%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP124-1.004 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 0.14s 0.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 63
% Syntax : Number of formulae : 258 ( 52 unt; 46 def)
% Number of atoms : 754 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 914 ( 418 ~; 450 |; 0 &)
% ( 46 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 50 ( 49 usr; 47 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 220 ( 220 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
group_element(e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
~ equalish(e_1,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
~ equalish(e_2,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X,Y] :
( product(X,Y,e_4)
| product(X,Y,e_3)
| product(X,Y,e_2)
| product(X,Y,e_1)
| ~ group_element(Y)
| ~ group_element(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [X] : product(X,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,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(f23,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(f24,plain,
group_element(e_1),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f25,plain,
group_element(e_2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f26,plain,
group_element(e_3),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f27,plain,
group_element(e_4),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f28,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f29,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f30,plain,
~ equalish(e_1,e_4),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f32,plain,
~ equalish(e_2,e_3),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f33,plain,
~ equalish(e_2,e_4),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f36,plain,
~ equalish(e_3,e_4),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f40,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)],[f17]) ).
fof(f41,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W) ) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f42,plain,
! [X0,X1,X2,X3] :
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f43,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product(X,Z,Y)
| ~ product(X,W,Y) ) ),
inference(miniscoping,[status(thm)],[f19]) ).
fof(f44,plain,
! [X0,X1,X2,X3] :
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f45,plain,
! [W,Z] :
( equalish(W,Z)
| ! [Y,X] :
( ~ product(Z,Y,X)
| ~ product(W,Y,X) ) ),
inference(miniscoping,[status(thm)],[f20]) ).
fof(f46,plain,
! [X0,X1,X2,X3] :
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f47,plain,
! [X0] : product(X0,X0,X0),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f48,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)],[f22]) ).
fof(f49,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)],[f48]) ).
fof(f50,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)],[f23]) ).
fof(f51,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)],[f50]) ).
fof(f52,plain,
! [X0,X1] :
( ~ product(e_2,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[f28,f46]) ).
fof(f53,plain,
! [X0,X1] :
( ~ product(X0,e_2,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f28,f44]) ).
fof(f54,plain,
! [X0,X1] :
( ~ product(X0,X1,e_2)
| ~ product(X0,X1,e_1) ),
inference(resolution,[status(thm)],[f28,f42]) ).
fof(f56,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)],[f28,f49]) ).
fof(f58,plain,
! [X0,X1] :
( ~ product(e_3,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[f29,f46]) ).
fof(f59,plain,
! [X0,X1] :
( ~ product(X0,e_3,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f29,f44]) ).
fof(f60,plain,
! [X0,X1] :
( ~ product(X0,X1,e_3)
| ~ product(X0,X1,e_1) ),
inference(resolution,[status(thm)],[f29,f42]) ).
fof(f62,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)],[f29,f49]) ).
fof(f63,plain,
! [X0,X1] :
( ~ product(e_4,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[f30,f46]) ).
fof(f64,plain,
! [X0,X1] :
( ~ product(X0,e_4,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f30,f44]) ).
fof(f67,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)],[f30,f49]) ).
fof(f73,plain,
! [X0,X1] :
( ~ product(e_3,X0,X1)
| ~ product(e_2,X0,X1) ),
inference(resolution,[status(thm)],[f32,f46]) ).
fof(f74,plain,
! [X0,X1] :
( ~ product(X0,e_3,X1)
| ~ product(X0,e_2,X1) ),
inference(resolution,[status(thm)],[f32,f44]) ).
fof(f75,plain,
! [X0,X1] :
( ~ product(X0,X1,e_3)
| ~ product(X0,X1,e_2) ),
inference(resolution,[status(thm)],[f32,f42]) ).
fof(f76,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)],[f32,f51]) ).
fof(f77,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)],[f32,f49]) ).
fof(f78,plain,
! [X0,X1] :
( ~ product(e_4,X0,X1)
| ~ product(e_2,X0,X1) ),
inference(resolution,[status(thm)],[f33,f46]) ).
fof(f79,plain,
! [X0,X1] :
( ~ product(X0,e_4,X1)
| ~ product(X0,e_2,X1) ),
inference(resolution,[status(thm)],[f33,f44]) ).
fof(f80,plain,
! [X0,X1] :
( ~ product(X0,X1,e_4)
| ~ product(X0,X1,e_2) ),
inference(resolution,[status(thm)],[f33,f42]) ).
fof(f82,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)],[f33,f49]) ).
fof(f93,plain,
! [X0,X1] :
( ~ product(e_4,X0,X1)
| ~ product(e_3,X0,X1) ),
inference(resolution,[status(thm)],[f36,f46]) ).
fof(f94,plain,
! [X0,X1] :
( ~ product(X0,e_4,X1)
| ~ product(X0,e_3,X1) ),
inference(resolution,[status(thm)],[f36,f44]) ).
fof(f96,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)],[f36,f51]) ).
fof(f97,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)],[f36,f49]) ).
fof(f113,plain,
! [X0] :
( ~ product(e_1,X0,e_4)
| product(e_2,X0,e_3)
| product(e_2,X0,e_2)
| product(e_2,X0,e_1)
| ~ group_element(X0)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[f40,f52]) ).
fof(f114,definition,
( sQ0_spl
<=> group_element(e_2) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f116,plain,
( sQ0_spl
| ~ group_element(e_2) ),
inference(component_clause,[status(thm)],[f114]) ).
fof(f117,definition,
! [X0] :
( sQ1_spl
<=> ( ~ product(e_1,X0,e_4)
| product(e_2,X0,e_3)
| product(e_2,X0,e_2)
| product(e_2,X0,e_1)
| ~ group_element(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f120,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f113,f114,f117]) ).
fof(f121,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f116,f25]) ).
fof(f122,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f121]) ).
fof(f124,plain,
! [X0,X1,X2] :
( product(e_2,X2,e_3)
| product(e_2,X2,e_2)
| product(e_2,X2,e_1)
| ~ group_element(X2)
| ~ group_element(e_2)
| ~ product(X1,e_2,X2)
| ~ product(X1,e_1,X0)
| ~ product(e_1,X0,e_4) ),
inference(resolution,[status(thm)],[f56,f40]) ).
fof(f125,plain,
! [X0,X1] :
( ~ product(X1,e_2,e_2)
| ~ product(X1,e_1,X0)
| ~ product(e_1,X0,e_2) ),
inference(resolution,[status(thm)],[f56,f47]) ).
fof(f126,definition,
! [X0,X1,X2] :
( sQ2_spl
<=> ( product(e_2,X2,e_3)
| product(e_2,X2,e_2)
| product(e_2,X2,e_1)
| ~ group_element(X2)
| ~ product(X1,e_2,X2)
| ~ product(X1,e_1,X0)
| ~ product(e_1,X0,e_4) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f129,plain,
( ~ sQ0_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f124,f126,f114]) ).
fof(f131,plain,
! [X0] :
( product(X0,e_2,e_3)
| product(X0,e_2,e_2)
| product(X0,e_2,e_1)
| ~ group_element(e_2)
| ~ group_element(X0)
| ~ product(X0,e_1,e_4) ),
inference(resolution,[status(thm)],[f53,f40]) ).
fof(f132,plain,
~ product(e_2,e_1,e_2),
inference(resolution,[status(thm)],[f53,f47]) ).
fof(f133,definition,
! [X0] :
( sQ3_spl
<=> ( product(X0,e_2,e_3)
| product(X0,e_2,e_2)
| product(X0,e_2,e_1)
| ~ group_element(X0)
| ~ product(X0,e_1,e_4) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f136,plain,
( ~ sQ0_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f131,f133,f114]) ).
fof(f137,plain,
~ product(e_2,e_2,e_1),
inference(resolution,[status(thm)],[f54,f47]) ).
fof(f138,plain,
! [X0] :
( product(e_3,X0,e_3)
| product(e_3,X0,e_2)
| product(e_3,X0,e_1)
| ~ group_element(X0)
| ~ group_element(e_3)
| ~ product(e_1,X0,e_4) ),
inference(resolution,[status(thm)],[f58,f40]) ).
fof(f140,definition,
! [X0] :
( sQ4_spl
<=> ( product(e_3,X0,e_3)
| product(e_3,X0,e_2)
| product(e_3,X0,e_1)
| ~ group_element(X0)
| ~ product(e_1,X0,e_4) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f143,definition,
( sQ5_spl
<=> group_element(e_3) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f145,plain,
( sQ5_spl
| ~ group_element(e_3) ),
inference(component_clause,[status(thm)],[f143]) ).
fof(f146,plain,
( ~ sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f138,f140,f143]) ).
fof(f147,plain,
! [X0] :
( product(X0,e_3,e_3)
| product(X0,e_3,e_2)
| product(X0,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(X0)
| ~ product(X0,e_1,e_4) ),
inference(resolution,[status(thm)],[f59,f40]) ).
fof(f148,plain,
~ product(e_3,e_1,e_3),
inference(resolution,[status(thm)],[f59,f47]) ).
fof(f149,definition,
! [X0] :
( sQ6_spl
<=> ( product(X0,e_3,e_3)
| product(X0,e_3,e_2)
| product(X0,e_3,e_1)
| ~ group_element(X0)
| ~ product(X0,e_1,e_4) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f152,plain,
( ~ sQ5_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f147,f149,f143]) ).
fof(f153,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f145,f26]) ).
fof(f154,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f153]) ).
fof(f155,plain,
~ product(e_3,e_3,e_1),
inference(resolution,[status(thm)],[f60,f47]) ).
fof(f156,plain,
! [X0] :
( product(e_4,X0,e_3)
| product(e_4,X0,e_2)
| product(e_4,X0,e_1)
| ~ group_element(X0)
| ~ group_element(e_4)
| ~ product(e_1,X0,e_4) ),
inference(resolution,[status(thm)],[f63,f40]) ).
fof(f157,plain,
~ product(e_1,e_4,e_4),
inference(resolution,[status(thm)],[f63,f47]) ).
fof(f158,definition,
! [X0] :
( sQ7_spl
<=> ( product(e_4,X0,e_3)
| product(e_4,X0,e_2)
| product(e_4,X0,e_1)
| ~ group_element(X0)
| ~ product(e_1,X0,e_4) ) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f161,definition,
( sQ8_spl
<=> group_element(e_4) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f163,plain,
( sQ8_spl
| ~ group_element(e_4) ),
inference(component_clause,[status(thm)],[f161]) ).
fof(f164,plain,
( ~ sQ8_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f156,f158,f161]) ).
fof(f165,plain,
( product(e_1,e_4,e_3)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_1)
| ~ group_element(e_4)
| ~ group_element(e_1) ),
inference(resolution,[status(thm)],[f157,f40]) ).
fof(f166,definition,
( sQ9_spl
<=> group_element(e_1) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f168,plain,
( sQ9_spl
| ~ group_element(e_1) ),
inference(component_clause,[status(thm)],[f166]) ).
fof(f169,definition,
( sQ10_spl
<=> product(e_1,e_4,e_1) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f170,plain,
( ~ sQ10_spl
| product(e_1,e_4,e_1) ),
inference(component_clause,[status(thm)],[f169]) ).
fof(f172,definition,
( sQ11_spl
<=> product(e_1,e_4,e_2) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f173,plain,
( ~ sQ11_spl
| product(e_1,e_4,e_2) ),
inference(component_clause,[status(thm)],[f172]) ).
fof(f175,definition,
( sQ12_spl
<=> product(e_1,e_4,e_3) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f176,plain,
( ~ sQ12_spl
| product(e_1,e_4,e_3) ),
inference(component_clause,[status(thm)],[f175]) ).
fof(f178,plain,
( sQ12_spl
| sQ11_spl
| sQ10_spl
| ~ sQ8_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f165,f166,f161,f169,f172,f175]) ).
fof(f179,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f163,f27]) ).
fof(f180,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f179]) ).
fof(f183,plain,
! [X0] :
( product(X0,e_1,e_3)
| product(X0,e_1,e_2)
| product(X0,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(X0)
| ~ product(X0,e_4,e_4) ),
inference(resolution,[status(thm)],[f64,f40]) ).
fof(f184,plain,
~ product(e_1,e_4,e_1),
inference(resolution,[status(thm)],[f64,f47]) ).
fof(f185,definition,
! [X0] :
( sQ13_spl
<=> ( product(X0,e_1,e_3)
| product(X0,e_1,e_2)
| product(X0,e_1,e_1)
| ~ group_element(X0)
| ~ product(X0,e_4,e_4) ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f188,plain,
( ~ sQ9_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f183,f185,f166]) ).
fof(f189,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f168,f24]) ).
fof(f190,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f189]) ).
fof(f191,plain,
! [X0,X1,X2] :
( product(e_3,X2,e_3)
| product(e_3,X2,e_2)
| product(e_3,X2,e_1)
| ~ group_element(X2)
| ~ group_element(e_3)
| ~ product(X1,e_3,X2)
| ~ product(X1,e_1,X0)
| ~ product(e_1,X0,e_4) ),
inference(resolution,[status(thm)],[f62,f40]) ).
fof(f192,plain,
! [X0,X1] :
( ~ product(X1,e_3,e_3)
| ~ product(X1,e_1,X0)
| ~ product(e_1,X0,e_3) ),
inference(resolution,[status(thm)],[f62,f47]) ).
fof(f193,definition,
! [X0,X1,X2] :
( sQ14_spl
<=> ( product(e_3,X2,e_3)
| product(e_3,X2,e_2)
| product(e_3,X2,e_1)
| ~ group_element(X2)
| ~ product(X1,e_3,X2)
| ~ product(X1,e_1,X0)
| ~ product(e_1,X0,e_4) ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f196,plain,
( ~ sQ5_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f191,f193,f143]) ).
fof(f213,plain,
! [X0,X1,X2] :
( product(e_4,X2,e_3)
| product(e_4,X2,e_2)
| product(e_4,X2,e_1)
| ~ group_element(X2)
| ~ group_element(e_4)
| ~ product(X1,e_4,X2)
| ~ product(X1,e_1,X0)
| ~ product(e_1,X0,e_4) ),
inference(resolution,[status(thm)],[f67,f40]) ).
fof(f215,definition,
! [X0,X1,X2] :
( sQ19_spl
<=> ( product(e_4,X2,e_3)
| product(e_4,X2,e_2)
| product(e_4,X2,e_1)
| ~ group_element(X2)
| ~ product(X1,e_4,X2)
| ~ product(X1,e_1,X0)
| ~ product(e_1,X0,e_4) ) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f218,plain,
( ~ sQ8_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f213,f215,f161]) ).
fof(f226,definition,
( sQ22_spl
<=> product(e_1,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f227,plain,
( ~ sQ22_spl
| product(e_1,e_1,e_3) ),
inference(component_clause,[status(thm)],[f226]) ).
fof(f245,plain,
! [X0] :
( ~ sQ11_spl
| ~ product(X0,e_2,e_2)
| ~ product(X0,e_1,e_4) ),
inference(resolution,[status(thm)],[f173,f125]) ).
fof(f249,plain,
( ~ sQ22_spl
| ~ product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f227,f60]) ).
fof(f251,plain,
( ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f249,f47]) ).
fof(f252,plain,
~ sQ22_spl,
inference(contradiction_clause,[status(thm)],[f251]) ).
fof(f259,plain,
( ~ sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f170,f184]) ).
fof(f260,plain,
~ sQ10_spl,
inference(contradiction_clause,[status(thm)],[f259]) ).
fof(f264,plain,
! [X0] :
( product(e_3,X0,e_3)
| product(e_3,X0,e_2)
| product(e_3,X0,e_1)
| ~ group_element(X0)
| ~ group_element(e_3)
| ~ product(e_2,X0,e_4) ),
inference(resolution,[status(thm)],[f73,f40]) ).
fof(f266,definition,
! [X0] :
( sQ23_spl
<=> ( product(e_3,X0,e_3)
| product(e_3,X0,e_2)
| product(e_3,X0,e_1)
| ~ group_element(X0)
| ~ product(e_2,X0,e_4) ) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f269,plain,
( ~ sQ5_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f264,f266,f143]) ).
fof(f270,plain,
! [X0] :
( product(X0,e_2,e_3)
| product(X0,e_2,e_2)
| product(X0,e_2,e_1)
| ~ group_element(e_2)
| ~ group_element(X0)
| ~ product(X0,e_3,e_4) ),
inference(resolution,[status(thm)],[f74,f40]) ).
fof(f272,definition,
! [X0] :
( sQ24_spl
<=> ( product(X0,e_2,e_3)
| product(X0,e_2,e_2)
| product(X0,e_2,e_1)
| ~ group_element(X0)
| ~ product(X0,e_3,e_4) ) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f275,plain,
( ~ sQ0_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f270,f272,f114]) ).
fof(f277,plain,
~ product(e_3,e_3,e_2),
inference(resolution,[status(thm)],[f75,f47]) ).
fof(f278,plain,
( ~ sQ11_spl
| ~ product(e_2,e_1,e_4) ),
inference(resolution,[status(thm)],[f245,f47]) ).
fof(f279,plain,
( ~ sQ11_spl
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[f278,f40]) ).
fof(f280,definition,
( sQ25_spl
<=> product(e_2,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f281,plain,
( ~ sQ25_spl
| product(e_2,e_1,e_1) ),
inference(component_clause,[status(thm)],[f280]) ).
fof(f283,definition,
( sQ26_spl
<=> product(e_2,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f284,plain,
( ~ sQ26_spl
| product(e_2,e_1,e_2) ),
inference(component_clause,[status(thm)],[f283]) ).
fof(f286,definition,
( sQ27_spl
<=> product(e_2,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f287,plain,
( ~ sQ27_spl
| product(e_2,e_1,e_3) ),
inference(component_clause,[status(thm)],[f286]) ).
fof(f289,plain,
( ~ sQ11_spl
| sQ27_spl
| sQ26_spl
| sQ25_spl
| ~ sQ9_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f279,f114,f166,f280,f283,f286,f172]) ).
fof(f290,plain,
( ~ sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f284,f132]) ).
fof(f291,plain,
~ sQ26_spl,
inference(contradiction_clause,[status(thm)],[f290]) ).
fof(f292,plain,
! [X0,X1,X2] :
( product(X2,e_2,e_3)
| product(X2,e_2,e_2)
| product(X2,e_2,e_1)
| ~ group_element(e_2)
| ~ group_element(X2)
| ~ product(X1,X0,e_3)
| ~ product(X1,X2,e_2)
| ~ product(X0,e_3,e_4) ),
inference(resolution,[status(thm)],[f76,f40]) ).
fof(f294,definition,
! [X0,X1,X2] :
( sQ28_spl
<=> ( product(X2,e_2,e_3)
| product(X2,e_2,e_2)
| product(X2,e_2,e_1)
| ~ group_element(X2)
| ~ product(X1,X0,e_3)
| ~ product(X1,X2,e_2)
| ~ product(X0,e_3,e_4) ) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f297,plain,
( ~ sQ0_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f292,f294,f114]) ).
fof(f300,plain,
( ~ sQ27_spl
| ~ product(e_2,e_4,e_3) ),
inference(resolution,[status(thm)],[f287,f64]) ).
fof(f306,plain,
( ~ sQ25_spl
| ~ product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f281,f52]) ).
fof(f310,plain,
( ~ sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f306,f47]) ).
fof(f311,plain,
~ sQ25_spl,
inference(contradiction_clause,[status(thm)],[f310]) ).
fof(f312,plain,
! [X0,X1,X2] :
( product(e_3,X2,e_3)
| product(e_3,X2,e_2)
| product(e_3,X2,e_1)
| ~ group_element(X2)
| ~ group_element(e_3)
| ~ product(X1,e_3,X2)
| ~ product(X1,e_2,X0)
| ~ product(e_2,X0,e_4) ),
inference(resolution,[status(thm)],[f77,f40]) ).
fof(f314,definition,
! [X0,X1,X2] :
( sQ29_spl
<=> ( product(e_3,X2,e_3)
| product(e_3,X2,e_2)
| product(e_3,X2,e_1)
| ~ group_element(X2)
| ~ product(X1,e_3,X2)
| ~ product(X1,e_2,X0)
| ~ product(e_2,X0,e_4) ) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f317,plain,
( ~ sQ5_spl
| sQ29_spl ),
inference(split_clause,[status(thm)],[f312,f314,f143]) ).
fof(f319,plain,
! [X0] :
( product(e_4,X0,e_3)
| product(e_4,X0,e_2)
| product(e_4,X0,e_1)
| ~ group_element(X0)
| ~ group_element(e_4)
| ~ product(e_2,X0,e_4) ),
inference(resolution,[status(thm)],[f78,f40]) ).
fof(f320,plain,
~ product(e_2,e_4,e_4),
inference(resolution,[status(thm)],[f78,f47]) ).
fof(f321,definition,
! [X0] :
( sQ30_spl
<=> ( product(e_4,X0,e_3)
| product(e_4,X0,e_2)
| product(e_4,X0,e_1)
| ~ group_element(X0)
| ~ product(e_2,X0,e_4) ) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f324,plain,
( ~ sQ8_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f319,f321,f161]) ).
fof(f325,plain,
( product(e_2,e_4,e_3)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1)
| ~ group_element(e_4)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[f320,f40]) ).
fof(f326,definition,
( sQ31_spl
<=> product(e_2,e_4,e_1) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f327,plain,
( ~ sQ31_spl
| product(e_2,e_4,e_1) ),
inference(component_clause,[status(thm)],[f326]) ).
fof(f329,definition,
( sQ32_spl
<=> product(e_2,e_4,e_2) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f330,plain,
( ~ sQ32_spl
| product(e_2,e_4,e_2) ),
inference(component_clause,[status(thm)],[f329]) ).
fof(f332,definition,
( sQ33_spl
<=> product(e_2,e_4,e_3) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f333,plain,
( ~ sQ33_spl
| product(e_2,e_4,e_3) ),
inference(component_clause,[status(thm)],[f332]) ).
fof(f335,plain,
( sQ33_spl
| sQ32_spl
| sQ31_spl
| ~ sQ8_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f325,f114,f161,f326,f329,f332]) ).
fof(f336,plain,
( ~ sQ33_spl
| ~ sQ27_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f333,f300]) ).
fof(f337,plain,
( ~ sQ33_spl
| ~ sQ27_spl ),
inference(contradiction_clause,[status(thm)],[f336]) ).
fof(f350,plain,
! [X0] :
( product(X0,e_2,e_3)
| product(X0,e_2,e_2)
| product(X0,e_2,e_1)
| ~ group_element(e_2)
| ~ group_element(X0)
| ~ product(X0,e_4,e_4) ),
inference(resolution,[status(thm)],[f79,f40]) ).
fof(f351,plain,
~ product(e_2,e_4,e_2),
inference(resolution,[status(thm)],[f79,f47]) ).
fof(f352,definition,
! [X0] :
( sQ34_spl
<=> ( product(X0,e_2,e_3)
| product(X0,e_2,e_2)
| product(X0,e_2,e_1)
| ~ group_element(X0)
| ~ product(X0,e_4,e_4) ) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f355,plain,
( ~ sQ0_spl
| sQ34_spl ),
inference(split_clause,[status(thm)],[f350,f352,f114]) ).
fof(f356,plain,
( ~ sQ32_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f351,f330]) ).
fof(f357,plain,
~ sQ32_spl,
inference(contradiction_clause,[status(thm)],[f356]) ).
fof(f358,plain,
~ product(e_2,e_2,e_4),
inference(resolution,[status(thm)],[f80,f47]) ).
fof(f364,definition,
( sQ36_spl
<=> product(e_4,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f365,plain,
( ~ sQ36_spl
| product(e_4,e_1,e_1) ),
inference(component_clause,[status(thm)],[f364]) ).
fof(f390,plain,
( ~ sQ36_spl
| ~ product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f365,f63]) ).
fof(f394,plain,
( ~ sQ36_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f390,f47]) ).
fof(f395,plain,
~ sQ36_spl,
inference(contradiction_clause,[status(thm)],[f394]) ).
fof(f396,plain,
! [X0,X1,X2] :
( product(e_4,X2,e_3)
| product(e_4,X2,e_2)
| product(e_4,X2,e_1)
| ~ group_element(X2)
| ~ group_element(e_4)
| ~ product(X1,e_4,X2)
| ~ product(X1,e_2,X0)
| ~ product(e_2,X0,e_4) ),
inference(resolution,[status(thm)],[f82,f40]) ).
fof(f398,definition,
! [X0,X1,X2] :
( sQ39_spl
<=> ( product(e_4,X2,e_3)
| product(e_4,X2,e_2)
| product(e_4,X2,e_1)
| ~ group_element(X2)
| ~ product(X1,e_4,X2)
| ~ product(X1,e_2,X0)
| ~ product(e_2,X0,e_4) ) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f401,plain,
( ~ sQ8_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f396,f398,f161]) ).
fof(f402,plain,
( product(e_2,e_2,e_3)
| product(e_2,e_2,e_2)
| product(e_2,e_2,e_1)
| ~ group_element(e_2)
| ~ group_element(e_2) ),
inference(resolution,[status(thm)],[f358,f40]) ).
fof(f403,definition,
( sQ40_spl
<=> product(e_2,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f404,plain,
( ~ sQ40_spl
| product(e_2,e_2,e_1) ),
inference(component_clause,[status(thm)],[f403]) ).
fof(f406,definition,
( sQ41_spl
<=> product(e_2,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f409,definition,
( sQ42_spl
<=> product(e_2,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f410,plain,
( ~ sQ42_spl
| product(e_2,e_2,e_3) ),
inference(component_clause,[status(thm)],[f409]) ).
fof(f412,plain,
( sQ42_spl
| sQ41_spl
| sQ40_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f402,f114,f403,f406,f409]) ).
fof(f413,plain,
( ~ sQ40_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f404,f137]) ).
fof(f414,plain,
~ sQ40_spl,
inference(contradiction_clause,[status(thm)],[f413]) ).
fof(f430,plain,
( ~ sQ42_spl
| ~ product(e_2,e_2,e_2) ),
inference(resolution,[status(thm)],[f410,f75]) ).
fof(f433,plain,
( ~ sQ42_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f430,f47]) ).
fof(f434,plain,
~ sQ42_spl,
inference(contradiction_clause,[status(thm)],[f433]) ).
fof(f437,plain,
! [X0] :
( ~ sQ12_spl
| ~ product(X0,e_3,e_3)
| ~ product(X0,e_1,e_4) ),
inference(resolution,[status(thm)],[f192,f176]) ).
fof(f438,plain,
( ~ sQ12_spl
| ~ product(e_3,e_1,e_4) ),
inference(resolution,[status(thm)],[f437,f47]) ).
fof(f439,plain,
( ~ sQ12_spl
| product(e_3,e_1,e_3)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1)
| ~ group_element(e_1)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[f438,f40]) ).
fof(f440,definition,
( sQ43_spl
<=> product(e_3,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f441,plain,
( ~ sQ43_spl
| product(e_3,e_1,e_1) ),
inference(component_clause,[status(thm)],[f440]) ).
fof(f443,definition,
( sQ44_spl
<=> product(e_3,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f444,plain,
( ~ sQ44_spl
| product(e_3,e_1,e_2) ),
inference(component_clause,[status(thm)],[f443]) ).
fof(f446,definition,
( sQ45_spl
<=> product(e_3,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f447,plain,
( ~ sQ45_spl
| product(e_3,e_1,e_3) ),
inference(component_clause,[status(thm)],[f446]) ).
fof(f449,plain,
( ~ sQ12_spl
| sQ45_spl
| sQ44_spl
| sQ43_spl
| ~ sQ9_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f439,f143,f166,f440,f443,f446,f175]) ).
fof(f450,plain,
( ~ sQ45_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f447,f148]) ).
fof(f451,plain,
~ sQ45_spl,
inference(contradiction_clause,[status(thm)],[f450]) ).
fof(f456,plain,
( ~ sQ44_spl
| ~ product(e_3,e_4,e_2) ),
inference(resolution,[status(thm)],[f444,f64]) ).
fof(f465,plain,
( ~ sQ43_spl
| ~ product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f441,f58]) ).
fof(f469,plain,
( ~ sQ43_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f465,f47]) ).
fof(f470,plain,
~ sQ43_spl,
inference(contradiction_clause,[status(thm)],[f469]) ).
fof(f472,plain,
! [X0] :
( product(e_4,X0,e_3)
| product(e_4,X0,e_2)
| product(e_4,X0,e_1)
| ~ group_element(X0)
| ~ group_element(e_4)
| ~ product(e_3,X0,e_4) ),
inference(resolution,[status(thm)],[f93,f40]) ).
fof(f473,plain,
~ product(e_3,e_4,e_4),
inference(resolution,[status(thm)],[f93,f47]) ).
fof(f474,definition,
! [X0] :
( sQ46_spl
<=> ( product(e_4,X0,e_3)
| product(e_4,X0,e_2)
| product(e_4,X0,e_1)
| ~ group_element(X0)
| ~ product(e_3,X0,e_4) ) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f477,plain,
( ~ sQ8_spl
| sQ46_spl ),
inference(split_clause,[status(thm)],[f472,f474,f161]) ).
fof(f478,plain,
( product(e_3,e_4,e_3)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1)
| ~ group_element(e_4)
| ~ group_element(e_3) ),
inference(resolution,[status(thm)],[f473,f40]) ).
fof(f479,definition,
( sQ47_spl
<=> product(e_3,e_4,e_1) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f480,plain,
( ~ sQ47_spl
| product(e_3,e_4,e_1) ),
inference(component_clause,[status(thm)],[f479]) ).
fof(f482,definition,
( sQ48_spl
<=> product(e_3,e_4,e_2) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f483,plain,
( ~ sQ48_spl
| product(e_3,e_4,e_2) ),
inference(component_clause,[status(thm)],[f482]) ).
fof(f485,definition,
( sQ49_spl
<=> product(e_3,e_4,e_3) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f486,plain,
( ~ sQ49_spl
| product(e_3,e_4,e_3) ),
inference(component_clause,[status(thm)],[f485]) ).
fof(f488,plain,
( sQ49_spl
| sQ48_spl
| sQ47_spl
| ~ sQ8_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f478,f143,f161,f479,f482,f485]) ).
fof(f489,plain,
( ~ sQ48_spl
| ~ sQ44_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f483,f456]) ).
fof(f490,plain,
( ~ sQ48_spl
| ~ sQ44_spl ),
inference(contradiction_clause,[status(thm)],[f489]) ).
fof(f502,plain,
( ~ sQ47_spl
| ~ product(e_2,e_4,e_1) ),
inference(resolution,[status(thm)],[f480,f73]) ).
fof(f507,plain,
( ~ sQ47_spl
| ~ sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f502,f327]) ).
fof(f508,plain,
( ~ sQ47_spl
| ~ sQ31_spl ),
inference(contradiction_clause,[status(thm)],[f507]) ).
fof(f510,plain,
! [X0] :
( product(X0,e_3,e_3)
| product(X0,e_3,e_2)
| product(X0,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(X0)
| ~ product(X0,e_4,e_4) ),
inference(resolution,[status(thm)],[f94,f40]) ).
fof(f511,plain,
~ product(e_3,e_4,e_3),
inference(resolution,[status(thm)],[f94,f47]) ).
fof(f512,definition,
! [X0] :
( sQ50_spl
<=> ( product(X0,e_3,e_3)
| product(X0,e_3,e_2)
| product(X0,e_3,e_1)
| ~ group_element(X0)
| ~ product(X0,e_4,e_4) ) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f515,plain,
( ~ sQ5_spl
| sQ50_spl ),
inference(split_clause,[status(thm)],[f510,f512,f143]) ).
fof(f524,definition,
( sQ52_spl
<=> product(e_3,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f525,plain,
( ~ sQ52_spl
| product(e_3,e_3,e_1) ),
inference(component_clause,[status(thm)],[f524]) ).
fof(f527,definition,
( sQ53_spl
<=> product(e_3,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f528,plain,
( ~ sQ53_spl
| product(e_3,e_3,e_2) ),
inference(component_clause,[status(thm)],[f527]) ).
fof(f534,plain,
( ~ sQ53_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f528,f277]) ).
fof(f535,plain,
~ sQ53_spl,
inference(contradiction_clause,[status(thm)],[f534]) ).
fof(f536,plain,
( ~ sQ52_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f525,f155]) ).
fof(f537,plain,
~ sQ52_spl,
inference(contradiction_clause,[status(thm)],[f536]) ).
fof(f540,plain,
! [X0,X1,X2] :
( product(X2,e_3,e_3)
| product(X2,e_3,e_2)
| product(X2,e_3,e_1)
| ~ group_element(e_3)
| ~ group_element(X2)
| ~ product(X1,X0,e_4)
| ~ product(X1,X2,e_3)
| ~ product(X0,e_4,e_4) ),
inference(resolution,[status(thm)],[f96,f40]) ).
fof(f542,definition,
! [X0,X1,X2] :
( sQ55_spl
<=> ( product(X2,e_3,e_3)
| product(X2,e_3,e_2)
| product(X2,e_3,e_1)
| ~ group_element(X2)
| ~ product(X1,X0,e_4)
| ~ product(X1,X2,e_3)
| ~ product(X0,e_4,e_4) ) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f545,plain,
( ~ sQ5_spl
| sQ55_spl ),
inference(split_clause,[status(thm)],[f540,f542,f143]) ).
fof(f547,plain,
( ~ sQ33_spl
| ~ product(e_1,e_4,e_3) ),
inference(resolution,[status(thm)],[f333,f52]) ).
fof(f551,plain,
( ~ sQ33_spl
| ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f547,f176]) ).
fof(f552,plain,
( ~ sQ33_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f551]) ).
fof(f558,plain,
! [X0,X1,X2] :
( product(e_4,X2,e_3)
| product(e_4,X2,e_2)
| product(e_4,X2,e_1)
| ~ group_element(X2)
| ~ group_element(e_4)
| ~ product(X1,e_4,X2)
| ~ product(X1,e_3,X0)
| ~ product(e_3,X0,e_4) ),
inference(resolution,[status(thm)],[f97,f40]) ).
fof(f560,definition,
! [X0,X1,X2] :
( sQ56_spl
<=> ( product(e_4,X2,e_3)
| product(e_4,X2,e_2)
| product(e_4,X2,e_1)
| ~ group_element(X2)
| ~ product(X1,e_4,X2)
| ~ product(X1,e_3,X0)
| ~ product(e_3,X0,e_4) ) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f563,plain,
( ~ sQ8_spl
| sQ56_spl ),
inference(split_clause,[status(thm)],[f558,f560,f161]) ).
fof(f580,plain,
( ~ sQ48_spl
| ~ product(e_1,e_4,e_2) ),
inference(resolution,[status(thm)],[f483,f58]) ).
fof(f585,plain,
( ~ sQ48_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f580,f172,f482]) ).
fof(f589,plain,
( ~ sQ49_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f486,f511]) ).
fof(f590,plain,
~ sQ49_spl,
inference(contradiction_clause,[status(thm)],[f589]) ).
fof(f591,plain,
$false,
inference(sat_refutation,[status(thm)],[f120,f122,f129,f136,f146,f152,f154,f164,f178,f180,f188,f190,f196,f218,f252,f260,f269,f275,f289,f291,f297,f311,f317,f324,f335,f337,f355,f357,f395,f401,f412,f414,f434,f449,f451,f470,f477,f488,f490,f508,f515,f535,f537,f545,f552,f563,f585,f590]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP124-1.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n020.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 20 19:59:32 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Drodi V4.1.1
% 0.14/0.40 % Refutation found
% 0.14/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.42 % Elapsed time: 0.049903 seconds
% 0.14/0.42 % CPU time: 0.199359 seconds
% 0.14/0.42 % Total memory used: 14.957 MB
% 0.14/0.42 % Net memory used: 14.682 MB
%------------------------------------------------------------------------------