%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP124-6.004 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 0.10s 0.42s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 81
% Syntax : Number of formulae : 390 ( 107 unt; 60 def)
% Number of atoms : 752 ( 0 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 766 ( 404 ~; 302 |; 0 &)
% ( 60 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 65 ( 64 usr; 61 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 175 ( 175 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
group_element(e_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
group_element(e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
group_element(e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
group_element(e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
~ equalish(e_1,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
~ equalish(e_2,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X,Y] :
( 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(f18,axiom,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product1(X,Y,Z)
| ~ product1(X,Y,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product1(X,Z,Y)
| ~ product1(X,W,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product1(Z,Y,X)
| ~ product1(W,Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [X] : product1(X,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,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(f23,axiom,
! [X,Y,W,Z] :
( equalish(W,Z)
| ~ product2(X,Y,Z)
| ~ product2(X,Y,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [X,W,Y,Z] :
( equalish(W,Z)
| ~ product2(X,Z,Y)
| ~ product2(X,W,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [W,Y,X,Z] :
( equalish(W,Z)
| ~ product2(Z,Y,X)
| ~ product2(W,Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [X] : product2(X,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,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(f28,plain,
group_element(e_1),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f29,plain,
group_element(e_2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f30,plain,
group_element(e_3),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f31,plain,
group_element(e_4),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f32,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f33,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f34,plain,
~ equalish(e_1,e_4),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f36,plain,
~ equalish(e_2,e_3),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f37,plain,
~ equalish(e_2,e_4),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f40,plain,
~ equalish(e_3,e_4),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f44,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)],[f17]) ).
fof(f45,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product1(X,Y,Z)
| ~ product1(X,Y,W) ) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f46,plain,
! [X0,X1,X2,X3] :
( equalish(X2,X3)
| ~ product1(X0,X1,X3)
| ~ product1(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f47,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product1(X,Z,Y)
| ~ product1(X,W,Y) ) ),
inference(miniscoping,[status(thm)],[f19]) ).
fof(f48,plain,
! [X0,X1,X2,X3] :
( equalish(X1,X3)
| ~ product1(X0,X3,X2)
| ~ product1(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f49,plain,
! [W,Z] :
( equalish(W,Z)
| ! [Y,X] :
( ~ product1(Z,Y,X)
| ~ product1(W,Y,X) ) ),
inference(miniscoping,[status(thm)],[f20]) ).
fof(f50,plain,
! [X0,X1,X2,X3] :
( equalish(X0,X3)
| ~ product1(X3,X1,X2)
| ~ product1(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f51,plain,
! [X0] : product1(X0,X0,X0),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f52,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)],[f22]) ).
fof(f53,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product2(X,Y,Z)
| ~ product2(X,Y,W) ) ),
inference(miniscoping,[status(thm)],[f23]) ).
fof(f54,plain,
! [X0,X1,X2,X3] :
( equalish(X2,X3)
| ~ product2(X0,X1,X3)
| ~ product2(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f55,plain,
! [W,Z] :
( equalish(W,Z)
| ! [X,Y] :
( ~ product2(X,Z,Y)
| ~ product2(X,W,Y) ) ),
inference(miniscoping,[status(thm)],[f24]) ).
fof(f56,plain,
! [X0,X1,X2,X3] :
( equalish(X1,X3)
| ~ product2(X0,X3,X2)
| ~ product2(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f57,plain,
! [W,Z] :
( equalish(W,Z)
| ! [Y,X] :
( ~ product2(Z,Y,X)
| ~ product2(W,Y,X) ) ),
inference(miniscoping,[status(thm)],[f25]) ).
fof(f58,plain,
! [X0,X1,X2,X3] :
( equalish(X0,X3)
| ~ product2(X3,X1,X2)
| ~ product2(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f59,plain,
! [X0] : product2(X0,X0,X0),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f60,plain,
! [X,Y,Z2] :
( product2(Z2,Y,X)
| ! [Z1] :
( ~ product1(Z1,X,Z2)
| ~ product1(X,Y,Z1) ) ),
inference(miniscoping,[status(thm)],[f27]) ).
fof(f61,plain,
! [X0,X1,X2,X3] :
( product2(X3,X1,X0)
| ~ product1(X2,X0,X3)
| ~ product1(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f62,plain,
! [X0,X1] :
( product2(X0,X1,X0)
| ~ product1(X0,X1,X0) ),
inference(resolution,[status(thm)],[f51,f61]) ).
fof(f63,plain,
! [X0,X1] :
( ~ product2(e_2,X0,X1)
| ~ product2(e_1,X0,X1) ),
inference(resolution,[status(thm)],[f32,f58]) ).
fof(f64,plain,
! [X0,X1] :
( ~ product2(X0,e_2,X1)
| ~ product2(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f32,f56]) ).
fof(f65,plain,
! [X0,X1] :
( ~ product2(X0,X1,e_2)
| ~ product2(X0,X1,e_1) ),
inference(resolution,[status(thm)],[f32,f54]) ).
fof(f66,plain,
! [X0,X1] :
( ~ product1(e_2,X0,X1)
| ~ product1(e_1,X0,X1) ),
inference(resolution,[status(thm)],[f32,f50]) ).
fof(f67,plain,
! [X0,X1] :
( ~ product1(X0,e_2,X1)
| ~ product1(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f32,f48]) ).
fof(f68,plain,
! [X0,X1] :
( ~ product1(X0,X1,e_2)
| ~ product1(X0,X1,e_1) ),
inference(resolution,[status(thm)],[f32,f46]) ).
fof(f69,plain,
! [X0,X1] :
( ~ product2(e_3,X0,X1)
| ~ product2(e_1,X0,X1) ),
inference(resolution,[status(thm)],[f33,f58]) ).
fof(f70,plain,
! [X0,X1] :
( ~ product2(X0,e_3,X1)
| ~ product2(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f33,f56]) ).
fof(f71,plain,
! [X0,X1] :
( ~ product2(X0,X1,e_3)
| ~ product2(X0,X1,e_1) ),
inference(resolution,[status(thm)],[f33,f54]) ).
fof(f72,plain,
! [X0,X1] :
( ~ product1(e_3,X0,X1)
| ~ product1(e_1,X0,X1) ),
inference(resolution,[status(thm)],[f33,f50]) ).
fof(f73,plain,
! [X0,X1] :
( ~ product1(X0,e_3,X1)
| ~ product1(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f33,f48]) ).
fof(f74,plain,
! [X0,X1] :
( ~ product1(X0,X1,e_3)
| ~ product1(X0,X1,e_1) ),
inference(resolution,[status(thm)],[f33,f46]) ).
fof(f75,plain,
! [X0,X1] :
( ~ product2(e_4,X0,X1)
| ~ product2(e_1,X0,X1) ),
inference(resolution,[status(thm)],[f34,f58]) ).
fof(f76,plain,
! [X0,X1] :
( ~ product2(X0,e_4,X1)
| ~ product2(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f34,f56]) ).
fof(f77,plain,
! [X0,X1] :
( ~ product2(X0,X1,e_4)
| ~ product2(X0,X1,e_1) ),
inference(resolution,[status(thm)],[f34,f54]) ).
fof(f78,plain,
! [X0,X1] :
( ~ product1(e_4,X0,X1)
| ~ product1(e_1,X0,X1) ),
inference(resolution,[status(thm)],[f34,f50]) ).
fof(f79,plain,
! [X0,X1] :
( ~ product1(X0,e_4,X1)
| ~ product1(X0,e_1,X1) ),
inference(resolution,[status(thm)],[f34,f48]) ).
fof(f88,plain,
~ product2(e_1,e_2,e_2),
inference(resolution,[status(thm)],[f63,f59]) ).
fof(f89,plain,
! [X0] :
( ~ product1(X0,e_2,X0)
| ~ product2(X0,e_1,X0) ),
inference(resolution,[status(thm)],[f64,f62]) ).
fof(f90,plain,
~ product2(e_2,e_1,e_2),
inference(resolution,[status(thm)],[f64,f59]) ).
fof(f92,plain,
~ product2(e_2,e_2,e_1),
inference(resolution,[status(thm)],[f65,f59]) ).
fof(f93,plain,
~ product1(e_1,e_2,e_2),
inference(resolution,[status(thm)],[f66,f51]) ).
fof(f94,plain,
~ product1(e_2,e_1,e_2),
inference(resolution,[status(thm)],[f67,f51]) ).
fof(f95,plain,
~ product1(e_2,e_2,e_1),
inference(resolution,[status(thm)],[f68,f51]) ).
fof(f97,plain,
~ product2(e_1,e_3,e_3),
inference(resolution,[status(thm)],[f69,f59]) ).
fof(f98,plain,
! [X0] :
( ~ product1(X0,e_3,X0)
| ~ product2(X0,e_1,X0) ),
inference(resolution,[status(thm)],[f70,f62]) ).
fof(f99,plain,
~ product2(e_3,e_1,e_3),
inference(resolution,[status(thm)],[f70,f59]) ).
fof(f101,plain,
~ product2(e_3,e_3,e_1),
inference(resolution,[status(thm)],[f71,f59]) ).
fof(f102,plain,
~ product1(e_1,e_3,e_3),
inference(resolution,[status(thm)],[f72,f51]) ).
fof(f103,plain,
~ product1(e_3,e_1,e_3),
inference(resolution,[status(thm)],[f73,f51]) ).
fof(f104,plain,
! [X0,X1] :
( ~ product2(e_3,X0,X1)
| ~ product2(e_2,X0,X1) ),
inference(resolution,[status(thm)],[f36,f58]) ).
fof(f105,plain,
! [X0,X1] :
( ~ product2(X0,e_3,X1)
| ~ product2(X0,e_2,X1) ),
inference(resolution,[status(thm)],[f36,f56]) ).
fof(f106,plain,
! [X0,X1] :
( ~ product2(X0,X1,e_3)
| ~ product2(X0,X1,e_2) ),
inference(resolution,[status(thm)],[f36,f54]) ).
fof(f107,plain,
! [X0,X1] :
( ~ product1(e_3,X0,X1)
| ~ product1(e_2,X0,X1) ),
inference(resolution,[status(thm)],[f36,f50]) ).
fof(f108,plain,
! [X0,X1] :
( ~ product1(X0,e_3,X1)
| ~ product1(X0,e_2,X1) ),
inference(resolution,[status(thm)],[f36,f48]) ).
fof(f109,plain,
! [X0,X1] :
( ~ product1(X0,X1,e_3)
| ~ product1(X0,X1,e_2) ),
inference(resolution,[status(thm)],[f36,f46]) ).
fof(f110,plain,
! [X0,X1] :
( ~ product2(e_4,X0,X1)
| ~ product2(e_2,X0,X1) ),
inference(resolution,[status(thm)],[f37,f58]) ).
fof(f111,plain,
! [X0,X1] :
( ~ product2(X0,e_4,X1)
| ~ product2(X0,e_2,X1) ),
inference(resolution,[status(thm)],[f37,f56]) ).
fof(f112,plain,
! [X0,X1] :
( ~ product2(X0,X1,e_4)
| ~ product2(X0,X1,e_2) ),
inference(resolution,[status(thm)],[f37,f54]) ).
fof(f113,plain,
! [X0,X1] :
( ~ product1(e_4,X0,X1)
| ~ product1(e_2,X0,X1) ),
inference(resolution,[status(thm)],[f37,f50]) ).
fof(f114,plain,
! [X0,X1] :
( ~ product1(X0,e_4,X1)
| ~ product1(X0,e_2,X1) ),
inference(resolution,[status(thm)],[f37,f48]) ).
fof(f128,plain,
! [X0,X1] :
( ~ product2(e_4,X0,X1)
| ~ product2(e_3,X0,X1) ),
inference(resolution,[status(thm)],[f40,f58]) ).
fof(f129,plain,
! [X0,X1] :
( ~ product2(X0,e_4,X1)
| ~ product2(X0,e_3,X1) ),
inference(resolution,[status(thm)],[f40,f56]) ).
fof(f130,plain,
! [X0,X1] :
( ~ product2(X0,X1,e_4)
| ~ product2(X0,X1,e_3) ),
inference(resolution,[status(thm)],[f40,f54]) ).
fof(f131,plain,
! [X0,X1] :
( ~ product1(e_4,X0,X1)
| ~ product1(e_3,X0,X1) ),
inference(resolution,[status(thm)],[f40,f50]) ).
fof(f132,plain,
! [X0,X1] :
( ~ product1(X0,e_4,X1)
| ~ product1(X0,e_3,X1) ),
inference(resolution,[status(thm)],[f40,f48]) ).
fof(f141,plain,
~ product1(e_3,e_3,e_1),
inference(resolution,[status(thm)],[f74,f51]) ).
fof(f143,plain,
~ product2(e_1,e_4,e_4),
inference(resolution,[status(thm)],[f75,f59]) ).
fof(f144,plain,
! [X0] :
( ~ product1(X0,e_4,X0)
| ~ product2(X0,e_1,X0) ),
inference(resolution,[status(thm)],[f76,f62]) ).
fof(f145,plain,
~ product2(e_4,e_1,e_4),
inference(resolution,[status(thm)],[f76,f59]) ).
fof(f147,plain,
~ product2(e_4,e_4,e_1),
inference(resolution,[status(thm)],[f77,f59]) ).
fof(f148,plain,
~ product1(e_1,e_4,e_4),
inference(resolution,[status(thm)],[f78,f51]) ).
fof(f149,plain,
~ product1(e_4,e_1,e_4),
inference(resolution,[status(thm)],[f79,f51]) ).
fof(f153,plain,
~ product2(e_2,e_3,e_3),
inference(resolution,[status(thm)],[f104,f59]) ).
fof(f166,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)],[f44,f31]) ).
fof(f167,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)],[f44,f30]) ).
fof(f170,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)],[f52,f31]) ).
fof(f174,plain,
! [X0] :
( ~ product1(X0,e_3,X0)
| ~ product2(X0,e_2,X0) ),
inference(resolution,[status(thm)],[f105,f62]) ).
fof(f175,plain,
~ product2(e_3,e_2,e_3),
inference(resolution,[status(thm)],[f105,f59]) ).
fof(f177,plain,
~ product2(e_3,e_3,e_2),
inference(resolution,[status(thm)],[f106,f59]) ).
fof(f179,plain,
~ product1(e_2,e_3,e_3),
inference(resolution,[status(thm)],[f107,f51]) ).
fof(f180,plain,
~ product1(e_3,e_2,e_3),
inference(resolution,[status(thm)],[f108,f51]) ).
fof(f181,plain,
~ product1(e_3,e_3,e_2),
inference(resolution,[status(thm)],[f109,f51]) ).
fof(f183,plain,
~ product2(e_2,e_4,e_4),
inference(resolution,[status(thm)],[f110,f59]) ).
fof(f184,plain,
! [X0] :
( ~ product1(X0,e_4,X0)
| ~ product2(X0,e_2,X0) ),
inference(resolution,[status(thm)],[f111,f62]) ).
fof(f185,plain,
~ product2(e_4,e_2,e_4),
inference(resolution,[status(thm)],[f111,f59]) ).
fof(f187,plain,
~ product2(e_4,e_4,e_2),
inference(resolution,[status(thm)],[f112,f59]) ).
fof(f188,plain,
~ product1(e_2,e_4,e_4),
inference(resolution,[status(thm)],[f113,f51]) ).
fof(f189,plain,
~ product1(e_4,e_2,e_4),
inference(resolution,[status(thm)],[f114,f51]) ).
fof(f192,plain,
~ product2(e_3,e_4,e_4),
inference(resolution,[status(thm)],[f128,f59]) ).
fof(f193,plain,
! [X0] :
( ~ product1(X0,e_4,X0)
| ~ product2(X0,e_3,X0) ),
inference(resolution,[status(thm)],[f129,f62]) ).
fof(f194,plain,
~ product2(e_4,e_3,e_4),
inference(resolution,[status(thm)],[f129,f59]) ).
fof(f196,plain,
~ product2(e_4,e_4,e_3),
inference(resolution,[status(thm)],[f130,f59]) ).
fof(f197,plain,
~ product1(e_3,e_4,e_4),
inference(resolution,[status(thm)],[f131,f51]) ).
fof(f198,plain,
~ product1(e_4,e_3,e_4),
inference(resolution,[status(thm)],[f132,f51]) ).
fof(f205,plain,
( product1(e_3,e_4,e_4)
| product1(e_3,e_4,e_3)
| product1(e_3,e_4,e_2)
| product1(e_3,e_4,e_1) ),
inference(resolution,[status(thm)],[f166,f30]) ).
fof(f206,plain,
( product1(e_2,e_4,e_4)
| product1(e_2,e_4,e_3)
| product1(e_2,e_4,e_2)
| product1(e_2,e_4,e_1) ),
inference(resolution,[status(thm)],[f166,f29]) ).
fof(f207,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)],[f166,f28]) ).
fof(f221,definition,
( sQ4_spl
<=> product1(e_3,e_4,e_1) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f222,plain,
( ~ sQ4_spl
| product1(e_3,e_4,e_1) ),
inference(component_clause,[status(thm)],[f221]) ).
fof(f224,definition,
( sQ5_spl
<=> product1(e_3,e_4,e_2) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f225,plain,
( ~ sQ5_spl
| product1(e_3,e_4,e_2) ),
inference(component_clause,[status(thm)],[f224]) ).
fof(f227,definition,
( sQ6_spl
<=> product1(e_3,e_4,e_3) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f228,plain,
( ~ sQ6_spl
| product1(e_3,e_4,e_3) ),
inference(component_clause,[status(thm)],[f227]) ).
fof(f230,definition,
( sQ7_spl
<=> product1(e_3,e_4,e_4) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f231,plain,
( ~ sQ7_spl
| product1(e_3,e_4,e_4) ),
inference(component_clause,[status(thm)],[f230]) ).
fof(f233,plain,
( sQ7_spl
| sQ6_spl
| sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f205,f221,f224,f227,f230]) ).
fof(f234,definition,
( sQ8_spl
<=> product1(e_2,e_4,e_1) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f235,plain,
( ~ sQ8_spl
| product1(e_2,e_4,e_1) ),
inference(component_clause,[status(thm)],[f234]) ).
fof(f237,definition,
( sQ9_spl
<=> product1(e_2,e_4,e_2) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f238,plain,
( ~ sQ9_spl
| product1(e_2,e_4,e_2) ),
inference(component_clause,[status(thm)],[f237]) ).
fof(f240,definition,
( sQ10_spl
<=> product1(e_2,e_4,e_3) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f241,plain,
( ~ sQ10_spl
| product1(e_2,e_4,e_3) ),
inference(component_clause,[status(thm)],[f240]) ).
fof(f243,definition,
( sQ11_spl
<=> product1(e_2,e_4,e_4) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f244,plain,
( ~ sQ11_spl
| product1(e_2,e_4,e_4) ),
inference(component_clause,[status(thm)],[f243]) ).
fof(f246,plain,
( sQ11_spl
| sQ10_spl
| sQ9_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f206,f234,f237,f240,f243]) ).
fof(f247,definition,
( sQ12_spl
<=> product1(e_1,e_4,e_1) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f248,plain,
( ~ sQ12_spl
| product1(e_1,e_4,e_1) ),
inference(component_clause,[status(thm)],[f247]) ).
fof(f250,definition,
( sQ13_spl
<=> product1(e_1,e_4,e_2) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f251,plain,
( ~ sQ13_spl
| product1(e_1,e_4,e_2) ),
inference(component_clause,[status(thm)],[f250]) ).
fof(f253,definition,
( sQ14_spl
<=> product1(e_1,e_4,e_3) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f254,plain,
( ~ sQ14_spl
| product1(e_1,e_4,e_3) ),
inference(component_clause,[status(thm)],[f253]) ).
fof(f256,definition,
( sQ15_spl
<=> product1(e_1,e_4,e_4) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f257,plain,
( ~ sQ15_spl
| product1(e_1,e_4,e_4) ),
inference(component_clause,[status(thm)],[f256]) ).
fof(f259,plain,
( sQ15_spl
| sQ14_spl
| sQ13_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f207,f247,f250,f253,f256]) ).
fof(f260,plain,
( ~ sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f257,f148]) ).
fof(f261,plain,
~ sQ15_spl,
inference(contradiction_clause,[status(thm)],[f260]) ).
fof(f262,plain,
( ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f244,f188]) ).
fof(f263,plain,
~ sQ11_spl,
inference(contradiction_clause,[status(thm)],[f262]) ).
fof(f264,plain,
( ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f231,f197]) ).
fof(f265,plain,
~ sQ7_spl,
inference(contradiction_clause,[status(thm)],[f264]) ).
fof(f268,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)],[f167,f29]) ).
fof(f269,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)],[f167,f28]) ).
fof(f276,definition,
( sQ18_spl
<=> product1(e_4,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f277,plain,
( ~ sQ18_spl
| product1(e_4,e_3,e_3) ),
inference(component_clause,[status(thm)],[f276]) ).
fof(f279,definition,
( sQ19_spl
<=> product1(e_4,e_3,e_4) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f280,plain,
( ~ sQ19_spl
| product1(e_4,e_3,e_4) ),
inference(component_clause,[status(thm)],[f279]) ).
fof(f283,definition,
( sQ20_spl
<=> product1(e_3,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f284,plain,
( ~ sQ20_spl
| product1(e_3,e_3,e_1) ),
inference(component_clause,[status(thm)],[f283]) ).
fof(f286,definition,
( sQ21_spl
<=> product1(e_3,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f287,plain,
( ~ sQ21_spl
| product1(e_3,e_3,e_2) ),
inference(component_clause,[status(thm)],[f286]) ).
fof(f296,definition,
( sQ24_spl
<=> product1(e_2,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f297,plain,
( ~ sQ24_spl
| product1(e_2,e_3,e_1) ),
inference(component_clause,[status(thm)],[f296]) ).
fof(f299,definition,
( sQ25_spl
<=> product1(e_2,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f300,plain,
( ~ sQ25_spl
| product1(e_2,e_3,e_2) ),
inference(component_clause,[status(thm)],[f299]) ).
fof(f302,definition,
( sQ26_spl
<=> product1(e_2,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f303,plain,
( ~ sQ26_spl
| product1(e_2,e_3,e_3) ),
inference(component_clause,[status(thm)],[f302]) ).
fof(f305,definition,
( sQ27_spl
<=> product1(e_2,e_3,e_4) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f306,plain,
( ~ sQ27_spl
| product1(e_2,e_3,e_4) ),
inference(component_clause,[status(thm)],[f305]) ).
fof(f308,plain,
( sQ27_spl
| sQ26_spl
| sQ25_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f268,f296,f299,f302,f305]) ).
fof(f309,definition,
( sQ28_spl
<=> product1(e_1,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f310,plain,
( ~ sQ28_spl
| product1(e_1,e_3,e_1) ),
inference(component_clause,[status(thm)],[f309]) ).
fof(f312,definition,
( sQ29_spl
<=> product1(e_1,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f313,plain,
( ~ sQ29_spl
| product1(e_1,e_3,e_2) ),
inference(component_clause,[status(thm)],[f312]) ).
fof(f315,definition,
( sQ30_spl
<=> product1(e_1,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f316,plain,
( ~ sQ30_spl
| product1(e_1,e_3,e_3) ),
inference(component_clause,[status(thm)],[f315]) ).
fof(f318,definition,
( sQ31_spl
<=> product1(e_1,e_3,e_4) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f319,plain,
( ~ sQ31_spl
| product1(e_1,e_3,e_4) ),
inference(component_clause,[status(thm)],[f318]) ).
fof(f321,plain,
( sQ31_spl
| sQ30_spl
| sQ29_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f269,f309,f312,f315,f318]) ).
fof(f322,plain,
( ~ sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f316,f102]) ).
fof(f323,plain,
~ sQ30_spl,
inference(contradiction_clause,[status(thm)],[f322]) ).
fof(f324,plain,
( ~ sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f303,f179]) ).
fof(f325,plain,
~ sQ26_spl,
inference(contradiction_clause,[status(thm)],[f324]) ).
fof(f326,plain,
( ~ sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f287,f181]) ).
fof(f327,plain,
~ sQ21_spl,
inference(contradiction_clause,[status(thm)],[f326]) ).
fof(f328,plain,
( ~ sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f284,f141]) ).
fof(f329,plain,
~ sQ20_spl,
inference(contradiction_clause,[status(thm)],[f328]) ).
fof(f330,plain,
( ~ sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f280,f198]) ).
fof(f331,plain,
~ sQ19_spl,
inference(contradiction_clause,[status(thm)],[f330]) ).
fof(f345,definition,
( sQ35_spl
<=> product1(e_4,e_2,e_4) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f346,plain,
( ~ sQ35_spl
| product1(e_4,e_2,e_4) ),
inference(component_clause,[status(thm)],[f345]) ).
fof(f355,definition,
( sQ38_spl
<=> product1(e_3,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f356,plain,
( ~ sQ38_spl
| product1(e_3,e_2,e_3) ),
inference(component_clause,[status(thm)],[f355]) ).
fof(f362,definition,
( sQ40_spl
<=> product1(e_2,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f363,plain,
( ~ sQ40_spl
| product1(e_2,e_2,e_1) ),
inference(component_clause,[status(thm)],[f362]) ).
fof(f375,definition,
( sQ44_spl
<=> product1(e_1,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f376,plain,
( ~ sQ44_spl
| product1(e_1,e_2,e_1) ),
inference(component_clause,[status(thm)],[f375]) ).
fof(f378,definition,
( sQ45_spl
<=> product1(e_1,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f379,plain,
( ~ sQ45_spl
| product1(e_1,e_2,e_2) ),
inference(component_clause,[status(thm)],[f378]) ).
fof(f388,plain,
( ~ sQ45_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f379,f93]) ).
fof(f389,plain,
~ sQ45_spl,
inference(contradiction_clause,[status(thm)],[f388]) ).
fof(f390,plain,
( ~ sQ40_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f363,f95]) ).
fof(f391,plain,
~ sQ40_spl,
inference(contradiction_clause,[status(thm)],[f390]) ).
fof(f392,plain,
( ~ sQ38_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f356,f180]) ).
fof(f393,plain,
~ sQ38_spl,
inference(contradiction_clause,[status(thm)],[f392]) ).
fof(f394,plain,
( ~ sQ35_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f346,f189]) ).
fof(f395,plain,
~ sQ35_spl,
inference(contradiction_clause,[status(thm)],[f394]) ).
fof(f400,definition,
( sQ48_spl
<=> product1(e_4,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f401,plain,
( ~ sQ48_spl
| product1(e_4,e_1,e_1) ),
inference(component_clause,[status(thm)],[f400]) ).
fof(f409,definition,
( sQ51_spl
<=> product1(e_4,e_1,e_4) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f410,plain,
( ~ sQ51_spl
| product1(e_4,e_1,e_4) ),
inference(component_clause,[status(thm)],[f409]) ).
fof(f419,definition,
( sQ54_spl
<=> product1(e_3,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f420,plain,
( ~ sQ54_spl
| product1(e_3,e_1,e_3) ),
inference(component_clause,[status(thm)],[f419]) ).
fof(f429,definition,
( sQ57_spl
<=> product1(e_2,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f430,plain,
( ~ sQ57_spl
| product1(e_2,e_1,e_2) ),
inference(component_clause,[status(thm)],[f429]) ).
fof(f452,plain,
( ~ sQ57_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f430,f94]) ).
fof(f453,plain,
~ sQ57_spl,
inference(contradiction_clause,[status(thm)],[f452]) ).
fof(f454,plain,
( ~ sQ54_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f420,f103]) ).
fof(f455,plain,
~ sQ54_spl,
inference(contradiction_clause,[status(thm)],[f454]) ).
fof(f456,plain,
( ~ sQ51_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f410,f149]) ).
fof(f457,plain,
~ sQ51_spl,
inference(contradiction_clause,[status(thm)],[f456]) ).
fof(f458,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)],[f170,f31]) ).
fof(f462,definition,
( sQ64_spl
<=> product2(e_4,e_4,e_1) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f463,plain,
( ~ sQ64_spl
| product2(e_4,e_4,e_1) ),
inference(component_clause,[status(thm)],[f462]) ).
fof(f465,definition,
( sQ65_spl
<=> product2(e_4,e_4,e_2) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f466,plain,
( ~ sQ65_spl
| product2(e_4,e_4,e_2) ),
inference(component_clause,[status(thm)],[f465]) ).
fof(f468,definition,
( sQ66_spl
<=> product2(e_4,e_4,e_3) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f469,plain,
( ~ sQ66_spl
| product2(e_4,e_4,e_3) ),
inference(component_clause,[status(thm)],[f468]) ).
fof(f471,definition,
( sQ67_spl
<=> product2(e_4,e_4,e_4) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f474,plain,
( sQ67_spl
| sQ66_spl
| sQ65_spl
| sQ64_spl ),
inference(split_clause,[status(thm)],[f458,f462,f465,f468,f471]) ).
fof(f481,definition,
( sQ70_spl
<=> product2(e_3,e_4,e_3) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f482,plain,
( ~ sQ70_spl
| product2(e_3,e_4,e_3) ),
inference(component_clause,[status(thm)],[f481]) ).
fof(f484,definition,
( sQ71_spl
<=> product2(e_3,e_4,e_4) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f485,plain,
( ~ sQ71_spl
| product2(e_3,e_4,e_4) ),
inference(component_clause,[status(thm)],[f484]) ).
fof(f497,definition,
( sQ75_spl
<=> product2(e_2,e_4,e_4) ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f498,plain,
( ~ sQ75_spl
| product2(e_2,e_4,e_4) ),
inference(component_clause,[status(thm)],[f497]) ).
fof(f501,definition,
( sQ76_spl
<=> product2(e_1,e_4,e_1) ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f502,plain,
( ~ sQ76_spl
| product2(e_1,e_4,e_1) ),
inference(component_clause,[status(thm)],[f501]) ).
fof(f510,definition,
( sQ79_spl
<=> product2(e_1,e_4,e_4) ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f511,plain,
( ~ sQ79_spl
| product2(e_1,e_4,e_4) ),
inference(component_clause,[status(thm)],[f510]) ).
fof(f514,plain,
( ~ sQ79_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f511,f143]) ).
fof(f515,plain,
~ sQ79_spl,
inference(contradiction_clause,[status(thm)],[f514]) ).
fof(f516,plain,
( ~ sQ75_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f498,f183]) ).
fof(f517,plain,
~ sQ75_spl,
inference(contradiction_clause,[status(thm)],[f516]) ).
fof(f518,plain,
( ~ sQ71_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f485,f192]) ).
fof(f519,plain,
~ sQ71_spl,
inference(contradiction_clause,[status(thm)],[f518]) ).
fof(f520,plain,
( ~ sQ66_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f469,f196]) ).
fof(f521,plain,
~ sQ66_spl,
inference(contradiction_clause,[status(thm)],[f520]) ).
fof(f522,plain,
( ~ sQ65_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f466,f187]) ).
fof(f523,plain,
~ sQ65_spl,
inference(contradiction_clause,[status(thm)],[f522]) ).
fof(f524,plain,
( ~ sQ64_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f463,f147]) ).
fof(f525,plain,
~ sQ64_spl,
inference(contradiction_clause,[status(thm)],[f524]) ).
fof(f536,definition,
( sQ82_spl
<=> product2(e_4,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f537,plain,
( ~ sQ82_spl
| product2(e_4,e_3,e_3) ),
inference(component_clause,[status(thm)],[f536]) ).
fof(f539,definition,
( sQ83_spl
<=> product2(e_4,e_3,e_4) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f540,plain,
( ~ sQ83_spl
| product2(e_4,e_3,e_4) ),
inference(component_clause,[status(thm)],[f539]) ).
fof(f543,definition,
( sQ84_spl
<=> product2(e_3,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f544,plain,
( ~ sQ84_spl
| product2(e_3,e_3,e_1) ),
inference(component_clause,[status(thm)],[f543]) ).
fof(f546,definition,
( sQ85_spl
<=> product2(e_3,e_3,e_2) ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f547,plain,
( ~ sQ85_spl
| product2(e_3,e_3,e_2) ),
inference(component_clause,[status(thm)],[f546]) ).
fof(f562,definition,
( sQ90_spl
<=> product2(e_2,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f563,plain,
( ~ sQ90_spl
| product2(e_2,e_3,e_3) ),
inference(component_clause,[status(thm)],[f562]) ).
fof(f569,definition,
( sQ92_spl
<=> product2(e_1,e_3,e_1) ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f570,plain,
( ~ sQ92_spl
| product2(e_1,e_3,e_1) ),
inference(component_clause,[status(thm)],[f569]) ).
fof(f575,definition,
( sQ94_spl
<=> product2(e_1,e_3,e_3) ),
introduced(definition,[new_symbols(definition,[sQ94_spl])],[split_symbol_definition]) ).
fof(f576,plain,
( ~ sQ94_spl
| product2(e_1,e_3,e_3) ),
inference(component_clause,[status(thm)],[f575]) ).
fof(f582,plain,
( ~ sQ94_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f576,f97]) ).
fof(f583,plain,
~ sQ94_spl,
inference(contradiction_clause,[status(thm)],[f582]) ).
fof(f584,plain,
( ~ sQ90_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f563,f153]) ).
fof(f585,plain,
~ sQ90_spl,
inference(contradiction_clause,[status(thm)],[f584]) ).
fof(f586,plain,
( ~ sQ85_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f547,f177]) ).
fof(f587,plain,
~ sQ85_spl,
inference(contradiction_clause,[status(thm)],[f586]) ).
fof(f588,plain,
( ~ sQ84_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f544,f101]) ).
fof(f589,plain,
~ sQ84_spl,
inference(contradiction_clause,[status(thm)],[f588]) ).
fof(f590,plain,
( ~ sQ83_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f540,f194]) ).
fof(f591,plain,
~ sQ83_spl,
inference(contradiction_clause,[status(thm)],[f590]) ).
fof(f607,definition,
( sQ99_spl
<=> product2(e_4,e_2,e_4) ),
introduced(definition,[new_symbols(definition,[sQ99_spl])],[split_symbol_definition]) ).
fof(f608,plain,
( ~ sQ99_spl
| product2(e_4,e_2,e_4) ),
inference(component_clause,[status(thm)],[f607]) ).
fof(f614,definition,
( sQ101_spl
<=> product2(e_3,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ101_spl])],[split_symbol_definition]) ).
fof(f615,plain,
( ~ sQ101_spl
| product2(e_3,e_2,e_2) ),
inference(component_clause,[status(thm)],[f614]) ).
fof(f617,definition,
( sQ102_spl
<=> product2(e_3,e_2,e_3) ),
introduced(definition,[new_symbols(definition,[sQ102_spl])],[split_symbol_definition]) ).
fof(f618,plain,
( ~ sQ102_spl
| product2(e_3,e_2,e_3) ),
inference(component_clause,[status(thm)],[f617]) ).
fof(f624,definition,
( sQ104_spl
<=> product2(e_2,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ104_spl])],[split_symbol_definition]) ).
fof(f625,plain,
( ~ sQ104_spl
| product2(e_2,e_2,e_1) ),
inference(component_clause,[status(thm)],[f624]) ).
fof(f637,definition,
( sQ108_spl
<=> product2(e_1,e_2,e_1) ),
introduced(definition,[new_symbols(definition,[sQ108_spl])],[split_symbol_definition]) ).
fof(f638,plain,
( ~ sQ108_spl
| product2(e_1,e_2,e_1) ),
inference(component_clause,[status(thm)],[f637]) ).
fof(f640,definition,
( sQ109_spl
<=> product2(e_1,e_2,e_2) ),
introduced(definition,[new_symbols(definition,[sQ109_spl])],[split_symbol_definition]) ).
fof(f641,plain,
( ~ sQ109_spl
| product2(e_1,e_2,e_2) ),
inference(component_clause,[status(thm)],[f640]) ).
fof(f650,plain,
( ~ sQ109_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f641,f88]) ).
fof(f651,plain,
~ sQ109_spl,
inference(contradiction_clause,[status(thm)],[f650]) ).
fof(f652,plain,
( ~ sQ104_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f625,f92]) ).
fof(f653,plain,
~ sQ104_spl,
inference(contradiction_clause,[status(thm)],[f652]) ).
fof(f654,plain,
( ~ sQ102_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f618,f175]) ).
fof(f655,plain,
~ sQ102_spl,
inference(contradiction_clause,[status(thm)],[f654]) ).
fof(f656,plain,
( ~ sQ99_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f608,f185]) ).
fof(f657,plain,
~ sQ99_spl,
inference(contradiction_clause,[status(thm)],[f656]) ).
fof(f662,definition,
( sQ112_spl
<=> product2(e_4,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ112_spl])],[split_symbol_definition]) ).
fof(f663,plain,
( ~ sQ112_spl
| product2(e_4,e_1,e_1) ),
inference(component_clause,[status(thm)],[f662]) ).
fof(f671,definition,
( sQ115_spl
<=> product2(e_4,e_1,e_4) ),
introduced(definition,[new_symbols(definition,[sQ115_spl])],[split_symbol_definition]) ).
fof(f672,plain,
( ~ sQ115_spl
| product2(e_4,e_1,e_4) ),
inference(component_clause,[status(thm)],[f671]) ).
fof(f681,definition,
( sQ118_spl
<=> product2(e_3,e_1,e_3) ),
introduced(definition,[new_symbols(definition,[sQ118_spl])],[split_symbol_definition]) ).
fof(f682,plain,
( ~ sQ118_spl
| product2(e_3,e_1,e_3) ),
inference(component_clause,[status(thm)],[f681]) ).
fof(f688,definition,
( sQ120_spl
<=> product2(e_2,e_1,e_1) ),
introduced(definition,[new_symbols(definition,[sQ120_spl])],[split_symbol_definition]) ).
fof(f689,plain,
( ~ sQ120_spl
| product2(e_2,e_1,e_1) ),
inference(component_clause,[status(thm)],[f688]) ).
fof(f691,definition,
( sQ121_spl
<=> product2(e_2,e_1,e_2) ),
introduced(definition,[new_symbols(definition,[sQ121_spl])],[split_symbol_definition]) ).
fof(f692,plain,
( ~ sQ121_spl
| product2(e_2,e_1,e_2) ),
inference(component_clause,[status(thm)],[f691]) ).
fof(f714,plain,
( ~ sQ121_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f692,f90]) ).
fof(f715,plain,
~ sQ121_spl,
inference(contradiction_clause,[status(thm)],[f714]) ).
fof(f716,plain,
( ~ sQ118_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f682,f99]) ).
fof(f717,plain,
~ sQ118_spl,
inference(contradiction_clause,[status(thm)],[f716]) ).
fof(f718,plain,
( ~ sQ115_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f672,f145]) ).
fof(f719,plain,
~ sQ115_spl,
inference(contradiction_clause,[status(thm)],[f718]) ).
fof(f731,plain,
( ~ sQ13_spl
| ~ product1(e_1,e_3,e_2) ),
inference(resolution,[status(thm)],[f251,f132]) ).
fof(f736,plain,
( ~ sQ13_spl
| ~ sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f731,f313]) ).
fof(f737,plain,
( ~ sQ13_spl
| ~ sQ29_spl ),
inference(contradiction_clause,[status(thm)],[f736]) ).
fof(f742,plain,
( ~ sQ12_spl
| ~ product2(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f248,f144]) ).
fof(f753,plain,
( ~ sQ10_spl
| ~ product1(e_1,e_4,e_3) ),
inference(resolution,[status(thm)],[f241,f66]) ).
fof(f764,plain,
( ~ sQ9_spl
| ~ product2(e_2,e_2,e_2) ),
inference(resolution,[status(thm)],[f238,f184]) ).
fof(f775,plain,
( ~ sQ8_spl
| ~ product1(e_2,e_3,e_1) ),
inference(resolution,[status(thm)],[f235,f132]) ).
fof(f779,plain,
( ~ sQ8_spl
| ~ sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f775,f297]) ).
fof(f780,plain,
( ~ sQ8_spl
| ~ sQ24_spl ),
inference(contradiction_clause,[status(thm)],[f779]) ).
fof(f787,plain,
( ~ sQ6_spl
| ~ product2(e_3,e_3,e_3) ),
inference(resolution,[status(thm)],[f228,f193]) ).
fof(f796,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f787,f59]) ).
fof(f797,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f796]) ).
fof(f799,plain,
( ~ sQ5_spl
| ~ product1(e_1,e_4,e_2) ),
inference(resolution,[status(thm)],[f225,f72]) ).
fof(f805,plain,
( ~ sQ5_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f799,f250,f224]) ).
fof(f808,plain,
( ~ sQ4_spl
| ~ product1(e_2,e_4,e_1) ),
inference(resolution,[status(thm)],[f222,f107]) ).
fof(f814,plain,
( ~ sQ4_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f808,f234,f221]) ).
fof(f820,plain,
( ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f742,f59]) ).
fof(f821,plain,
~ sQ12_spl,
inference(contradiction_clause,[status(thm)],[f820]) ).
fof(f829,plain,
! [X0] :
( ~ sQ31_spl
| product2(e_4,X0,e_3)
| ~ product1(e_3,X0,e_1) ),
inference(resolution,[status(thm)],[f319,f61]) ).
fof(f838,plain,
! [X0] :
( ~ sQ27_spl
| product2(e_4,X0,e_3)
| ~ product1(e_3,X0,e_2) ),
inference(resolution,[status(thm)],[f306,f61]) ).
fof(f842,plain,
( ~ sQ25_spl
| ~ product2(e_2,e_2,e_2) ),
inference(resolution,[status(thm)],[f300,f174]) ).
fof(f848,plain,
( ~ sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f842,f59]) ).
fof(f849,plain,
~ sQ25_spl,
inference(contradiction_clause,[status(thm)],[f848]) ).
fof(f860,plain,
( ~ sQ18_spl
| ~ product1(e_3,e_3,e_3) ),
inference(resolution,[status(thm)],[f277,f131]) ).
fof(f868,plain,
( ~ sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f860,f51]) ).
fof(f869,plain,
~ sQ18_spl,
inference(contradiction_clause,[status(thm)],[f868]) ).
fof(f928,plain,
( ~ sQ48_spl
| ~ product1(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f401,f78]) ).
fof(f931,plain,
( ~ sQ48_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f928,f51]) ).
fof(f932,plain,
~ sQ48_spl,
inference(contradiction_clause,[status(thm)],[f931]) ).
fof(f950,plain,
( ~ sQ76_spl
| ~ product2(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f502,f76]) ).
fof(f951,plain,
( ~ sQ76_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f950,f59]) ).
fof(f952,plain,
~ sQ76_spl,
inference(contradiction_clause,[status(thm)],[f951]) ).
fof(f982,plain,
( ~ sQ70_spl
| ~ product2(e_3,e_3,e_3) ),
inference(resolution,[status(thm)],[f482,f129]) ).
fof(f987,plain,
( ~ sQ70_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f982,f59]) ).
fof(f988,plain,
~ sQ70_spl,
inference(contradiction_clause,[status(thm)],[f987]) ).
fof(f1042,plain,
( ~ sQ82_spl
| ~ product2(e_3,e_3,e_3) ),
inference(resolution,[status(thm)],[f537,f128]) ).
fof(f1049,plain,
( ~ sQ82_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1042,f59]) ).
fof(f1050,plain,
~ sQ82_spl,
inference(contradiction_clause,[status(thm)],[f1049]) ).
fof(f1074,plain,
( ~ sQ101_spl
| ~ product2(e_2,e_2,e_2) ),
inference(resolution,[status(thm)],[f615,f104]) ).
fof(f1078,plain,
( ~ sQ101_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1074,f59]) ).
fof(f1079,plain,
~ sQ101_spl,
inference(contradiction_clause,[status(thm)],[f1078]) ).
fof(f1110,plain,
( ~ sQ112_spl
| ~ product2(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f663,f75]) ).
fof(f1112,plain,
( ~ sQ112_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1110,f59]) ).
fof(f1113,plain,
~ sQ112_spl,
inference(contradiction_clause,[status(thm)],[f1112]) ).
fof(f1128,plain,
( ~ sQ28_spl
| ~ product2(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f310,f98]) ).
fof(f1133,plain,
( ~ sQ28_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1128,f59]) ).
fof(f1134,plain,
~ sQ28_spl,
inference(contradiction_clause,[status(thm)],[f1133]) ).
fof(f1135,plain,
( ~ sQ4_spl
| ~ sQ31_spl
| product2(e_4,e_4,e_3) ),
inference(resolution,[status(thm)],[f829,f222]) ).
fof(f1136,plain,
( ~ sQ4_spl
| ~ sQ31_spl
| sQ66_spl ),
inference(split_clause,[status(thm)],[f1135,f468,f318,f221]) ).
fof(f1141,plain,
( ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f764,f59]) ).
fof(f1142,plain,
~ sQ9_spl,
inference(contradiction_clause,[status(thm)],[f1141]) ).
fof(f1145,plain,
( ~ sQ10_spl
| ~ sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f753,f254]) ).
fof(f1146,plain,
( ~ sQ10_spl
| ~ sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f1145]) ).
fof(f1147,plain,
( ~ sQ44_spl
| ~ product2(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f376,f89]) ).
fof(f1150,plain,
( ~ sQ44_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1147,f59]) ).
fof(f1151,plain,
~ sQ44_spl,
inference(contradiction_clause,[status(thm)],[f1150]) ).
fof(f1168,plain,
( ~ sQ92_spl
| ~ product2(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f570,f70]) ).
fof(f1170,plain,
( ~ sQ92_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1168,f59]) ).
fof(f1171,plain,
~ sQ92_spl,
inference(contradiction_clause,[status(thm)],[f1170]) ).
fof(f1175,plain,
( ~ sQ108_spl
| ~ product2(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f638,f64]) ).
fof(f1176,plain,
( ~ sQ108_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1175,f59]) ).
fof(f1177,plain,
~ sQ108_spl,
inference(contradiction_clause,[status(thm)],[f1176]) ).
fof(f1179,plain,
( ~ sQ120_spl
| ~ product2(e_1,e_1,e_1) ),
inference(resolution,[status(thm)],[f689,f63]) ).
fof(f1180,plain,
( ~ sQ120_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1179,f59]) ).
fof(f1181,plain,
~ sQ120_spl,
inference(contradiction_clause,[status(thm)],[f1180]) ).
fof(f1189,plain,
( ~ sQ27_spl
| ~ sQ5_spl
| product2(e_4,e_4,e_3) ),
inference(resolution,[status(thm)],[f225,f838]) ).
fof(f1197,plain,
( ~ sQ27_spl
| ~ sQ5_spl
| sQ66_spl ),
inference(split_clause,[status(thm)],[f1189,f468,f224,f305]) ).
fof(f1198,plain,
$false,
inference(sat_refutation,[status(thm)],[f233,f246,f259,f261,f263,f265,f308,f321,f323,f325,f327,f329,f331,f389,f391,f393,f395,f453,f455,f457,f474,f515,f517,f519,f521,f523,f525,f583,f585,f587,f589,f591,f651,f653,f655,f657,f715,f717,f719,f737,f780,f797,f805,f814,f821,f849,f869,f932,f952,f988,f1050,f1079,f1113,f1134,f1136,f1142,f1146,f1151,f1171,f1177,f1181,f1197]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP124-6.004 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 19:59:27 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.42 % Refutation found
% 0.10/0.42 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.44 % Elapsed time: 0.065507 seconds
% 0.10/0.44 % CPU time: 0.279900 seconds
% 0.10/0.44 % Total memory used: 20.343 MB
% 0.10/0.44 % Net memory used: 19.995 MB
%------------------------------------------------------------------------------