%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP130-4.003 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 12:32:48 PM UTC 2026
% Result : Unsatisfiable 0.17s 0.49s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 41
% Syntax : Number of formulae : 194 ( 15 unt; 27 def)
% Number of atoms : 479 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 504 ( 219 ~; 258 |; 0 &)
% ( 27 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 31 ( 30 usr; 28 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 109 ( 109 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [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_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,negated_conjecture,
! [X,Y,Z1,Z2] :
( ~ product(X,Z1,Z2)
| ~ product(Z2,Y,X)
| product(X,Y,Z1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X,Y] :
( 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(f15,axiom,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
! [X,Y,Z1,Z2] :
( product(Z2,Y,X)
| ~ product(X,Z1,Z2)
| ~ product(X,Y,Z1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,plain,
! [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(f20,plain,
! [X0,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(f21,plain,
! [X,Z1,Z2] :
( ~ product(X,Z1,Z2)
| ! [Y] :
( ~ product(Z2,Y,X)
| product(X,Y,Z1) ) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f22,plain,
! [X0,X1,X2,X3] :
( ~ product(X0,X2,X3)
| ~ product(X3,X1,X0)
| product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f25,plain,
group_element(e_1),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f26,plain,
group_element(e_2),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f27,plain,
group_element(e_3),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f28,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f29,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f31,plain,
~ equalish(e_2,e_3),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f34,plain,
! [X0,X1] :
( 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)],[f14]) ).
fof(f35,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W) ) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f36,plain,
! [X0,X1,X2,X3] :
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f37,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product(X,Z,Y)
| ~ product(X,W,Y) ) ),
inference(miniscoping,[status(thm)],[f16]) ).
fof(f38,plain,
! [X0,X1,X2,X3] :
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f39,plain,
! [W,Z] :
( equalish(W,Z)
| ! [Y,X] :
( ~ product(Z,Y,X)
| ~ product(W,Y,X) ) ),
inference(miniscoping,[status(thm)],[f17]) ).
fof(f40,plain,
! [X0,X1,X2,X3] :
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f41,plain,
! [X,Y,Z2] :
( product(Z2,Y,X)
| ! [Z1] :
( ~ product(X,Z1,Z2)
| ~ product(X,Y,Z1) ) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f42,plain,
! [X0,X1,X2,X3] :
( product(X3,X1,X0)
| ~ product(X0,X2,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f43,plain,
! [X0] :
( product(X0,e_3,e_1)
| product(X0,e_2,e_1)
| product(X0,e_1,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f25,f20]) ).
fof(f44,plain,
! [X0] :
( product(e_3,X0,e_1)
| product(e_2,X0,e_1)
| product(e_1,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f25,f19]) ).
fof(f45,plain,
! [X0] :
( product(X0,e_3,e_2)
| product(X0,e_2,e_2)
| product(X0,e_1,e_2)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f26,f20]) ).
fof(f46,plain,
! [X0] :
( product(e_3,X0,e_2)
| product(e_2,X0,e_2)
| product(e_1,X0,e_2)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f26,f19]) ).
fof(f47,plain,
! [X0] :
( product(X0,e_3,e_3)
| product(X0,e_2,e_3)
| product(X0,e_1,e_3)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f27,f20]) ).
fof(f48,plain,
! [X0] :
( product(e_3,X0,e_3)
| product(e_2,X0,e_3)
| product(e_1,X0,e_3)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f27,f19]) ).
fof(f49,plain,
! [X0,X1] :
( ~ product(e_2,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[f28,f40]) ).
fof(f51,plain,
! [X0,X1] :
( ~ product(X0,X1,e_2)
| ~ product(X0,X1,e_1) ),
inference(resolution,[status(thm)],[f28,f36]) ).
fof(f52,plain,
! [X0,X1] :
( ~ product(e_3,X0,X1)
| ~ product(e_1,X0,X1) ),
inference(resolution,[status(thm)],[f29,f40]) ).
fof(f53,plain,
! [X0,X1] :
( ~ product(X0,e_3,X1)
| ~ product(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f29,f38]) ).
fof(f54,plain,
! [X0,X1] :
( ~ product(X0,X1,e_3)
| ~ product(X0,X1,e_1) ),
inference(resolution,[status(thm)],[f29,f36]) ).
fof(f58,plain,
! [X0,X1] :
( ~ product(e_3,X0,X1)
| ~ product(e_2,X0,X1) ),
inference(resolution,[status(thm)],[f31,f40]) ).
fof(f59,plain,
! [X0,X1] :
( ~ product(X0,e_3,X1)
| ~ product(X0,e_2,X1) ),
inference(resolution,[status(thm)],[f31,f38]) ).
fof(f60,plain,
! [X0,X1] :
( ~ product(X0,X1,e_3)
| ~ product(X0,X1,e_2) ),
inference(resolution,[status(thm)],[f31,f36]) ).
fof(f67,plain,
! [X0] :
( 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)],[f34,f27]) ).
fof(f68,plain,
! [X0] :
( 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)],[f34,f26]) ).
fof(f69,plain,
! [X0] :
( 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)],[f34,f25]) ).
fof(f70,plain,
( product(e_3,e_3,e_1)
| product(e_3,e_2,e_1)
| product(e_3,e_1,e_1) ),
inference(resolution,[status(thm)],[f43,f27]) ).
fof(f72,plain,
( product(e_1,e_3,e_1)
| product(e_1,e_2,e_1)
| product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f43,f25]) ).
fof(f73,definition,
( sQ0_spl
<=> product(e_3,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f74,plain,
( ~ sQ0_spl
| product(e_3,e_1,e_1) ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f76,definition,
( sQ1_spl
<=> product(e_3,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f77,plain,
( ~ sQ1_spl
| product(e_3,e_2,e_1) ),
inference(component_clause,[status(thm)],[f76]) ).
fof(f79,definition,
( sQ2_spl
<=> product(e_3,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f80,plain,
( ~ sQ2_spl
| product(e_3,e_3,e_1) ),
inference(component_clause,[status(thm)],[f79]) ).
fof(f82,plain,
( sQ2_spl
| sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f70,f73,f76,f79]) ).
fof(f83,definition,
( sQ3_spl
<=> product(e_2,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f84,plain,
( ~ sQ3_spl
| product(e_2,e_1,e_1) ),
inference(component_clause,[status(thm)],[f83]) ).
fof(f86,definition,
( sQ4_spl
<=> product(e_2,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f89,definition,
( sQ5_spl
<=> product(e_2,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f90,plain,
( ~ sQ5_spl
| product(e_2,e_3,e_1) ),
inference(component_clause,[status(thm)],[f89]) ).
fof(f93,definition,
( sQ6_spl
<=> product(e_1,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ6_spl
| product(e_1,e_1,e_1) ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f96,definition,
( sQ7_spl
<=> product(e_1,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f97,plain,
( ~ sQ7_spl
| product(e_1,e_2,e_1) ),
inference(component_clause,[status(thm)],[f96]) ).
fof(f99,definition,
( sQ8_spl
<=> product(e_1,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f100,plain,
( ~ sQ8_spl
| product(e_1,e_3,e_1) ),
inference(component_clause,[status(thm)],[f99]) ).
fof(f102,plain,
( sQ8_spl
| sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f72,f93,f96,f99]) ).
fof(f103,plain,
( product(e_3,e_3,e_1)
| product(e_2,e_3,e_1)
| product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[f44,f27]) ).
fof(f106,plain,
( sQ2_spl
| sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f103,f99,f89,f79]) ).
fof(f110,plain,
( product(e_2,e_3,e_2)
| product(e_2,e_2,e_2)
| product(e_2,e_1,e_2) ),
inference(resolution,[status(thm)],[f45,f26]) ).
fof(f112,definition,
( sQ9_spl
<=> product(e_3,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f113,plain,
( ~ sQ9_spl
| product(e_3,e_1,e_2) ),
inference(component_clause,[status(thm)],[f112]) ).
fof(f115,definition,
( sQ10_spl
<=> product(e_3,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f116,plain,
( ~ sQ10_spl
| product(e_3,e_2,e_2) ),
inference(component_clause,[status(thm)],[f115]) ).
fof(f118,definition,
( sQ11_spl
<=> product(e_3,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f119,plain,
( ~ sQ11_spl
| product(e_3,e_3,e_2) ),
inference(component_clause,[status(thm)],[f118]) ).
fof(f122,definition,
( sQ12_spl
<=> product(e_2,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f123,plain,
( ~ sQ12_spl
| product(e_2,e_1,e_2) ),
inference(component_clause,[status(thm)],[f122]) ).
fof(f125,definition,
( sQ13_spl
<=> product(e_2,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f126,plain,
( ~ sQ13_spl
| product(e_2,e_2,e_2) ),
inference(component_clause,[status(thm)],[f125]) ).
fof(f128,definition,
( sQ14_spl
<=> product(e_2,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f129,plain,
( ~ sQ14_spl
| product(e_2,e_3,e_2) ),
inference(component_clause,[status(thm)],[f128]) ).
fof(f131,plain,
( sQ14_spl
| sQ13_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f110,f122,f125,f128]) ).
fof(f132,definition,
( sQ15_spl
<=> product(e_1,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f133,plain,
( ~ sQ15_spl
| product(e_1,e_1,e_2) ),
inference(component_clause,[status(thm)],[f132]) ).
fof(f135,definition,
( sQ16_spl
<=> product(e_1,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f136,plain,
( ~ sQ16_spl
| product(e_1,e_2,e_2) ),
inference(component_clause,[status(thm)],[f135]) ).
fof(f138,definition,
( sQ17_spl
<=> product(e_1,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f139,plain,
( ~ sQ17_spl
| product(e_1,e_3,e_2) ),
inference(component_clause,[status(thm)],[f138]) ).
fof(f142,plain,
( product(e_3,e_3,e_2)
| product(e_2,e_3,e_2)
| product(e_1,e_3,e_2) ),
inference(resolution,[status(thm)],[f46,f27]) ).
fof(f144,plain,
( product(e_3,e_1,e_2)
| product(e_2,e_1,e_2)
| product(e_1,e_1,e_2) ),
inference(resolution,[status(thm)],[f46,f25]) ).
fof(f145,plain,
( sQ11_spl
| sQ14_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f142,f138,f128,f118]) ).
fof(f147,plain,
( sQ9_spl
| sQ12_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f144,f132,f122,f112]) ).
fof(f149,plain,
( product(e_2,e_3,e_3)
| product(e_2,e_2,e_3)
| product(e_2,e_1,e_3) ),
inference(resolution,[status(thm)],[f47,f26]) ).
fof(f150,plain,
( product(e_1,e_3,e_3)
| product(e_1,e_2,e_3)
| product(e_1,e_1,e_3) ),
inference(resolution,[status(thm)],[f47,f25]) ).
fof(f151,definition,
( sQ18_spl
<=> product(e_3,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f154,definition,
( sQ19_spl
<=> product(e_3,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f155,plain,
( ~ sQ19_spl
| product(e_3,e_2,e_3) ),
inference(component_clause,[status(thm)],[f154]) ).
fof(f157,definition,
( sQ20_spl
<=> product(e_3,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f158,plain,
( ~ sQ20_spl
| product(e_3,e_3,e_3) ),
inference(component_clause,[status(thm)],[f157]) ).
fof(f161,definition,
( sQ21_spl
<=> product(e_2,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f162,plain,
( ~ sQ21_spl
| product(e_2,e_1,e_3) ),
inference(component_clause,[status(thm)],[f161]) ).
fof(f164,definition,
( sQ22_spl
<=> product(e_2,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f167,definition,
( sQ23_spl
<=> product(e_2,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f170,plain,
( sQ23_spl
| sQ22_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f149,f161,f164,f167]) ).
fof(f171,definition,
( sQ24_spl
<=> product(e_1,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f174,definition,
( sQ25_spl
<=> product(e_1,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f175,plain,
( ~ sQ25_spl
| product(e_1,e_2,e_3) ),
inference(component_clause,[status(thm)],[f174]) ).
fof(f177,definition,
( sQ26_spl
<=> product(e_1,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f178,plain,
( ~ sQ26_spl
| product(e_1,e_3,e_3) ),
inference(component_clause,[status(thm)],[f177]) ).
fof(f180,plain,
( sQ26_spl
| sQ25_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f150,f171,f174,f177]) ).
fof(f182,plain,
( product(e_3,e_2,e_3)
| product(e_2,e_2,e_3)
| product(e_1,e_2,e_3) ),
inference(resolution,[status(thm)],[f48,f26]) ).
fof(f183,plain,
( product(e_3,e_1,e_3)
| product(e_2,e_1,e_3)
| product(e_1,e_1,e_3) ),
inference(resolution,[status(thm)],[f48,f25]) ).
fof(f185,plain,
( sQ19_spl
| sQ22_spl
| sQ25_spl ),
inference(split_clause,[status(thm)],[f182,f174,f164,f154]) ).
fof(f186,plain,
( sQ18_spl
| sQ21_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f183,f171,f161,f151]) ).
fof(f187,plain,
( product(e_3,e_3,e_3)
| product(e_3,e_3,e_2)
| product(e_3,e_3,e_1) ),
inference(resolution,[status(thm)],[f67,f27]) ).
fof(f190,plain,
( sQ20_spl
| sQ11_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f187,f79,f118,f157]) ).
fof(f193,plain,
( product(e_3,e_2,e_3)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[f68,f27]) ).
fof(f195,plain,
( 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)],[f68,f25]) ).
fof(f196,plain,
( sQ19_spl
| sQ10_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f193,f76,f115,f154]) ).
fof(f198,plain,
( sQ25_spl
| sQ16_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f195,f96,f135,f174]) ).
fof(f200,plain,
( product(e_2,e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[f69,f26]) ).
fof(f201,plain,
( 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)],[f69,f25]) ).
fof(f203,plain,
( sQ21_spl
| sQ12_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f200,f83,f122,f161]) ).
fof(f204,plain,
( sQ24_spl
| sQ15_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f201,f93,f132,f171]) ).
fof(f205,plain,
( ~ sQ0_spl
| ~ product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[f74,f58]) ).
fof(f211,plain,
( ~ sQ0_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f205,f84]) ).
fof(f212,plain,
( ~ sQ0_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f211]) ).
fof(f214,plain,
( ~ sQ1_spl
| ~ product(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[f77,f52]) ).
fof(f222,plain,
( ~ sQ17_spl
| ~ product(e_1,e_2,e_2) ),
inference(resolution,[status(thm)],[f139,f59]) ).
fof(f224,plain,
( ~ sQ17_spl
| ~ product(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[f139,f51]) ).
fof(f228,plain,
! [X0] :
( ~ sQ17_spl
| ~ product(e_2,X0,e_1)
| product(e_2,e_3,X0) ),
inference(resolution,[status(thm)],[f139,f22]) ).
fof(f229,plain,
( ~ sQ17_spl
| ~ sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f222,f136]) ).
fof(f230,plain,
( ~ sQ17_spl
| ~ sQ16_spl ),
inference(contradiction_clause,[status(thm)],[f229]) ).
fof(f231,plain,
( ~ sQ15_spl
| ~ product(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f133,f51]) ).
fof(f232,plain,
! [X0] :
( ~ sQ15_spl
| product(e_2,X0,e_1)
| ~ product(e_1,X0,e_1) ),
inference(resolution,[status(thm)],[f133,f42]) ).
fof(f234,plain,
! [X0] :
( ~ sQ15_spl
| ~ product(e_2,X0,e_1)
| product(e_1,X0,e_1) ),
inference(resolution,[status(thm)],[f133,f22]) ).
fof(f236,plain,
( ~ sQ15_spl
| ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f231,f94]) ).
fof(f237,plain,
( ~ sQ15_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f236]) ).
fof(f239,plain,
( ~ sQ8_spl
| ~ sQ15_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f100,f241]) ).
fof(f240,plain,
( ~ sQ7_spl
| ~ sQ15_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f97,f241]) ).
fof(f241,plain,
! [X0] :
( ~ sQ15_spl
| ~ product(e_1,X0,e_1) ),
inference(forward_subsumption_resolution,[status(thm)],[f232,f49]) ).
fof(f244,plain,
! [X0] :
( ~ sQ15_spl
| ~ product(e_2,X0,e_1) ),
inference(forward_subsumption_resolution,[status(thm)],[f234,f49]) ).
fof(f245,plain,
( ~ sQ3_spl
| ~ sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f84,f244]) ).
fof(f246,plain,
( ~ sQ3_spl
| ~ sQ15_spl ),
inference(contradiction_clause,[status(thm)],[f245]) ).
fof(f251,plain,
! [X0] :
( ~ sQ14_spl
| product(e_2,X0,e_2)
| ~ product(e_2,X0,e_3) ),
inference(resolution,[status(thm)],[f129,f42]) ).
fof(f253,plain,
( ~ sQ14_spl
| product(e_2,e_3,e_3) ),
inference(resolution,[status(thm)],[f129,f22]) ).
fof(f259,plain,
( ~ sQ17_spl
| ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f224,f100]) ).
fof(f260,plain,
( ~ sQ17_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f259]) ).
fof(f261,plain,
( ~ sQ7_spl
| ~ sQ15_spl ),
inference(contradiction_clause,[status(thm)],[f240]) ).
fof(f269,plain,
( ~ sQ12_spl
| ~ product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[f123,f51]) ).
fof(f272,plain,
( ~ sQ12_spl
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[f123,f22]) ).
fof(f280,plain,
( ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f272,f269]) ).
fof(f281,plain,
~ sQ12_spl,
inference(contradiction_clause,[status(thm)],[f280]) ).
fof(f294,plain,
! [X0] :
( ~ sQ9_spl
| ~ product(e_2,X0,e_3)
| product(e_2,e_1,X0) ),
inference(resolution,[status(thm)],[f113,f22]) ).
fof(f295,plain,
( ~ sQ10_spl
| ~ product(e_2,e_2,e_2) ),
inference(resolution,[status(thm)],[f116,f58]) ).
fof(f303,plain,
( ~ sQ10_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f295,f125,f115]) ).
fof(f312,plain,
! [X0] :
( ~ sQ14_spl
| ~ product(e_2,X0,e_3) ),
inference(forward_subsumption_resolution,[status(thm)],[f251,f60]) ).
fof(f313,plain,
( ~ sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f253,f312]) ).
fof(f314,plain,
~ sQ14_spl,
inference(contradiction_clause,[status(thm)],[f313]) ).
fof(f315,plain,
( ~ sQ26_spl
| ~ product(e_1,e_2,e_3) ),
inference(resolution,[status(thm)],[f178,f59]) ).
fof(f323,plain,
( ~ sQ26_spl
| ~ sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f315,f175]) ).
fof(f324,plain,
( ~ sQ26_spl
| ~ sQ25_spl ),
inference(contradiction_clause,[status(thm)],[f323]) ).
fof(f325,plain,
( ~ sQ2_spl
| ~ product(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[f80,f58]) ).
fof(f329,plain,
! [X0] :
( ~ sQ2_spl
| product(e_1,X0,e_3)
| ~ product(e_3,X0,e_3) ),
inference(resolution,[status(thm)],[f80,f42]) ).
fof(f331,plain,
! [X0] :
( ~ sQ2_spl
| ~ product(e_1,X0,e_3)
| product(e_3,X0,e_3) ),
inference(resolution,[status(thm)],[f80,f22]) ).
fof(f333,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f325,f90]) ).
fof(f334,plain,
( ~ sQ2_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f333]) ).
fof(f345,plain,
( ~ sQ11_spl
| ~ product(e_3,e_1,e_2) ),
inference(resolution,[status(thm)],[f119,f53]) ).
fof(f351,plain,
( ~ sQ11_spl
| ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f345,f113]) ).
fof(f352,plain,
( ~ sQ11_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f351]) ).
fof(f364,plain,
( ~ sQ8_spl
| ~ sQ15_spl ),
inference(contradiction_clause,[status(thm)],[f239]) ).
fof(f365,plain,
( ~ sQ1_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f214,f96,f76]) ).
fof(f380,plain,
( ~ sQ13_spl
| ~ product(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[f126,f51]) ).
fof(f387,plain,
( ~ sQ20_spl
| ~ product(e_2,e_3,e_3) ),
inference(resolution,[status(thm)],[f158,f58]) ).
fof(f399,plain,
( ~ sQ9_spl
| ~ sQ21_spl
| product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[f162,f294]) ).
fof(f402,plain,
( ~ sQ21_spl
| ~ product(e_2,e_1,e_1) ),
inference(resolution,[status(thm)],[f162,f54]) ).
fof(f407,plain,
( ~ sQ21_spl
| ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f402,f399]) ).
fof(f408,plain,
( ~ sQ21_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f407]) ).
fof(f416,plain,
( ~ sQ17_spl
| ~ sQ5_spl
| product(e_2,e_3,e_3) ),
inference(resolution,[status(thm)],[f90,f228]) ).
fof(f425,plain,
( ~ sQ17_spl
| ~ sQ5_spl
| ~ sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f416,f387]) ).
fof(f426,plain,
( ~ sQ17_spl
| ~ sQ5_spl
| ~ sQ20_spl ),
inference(contradiction_clause,[status(thm)],[f425]) ).
fof(f428,plain,
( ~ sQ19_spl
| ~ sQ2_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f155,f429]) ).
fof(f429,plain,
! [X0] :
( ~ sQ2_spl
| ~ product(e_3,X0,e_3) ),
inference(forward_subsumption_resolution,[status(thm)],[f329,f52]) ).
fof(f431,plain,
( ~ sQ25_spl
| ~ sQ2_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f175,f434]) ).
fof(f434,plain,
! [X0] :
( ~ sQ2_spl
| ~ product(e_1,X0,e_3) ),
inference(forward_subsumption_resolution,[status(thm)],[f331,f52]) ).
fof(f435,plain,
( ~ sQ13_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f380,f86,f125]) ).
fof(f437,plain,
( ~ sQ19_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f428]) ).
fof(f441,plain,
( ~ sQ25_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f431]) ).
fof(f442,plain,
$false,
inference(sat_refutation,[status(thm)],[f82,f102,f106,f131,f145,f147,f170,f180,f185,f186,f190,f196,f198,f203,f204,f212,f230,f237,f246,f260,f261,f281,f303,f314,f324,f334,f352,f364,f365,f408,f426,f435,f437,f441]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP130-4.003 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n019.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sun Sep 20 20:01:21 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.47 % Drodi V4.1.1
% 0.17/0.49 % Refutation found
% 0.17/0.49 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.17/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.55 % Elapsed time: 0.089422 seconds
% 0.17/0.55 % CPU time: 0.134226 seconds
% 0.17/0.55 % Total memory used: 4.621 MB
% 0.17/0.55 % Net memory used: 4.551 MB
%------------------------------------------------------------------------------