%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP127-3.004 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:32:45 PM UTC 2026
% Result : Unsatisfiable 3.73s 0.91s
% Output : CNFRefutation 4.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 180
% Syntax : Number of formulae : 641 ( 109 unt; 140 def)
% Number of atoms : 2257 ( 0 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 2485 ( 869 ~;1476 |; 0 &)
% ( 140 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 147 ( 146 usr; 141 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 310 ( 310 !; 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(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(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,
! [Y,X,Z1,Z2] :
( product(Z2,Y,X)
| ~ product(Z1,Y,Z2)
| ~ product(Y,X,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(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(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,X,Z2] :
( product(Z2,Y,X)
| ! [Z1] :
( ~ product(Z1,Y,Z2)
| ~ product(Y,X,Z1) ) ),
inference(miniscoping,[status(thm)],[f43]) ).
fof(f94,plain,
! [X0,X1,X2,X3] :
( product(X3,X0,X1)
| ~ product(X2,X0,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f93]) ).
fof(f95,plain,
! [X0,X1] :
( product(X0,X0,X1)
| ~ product(X0,X1,X0) ),
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(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(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(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(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(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(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(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(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(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(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,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)],[f85,f95]) ).
fof(f365,plain,
! [X0,X1,X2] :
( product(e_2,X1,X2)
| ~ product(X1,X2,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)],[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,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)],[f85,f95]) ).
fof(f375,plain,
! [X0,X1,X2] :
( product(e_3,X1,X2)
| ~ product(X1,X2,X0)
| 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(f384,plain,
! [X0] :
( product(e_4,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)],[f85,f95]) ).
fof(f385,plain,
! [X0,X1,X2] :
( product(e_4,X1,X2)
| ~ product(X1,X2,X0)
| 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(f403,definition,
! [X0] :
( sQ43_spl
<=> ( product(e_2,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,[sQ43_spl])],[split_symbol_definition]) ).
fof(f404,plain,
! [X0] :
( ~ sQ43_spl
| product(e_2,e_2,X0)
| product(e_2,X0,e_4)
| product(e_2,X0,e_3)
| product(e_2,X0,e_1)
| ~ group_element(X0) ),
inference(component_clause,[status(thm)],[f403]) ).
fof(f406,plain,
( sQ43_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f364,f246,f403]) ).
fof(f407,definition,
! [X0,X1,X2] :
( sQ44_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,[sQ44_spl])],[split_symbol_definition]) ).
fof(f410,plain,
( ~ sQ22_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f366,f407,f216]) ).
fof(f411,definition,
! [X0] :
( sQ45_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,[sQ45_spl])],[split_symbol_definition]) ).
fof(f414,plain,
( ~ sQ22_spl
| sQ45_spl ),
inference(split_clause,[status(thm)],[f367,f411,f216]) ).
fof(f415,definition,
! [X0] :
( sQ46_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,[sQ46_spl])],[split_symbol_definition]) ).
fof(f418,plain,
( ~ sQ33_spl
| sQ46_spl ),
inference(split_clause,[status(thm)],[f368,f415,f259]) ).
fof(f419,definition,
! [X0] :
( sQ47_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,[sQ47_spl])],[split_symbol_definition]) ).
fof(f422,plain,
( sQ47_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f370,f259,f419]) ).
fof(f424,definition,
! [X0] :
( sQ48_spl
<=> ( product(e_3,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,[sQ48_spl])],[split_symbol_definition]) ).
fof(f425,plain,
! [X0] :
( ~ sQ48_spl
| product(e_3,e_3,X0)
| product(e_3,X0,e_4)
| product(e_3,X0,e_2)
| product(e_3,X0,e_1)
| ~ group_element(X0) ),
inference(component_clause,[status(thm)],[f424]) ).
fof(f427,plain,
( sQ48_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f374,f259,f424]) ).
fof(f428,definition,
! [X0,X1,X2] :
( sQ49_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,[sQ49_spl])],[split_symbol_definition]) ).
fof(f431,plain,
( ~ sQ22_spl
| sQ49_spl ),
inference(split_clause,[status(thm)],[f376,f428,f216]) ).
fof(f432,definition,
! [X0] :
( sQ50_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,[sQ50_spl])],[split_symbol_definition]) ).
fof(f435,plain,
( ~ sQ22_spl
| sQ50_spl ),
inference(split_clause,[status(thm)],[f377,f432,f216]) ).
fof(f436,definition,
! [X0] :
( sQ51_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,[sQ51_spl])],[split_symbol_definition]) ).
fof(f439,plain,
( ~ sQ9_spl
| sQ51_spl ),
inference(split_clause,[status(thm)],[f378,f436,f152]) ).
fof(f440,definition,
! [X0] :
( sQ52_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,[sQ52_spl])],[split_symbol_definition]) ).
fof(f443,plain,
( sQ52_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f380,f152,f440]) ).
fof(f445,definition,
! [X0] :
( sQ53_spl
<=> ( product(e_4,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,[sQ53_spl])],[split_symbol_definition]) ).
fof(f446,plain,
! [X0] :
( ~ sQ53_spl
| product(e_4,e_4,X0)
| product(e_4,X0,e_3)
| product(e_4,X0,e_2)
| product(e_4,X0,e_1)
| ~ group_element(X0) ),
inference(component_clause,[status(thm)],[f445]) ).
fof(f448,plain,
( sQ53_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f384,f152,f445]) ).
fof(f478,plain,
( ~ sQ43_spl
| equalish(e_3,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_4)
| product(e_2,e_2,e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[f404,f97]) ).
fof(f481,plain,
! [X0,X1] :
( ~ sQ43_spl
| equalish(e_4,X1)
| ~ next(e_2,X1)
| ~ greater(X0,e_0)
| ~ cycle(e_2,X0)
| product(e_2,e_2,e_1)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_1)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[f404,f68]) ).
fof(f482,plain,
( ~ sQ43_spl
| ~ greater(e_4,e_2)
| ~ cycle(e_2,e_0)
| product(e_2,e_2,e_1)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_1)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[f404,f66]) ).
fof(f489,plain,
( ~ sQ43_spl
| 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)],[f404,f101]) ).
fof(f497,definition,
( sQ57_spl
<=> product(e_2,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f498,plain,
( ~ sQ57_spl
| product(e_2,e_1,e_1) ),
inference(component_clause,[status(thm)],[f497]) ).
fof(f500,definition,
( sQ58_spl
<=> product(e_2,e_1,e_4) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f501,plain,
( ~ sQ58_spl
| product(e_2,e_1,e_4) ),
inference(component_clause,[status(thm)],[f500]) ).
fof(f503,definition,
( sQ59_spl
<=> product(e_2,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f504,plain,
( ~ sQ59_spl
| product(e_2,e_2,e_1) ),
inference(component_clause,[status(thm)],[f503]) ).
fof(f506,definition,
! [X0] :
( sQ60_spl
<=> ( ~ greater(X0,e_0)
| ~ cycle(e_2,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f507,plain,
! [X0] :
( ~ sQ60_spl
| ~ greater(X0,e_0)
| ~ cycle(e_2,X0) ),
inference(component_clause,[status(thm)],[f506]) ).
fof(f513,definition,
( sQ62_spl
<=> greater(e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f515,plain,
( sQ62_spl
| ~ greater(e_3,e_2) ),
inference(component_clause,[status(thm)],[f513]) ).
fof(f517,definition,
( sQ63_spl
<=> product(e_2,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f518,plain,
( ~ sQ63_spl
| product(e_2,e_3,e_1) ),
inference(component_clause,[status(thm)],[f517]) ).
fof(f523,definition,
( sQ65_spl
<=> product(e_2,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f524,plain,
( ~ sQ65_spl
| product(e_2,e_2,e_3) ),
inference(component_clause,[status(thm)],[f523]) ).
fof(f526,definition,
( sQ66_spl
<=> equalish(e_2,e_3) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f527,plain,
( ~ sQ66_spl
| equalish(e_2,e_3) ),
inference(component_clause,[status(thm)],[f526]) ).
fof(f530,definition,
( sQ67_spl
<=> product(e_2,e_2,e_4) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f531,plain,
( ~ sQ67_spl
| product(e_2,e_2,e_4) ),
inference(component_clause,[status(thm)],[f530]) ).
fof(f533,definition,
( sQ68_spl
<=> product(e_2,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f536,definition,
( sQ69_spl
<=> equalish(e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f537,plain,
( ~ sQ69_spl
| equalish(e_3,e_2) ),
inference(component_clause,[status(thm)],[f536]) ).
fof(f539,plain,
( ~ sQ43_spl
| sQ69_spl
| sQ68_spl
| sQ67_spl
| sQ59_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f478,f246,f503,f530,f533,f536,f403]) ).
fof(f540,definition,
( sQ70_spl
<=> product(e_2,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f541,plain,
( ~ sQ70_spl
| product(e_2,e_1,e_3) ),
inference(component_clause,[status(thm)],[f540]) ).
fof(f543,definition,
! [X1] :
( sQ71_spl
<=> ( equalish(e_4,X1)
| ~ next(e_2,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f544,plain,
! [X0] :
( ~ sQ71_spl
| equalish(e_4,X0)
| ~ next(e_2,X0) ),
inference(component_clause,[status(thm)],[f543]) ).
fof(f546,plain,
( ~ sQ43_spl
| sQ71_spl
| sQ60_spl
| sQ59_spl
| sQ70_spl
| sQ57_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f481,f216,f497,f540,f503,f506,f543,f403]) ).
fof(f547,definition,
( sQ72_spl
<=> greater(e_4,e_2) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f549,plain,
( sQ72_spl
| ~ greater(e_4,e_2) ),
inference(component_clause,[status(thm)],[f547]) ).
fof(f550,plain,
( ~ sQ43_spl
| ~ sQ72_spl
| ~ sQ18_spl
| sQ59_spl
| sQ70_spl
| sQ57_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f482,f216,f497,f540,f503,f200,f547,f403]) ).
fof(f557,definition,
( sQ75_spl
<=> equalish(e_2,e_4) ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f558,plain,
( ~ sQ75_spl
| equalish(e_2,e_4) ),
inference(component_clause,[status(thm)],[f557]) ).
fof(f561,definition,
( sQ76_spl
<=> equalish(e_4,e_2) ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f562,plain,
( ~ sQ76_spl
| equalish(e_4,e_2) ),
inference(component_clause,[status(thm)],[f561]) ).
fof(f565,definition,
( sQ77_spl
<=> equalish(e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f568,plain,
( ~ sQ43_spl
| sQ77_spl
| sQ67_spl
| sQ65_spl
| sQ59_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f489,f246,f503,f523,f530,f565,f403]) ).
fof(f571,plain,
( ~ sQ76_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f562,f83]) ).
fof(f572,plain,
~ sQ76_spl,
inference(contradiction_clause,[status(thm)],[f571]) ).
fof(f573,plain,
( ~ sQ75_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f558,f78]) ).
fof(f574,plain,
~ sQ75_spl,
inference(contradiction_clause,[status(thm)],[f573]) ).
fof(f575,plain,
( sQ72_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f549,f56]) ).
fof(f576,plain,
sQ72_spl,
inference(contradiction_clause,[status(thm)],[f575]) ).
fof(f577,plain,
( ~ sQ69_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f537,f80]) ).
fof(f578,plain,
~ sQ69_spl,
inference(contradiction_clause,[status(thm)],[f577]) ).
fof(f579,plain,
( ~ sQ66_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f527,f77]) ).
fof(f580,plain,
~ sQ66_spl,
inference(contradiction_clause,[status(thm)],[f579]) ).
fof(f581,plain,
( sQ62_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f515,f55]) ).
fof(f582,plain,
sQ62_spl,
inference(contradiction_clause,[status(thm)],[f581]) ).
fof(f585,plain,
( ~ sQ59_spl
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[f504,f97]) ).
fof(f588,plain,
( ~ sQ59_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f585,f73]) ).
fof(f589,plain,
~ sQ59_spl,
inference(contradiction_clause,[status(thm)],[f588]) ).
fof(f592,plain,
( ~ sQ67_spl
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[f531,f97]) ).
fof(f595,plain,
( ~ sQ67_spl
| sQ76_spl ),
inference(split_clause,[status(thm)],[f592,f561,f530]) ).
fof(f598,plain,
( ~ sQ65_spl
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[f524,f97]) ).
fof(f601,plain,
( ~ sQ65_spl
| sQ69_spl ),
inference(split_clause,[status(thm)],[f598,f536,f523]) ).
fof(f604,plain,
( ~ sQ57_spl
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[f498,f101]) ).
fof(f617,plain,
( ~ sQ57_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f604,f76]) ).
fof(f618,plain,
~ sQ57_spl,
inference(contradiction_clause,[status(thm)],[f617]) ).
fof(f622,plain,
! [X0,X1] :
( product(X0,X1,e_3)
| product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0)
| product(e_2,X0,X1)
| 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)],[f365,f85]) ).
fof(f623,plain,
! [X0,X1] :
( product(X0,X1,e_4)
| product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0)
| product(e_2,X0,X1)
| 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) ),
inference(resolution,[status(thm)],[f365,f85]) ).
fof(f624,plain,
! [X0,X1] :
( product(X0,X1,e_4)
| product(X0,X1,e_3)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0)
| product(e_2,X0,X1)
| 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)],[f365,f85]) ).
fof(f630,definition,
( sQ81_spl
<=> product(e_4,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f631,plain,
( ~ sQ81_spl
| product(e_4,e_2,e_1) ),
inference(component_clause,[status(thm)],[f630]) ).
fof(f633,definition,
( sQ82_spl
<=> product(e_4,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f634,plain,
( ~ sQ82_spl
| product(e_4,e_2,e_3) ),
inference(component_clause,[status(thm)],[f633]) ).
fof(f636,definition,
( sQ83_spl
<=> product(e_4,e_2,e_4) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f637,plain,
( ~ sQ83_spl
| product(e_4,e_2,e_4) ),
inference(component_clause,[status(thm)],[f636]) ).
fof(f638,plain,
( sQ83_spl
| ~ product(e_4,e_2,e_4) ),
inference(component_clause,[status(thm)],[f636]) ).
fof(f643,definition,
( sQ85_spl
<=> product(e_3,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f644,plain,
( ~ sQ85_spl
| product(e_3,e_2,e_1) ),
inference(component_clause,[status(thm)],[f643]) ).
fof(f646,definition,
( sQ86_spl
<=> product(e_3,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f647,plain,
( ~ sQ86_spl
| product(e_3,e_2,e_3) ),
inference(component_clause,[status(thm)],[f646]) ).
fof(f649,definition,
( sQ87_spl
<=> product(e_3,e_2,e_4) ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f650,plain,
( ~ sQ87_spl
| product(e_3,e_2,e_4) ),
inference(component_clause,[status(thm)],[f649]) ).
fof(f656,definition,
! [X0,X1] :
( sQ89_spl
<=> ( product(X0,X1,e_3)
| product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0)
| product(e_2,X0,X1)
| 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,[sQ89_spl])],[split_symbol_definition]) ).
fof(f659,plain,
( sQ89_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f622,f152,f656]) ).
fof(f660,definition,
! [X0,X1] :
( sQ90_spl
<=> ( product(X0,X1,e_4)
| product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0)
| product(e_2,X0,X1)
| product(e_3,X0,e_4)
| product(e_3,X0,e_3)
| product(e_3,X0,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f663,plain,
( sQ90_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f623,f259,f660]) ).
fof(f664,definition,
! [X0,X1] :
( sQ91_spl
<=> ( product(X0,X1,e_4)
| product(X0,X1,e_3)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0)
| product(e_2,X0,X1)
| 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,[sQ91_spl])],[split_symbol_definition]) ).
fof(f667,plain,
( sQ91_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f624,f246,f664]) ).
fof(f676,plain,
( ~ sQ70_spl
| ~ greater(e_3,e_2)
| ~ cycle(e_2,e_0) ),
inference(resolution,[status(thm)],[f541,f66]) ).
fof(f677,plain,
( ~ sQ70_spl
| product(e_2,e_2,e_1)
| product(e_3,e_2,e_4)
| product(e_3,e_2,e_3)
| product(e_3,e_2,e_1)
| ~ group_element(e_2)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[f541,f365]) ).
fof(f683,plain,
( ~ sQ70_spl
| ~ sQ62_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f676,f200,f513,f540]) ).
fof(f684,plain,
( ~ sQ70_spl
| sQ59_spl
| sQ87_spl
| sQ86_spl
| sQ85_spl
| ~ sQ30_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f677,f259,f246,f643,f646,f649,f503,f540]) ).
fof(f685,plain,
! [X0,X1] :
( ~ sQ58_spl
| equalish(e_4,X1)
| ~ next(e_2,X1)
| ~ greater(X0,e_0)
| ~ cycle(e_2,X0) ),
inference(resolution,[status(thm)],[f501,f68]) ).
fof(f692,plain,
( ~ sQ58_spl
| sQ71_spl
| sQ60_spl ),
inference(split_clause,[status(thm)],[f685,f506,f543,f500]) ).
fof(f706,definition,
( sQ92_spl
<=> product(e_1,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f707,plain,
( ~ sQ92_spl
| product(e_1,e_2,e_1) ),
inference(component_clause,[status(thm)],[f706]) ).
fof(f733,definition,
( sQ95_spl
<=> product(e_2,e_4,e_4) ),
introduced(definition,[new_symbols(definition,[sQ95_spl])],[split_symbol_definition]) ).
fof(f734,plain,
( ~ sQ95_spl
| product(e_2,e_4,e_4) ),
inference(component_clause,[status(thm)],[f733]) ).
fof(f742,definition,
( sQ96_spl
<=> product(e_2,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ96_spl])],[split_symbol_definition]) ).
fof(f743,plain,
( ~ sQ96_spl
| product(e_2,e_3,e_3) ),
inference(component_clause,[status(thm)],[f742]) ).
fof(f748,plain,
( ~ sQ87_spl
| product(e_2,e_3,e_2)
| product(e_4,e_3,e_4)
| product(e_4,e_3,e_3)
| product(e_4,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(e_4) ),
inference(resolution,[status(thm)],[f650,f365]) ).
fof(f753,definition,
( sQ97_spl
<=> product(e_4,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ97_spl])],[split_symbol_definition]) ).
fof(f754,plain,
( ~ sQ97_spl
| product(e_4,e_3,e_1) ),
inference(component_clause,[status(thm)],[f753]) ).
fof(f756,definition,
( sQ98_spl
<=> product(e_4,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ98_spl])],[split_symbol_definition]) ).
fof(f757,plain,
( ~ sQ98_spl
| product(e_4,e_3,e_3) ),
inference(component_clause,[status(thm)],[f756]) ).
fof(f759,definition,
( sQ99_spl
<=> product(e_4,e_3,e_4) ),
introduced(definition,[new_symbols(definition,[sQ99_spl])],[split_symbol_definition]) ).
fof(f760,plain,
( ~ sQ99_spl
| product(e_4,e_3,e_4) ),
inference(component_clause,[status(thm)],[f759]) ).
fof(f762,definition,
( sQ100_spl
<=> product(e_2,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ100_spl])],[split_symbol_definition]) ).
fof(f763,plain,
( ~ sQ100_spl
| product(e_2,e_3,e_2) ),
inference(component_clause,[status(thm)],[f762]) ).
fof(f765,plain,
( ~ sQ87_spl
| sQ100_spl
| sQ99_spl
| sQ98_spl
| sQ97_spl
| ~ sQ33_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f748,f152,f259,f753,f756,f759,f762,f649]) ).
fof(f768,plain,
( ~ sQ86_spl
| equalish(e_2,e_3) ),
inference(resolution,[status(thm)],[f647,f99]) ).
fof(f773,definition,
( sQ101_spl
<=> product(e_3,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ101_spl])],[split_symbol_definition]) ).
fof(f774,plain,
( ~ sQ101_spl
| product(e_3,e_3,e_1) ),
inference(component_clause,[status(thm)],[f773]) ).
fof(f776,definition,
( sQ102_spl
<=> product(e_3,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ102_spl])],[split_symbol_definition]) ).
fof(f779,definition,
( sQ103_spl
<=> product(e_3,e_3,e_4) ),
introduced(definition,[new_symbols(definition,[sQ103_spl])],[split_symbol_definition]) ).
fof(f780,plain,
( ~ sQ103_spl
| product(e_3,e_3,e_4) ),
inference(component_clause,[status(thm)],[f779]) ).
fof(f783,plain,
( ~ sQ86_spl
| sQ66_spl ),
inference(split_clause,[status(thm)],[f768,f526,f646]) ).
fof(f784,plain,
( ~ sQ24_spl
| ~ sQ37_spl
| ~ greater(e_2,e_0) ),
inference(resolution,[status(thm)],[f350,f223]) ).
fof(f786,plain,
( ~ sQ24_spl
| ~ sQ37_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f784,f49]) ).
fof(f787,plain,
( ~ sQ24_spl
| ~ sQ37_spl ),
inference(contradiction_clause,[status(thm)],[f786]) ).
fof(f788,plain,
( ~ sQ38_spl
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[f353,f45]) ).
fof(f789,plain,
( ~ sQ38_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f788,f73]) ).
fof(f790,plain,
~ sQ38_spl,
inference(contradiction_clause,[status(thm)],[f789]) ).
fof(f828,definition,
( sQ107_spl
<=> product(e_1,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ107_spl])],[split_symbol_definition]) ).
fof(f829,plain,
( ~ sQ107_spl
| product(e_1,e_3,e_1) ),
inference(component_clause,[status(thm)],[f828]) ).
fof(f831,definition,
( sQ108_spl
<=> product(e_1,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ108_spl])],[split_symbol_definition]) ).
fof(f832,plain,
( ~ sQ108_spl
| product(e_1,e_3,e_3) ),
inference(component_clause,[status(thm)],[f831]) ).
fof(f840,plain,
( ~ sQ83_spl
| equalish(e_2,e_4) ),
inference(resolution,[status(thm)],[f637,f99]) ).
fof(f845,definition,
( sQ110_spl
<=> product(e_4,e_4,e_1) ),
introduced(definition,[new_symbols(definition,[sQ110_spl])],[split_symbol_definition]) ).
fof(f846,plain,
( ~ sQ110_spl
| product(e_4,e_4,e_1) ),
inference(component_clause,[status(thm)],[f845]) ).
fof(f848,definition,
( sQ111_spl
<=> product(e_4,e_4,e_3) ),
introduced(definition,[new_symbols(definition,[sQ111_spl])],[split_symbol_definition]) ).
fof(f849,plain,
( ~ sQ111_spl
| product(e_4,e_4,e_3) ),
inference(component_clause,[status(thm)],[f848]) ).
fof(f851,definition,
( sQ112_spl
<=> product(e_4,e_4,e_4) ),
introduced(definition,[new_symbols(definition,[sQ112_spl])],[split_symbol_definition]) ).
fof(f854,definition,
( sQ113_spl
<=> product(e_2,e_4,e_2) ),
introduced(definition,[new_symbols(definition,[sQ113_spl])],[split_symbol_definition]) ).
fof(f855,plain,
( ~ sQ113_spl
| product(e_2,e_4,e_2) ),
inference(component_clause,[status(thm)],[f854]) ).
fof(f858,plain,
( ~ sQ83_spl
| sQ75_spl ),
inference(split_clause,[status(thm)],[f840,f557,f636]) ).
fof(f859,plain,
( ~ sQ82_spl
| product(e_2,e_4,e_2)
| 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)],[f634,f365]) ).
fof(f864,definition,
( sQ114_spl
<=> product(e_3,e_4,e_1) ),
introduced(definition,[new_symbols(definition,[sQ114_spl])],[split_symbol_definition]) ).
fof(f865,plain,
( ~ sQ114_spl
| product(e_3,e_4,e_1) ),
inference(component_clause,[status(thm)],[f864]) ).
fof(f867,definition,
( sQ115_spl
<=> product(e_3,e_4,e_3) ),
introduced(definition,[new_symbols(definition,[sQ115_spl])],[split_symbol_definition]) ).
fof(f868,plain,
( ~ sQ115_spl
| product(e_3,e_4,e_3) ),
inference(component_clause,[status(thm)],[f867]) ).
fof(f870,definition,
( sQ116_spl
<=> product(e_3,e_4,e_4) ),
introduced(definition,[new_symbols(definition,[sQ116_spl])],[split_symbol_definition]) ).
fof(f871,plain,
( ~ sQ116_spl
| product(e_3,e_4,e_4) ),
inference(component_clause,[status(thm)],[f870]) ).
fof(f873,plain,
( ~ sQ82_spl
| sQ113_spl
| sQ116_spl
| sQ115_spl
| sQ114_spl
| ~ sQ9_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f859,f259,f152,f864,f867,f870,f854,f633]) ).
fof(f875,plain,
! [X0] :
( ~ sQ81_spl
| equalish(X0,e_4)
| ~ product(X0,e_2,e_1) ),
inference(resolution,[status(thm)],[f631,f91]) ).
fof(f879,definition,
( sQ117_spl
<=> product(e_1,e_4,e_1) ),
introduced(definition,[new_symbols(definition,[sQ117_spl])],[split_symbol_definition]) ).
fof(f880,plain,
( ~ sQ117_spl
| product(e_1,e_4,e_1) ),
inference(component_clause,[status(thm)],[f879]) ).
fof(f885,definition,
( sQ119_spl
<=> product(e_1,e_4,e_4) ),
introduced(definition,[new_symbols(definition,[sQ119_spl])],[split_symbol_definition]) ).
fof(f886,plain,
( ~ sQ119_spl
| product(e_1,e_4,e_4) ),
inference(component_clause,[status(thm)],[f885]) ).
fof(f894,definition,
( sQ120_spl
<=> product(e_4,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ120_spl])],[split_symbol_definition]) ).
fof(f895,plain,
( ~ sQ120_spl
| product(e_4,e_1,e_1) ),
inference(component_clause,[status(thm)],[f894]) ).
fof(f900,definition,
( sQ122_spl
<=> product(e_4,e_1,e_4) ),
introduced(definition,[new_symbols(definition,[sQ122_spl])],[split_symbol_definition]) ).
fof(f901,plain,
( ~ sQ122_spl
| product(e_4,e_1,e_4) ),
inference(component_clause,[status(thm)],[f900]) ).
fof(f903,definition,
( sQ123_spl
<=> product(e_2,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ123_spl])],[split_symbol_definition]) ).
fof(f904,plain,
( ~ sQ123_spl
| product(e_2,e_1,e_2) ),
inference(component_clause,[status(thm)],[f903]) ).
fof(f912,definition,
( sQ124_spl
<=> product(e_3,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ124_spl])],[split_symbol_definition]) ).
fof(f913,plain,
( ~ sQ124_spl
| product(e_3,e_1,e_1) ),
inference(component_clause,[status(thm)],[f912]) ).
fof(f915,definition,
( sQ125_spl
<=> product(e_3,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[sQ125_spl])],[split_symbol_definition]) ).
fof(f916,plain,
( ~ sQ125_spl
| product(e_3,e_1,e_3) ),
inference(component_clause,[status(thm)],[f915]) ).
fof(f924,plain,
( ~ sQ92_spl
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[f707,f99]) ).
fof(f929,definition,
( sQ127_spl
<=> product(e_1,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ127_spl])],[split_symbol_definition]) ).
fof(f932,definition,
( sQ128_spl
<=> product(e_1,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[sQ128_spl])],[split_symbol_definition]) ).
fof(f933,plain,
( ~ sQ128_spl
| product(e_1,e_1,e_3) ),
inference(component_clause,[status(thm)],[f932]) ).
fof(f935,definition,
( sQ129_spl
<=> product(e_1,e_1,e_4) ),
introduced(definition,[new_symbols(definition,[sQ129_spl])],[split_symbol_definition]) ).
fof(f936,plain,
( ~ sQ129_spl
| product(e_1,e_1,e_4) ),
inference(component_clause,[status(thm)],[f935]) ).
fof(f937,plain,
( sQ129_spl
| ~ product(e_1,e_1,e_4) ),
inference(component_clause,[status(thm)],[f935]) ).
fof(f939,plain,
( ~ sQ92_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f924,f76]) ).
fof(f940,plain,
~ sQ92_spl,
inference(contradiction_clause,[status(thm)],[f939]) ).
fof(f962,plain,
( ~ sQ95_spl
| equalish(e_2,e_4) ),
inference(resolution,[status(thm)],[f734,f101]) ).
fof(f968,plain,
( ~ sQ95_spl
| sQ75_spl ),
inference(split_clause,[status(thm)],[f962,f557,f733]) ).
fof(f999,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(f1010,definition,
! [X0] :
( sQ136_spl
<=> ( equalish(X0,e_1)
| ~ greater(X0,e_0)
| ~ cycle(e_3,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ136_spl])],[split_symbol_definition]) ).
fof(f1013,definition,
( sQ137_spl
<=> cycle(e_4,e_0) ),
introduced(definition,[new_symbols(definition,[sQ137_spl])],[split_symbol_definition]) ).
fof(f1015,plain,
( sQ137_spl
| ~ cycle(e_4,e_0) ),
inference(component_clause,[status(thm)],[f1013]) ).
fof(f1016,plain,
( ~ sQ137_spl
| sQ136_spl ),
inference(split_clause,[status(thm)],[f999,f1010,f1013]) ).
fof(f1017,plain,
( sQ137_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1015,f61]) ).
fof(f1018,plain,
sQ137_spl,
inference(contradiction_clause,[status(thm)],[f1017]) ).
fof(f1020,plain,
( ~ sQ96_spl
| equalish(e_2,e_3) ),
inference(resolution,[status(thm)],[f743,f101]) ).
fof(f1026,plain,
( ~ sQ96_spl
| sQ66_spl ),
inference(split_clause,[status(thm)],[f1020,f526,f742]) ).
fof(f1032,plain,
( ~ sQ100_spl
| product(e_2,e_2,e_3) ),
inference(resolution,[status(thm)],[f763,f95]) ).
fof(f1036,plain,
( ~ sQ100_spl
| sQ65_spl ),
inference(split_clause,[status(thm)],[f1032,f523,f762]) ).
fof(f1039,plain,
( ~ sQ99_spl
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[f760,f99]) ).
fof(f1045,plain,
( ~ sQ99_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1039,f81]) ).
fof(f1046,plain,
~ sQ99_spl,
inference(contradiction_clause,[status(thm)],[f1045]) ).
fof(f1048,plain,
( ~ sQ98_spl
| equalish(e_4,e_3) ),
inference(resolution,[status(thm)],[f757,f101]) ).
fof(f1054,plain,
( ~ sQ98_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1048,f84]) ).
fof(f1055,plain,
~ sQ98_spl,
inference(contradiction_clause,[status(thm)],[f1054]) ).
fof(f1057,plain,
! [X0] :
( ~ sQ97_spl
| equalish(X0,e_4)
| ~ product(X0,e_3,e_1) ),
inference(resolution,[status(thm)],[f754,f91]) ).
fof(f1065,plain,
( ~ sQ103_spl
| equalish(e_4,e_3) ),
inference(resolution,[status(thm)],[f780,f97]) ).
fof(f1069,plain,
( ~ sQ103_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1065,f84]) ).
fof(f1070,plain,
~ sQ103_spl,
inference(contradiction_clause,[status(thm)],[f1069]) ).
fof(f1078,plain,
! [X0] :
( ~ sQ43_spl
| product(e_2,X0,e_4)
| product(e_2,X0,e_3)
| product(e_2,X0,e_1)
| ~ group_element(X0)
| product(e_3,e_2,e_2)
| 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,f404]) ).
fof(f1081,plain,
! [X0,X1] :
( product(X0,X1,e_3)
| product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0)
| product(e_3,X0,X1)
| 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) ),
inference(resolution,[status(thm)],[f375,f85]) ).
fof(f1082,plain,
! [X0,X1] :
( product(X0,X1,e_4)
| product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0)
| product(e_3,X0,X1)
| 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)],[f375,f85]) ).
fof(f1083,plain,
! [X0,X1] :
( product(X0,X1,e_4)
| product(X0,X1,e_3)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0)
| product(e_3,X0,X1)
| 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)],[f375,f85]) ).
fof(f1092,definition,
( sQ140_spl
<=> product(e_3,e_4,e_2) ),
introduced(definition,[new_symbols(definition,[sQ140_spl])],[split_symbol_definition]) ).
fof(f1093,plain,
( ~ sQ140_spl
| product(e_3,e_4,e_2) ),
inference(component_clause,[status(thm)],[f1092]) ).
fof(f1097,definition,
( sQ141_spl
<=> product(e_1,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ141_spl])],[split_symbol_definition]) ).
fof(f1098,plain,
( ~ sQ141_spl
| product(e_1,e_3,e_2) ),
inference(component_clause,[status(thm)],[f1097]) ).
fof(f1100,definition,
( sQ142_spl
<=> product(e_3,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ142_spl])],[split_symbol_definition]) ).
fof(f1101,plain,
( ~ sQ142_spl
| product(e_3,e_3,e_2) ),
inference(component_clause,[status(thm)],[f1100]) ).
fof(f1104,definition,
( sQ143_spl
<=> product(e_3,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ143_spl])],[split_symbol_definition]) ).
fof(f1105,plain,
( ~ sQ143_spl
| product(e_3,e_2,e_2) ),
inference(component_clause,[status(thm)],[f1104]) ).
fof(f1108,definition,
( sQ144_spl
<=> product(e_1,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ144_spl])],[split_symbol_definition]) ).
fof(f1109,plain,
( ~ sQ144_spl
| product(e_1,e_2,e_2) ),
inference(component_clause,[status(thm)],[f1108]) ).
fof(f1113,definition,
! [X0] :
( sQ145_spl
<=> ( product(e_2,X0,e_4)
| product(e_2,X0,e_3)
| product(e_2,X0,e_1)
| ~ group_element(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,[sQ145_spl])],[split_symbol_definition]) ).
fof(f1116,plain,
( ~ sQ43_spl
| sQ143_spl
| ~ sQ30_spl
| sQ145_spl ),
inference(split_clause,[status(thm)],[f1078,f1113,f246,f1104,f403]) ).
fof(f1117,definition,
( sQ146_spl
<=> product(e_4,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ146_spl])],[split_symbol_definition]) ).
fof(f1118,plain,
( ~ sQ146_spl
| product(e_4,e_2,e_2) ),
inference(component_clause,[status(thm)],[f1117]) ).
fof(f1128,definition,
! [X0,X1] :
( sQ149_spl
<=> ( product(X0,X1,e_3)
| product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0)
| product(e_3,X0,X1)
| product(e_4,X0,e_4)
| product(e_4,X0,e_2)
| product(e_4,X0,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ149_spl])],[split_symbol_definition]) ).
fof(f1131,plain,
( sQ149_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f1081,f152,f1128]) ).
fof(f1132,definition,
! [X0,X1] :
( sQ150_spl
<=> ( product(X0,X1,e_4)
| product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0)
| product(e_3,X0,X1)
| 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,[sQ150_spl])],[split_symbol_definition]) ).
fof(f1135,plain,
( sQ150_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f1082,f259,f1132]) ).
fof(f1136,definition,
! [X0,X1] :
( sQ151_spl
<=> ( product(X0,X1,e_4)
| product(X0,X1,e_3)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0)
| product(e_3,X0,X1)
| 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,[sQ151_spl])],[split_symbol_definition]) ).
fof(f1139,plain,
( sQ151_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f1083,f246,f1136]) ).
fof(f1149,plain,
( ~ sQ101_spl
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[f774,f97]) ).
fof(f1154,plain,
( ~ sQ101_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1149,f74]) ).
fof(f1155,plain,
~ sQ101_spl,
inference(contradiction_clause,[status(thm)],[f1154]) ).
fof(f1171,plain,
( ~ sQ108_spl
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[f832,f101]) ).
fof(f1178,plain,
( ~ sQ108_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1171,f74]) ).
fof(f1179,plain,
~ sQ108_spl,
inference(contradiction_clause,[status(thm)],[f1178]) ).
fof(f1183,plain,
( ~ sQ107_spl
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[f829,f99]) ).
fof(f1188,definition,
( sQ153_spl
<=> product(e_1,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ153_spl])],[split_symbol_definition]) ).
fof(f1189,plain,
( ~ sQ153_spl
| product(e_1,e_1,e_2) ),
inference(component_clause,[status(thm)],[f1188]) ).
fof(f1193,plain,
( ~ sQ107_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1183,f79]) ).
fof(f1194,plain,
~ sQ107_spl,
inference(contradiction_clause,[status(thm)],[f1193]) ).
fof(f1201,plain,
( ~ sQ113_spl
| product(e_2,e_2,e_4) ),
inference(resolution,[status(thm)],[f855,f95]) ).
fof(f1206,plain,
( ~ sQ113_spl
| sQ67_spl ),
inference(split_clause,[status(thm)],[f1201,f530,f854]) ).
fof(f1211,plain,
( ~ sQ111_spl
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[f849,f97]) ).
fof(f1216,plain,
( ~ sQ111_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1211,f81]) ).
fof(f1217,plain,
~ sQ111_spl,
inference(contradiction_clause,[status(thm)],[f1216]) ).
fof(f1222,plain,
( ~ sQ110_spl
| equalish(e_1,e_4) ),
inference(resolution,[status(thm)],[f846,f97]) ).
fof(f1227,plain,
( ~ sQ110_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1222,f75]) ).
fof(f1228,plain,
~ sQ110_spl,
inference(contradiction_clause,[status(thm)],[f1227]) ).
fof(f1229,plain,
( sQ83_spl
| product(e_4,e_2,e_3)
| 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)],[f638,f85]) ).
fof(f1230,plain,
( sQ83_spl
| sQ82_spl
| sQ146_spl
| sQ81_spl
| ~ sQ30_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f1229,f152,f246,f630,f1117,f633,f636]) ).
fof(f1233,plain,
( ~ sQ116_spl
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[f871,f101]) ).
fof(f1243,plain,
( ~ sQ116_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1233,f81]) ).
fof(f1244,plain,
~ sQ116_spl,
inference(contradiction_clause,[status(thm)],[f1243]) ).
fof(f1248,plain,
( ~ sQ115_spl
| equalish(e_4,e_3) ),
inference(resolution,[status(thm)],[f868,f99]) ).
fof(f1255,plain,
( ~ sQ115_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1248,f84]) ).
fof(f1256,plain,
~ sQ115_spl,
inference(contradiction_clause,[status(thm)],[f1255]) ).
fof(f1267,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(f1268,definition,
! [X0] :
( sQ155_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,[sQ155_spl])],[split_symbol_definition]) ).
fof(f1273,plain,
( ~ sQ30_spl
| sQ155_spl ),
inference(split_clause,[status(thm)],[f1267,f1268,f246]) ).
fof(f1276,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(f1277,definition,
! [X0] :
( sQ156_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,[sQ156_spl])],[split_symbol_definition]) ).
fof(f1282,plain,
( sQ156_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f1276,f246,f1277]) ).
fof(f1297,plain,
( ~ sQ119_spl
| equalish(e_1,e_4) ),
inference(resolution,[status(thm)],[f886,f101]) ).
fof(f1304,plain,
( ~ sQ119_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1297,f75]) ).
fof(f1305,plain,
~ sQ119_spl,
inference(contradiction_clause,[status(thm)],[f1304]) ).
fof(f1317,plain,
( ~ sQ117_spl
| equalish(e_4,e_1) ),
inference(resolution,[status(thm)],[f880,f99]) ).
fof(f1324,plain,
( ~ sQ117_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1317,f82]) ).
fof(f1325,plain,
~ sQ117_spl,
inference(contradiction_clause,[status(thm)],[f1324]) ).
fof(f1333,plain,
( ~ sQ123_spl
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[f904,f99]) ).
fof(f1338,definition,
! [X1] :
( sQ157_spl
<=> ( equalish(e_2,X1)
| ~ next(e_2,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ157_spl])],[split_symbol_definition]) ).
fof(f1339,plain,
! [X0] :
( ~ sQ157_spl
| equalish(e_2,X0)
| ~ next(e_2,X0) ),
inference(component_clause,[status(thm)],[f1338]) ).
fof(f1356,plain,
( ~ sQ123_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1333,f73]) ).
fof(f1357,plain,
~ sQ123_spl,
inference(contradiction_clause,[status(thm)],[f1356]) ).
fof(f1363,plain,
( ~ sQ122_spl
| equalish(e_1,e_4) ),
inference(resolution,[status(thm)],[f901,f99]) ).
fof(f1379,definition,
( sQ164_spl
<=> product(e_4,e_4,e_2) ),
introduced(definition,[new_symbols(definition,[sQ164_spl])],[split_symbol_definition]) ).
fof(f1380,plain,
( ~ sQ164_spl
| product(e_4,e_4,e_2) ),
inference(component_clause,[status(thm)],[f1379]) ).
fof(f1384,plain,
( ~ sQ122_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1363,f75]) ).
fof(f1385,plain,
~ sQ122_spl,
inference(contradiction_clause,[status(thm)],[f1384]) ).
fof(f1408,plain,
( ~ sQ120_spl
| equalish(e_4,e_1) ),
inference(resolution,[status(thm)],[f895,f101]) ).
fof(f1423,plain,
( ~ sQ120_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1408,f82]) ).
fof(f1424,plain,
~ sQ120_spl,
inference(contradiction_clause,[status(thm)],[f1423]) ).
fof(f1440,definition,
( sQ171_spl
<=> greater(e_4,e_3) ),
introduced(definition,[new_symbols(definition,[sQ171_spl])],[split_symbol_definition]) ).
fof(f1442,plain,
( sQ171_spl
| ~ greater(e_4,e_3) ),
inference(component_clause,[status(thm)],[f1440]) ).
fof(f1446,plain,
( sQ171_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1442,f57]) ).
fof(f1447,plain,
sQ171_spl,
inference(contradiction_clause,[status(thm)],[f1446]) ).
fof(f1460,plain,
( ~ sQ125_spl
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[f916,f99]) ).
fof(f1475,plain,
( ~ sQ125_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1460,f74]) ).
fof(f1476,plain,
~ sQ125_spl,
inference(contradiction_clause,[status(thm)],[f1475]) ).
fof(f1542,plain,
( ~ sQ124_spl
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[f913,f101]) ).
fof(f1557,plain,
( ~ sQ124_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1542,f79]) ).
fof(f1558,plain,
~ sQ124_spl,
inference(contradiction_clause,[status(thm)],[f1557]) ).
fof(f1565,plain,
( ~ sQ129_spl
| equalish(e_4,e_1) ),
inference(resolution,[status(thm)],[f936,f97]) ).
fof(f1572,definition,
( sQ187_spl
<=> greater(e_4,e_1) ),
introduced(definition,[new_symbols(definition,[sQ187_spl])],[split_symbol_definition]) ).
fof(f1574,plain,
( sQ187_spl
| ~ greater(e_4,e_1) ),
inference(component_clause,[status(thm)],[f1572]) ).
fof(f1578,plain,
( ~ sQ129_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1565,f82]) ).
fof(f1579,plain,
~ sQ129_spl,
inference(contradiction_clause,[status(thm)],[f1578]) ).
fof(f1580,plain,
( sQ187_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1574,f54]) ).
fof(f1581,plain,
sQ187_spl,
inference(contradiction_clause,[status(thm)],[f1580]) ).
fof(f1588,plain,
( ~ sQ128_spl
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[f933,f97]) ).
fof(f1595,definition,
( sQ189_spl
<=> greater(e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ189_spl])],[split_symbol_definition]) ).
fof(f1597,plain,
( sQ189_spl
| ~ greater(e_3,e_1) ),
inference(component_clause,[status(thm)],[f1595]) ).
fof(f1601,plain,
( ~ sQ128_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1588,f79]) ).
fof(f1602,plain,
~ sQ128_spl,
inference(contradiction_clause,[status(thm)],[f1601]) ).
fof(f1603,plain,
( sQ189_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1597,f53]) ).
fof(f1604,plain,
sQ189_spl,
inference(contradiction_clause,[status(thm)],[f1603]) ).
fof(f1608,plain,
( ~ sQ114_spl
| product(e_4,e_3,e_4)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[f385,f865]) ).
fof(f1610,plain,
! [X0] :
( ~ sQ43_spl
| product(e_2,X0,e_4)
| product(e_2,X0,e_3)
| product(e_2,X0,e_1)
| ~ group_element(X0)
| product(e_4,e_2,e_2)
| 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,f404]) ).
fof(f1613,plain,
! [X0,X1] :
( product(X0,X1,e_3)
| product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0)
| product(e_4,X0,X1)
| 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)],[f385,f85]) ).
fof(f1614,plain,
! [X0,X1] :
( product(X0,X1,e_4)
| product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0)
| product(e_4,X0,X1)
| 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)],[f385,f85]) ).
fof(f1615,plain,
! [X0,X1] :
( product(X0,X1,e_4)
| product(X0,X1,e_3)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0)
| product(e_4,X0,X1)
| 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)],[f385,f85]) ).
fof(f1620,plain,
( ~ sQ114_spl
| sQ99_spl
| sQ108_spl
| sQ141_spl
| sQ107_spl
| ~ sQ33_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f1608,f216,f259,f828,f1097,f831,f759,f864]) ).
fof(f1622,definition,
! [X0] :
( sQ190_spl
<=> ( product(e_2,X0,e_4)
| product(e_2,X0,e_3)
| product(e_2,X0,e_1)
| ~ group_element(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,[sQ190_spl])],[split_symbol_definition]) ).
fof(f1625,plain,
( ~ sQ43_spl
| sQ146_spl
| ~ sQ30_spl
| sQ190_spl ),
inference(split_clause,[status(thm)],[f1610,f1622,f246,f1117,f403]) ).
fof(f1634,definition,
! [X0,X1] :
( sQ193_spl
<=> ( product(X0,X1,e_3)
| product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0)
| product(e_4,X0,X1)
| 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,[sQ193_spl])],[split_symbol_definition]) ).
fof(f1637,plain,
( sQ193_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f1613,f152,f1634]) ).
fof(f1638,definition,
! [X0,X1] :
( sQ194_spl
<=> ( product(X0,X1,e_4)
| product(X0,X1,e_2)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0)
| product(e_4,X0,X1)
| 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,[sQ194_spl])],[split_symbol_definition]) ).
fof(f1641,plain,
( sQ194_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f1614,f259,f1638]) ).
fof(f1642,definition,
! [X0,X1] :
( sQ195_spl
<=> ( product(X0,X1,e_4)
| product(X0,X1,e_3)
| product(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0)
| product(e_4,X0,X1)
| 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,[sQ195_spl])],[split_symbol_definition]) ).
fof(f1645,plain,
( sQ195_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f1615,f246,f1642]) ).
fof(f1692,plain,
( ~ sQ143_spl
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[f1105,f101]) ).
fof(f1708,plain,
( ~ sQ143_spl
| sQ69_spl ),
inference(split_clause,[status(thm)],[f1692,f536,f1104]) ).
fof(f1714,plain,
( ~ sQ144_spl
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[f1109,f101]) ).
fof(f1730,plain,
( ~ sQ144_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1714,f73]) ).
fof(f1731,plain,
~ sQ144_spl,
inference(contradiction_clause,[status(thm)],[f1730]) ).
fof(f1734,plain,
( ~ sQ140_spl
| product(e_4,e_3,e_4)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[f1093,f385]) ).
fof(f1749,plain,
( ~ sQ140_spl
| sQ99_spl
| sQ96_spl
| sQ100_spl
| sQ63_spl
| ~ sQ33_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f1734,f246,f259,f517,f762,f742,f759,f1092]) ).
fof(f1757,plain,
( ~ sQ146_spl
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[f1118,f101]) ).
fof(f1773,plain,
( ~ sQ146_spl
| sQ76_spl ),
inference(split_clause,[status(thm)],[f1757,f561,f1117]) ).
fof(f1779,plain,
! [X0] :
( ~ sQ43_spl
| product(e_2,e_2,X0)
| product(e_2,X0,e_3)
| product(e_2,X0,e_1)
| ~ group_element(X0)
| equalish(e_4,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,f404]) ).
fof(f1780,plain,
! [X0] :
( ~ sQ43_spl
| product(e_2,e_2,X0)
| product(e_2,X0,e_4)
| product(e_2,X0,e_1)
| ~ group_element(X0)
| equalish(e_3,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,f404]) ).
fof(f1781,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(f1782,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(f1786,definition,
( sQ204_spl
<=> equalish(e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ204_spl])],[split_symbol_definition]) ).
fof(f1787,plain,
( ~ sQ204_spl
| equalish(e_1,e_2) ),
inference(component_clause,[status(thm)],[f1786]) ).
fof(f1793,definition,
! [X0] :
( sQ205_spl
<=> ( product(e_2,e_2,X0)
| product(e_2,X0,e_3)
| product(e_2,X0,e_1)
| ~ group_element(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,[sQ205_spl])],[split_symbol_definition]) ).
fof(f1796,plain,
( ~ sQ43_spl
| sQ76_spl
| sQ205_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f1779,f246,f1793,f561,f403]) ).
fof(f1797,definition,
! [X0] :
( sQ206_spl
<=> ( product(e_2,e_2,X0)
| product(e_2,X0,e_4)
| product(e_2,X0,e_1)
| ~ group_element(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,[sQ206_spl])],[split_symbol_definition]) ).
fof(f1800,plain,
( ~ sQ43_spl
| sQ69_spl
| sQ206_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f1780,f246,f1797,f536,f403]) ).
fof(f1801,definition,
! [X0,X1] :
( sQ207_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,[sQ207_spl])],[split_symbol_definition]) ).
fof(f1804,plain,
( sQ76_spl
| sQ207_spl ),
inference(split_clause,[status(thm)],[f1781,f1801,f561]) ).
fof(f1805,definition,
! [X0,X1] :
( sQ208_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,[sQ208_spl])],[split_symbol_definition]) ).
fof(f1808,plain,
( sQ69_spl
| sQ208_spl ),
inference(split_clause,[status(thm)],[f1782,f1805,f536]) ).
fof(f1823,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(f1834,definition,
! [X0] :
( sQ212_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,[sQ212_spl])],[split_symbol_definition]) ).
fof(f1837,plain,
( ~ sQ33_spl
| sQ212_spl ),
inference(split_clause,[status(thm)],[f1823,f1834,f259]) ).
fof(f1867,plain,
( ~ sQ142_spl
| equalish(e_2,e_3) ),
inference(resolution,[status(thm)],[f1101,f97]) ).
fof(f1882,plain,
( ~ sQ142_spl
| sQ66_spl ),
inference(split_clause,[status(thm)],[f1867,f526,f1100]) ).
fof(f1887,plain,
( ~ sQ141_spl
| product(e_3,e_1,e_3)
| 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)],[f1098,f375]) ).
fof(f1903,plain,
( ~ sQ141_spl
| sQ125_spl
| sQ58_spl
| sQ123_spl
| sQ57_spl
| ~ sQ22_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f1887,f246,f216,f497,f903,f500,f915,f1097]) ).
fof(f2003,plain,
( ~ sQ153_spl
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[f1189,f97]) ).
fof(f2010,definition,
( sQ228_spl
<=> greater(e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ228_spl])],[split_symbol_definition]) ).
fof(f2012,plain,
( sQ228_spl
| ~ greater(e_2,e_1) ),
inference(component_clause,[status(thm)],[f2010]) ).
fof(f2026,plain,
( ~ sQ153_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2003,f76]) ).
fof(f2027,plain,
~ sQ153_spl,
inference(contradiction_clause,[status(thm)],[f2026]) ).
fof(f2028,plain,
( sQ228_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2012,f52]) ).
fof(f2029,plain,
sQ228_spl,
inference(contradiction_clause,[status(thm)],[f2028]) ).
fof(f2094,plain,
! [X0,X1] :
( ~ sQ48_spl
| equalish(X0,X1)
| product(e_3,X1,e_4)
| product(e_3,X1,e_3)
| product(e_3,X1,e_1)
| ~ group_element(X1)
| ~ group_element(e_3)
| product(e_3,e_3,X0)
| product(e_3,X0,e_4)
| product(e_3,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f425,f361]) ).
fof(f2103,plain,
( ~ sQ48_spl
| equalish(e_2,e_3)
| product(e_3,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)],[f425,f97]) ).
fof(f2110,plain,
! [X0] :
( ~ sQ48_spl
| equalish(e_4,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(e_3,e_3,X0)
| product(e_3,X0,e_2)
| product(e_3,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f425,f363]) ).
fof(f2114,plain,
( ~ sQ48_spl
| equalish(e_3,e_4)
| product(e_3,e_3,e_4)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1)
| ~ group_element(e_4) ),
inference(resolution,[status(thm)],[f425,f101]) ).
fof(f2126,plain,
! [X0] :
( ~ sQ48_spl
| product(e_4,e_3,e_3)
| 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(e_3,X0,e_4)
| product(e_3,X0,e_2)
| product(e_3,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f425,f385]) ).
fof(f2128,plain,
! [X0] :
( ~ sQ48_spl
| product(e_2,e_3,e_3)
| 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(e_3,X0,e_4)
| product(e_3,X0,e_2)
| product(e_3,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f425,f365]) ).
fof(f2129,plain,
( ~ sQ48_spl
| equalish(e_3,e_3)
| product(e_3,e_3,e_4)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_1)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[f425,f101]) ).
fof(f2139,definition,
! [X0,X1] :
( sQ233_spl
<=> ( equalish(X0,X1)
| product(e_3,X1,e_4)
| product(e_3,X1,e_3)
| product(e_3,X1,e_1)
| ~ group_element(X1)
| product(e_3,e_3,X0)
| product(e_3,X0,e_4)
| product(e_3,X0,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ233_spl])],[split_symbol_definition]) ).
fof(f2142,plain,
( ~ sQ48_spl
| ~ sQ33_spl
| sQ233_spl ),
inference(split_clause,[status(thm)],[f2094,f2139,f259,f424]) ).
fof(f2161,plain,
( ~ sQ48_spl
| sQ66_spl
| sQ102_spl
| sQ103_spl
| sQ101_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f2103,f259,f773,f779,f776,f526,f424]) ).
fof(f2166,definition,
! [X0] :
( sQ238_spl
<=> ( product(e_3,X0,e_4)
| product(e_3,X0,e_3)
| product(e_3,X0,e_1)
| ~ group_element(X0)
| product(e_3,e_3,X0)
| product(e_3,X0,e_2)
| product(e_3,X0,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ238_spl])],[split_symbol_definition]) ).
fof(f2169,plain,
( ~ sQ48_spl
| sQ76_spl
| ~ sQ33_spl
| sQ238_spl ),
inference(split_clause,[status(thm)],[f2110,f2166,f259,f561,f424]) ).
fof(f2182,definition,
( sQ242_spl
<=> equalish(e_3,e_4) ),
introduced(definition,[new_symbols(definition,[sQ242_spl])],[split_symbol_definition]) ).
fof(f2183,plain,
( ~ sQ242_spl
| equalish(e_3,e_4) ),
inference(component_clause,[status(thm)],[f2182]) ).
fof(f2185,plain,
( ~ sQ48_spl
| sQ242_spl
| sQ103_spl
| sQ140_spl
| sQ114_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f2114,f152,f864,f1092,f779,f2182,f424]) ).
fof(f2186,definition,
( sQ243_spl
<=> equalish(e_4,e_3) ),
introduced(definition,[new_symbols(definition,[sQ243_spl])],[split_symbol_definition]) ).
fof(f2187,plain,
( ~ sQ243_spl
| equalish(e_4,e_3) ),
inference(component_clause,[status(thm)],[f2186]) ).
fof(f2199,definition,
! [X0] :
( sQ245_spl
<=> ( product(X0,e_3,e_3)
| product(X0,e_3,e_2)
| product(X0,e_3,e_1)
| ~ group_element(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,[sQ245_spl])],[split_symbol_definition]) ).
fof(f2202,plain,
( ~ sQ48_spl
| sQ98_spl
| ~ sQ33_spl
| sQ245_spl ),
inference(split_clause,[status(thm)],[f2126,f2199,f259,f756,f424]) ).
fof(f2207,definition,
! [X0] :
( sQ247_spl
<=> ( product(X0,e_3,e_4)
| product(X0,e_3,e_3)
| product(X0,e_3,e_1)
| ~ group_element(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,[sQ247_spl])],[split_symbol_definition]) ).
fof(f2210,plain,
( ~ sQ48_spl
| sQ96_spl
| ~ sQ33_spl
| sQ247_spl ),
inference(split_clause,[status(thm)],[f2128,f2207,f259,f742,f424]) ).
fof(f2211,definition,
( sQ248_spl
<=> equalish(e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ248_spl])],[split_symbol_definition]) ).
fof(f2214,plain,
( ~ sQ48_spl
| sQ248_spl
| sQ103_spl
| sQ142_spl
| sQ101_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f2129,f259,f773,f1100,f779,f2211,f424]) ).
fof(f2221,plain,
( ~ sQ243_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2187,f84]) ).
fof(f2222,plain,
~ sQ243_spl,
inference(contradiction_clause,[status(thm)],[f2221]) ).
fof(f2223,plain,
( ~ sQ242_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2183,f81]) ).
fof(f2224,plain,
~ sQ242_spl,
inference(contradiction_clause,[status(thm)],[f2223]) ).
fof(f2237,plain,
( ~ sQ164_spl
| equalish(e_2,e_4) ),
inference(resolution,[status(thm)],[f1380,f97]) ).
fof(f2252,plain,
( ~ sQ164_spl
| sQ75_spl ),
inference(split_clause,[status(thm)],[f2237,f557,f1379]) ).
fof(f2273,plain,
( sQ129_spl
| product(e_1,e_1,e_3)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[f937,f85]) ).
fof(f2274,plain,
( sQ129_spl
| sQ128_spl
| sQ153_spl
| sQ127_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f2273,f216,f929,f1188,f932,f935]) ).
fof(f2342,plain,
! [X0,X1] :
( ~ sQ43_spl
| product(e_2,e_2,X1)
| product(e_2,X1,e_4)
| product(e_2,X1,e_1)
| ~ group_element(X1)
| equalish(X1,X0)
| 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)],[f371,f404]) ).
fof(f2344,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(f2353,definition,
! [X0] :
( sQ254_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,[sQ254_spl])],[split_symbol_definition]) ).
fof(f2361,definition,
! [X0,X1] :
( sQ256_spl
<=> ( product(e_2,e_2,X1)
| product(e_2,X1,e_4)
| product(e_2,X1,e_1)
| ~ group_element(X1)
| equalish(X1,X0)
| 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,[sQ256_spl])],[split_symbol_definition]) ).
fof(f2364,plain,
( ~ sQ43_spl
| sQ256_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f2342,f246,f2361,f403]) ).
fof(f2366,plain,
( sQ254_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f2344,f259,f2353]) ).
fof(f2379,plain,
! [X0] :
( ~ sQ48_spl
| product(e_3,e_3,X0)
| product(e_3,X0,e_2)
| product(e_3,X0,e_1)
| ~ group_element(X0)
| equalish(e_4,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,f425]) ).
fof(f2380,plain,
! [X0] :
( ~ sQ48_spl
| product(e_3,e_3,X0)
| product(e_3,X0,e_4)
| product(e_3,X0,e_1)
| ~ group_element(X0)
| equalish(e_2,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,f425]) ).
fof(f2384,plain,
! [X0] :
( ~ sQ43_spl
| product(e_2,e_2,X0)
| product(e_2,X0,e_3)
| product(e_2,X0,e_1)
| ~ group_element(X0)
| equalish(e_4,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,f404]) ).
fof(f2386,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(f2405,definition,
! [X0] :
( sQ258_spl
<=> ( product(e_3,e_3,X0)
| product(e_3,X0,e_2)
| product(e_3,X0,e_1)
| ~ group_element(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,[sQ258_spl])],[split_symbol_definition]) ).
fof(f2408,plain,
( ~ sQ48_spl
| sQ243_spl
| sQ258_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f2379,f259,f2405,f2186,f424]) ).
fof(f2409,definition,
! [X0] :
( sQ259_spl
<=> ( product(e_3,e_3,X0)
| product(e_3,X0,e_4)
| product(e_3,X0,e_1)
| ~ group_element(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,[sQ259_spl])],[split_symbol_definition]) ).
fof(f2412,plain,
( ~ sQ48_spl
| sQ66_spl
| sQ259_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f2380,f259,f2409,f526,f424]) ).
fof(f2419,definition,
! [X0] :
( sQ261_spl
<=> ( product(e_2,e_2,X0)
| product(e_2,X0,e_3)
| product(e_2,X0,e_1)
| ~ group_element(X0)
| 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,[sQ261_spl])],[split_symbol_definition]) ).
fof(f2422,plain,
( ~ sQ43_spl
| sQ243_spl
| sQ261_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f2384,f246,f2419,f2186,f403]) ).
fof(f2427,definition,
! [X0,X1] :
( sQ263_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,[sQ263_spl])],[split_symbol_definition]) ).
fof(f2430,plain,
( sQ243_spl
| sQ263_spl ),
inference(split_clause,[status(thm)],[f2386,f2427,f2186]) ).
fof(f2502,plain,
! [X0] :
( ~ sQ70_spl
| equalish(e_1,X0)
| 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)],[f541,f371]) ).
fof(f2503,plain,
! [X0] :
( ~ sQ70_spl
| equalish(e_2,X0)
| 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)],[f541,f369]) ).
fof(f2515,definition,
! [X0] :
( sQ265_spl
<=> ( equalish(e_1,X0)
| 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,[sQ265_spl])],[split_symbol_definition]) ).
fof(f2518,plain,
( ~ sQ70_spl
| sQ265_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f2502,f246,f2515,f540]) ).
fof(f2519,definition,
! [X0] :
( sQ266_spl
<=> ( equalish(e_2,X0)
| 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,[sQ266_spl])],[split_symbol_definition]) ).
fof(f2522,plain,
( ~ sQ70_spl
| ~ sQ22_spl
| sQ266_spl ),
inference(split_clause,[status(thm)],[f2503,f2519,f216,f540]) ).
fof(f2616,plain,
( ~ sQ5_spl
| ~ sQ60_spl
| ~ greater(e_1,e_0) ),
inference(resolution,[status(thm)],[f507,f137]) ).
fof(f2618,plain,
( ~ sQ5_spl
| ~ sQ60_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2616,f48]) ).
fof(f2619,plain,
( ~ sQ5_spl
| ~ sQ60_spl ),
inference(contradiction_clause,[status(thm)],[f2618]) ).
fof(f2621,plain,
( ~ sQ60_spl
| ~ sQ31_spl
| ~ greater(e_2,e_0) ),
inference(resolution,[status(thm)],[f250,f507]) ).
fof(f2628,plain,
( ~ sQ60_spl
| ~ sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2621,f49]) ).
fof(f2629,plain,
( ~ sQ60_spl
| ~ sQ31_spl ),
inference(contradiction_clause,[status(thm)],[f2628]) ).
fof(f2644,definition,
( sQ271_spl
<=> greater(e_2,e_0) ),
introduced(definition,[new_symbols(definition,[sQ271_spl])],[split_symbol_definition]) ).
fof(f2646,plain,
( sQ271_spl
| ~ greater(e_2,e_0) ),
inference(component_clause,[status(thm)],[f2644]) ).
fof(f2647,definition,
( sQ272_spl
<=> equalish(e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ272_spl])],[split_symbol_definition]) ).
fof(f2648,plain,
( ~ sQ272_spl
| equalish(e_2,e_1) ),
inference(component_clause,[status(thm)],[f2647]) ).
fof(f2655,plain,
( ~ sQ272_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2648,f76]) ).
fof(f2656,plain,
~ sQ272_spl,
inference(contradiction_clause,[status(thm)],[f2655]) ).
fof(f2657,plain,
( sQ271_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2646,f49]) ).
fof(f2658,plain,
sQ271_spl,
inference(contradiction_clause,[status(thm)],[f2657]) ).
fof(f2662,definition,
( sQ274_spl
<=> greater(e_1,e_0) ),
introduced(definition,[new_symbols(definition,[sQ274_spl])],[split_symbol_definition]) ).
fof(f2664,plain,
( sQ274_spl
| ~ greater(e_1,e_0) ),
inference(component_clause,[status(thm)],[f2662]) ).
fof(f2668,plain,
( ~ sQ204_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1787,f73]) ).
fof(f2669,plain,
~ sQ204_spl,
inference(contradiction_clause,[status(thm)],[f2668]) ).
fof(f2670,plain,
( sQ274_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2664,f48]) ).
fof(f2671,plain,
sQ274_spl,
inference(contradiction_clause,[status(thm)],[f2670]) ).
fof(f2672,plain,
( ~ sQ71_spl
| equalish(e_4,e_3) ),
inference(resolution,[status(thm)],[f544,f46]) ).
fof(f2673,plain,
( ~ sQ71_spl
| sQ243_spl ),
inference(split_clause,[status(thm)],[f2672,f2186,f543]) ).
fof(f2675,plain,
( ~ sQ157_spl
| equalish(e_2,e_3) ),
inference(resolution,[status(thm)],[f1339,f46]) ).
fof(f2676,plain,
( ~ sQ157_spl
| sQ66_spl ),
inference(split_clause,[status(thm)],[f2675,f526,f1338]) ).
fof(f2688,plain,
! [X0,X1] :
( ~ sQ53_spl
| equalish(X0,X1)
| product(e_4,X1,e_4)
| product(e_4,X1,e_3)
| product(e_4,X1,e_1)
| ~ group_element(X1)
| ~ group_element(e_4)
| product(e_4,e_4,X0)
| product(e_4,X0,e_3)
| product(e_4,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f446,f361]) ).
fof(f2690,plain,
! [X0] :
( ~ sQ53_spl
| equalish(e_2,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(e_4,e_4,X0)
| product(e_4,X0,e_3)
| product(e_4,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f446,f373]) ).
fof(f2698,plain,
( ~ sQ53_spl
| equalish(e_2,e_4)
| 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)],[f446,f97]) ).
fof(f2705,plain,
! [X0,X1] :
( ~ sQ53_spl
| equalish(X0,X1)
| product(e_4,X1,e_4)
| product(e_4,X1,e_2)
| product(e_4,X1,e_1)
| ~ group_element(X1)
| ~ group_element(e_4)
| product(e_4,e_4,X0)
| product(e_4,X0,e_2)
| product(e_4,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f446,f371]) ).
fof(f2728,plain,
! [X0] :
( ~ sQ53_spl
| product(e_3,e_4,e_4)
| 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(e_4,X0,e_3)
| product(e_4,X0,e_2)
| product(e_4,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f446,f375]) ).
fof(f2729,plain,
! [X0] :
( ~ sQ53_spl
| product(e_2,e_4,e_4)
| 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(e_4,X0,e_3)
| product(e_4,X0,e_2)
| product(e_4,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f446,f365]) ).
fof(f2730,plain,
( ~ sQ53_spl
| equalish(e_4,e_4)
| product(e_4,e_4,e_3)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_1)
| ~ group_element(e_4) ),
inference(resolution,[status(thm)],[f446,f101]) ).
fof(f2742,definition,
! [X0,X1] :
( sQ275_spl
<=> ( equalish(X0,X1)
| product(e_4,X1,e_4)
| product(e_4,X1,e_3)
| product(e_4,X1,e_1)
| ~ group_element(X1)
| product(e_4,e_4,X0)
| product(e_4,X0,e_3)
| product(e_4,X0,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ275_spl])],[split_symbol_definition]) ).
fof(f2745,plain,
( ~ sQ53_spl
| ~ sQ9_spl
| sQ275_spl ),
inference(split_clause,[status(thm)],[f2688,f2742,f152,f445]) ).
fof(f2747,definition,
! [X0] :
( sQ276_spl
<=> ( product(e_4,X0,e_4)
| product(e_4,X0,e_2)
| product(e_4,X0,e_1)
| ~ group_element(X0)
| product(e_4,e_4,X0)
| product(e_4,X0,e_3)
| product(e_4,X0,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ276_spl])],[split_symbol_definition]) ).
fof(f2750,plain,
( ~ sQ53_spl
| sQ66_spl
| ~ sQ9_spl
| sQ276_spl ),
inference(split_clause,[status(thm)],[f2690,f2747,f152,f526,f445]) ).
fof(f2768,plain,
( ~ sQ53_spl
| sQ75_spl
| sQ112_spl
| sQ111_spl
| sQ110_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f2698,f152,f845,f848,f851,f557,f445]) ).
fof(f2773,definition,
! [X0,X1] :
( sQ281_spl
<=> ( equalish(X0,X1)
| product(e_4,X1,e_4)
| product(e_4,X1,e_2)
| product(e_4,X1,e_1)
| ~ group_element(X1)
| product(e_4,e_4,X0)
| product(e_4,X0,e_2)
| product(e_4,X0,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ281_spl])],[split_symbol_definition]) ).
fof(f2776,plain,
( ~ sQ53_spl
| ~ sQ9_spl
| sQ281_spl ),
inference(split_clause,[status(thm)],[f2705,f2773,f152,f445]) ).
fof(f2822,definition,
! [X0] :
( sQ291_spl
<=> ( product(X0,e_4,e_4)
| product(X0,e_4,e_2)
| product(X0,e_4,e_1)
| ~ group_element(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,[sQ291_spl])],[split_symbol_definition]) ).
fof(f2825,plain,
( ~ sQ53_spl
| sQ116_spl
| ~ sQ9_spl
| sQ291_spl ),
inference(split_clause,[status(thm)],[f2728,f2822,f152,f870,f445]) ).
fof(f2826,definition,
! [X0] :
( sQ292_spl
<=> ( product(X0,e_4,e_4)
| product(X0,e_4,e_3)
| product(X0,e_4,e_1)
| ~ group_element(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,[sQ292_spl])],[split_symbol_definition]) ).
fof(f2829,plain,
( ~ sQ53_spl
| sQ95_spl
| ~ sQ9_spl
| sQ292_spl ),
inference(split_clause,[status(thm)],[f2729,f2826,f152,f733,f445]) ).
fof(f2830,definition,
( sQ293_spl
<=> equalish(e_4,e_4) ),
introduced(definition,[new_symbols(definition,[sQ293_spl])],[split_symbol_definition]) ).
fof(f2833,plain,
( ~ sQ53_spl
| sQ293_spl
| sQ111_spl
| sQ164_spl
| sQ110_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f2730,f152,f845,f1379,f848,f2830,f445]) ).
fof(f2843,plain,
( ~ sQ85_spl
| ~ sQ81_spl
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[f875,f644]) ).
fof(f2845,plain,
( ~ sQ85_spl
| ~ sQ81_spl
| sQ242_spl ),
inference(split_clause,[status(thm)],[f2843,f2182,f630,f643]) ).
fof(f2879,plain,
( ~ sQ63_spl
| ~ sQ97_spl
| equalish(e_2,e_4) ),
inference(resolution,[status(thm)],[f1057,f518]) ).
fof(f2881,plain,
( ~ sQ63_spl
| ~ sQ97_spl
| sQ75_spl ),
inference(split_clause,[status(thm)],[f2879,f557,f753,f517]) ).
fof(f2919,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(f2924,definition,
! [X0] :
( sQ297_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,[sQ297_spl])],[split_symbol_definition]) ).
fof(f2947,plain,
( ~ sQ9_spl
| sQ297_spl ),
inference(split_clause,[status(thm)],[f2919,f2924,f152]) ).
fof(f2952,plain,
! [X0,X1] :
( ~ sQ48_spl
| product(e_3,e_3,X1)
| product(e_3,X1,e_2)
| product(e_3,X1,e_1)
| ~ group_element(X1)
| equalish(X1,X0)
| 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)],[f381,f425]) ).
fof(f2955,plain,
! [X0,X1] :
( ~ sQ43_spl
| product(e_2,e_2,X1)
| product(e_2,X1,e_3)
| product(e_2,X1,e_1)
| ~ group_element(X1)
| equalish(X1,X0)
| 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)],[f381,f404]) ).
fof(f2957,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(f2962,definition,
! [X0] :
( sQ303_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,[sQ303_spl])],[split_symbol_definition]) ).
fof(f2974,definition,
! [X0,X1] :
( sQ306_spl
<=> ( product(e_3,e_3,X1)
| product(e_3,X1,e_2)
| product(e_3,X1,e_1)
| ~ group_element(X1)
| equalish(X1,X0)
| 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,[sQ306_spl])],[split_symbol_definition]) ).
fof(f2977,plain,
( ~ sQ48_spl
| sQ306_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f2952,f259,f2974,f424]) ).
fof(f2986,definition,
! [X0,X1] :
( sQ309_spl
<=> ( product(e_2,e_2,X1)
| product(e_2,X1,e_3)
| product(e_2,X1,e_1)
| ~ group_element(X1)
| equalish(X1,X0)
| 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,[sQ309_spl])],[split_symbol_definition]) ).
fof(f2989,plain,
( ~ sQ43_spl
| sQ309_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f2955,f246,f2986,f403]) ).
fof(f2991,plain,
( sQ303_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f2957,f152,f2962]) ).
fof(f2992,plain,
( ~ sQ60_spl
| ~ sQ32_spl
| ~ greater(e_3,e_0) ),
inference(resolution,[status(thm)],[f253,f507]) ).
fof(f2998,plain,
( ~ sQ60_spl
| ~ sQ32_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2992,f50]) ).
fof(f2999,plain,
( ~ sQ60_spl
| ~ sQ32_spl ),
inference(contradiction_clause,[status(thm)],[f2998]) ).
fof(f3000,plain,
$false,
inference(sat_refutation,[status(thm)],[f230,f255,f257,f270,f332,f355,f389,f393,f397,f401,f406,f410,f414,f418,f422,f427,f431,f435,f439,f443,f448,f539,f546,f550,f568,f572,f574,f576,f578,f580,f582,f589,f595,f601,f618,f659,f663,f667,f683,f684,f692,f765,f783,f787,f790,f858,f873,f940,f968,f1016,f1018,f1026,f1036,f1046,f1055,f1070,f1116,f1131,f1135,f1139,f1155,f1179,f1194,f1206,f1217,f1228,f1230,f1244,f1256,f1273,f1282,f1305,f1325,f1357,f1385,f1424,f1447,f1476,f1558,f1579,f1581,f1602,f1604,f1620,f1625,f1637,f1641,f1645,f1708,f1731,f1749,f1773,f1796,f1800,f1804,f1808,f1837,f1882,f1903,f2027,f2029,f2142,f2161,f2169,f2185,f2202,f2210,f2214,f2222,f2224,f2252,f2274,f2364,f2366,f2408,f2412,f2422,f2430,f2518,f2522,f2619,f2629,f2656,f2658,f2669,f2671,f2673,f2676,f2745,f2750,f2768,f2776,f2825,f2829,f2833,f2845,f2881,f2947,f2977,f2989,f2991,f2999]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP127-3.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n005.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sun Sep 20 20:00:02 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.35 % Drodi V4.1.1
% 3.73/0.91 % Refutation found
% 3.73/0.91 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 3.73/0.91 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.14/0.94 % Elapsed time: 0.597876 seconds
% 4.14/0.94 % CPU time: 4.471937 seconds
% 4.14/0.94 % Total memory used: 32.622 MB
% 4.14/0.94 % Net memory used: 30.298 MB
%------------------------------------------------------------------------------