%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP124-3.004 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 12:32:41 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.44s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 89
% Syntax : Number of formulae : 386 ( 90 unt; 62 def)
% Number of atoms : 842 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 890 ( 434 ~; 394 |; 0 &)
% ( 62 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 69 ( 68 usr; 63 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 167 ( 167 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
next(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
greater(e_1,e_0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
greater(e_2,e_0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
greater(e_3,e_0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
greater(e_2,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
greater(e_3,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
greater(e_4,e_1),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [X,Y] :
( ~ greater(Y,X)
| ~ product(X,e_1,Y)
| ~ cycle(X,e_0) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
group_element(e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
~ equalish(e_1,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,axiom,
~ equalish(e_2,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,axiom,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,axiom,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,axiom,
! [X] : product(X,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,negated_conjecture,
! [X1,Y1,Z1,X2,Y2,Z2] :
( equalish(X1,X2)
| ~ product(Z2,X2,Y2)
| ~ product(Z2,X1,Y1)
| ~ product(X2,Y2,Z1)
| ~ product(X1,Y1,Z1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
! [X1,Y1,Z1,X2,Y2,Z2] :
( equalish(Y1,Y2)
| ~ product(Z2,X2,Y2)
| ~ product(Z2,X1,Y1)
| ~ product(X2,Y2,Z1)
| ~ product(X1,Y1,Z1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,plain,
next(e_1,e_2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f49,plain,
greater(e_1,e_0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f50,plain,
greater(e_2,e_0),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f51,plain,
greater(e_3,e_0),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f53,plain,
greater(e_2,e_1),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f54,plain,
greater(e_3,e_1),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f55,plain,
greater(e_4,e_1),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f61,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(f67,plain,
! [X0,X1] :
( ~ greater(X1,X0)
| ~ product(X0,e_1,X1)
| ~ cycle(X0,e_0) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f68,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(f69,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)],[f68]) ).
fof(f70,plain,
group_element(e_1),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f71,plain,
group_element(e_2),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f72,plain,
group_element(e_3),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f73,plain,
group_element(e_4),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f74,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f75,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f76,plain,
~ equalish(e_1,e_4),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f78,plain,
~ equalish(e_2,e_3),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f79,plain,
~ equalish(e_2,e_4),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f82,plain,
~ equalish(e_3,e_4),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f86,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(f87,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W) ) ),
inference(miniscoping,[status(thm)],[f39]) ).
fof(f88,plain,
! [X0,X1,X2,X3] :
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f87]) ).
fof(f89,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product(X,Z,Y)
| ~ product(X,W,Y) ) ),
inference(miniscoping,[status(thm)],[f40]) ).
fof(f90,plain,
! [X0,X1,X2,X3] :
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f89]) ).
fof(f91,plain,
! [W,Z] :
( equalish(W,Z)
| ! [Y,X] :
( ~ product(Z,Y,X)
| ~ product(W,Y,X) ) ),
inference(miniscoping,[status(thm)],[f41]) ).
fof(f92,plain,
! [X0,X1,X2,X3] :
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f93,plain,
! [X0] : product(X0,X0,X0),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f94,plain,
! [X1,X2] :
( equalish(X1,X2)
| ! [Y2,Z2] :
( ~ product(Z2,X2,Y2)
| ! [Y1] :
( ~ product(Z2,X1,Y1)
| ! [Z1] :
( ~ product(X2,Y2,Z1)
| ~ product(X1,Y1,Z1) ) ) ) ),
inference(miniscoping,[status(thm)],[f43]) ).
fof(f95,plain,
! [X0,X1,X2,X3,X4,X5] :
( equalish(X0,X3)
| ~ product(X5,X3,X4)
| ~ product(X5,X0,X1)
| ~ product(X3,X4,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f94]) ).
fof(f96,plain,
! [Y1,Y2] :
( equalish(Y1,Y2)
| ! [X2,Z2] :
( ~ product(Z2,X2,Y2)
| ! [X1] :
( ~ product(Z2,X1,Y1)
| ! [Z1] :
( ~ product(X2,Y2,Z1)
| ~ product(X1,Y1,Z1) ) ) ) ),
inference(miniscoping,[status(thm)],[f44]) ).
fof(f97,plain,
! [X0,X1,X2,X3,X4,X5] :
( equalish(X1,X4)
| ~ product(X5,X3,X4)
| ~ product(X5,X0,X1)
| ~ product(X3,X4,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f96]) ).
fof(f98,plain,
! [X0,X1] :
( ~ product(e_2,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[f74,f92]) ).
fof(f99,plain,
! [X0,X1] :
( ~ product(X0,e_2,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f74,f90]) ).
fof(f100,plain,
! [X0,X1] :
( ~ product(X0,X1,e_2)
| ~ product(X0,X1,e_1) ),
inference(resolution,[status(thm)],[f74,f88]) ).
fof(f101,plain,
! [X0,X1,X2,X3] :
( ~ product(X3,X2,e_2)
| ~ product(X3,X0,e_1)
| ~ product(X2,e_2,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f74,f97]) ).
fof(f103,plain,
! [X0,X1] :
( ~ product(X1,e_2,e_2)
| ~ product(X1,X0,e_1)
| ~ product(X0,e_1,e_2) ),
inference(resolution,[status(thm)],[f101,f93]) ).
fof(f105,plain,
~ product(e_1,e_2,e_2),
inference(resolution,[status(thm)],[f98,f93]) ).
fof(f106,plain,
~ product(e_2,e_1,e_2),
inference(resolution,[status(thm)],[f99,f93]) ).
fof(f107,plain,
~ product(e_2,e_2,e_1),
inference(resolution,[status(thm)],[f100,f93]) ).
fof(f108,plain,
! [X0,X1] :
( ~ product(e_3,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[f75,f92]) ).
fof(f109,plain,
! [X0,X1] :
( ~ product(X0,e_3,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f75,f90]) ).
fof(f110,plain,
! [X0,X1] :
( ~ product(X0,X1,e_3)
| ~ product(X0,X1,e_1) ),
inference(resolution,[status(thm)],[f75,f88]) ).
fof(f112,plain,
! [X0,X1,X2,X3] :
( ~ product(X3,e_3,X2)
| ~ product(X3,e_1,X0)
| ~ product(e_3,X2,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[f75,f95]) ).
fof(f113,plain,
! [X0,X1] :
( ~ product(e_4,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[f76,f92]) ).
fof(f114,plain,
! [X0,X1] :
( ~ product(X0,e_4,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f76,f90]) ).
fof(f115,plain,
! [X0,X1] :
( ~ product(X0,X1,e_4)
| ~ product(X0,X1,e_1) ),
inference(resolution,[status(thm)],[f76,f88]) ).
fof(f123,plain,
! [X0,X1] :
( ~ product(e_3,X0,X1)
| ~ product(e_2,X0,X1) ),
inference(resolution,[status(thm)],[f78,f92]) ).
fof(f124,plain,
! [X0,X1] :
( ~ product(X0,e_3,X1)
| ~ product(X0,e_2,X1) ),
inference(resolution,[status(thm)],[f78,f90]) ).
fof(f125,plain,
! [X0,X1] :
( ~ product(X0,X1,e_3)
| ~ product(X0,X1,e_2) ),
inference(resolution,[status(thm)],[f78,f88]) ).
fof(f128,plain,
! [X0,X1] :
( ~ product(e_4,X0,X1)
| ~ product(e_2,X0,X1) ),
inference(resolution,[status(thm)],[f79,f92]) ).
fof(f129,plain,
! [X0,X1] :
( ~ product(X0,e_4,X1)
| ~ product(X0,e_2,X1) ),
inference(resolution,[status(thm)],[f79,f90]) ).
fof(f130,plain,
! [X0,X1] :
( ~ product(X0,X1,e_4)
| ~ product(X0,X1,e_2) ),
inference(resolution,[status(thm)],[f79,f88]) ).
fof(f143,plain,
! [X0,X1] :
( ~ product(e_4,X0,X1)
| ~ product(e_3,X0,X1) ),
inference(resolution,[status(thm)],[f82,f92]) ).
fof(f144,plain,
! [X0,X1] :
( ~ product(X0,e_4,X1)
| ~ product(X0,e_3,X1) ),
inference(resolution,[status(thm)],[f82,f90]) ).
fof(f145,plain,
! [X0,X1] :
( ~ product(X0,X1,e_4)
| ~ product(X0,X1,e_3) ),
inference(resolution,[status(thm)],[f82,f88]) ).
fof(f146,plain,
! [X0,X1,X2,X3] :
( ~ product(X3,X2,e_4)
| ~ product(X3,X0,e_3)
| ~ product(X2,e_4,X1)
| ~ product(X0,e_3,X1) ),
inference(resolution,[status(thm)],[f82,f97]) ).
fof(f158,plain,
! [X0,X1] :
( ~ product(X1,e_3,e_3)
| ~ product(X1,e_1,X0)
| ~ product(e_1,X0,e_3) ),
inference(resolution,[status(thm)],[f112,f93]) ).
fof(f160,plain,
~ product(e_1,e_3,e_3),
inference(resolution,[status(thm)],[f108,f93]) ).
fof(f161,plain,
~ product(e_3,e_1,e_3),
inference(resolution,[status(thm)],[f109,f93]) ).
fof(f162,plain,
~ product(e_3,e_3,e_1),
inference(resolution,[status(thm)],[f110,f93]) ).
fof(f163,plain,
~ product(e_1,e_4,e_4),
inference(resolution,[status(thm)],[f113,f93]) ).
fof(f164,plain,
~ product(e_4,e_1,e_4),
inference(resolution,[status(thm)],[f114,f93]) ).
fof(f175,plain,
~ product(e_4,e_4,e_1),
inference(resolution,[status(thm)],[f115,f93]) ).
fof(f176,plain,
~ product(e_2,e_3,e_3),
inference(resolution,[status(thm)],[f123,f93]) ).
fof(f179,plain,
! [X0,X1] :
( equalish(e_1,X1)
| ~ next(e_1,X1)
| ~ greater(X0,e_0)
| ~ cycle(e_1,X0) ),
inference(resolution,[status(thm)],[f69,f93]) ).
fof(f180,definition,
! [X0] :
( sQ0_spl
<=> ( ~ greater(X0,e_0)
| ~ cycle(e_1,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f181,plain,
! [X0] :
( ~ sQ0_spl
| ~ greater(X0,e_0)
| ~ cycle(e_1,X0) ),
inference(component_clause,[status(thm)],[f180]) ).
fof(f183,definition,
! [X1] :
( sQ1_spl
<=> ( equalish(e_1,X1)
| ~ next(e_1,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f184,plain,
! [X0] :
( ~ sQ1_spl
| equalish(e_1,X0)
| ~ next(e_1,X0) ),
inference(component_clause,[status(thm)],[f183]) ).
fof(f186,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f179,f180,f183]) ).
fof(f189,plain,
( ~ sQ0_spl
| cycle(e_1,e_2)
| cycle(e_1,e_1)
| cycle(e_1,e_0)
| ~ group_element(e_1)
| ~ greater(e_3,e_0) ),
inference(resolution,[status(thm)],[f181,f61]) ).
fof(f190,definition,
( sQ2_spl
<=> greater(e_3,e_0) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f192,plain,
( sQ2_spl
| ~ greater(e_3,e_0) ),
inference(component_clause,[status(thm)],[f190]) ).
fof(f193,definition,
( sQ3_spl
<=> group_element(e_1) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f195,plain,
( sQ3_spl
| ~ group_element(e_1) ),
inference(component_clause,[status(thm)],[f193]) ).
fof(f196,definition,
( sQ4_spl
<=> cycle(e_1,e_0) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f197,plain,
( ~ sQ4_spl
| cycle(e_1,e_0) ),
inference(component_clause,[status(thm)],[f196]) ).
fof(f199,definition,
( sQ5_spl
<=> cycle(e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f200,plain,
( ~ sQ5_spl
| cycle(e_1,e_1) ),
inference(component_clause,[status(thm)],[f199]) ).
fof(f202,definition,
( sQ6_spl
<=> cycle(e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f203,plain,
( ~ sQ6_spl
| cycle(e_1,e_2) ),
inference(component_clause,[status(thm)],[f202]) ).
fof(f205,plain,
( ~ sQ0_spl
| sQ6_spl
| sQ5_spl
| sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f189,f190,f193,f196,f199,f202,f180]) ).
fof(f208,plain,
( ~ sQ1_spl
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[f184,f46]) ).
fof(f209,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f208,f74]) ).
fof(f210,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f209]) ).
fof(f217,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| ~ greater(e_2,e_0) ),
inference(resolution,[status(thm)],[f181,f203]) ).
fof(f219,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f217,f50]) ).
fof(f220,plain,
( ~ sQ6_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f219]) ).
fof(f222,plain,
~ product(e_3,e_2,e_3),
inference(resolution,[status(thm)],[f124,f93]) ).
fof(f223,plain,
~ product(e_3,e_3,e_2),
inference(resolution,[status(thm)],[f125,f93]) ).
fof(f224,plain,
( ~ sQ0_spl
| ~ sQ5_spl
| ~ greater(e_1,e_0) ),
inference(resolution,[status(thm)],[f200,f181]) ).
fof(f227,plain,
( ~ sQ0_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f224,f49]) ).
fof(f228,plain,
( ~ sQ0_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f227]) ).
fof(f230,plain,
! [X0] :
( ~ sQ4_spl
| ~ greater(X0,e_1)
| ~ product(e_1,e_1,X0) ),
inference(resolution,[status(thm)],[f197,f67]) ).
fof(f234,plain,
~ product(e_2,e_4,e_4),
inference(resolution,[status(thm)],[f128,f93]) ).
fof(f235,plain,
! [X0] :
( product(X0,e_4,e_4)
| product(X0,e_4,e_3)
| product(X0,e_4,e_2)
| product(X0,e_4,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f86,f73]) ).
fof(f236,plain,
! [X0] :
( product(X0,e_3,e_4)
| product(X0,e_3,e_3)
| product(X0,e_3,e_2)
| product(X0,e_3,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f86,f72]) ).
fof(f237,plain,
! [X0] :
( product(X0,e_2,e_4)
| product(X0,e_2,e_3)
| product(X0,e_2,e_2)
| product(X0,e_2,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f86,f71]) ).
fof(f238,plain,
! [X0] :
( product(X0,e_1,e_4)
| product(X0,e_1,e_3)
| product(X0,e_1,e_2)
| product(X0,e_1,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f86,f70]) ).
fof(f240,plain,
~ product(e_4,e_2,e_4),
inference(resolution,[status(thm)],[f129,f93]) ).
fof(f242,plain,
~ product(e_4,e_4,e_2),
inference(resolution,[status(thm)],[f130,f93]) ).
fof(f244,plain,
~ product(e_3,e_4,e_4),
inference(resolution,[status(thm)],[f143,f93]) ).
fof(f245,plain,
~ product(e_4,e_3,e_4),
inference(resolution,[status(thm)],[f144,f93]) ).
fof(f246,plain,
~ product(e_4,e_4,e_3),
inference(resolution,[status(thm)],[f145,f93]) ).
fof(f247,plain,
! [X0,X1] :
( ~ product(X1,e_4,e_4)
| ~ product(X1,X0,e_3)
| ~ product(X0,e_3,e_4) ),
inference(resolution,[status(thm)],[f146,f93]) ).
fof(f257,definition,
( sQ9_spl
<=> group_element(e_4) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f259,plain,
( sQ9_spl
| ~ group_element(e_4) ),
inference(component_clause,[status(thm)],[f257]) ).
fof(f278,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f259,f73]) ).
fof(f279,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f278]) ).
fof(f299,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f195,f70]) ).
fof(f300,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f299]) ).
fof(f301,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f192,f51]) ).
fof(f302,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f301]) ).
fof(f337,plain,
( product(e_4,e_4,e_4)
| product(e_4,e_4,e_3)
| product(e_4,e_4,e_2)
| product(e_4,e_4,e_1) ),
inference(resolution,[status(thm)],[f235,f73]) ).
fof(f338,plain,
( product(e_3,e_4,e_4)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[f235,f72]) ).
fof(f340,plain,
( product(e_1,e_4,e_4)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_1) ),
inference(resolution,[status(thm)],[f235,f70]) ).
fof(f341,definition,
( sQ22_spl
<=> product(e_4,e_4,e_1) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f342,plain,
( ~ sQ22_spl
| product(e_4,e_4,e_1) ),
inference(component_clause,[status(thm)],[f341]) ).
fof(f344,definition,
( sQ23_spl
<=> product(e_4,e_4,e_2) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f345,plain,
( ~ sQ23_spl
| product(e_4,e_4,e_2) ),
inference(component_clause,[status(thm)],[f344]) ).
fof(f347,definition,
( sQ24_spl
<=> product(e_4,e_4,e_3) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f348,plain,
( ~ sQ24_spl
| product(e_4,e_4,e_3) ),
inference(component_clause,[status(thm)],[f347]) ).
fof(f350,definition,
( sQ25_spl
<=> product(e_4,e_4,e_4) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f353,plain,
( sQ25_spl
| sQ24_spl
| sQ23_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f337,f341,f344,f347,f350]) ).
fof(f354,definition,
( sQ26_spl
<=> product(e_3,e_4,e_1) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f355,plain,
( ~ sQ26_spl
| product(e_3,e_4,e_1) ),
inference(component_clause,[status(thm)],[f354]) ).
fof(f357,definition,
( sQ27_spl
<=> product(e_3,e_4,e_2) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f358,plain,
( ~ sQ27_spl
| product(e_3,e_4,e_2) ),
inference(component_clause,[status(thm)],[f357]) ).
fof(f360,definition,
( sQ28_spl
<=> product(e_3,e_4,e_3) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f361,plain,
( ~ sQ28_spl
| product(e_3,e_4,e_3) ),
inference(component_clause,[status(thm)],[f360]) ).
fof(f363,definition,
( sQ29_spl
<=> product(e_3,e_4,e_4) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f364,plain,
( ~ sQ29_spl
| product(e_3,e_4,e_4) ),
inference(component_clause,[status(thm)],[f363]) ).
fof(f366,plain,
( sQ29_spl
| sQ28_spl
| sQ27_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f338,f354,f357,f360,f363]) ).
fof(f376,definition,
( sQ33_spl
<=> product(e_2,e_4,e_4) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f377,plain,
( ~ sQ33_spl
| product(e_2,e_4,e_4) ),
inference(component_clause,[status(thm)],[f376]) ).
fof(f380,definition,
( sQ34_spl
<=> product(e_1,e_4,e_1) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f381,plain,
( ~ sQ34_spl
| product(e_1,e_4,e_1) ),
inference(component_clause,[status(thm)],[f380]) ).
fof(f383,definition,
( sQ35_spl
<=> product(e_1,e_4,e_2) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f384,plain,
( ~ sQ35_spl
| product(e_1,e_4,e_2) ),
inference(component_clause,[status(thm)],[f383]) ).
fof(f386,definition,
( sQ36_spl
<=> product(e_1,e_4,e_3) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f387,plain,
( ~ sQ36_spl
| product(e_1,e_4,e_3) ),
inference(component_clause,[status(thm)],[f386]) ).
fof(f389,definition,
( sQ37_spl
<=> product(e_1,e_4,e_4) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f390,plain,
( ~ sQ37_spl
| product(e_1,e_4,e_4) ),
inference(component_clause,[status(thm)],[f389]) ).
fof(f392,plain,
( sQ37_spl
| sQ36_spl
| sQ35_spl
| sQ34_spl ),
inference(split_clause,[status(thm)],[f340,f380,f383,f386,f389]) ).
fof(f393,plain,
( ~ sQ37_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f390,f163]) ).
fof(f394,plain,
~ sQ37_spl,
inference(contradiction_clause,[status(thm)],[f393]) ).
fof(f395,plain,
( ~ sQ33_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f377,f234]) ).
fof(f396,plain,
~ sQ33_spl,
inference(contradiction_clause,[status(thm)],[f395]) ).
fof(f397,plain,
( ~ sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f364,f244]) ).
fof(f398,plain,
~ sQ29_spl,
inference(contradiction_clause,[status(thm)],[f397]) ).
fof(f399,plain,
( ~ sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f348,f246]) ).
fof(f400,plain,
~ sQ24_spl,
inference(contradiction_clause,[status(thm)],[f399]) ).
fof(f401,plain,
( ~ sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f345,f242]) ).
fof(f402,plain,
~ sQ23_spl,
inference(contradiction_clause,[status(thm)],[f401]) ).
fof(f403,plain,
( ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f342,f175]) ).
fof(f404,plain,
~ sQ22_spl,
inference(contradiction_clause,[status(thm)],[f403]) ).
fof(f405,plain,
( product(e_4,e_3,e_4)
| product(e_4,e_3,e_3)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_1) ),
inference(resolution,[status(thm)],[f236,f73]) ).
fof(f407,plain,
( product(e_2,e_3,e_4)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[f236,f71]) ).
fof(f408,plain,
( product(e_1,e_3,e_4)
| product(e_1,e_3,e_3)
| product(e_1,e_3,e_2)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[f236,f70]) ).
fof(f409,definition,
( sQ38_spl
<=> product(e_4,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f410,plain,
( ~ sQ38_spl
| product(e_4,e_3,e_1) ),
inference(component_clause,[status(thm)],[f409]) ).
fof(f412,definition,
( sQ39_spl
<=> product(e_4,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f413,plain,
( ~ sQ39_spl
| product(e_4,e_3,e_2) ),
inference(component_clause,[status(thm)],[f412]) ).
fof(f415,definition,
( sQ40_spl
<=> product(e_4,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f416,plain,
( ~ sQ40_spl
| product(e_4,e_3,e_3) ),
inference(component_clause,[status(thm)],[f415]) ).
fof(f418,definition,
( sQ41_spl
<=> product(e_4,e_3,e_4) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f419,plain,
( ~ sQ41_spl
| product(e_4,e_3,e_4) ),
inference(component_clause,[status(thm)],[f418]) ).
fof(f421,plain,
( sQ41_spl
| sQ40_spl
| sQ39_spl
| sQ38_spl ),
inference(split_clause,[status(thm)],[f405,f409,f412,f415,f418]) ).
fof(f422,definition,
( sQ42_spl
<=> product(e_3,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f423,plain,
( ~ sQ42_spl
| product(e_3,e_3,e_1) ),
inference(component_clause,[status(thm)],[f422]) ).
fof(f425,definition,
( sQ43_spl
<=> product(e_3,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f426,plain,
( ~ sQ43_spl
| product(e_3,e_3,e_2) ),
inference(component_clause,[status(thm)],[f425]) ).
fof(f435,definition,
( sQ46_spl
<=> product(e_2,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f436,plain,
( ~ sQ46_spl
| product(e_2,e_3,e_1) ),
inference(component_clause,[status(thm)],[f435]) ).
fof(f438,definition,
( sQ47_spl
<=> product(e_2,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f439,plain,
( ~ sQ47_spl
| product(e_2,e_3,e_2) ),
inference(component_clause,[status(thm)],[f438]) ).
fof(f441,definition,
( sQ48_spl
<=> product(e_2,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f442,plain,
( ~ sQ48_spl
| product(e_2,e_3,e_3) ),
inference(component_clause,[status(thm)],[f441]) ).
fof(f444,definition,
( sQ49_spl
<=> product(e_2,e_3,e_4) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f445,plain,
( ~ sQ49_spl
| product(e_2,e_3,e_4) ),
inference(component_clause,[status(thm)],[f444]) ).
fof(f447,plain,
( sQ49_spl
| sQ48_spl
| sQ47_spl
| sQ46_spl ),
inference(split_clause,[status(thm)],[f407,f435,f438,f441,f444]) ).
fof(f448,definition,
( sQ50_spl
<=> product(e_1,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f449,plain,
( ~ sQ50_spl
| product(e_1,e_3,e_1) ),
inference(component_clause,[status(thm)],[f448]) ).
fof(f451,definition,
( sQ51_spl
<=> product(e_1,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f452,plain,
( ~ sQ51_spl
| product(e_1,e_3,e_2) ),
inference(component_clause,[status(thm)],[f451]) ).
fof(f454,definition,
( sQ52_spl
<=> product(e_1,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f455,plain,
( ~ sQ52_spl
| product(e_1,e_3,e_3) ),
inference(component_clause,[status(thm)],[f454]) ).
fof(f457,definition,
( sQ53_spl
<=> product(e_1,e_3,e_4) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f458,plain,
( ~ sQ53_spl
| product(e_1,e_3,e_4) ),
inference(component_clause,[status(thm)],[f457]) ).
fof(f460,plain,
( sQ53_spl
| sQ52_spl
| sQ51_spl
| sQ50_spl ),
inference(split_clause,[status(thm)],[f408,f448,f451,f454,f457]) ).
fof(f461,plain,
( ~ sQ52_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f455,f160]) ).
fof(f462,plain,
~ sQ52_spl,
inference(contradiction_clause,[status(thm)],[f461]) ).
fof(f463,plain,
( ~ sQ48_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f442,f176]) ).
fof(f464,plain,
~ sQ48_spl,
inference(contradiction_clause,[status(thm)],[f463]) ).
fof(f465,plain,
( ~ sQ43_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f426,f223]) ).
fof(f466,plain,
~ sQ43_spl,
inference(contradiction_clause,[status(thm)],[f465]) ).
fof(f467,plain,
( ~ sQ42_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f423,f162]) ).
fof(f468,plain,
~ sQ42_spl,
inference(contradiction_clause,[status(thm)],[f467]) ).
fof(f469,plain,
( ~ sQ41_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f419,f245]) ).
fof(f470,plain,
~ sQ41_spl,
inference(contradiction_clause,[status(thm)],[f469]) ).
fof(f478,definition,
( sQ55_spl
<=> group_element(e_2) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f480,plain,
( sQ55_spl
| ~ group_element(e_2) ),
inference(component_clause,[status(thm)],[f478]) ).
fof(f491,plain,
( sQ55_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f480,f71]) ).
fof(f492,plain,
sQ55_spl,
inference(contradiction_clause,[status(thm)],[f491]) ).
fof(f507,plain,
! [X0] :
( ~ sQ36_spl
| ~ product(X0,e_3,e_3)
| ~ product(X0,e_1,e_4) ),
inference(resolution,[status(thm)],[f387,f158]) ).
fof(f511,plain,
( ~ sQ36_spl
| ~ product(e_1,e_2,e_3) ),
inference(resolution,[status(thm)],[f387,f129]) ).
fof(f518,plain,
( ~ sQ35_spl
| ~ product(e_1,e_3,e_2) ),
inference(resolution,[status(thm)],[f384,f144]) ).
fof(f528,plain,
( ~ sQ34_spl
| ~ product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f381,f114]) ).
fof(f530,plain,
( ~ sQ34_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f528,f93]) ).
fof(f531,plain,
~ sQ34_spl,
inference(contradiction_clause,[status(thm)],[f530]) ).
fof(f569,plain,
( ~ sQ28_spl
| ~ product(e_3,e_3,e_3) ),
inference(resolution,[status(thm)],[f361,f144]) ).
fof(f576,plain,
( ~ sQ28_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f569,f93]) ).
fof(f577,plain,
~ sQ28_spl,
inference(contradiction_clause,[status(thm)],[f576]) ).
fof(f580,plain,
( ~ sQ27_spl
| ~ product(e_1,e_4,e_2) ),
inference(resolution,[status(thm)],[f358,f108]) ).
fof(f589,plain,
( ~ sQ27_spl
| ~ sQ35_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f580,f384]) ).
fof(f590,plain,
( ~ sQ27_spl
| ~ sQ35_spl ),
inference(contradiction_clause,[status(thm)],[f589]) ).
fof(f591,plain,
( product(e_4,e_2,e_4)
| product(e_4,e_2,e_3)
| product(e_4,e_2,e_2)
| product(e_4,e_2,e_1) ),
inference(resolution,[status(thm)],[f237,f73]) ).
fof(f593,plain,
( product(e_2,e_2,e_4)
| product(e_2,e_2,e_3)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[f237,f71]) ).
fof(f594,plain,
( product(e_1,e_2,e_4)
| product(e_1,e_2,e_3)
| product(e_1,e_2,e_2)
| product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[f237,f70]) ).
fof(f595,definition,
( sQ59_spl
<=> product(e_4,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f596,plain,
( ~ sQ59_spl
| product(e_4,e_2,e_1) ),
inference(component_clause,[status(thm)],[f595]) ).
fof(f598,definition,
( sQ60_spl
<=> product(e_4,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f601,definition,
( sQ61_spl
<=> product(e_4,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f602,plain,
( ~ sQ61_spl
| product(e_4,e_2,e_3) ),
inference(component_clause,[status(thm)],[f601]) ).
fof(f604,definition,
( sQ62_spl
<=> product(e_4,e_2,e_4) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f605,plain,
( ~ sQ62_spl
| product(e_4,e_2,e_4) ),
inference(component_clause,[status(thm)],[f604]) ).
fof(f607,plain,
( sQ62_spl
| sQ61_spl
| sQ60_spl
| sQ59_spl ),
inference(split_clause,[status(thm)],[f591,f595,f598,f601,f604]) ).
fof(f611,definition,
( sQ64_spl
<=> product(e_3,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f612,plain,
( ~ sQ64_spl
| product(e_3,e_2,e_2) ),
inference(component_clause,[status(thm)],[f611]) ).
fof(f614,definition,
( sQ65_spl
<=> product(e_3,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f615,plain,
( ~ sQ65_spl
| product(e_3,e_2,e_3) ),
inference(component_clause,[status(thm)],[f614]) ).
fof(f621,definition,
( sQ67_spl
<=> product(e_2,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f622,plain,
( ~ sQ67_spl
| product(e_2,e_2,e_1) ),
inference(component_clause,[status(thm)],[f621]) ).
fof(f624,definition,
( sQ68_spl
<=> product(e_2,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f627,definition,
( sQ69_spl
<=> product(e_2,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f628,plain,
( ~ sQ69_spl
| product(e_2,e_2,e_3) ),
inference(component_clause,[status(thm)],[f627]) ).
fof(f630,definition,
( sQ70_spl
<=> product(e_2,e_2,e_4) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f631,plain,
( ~ sQ70_spl
| product(e_2,e_2,e_4) ),
inference(component_clause,[status(thm)],[f630]) ).
fof(f633,plain,
( sQ70_spl
| sQ69_spl
| sQ68_spl
| sQ67_spl ),
inference(split_clause,[status(thm)],[f593,f621,f624,f627,f630]) ).
fof(f634,definition,
( sQ71_spl
<=> product(e_1,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f635,plain,
( ~ sQ71_spl
| product(e_1,e_2,e_1) ),
inference(component_clause,[status(thm)],[f634]) ).
fof(f637,definition,
( sQ72_spl
<=> product(e_1,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f638,plain,
( ~ sQ72_spl
| product(e_1,e_2,e_2) ),
inference(component_clause,[status(thm)],[f637]) ).
fof(f640,definition,
( sQ73_spl
<=> product(e_1,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f641,plain,
( ~ sQ73_spl
| product(e_1,e_2,e_3) ),
inference(component_clause,[status(thm)],[f640]) ).
fof(f643,definition,
( sQ74_spl
<=> product(e_1,e_2,e_4) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f646,plain,
( sQ74_spl
| sQ73_spl
| sQ72_spl
| sQ71_spl ),
inference(split_clause,[status(thm)],[f594,f634,f637,f640,f643]) ).
fof(f647,plain,
( ~ sQ72_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f638,f105]) ).
fof(f648,plain,
~ sQ72_spl,
inference(contradiction_clause,[status(thm)],[f647]) ).
fof(f649,plain,
( ~ sQ67_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f622,f107]) ).
fof(f650,plain,
~ sQ67_spl,
inference(contradiction_clause,[status(thm)],[f649]) ).
fof(f651,plain,
( ~ sQ65_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f615,f222]) ).
fof(f652,plain,
~ sQ65_spl,
inference(contradiction_clause,[status(thm)],[f651]) ).
fof(f653,plain,
( ~ sQ62_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f605,f240]) ).
fof(f654,plain,
~ sQ62_spl,
inference(contradiction_clause,[status(thm)],[f653]) ).
fof(f656,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_1,e_3)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(resolution,[status(thm)],[f238,f72]) ).
fof(f658,plain,
( product(e_1,e_1,e_4)
| product(e_1,e_1,e_3)
| product(e_1,e_1,e_2)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f238,f70]) ).
fof(f659,definition,
( sQ75_spl
<=> product(e_4,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f660,plain,
( ~ sQ75_spl
| product(e_4,e_1,e_1) ),
inference(component_clause,[status(thm)],[f659]) ).
fof(f668,definition,
( sQ78_spl
<=> product(e_4,e_1,e_4) ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f669,plain,
( ~ sQ78_spl
| product(e_4,e_1,e_4) ),
inference(component_clause,[status(thm)],[f668]) ).
fof(f672,definition,
( sQ79_spl
<=> product(e_3,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f673,plain,
( ~ sQ79_spl
| product(e_3,e_1,e_1) ),
inference(component_clause,[status(thm)],[f672]) ).
fof(f675,definition,
( sQ80_spl
<=> product(e_3,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f676,plain,
( ~ sQ80_spl
| product(e_3,e_1,e_2) ),
inference(component_clause,[status(thm)],[f675]) ).
fof(f678,definition,
( sQ81_spl
<=> product(e_3,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f679,plain,
( ~ sQ81_spl
| product(e_3,e_1,e_3) ),
inference(component_clause,[status(thm)],[f678]) ).
fof(f681,definition,
( sQ82_spl
<=> product(e_3,e_1,e_4) ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f682,plain,
( ~ sQ82_spl
| product(e_3,e_1,e_4) ),
inference(component_clause,[status(thm)],[f681]) ).
fof(f684,plain,
( sQ82_spl
| sQ81_spl
| sQ80_spl
| sQ79_spl ),
inference(split_clause,[status(thm)],[f656,f672,f675,f678,f681]) ).
fof(f685,definition,
( sQ83_spl
<=> product(e_2,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f686,plain,
( ~ sQ83_spl
| product(e_2,e_1,e_1) ),
inference(component_clause,[status(thm)],[f685]) ).
fof(f688,definition,
( sQ84_spl
<=> product(e_2,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f689,plain,
( ~ sQ84_spl
| product(e_2,e_1,e_2) ),
inference(component_clause,[status(thm)],[f688]) ).
fof(f698,definition,
( sQ87_spl
<=> product(e_1,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f701,definition,
( sQ88_spl
<=> product(e_1,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition]) ).
fof(f702,plain,
( ~ sQ88_spl
| product(e_1,e_1,e_2) ),
inference(component_clause,[status(thm)],[f701]) ).
fof(f704,definition,
( sQ89_spl
<=> product(e_1,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[sQ89_spl])],[split_symbol_definition]) ).
fof(f705,plain,
( ~ sQ89_spl
| product(e_1,e_1,e_3) ),
inference(component_clause,[status(thm)],[f704]) ).
fof(f707,definition,
( sQ90_spl
<=> product(e_1,e_1,e_4) ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f708,plain,
( ~ sQ90_spl
| product(e_1,e_1,e_4) ),
inference(component_clause,[status(thm)],[f707]) ).
fof(f710,plain,
( sQ90_spl
| sQ89_spl
| sQ88_spl
| sQ87_spl ),
inference(split_clause,[status(thm)],[f658,f698,f701,f704,f707]) ).
fof(f711,plain,
( ~ sQ84_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f689,f106]) ).
fof(f712,plain,
~ sQ84_spl,
inference(contradiction_clause,[status(thm)],[f711]) ).
fof(f713,plain,
( ~ sQ81_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f679,f161]) ).
fof(f714,plain,
~ sQ81_spl,
inference(contradiction_clause,[status(thm)],[f713]) ).
fof(f715,plain,
( ~ sQ78_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f669,f164]) ).
fof(f716,plain,
~ sQ78_spl,
inference(contradiction_clause,[status(thm)],[f715]) ).
fof(f749,plain,
! [X0,X1] :
( ~ sQ26_spl
| ~ product(X1,e_3,e_4)
| ~ product(X1,e_1,X0)
| ~ product(e_1,X0,e_1) ),
inference(resolution,[status(thm)],[f355,f112]) ).
fof(f760,plain,
( ~ sQ53_spl
| ~ product(e_1,e_2,e_4) ),
inference(resolution,[status(thm)],[f458,f124]) ).
fof(f767,plain,
( ~ sQ51_spl
| ~ sQ35_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f452,f518]) ).
fof(f768,plain,
( ~ sQ51_spl
| ~ sQ35_spl ),
inference(contradiction_clause,[status(thm)],[f767]) ).
fof(f771,plain,
( ~ sQ50_spl
| ~ product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f449,f109]) ).
fof(f773,plain,
( ~ sQ50_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f771,f93]) ).
fof(f774,plain,
~ sQ50_spl,
inference(contradiction_clause,[status(thm)],[f773]) ).
fof(f779,plain,
! [X0] :
( ~ sQ49_spl
| ~ product(X0,e_4,e_4)
| ~ product(X0,e_2,e_3) ),
inference(resolution,[status(thm)],[f445,f247]) ).
fof(f789,plain,
! [X0] :
( ~ sQ26_spl
| ~ product(X0,e_3,e_4)
| ~ product(X0,e_1,e_1) ),
inference(resolution,[status(thm)],[f749,f93]) ).
fof(f793,plain,
( ~ sQ47_spl
| ~ product(e_2,e_2,e_2) ),
inference(resolution,[status(thm)],[f439,f124]) ).
fof(f798,plain,
( ~ sQ47_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f793,f93]) ).
fof(f799,plain,
~ sQ47_spl,
inference(contradiction_clause,[status(thm)],[f798]) ).
fof(f824,plain,
( ~ sQ40_spl
| ~ product(e_3,e_3,e_3) ),
inference(resolution,[status(thm)],[f416,f143]) ).
fof(f835,plain,
( ~ sQ40_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f824,f93]) ).
fof(f836,plain,
~ sQ40_spl,
inference(contradiction_clause,[status(thm)],[f835]) ).
fof(f842,plain,
( ~ sQ39_spl
| ~ product(e_1,e_3,e_2) ),
inference(resolution,[status(thm)],[f413,f113]) ).
fof(f852,plain,
( ~ sQ38_spl
| ~ product(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[f410,f128]) ).
fof(f856,plain,
( ~ sQ38_spl
| ~ product(e_4,e_2,e_1) ),
inference(resolution,[status(thm)],[f410,f124]) ).
fof(f860,plain,
( ~ sQ38_spl
| ~ sQ46_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f852,f436]) ).
fof(f861,plain,
( ~ sQ38_spl
| ~ sQ46_spl ),
inference(contradiction_clause,[status(thm)],[f860]) ).
fof(f870,plain,
( ~ sQ53_spl
| ~ sQ26_spl
| ~ product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f789,f458]) ).
fof(f871,plain,
( ~ sQ53_spl
| ~ sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f870,f93]) ).
fof(f872,plain,
( ~ sQ53_spl
| ~ sQ26_spl ),
inference(contradiction_clause,[status(thm)],[f871]) ).
fof(f877,plain,
( ~ sQ71_spl
| ~ product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f635,f99]) ).
fof(f879,plain,
( ~ sQ71_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f877,f93]) ).
fof(f880,plain,
~ sQ71_spl,
inference(contradiction_clause,[status(thm)],[f879]) ).
fof(f888,plain,
( ~ sQ70_spl
| ~ product(e_2,e_2,e_2) ),
inference(resolution,[status(thm)],[f631,f130]) ).
fof(f890,plain,
( ~ sQ70_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f888,f93]) ).
fof(f891,plain,
~ sQ70_spl,
inference(contradiction_clause,[status(thm)],[f890]) ).
fof(f898,plain,
( ~ sQ69_spl
| ~ product(e_2,e_2,e_2) ),
inference(resolution,[status(thm)],[f628,f125]) ).
fof(f900,plain,
( ~ sQ69_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f898,f93]) ).
fof(f901,plain,
~ sQ69_spl,
inference(contradiction_clause,[status(thm)],[f900]) ).
fof(f915,plain,
( ~ sQ64_spl
| ~ product(e_2,e_2,e_2) ),
inference(resolution,[status(thm)],[f612,f123]) ).
fof(f921,plain,
( ~ sQ64_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f915,f93]) ).
fof(f922,plain,
~ sQ64_spl,
inference(contradiction_clause,[status(thm)],[f921]) ).
fof(f952,plain,
( ~ sQ4_spl
| ~ sQ90_spl
| ~ greater(e_4,e_1) ),
inference(resolution,[status(thm)],[f708,f230]) ).
fof(f959,plain,
( ~ sQ4_spl
| ~ sQ90_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f952,f55]) ).
fof(f960,plain,
( ~ sQ4_spl
| ~ sQ90_spl ),
inference(contradiction_clause,[status(thm)],[f959]) ).
fof(f961,plain,
( ~ sQ4_spl
| ~ sQ89_spl
| ~ greater(e_3,e_1) ),
inference(resolution,[status(thm)],[f705,f230]) ).
fof(f967,plain,
( ~ sQ4_spl
| ~ sQ89_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f961,f54]) ).
fof(f968,plain,
( ~ sQ4_spl
| ~ sQ89_spl ),
inference(contradiction_clause,[status(thm)],[f967]) ).
fof(f969,plain,
( ~ sQ49_spl
| ~ product(e_4,e_2,e_3) ),
inference(resolution,[status(thm)],[f779,f93]) ).
fof(f970,plain,
( ~ sQ49_spl
| ~ sQ61_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f969,f602]) ).
fof(f971,plain,
( ~ sQ49_spl
| ~ sQ61_spl ),
inference(contradiction_clause,[status(thm)],[f970]) ).
fof(f972,plain,
( ~ sQ4_spl
| ~ sQ88_spl
| ~ greater(e_2,e_1) ),
inference(resolution,[status(thm)],[f702,f230]) ).
fof(f977,plain,
( ~ sQ4_spl
| ~ sQ88_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f972,f53]) ).
fof(f978,plain,
( ~ sQ4_spl
| ~ sQ88_spl ),
inference(contradiction_clause,[status(thm)],[f977]) ).
fof(f1008,plain,
( ~ sQ83_spl
| ~ product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f686,f98]) ).
fof(f1011,plain,
( ~ sQ83_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1008,f93]) ).
fof(f1012,plain,
~ sQ83_spl,
inference(contradiction_clause,[status(thm)],[f1011]) ).
fof(f1020,plain,
( ~ sQ36_spl
| ~ sQ82_spl
| ~ product(e_3,e_3,e_3) ),
inference(resolution,[status(thm)],[f682,f507]) ).
fof(f1026,plain,
( ~ sQ36_spl
| ~ sQ82_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1020,f93]) ).
fof(f1027,plain,
( ~ sQ36_spl
| ~ sQ82_spl ),
inference(contradiction_clause,[status(thm)],[f1026]) ).
fof(f1032,plain,
! [X0] :
( ~ sQ80_spl
| ~ product(X0,e_2,e_2)
| ~ product(X0,e_3,e_1) ),
inference(resolution,[status(thm)],[f676,f103]) ).
fof(f1044,plain,
( ~ sQ79_spl
| ~ product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f673,f108]) ).
fof(f1047,plain,
( ~ sQ79_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1044,f93]) ).
fof(f1048,plain,
~ sQ79_spl,
inference(contradiction_clause,[status(thm)],[f1047]) ).
fof(f1084,plain,
( ~ sQ75_spl
| ~ product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f660,f113]) ).
fof(f1086,plain,
( ~ sQ75_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1084,f93]) ).
fof(f1087,plain,
~ sQ75_spl,
inference(contradiction_clause,[status(thm)],[f1086]) ).
fof(f1138,plain,
( ~ sQ73_spl
| ~ sQ36_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f641,f511]) ).
fof(f1139,plain,
( ~ sQ73_spl
| ~ sQ36_spl ),
inference(contradiction_clause,[status(thm)],[f1138]) ).
fof(f1147,plain,
( ~ sQ80_spl
| ~ sQ38_spl
| ~ product(e_4,e_2,e_2) ),
inference(resolution,[status(thm)],[f410,f1032]) ).
fof(f1157,plain,
( ~ sQ59_spl
| ~ sQ38_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f596,f856]) ).
fof(f1158,plain,
( ~ sQ59_spl
| ~ sQ38_spl ),
inference(contradiction_clause,[status(thm)],[f1157]) ).
fof(f1159,plain,
( ~ sQ39_spl
| ~ sQ51_spl ),
inference(split_clause,[status(thm)],[f842,f451,f412]) ).
fof(f1160,plain,
( ~ sQ80_spl
| ~ sQ38_spl
| ~ sQ60_spl ),
inference(split_clause,[status(thm)],[f1147,f598,f409,f675]) ).
fof(f1161,plain,
( ~ sQ53_spl
| ~ sQ74_spl ),
inference(split_clause,[status(thm)],[f760,f643,f457]) ).
fof(f1165,plain,
$false,
inference(sat_refutation,[status(thm)],[f186,f205,f210,f220,f228,f279,f300,f302,f353,f366,f392,f394,f396,f398,f400,f402,f404,f421,f447,f460,f462,f464,f466,f468,f470,f492,f531,f577,f590,f607,f633,f646,f648,f650,f652,f654,f684,f710,f712,f714,f716,f768,f774,f799,f836,f861,f872,f880,f891,f901,f922,f960,f968,f971,f978,f1012,f1027,f1048,f1087,f1139,f1158,f1159,f1160,f1161]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP124-3.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.38 % Computer : n011.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 20 19:58:40 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.39 % Drodi V4.1.1
% 0.12/0.44 % Refutation found
% 0.12/0.44 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.47 % Elapsed time: 0.077682 seconds
% 0.12/0.47 % CPU time: 0.343234 seconds
% 0.12/0.47 % Total memory used: 21.271 MB
% 0.12/0.47 % Net memory used: 20.871 MB
%------------------------------------------------------------------------------