%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP124-8.004 : 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 12:32:42 PM UTC 2026
% Result : Unsatisfiable 0.17s 0.51s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 84
% Syntax : Number of formulae : 402 ( 107 unt; 63 def)
% Number of atoms : 793 ( 0 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 798 ( 407 ~; 328 |; 0 &)
% ( 63 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 68 ( 67 usr; 64 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 176 ( 176 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f22,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
group_element(e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
~ equalish(e_1,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,axiom,
~ equalish(e_2,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [X,Y] :
( product1(X,Y,e_4)
| product1(X,Y,e_3)
| product1(X,Y,e_2)
| product1(X,Y,e_1)
| ~ group_element(Y)
| ~ group_element(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product1(X,Y,Z)
| ~ product1(X,Y,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,axiom,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product1(X,Z,Y)
| ~ product1(X,W,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,axiom,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product1(Z,Y,X)
| ~ product1(W,Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,axiom,
! [X] : product1(X,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,axiom,
! [X,Y] :
( product2(X,Y,e_4)
| product2(X,Y,e_3)
| product2(X,Y,e_2)
| product2(X,Y,e_1)
| ~ group_element(Y)
| ~ group_element(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,axiom,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product2(X,Y,Z)
| ~ product2(X,Y,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,axiom,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product2(X,Z,Y)
| ~ product2(X,W,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,axiom,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product2(Z,Y,X)
| ~ product2(W,Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,axiom,
! [X] : product2(X,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,negated_conjecture,
! [X,Y,Z1,Z2] :
( product2(Z2,Y,X)
| ~ product1(Z1,X,Z2)
| ~ product1(X,Y,Z1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f74,plain,
group_element(e_1),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f75,plain,
group_element(e_2),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f76,plain,
group_element(e_3),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f77,plain,
group_element(e_4),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f78,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f79,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f80,plain,
~ equalish(e_1,e_4),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f82,plain,
~ equalish(e_2,e_3),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f83,plain,
~ equalish(e_2,e_4),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f86,plain,
~ equalish(e_3,e_4),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f90,plain,
! [X0,X1] :
( product1(X0,X1,e_4)
| product1(X0,X1,e_3)
| product1(X0,X1,e_2)
| product1(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f91,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product1(X,Y,Z)
| ~ product1(X,Y,W) ) ),
inference(miniscoping,[status(thm)],[f39]) ).
fof(f92,plain,
! [X0,X1,X2,X3] :
( equalish(X2,X3)
| ~ product1(X0,X1,X3)
| ~ product1(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f93,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product1(X,Z,Y)
| ~ product1(X,W,Y) ) ),
inference(miniscoping,[status(thm)],[f40]) ).
fof(f94,plain,
! [X0,X1,X2,X3] :
( equalish(X1,X3)
| ~ product1(X0,X3,X2)
| ~ product1(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f93]) ).
fof(f95,plain,
! [W,Z] :
( equalish(W,Z)
| ! [Y,X] :
( ~ product1(Z,Y,X)
| ~ product1(W,Y,X) ) ),
inference(miniscoping,[status(thm)],[f41]) ).
fof(f96,plain,
! [X0,X1,X2,X3] :
( equalish(X0,X3)
| ~ product1(X3,X1,X2)
| ~ product1(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f97,plain,
! [X0] : product1(X0,X0,X0),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f98,plain,
! [X0,X1] :
( product2(X0,X1,e_4)
| product2(X0,X1,e_3)
| product2(X0,X1,e_2)
| product2(X0,X1,e_1)
| ~ group_element(X1)
| ~ group_element(X0) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f99,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product2(X,Y,Z)
| ~ product2(X,Y,W) ) ),
inference(miniscoping,[status(thm)],[f44]) ).
fof(f100,plain,
! [X0,X1,X2,X3] :
( equalish(X2,X3)
| ~ product2(X0,X1,X3)
| ~ product2(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f99]) ).
fof(f101,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product2(X,Z,Y)
| ~ product2(X,W,Y) ) ),
inference(miniscoping,[status(thm)],[f45]) ).
fof(f102,plain,
! [X0,X1,X2,X3] :
( equalish(X1,X3)
| ~ product2(X0,X3,X2)
| ~ product2(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f101]) ).
fof(f103,plain,
! [W,Z] :
( equalish(W,Z)
| ! [Y,X] :
( ~ product2(Z,Y,X)
| ~ product2(W,Y,X) ) ),
inference(miniscoping,[status(thm)],[f46]) ).
fof(f104,plain,
! [X0,X1,X2,X3] :
( equalish(X0,X3)
| ~ product2(X3,X1,X2)
| ~ product2(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f103]) ).
fof(f105,plain,
! [X0] : product2(X0,X0,X0),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f106,plain,
! [X,Y,Z2] :
( product2(Z2,Y,X)
| ! [Z1] :
( ~ product1(Z1,X,Z2)
| ~ product1(X,Y,Z1) ) ),
inference(miniscoping,[status(thm)],[f48]) ).
fof(f107,plain,
! [X0,X1,X2,X3] :
( product2(X3,X1,X0)
| ~ product1(X2,X0,X3)
| ~ product1(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f108,plain,
! [X0,X1] :
( product2(X0,X1,X0)
| ~ product1(X0,X1,X0) ),
inference(resolution,[status(thm)],[f97,f107]) ).
fof(f109,plain,
! [X0,X1] :
( ~ product2(e_2,X0,X1)
| ~ product2(e_1,X0,X1) ),
inference(resolution,[status(thm)],[f78,f104]) ).
fof(f110,plain,
! [X0,X1] :
( ~ product2(X0,e_2,X1)
| ~ product2(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f78,f102]) ).
fof(f111,plain,
! [X0,X1] :
( ~ product2(X0,X1,e_2)
| ~ product2(X0,X1,e_1) ),
inference(resolution,[status(thm)],[f78,f100]) ).
fof(f112,plain,
! [X0,X1] :
( ~ product1(e_2,X0,X1)
| ~ product1(e_1,X0,X1) ),
inference(resolution,[status(thm)],[f78,f96]) ).
fof(f113,plain,
! [X0,X1] :
( ~ product1(X0,e_2,X1)
| ~ product1(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f78,f94]) ).
fof(f114,plain,
! [X0,X1] :
( ~ product1(X0,X1,e_2)
| ~ product1(X0,X1,e_1) ),
inference(resolution,[status(thm)],[f78,f92]) ).
fof(f115,plain,
~ product2(e_1,e_2,e_2),
inference(resolution,[status(thm)],[f109,f105]) ).
fof(f119,plain,
~ product2(e_2,e_1,e_2),
inference(resolution,[status(thm)],[f110,f105]) ).
fof(f122,plain,
~ product1(e_2,e_1,e_2),
inference(resolution,[status(thm)],[f119,f108]) ).
fof(f124,plain,
~ product2(e_2,e_2,e_1),
inference(resolution,[status(thm)],[f111,f105]) ).
fof(f127,plain,
~ product1(e_1,e_2,e_2),
inference(resolution,[status(thm)],[f112,f97]) ).
fof(f128,plain,
! [X0,X1] :
( ~ product2(e_3,X0,X1)
| ~ product2(e_1,X0,X1) ),
inference(resolution,[status(thm)],[f79,f104]) ).
fof(f129,plain,
! [X0,X1] :
( ~ product2(X0,e_3,X1)
| ~ product2(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f79,f102]) ).
fof(f130,plain,
! [X0,X1] :
( ~ product2(X0,X1,e_3)
| ~ product2(X0,X1,e_1) ),
inference(resolution,[status(thm)],[f79,f100]) ).
fof(f131,plain,
! [X0,X1] :
( ~ product1(e_3,X0,X1)
| ~ product1(e_1,X0,X1) ),
inference(resolution,[status(thm)],[f79,f96]) ).
fof(f132,plain,
! [X0,X1] :
( ~ product1(X0,e_3,X1)
| ~ product1(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f79,f94]) ).
fof(f133,plain,
! [X0,X1] :
( ~ product1(X0,X1,e_3)
| ~ product1(X0,X1,e_1) ),
inference(resolution,[status(thm)],[f79,f92]) ).
fof(f134,plain,
! [X0,X1] :
( ~ product2(e_4,X0,X1)
| ~ product2(e_1,X0,X1) ),
inference(resolution,[status(thm)],[f80,f104]) ).
fof(f135,plain,
! [X0,X1] :
( ~ product2(X0,e_4,X1)
| ~ product2(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f80,f102]) ).
fof(f136,plain,
! [X0,X1] :
( ~ product2(X0,X1,e_4)
| ~ product2(X0,X1,e_1) ),
inference(resolution,[status(thm)],[f80,f100]) ).
fof(f137,plain,
! [X0,X1] :
( ~ product1(e_4,X0,X1)
| ~ product1(e_1,X0,X1) ),
inference(resolution,[status(thm)],[f80,f96]) ).
fof(f139,plain,
! [X0,X1] :
( ~ product1(X0,X1,e_4)
| ~ product1(X0,X1,e_1) ),
inference(resolution,[status(thm)],[f80,f92]) ).
fof(f146,plain,
! [X0,X1] :
( ~ product2(e_3,X0,X1)
| ~ product2(e_2,X0,X1) ),
inference(resolution,[status(thm)],[f82,f104]) ).
fof(f147,plain,
! [X0,X1] :
( ~ product2(X0,e_3,X1)
| ~ product2(X0,e_2,X1) ),
inference(resolution,[status(thm)],[f82,f102]) ).
fof(f148,plain,
! [X0,X1] :
( ~ product2(X0,X1,e_3)
| ~ product2(X0,X1,e_2) ),
inference(resolution,[status(thm)],[f82,f100]) ).
fof(f149,plain,
! [X0,X1] :
( ~ product1(e_3,X0,X1)
| ~ product1(e_2,X0,X1) ),
inference(resolution,[status(thm)],[f82,f96]) ).
fof(f150,plain,
! [X0,X1] :
( ~ product1(X0,e_3,X1)
| ~ product1(X0,e_2,X1) ),
inference(resolution,[status(thm)],[f82,f94]) ).
fof(f151,plain,
! [X0,X1] :
( ~ product1(X0,X1,e_3)
| ~ product1(X0,X1,e_2) ),
inference(resolution,[status(thm)],[f82,f92]) ).
fof(f152,plain,
! [X0,X1] :
( ~ product2(e_4,X0,X1)
| ~ product2(e_2,X0,X1) ),
inference(resolution,[status(thm)],[f83,f104]) ).
fof(f153,plain,
! [X0,X1] :
( ~ product2(X0,e_4,X1)
| ~ product2(X0,e_2,X1) ),
inference(resolution,[status(thm)],[f83,f102]) ).
fof(f154,plain,
! [X0,X1] :
( ~ product2(X0,X1,e_4)
| ~ product2(X0,X1,e_2) ),
inference(resolution,[status(thm)],[f83,f100]) ).
fof(f155,plain,
! [X0,X1] :
( ~ product1(e_4,X0,X1)
| ~ product1(e_2,X0,X1) ),
inference(resolution,[status(thm)],[f83,f96]) ).
fof(f156,plain,
! [X0,X1] :
( ~ product1(X0,e_4,X1)
| ~ product1(X0,e_2,X1) ),
inference(resolution,[status(thm)],[f83,f94]) ).
fof(f157,plain,
! [X0,X1] :
( ~ product1(X0,X1,e_4)
| ~ product1(X0,X1,e_2) ),
inference(resolution,[status(thm)],[f83,f92]) ).
fof(f170,plain,
! [X0,X1] :
( ~ product2(e_4,X0,X1)
| ~ product2(e_3,X0,X1) ),
inference(resolution,[status(thm)],[f86,f104]) ).
fof(f171,plain,
! [X0,X1] :
( ~ product2(X0,e_4,X1)
| ~ product2(X0,e_3,X1) ),
inference(resolution,[status(thm)],[f86,f102]) ).
fof(f172,plain,
! [X0,X1] :
( ~ product2(X0,X1,e_4)
| ~ product2(X0,X1,e_3) ),
inference(resolution,[status(thm)],[f86,f100]) ).
fof(f173,plain,
! [X0,X1] :
( ~ product1(e_4,X0,X1)
| ~ product1(e_3,X0,X1) ),
inference(resolution,[status(thm)],[f86,f96]) ).
fof(f174,plain,
! [X0,X1] :
( ~ product1(X0,e_4,X1)
| ~ product1(X0,e_3,X1) ),
inference(resolution,[status(thm)],[f86,f94]) ).
fof(f175,plain,
! [X0,X1] :
( ~ product1(X0,X1,e_4)
| ~ product1(X0,X1,e_3) ),
inference(resolution,[status(thm)],[f86,f92]) ).
fof(f191,plain,
~ product1(e_2,e_2,e_1),
inference(resolution,[status(thm)],[f114,f97]) ).
fof(f192,plain,
~ product2(e_1,e_3,e_3),
inference(resolution,[status(thm)],[f128,f105]) ).
fof(f195,plain,
~ product2(e_3,e_1,e_3),
inference(resolution,[status(thm)],[f129,f105]) ).
fof(f198,plain,
~ product2(e_3,e_3,e_1),
inference(resolution,[status(thm)],[f130,f105]) ).
fof(f214,plain,
~ product1(e_3,e_1,e_3),
inference(resolution,[status(thm)],[f195,f108]) ).
fof(f217,plain,
~ product1(e_1,e_3,e_3),
inference(resolution,[status(thm)],[f131,f97]) ).
fof(f222,plain,
~ product1(e_3,e_3,e_1),
inference(resolution,[status(thm)],[f133,f97]) ).
fof(f223,plain,
~ product2(e_1,e_4,e_4),
inference(resolution,[status(thm)],[f134,f105]) ).
fof(f227,plain,
~ product2(e_4,e_1,e_4),
inference(resolution,[status(thm)],[f135,f105]) ).
fof(f228,plain,
! [X0] :
( ~ product1(X0,e_4,X0)
| ~ product2(X0,e_1,X0) ),
inference(resolution,[status(thm)],[f135,f108]) ).
fof(f230,plain,
~ product2(e_4,e_4,e_1),
inference(resolution,[status(thm)],[f136,f105]) ).
fof(f233,plain,
~ product1(e_1,e_4,e_4),
inference(resolution,[status(thm)],[f137,f97]) ).
fof(f234,plain,
~ product1(e_4,e_1,e_4),
inference(resolution,[status(thm)],[f227,f108]) ).
fof(f238,plain,
~ product1(e_4,e_4,e_1),
inference(resolution,[status(thm)],[f139,f97]) ).
fof(f239,plain,
! [X0] :
( product1(X0,e_4,e_4)
| product1(X0,e_4,e_3)
| product1(X0,e_4,e_2)
| product1(X0,e_4,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f90,f77]) ).
fof(f240,plain,
! [X0] :
( product1(X0,e_3,e_4)
| product1(X0,e_3,e_3)
| product1(X0,e_3,e_2)
| product1(X0,e_3,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f90,f76]) ).
fof(f241,plain,
! [X0] :
( product1(X0,e_2,e_4)
| product1(X0,e_2,e_3)
| product1(X0,e_2,e_2)
| product1(X0,e_2,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f90,f75]) ).
fof(f243,plain,
! [X0] :
( product2(X0,e_4,e_4)
| product2(X0,e_4,e_3)
| product2(X0,e_4,e_2)
| product2(X0,e_4,e_1)
| ~ group_element(X0) ),
inference(resolution,[status(thm)],[f98,f77]) ).
fof(f247,plain,
~ product2(e_2,e_3,e_3),
inference(resolution,[status(thm)],[f146,f105]) ).
fof(f254,plain,
~ product2(e_3,e_2,e_3),
inference(resolution,[status(thm)],[f147,f105]) ).
fof(f255,plain,
! [X0] :
( ~ product1(X0,e_3,X0)
| ~ product2(X0,e_2,X0) ),
inference(resolution,[status(thm)],[f147,f108]) ).
fof(f257,plain,
~ product1(e_3,e_2,e_3),
inference(resolution,[status(thm)],[f254,f108]) ).
fof(f259,plain,
~ product2(e_3,e_3,e_2),
inference(resolution,[status(thm)],[f148,f105]) ).
fof(f262,plain,
! [X0] :
( ~ product1(X0,e_2,e_3)
| ~ product1(e_2,e_3,X0) ),
inference(resolution,[status(thm)],[f259,f107]) ).
fof(f263,plain,
~ product1(e_2,e_3,e_3),
inference(resolution,[status(thm)],[f149,f97]) ).
fof(f265,plain,
~ product1(e_3,e_3,e_2),
inference(resolution,[status(thm)],[f151,f97]) ).
fof(f266,plain,
~ product2(e_2,e_4,e_4),
inference(resolution,[status(thm)],[f152,f105]) ).
fof(f270,plain,
~ product2(e_4,e_2,e_4),
inference(resolution,[status(thm)],[f153,f105]) ).
fof(f273,plain,
~ product1(e_4,e_2,e_4),
inference(resolution,[status(thm)],[f270,f108]) ).
fof(f275,plain,
~ product2(e_4,e_4,e_2),
inference(resolution,[status(thm)],[f154,f105]) ).
fof(f278,plain,
~ product1(e_2,e_4,e_4),
inference(resolution,[status(thm)],[f155,f97]) ).
fof(f280,plain,
~ product1(e_4,e_4,e_2),
inference(resolution,[status(thm)],[f157,f97]) ).
fof(f286,plain,
~ product2(e_3,e_4,e_4),
inference(resolution,[status(thm)],[f170,f105]) ).
fof(f291,plain,
! [X0] :
( ~ product1(X0,e_4,X0)
| ~ product2(X0,e_3,X0) ),
inference(resolution,[status(thm)],[f171,f108]) ).
fof(f293,plain,
~ product2(e_4,e_4,e_3),
inference(resolution,[status(thm)],[f172,f105]) ).
fof(f296,plain,
~ product1(e_3,e_4,e_4),
inference(resolution,[status(thm)],[f173,f97]) ).
fof(f297,plain,
~ product2(e_4,e_3,e_4),
inference(resolution,[status(thm)],[f291,f97]) ).
fof(f298,plain,
~ product1(e_4,e_3,e_4),
inference(resolution,[status(thm)],[f297,f108]) ).
fof(f303,plain,
~ product1(e_4,e_4,e_3),
inference(resolution,[status(thm)],[f175,f97]) ).
fof(f338,plain,
( product1(e_4,e_4,e_4)
| product1(e_4,e_4,e_3)
| product1(e_4,e_4,e_2)
| product1(e_4,e_4,e_1) ),
inference(resolution,[status(thm)],[f239,f77]) ).
fof(f341,plain,
( product1(e_1,e_4,e_4)
| product1(e_1,e_4,e_3)
| product1(e_1,e_4,e_2)
| product1(e_1,e_4,e_1) ),
inference(resolution,[status(thm)],[f239,f74]) ).
fof(f342,definition,
( sQ7_spl
<=> product1(e_4,e_4,e_1) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f343,plain,
( ~ sQ7_spl
| product1(e_4,e_4,e_1) ),
inference(component_clause,[status(thm)],[f342]) ).
fof(f345,definition,
( sQ8_spl
<=> product1(e_4,e_4,e_2) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f346,plain,
( ~ sQ8_spl
| product1(e_4,e_4,e_2) ),
inference(component_clause,[status(thm)],[f345]) ).
fof(f348,definition,
( sQ9_spl
<=> product1(e_4,e_4,e_3) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f349,plain,
( ~ sQ9_spl
| product1(e_4,e_4,e_3) ),
inference(component_clause,[status(thm)],[f348]) ).
fof(f351,definition,
( sQ10_spl
<=> product1(e_4,e_4,e_4) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f354,plain,
( sQ10_spl
| sQ9_spl
| sQ8_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f338,f342,f345,f348,f351]) ).
fof(f361,definition,
( sQ13_spl
<=> product1(e_3,e_4,e_3) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f362,plain,
( ~ sQ13_spl
| product1(e_3,e_4,e_3) ),
inference(component_clause,[status(thm)],[f361]) ).
fof(f364,definition,
( sQ14_spl
<=> product1(e_3,e_4,e_4) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f365,plain,
( ~ sQ14_spl
| product1(e_3,e_4,e_4) ),
inference(component_clause,[status(thm)],[f364]) ).
fof(f377,definition,
( sQ18_spl
<=> product1(e_2,e_4,e_4) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f378,plain,
( ~ sQ18_spl
| product1(e_2,e_4,e_4) ),
inference(component_clause,[status(thm)],[f377]) ).
fof(f381,definition,
( sQ19_spl
<=> product1(e_1,e_4,e_1) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f382,plain,
( ~ sQ19_spl
| product1(e_1,e_4,e_1) ),
inference(component_clause,[status(thm)],[f381]) ).
fof(f384,definition,
( sQ20_spl
<=> product1(e_1,e_4,e_2) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f385,plain,
( ~ sQ20_spl
| product1(e_1,e_4,e_2) ),
inference(component_clause,[status(thm)],[f384]) ).
fof(f387,definition,
( sQ21_spl
<=> product1(e_1,e_4,e_3) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f388,plain,
( ~ sQ21_spl
| product1(e_1,e_4,e_3) ),
inference(component_clause,[status(thm)],[f387]) ).
fof(f390,definition,
( sQ22_spl
<=> product1(e_1,e_4,e_4) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f391,plain,
( ~ sQ22_spl
| product1(e_1,e_4,e_4) ),
inference(component_clause,[status(thm)],[f390]) ).
fof(f393,plain,
( sQ22_spl
| sQ21_spl
| sQ20_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f341,f381,f384,f387,f390]) ).
fof(f394,plain,
( ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f391,f233]) ).
fof(f395,plain,
~ sQ22_spl,
inference(contradiction_clause,[status(thm)],[f394]) ).
fof(f396,plain,
( ~ sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f378,f278]) ).
fof(f397,plain,
~ sQ18_spl,
inference(contradiction_clause,[status(thm)],[f396]) ).
fof(f398,plain,
( ~ sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f365,f296]) ).
fof(f399,plain,
~ sQ14_spl,
inference(contradiction_clause,[status(thm)],[f398]) ).
fof(f400,plain,
( ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f349,f303]) ).
fof(f401,plain,
~ sQ9_spl,
inference(contradiction_clause,[status(thm)],[f400]) ).
fof(f402,plain,
( ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f346,f280]) ).
fof(f403,plain,
~ sQ8_spl,
inference(contradiction_clause,[status(thm)],[f402]) ).
fof(f404,plain,
( ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f343,f238]) ).
fof(f405,plain,
~ sQ7_spl,
inference(contradiction_clause,[status(thm)],[f404]) ).
fof(f406,plain,
( product1(e_4,e_3,e_4)
| product1(e_4,e_3,e_3)
| product1(e_4,e_3,e_2)
| product1(e_4,e_3,e_1) ),
inference(resolution,[status(thm)],[f240,f77]) ).
fof(f408,plain,
( product1(e_2,e_3,e_4)
| product1(e_2,e_3,e_3)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[f240,f75]) ).
fof(f409,plain,
( product1(e_1,e_3,e_4)
| product1(e_1,e_3,e_3)
| product1(e_1,e_3,e_2)
| product1(e_1,e_3,e_1) ),
inference(resolution,[status(thm)],[f240,f74]) ).
fof(f410,definition,
( sQ23_spl
<=> product1(e_4,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f411,plain,
( ~ sQ23_spl
| product1(e_4,e_3,e_1) ),
inference(component_clause,[status(thm)],[f410]) ).
fof(f413,definition,
( sQ24_spl
<=> product1(e_4,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f414,plain,
( ~ sQ24_spl
| product1(e_4,e_3,e_2) ),
inference(component_clause,[status(thm)],[f413]) ).
fof(f416,definition,
( sQ25_spl
<=> product1(e_4,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f417,plain,
( ~ sQ25_spl
| product1(e_4,e_3,e_3) ),
inference(component_clause,[status(thm)],[f416]) ).
fof(f419,definition,
( sQ26_spl
<=> product1(e_4,e_3,e_4) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f420,plain,
( ~ sQ26_spl
| product1(e_4,e_3,e_4) ),
inference(component_clause,[status(thm)],[f419]) ).
fof(f422,plain,
( sQ26_spl
| sQ25_spl
| sQ24_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f406,f410,f413,f416,f419]) ).
fof(f423,definition,
( sQ27_spl
<=> product1(e_3,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f424,plain,
( ~ sQ27_spl
| product1(e_3,e_3,e_1) ),
inference(component_clause,[status(thm)],[f423]) ).
fof(f426,definition,
( sQ28_spl
<=> product1(e_3,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f427,plain,
( ~ sQ28_spl
| product1(e_3,e_3,e_2) ),
inference(component_clause,[status(thm)],[f426]) ).
fof(f436,definition,
( sQ31_spl
<=> product1(e_2,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f437,plain,
( ~ sQ31_spl
| product1(e_2,e_3,e_1) ),
inference(component_clause,[status(thm)],[f436]) ).
fof(f439,definition,
( sQ32_spl
<=> product1(e_2,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f440,plain,
( ~ sQ32_spl
| product1(e_2,e_3,e_2) ),
inference(component_clause,[status(thm)],[f439]) ).
fof(f442,definition,
( sQ33_spl
<=> product1(e_2,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f443,plain,
( ~ sQ33_spl
| product1(e_2,e_3,e_3) ),
inference(component_clause,[status(thm)],[f442]) ).
fof(f445,definition,
( sQ34_spl
<=> product1(e_2,e_3,e_4) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f446,plain,
( ~ sQ34_spl
| product1(e_2,e_3,e_4) ),
inference(component_clause,[status(thm)],[f445]) ).
fof(f448,plain,
( sQ34_spl
| sQ33_spl
| sQ32_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f408,f436,f439,f442,f445]) ).
fof(f449,definition,
( sQ35_spl
<=> product1(e_1,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f450,plain,
( ~ sQ35_spl
| product1(e_1,e_3,e_1) ),
inference(component_clause,[status(thm)],[f449]) ).
fof(f452,definition,
( sQ36_spl
<=> product1(e_1,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f453,plain,
( ~ sQ36_spl
| product1(e_1,e_3,e_2) ),
inference(component_clause,[status(thm)],[f452]) ).
fof(f455,definition,
( sQ37_spl
<=> product1(e_1,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f456,plain,
( ~ sQ37_spl
| product1(e_1,e_3,e_3) ),
inference(component_clause,[status(thm)],[f455]) ).
fof(f458,definition,
( sQ38_spl
<=> product1(e_1,e_3,e_4) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f459,plain,
( ~ sQ38_spl
| product1(e_1,e_3,e_4) ),
inference(component_clause,[status(thm)],[f458]) ).
fof(f461,plain,
( sQ38_spl
| sQ37_spl
| sQ36_spl
| sQ35_spl ),
inference(split_clause,[status(thm)],[f409,f449,f452,f455,f458]) ).
fof(f462,plain,
( ~ sQ37_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f456,f217]) ).
fof(f463,plain,
~ sQ37_spl,
inference(contradiction_clause,[status(thm)],[f462]) ).
fof(f464,plain,
( ~ sQ33_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f443,f263]) ).
fof(f465,plain,
~ sQ33_spl,
inference(contradiction_clause,[status(thm)],[f464]) ).
fof(f466,plain,
( ~ sQ28_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f427,f265]) ).
fof(f467,plain,
~ sQ28_spl,
inference(contradiction_clause,[status(thm)],[f466]) ).
fof(f468,plain,
( ~ sQ27_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f424,f222]) ).
fof(f469,plain,
~ sQ27_spl,
inference(contradiction_clause,[status(thm)],[f468]) ).
fof(f470,plain,
( ~ sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f420,f298]) ).
fof(f471,plain,
~ sQ26_spl,
inference(contradiction_clause,[status(thm)],[f470]) ).
fof(f482,plain,
( ~ sQ21_spl
| ~ product1(e_1,e_2,e_3) ),
inference(resolution,[status(thm)],[f388,f156]) ).
fof(f491,plain,
( ~ sQ20_spl
| ~ product1(e_1,e_3,e_2) ),
inference(resolution,[status(thm)],[f385,f174]) ).
fof(f504,plain,
( ~ sQ19_spl
| ~ product2(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f382,f228]) ).
fof(f507,plain,
( ~ sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f504,f105]) ).
fof(f508,plain,
~ sQ19_spl,
inference(contradiction_clause,[status(thm)],[f507]) ).
fof(f548,plain,
( ~ sQ13_spl
| ~ product1(e_3,e_3,e_3) ),
inference(resolution,[status(thm)],[f362,f174]) ).
fof(f558,plain,
( ~ sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f548,f97]) ).
fof(f559,plain,
~ sQ13_spl,
inference(contradiction_clause,[status(thm)],[f558]) ).
fof(f584,plain,
( product1(e_4,e_2,e_4)
| product1(e_4,e_2,e_3)
| product1(e_4,e_2,e_2)
| product1(e_4,e_2,e_1) ),
inference(resolution,[status(thm)],[f241,f77]) ).
fof(f585,plain,
( product1(e_3,e_2,e_4)
| product1(e_3,e_2,e_3)
| product1(e_3,e_2,e_2)
| product1(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[f241,f76]) ).
fof(f586,plain,
( product1(e_2,e_2,e_4)
| product1(e_2,e_2,e_3)
| product1(e_2,e_2,e_2)
| product1(e_2,e_2,e_1) ),
inference(resolution,[status(thm)],[f241,f75]) ).
fof(f587,plain,
( product1(e_1,e_2,e_4)
| product1(e_1,e_2,e_3)
| product1(e_1,e_2,e_2)
| product1(e_1,e_2,e_1) ),
inference(resolution,[status(thm)],[f241,f74]) ).
fof(f588,definition,
( sQ39_spl
<=> product1(e_4,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f589,plain,
( ~ sQ39_spl
| product1(e_4,e_2,e_1) ),
inference(component_clause,[status(thm)],[f588]) ).
fof(f591,definition,
( sQ40_spl
<=> product1(e_4,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f592,plain,
( ~ sQ40_spl
| product1(e_4,e_2,e_2) ),
inference(component_clause,[status(thm)],[f591]) ).
fof(f594,definition,
( sQ41_spl
<=> product1(e_4,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f595,plain,
( ~ sQ41_spl
| product1(e_4,e_2,e_3) ),
inference(component_clause,[status(thm)],[f594]) ).
fof(f597,definition,
( sQ42_spl
<=> product1(e_4,e_2,e_4) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f598,plain,
( ~ sQ42_spl
| product1(e_4,e_2,e_4) ),
inference(component_clause,[status(thm)],[f597]) ).
fof(f600,plain,
( sQ42_spl
| sQ41_spl
| sQ40_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f584,f588,f591,f594,f597]) ).
fof(f601,definition,
( sQ43_spl
<=> product1(e_3,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f602,plain,
( ~ sQ43_spl
| product1(e_3,e_2,e_1) ),
inference(component_clause,[status(thm)],[f601]) ).
fof(f604,definition,
( sQ44_spl
<=> product1(e_3,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f605,plain,
( ~ sQ44_spl
| product1(e_3,e_2,e_2) ),
inference(component_clause,[status(thm)],[f604]) ).
fof(f607,definition,
( sQ45_spl
<=> product1(e_3,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f608,plain,
( ~ sQ45_spl
| product1(e_3,e_2,e_3) ),
inference(component_clause,[status(thm)],[f607]) ).
fof(f610,definition,
( sQ46_spl
<=> product1(e_3,e_2,e_4) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f611,plain,
( ~ sQ46_spl
| product1(e_3,e_2,e_4) ),
inference(component_clause,[status(thm)],[f610]) ).
fof(f613,plain,
( sQ46_spl
| sQ45_spl
| sQ44_spl
| sQ43_spl ),
inference(split_clause,[status(thm)],[f585,f601,f604,f607,f610]) ).
fof(f614,definition,
( sQ47_spl
<=> product1(e_2,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f615,plain,
( ~ sQ47_spl
| product1(e_2,e_2,e_1) ),
inference(component_clause,[status(thm)],[f614]) ).
fof(f617,definition,
( sQ48_spl
<=> product1(e_2,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f620,definition,
( sQ49_spl
<=> product1(e_2,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f621,plain,
( ~ sQ49_spl
| product1(e_2,e_2,e_3) ),
inference(component_clause,[status(thm)],[f620]) ).
fof(f623,definition,
( sQ50_spl
<=> product1(e_2,e_2,e_4) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f624,plain,
( ~ sQ50_spl
| product1(e_2,e_2,e_4) ),
inference(component_clause,[status(thm)],[f623]) ).
fof(f626,plain,
( sQ50_spl
| sQ49_spl
| sQ48_spl
| sQ47_spl ),
inference(split_clause,[status(thm)],[f586,f614,f617,f620,f623]) ).
fof(f627,definition,
( sQ51_spl
<=> product1(e_1,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f628,plain,
( ~ sQ51_spl
| product1(e_1,e_2,e_1) ),
inference(component_clause,[status(thm)],[f627]) ).
fof(f630,definition,
( sQ52_spl
<=> product1(e_1,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f631,plain,
( ~ sQ52_spl
| product1(e_1,e_2,e_2) ),
inference(component_clause,[status(thm)],[f630]) ).
fof(f633,definition,
( sQ53_spl
<=> product1(e_1,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f634,plain,
( ~ sQ53_spl
| product1(e_1,e_2,e_3) ),
inference(component_clause,[status(thm)],[f633]) ).
fof(f636,definition,
( sQ54_spl
<=> product1(e_1,e_2,e_4) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f637,plain,
( ~ sQ54_spl
| product1(e_1,e_2,e_4) ),
inference(component_clause,[status(thm)],[f636]) ).
fof(f639,plain,
( sQ54_spl
| sQ53_spl
| sQ52_spl
| sQ51_spl ),
inference(split_clause,[status(thm)],[f587,f627,f630,f633,f636]) ).
fof(f640,plain,
( ~ sQ52_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f631,f127]) ).
fof(f641,plain,
~ sQ52_spl,
inference(contradiction_clause,[status(thm)],[f640]) ).
fof(f642,plain,
( ~ sQ47_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f615,f191]) ).
fof(f643,plain,
~ sQ47_spl,
inference(contradiction_clause,[status(thm)],[f642]) ).
fof(f644,plain,
( ~ sQ45_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f608,f257]) ).
fof(f645,plain,
~ sQ45_spl,
inference(contradiction_clause,[status(thm)],[f644]) ).
fof(f646,plain,
( ~ sQ42_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f598,f273]) ).
fof(f647,plain,
~ sQ42_spl,
inference(contradiction_clause,[status(thm)],[f646]) ).
fof(f661,definition,
( sQ58_spl
<=> product1(e_4,e_1,e_4) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f662,plain,
( ~ sQ58_spl
| product1(e_4,e_1,e_4) ),
inference(component_clause,[status(thm)],[f661]) ).
fof(f671,definition,
( sQ61_spl
<=> product1(e_3,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f672,plain,
( ~ sQ61_spl
| product1(e_3,e_1,e_3) ),
inference(component_clause,[status(thm)],[f671]) ).
fof(f681,definition,
( sQ64_spl
<=> product1(e_2,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f682,plain,
( ~ sQ64_spl
| product1(e_2,e_1,e_2) ),
inference(component_clause,[status(thm)],[f681]) ).
fof(f704,plain,
( ~ sQ64_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f682,f122]) ).
fof(f705,plain,
~ sQ64_spl,
inference(contradiction_clause,[status(thm)],[f704]) ).
fof(f706,plain,
( ~ sQ61_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f672,f214]) ).
fof(f707,plain,
~ sQ61_spl,
inference(contradiction_clause,[status(thm)],[f706]) ).
fof(f708,plain,
( ~ sQ58_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f662,f234]) ).
fof(f709,plain,
~ sQ58_spl,
inference(contradiction_clause,[status(thm)],[f708]) ).
fof(f710,plain,
( product2(e_4,e_4,e_4)
| product2(e_4,e_4,e_3)
| product2(e_4,e_4,e_2)
| product2(e_4,e_4,e_1) ),
inference(resolution,[status(thm)],[f243,f77]) ).
fof(f714,definition,
( sQ71_spl
<=> product2(e_4,e_4,e_1) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f715,plain,
( ~ sQ71_spl
| product2(e_4,e_4,e_1) ),
inference(component_clause,[status(thm)],[f714]) ).
fof(f717,definition,
( sQ72_spl
<=> product2(e_4,e_4,e_2) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f718,plain,
( ~ sQ72_spl
| product2(e_4,e_4,e_2) ),
inference(component_clause,[status(thm)],[f717]) ).
fof(f720,definition,
( sQ73_spl
<=> product2(e_4,e_4,e_3) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f721,plain,
( ~ sQ73_spl
| product2(e_4,e_4,e_3) ),
inference(component_clause,[status(thm)],[f720]) ).
fof(f723,definition,
( sQ74_spl
<=> product2(e_4,e_4,e_4) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f726,plain,
( sQ74_spl
| sQ73_spl
| sQ72_spl
| sQ71_spl ),
inference(split_clause,[status(thm)],[f710,f714,f717,f720,f723]) ).
fof(f736,definition,
( sQ78_spl
<=> product2(e_3,e_4,e_4) ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f737,plain,
( ~ sQ78_spl
| product2(e_3,e_4,e_4) ),
inference(component_clause,[status(thm)],[f736]) ).
fof(f749,definition,
( sQ82_spl
<=> product2(e_2,e_4,e_4) ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f750,plain,
( ~ sQ82_spl
| product2(e_2,e_4,e_4) ),
inference(component_clause,[status(thm)],[f749]) ).
fof(f762,definition,
( sQ86_spl
<=> product2(e_1,e_4,e_4) ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f763,plain,
( ~ sQ86_spl
| product2(e_1,e_4,e_4) ),
inference(component_clause,[status(thm)],[f762]) ).
fof(f766,plain,
( ~ sQ86_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f763,f223]) ).
fof(f767,plain,
~ sQ86_spl,
inference(contradiction_clause,[status(thm)],[f766]) ).
fof(f768,plain,
( ~ sQ82_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f750,f266]) ).
fof(f769,plain,
~ sQ82_spl,
inference(contradiction_clause,[status(thm)],[f768]) ).
fof(f770,plain,
( ~ sQ78_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f737,f286]) ).
fof(f771,plain,
~ sQ78_spl,
inference(contradiction_clause,[status(thm)],[f770]) ).
fof(f772,plain,
( ~ sQ73_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f721,f293]) ).
fof(f773,plain,
~ sQ73_spl,
inference(contradiction_clause,[status(thm)],[f772]) ).
fof(f774,plain,
( ~ sQ72_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f718,f275]) ).
fof(f775,plain,
~ sQ72_spl,
inference(contradiction_clause,[status(thm)],[f774]) ).
fof(f776,plain,
( ~ sQ71_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f715,f230]) ).
fof(f777,plain,
~ sQ71_spl,
inference(contradiction_clause,[status(thm)],[f776]) ).
fof(f786,plain,
( ~ sQ38_spl
| ~ product1(e_1,e_2,e_4) ),
inference(resolution,[status(thm)],[f459,f150]) ).
fof(f793,plain,
( ~ sQ36_spl
| ~ sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f453,f491]) ).
fof(f794,plain,
( ~ sQ36_spl
| ~ sQ20_spl ),
inference(contradiction_clause,[status(thm)],[f793]) ).
fof(f802,plain,
( ~ sQ35_spl
| ~ product1(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f450,f132]) ).
fof(f805,plain,
( ~ sQ35_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f802,f97]) ).
fof(f806,plain,
~ sQ35_spl,
inference(contradiction_clause,[status(thm)],[f805]) ).
fof(f807,plain,
( ~ sQ34_spl
| ~ product1(e_4,e_2,e_3) ),
inference(resolution,[status(thm)],[f446,f262]) ).
fof(f809,plain,
( ~ sQ34_spl
| ~ product1(e_1,e_3,e_4) ),
inference(resolution,[status(thm)],[f446,f112]) ).
fof(f820,plain,
( ~ sQ34_spl
| ~ sQ38_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f809,f459]) ).
fof(f821,plain,
( ~ sQ34_spl
| ~ sQ38_spl ),
inference(contradiction_clause,[status(thm)],[f820]) ).
fof(f829,plain,
( ~ sQ32_spl
| ~ product2(e_2,e_2,e_2) ),
inference(resolution,[status(thm)],[f440,f255]) ).
fof(f836,plain,
( ~ sQ32_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f829,f105]) ).
fof(f837,plain,
~ sQ32_spl,
inference(contradiction_clause,[status(thm)],[f836]) ).
fof(f838,plain,
( ~ sQ31_spl
| ~ product1(e_1,e_2,e_3) ),
inference(resolution,[status(thm)],[f437,f262]) ).
fof(f864,plain,
( ~ sQ25_spl
| ~ product1(e_3,e_3,e_3) ),
inference(resolution,[status(thm)],[f417,f173]) ).
fof(f877,plain,
( ~ sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f864,f97]) ).
fof(f878,plain,
~ sQ25_spl,
inference(contradiction_clause,[status(thm)],[f877]) ).
fof(f882,plain,
( ~ sQ24_spl
| ~ product1(e_1,e_3,e_2) ),
inference(resolution,[status(thm)],[f414,f137]) ).
fof(f905,definition,
( sQ90_spl
<=> product2(e_4,e_3,e_4) ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f906,plain,
( ~ sQ90_spl
| product2(e_4,e_3,e_4) ),
inference(component_clause,[status(thm)],[f905]) ).
fof(f909,definition,
( sQ91_spl
<=> product2(e_3,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ91_spl])],[split_symbol_definition]) ).
fof(f910,plain,
( ~ sQ91_spl
| product2(e_3,e_3,e_1) ),
inference(component_clause,[status(thm)],[f909]) ).
fof(f912,definition,
( sQ92_spl
<=> product2(e_3,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f913,plain,
( ~ sQ92_spl
| product2(e_3,e_3,e_2) ),
inference(component_clause,[status(thm)],[f912]) ).
fof(f928,definition,
( sQ97_spl
<=> product2(e_2,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ97_spl])],[split_symbol_definition]) ).
fof(f929,plain,
( ~ sQ97_spl
| product2(e_2,e_3,e_3) ),
inference(component_clause,[status(thm)],[f928]) ).
fof(f941,definition,
( sQ101_spl
<=> product2(e_1,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ101_spl])],[split_symbol_definition]) ).
fof(f942,plain,
( ~ sQ101_spl
| product2(e_1,e_3,e_3) ),
inference(component_clause,[status(thm)],[f941]) ).
fof(f948,plain,
( ~ sQ101_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f942,f192]) ).
fof(f949,plain,
~ sQ101_spl,
inference(contradiction_clause,[status(thm)],[f948]) ).
fof(f950,plain,
( ~ sQ97_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f929,f247]) ).
fof(f951,plain,
~ sQ97_spl,
inference(contradiction_clause,[status(thm)],[f950]) ).
fof(f952,plain,
( ~ sQ92_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f913,f259]) ).
fof(f953,plain,
~ sQ92_spl,
inference(contradiction_clause,[status(thm)],[f952]) ).
fof(f954,plain,
( ~ sQ91_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f910,f198]) ).
fof(f955,plain,
~ sQ91_spl,
inference(contradiction_clause,[status(thm)],[f954]) ).
fof(f956,plain,
( ~ sQ90_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f906,f297]) ).
fof(f957,plain,
~ sQ90_spl,
inference(contradiction_clause,[status(thm)],[f956]) ).
fof(f971,definition,
( sQ106_spl
<=> product2(e_4,e_2,e_4) ),
introduced(definition,[new_symbols(definition,[sQ106_spl])],[split_symbol_definition]) ).
fof(f972,plain,
( ~ sQ106_spl
| product2(e_4,e_2,e_4) ),
inference(component_clause,[status(thm)],[f971]) ).
fof(f981,definition,
( sQ109_spl
<=> product2(e_3,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[sQ109_spl])],[split_symbol_definition]) ).
fof(f982,plain,
( ~ sQ109_spl
| product2(e_3,e_2,e_3) ),
inference(component_clause,[status(thm)],[f981]) ).
fof(f988,definition,
( sQ111_spl
<=> product2(e_2,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ111_spl])],[split_symbol_definition]) ).
fof(f989,plain,
( ~ sQ111_spl
| product2(e_2,e_2,e_1) ),
inference(component_clause,[status(thm)],[f988]) ).
fof(f1004,definition,
( sQ116_spl
<=> product2(e_1,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ116_spl])],[split_symbol_definition]) ).
fof(f1005,plain,
( ~ sQ116_spl
| product2(e_1,e_2,e_2) ),
inference(component_clause,[status(thm)],[f1004]) ).
fof(f1014,plain,
( ~ sQ116_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1005,f115]) ).
fof(f1015,plain,
~ sQ116_spl,
inference(contradiction_clause,[status(thm)],[f1014]) ).
fof(f1016,plain,
( ~ sQ111_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f989,f124]) ).
fof(f1017,plain,
~ sQ111_spl,
inference(contradiction_clause,[status(thm)],[f1016]) ).
fof(f1018,plain,
( ~ sQ109_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f982,f254]) ).
fof(f1019,plain,
~ sQ109_spl,
inference(contradiction_clause,[status(thm)],[f1018]) ).
fof(f1020,plain,
( ~ sQ106_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f972,f270]) ).
fof(f1021,plain,
~ sQ106_spl,
inference(contradiction_clause,[status(thm)],[f1020]) ).
fof(f1035,definition,
( sQ122_spl
<=> product2(e_4,e_1,e_4) ),
introduced(definition,[new_symbols(definition,[sQ122_spl])],[split_symbol_definition]) ).
fof(f1036,plain,
( ~ sQ122_spl
| product2(e_4,e_1,e_4) ),
inference(component_clause,[status(thm)],[f1035]) ).
fof(f1045,definition,
( sQ125_spl
<=> product2(e_3,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[sQ125_spl])],[split_symbol_definition]) ).
fof(f1046,plain,
( ~ sQ125_spl
| product2(e_3,e_1,e_3) ),
inference(component_clause,[status(thm)],[f1045]) ).
fof(f1055,definition,
( sQ128_spl
<=> product2(e_2,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ128_spl])],[split_symbol_definition]) ).
fof(f1056,plain,
( ~ sQ128_spl
| product2(e_2,e_1,e_2) ),
inference(component_clause,[status(thm)],[f1055]) ).
fof(f1078,plain,
( ~ sQ128_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1056,f119]) ).
fof(f1079,plain,
~ sQ128_spl,
inference(contradiction_clause,[status(thm)],[f1078]) ).
fof(f1080,plain,
( ~ sQ125_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1046,f195]) ).
fof(f1081,plain,
~ sQ125_spl,
inference(contradiction_clause,[status(thm)],[f1080]) ).
fof(f1082,plain,
( ~ sQ122_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1036,f227]) ).
fof(f1083,plain,
~ sQ122_spl,
inference(contradiction_clause,[status(thm)],[f1082]) ).
fof(f1094,plain,
( ~ sQ23_spl
| ~ product1(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[f411,f155]) ).
fof(f1103,plain,
( ~ sQ23_spl
| ~ sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1094,f437]) ).
fof(f1104,plain,
( ~ sQ23_spl
| ~ sQ31_spl ),
inference(contradiction_clause,[status(thm)],[f1103]) ).
fof(f1136,plain,
( ~ sQ38_spl
| ~ sQ54_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f786,f637]) ).
fof(f1137,plain,
( ~ sQ38_spl
| ~ sQ54_spl ),
inference(contradiction_clause,[status(thm)],[f1136]) ).
fof(f1138,plain,
( ~ sQ53_spl
| ~ sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f634,f838]) ).
fof(f1139,plain,
( ~ sQ53_spl
| ~ sQ31_spl ),
inference(contradiction_clause,[status(thm)],[f1138]) ).
fof(f1144,plain,
( ~ sQ51_spl
| ~ product1(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f628,f113]) ).
fof(f1147,plain,
( ~ sQ51_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1144,f97]) ).
fof(f1148,plain,
~ sQ51_spl,
inference(contradiction_clause,[status(thm)],[f1147]) ).
fof(f1149,plain,
( ~ sQ24_spl
| ~ sQ36_spl ),
inference(split_clause,[status(thm)],[f882,f452,f413]) ).
fof(f1152,plain,
( ~ sQ21_spl
| ~ sQ53_spl ),
inference(split_clause,[status(thm)],[f482,f633,f387]) ).
fof(f1162,plain,
( ~ sQ50_spl
| ~ product1(e_2,e_2,e_2) ),
inference(resolution,[status(thm)],[f624,f157]) ).
fof(f1167,plain,
( ~ sQ50_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1162,f97]) ).
fof(f1168,plain,
~ sQ50_spl,
inference(contradiction_clause,[status(thm)],[f1167]) ).
fof(f1177,plain,
( ~ sQ49_spl
| ~ product1(e_2,e_2,e_2) ),
inference(resolution,[status(thm)],[f621,f151]) ).
fof(f1181,plain,
( ~ sQ49_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1177,f97]) ).
fof(f1182,plain,
~ sQ49_spl,
inference(contradiction_clause,[status(thm)],[f1181]) ).
fof(f1186,plain,
( ~ sQ46_spl
| ~ product1(e_1,e_2,e_4) ),
inference(resolution,[status(thm)],[f611,f131]) ).
fof(f1195,plain,
( ~ sQ46_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f1186,f636,f610]) ).
fof(f1198,plain,
( ~ sQ44_spl
| ~ product1(e_2,e_2,e_2) ),
inference(resolution,[status(thm)],[f605,f149]) ).
fof(f1205,plain,
( ~ sQ44_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1198,f97]) ).
fof(f1206,plain,
~ sQ44_spl,
inference(contradiction_clause,[status(thm)],[f1205]) ).
fof(f1235,plain,
( ~ sQ40_spl
| ~ product1(e_2,e_2,e_2) ),
inference(resolution,[status(thm)],[f592,f155]) ).
fof(f1242,plain,
( ~ sQ40_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1235,f97]) ).
fof(f1243,plain,
~ sQ40_spl,
inference(contradiction_clause,[status(thm)],[f1242]) ).
fof(f1247,plain,
( ~ sQ34_spl
| ~ sQ41_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f807,f595]) ).
fof(f1248,plain,
( ~ sQ34_spl
| ~ sQ41_spl ),
inference(contradiction_clause,[status(thm)],[f1247]) ).
fof(f1254,plain,
( ~ sQ39_spl
| ~ product1(e_3,e_2,e_1) ),
inference(resolution,[status(thm)],[f589,f173]) ).
fof(f1262,plain,
( ~ sQ39_spl
| ~ sQ43_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1254,f602]) ).
fof(f1263,plain,
( ~ sQ39_spl
| ~ sQ43_spl ),
inference(contradiction_clause,[status(thm)],[f1262]) ).
fof(f1264,plain,
$false,
inference(sat_refutation,[status(thm)],[f354,f393,f395,f397,f399,f401,f403,f405,f422,f448,f461,f463,f465,f467,f469,f471,f508,f559,f600,f613,f626,f639,f641,f643,f645,f647,f705,f707,f709,f726,f767,f769,f771,f773,f775,f777,f794,f806,f821,f837,f878,f949,f951,f953,f955,f957,f1015,f1017,f1019,f1021,f1079,f1081,f1083,f1104,f1137,f1139,f1148,f1149,f1152,f1168,f1182,f1195,f1206,f1243,f1248,f1263]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP124-8.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n001.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Sun Sep 20 20:04:42 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.44 % Drodi V4.1.1
% 0.17/0.51 % Refutation found
% 0.17/0.51 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.17/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.53 % Elapsed time: 0.095009 seconds
% 0.17/0.53 % CPU time: 0.448342 seconds
% 0.17/0.53 % Total memory used: 21.830 MB
% 0.17/0.53 % Net memory used: 21.514 MB
%------------------------------------------------------------------------------