%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP124-4.004 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 12:32:42 PM UTC 2026
% Result : Unsatisfiable 0.16s 0.46s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 87
% Syntax : Number of formulae : 339 ( 58 unt; 69 def)
% Number of atoms : 1089 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 1333 ( 583 ~; 681 |; 0 &)
% ( 69 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 73 ( 72 usr; 70 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 292 ( 292 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( product(e_4,X,Y)
| product(e_3,X,Y)
| product(e_2,X,Y)
| product(e_1,X,Y)
| ~ group_element(Y)
| ~ group_element(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] :
( product(X,e_4,Y)
| product(X,e_3,Y)
| product(X,e_2,Y)
| product(X,e_1,Y)
| ~ group_element(Y)
| ~ group_element(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
group_element(e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
~ equalish(e_1,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
~ equalish(e_2,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [X] : product(X,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,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/sandbox/benchmark/theBenchmark.p') ).
fof(f25,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/sandbox/benchmark/theBenchmark.p') ).
fof(f26,plain,
! [X0,X1] :
( product(e_4,X0,X1)
| product(e_3,X0,X1)
| product(e_2,X0,X1)
| product(e_1,X0,X1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f27,plain,
! [X0,X1] :
( product(X0,e_4,X1)
| product(X0,e_3,X1)
| product(X0,e_2,X1)
| product(X0,e_1,X1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f28,plain,
group_element(e_1),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f29,plain,
group_element(e_2),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f30,plain,
group_element(e_3),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f31,plain,
group_element(e_4),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f32,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f33,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f34,plain,
~ equalish(e_1,e_4),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f36,plain,
~ equalish(e_2,e_3),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f37,plain,
~ equalish(e_2,e_4),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f40,plain,
~ equalish(e_3,e_4),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f45,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W) ) ),
inference(miniscoping,[status(thm)],[f20]) ).
fof(f46,plain,
! [X0,X1,X2,X3] :
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f47,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product(X,Z,Y)
| ~ product(X,W,Y) ) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f48,plain,
! [X0,X1,X2,X3] :
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f49,plain,
! [W,Z] :
( equalish(W,Z)
| ! [Y,X] :
( ~ product(Z,Y,X)
| ~ product(W,Y,X) ) ),
inference(miniscoping,[status(thm)],[f22]) ).
fof(f50,plain,
! [X0,X1,X2,X3] :
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f51,plain,
! [X0] : product(X0,X0,X0),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f52,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)],[f24]) ).
fof(f53,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)],[f52]) ).
fof(f54,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)],[f25]) ).
fof(f55,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)],[f54]) ).
fof(f56,plain,
! [X0,X1] :
( ~ product(e_2,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[f32,f50]) ).
fof(f57,plain,
! [X0,X1] :
( ~ product(X0,e_2,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f32,f48]) ).
fof(f58,plain,
! [X0,X1] :
( ~ product(X0,X1,e_2)
| ~ product(X0,X1,e_1) ),
inference(resolution,[status(thm)],[f32,f46]) ).
fof(f59,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)],[f32,f55]) ).
fof(f60,plain,
! [X0,X1,X2,X3] :
( ~ product(X3,e_2,X2)
| ~ product(X3,e_1,X0)
| ~ product(e_2,X2,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[f32,f53]) ).
fof(f61,plain,
! [X0,X1] :
( ~ product(e_3,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[f33,f50]) ).
fof(f62,plain,
! [X0,X1] :
( ~ product(X0,e_3,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f33,f48]) ).
fof(f63,plain,
! [X0,X1] :
( ~ product(X0,X1,e_3)
| ~ product(X0,X1,e_1) ),
inference(resolution,[status(thm)],[f33,f46]) ).
fof(f64,plain,
! [X0,X1,X2,X3] :
( ~ product(X3,X2,e_3)
| ~ product(X3,X0,e_1)
| ~ product(X2,e_3,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f33,f55]) ).
fof(f65,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)],[f33,f53]) ).
fof(f66,plain,
! [X0,X1] :
( ~ product(e_4,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[f34,f50]) ).
fof(f67,plain,
! [X0,X1] :
( ~ product(X0,e_4,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f34,f48]) ).
fof(f68,plain,
! [X0,X1] :
( ~ product(X0,X1,e_4)
| ~ product(X0,X1,e_1) ),
inference(resolution,[status(thm)],[f34,f46]) ).
fof(f69,plain,
! [X0,X1,X2,X3] :
( ~ product(X3,X2,e_4)
| ~ product(X3,X0,e_1)
| ~ product(X2,e_4,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f34,f55]) ).
fof(f70,plain,
! [X0,X1,X2,X3] :
( ~ product(X3,e_4,X2)
| ~ product(X3,e_1,X0)
| ~ product(e_4,X2,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[f34,f53]) ).
fof(f76,plain,
! [X0,X1] :
( ~ product(e_3,X0,X1)
| ~ product(e_2,X0,X1) ),
inference(resolution,[status(thm)],[f36,f50]) ).
fof(f77,plain,
! [X0,X1] :
( ~ product(X0,e_3,X1)
| ~ product(X0,e_2,X1) ),
inference(resolution,[status(thm)],[f36,f48]) ).
fof(f78,plain,
! [X0,X1] :
( ~ product(X0,X1,e_3)
| ~ product(X0,X1,e_2) ),
inference(resolution,[status(thm)],[f36,f46]) ).
fof(f79,plain,
! [X0,X1,X2,X3] :
( ~ product(X3,X2,e_3)
| ~ product(X3,X0,e_2)
| ~ product(X2,e_3,X1)
| ~ product(X0,e_2,X1) ),
inference(resolution,[status(thm)],[f36,f55]) ).
fof(f80,plain,
! [X0,X1,X2,X3] :
( ~ product(X3,e_3,X2)
| ~ product(X3,e_2,X0)
| ~ product(e_3,X2,X1)
| ~ product(e_2,X0,X1) ),
inference(resolution,[status(thm)],[f36,f53]) ).
fof(f81,plain,
! [X0,X1] :
( ~ product(e_4,X0,X1)
| ~ product(e_2,X0,X1) ),
inference(resolution,[status(thm)],[f37,f50]) ).
fof(f82,plain,
! [X0,X1] :
( ~ product(X0,e_4,X1)
| ~ product(X0,e_2,X1) ),
inference(resolution,[status(thm)],[f37,f48]) ).
fof(f83,plain,
! [X0,X1] :
( ~ product(X0,X1,e_4)
| ~ product(X0,X1,e_2) ),
inference(resolution,[status(thm)],[f37,f46]) ).
fof(f84,plain,
! [X0,X1,X2,X3] :
( ~ product(X3,X2,e_4)
| ~ product(X3,X0,e_2)
| ~ product(X2,e_4,X1)
| ~ product(X0,e_2,X1) ),
inference(resolution,[status(thm)],[f37,f55]) ).
fof(f85,plain,
! [X0,X1,X2,X3] :
( ~ product(X3,e_4,X2)
| ~ product(X3,e_2,X0)
| ~ product(e_4,X2,X1)
| ~ product(e_2,X0,X1) ),
inference(resolution,[status(thm)],[f37,f53]) ).
fof(f96,plain,
! [X0,X1] :
( ~ product(e_4,X0,X1)
| ~ product(e_3,X0,X1) ),
inference(resolution,[status(thm)],[f40,f50]) ).
fof(f97,plain,
! [X0,X1] :
( ~ product(X0,e_4,X1)
| ~ product(X0,e_3,X1) ),
inference(resolution,[status(thm)],[f40,f48]) ).
fof(f98,plain,
! [X0,X1] :
( ~ product(X0,X1,e_4)
| ~ product(X0,X1,e_3) ),
inference(resolution,[status(thm)],[f40,f46]) ).
fof(f99,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)],[f40,f55]) ).
fof(f100,plain,
! [X0,X1,X2,X3] :
( ~ product(X3,e_4,X2)
| ~ product(X3,e_3,X0)
| ~ product(e_4,X2,X1)
| ~ product(e_3,X0,X1) ),
inference(resolution,[status(thm)],[f40,f53]) ).
fof(f116,plain,
! [X0,X1,X2] :
( product(e_3,e_2,X1)
| product(e_2,e_2,X1)
| product(e_1,e_2,X1)
| ~ group_element(X1)
| ~ group_element(e_2)
| ~ product(X2,e_4,e_2)
| ~ product(X2,X0,e_1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f59,f26]) ).
fof(f117,plain,
! [X0,X1] :
( ~ product(X1,e_2,e_2)
| ~ product(X1,X0,e_1)
| ~ product(X0,e_1,e_2) ),
inference(resolution,[status(thm)],[f59,f51]) ).
fof(f118,definition,
! [X0,X1,X2] :
( sQ0_spl
<=> ( product(e_3,e_2,X1)
| product(e_2,e_2,X1)
| product(e_1,e_2,X1)
| ~ group_element(X1)
| ~ product(X2,e_4,e_2)
| ~ product(X2,X0,e_1)
| ~ product(X0,e_1,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f121,definition,
( sQ1_spl
<=> group_element(e_2) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f123,plain,
( sQ1_spl
| ~ group_element(e_2) ),
inference(component_clause,[status(thm)],[f121]) ).
fof(f124,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f116,f118,f121]) ).
fof(f125,plain,
! [X0] :
( product(e_3,e_1,e_2)
| product(e_2,e_1,e_2)
| product(e_1,e_1,e_2)
| ~ group_element(e_2)
| ~ group_element(e_1)
| ~ product(X0,e_2,e_2)
| ~ product(X0,e_4,e_1) ),
inference(resolution,[status(thm)],[f117,f26]) ).
fof(f126,definition,
! [X0] :
( sQ2_spl
<=> ( ~ product(X0,e_2,e_2)
| ~ product(X0,e_4,e_1) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f127,plain,
! [X0] :
( ~ sQ2_spl
| ~ product(X0,e_2,e_2)
| ~ product(X0,e_4,e_1) ),
inference(component_clause,[status(thm)],[f126]) ).
fof(f129,definition,
( sQ3_spl
<=> group_element(e_1) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f131,plain,
( sQ3_spl
| ~ group_element(e_1) ),
inference(component_clause,[status(thm)],[f129]) ).
fof(f132,definition,
( sQ4_spl
<=> product(e_1,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f133,plain,
( ~ sQ4_spl
| product(e_1,e_1,e_2) ),
inference(component_clause,[status(thm)],[f132]) ).
fof(f135,definition,
( sQ5_spl
<=> product(e_2,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f136,plain,
( ~ sQ5_spl
| product(e_2,e_1,e_2) ),
inference(component_clause,[status(thm)],[f135]) ).
fof(f138,definition,
( sQ6_spl
<=> product(e_3,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f139,plain,
( ~ sQ6_spl
| product(e_3,e_1,e_2) ),
inference(component_clause,[status(thm)],[f138]) ).
fof(f141,plain,
( sQ6_spl
| sQ5_spl
| sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f125,f126,f129,f121,f132,f135,f138]) ).
fof(f142,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f123,f29]) ).
fof(f143,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f142]) ).
fof(f145,plain,
! [X0,X1,X2] :
( product(e_2,e_3,X1)
| product(e_2,e_2,X1)
| product(e_2,e_1,X1)
| ~ group_element(X1)
| ~ group_element(e_2)
| ~ product(X2,e_2,e_4)
| ~ product(X2,e_1,X0)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[f60,f27]) ).
fof(f147,definition,
! [X0,X1,X2] :
( sQ7_spl
<=> ( product(e_2,e_3,X1)
| product(e_2,e_2,X1)
| product(e_2,e_1,X1)
| ~ group_element(X1)
| ~ product(X2,e_2,e_4)
| ~ product(X2,e_1,X0)
| ~ product(e_1,X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f150,plain,
( ~ sQ1_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f145,f147,f121]) ).
fof(f151,plain,
! [X0] :
( product(e_2,e_3,X0)
| product(e_2,e_2,X0)
| product(e_2,e_1,X0)
| ~ group_element(X0)
| ~ group_element(e_2)
| ~ product(e_1,e_4,X0) ),
inference(resolution,[status(thm)],[f56,f27]) ).
fof(f152,plain,
~ product(e_1,e_2,e_2),
inference(resolution,[status(thm)],[f56,f51]) ).
fof(f153,definition,
! [X0] :
( sQ8_spl
<=> ( product(e_2,e_3,X0)
| product(e_2,e_2,X0)
| product(e_2,e_1,X0)
| ~ group_element(X0)
| ~ product(e_1,e_4,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f156,plain,
( ~ sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f151,f153,f121]) ).
fof(f157,plain,
! [X0] :
( product(e_3,e_2,X0)
| product(e_2,e_2,X0)
| product(e_1,e_2,X0)
| ~ group_element(X0)
| ~ group_element(e_2)
| ~ product(e_4,e_1,X0) ),
inference(resolution,[status(thm)],[f57,f26]) ).
fof(f158,plain,
~ product(e_2,e_1,e_2),
inference(resolution,[status(thm)],[f57,f51]) ).
fof(f159,definition,
! [X0] :
( sQ9_spl
<=> ( product(e_3,e_2,X0)
| product(e_2,e_2,X0)
| product(e_1,e_2,X0)
| ~ group_element(X0)
| ~ product(e_4,e_1,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f162,plain,
( ~ sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f157,f159,f121]) ).
fof(f163,plain,
! [X0] :
( product(e_3,X0,e_1)
| product(e_2,X0,e_1)
| product(e_1,X0,e_1)
| ~ group_element(e_1)
| ~ group_element(X0)
| ~ product(e_4,X0,e_2) ),
inference(resolution,[status(thm)],[f58,f26]) ).
fof(f164,plain,
! [X0] :
( product(X0,e_3,e_1)
| product(X0,e_2,e_1)
| product(X0,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(X0)
| ~ product(X0,e_4,e_2) ),
inference(resolution,[status(thm)],[f58,f27]) ).
fof(f165,plain,
~ product(e_1,e_1,e_2),
inference(resolution,[status(thm)],[f58,f51]) ).
fof(f166,definition,
! [X0] :
( sQ10_spl
<=> ( product(e_3,X0,e_1)
| product(e_2,X0,e_1)
| product(e_1,X0,e_1)
| ~ group_element(X0)
| ~ product(e_4,X0,e_2) ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f169,plain,
( ~ sQ3_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f163,f166,f129]) ).
fof(f170,definition,
! [X0] :
( sQ11_spl
<=> ( product(X0,e_3,e_1)
| product(X0,e_2,e_1)
| product(X0,e_1,e_1)
| ~ group_element(X0)
| ~ product(X0,e_4,e_2) ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f173,plain,
( ~ sQ3_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f164,f170,f129]) ).
fof(f174,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f131,f28]) ).
fof(f175,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f174]) ).
fof(f176,plain,
! [X0] :
( product(e_3,e_3,X0)
| product(e_3,e_2,X0)
| product(e_3,e_1,X0)
| ~ group_element(X0)
| ~ group_element(e_3)
| ~ product(e_1,e_4,X0) ),
inference(resolution,[status(thm)],[f61,f27]) ).
fof(f177,plain,
~ product(e_1,e_3,e_3),
inference(resolution,[status(thm)],[f61,f51]) ).
fof(f178,definition,
! [X0] :
( sQ12_spl
<=> ( product(e_3,e_3,X0)
| product(e_3,e_2,X0)
| product(e_3,e_1,X0)
| ~ group_element(X0)
| ~ product(e_1,e_4,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f181,definition,
( sQ13_spl
<=> group_element(e_3) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f183,plain,
( sQ13_spl
| ~ group_element(e_3) ),
inference(component_clause,[status(thm)],[f181]) ).
fof(f184,plain,
( ~ sQ13_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f176,f178,f181]) ).
fof(f185,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f183,f30]) ).
fof(f186,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f185]) ).
fof(f187,plain,
! [X0] :
( product(e_3,e_3,X0)
| product(e_2,e_3,X0)
| product(e_1,e_3,X0)
| ~ group_element(X0)
| ~ group_element(e_3)
| ~ product(e_4,e_1,X0) ),
inference(resolution,[status(thm)],[f62,f26]) ).
fof(f188,plain,
~ product(e_3,e_1,e_3),
inference(resolution,[status(thm)],[f62,f51]) ).
fof(f189,definition,
! [X0] :
( sQ14_spl
<=> ( product(e_3,e_3,X0)
| product(e_2,e_3,X0)
| product(e_1,e_3,X0)
| ~ group_element(X0)
| ~ product(e_4,e_1,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f192,plain,
( ~ sQ13_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f187,f189,f181]) ).
fof(f194,plain,
! [X0] :
( ~ sQ6_spl
| ~ product(X0,e_2,e_2)
| ~ product(X0,e_3,e_1) ),
inference(resolution,[status(thm)],[f139,f117]) ).
fof(f195,plain,
! [X0] :
( product(e_3,X0,e_3)
| product(e_2,X0,e_3)
| product(e_1,X0,e_3)
| ~ group_element(e_3)
| ~ group_element(X0)
| ~ product(e_4,X0,e_1) ),
inference(resolution,[status(thm)],[f63,f26]) ).
fof(f196,plain,
! [X0] :
( product(X0,e_3,e_3)
| product(X0,e_2,e_3)
| product(X0,e_1,e_3)
| ~ group_element(e_3)
| ~ group_element(X0)
| ~ product(X0,e_4,e_1) ),
inference(resolution,[status(thm)],[f63,f27]) ).
fof(f197,plain,
~ product(e_3,e_3,e_1),
inference(resolution,[status(thm)],[f63,f51]) ).
fof(f198,definition,
! [X0] :
( sQ15_spl
<=> ( product(e_3,X0,e_3)
| product(e_2,X0,e_3)
| product(e_1,X0,e_3)
| ~ group_element(X0)
| ~ product(e_4,X0,e_1) ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f201,plain,
( ~ sQ13_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f195,f198,f181]) ).
fof(f202,definition,
! [X0] :
( sQ16_spl
<=> ( product(X0,e_3,e_3)
| product(X0,e_2,e_3)
| product(X0,e_1,e_3)
| ~ group_element(X0)
| ~ product(X0,e_4,e_1) ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f205,plain,
( ~ sQ13_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f196,f202,f181]) ).
fof(f206,plain,
! [X0] :
( product(e_1,e_3,X0)
| product(e_1,e_2,X0)
| product(e_1,e_1,X0)
| ~ group_element(X0)
| ~ group_element(e_1)
| ~ product(e_4,e_4,X0) ),
inference(resolution,[status(thm)],[f66,f27]) ).
fof(f207,plain,
~ product(e_4,e_1,e_1),
inference(resolution,[status(thm)],[f66,f51]) ).
fof(f208,definition,
! [X0] :
( sQ17_spl
<=> ( product(e_1,e_3,X0)
| product(e_1,e_2,X0)
| product(e_1,e_1,X0)
| ~ group_element(X0)
| ~ product(e_4,e_4,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f211,plain,
( ~ sQ3_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f206,f208,f129]) ).
fof(f212,plain,
( product(e_3,e_1,e_1)
| product(e_2,e_1,e_1)
| product(e_1,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[f207,f26]) ).
fof(f213,definition,
( sQ18_spl
<=> product(e_1,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f216,definition,
( sQ19_spl
<=> product(e_2,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f217,plain,
( ~ sQ19_spl
| product(e_2,e_1,e_1) ),
inference(component_clause,[status(thm)],[f216]) ).
fof(f219,definition,
( sQ20_spl
<=> product(e_3,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f220,plain,
( ~ sQ20_spl
| product(e_3,e_1,e_1) ),
inference(component_clause,[status(thm)],[f219]) ).
fof(f222,plain,
( sQ20_spl
| sQ19_spl
| sQ18_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f212,f129,f213,f216,f219]) ).
fof(f223,plain,
( ~ sQ20_spl
| ~ product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f220,f61]) ).
fof(f225,plain,
( ~ sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f223,f51]) ).
fof(f226,plain,
~ sQ20_spl,
inference(contradiction_clause,[status(thm)],[f225]) ).
fof(f227,plain,
( ~ sQ19_spl
| ~ product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f217,f56]) ).
fof(f230,plain,
( ~ sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f227,f51]) ).
fof(f231,plain,
~ sQ19_spl,
inference(contradiction_clause,[status(thm)],[f230]) ).
fof(f236,plain,
! [X0,X1,X2] :
( product(e_3,e_3,X1)
| product(e_2,e_3,X1)
| product(e_1,e_3,X1)
| ~ group_element(X1)
| ~ group_element(e_3)
| ~ product(X2,e_4,e_3)
| ~ product(X2,X0,e_1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f64,f26]) ).
fof(f238,definition,
! [X0,X1,X2] :
( sQ21_spl
<=> ( product(e_3,e_3,X1)
| product(e_2,e_3,X1)
| product(e_1,e_3,X1)
| ~ group_element(X1)
| ~ product(X2,e_4,e_3)
| ~ product(X2,X0,e_1)
| ~ product(X0,e_1,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f241,plain,
( ~ sQ13_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f236,f238,f181]) ).
fof(f242,plain,
! [X0,X1,X2] :
( product(e_1,e_3,X1)
| product(e_1,e_2,X1)
| product(e_1,e_1,X1)
| ~ group_element(X1)
| ~ group_element(e_1)
| ~ product(X2,e_3,X0)
| ~ product(X2,e_1,e_4)
| ~ product(e_3,X0,X1) ),
inference(resolution,[status(thm)],[f65,f27]) ).
fof(f244,definition,
! [X0,X1,X2] :
( sQ22_spl
<=> ( product(e_1,e_3,X1)
| product(e_1,e_2,X1)
| product(e_1,e_1,X1)
| ~ group_element(X1)
| ~ product(X2,e_3,X0)
| ~ product(X2,e_1,e_4)
| ~ product(e_3,X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f247,plain,
( ~ sQ3_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f242,f244,f129]) ).
fof(f249,definition,
( sQ23_spl
<=> product(e_4,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f250,plain,
( ~ sQ23_spl
| product(e_4,e_2,e_2) ),
inference(component_clause,[status(thm)],[f249]) ).
fof(f252,definition,
( sQ24_spl
<=> product(e_1,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f253,plain,
( ~ sQ24_spl
| product(e_1,e_3,e_1) ),
inference(component_clause,[status(thm)],[f252]) ).
fof(f255,definition,
( sQ25_spl
<=> product(e_2,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f256,plain,
( ~ sQ25_spl
| product(e_2,e_3,e_1) ),
inference(component_clause,[status(thm)],[f255]) ).
fof(f258,definition,
( sQ26_spl
<=> product(e_3,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f259,plain,
( ~ sQ26_spl
| product(e_3,e_3,e_1) ),
inference(component_clause,[status(thm)],[f258]) ).
fof(f262,plain,
( ~ sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f259,f197]) ).
fof(f263,plain,
~ sQ26_spl,
inference(contradiction_clause,[status(thm)],[f262]) ).
fof(f264,plain,
( ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f136,f158]) ).
fof(f265,plain,
~ sQ5_spl,
inference(contradiction_clause,[status(thm)],[f264]) ).
fof(f266,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f133,f165]) ).
fof(f267,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f266]) ).
fof(f273,plain,
! [X0,X1,X2] :
( product(e_3,e_1,X1)
| product(e_2,e_1,X1)
| product(e_1,e_1,X1)
| ~ group_element(X1)
| ~ group_element(e_1)
| ~ product(X2,X0,e_4)
| ~ product(X2,e_4,e_1)
| ~ product(X0,e_4,X1) ),
inference(resolution,[status(thm)],[f69,f26]) ).
fof(f275,definition,
! [X0,X1,X2] :
( sQ27_spl
<=> ( product(e_3,e_1,X1)
| product(e_2,e_1,X1)
| product(e_1,e_1,X1)
| ~ group_element(X1)
| ~ product(X2,X0,e_4)
| ~ product(X2,e_4,e_1)
| ~ product(X0,e_4,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f278,plain,
( ~ sQ3_spl
| sQ27_spl ),
inference(split_clause,[status(thm)],[f273,f275,f129]) ).
fof(f279,plain,
! [X0] :
( product(e_3,e_1,X0)
| product(e_2,e_1,X0)
| product(e_1,e_1,X0)
| ~ group_element(X0)
| ~ group_element(e_1)
| ~ product(e_4,e_4,X0) ),
inference(resolution,[status(thm)],[f67,f26]) ).
fof(f280,plain,
~ product(e_1,e_4,e_1),
inference(resolution,[status(thm)],[f67,f51]) ).
fof(f281,definition,
! [X0] :
( sQ28_spl
<=> ( product(e_3,e_1,X0)
| product(e_2,e_1,X0)
| product(e_1,e_1,X0)
| ~ group_element(X0)
| ~ product(e_4,e_4,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f284,plain,
( ~ sQ3_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f279,f281,f129]) ).
fof(f286,definition,
( sQ29_spl
<=> product(e_1,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f287,plain,
( ~ sQ29_spl
| product(e_1,e_2,e_1) ),
inference(component_clause,[status(thm)],[f286]) ).
fof(f290,plain,
! [X0] :
( product(e_3,X0,e_4)
| product(e_2,X0,e_4)
| product(e_1,X0,e_4)
| ~ group_element(e_4)
| ~ group_element(X0)
| ~ product(e_4,X0,e_1) ),
inference(resolution,[status(thm)],[f68,f26]) ).
fof(f291,plain,
! [X0] :
( product(X0,e_3,e_4)
| product(X0,e_2,e_4)
| product(X0,e_1,e_4)
| ~ group_element(e_4)
| ~ group_element(X0)
| ~ product(X0,e_4,e_1) ),
inference(resolution,[status(thm)],[f68,f27]) ).
fof(f292,plain,
~ product(e_4,e_4,e_1),
inference(resolution,[status(thm)],[f68,f51]) ).
fof(f293,definition,
! [X0] :
( sQ30_spl
<=> ( product(e_3,X0,e_4)
| product(e_2,X0,e_4)
| product(e_1,X0,e_4)
| ~ group_element(X0)
| ~ product(e_4,X0,e_1) ) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f296,definition,
( sQ31_spl
<=> group_element(e_4) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f298,plain,
( sQ31_spl
| ~ group_element(e_4) ),
inference(component_clause,[status(thm)],[f296]) ).
fof(f299,plain,
( ~ sQ31_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f290,f293,f296]) ).
fof(f300,definition,
! [X0] :
( sQ32_spl
<=> ( product(X0,e_3,e_4)
| product(X0,e_2,e_4)
| product(X0,e_1,e_4)
| ~ group_element(X0)
| ~ product(X0,e_4,e_1) ) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f303,plain,
( ~ sQ31_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f291,f300,f296]) ).
fof(f304,plain,
( sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f298,f31]) ).
fof(f305,plain,
sQ31_spl,
inference(contradiction_clause,[status(thm)],[f304]) ).
fof(f306,plain,
! [X0,X1,X2] :
( product(e_1,e_3,X1)
| product(e_1,e_2,X1)
| product(e_1,e_1,X1)
| ~ group_element(X1)
| ~ group_element(e_1)
| ~ product(X2,e_4,X0)
| ~ product(X2,e_1,e_4)
| ~ product(e_4,X0,X1) ),
inference(resolution,[status(thm)],[f70,f27]) ).
fof(f308,definition,
! [X0,X1,X2] :
( sQ33_spl
<=> ( product(e_1,e_3,X1)
| product(e_1,e_2,X1)
| product(e_1,e_1,X1)
| ~ group_element(X1)
| ~ product(X2,e_4,X0)
| ~ product(X2,e_1,e_4)
| ~ product(e_4,X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f311,plain,
( ~ sQ3_spl
| sQ33_spl ),
inference(split_clause,[status(thm)],[f306,f308,f129]) ).
fof(f316,plain,
( ~ sQ24_spl
| ~ product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f253,f62]) ).
fof(f318,plain,
( ~ sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f316,f51]) ).
fof(f319,plain,
~ sQ24_spl,
inference(contradiction_clause,[status(thm)],[f318]) ).
fof(f320,plain,
( product(e_3,e_4,e_1)
| product(e_2,e_4,e_1)
| product(e_1,e_4,e_1)
| ~ group_element(e_1)
| ~ group_element(e_4) ),
inference(resolution,[status(thm)],[f292,f26]) ).
fof(f321,plain,
( product(e_4,e_3,e_1)
| product(e_4,e_2,e_1)
| product(e_4,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(e_4) ),
inference(resolution,[status(thm)],[f292,f27]) ).
fof(f322,definition,
( sQ34_spl
<=> product(e_1,e_4,e_1) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f323,plain,
( ~ sQ34_spl
| product(e_1,e_4,e_1) ),
inference(component_clause,[status(thm)],[f322]) ).
fof(f325,definition,
( sQ35_spl
<=> product(e_2,e_4,e_1) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f326,plain,
( ~ sQ35_spl
| product(e_2,e_4,e_1) ),
inference(component_clause,[status(thm)],[f325]) ).
fof(f328,definition,
( sQ36_spl
<=> product(e_3,e_4,e_1) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f329,plain,
( ~ sQ36_spl
| product(e_3,e_4,e_1) ),
inference(component_clause,[status(thm)],[f328]) ).
fof(f331,plain,
( sQ36_spl
| sQ35_spl
| sQ34_spl
| ~ sQ3_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f320,f296,f129,f322,f325,f328]) ).
fof(f332,definition,
( sQ37_spl
<=> product(e_4,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f333,plain,
( ~ sQ37_spl
| product(e_4,e_1,e_1) ),
inference(component_clause,[status(thm)],[f332]) ).
fof(f335,definition,
( sQ38_spl
<=> product(e_4,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f336,plain,
( ~ sQ38_spl
| product(e_4,e_2,e_1) ),
inference(component_clause,[status(thm)],[f335]) ).
fof(f338,definition,
( sQ39_spl
<=> product(e_4,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f339,plain,
( ~ sQ39_spl
| product(e_4,e_3,e_1) ),
inference(component_clause,[status(thm)],[f338]) ).
fof(f341,plain,
( sQ39_spl
| sQ38_spl
| sQ37_spl
| ~ sQ3_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f321,f296,f129,f332,f335,f338]) ).
fof(f342,plain,
( ~ sQ37_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f333,f207]) ).
fof(f343,plain,
~ sQ37_spl,
inference(contradiction_clause,[status(thm)],[f342]) ).
fof(f344,plain,
( ~ sQ34_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f323,f280]) ).
fof(f345,plain,
~ sQ34_spl,
inference(contradiction_clause,[status(thm)],[f344]) ).
fof(f349,plain,
( ~ sQ29_spl
| ~ product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f287,f57]) ).
fof(f352,plain,
( ~ sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f349,f51]) ).
fof(f353,plain,
~ sQ29_spl,
inference(contradiction_clause,[status(thm)],[f352]) ).
fof(f361,plain,
( ~ sQ39_spl
| ~ product(e_4,e_3,e_2) ),
inference(resolution,[status(thm)],[f339,f58]) ).
fof(f374,plain,
( ~ sQ2_spl
| ~ sQ36_spl
| ~ product(e_3,e_2,e_2) ),
inference(resolution,[status(thm)],[f329,f127]) ).
fof(f375,plain,
( ~ sQ36_spl
| ~ product(e_3,e_4,e_2) ),
inference(resolution,[status(thm)],[f329,f58]) ).
fof(f378,plain,
( ~ sQ2_spl
| ~ sQ35_spl
| ~ product(e_2,e_2,e_2) ),
inference(resolution,[status(thm)],[f326,f127]) ).
fof(f380,plain,
( ~ sQ2_spl
| ~ sQ35_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f378,f51]) ).
fof(f381,plain,
( ~ sQ2_spl
| ~ sQ35_spl ),
inference(contradiction_clause,[status(thm)],[f380]) ).
fof(f383,definition,
( sQ41_spl
<=> product(e_1,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f384,plain,
( ~ sQ41_spl
| product(e_1,e_2,e_2) ),
inference(component_clause,[status(thm)],[f383]) ).
fof(f389,definition,
( sQ43_spl
<=> product(e_3,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f390,plain,
( ~ sQ43_spl
| product(e_3,e_2,e_2) ),
inference(component_clause,[status(thm)],[f389]) ).
fof(f395,plain,
( ~ sQ41_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f384,f152]) ).
fof(f396,plain,
~ sQ41_spl,
inference(contradiction_clause,[status(thm)],[f395]) ).
fof(f397,plain,
! [X0] :
( product(e_2,e_3,X0)
| product(e_2,e_2,X0)
| product(e_2,e_1,X0)
| ~ group_element(X0)
| ~ group_element(e_2)
| ~ product(e_3,e_4,X0) ),
inference(resolution,[status(thm)],[f76,f27]) ).
fof(f399,definition,
! [X0] :
( sQ44_spl
<=> ( product(e_2,e_3,X0)
| product(e_2,e_2,X0)
| product(e_2,e_1,X0)
| ~ group_element(X0)
| ~ product(e_3,e_4,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f402,plain,
( ~ sQ1_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f397,f399,f121]) ).
fof(f403,plain,
( ~ sQ36_spl
| product(e_3,e_3,e_2)
| product(e_3,e_2,e_2)
| product(e_3,e_1,e_2)
| ~ group_element(e_2)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[f375,f27]) ).
fof(f404,definition,
( sQ45_spl
<=> product(e_3,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f405,plain,
( ~ sQ45_spl
| product(e_3,e_3,e_2) ),
inference(component_clause,[status(thm)],[f404]) ).
fof(f407,plain,
( ~ sQ36_spl
| sQ45_spl
| sQ43_spl
| sQ6_spl
| ~ sQ1_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f403,f181,f121,f138,f389,f404,f328]) ).
fof(f409,definition,
( sQ46_spl
<=> product(e_2,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f410,plain,
( ~ sQ46_spl
| product(e_2,e_2,e_1) ),
inference(component_clause,[status(thm)],[f409]) ).
fof(f424,plain,
( ~ sQ43_spl
| ~ sQ2_spl
| ~ sQ36_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f390,f374]) ).
fof(f425,plain,
( ~ sQ43_spl
| ~ sQ2_spl
| ~ sQ36_spl ),
inference(contradiction_clause,[status(thm)],[f424]) ).
fof(f432,plain,
! [X0] :
( product(e_3,e_2,X0)
| product(e_2,e_2,X0)
| product(e_1,e_2,X0)
| ~ group_element(X0)
| ~ group_element(e_2)
| ~ product(e_4,e_3,X0) ),
inference(resolution,[status(thm)],[f77,f26]) ).
fof(f434,definition,
! [X0] :
( sQ49_spl
<=> ( product(e_3,e_2,X0)
| product(e_2,e_2,X0)
| product(e_1,e_2,X0)
| ~ group_element(X0)
| ~ product(e_4,e_3,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f437,plain,
( ~ sQ1_spl
| sQ49_spl ),
inference(split_clause,[status(thm)],[f432,f434,f121]) ).
fof(f438,plain,
! [X0] :
( product(e_3,X0,e_3)
| product(e_2,X0,e_3)
| product(e_1,X0,e_3)
| ~ group_element(e_3)
| ~ group_element(X0)
| ~ product(e_4,X0,e_2) ),
inference(resolution,[status(thm)],[f78,f26]) ).
fof(f439,plain,
! [X0] :
( product(X0,e_3,e_3)
| product(X0,e_2,e_3)
| product(X0,e_1,e_3)
| ~ group_element(e_3)
| ~ group_element(X0)
| ~ product(X0,e_4,e_2) ),
inference(resolution,[status(thm)],[f78,f27]) ).
fof(f440,plain,
~ product(e_3,e_3,e_2),
inference(resolution,[status(thm)],[f78,f51]) ).
fof(f441,definition,
! [X0] :
( sQ50_spl
<=> ( product(e_3,X0,e_3)
| product(e_2,X0,e_3)
| product(e_1,X0,e_3)
| ~ group_element(X0)
| ~ product(e_4,X0,e_2) ) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f444,plain,
( ~ sQ13_spl
| sQ50_spl ),
inference(split_clause,[status(thm)],[f438,f441,f181]) ).
fof(f445,definition,
! [X0] :
( sQ51_spl
<=> ( product(X0,e_3,e_3)
| product(X0,e_2,e_3)
| product(X0,e_1,e_3)
| ~ group_element(X0)
| ~ product(X0,e_4,e_2) ) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f448,plain,
( ~ sQ13_spl
| sQ51_spl ),
inference(split_clause,[status(thm)],[f439,f445,f181]) ).
fof(f449,plain,
! [X0,X1,X2] :
( product(e_3,e_2,X1)
| product(e_2,e_2,X1)
| product(e_1,e_2,X1)
| ~ group_element(X1)
| ~ group_element(e_2)
| ~ product(X2,X0,e_3)
| ~ product(X2,e_4,e_2)
| ~ product(X0,e_3,X1) ),
inference(resolution,[status(thm)],[f79,f26]) ).
fof(f451,definition,
! [X0,X1,X2] :
( sQ52_spl
<=> ( product(e_3,e_2,X1)
| product(e_2,e_2,X1)
| product(e_1,e_2,X1)
| ~ group_element(X1)
| ~ product(X2,X0,e_3)
| ~ product(X2,e_4,e_2)
| ~ product(X0,e_3,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f454,plain,
( ~ sQ1_spl
| sQ52_spl ),
inference(split_clause,[status(thm)],[f449,f451,f121]) ).
fof(f470,definition,
( sQ57_spl
<=> product(e_3,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f471,plain,
( ~ sQ57_spl
| product(e_3,e_1,e_3) ),
inference(component_clause,[status(thm)],[f470]) ).
fof(f474,plain,
( ~ sQ57_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f471,f188]) ).
fof(f475,plain,
~ sQ57_spl,
inference(contradiction_clause,[status(thm)],[f474]) ).
fof(f476,plain,
! [X0,X1,X2] :
( product(e_3,e_2,X0)
| product(e_2,e_2,X0)
| product(e_1,e_2,X0)
| ~ group_element(X0)
| ~ group_element(e_2)
| ~ product(e_4,e_3,X2)
| ~ product(e_3,X2,X1)
| ~ product(e_2,X0,X1) ),
inference(resolution,[status(thm)],[f80,f26]) ).
fof(f478,definition,
! [X0,X1,X2] :
( sQ58_spl
<=> ( product(e_3,e_2,X0)
| product(e_2,e_2,X0)
| product(e_1,e_2,X0)
| ~ group_element(X0)
| ~ product(e_4,e_3,X2)
| ~ product(e_3,X2,X1)
| ~ product(e_2,X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f481,plain,
( ~ sQ1_spl
| sQ58_spl ),
inference(split_clause,[status(thm)],[f476,f478,f121]) ).
fof(f487,plain,
( ~ sQ38_spl
| ~ product(e_4,e_3,e_1) ),
inference(resolution,[status(thm)],[f336,f77]) ).
fof(f493,plain,
( ~ sQ45_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f440,f405]) ).
fof(f494,plain,
~ sQ45_spl,
inference(contradiction_clause,[status(thm)],[f493]) ).
fof(f502,plain,
! [X0] :
( product(e_2,e_3,X0)
| product(e_2,e_2,X0)
| product(e_2,e_1,X0)
| ~ group_element(X0)
| ~ group_element(e_2)
| ~ product(e_4,e_4,X0) ),
inference(resolution,[status(thm)],[f81,f27]) ).
fof(f503,plain,
~ product(e_4,e_2,e_2),
inference(resolution,[status(thm)],[f81,f51]) ).
fof(f504,definition,
! [X0] :
( sQ59_spl
<=> ( product(e_2,e_3,X0)
| product(e_2,e_2,X0)
| product(e_2,e_1,X0)
| ~ group_element(X0)
| ~ product(e_4,e_4,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f507,plain,
( ~ sQ1_spl
| sQ59_spl ),
inference(split_clause,[status(thm)],[f502,f504,f121]) ).
fof(f509,plain,
! [X0] :
( product(e_3,e_2,X0)
| product(e_2,e_2,X0)
| product(e_1,e_2,X0)
| ~ group_element(X0)
| ~ group_element(e_2)
| ~ product(e_4,e_4,X0) ),
inference(resolution,[status(thm)],[f82,f26]) ).
fof(f510,plain,
~ product(e_2,e_4,e_2),
inference(resolution,[status(thm)],[f82,f51]) ).
fof(f511,definition,
! [X0] :
( sQ60_spl
<=> ( product(e_3,e_2,X0)
| product(e_2,e_2,X0)
| product(e_1,e_2,X0)
| ~ group_element(X0)
| ~ product(e_4,e_4,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f514,plain,
( ~ sQ1_spl
| sQ60_spl ),
inference(split_clause,[status(thm)],[f509,f511,f121]) ).
fof(f524,plain,
( ~ sQ38_spl
| product(e_3,e_3,e_1)
| product(e_2,e_3,e_1)
| product(e_1,e_3,e_1)
| ~ group_element(e_1)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[f487,f26]) ).
fof(f525,plain,
( ~ sQ38_spl
| sQ26_spl
| sQ25_spl
| sQ24_spl
| ~ sQ3_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f524,f181,f129,f252,f255,f258,f335]) ).
fof(f536,plain,
! [X0] :
( product(e_3,X0,e_4)
| product(e_2,X0,e_4)
| product(e_1,X0,e_4)
| ~ group_element(e_4)
| ~ group_element(X0)
| ~ product(e_4,X0,e_2) ),
inference(resolution,[status(thm)],[f83,f26]) ).
fof(f537,plain,
! [X0] :
( product(X0,e_3,e_4)
| product(X0,e_2,e_4)
| product(X0,e_1,e_4)
| ~ group_element(e_4)
| ~ group_element(X0)
| ~ product(X0,e_4,e_2) ),
inference(resolution,[status(thm)],[f83,f27]) ).
fof(f538,plain,
~ product(e_4,e_4,e_2),
inference(resolution,[status(thm)],[f83,f51]) ).
fof(f539,definition,
! [X0] :
( sQ61_spl
<=> ( product(e_3,X0,e_4)
| product(e_2,X0,e_4)
| product(e_1,X0,e_4)
| ~ group_element(X0)
| ~ product(e_4,X0,e_2) ) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f542,plain,
( ~ sQ31_spl
| sQ61_spl ),
inference(split_clause,[status(thm)],[f536,f539,f296]) ).
fof(f543,definition,
! [X0] :
( sQ62_spl
<=> ( product(X0,e_3,e_4)
| product(X0,e_2,e_4)
| product(X0,e_1,e_4)
| ~ group_element(X0)
| ~ product(X0,e_4,e_2) ) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f546,plain,
( ~ sQ31_spl
| sQ62_spl ),
inference(split_clause,[status(thm)],[f537,f543,f296]) ).
fof(f548,plain,
! [X0,X1,X2] :
( product(e_3,e_2,X1)
| product(e_2,e_2,X1)
| product(e_1,e_2,X1)
| ~ group_element(X1)
| ~ group_element(e_2)
| ~ product(X2,X0,e_4)
| ~ product(X2,e_4,e_2)
| ~ product(X0,e_4,X1) ),
inference(resolution,[status(thm)],[f84,f26]) ).
fof(f550,definition,
! [X0,X1,X2] :
( sQ63_spl
<=> ( product(e_3,e_2,X1)
| product(e_2,e_2,X1)
| product(e_1,e_2,X1)
| ~ group_element(X1)
| ~ product(X2,X0,e_4)
| ~ product(X2,e_4,e_2)
| ~ product(X0,e_4,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f553,plain,
( ~ sQ1_spl
| sQ63_spl ),
inference(split_clause,[status(thm)],[f548,f550,f121]) ).
fof(f555,plain,
! [X0,X1,X2] :
( product(e_3,e_2,X0)
| product(e_2,e_2,X0)
| product(e_1,e_2,X0)
| ~ group_element(X0)
| ~ group_element(e_2)
| ~ product(e_4,e_4,X2)
| ~ product(e_4,X2,X1)
| ~ product(e_2,X0,X1) ),
inference(resolution,[status(thm)],[f85,f26]) ).
fof(f557,definition,
! [X0,X1,X2] :
( sQ64_spl
<=> ( product(e_3,e_2,X0)
| product(e_2,e_2,X0)
| product(e_1,e_2,X0)
| ~ group_element(X0)
| ~ product(e_4,e_4,X2)
| ~ product(e_4,X2,X1)
| ~ product(e_2,X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f560,plain,
( ~ sQ1_spl
| sQ64_spl ),
inference(split_clause,[status(thm)],[f555,f557,f121]) ).
fof(f567,definition,
( sQ66_spl
<=> product(e_2,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f568,plain,
( ~ sQ66_spl
| product(e_2,e_3,e_3) ),
inference(component_clause,[status(thm)],[f567]) ).
fof(f572,plain,
( product(e_4,e_3,e_2)
| product(e_4,e_2,e_2)
| product(e_4,e_1,e_2)
| ~ group_element(e_2)
| ~ group_element(e_4) ),
inference(resolution,[status(thm)],[f538,f27]) ).
fof(f576,definition,
( sQ68_spl
<=> product(e_2,e_4,e_2) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f577,plain,
( ~ sQ68_spl
| product(e_2,e_4,e_2) ),
inference(component_clause,[status(thm)],[f576]) ).
fof(f583,definition,
( sQ70_spl
<=> product(e_4,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f584,plain,
( ~ sQ70_spl
| product(e_4,e_1,e_2) ),
inference(component_clause,[status(thm)],[f583]) ).
fof(f586,definition,
( sQ71_spl
<=> product(e_4,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f589,plain,
( sQ71_spl
| sQ23_spl
| sQ70_spl
| ~ sQ1_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f572,f296,f121,f583,f249,f586]) ).
fof(f594,plain,
( ~ sQ68_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f577,f510]) ).
fof(f595,plain,
~ sQ68_spl,
inference(contradiction_clause,[status(thm)],[f594]) ).
fof(f603,plain,
( ~ sQ6_spl
| ~ product(e_4,e_1,e_2) ),
inference(resolution,[status(thm)],[f96,f139]) ).
fof(f605,plain,
! [X0] :
( product(e_3,e_3,X0)
| product(e_3,e_2,X0)
| product(e_3,e_1,X0)
| ~ group_element(X0)
| ~ group_element(e_3)
| ~ product(e_4,e_4,X0) ),
inference(resolution,[status(thm)],[f96,f27]) ).
fof(f606,plain,
~ product(e_4,e_3,e_3),
inference(resolution,[status(thm)],[f96,f51]) ).
fof(f607,plain,
( ~ sQ6_spl
| ~ sQ70_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f603,f584]) ).
fof(f608,plain,
( ~ sQ6_spl
| ~ sQ70_spl ),
inference(contradiction_clause,[status(thm)],[f607]) ).
fof(f609,definition,
! [X0] :
( sQ72_spl
<=> ( product(e_3,e_3,X0)
| product(e_3,e_2,X0)
| product(e_3,e_1,X0)
| ~ group_element(X0)
| ~ product(e_4,e_4,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f612,plain,
( ~ sQ13_spl
| sQ72_spl ),
inference(split_clause,[status(thm)],[f605,f609,f181]) ).
fof(f615,plain,
( product(e_3,e_3,e_3)
| product(e_2,e_3,e_3)
| product(e_1,e_3,e_3)
| ~ group_element(e_3)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[f606,f26]) ).
fof(f616,definition,
( sQ73_spl
<=> product(e_1,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f617,plain,
( ~ sQ73_spl
| product(e_1,e_3,e_3) ),
inference(component_clause,[status(thm)],[f616]) ).
fof(f619,definition,
( sQ74_spl
<=> product(e_3,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f622,plain,
( sQ74_spl
| sQ66_spl
| sQ73_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f615,f181,f616,f567,f619]) ).
fof(f623,plain,
( ~ sQ73_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f617,f177]) ).
fof(f624,plain,
~ sQ73_spl,
inference(contradiction_clause,[status(thm)],[f623]) ).
fof(f637,plain,
( ~ sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f503,f250]) ).
fof(f638,plain,
~ sQ23_spl,
inference(contradiction_clause,[status(thm)],[f637]) ).
fof(f639,plain,
( ~ sQ39_spl
| ~ sQ71_spl ),
inference(split_clause,[status(thm)],[f361,f586,f338]) ).
fof(f641,plain,
! [X0] :
( product(e_3,e_3,X0)
| product(e_2,e_3,X0)
| product(e_1,e_3,X0)
| ~ group_element(X0)
| ~ group_element(e_3)
| ~ product(e_4,e_4,X0) ),
inference(resolution,[status(thm)],[f97,f26]) ).
fof(f643,definition,
! [X0] :
( sQ75_spl
<=> ( product(e_3,e_3,X0)
| product(e_2,e_3,X0)
| product(e_1,e_3,X0)
| ~ group_element(X0)
| ~ product(e_4,e_4,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f646,plain,
( ~ sQ13_spl
| sQ75_spl ),
inference(split_clause,[status(thm)],[f641,f643,f181]) ).
fof(f648,plain,
( ~ sQ66_spl
| ~ product(e_3,e_3,e_3) ),
inference(resolution,[status(thm)],[f568,f76]) ).
fof(f656,plain,
( ~ sQ66_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f648,f51]) ).
fof(f657,plain,
~ sQ66_spl,
inference(contradiction_clause,[status(thm)],[f656]) ).
fof(f669,plain,
! [X0,X1,X2] :
( product(e_3,e_3,X1)
| product(e_2,e_3,X1)
| product(e_1,e_3,X1)
| ~ group_element(X1)
| ~ group_element(e_3)
| ~ product(X2,X0,e_4)
| ~ product(X2,e_4,e_3)
| ~ product(X0,e_4,X1) ),
inference(resolution,[status(thm)],[f99,f26]) ).
fof(f671,definition,
! [X0,X1,X2] :
( sQ76_spl
<=> ( product(e_3,e_3,X1)
| product(e_2,e_3,X1)
| product(e_1,e_3,X1)
| ~ group_element(X1)
| ~ product(X2,X0,e_4)
| ~ product(X2,e_4,e_3)
| ~ product(X0,e_4,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f674,plain,
( ~ sQ13_spl
| sQ76_spl ),
inference(split_clause,[status(thm)],[f669,f671,f181]) ).
fof(f687,plain,
( ~ sQ46_spl
| ~ product(e_2,e_2,e_2) ),
inference(resolution,[status(thm)],[f410,f58]) ).
fof(f690,plain,
( ~ sQ46_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f687,f51]) ).
fof(f691,plain,
~ sQ46_spl,
inference(contradiction_clause,[status(thm)],[f690]) ).
fof(f705,plain,
! [X0] :
( product(e_3,X0,e_4)
| product(e_2,X0,e_4)
| product(e_1,X0,e_4)
| ~ group_element(e_4)
| ~ group_element(X0)
| ~ product(e_4,X0,e_3) ),
inference(resolution,[status(thm)],[f98,f26]) ).
fof(f706,plain,
! [X0] :
( product(X0,e_3,e_4)
| product(X0,e_2,e_4)
| product(X0,e_1,e_4)
| ~ group_element(e_4)
| ~ group_element(X0)
| ~ product(X0,e_4,e_3) ),
inference(resolution,[status(thm)],[f98,f27]) ).
fof(f708,definition,
! [X0] :
( sQ77_spl
<=> ( product(e_3,X0,e_4)
| product(e_2,X0,e_4)
| product(e_1,X0,e_4)
| ~ group_element(X0)
| ~ product(e_4,X0,e_3) ) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f711,plain,
( ~ sQ31_spl
| sQ77_spl ),
inference(split_clause,[status(thm)],[f705,f708,f296]) ).
fof(f712,definition,
! [X0] :
( sQ78_spl
<=> ( product(X0,e_3,e_4)
| product(X0,e_2,e_4)
| product(X0,e_1,e_4)
| ~ group_element(X0)
| ~ product(X0,e_4,e_3) ) ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f715,plain,
( ~ sQ31_spl
| sQ78_spl ),
inference(split_clause,[status(thm)],[f706,f712,f296]) ).
fof(f718,plain,
! [X0,X1,X2] :
( product(e_3,e_3,X1)
| product(e_3,e_2,X1)
| product(e_3,e_1,X1)
| ~ group_element(X1)
| ~ group_element(e_3)
| ~ product(X2,e_4,X0)
| ~ product(X2,e_3,e_4)
| ~ product(e_4,X0,X1) ),
inference(resolution,[status(thm)],[f100,f27]) ).
fof(f720,definition,
! [X0,X1,X2] :
( sQ79_spl
<=> ( product(e_3,e_3,X1)
| product(e_3,e_2,X1)
| product(e_3,e_1,X1)
| ~ group_element(X1)
| ~ product(X2,e_4,X0)
| ~ product(X2,e_3,e_4)
| ~ product(e_4,X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f723,plain,
( ~ sQ13_spl
| sQ79_spl ),
inference(split_clause,[status(thm)],[f718,f720,f181]) ).
fof(f731,plain,
( ~ sQ25_spl
| ~ sQ6_spl
| ~ product(e_2,e_2,e_2) ),
inference(resolution,[status(thm)],[f194,f256]) ).
fof(f733,plain,
( ~ sQ25_spl
| ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f731,f51]) ).
fof(f734,plain,
( ~ sQ25_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f733]) ).
fof(f735,plain,
$false,
inference(sat_refutation,[status(thm)],[f124,f141,f143,f150,f156,f162,f169,f173,f175,f184,f186,f192,f201,f205,f211,f222,f226,f231,f241,f247,f263,f265,f267,f278,f284,f299,f303,f305,f311,f319,f331,f341,f343,f345,f353,f381,f396,f402,f407,f425,f437,f444,f448,f454,f475,f481,f494,f507,f514,f525,f542,f546,f553,f560,f589,f595,f608,f612,f622,f624,f638,f639,f646,f657,f674,f691,f711,f715,f723,f734]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP124-4.004 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n001.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 20:04:58 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 0.16/0.46 % Refutation found
% 0.16/0.46 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.16/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.48 % Elapsed time: 0.103151 seconds
% 0.16/0.48 % CPU time: 0.445729 seconds
% 0.16/0.48 % Total memory used: 20.426 MB
% 0.16/0.48 % Net memory used: 20.021 MB
%------------------------------------------------------------------------------