%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP126-2.004 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : 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 12:32:44 PM UTC 2026
% Result : Unsatisfiable 0.26s 0.62s
% Output : CNFRefutation 0.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 57
% Syntax : Number of formulae : 232 ( 54 unt; 32 def)
% Number of atoms : 516 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 533 ( 249 ~; 252 |; 0 &)
% ( 32 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 38 ( 37 usr; 33 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 83 ( 83 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
next(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
greater(e_4,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y,X1] :
( ~ greater(Y,X1)
| ~ next(X,X1)
| ~ product(X,e_1,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
group_element(e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
~ equalish(e_1,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
~ equalish(e_2,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
~ equalish(e_4,e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
~ equalish(e_4,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
~ equalish(e_4,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,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(f28,axiom,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product(X,Y,Z)
| ~ product(X,Y,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product(X,Z,Y)
| ~ product(X,W,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product(Z,Y,X)
| ~ product(W,Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [X] : product(X,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
! [X,Y,Z1,Z2] :
( product(Z1,Z2,Y)
| ~ product(Y,X,Z2)
| ~ product(X,Y,Z1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,plain,
next(e_2,e_3),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f41,plain,
greater(e_4,e_3),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f42,plain,
! [Y,X1] :
( ~ greater(Y,X1)
| ! [X] :
( ~ next(X,X1)
| ~ product(X,e_1,Y) ) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ~ greater(X1,X2)
| ~ next(X0,X2)
| ~ product(X0,e_1,X1) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f44,plain,
group_element(e_1),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f45,plain,
group_element(e_2),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f46,plain,
group_element(e_3),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f47,plain,
group_element(e_4),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f48,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f49,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f50,plain,
~ equalish(e_1,e_4),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f51,plain,
~ equalish(e_2,e_1),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f52,plain,
~ equalish(e_2,e_3),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f53,plain,
~ equalish(e_2,e_4),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f54,plain,
~ equalish(e_3,e_1),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f55,plain,
~ equalish(e_3,e_2),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f56,plain,
~ equalish(e_3,e_4),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f57,plain,
~ equalish(e_4,e_1),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f58,plain,
~ equalish(e_4,e_2),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f59,plain,
~ equalish(e_4,e_3),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f60,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)],[f27]) ).
fof(f61,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W) ) ),
inference(miniscoping,[status(thm)],[f28]) ).
fof(f62,plain,
! [X0,X1,X2,X3] :
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f63,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product(X,Z,Y)
| ~ product(X,W,Y) ) ),
inference(miniscoping,[status(thm)],[f29]) ).
fof(f64,plain,
! [X0,X1,X2,X3] :
( equalish(X1,X3)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f65,plain,
! [W,Z] :
( equalish(W,Z)
| ! [Y,X] :
( ~ product(Z,Y,X)
| ~ product(W,Y,X) ) ),
inference(miniscoping,[status(thm)],[f30]) ).
fof(f66,plain,
! [X0,X1,X2,X3] :
( equalish(X0,X3)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f67,plain,
! [X0] : product(X0,X0,X0),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f68,plain,
! [Y,Z1,Z2] :
( product(Z1,Z2,Y)
| ! [X] :
( ~ product(Y,X,Z2)
| ~ product(X,Y,Z1) ) ),
inference(miniscoping,[status(thm)],[f32]) ).
fof(f69,plain,
! [X0,X1,X2,X3] :
( product(X2,X3,X1)
| ~ product(X1,X0,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f72,plain,
! [X0,X1] :
( equalish(X1,X0)
| ~ product(X0,X0,X1) ),
inference(resolution,[status(thm)],[f62,f67]) ).
fof(f74,plain,
! [X0,X1] :
( equalish(X1,X0)
| ~ product(X0,X1,X0) ),
inference(resolution,[status(thm)],[f64,f67]) ).
fof(f75,plain,
! [X0,X1] :
( equalish(X0,X1)
| ~ product(X0,X1,X1) ),
inference(resolution,[status(thm)],[f66,f67]) ).
fof(f77,plain,
! [X0] :
( product(e_4,X0,e_4)
| product(e_4,X0,e_3)
| product(e_4,X0,e_2)
| product(e_4,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f60,f47]) ).
fof(f78,plain,
! [X0] :
( product(e_3,X0,e_4)
| product(e_3,X0,e_3)
| product(e_3,X0,e_2)
| product(e_3,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f60,f46]) ).
fof(f79,plain,
! [X0] :
( product(e_2,X0,e_4)
| product(e_2,X0,e_3)
| product(e_2,X0,e_2)
| product(e_2,X0,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f60,f45]) ).
fof(f82,plain,
( product(e_4,e_3,e_4)
| product(e_4,e_3,e_3)
| product(e_4,e_3,e_2)
| product(e_4,e_3,e_1) ),
inference(resolution,[status(thm)],[f77,f46]) ).
fof(f84,plain,
( product(e_4,e_1,e_4)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_1) ),
inference(resolution,[status(thm)],[f77,f44]) ).
fof(f98,definition,
( sQ4_spl
<=> product(e_4,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f99,plain,
( ~ sQ4_spl
| product(e_4,e_3,e_1) ),
inference(component_clause,[status(thm)],[f98]) ).
fof(f101,definition,
( sQ5_spl
<=> product(e_4,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f102,plain,
( ~ sQ5_spl
| product(e_4,e_3,e_2) ),
inference(component_clause,[status(thm)],[f101]) ).
fof(f104,definition,
( sQ6_spl
<=> product(e_4,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f105,plain,
( ~ sQ6_spl
| product(e_4,e_3,e_3) ),
inference(component_clause,[status(thm)],[f104]) ).
fof(f107,definition,
( sQ7_spl
<=> product(e_4,e_3,e_4) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f108,plain,
( ~ sQ7_spl
| product(e_4,e_3,e_4) ),
inference(component_clause,[status(thm)],[f107]) ).
fof(f110,plain,
( sQ7_spl
| sQ6_spl
| sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f82,f98,f101,f104,f107]) ).
fof(f114,definition,
( sQ9_spl
<=> product(e_4,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f115,plain,
( ~ sQ9_spl
| product(e_4,e_2,e_2) ),
inference(component_clause,[status(thm)],[f114]) ).
fof(f120,definition,
( sQ11_spl
<=> product(e_4,e_2,e_4) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f121,plain,
( ~ sQ11_spl
| product(e_4,e_2,e_4) ),
inference(component_clause,[status(thm)],[f120]) ).
fof(f124,definition,
( sQ12_spl
<=> product(e_4,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f125,plain,
( ~ sQ12_spl
| product(e_4,e_1,e_1) ),
inference(component_clause,[status(thm)],[f124]) ).
fof(f127,definition,
( sQ13_spl
<=> product(e_4,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f128,plain,
( ~ sQ13_spl
| product(e_4,e_1,e_2) ),
inference(component_clause,[status(thm)],[f127]) ).
fof(f130,definition,
( sQ14_spl
<=> product(e_4,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f131,plain,
( ~ sQ14_spl
| product(e_4,e_1,e_3) ),
inference(component_clause,[status(thm)],[f130]) ).
fof(f133,definition,
( sQ15_spl
<=> product(e_4,e_1,e_4) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f134,plain,
( ~ sQ15_spl
| product(e_4,e_1,e_4) ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,plain,
( sQ15_spl
| sQ14_spl
| sQ13_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f84,f124,f127,f130,f133]) ).
fof(f137,plain,
( product(e_3,e_4,e_4)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[f78,f47]) ).
fof(f139,plain,
( product(e_3,e_2,e_4)
| 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)],[f78,f45]) ).
fof(f140,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_1,e_3)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_1) ),
inference(resolution,[status(thm)],[f78,f44]) ).
fof(f141,definition,
( sQ16_spl
<=> product(e_3,e_4,e_1) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f142,plain,
( ~ sQ16_spl
| product(e_3,e_4,e_1) ),
inference(component_clause,[status(thm)],[f141]) ).
fof(f144,definition,
( sQ17_spl
<=> product(e_3,e_4,e_2) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f145,plain,
( ~ sQ17_spl
| product(e_3,e_4,e_2) ),
inference(component_clause,[status(thm)],[f144]) ).
fof(f147,definition,
( sQ18_spl
<=> product(e_3,e_4,e_3) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f148,plain,
( ~ sQ18_spl
| product(e_3,e_4,e_3) ),
inference(component_clause,[status(thm)],[f147]) ).
fof(f150,definition,
( sQ19_spl
<=> product(e_3,e_4,e_4) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f151,plain,
( ~ sQ19_spl
| product(e_3,e_4,e_4) ),
inference(component_clause,[status(thm)],[f150]) ).
fof(f153,plain,
( sQ19_spl
| sQ18_spl
| sQ17_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f137,f141,f144,f147,f150]) ).
fof(f157,definition,
( sQ21_spl
<=> product(e_3,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f158,plain,
( ~ sQ21_spl
| product(e_3,e_3,e_2) ),
inference(component_clause,[status(thm)],[f157]) ).
fof(f167,definition,
( sQ24_spl
<=> product(e_3,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f168,plain,
( ~ sQ24_spl
| product(e_3,e_2,e_1) ),
inference(component_clause,[status(thm)],[f167]) ).
fof(f170,definition,
( sQ25_spl
<=> product(e_3,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f171,plain,
( ~ sQ25_spl
| product(e_3,e_2,e_2) ),
inference(component_clause,[status(thm)],[f170]) ).
fof(f173,definition,
( sQ26_spl
<=> product(e_3,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f174,plain,
( ~ sQ26_spl
| product(e_3,e_2,e_3) ),
inference(component_clause,[status(thm)],[f173]) ).
fof(f176,definition,
( sQ27_spl
<=> product(e_3,e_2,e_4) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f177,plain,
( ~ sQ27_spl
| product(e_3,e_2,e_4) ),
inference(component_clause,[status(thm)],[f176]) ).
fof(f179,plain,
( sQ27_spl
| sQ26_spl
| sQ25_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f139,f167,f170,f173,f176]) ).
fof(f180,definition,
( sQ28_spl
<=> product(e_3,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f181,plain,
( ~ sQ28_spl
| product(e_3,e_1,e_1) ),
inference(component_clause,[status(thm)],[f180]) ).
fof(f183,definition,
( sQ29_spl
<=> product(e_3,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f186,definition,
( sQ30_spl
<=> product(e_3,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f187,plain,
( ~ sQ30_spl
| product(e_3,e_1,e_3) ),
inference(component_clause,[status(thm)],[f186]) ).
fof(f189,definition,
( sQ31_spl
<=> product(e_3,e_1,e_4) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f190,plain,
( ~ sQ31_spl
| product(e_3,e_1,e_4) ),
inference(component_clause,[status(thm)],[f189]) ).
fof(f192,plain,
( sQ31_spl
| sQ30_spl
| sQ29_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f140,f180,f183,f186,f189]) ).
fof(f194,plain,
( product(e_2,e_3,e_4)
| product(e_2,e_3,e_3)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[f79,f46]) ).
fof(f196,plain,
( product(e_2,e_1,e_4)
| 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)],[f79,f44]) ).
fof(f210,definition,
( sQ36_spl
<=> product(e_2,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f211,plain,
( ~ sQ36_spl
| product(e_2,e_3,e_1) ),
inference(component_clause,[status(thm)],[f210]) ).
fof(f213,definition,
( sQ37_spl
<=> product(e_2,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f214,plain,
( ~ sQ37_spl
| product(e_2,e_3,e_2) ),
inference(component_clause,[status(thm)],[f213]) ).
fof(f216,definition,
( sQ38_spl
<=> product(e_2,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f217,plain,
( ~ sQ38_spl
| product(e_2,e_3,e_3) ),
inference(component_clause,[status(thm)],[f216]) ).
fof(f219,definition,
( sQ39_spl
<=> product(e_2,e_3,e_4) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f220,plain,
( ~ sQ39_spl
| product(e_2,e_3,e_4) ),
inference(component_clause,[status(thm)],[f219]) ).
fof(f222,plain,
( sQ39_spl
| sQ38_spl
| sQ37_spl
| sQ36_spl ),
inference(split_clause,[status(thm)],[f194,f210,f213,f216,f219]) ).
fof(f232,definition,
( sQ43_spl
<=> product(e_2,e_2,e_4) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f233,plain,
( ~ sQ43_spl
| product(e_2,e_2,e_4) ),
inference(component_clause,[status(thm)],[f232]) ).
fof(f236,definition,
( sQ44_spl
<=> product(e_2,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f237,plain,
( ~ sQ44_spl
| product(e_2,e_1,e_1) ),
inference(component_clause,[status(thm)],[f236]) ).
fof(f239,definition,
( sQ45_spl
<=> product(e_2,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f240,plain,
( ~ sQ45_spl
| product(e_2,e_1,e_2) ),
inference(component_clause,[status(thm)],[f239]) ).
fof(f242,definition,
( sQ46_spl
<=> product(e_2,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f243,plain,
( ~ sQ46_spl
| product(e_2,e_1,e_3) ),
inference(component_clause,[status(thm)],[f242]) ).
fof(f245,definition,
( sQ47_spl
<=> product(e_2,e_1,e_4) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f246,plain,
( ~ sQ47_spl
| product(e_2,e_1,e_4) ),
inference(component_clause,[status(thm)],[f245]) ).
fof(f248,plain,
( sQ47_spl
| sQ46_spl
| sQ45_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f196,f236,f239,f242,f245]) ).
fof(f308,plain,
( ~ sQ15_spl
| equalish(e_1,e_4) ),
inference(resolution,[status(thm)],[f134,f74]) ).
fof(f313,plain,
( ~ sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f308,f50]) ).
fof(f314,plain,
~ sQ15_spl,
inference(contradiction_clause,[status(thm)],[f313]) ).
fof(f316,plain,
! [X0] :
( ~ sQ14_spl
| equalish(X0,e_4)
| ~ product(X0,e_1,e_3) ),
inference(resolution,[status(thm)],[f131,f66]) ).
fof(f319,plain,
! [X0] :
( ~ sQ14_spl
| product(X0,e_3,e_4)
| ~ product(e_1,e_4,X0) ),
inference(resolution,[status(thm)],[f131,f69]) ).
fof(f326,plain,
! [X0] :
( ~ sQ13_spl
| equalish(X0,e_1)
| ~ product(e_4,X0,e_2) ),
inference(resolution,[status(thm)],[f128,f64]) ).
fof(f332,plain,
( ~ sQ12_spl
| equalish(e_4,e_1) ),
inference(resolution,[status(thm)],[f125,f75]) ).
fof(f337,plain,
( ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f332,f57]) ).
fof(f338,plain,
~ sQ12_spl,
inference(contradiction_clause,[status(thm)],[f337]) ).
fof(f339,plain,
( ~ sQ11_spl
| equalish(e_2,e_4) ),
inference(resolution,[status(thm)],[f121,f74]) ).
fof(f344,plain,
( ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f339,f53]) ).
fof(f345,plain,
~ sQ11_spl,
inference(contradiction_clause,[status(thm)],[f344]) ).
fof(f355,plain,
( ~ sQ9_spl
| equalish(e_4,e_2) ),
inference(resolution,[status(thm)],[f115,f75]) ).
fof(f369,plain,
( ~ sQ7_spl
| equalish(e_3,e_4) ),
inference(resolution,[status(thm)],[f108,f74]) ).
fof(f374,plain,
( ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f369,f56]) ).
fof(f375,plain,
~ sQ7_spl,
inference(contradiction_clause,[status(thm)],[f374]) ).
fof(f376,plain,
( ~ sQ6_spl
| equalish(e_4,e_3) ),
inference(resolution,[status(thm)],[f105,f75]) ).
fof(f381,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f376,f59]) ).
fof(f382,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f381]) ).
fof(f383,plain,
( ~ sQ13_spl
| ~ sQ5_spl
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[f102,f326]) ).
fof(f384,plain,
! [X0] :
( ~ sQ5_spl
| equalish(X0,e_4)
| ~ product(X0,e_3,e_2) ),
inference(resolution,[status(thm)],[f102,f66]) ).
fof(f388,plain,
( ~ sQ13_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f383,f54]) ).
fof(f389,plain,
( ~ sQ13_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f388]) ).
fof(f394,plain,
! [X0] :
( ~ sQ4_spl
| product(X0,e_1,e_4)
| ~ product(e_3,e_4,X0) ),
inference(resolution,[status(thm)],[f99,f69]) ).
fof(f403,plain,
! [X0] :
( ~ sQ31_spl
| equalish(X0,e_3)
| ~ product(X0,e_1,e_4) ),
inference(resolution,[status(thm)],[f190,f66]) ).
fof(f412,plain,
( ~ sQ30_spl
| equalish(e_1,e_3) ),
inference(resolution,[status(thm)],[f187,f74]) ).
fof(f428,plain,
( ~ sQ28_spl
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[f181,f75]) ).
fof(f433,plain,
( ~ sQ28_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f428,f54]) ).
fof(f434,plain,
~ sQ28_spl,
inference(contradiction_clause,[status(thm)],[f433]) ).
fof(f435,plain,
( ~ sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f412,f49]) ).
fof(f436,plain,
~ sQ30_spl,
inference(contradiction_clause,[status(thm)],[f435]) ).
fof(f439,plain,
! [X0] :
( ~ sQ27_spl
| equalish(X0,e_2)
| ~ product(e_3,X0,e_4) ),
inference(resolution,[status(thm)],[f177,f64]) ).
fof(f441,plain,
! [X0] :
( ~ sQ27_spl
| product(X0,e_4,e_3)
| ~ product(e_2,e_3,X0) ),
inference(resolution,[status(thm)],[f177,f69]) ).
fof(f445,plain,
( ~ sQ26_spl
| equalish(e_2,e_3) ),
inference(resolution,[status(thm)],[f174,f74]) ).
fof(f452,plain,
( ~ sQ25_spl
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[f171,f75]) ).
fof(f457,plain,
( ~ sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f452,f55]) ).
fof(f458,plain,
~ sQ25_spl,
inference(contradiction_clause,[status(thm)],[f457]) ).
fof(f462,plain,
! [X0] :
( ~ sQ24_spl
| product(X0,e_1,e_3)
| ~ product(e_2,e_3,X0) ),
inference(resolution,[status(thm)],[f168,f69]) ).
fof(f477,plain,
( ~ sQ21_spl
| equalish(e_2,e_3) ),
inference(resolution,[status(thm)],[f158,f72]) ).
fof(f481,plain,
( ~ sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f477,f52]) ).
fof(f482,plain,
~ sQ21_spl,
inference(contradiction_clause,[status(thm)],[f481]) ).
fof(f493,plain,
( ~ sQ4_spl
| ~ sQ19_spl
| product(e_4,e_1,e_4) ),
inference(resolution,[status(thm)],[f151,f394]) ).
fof(f500,plain,
( ~ sQ4_spl
| ~ sQ19_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f493,f133,f150,f98]) ).
fof(f504,plain,
( ~ sQ18_spl
| equalish(e_4,e_3) ),
inference(resolution,[status(thm)],[f148,f74]) ).
fof(f509,plain,
( ~ sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f504,f59]) ).
fof(f510,plain,
~ sQ18_spl,
inference(contradiction_clause,[status(thm)],[f509]) ).
fof(f511,plain,
( ~ sQ4_spl
| ~ sQ17_spl
| product(e_2,e_1,e_4) ),
inference(resolution,[status(thm)],[f145,f394]) ).
fof(f516,plain,
( ~ sQ4_spl
| ~ sQ16_spl
| product(e_1,e_1,e_4) ),
inference(resolution,[status(thm)],[f142,f394]) ).
fof(f524,plain,
( ~ sQ31_spl
| ~ sQ47_spl
| equalish(e_2,e_3) ),
inference(resolution,[status(thm)],[f246,f403]) ).
fof(f527,plain,
! [X0] :
( ~ sQ47_spl
| equalish(X0,e_1)
| ~ product(e_2,X0,e_4) ),
inference(resolution,[status(thm)],[f246,f64]) ).
fof(f530,plain,
( ~ sQ31_spl
| ~ sQ47_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f524,f52]) ).
fof(f531,plain,
( ~ sQ31_spl
| ~ sQ47_spl ),
inference(contradiction_clause,[status(thm)],[f530]) ).
fof(f539,plain,
( ~ sQ45_spl
| equalish(e_1,e_2) ),
inference(resolution,[status(thm)],[f240,f74]) ).
fof(f547,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ17_spl
| ~ greater(e_4,X0)
| ~ next(e_2,X0) ),
inference(resolution,[status(thm)],[f511,f43]) ).
fof(f554,plain,
( ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f355,f58]) ).
fof(f555,plain,
~ sQ9_spl,
inference(contradiction_clause,[status(thm)],[f554]) ).
fof(f559,plain,
( ~ sQ4_spl
| ~ sQ16_spl
| equalish(e_4,e_1) ),
inference(resolution,[status(thm)],[f516,f72]) ).
fof(f563,plain,
( ~ sQ4_spl
| ~ sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f559,f57]) ).
fof(f564,plain,
( ~ sQ4_spl
| ~ sQ16_spl ),
inference(contradiction_clause,[status(thm)],[f563]) ).
fof(f570,plain,
( ~ sQ4_spl
| ~ sQ17_spl
| ~ next(e_2,e_3) ),
inference(resolution,[status(thm)],[f547,f41]) ).
fof(f573,plain,
( ~ sQ4_spl
| ~ sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f570,f34]) ).
fof(f574,plain,
( ~ sQ4_spl
| ~ sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f573]) ).
fof(f578,plain,
( ~ sQ46_spl
| ~ sQ14_spl
| equalish(e_2,e_4) ),
inference(resolution,[status(thm)],[f316,f243]) ).
fof(f579,plain,
( ~ sQ46_spl
| ~ sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f578,f53]) ).
fof(f580,plain,
( ~ sQ46_spl
| ~ sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f579]) ).
fof(f582,plain,
( ~ sQ44_spl
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[f237,f75]) ).
fof(f587,plain,
( ~ sQ44_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f582,f51]) ).
fof(f588,plain,
~ sQ44_spl,
inference(contradiction_clause,[status(thm)],[f587]) ).
fof(f589,plain,
( ~ sQ45_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f539,f48]) ).
fof(f590,plain,
~ sQ45_spl,
inference(contradiction_clause,[status(thm)],[f589]) ).
fof(f591,plain,
( ~ sQ47_spl
| ~ sQ43_spl
| equalish(e_2,e_1) ),
inference(resolution,[status(thm)],[f233,f527]) ).
fof(f598,plain,
( ~ sQ47_spl
| ~ sQ43_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f591,f51]) ).
fof(f599,plain,
( ~ sQ47_spl
| ~ sQ43_spl ),
inference(contradiction_clause,[status(thm)],[f598]) ).
fof(f619,plain,
( ~ sQ47_spl
| ~ sQ39_spl
| equalish(e_3,e_1) ),
inference(resolution,[status(thm)],[f220,f527]) ).
fof(f624,plain,
( ~ sQ47_spl
| ~ sQ39_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f619,f54]) ).
fof(f625,plain,
( ~ sQ47_spl
| ~ sQ39_spl ),
inference(contradiction_clause,[status(thm)],[f624]) ).
fof(f627,plain,
( ~ sQ38_spl
| equalish(e_2,e_3) ),
inference(resolution,[status(thm)],[f217,f75]) ).
fof(f633,plain,
( ~ sQ38_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f627,f52]) ).
fof(f634,plain,
~ sQ38_spl,
inference(contradiction_clause,[status(thm)],[f633]) ).
fof(f636,plain,
( ~ sQ5_spl
| ~ sQ37_spl
| equalish(e_2,e_4) ),
inference(resolution,[status(thm)],[f214,f384]) ).
fof(f643,plain,
( ~ sQ5_spl
| ~ sQ37_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f636,f53]) ).
fof(f644,plain,
( ~ sQ5_spl
| ~ sQ37_spl ),
inference(contradiction_clause,[status(thm)],[f643]) ).
fof(f645,plain,
( ~ sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f445,f52]) ).
fof(f646,plain,
~ sQ26_spl,
inference(contradiction_clause,[status(thm)],[f645]) ).
fof(f647,plain,
( ~ sQ27_spl
| ~ sQ36_spl
| product(e_1,e_4,e_3) ),
inference(resolution,[status(thm)],[f211,f441]) ).
fof(f652,plain,
( ~ sQ14_spl
| ~ sQ27_spl
| ~ sQ36_spl
| product(e_3,e_3,e_4) ),
inference(resolution,[status(thm)],[f647,f319]) ).
fof(f657,plain,
( ~ sQ27_spl
| ~ sQ14_spl
| ~ sQ36_spl
| equalish(e_3,e_2) ),
inference(resolution,[status(thm)],[f652,f439]) ).
fof(f664,plain,
( ~ sQ27_spl
| ~ sQ14_spl
| ~ sQ36_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f657,f55]) ).
fof(f665,plain,
( ~ sQ27_spl
| ~ sQ14_spl
| ~ sQ36_spl ),
inference(contradiction_clause,[status(thm)],[f664]) ).
fof(f666,plain,
( ~ sQ36_spl
| ~ sQ24_spl
| product(e_1,e_1,e_3) ),
inference(resolution,[status(thm)],[f462,f211]) ).
fof(f667,plain,
( ~ sQ14_spl
| ~ sQ36_spl
| ~ sQ24_spl
| equalish(e_1,e_4) ),
inference(resolution,[status(thm)],[f666,f316]) ).
fof(f675,plain,
( ~ sQ14_spl
| ~ sQ36_spl
| ~ sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f667,f50]) ).
fof(f676,plain,
( ~ sQ14_spl
| ~ sQ36_spl
| ~ sQ24_spl ),
inference(contradiction_clause,[status(thm)],[f675]) ).
fof(f677,plain,
$false,
inference(sat_refutation,[status(thm)],[f110,f136,f153,f179,f192,f222,f248,f314,f338,f345,f375,f382,f389,f434,f436,f458,f482,f500,f510,f531,f555,f564,f574,f580,f588,f590,f599,f625,f634,f644,f646,f665,f676]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP126-2.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n001.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Sun Sep 20 20:05:13 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.46 % Drodi V4.1.1
% 0.26/0.62 % Refutation found
% 0.26/0.62 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.26/0.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.26/0.65 % Elapsed time: 0.187509 seconds
% 0.26/0.65 % CPU time: 1.233362 seconds
% 0.26/0.65 % Total memory used: 22.663 MB
% 0.26/0.65 % Net memory used: 21.886 MB
%------------------------------------------------------------------------------