TSTP Solution File: GRP124-9.004 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : GRP124-9.004 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed May 31 12:10:31 EDT 2023
% Result : Unsatisfiable 0.20s 0.41s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 79
% Syntax : Number of formulae : 376 ( 107 unt; 0 def)
% Number of atoms : 724 ( 0 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 730 ( 382 ~; 290 |; 0 &)
% ( 58 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 63 ( 62 usr; 59 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 170 (; 170 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
group_element(e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
~ equalish(e_1,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
~ equalish(e_1,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
~ equalish(e_1,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
~ equalish(e_2,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X,Y] :
( ~ group_element(X)
| ~ group_element(Y)
| product1(X,Y,e_1)
| product1(X,Y,e_2)
| product1(X,Y,e_3)
| product1(X,Y,e_4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [X,Y,W,Z] :
( ~ product1(X,Y,W)
| ~ product1(X,Y,Z)
| equalish(W,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [X,W,Y,Z] :
( ~ product1(X,W,Y)
| ~ product1(X,Z,Y)
| equalish(W,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [W,Y,X,Z] :
( ~ product1(W,Y,X)
| ~ product1(Z,Y,X)
| equalish(W,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [X] : product1(X,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [X,Y] :
( ~ group_element(X)
| ~ group_element(Y)
| product2(X,Y,e_1)
| product2(X,Y,e_2)
| product2(X,Y,e_3)
| product2(X,Y,e_4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [X,Y,W,Z] :
( ~ product2(X,Y,W)
| ~ product2(X,Y,Z)
| equalish(W,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [X,W,Y,Z] :
( ~ product2(X,W,Y)
| ~ product2(X,Z,Y)
| equalish(W,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [W,Y,X,Z] :
( ~ product2(W,Y,X)
| ~ product2(Z,Y,X)
| equalish(W,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [X] : product2(X,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
! [X,Y,Z1,Z2] :
( ~ product1(X,Y,Z1)
| ~ product1(Z1,X,Z2)
| product2(Z2,Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,plain,
group_element(e_1),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f33,plain,
group_element(e_2),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f34,plain,
group_element(e_3),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f35,plain,
group_element(e_4),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f36,plain,
~ equalish(e_1,e_2),
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f37,plain,
~ equalish(e_1,e_3),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f38,plain,
~ equalish(e_1,e_4),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f40,plain,
~ equalish(e_2,e_3),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f41,plain,
~ equalish(e_2,e_4),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f44,plain,
~ equalish(e_3,e_4),
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f48,plain,
! [X0,X1] :
( ~ group_element(X0)
| ~ group_element(X1)
| product1(X0,X1,e_1)
| product1(X0,X1,e_2)
| product1(X0,X1,e_3)
| product1(X0,X1,e_4) ),
inference(cnf_transformation,[status(esa)],[f19]) ).
fof(f49,plain,
! [W,Z] :
( ! [X,Y] :
( ~ product1(X,Y,W)
| ~ product1(X,Y,Z) )
| equalish(W,Z) ),
inference(miniscoping,[status(esa)],[f20]) ).
fof(f50,plain,
! [X0,X1,X2,X3] :
( ~ product1(X0,X1,X2)
| ~ product1(X0,X1,X3)
| equalish(X2,X3) ),
inference(cnf_transformation,[status(esa)],[f49]) ).
fof(f51,plain,
! [W,Z] :
( ! [X,Y] :
( ~ product1(X,W,Y)
| ~ product1(X,Z,Y) )
| equalish(W,Z) ),
inference(miniscoping,[status(esa)],[f21]) ).
fof(f52,plain,
! [X0,X1,X2,X3] :
( ~ product1(X0,X1,X2)
| ~ product1(X0,X3,X2)
| equalish(X1,X3) ),
inference(cnf_transformation,[status(esa)],[f51]) ).
fof(f53,plain,
! [W,Z] :
( ! [Y,X] :
( ~ product1(W,Y,X)
| ~ product1(Z,Y,X) )
| equalish(W,Z) ),
inference(miniscoping,[status(esa)],[f22]) ).
fof(f54,plain,
! [X0,X1,X2,X3] :
( ~ product1(X0,X1,X2)
| ~ product1(X3,X1,X2)
| equalish(X0,X3) ),
inference(cnf_transformation,[status(esa)],[f53]) ).
fof(f55,plain,
! [X0] : product1(X0,X0,X0),
inference(cnf_transformation,[status(esa)],[f23]) ).
fof(f56,plain,
! [X0,X1] :
( ~ group_element(X0)
| ~ group_element(X1)
| product2(X0,X1,e_1)
| product2(X0,X1,e_2)
| product2(X0,X1,e_3)
| product2(X0,X1,e_4) ),
inference(cnf_transformation,[status(esa)],[f24]) ).
fof(f57,plain,
! [W,Z] :
( ! [X,Y] :
( ~ product2(X,Y,W)
| ~ product2(X,Y,Z) )
| equalish(W,Z) ),
inference(miniscoping,[status(esa)],[f25]) ).
fof(f58,plain,
! [X0,X1,X2,X3] :
( ~ product2(X0,X1,X2)
| ~ product2(X0,X1,X3)
| equalish(X2,X3) ),
inference(cnf_transformation,[status(esa)],[f57]) ).
fof(f59,plain,
! [W,Z] :
( ! [X,Y] :
( ~ product2(X,W,Y)
| ~ product2(X,Z,Y) )
| equalish(W,Z) ),
inference(miniscoping,[status(esa)],[f26]) ).
fof(f60,plain,
! [X0,X1,X2,X3] :
( ~ product2(X0,X1,X2)
| ~ product2(X0,X3,X2)
| equalish(X1,X3) ),
inference(cnf_transformation,[status(esa)],[f59]) ).
fof(f61,plain,
! [W,Z] :
( ! [Y,X] :
( ~ product2(W,Y,X)
| ~ product2(Z,Y,X) )
| equalish(W,Z) ),
inference(miniscoping,[status(esa)],[f27]) ).
fof(f62,plain,
! [X0,X1,X2,X3] :
( ~ product2(X0,X1,X2)
| ~ product2(X3,X1,X2)
| equalish(X0,X3) ),
inference(cnf_transformation,[status(esa)],[f61]) ).
fof(f63,plain,
! [X0] : product2(X0,X0,X0),
inference(cnf_transformation,[status(esa)],[f28]) ).
fof(f64,plain,
! [X,Y,Z2] :
( ! [Z1] :
( ~ product1(X,Y,Z1)
| ~ product1(Z1,X,Z2) )
| product2(Z2,Y,X) ),
inference(miniscoping,[status(esa)],[f29]) ).
fof(f65,plain,
! [X0,X1,X2,X3] :
( ~ product1(X0,X1,X2)
| ~ product1(X2,X0,X3)
| product2(X3,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f64]) ).
fof(f66,plain,
! [X0,X1] :
( ~ product1(X0,X1,X0)
| product2(X0,X1,X0) ),
inference(resolution,[status(thm)],[f55,f65]) ).
fof(f67,plain,
! [X0,X1] :
( ~ product2(e_1,X0,X1)
| ~ product2(e_2,X0,X1) ),
inference(resolution,[status(thm)],[f36,f62]) ).
fof(f68,plain,
! [X0,X1] :
( ~ product2(X0,e_1,X1)
| ~ product2(X0,e_2,X1) ),
inference(resolution,[status(thm)],[f36,f60]) ).
fof(f69,plain,
! [X0,X1] :
( ~ product2(X0,X1,e_1)
| ~ product2(X0,X1,e_2) ),
inference(resolution,[status(thm)],[f36,f58]) ).
fof(f70,plain,
! [X0,X1] :
( ~ product1(e_1,X0,X1)
| ~ product1(e_2,X0,X1) ),
inference(resolution,[status(thm)],[f36,f54]) ).
fof(f72,plain,
! [X0,X1] :
( ~ product1(X0,X1,e_1)
| ~ product1(X0,X1,e_2) ),
inference(resolution,[status(thm)],[f36,f50]) ).
fof(f73,plain,
~ product2(e_1,e_2,e_2),
inference(resolution,[status(thm)],[f67,f63]) ).
fof(f79,plain,
~ product2(e_2,e_1,e_2),
inference(resolution,[status(thm)],[f68,f63]) ).
fof(f85,plain,
~ product1(e_2,e_1,e_2),
inference(resolution,[status(thm)],[f79,f66]) ).
fof(f87,plain,
~ product2(e_2,e_2,e_1),
inference(resolution,[status(thm)],[f69,f63]) ).
fof(f93,plain,
~ product1(e_1,e_2,e_2),
inference(resolution,[status(thm)],[f70,f55]) ).
fof(f95,plain,
~ product1(e_2,e_2,e_1),
inference(resolution,[status(thm)],[f72,f55]) ).
fof(f97,plain,
! [X0,X1] :
( ~ product2(e_1,X0,X1)
| ~ product2(e_3,X0,X1) ),
inference(resolution,[status(thm)],[f37,f62]) ).
fof(f98,plain,
! [X0,X1] :
( ~ product2(X0,e_1,X1)
| ~ product2(X0,e_3,X1) ),
inference(resolution,[status(thm)],[f37,f60]) ).
fof(f99,plain,
! [X0,X1] :
( ~ product2(X0,X1,e_1)
| ~ product2(X0,X1,e_3) ),
inference(resolution,[status(thm)],[f37,f58]) ).
fof(f100,plain,
! [X0,X1] :
( ~ product1(e_1,X0,X1)
| ~ product1(e_3,X0,X1) ),
inference(resolution,[status(thm)],[f37,f54]) ).
fof(f101,plain,
! [X0,X1] :
( ~ product1(X0,e_1,X1)
| ~ product1(X0,e_3,X1) ),
inference(resolution,[status(thm)],[f37,f52]) ).
fof(f102,plain,
! [X0,X1] :
( ~ product1(X0,X1,e_1)
| ~ product1(X0,X1,e_3) ),
inference(resolution,[status(thm)],[f37,f50]) ).
fof(f103,plain,
~ product2(e_1,e_3,e_3),
inference(resolution,[status(thm)],[f97,f63]) ).
fof(f109,plain,
~ product2(e_3,e_1,e_3),
inference(resolution,[status(thm)],[f98,f63]) ).
fof(f115,plain,
~ product1(e_3,e_1,e_3),
inference(resolution,[status(thm)],[f109,f66]) ).
fof(f117,plain,
~ product2(e_3,e_3,e_1),
inference(resolution,[status(thm)],[f99,f63]) ).
fof(f123,plain,
~ product1(e_1,e_3,e_3),
inference(resolution,[status(thm)],[f100,f55]) ).
fof(f126,plain,
~ product1(e_3,e_3,e_1),
inference(resolution,[status(thm)],[f102,f55]) ).
fof(f127,plain,
! [X0,X1] :
( ~ product2(e_1,X0,X1)
| ~ product2(e_4,X0,X1) ),
inference(resolution,[status(thm)],[f38,f62]) ).
fof(f128,plain,
! [X0,X1] :
( ~ product2(X0,e_1,X1)
| ~ product2(X0,e_4,X1) ),
inference(resolution,[status(thm)],[f38,f60]) ).
fof(f129,plain,
! [X0,X1] :
( ~ product2(X0,X1,e_1)
| ~ product2(X0,X1,e_4) ),
inference(resolution,[status(thm)],[f38,f58]) ).
fof(f130,plain,
! [X0,X1] :
( ~ product1(e_1,X0,X1)
| ~ product1(e_4,X0,X1) ),
inference(resolution,[status(thm)],[f38,f54]) ).
fof(f132,plain,
! [X0,X1] :
( ~ product1(X0,X1,e_1)
| ~ product1(X0,X1,e_4) ),
inference(resolution,[status(thm)],[f38,f50]) ).
fof(f133,plain,
~ product2(e_1,e_4,e_4),
inference(resolution,[status(thm)],[f127,f63]) ).
fof(f137,plain,
~ product2(e_4,e_1,e_4),
inference(resolution,[status(thm)],[f128,f63]) ).
fof(f138,plain,
! [X0] :
( ~ product2(X0,e_1,X0)
| ~ product1(X0,e_4,X0) ),
inference(resolution,[status(thm)],[f128,f66]) ).
fof(f140,plain,
~ product1(e_4,e_1,e_4),
inference(resolution,[status(thm)],[f137,f66]) ).
fof(f142,plain,
~ product2(e_4,e_4,e_1),
inference(resolution,[status(thm)],[f129,f63]) ).
fof(f146,plain,
~ product1(e_1,e_4,e_4),
inference(resolution,[status(thm)],[f130,f55]) ).
fof(f148,plain,
~ product1(e_4,e_4,e_1),
inference(resolution,[status(thm)],[f132,f55]) ).
fof(f163,plain,
! [X0,X1] :
( ~ product2(e_2,X0,X1)
| ~ product2(e_3,X0,X1) ),
inference(resolution,[status(thm)],[f40,f62]) ).
fof(f164,plain,
! [X0,X1] :
( ~ product2(X0,e_2,X1)
| ~ product2(X0,e_3,X1) ),
inference(resolution,[status(thm)],[f40,f60]) ).
fof(f165,plain,
! [X0,X1] :
( ~ product2(X0,X1,e_2)
| ~ product2(X0,X1,e_3) ),
inference(resolution,[status(thm)],[f40,f58]) ).
fof(f166,plain,
! [X0,X1] :
( ~ product1(e_2,X0,X1)
| ~ product1(e_3,X0,X1) ),
inference(resolution,[status(thm)],[f40,f54]) ).
fof(f168,plain,
! [X0,X1] :
( ~ product1(X0,X1,e_2)
| ~ product1(X0,X1,e_3) ),
inference(resolution,[status(thm)],[f40,f50]) ).
fof(f169,plain,
~ product2(e_2,e_3,e_3),
inference(resolution,[status(thm)],[f163,f63]) ).
fof(f173,plain,
~ product2(e_3,e_2,e_3),
inference(resolution,[status(thm)],[f164,f63]) ).
fof(f174,plain,
! [X0] :
( ~ product2(X0,e_2,X0)
| ~ product1(X0,e_3,X0) ),
inference(resolution,[status(thm)],[f164,f66]) ).
fof(f176,plain,
~ product1(e_3,e_2,e_3),
inference(resolution,[status(thm)],[f173,f66]) ).
fof(f178,plain,
~ product2(e_3,e_3,e_2),
inference(resolution,[status(thm)],[f165,f63]) ).
fof(f181,plain,
~ product1(e_2,e_3,e_3),
inference(resolution,[status(thm)],[f166,f55]) ).
fof(f183,plain,
~ product1(e_3,e_3,e_2),
inference(resolution,[status(thm)],[f168,f55]) ).
fof(f189,plain,
! [X0,X1] :
( ~ product2(e_2,X0,X1)
| ~ product2(e_4,X0,X1) ),
inference(resolution,[status(thm)],[f41,f62]) ).
fof(f190,plain,
! [X0,X1] :
( ~ product2(X0,e_2,X1)
| ~ product2(X0,e_4,X1) ),
inference(resolution,[status(thm)],[f41,f60]) ).
fof(f191,plain,
! [X0,X1] :
( ~ product2(X0,X1,e_2)
| ~ product2(X0,X1,e_4) ),
inference(resolution,[status(thm)],[f41,f58]) ).
fof(f192,plain,
! [X0,X1] :
( ~ product1(e_2,X0,X1)
| ~ product1(e_4,X0,X1) ),
inference(resolution,[status(thm)],[f41,f54]) ).
fof(f194,plain,
! [X0,X1] :
( ~ product1(X0,X1,e_2)
| ~ product1(X0,X1,e_4) ),
inference(resolution,[status(thm)],[f41,f50]) ).
fof(f207,plain,
! [X0,X1] :
( ~ product2(e_3,X0,X1)
| ~ product2(e_4,X0,X1) ),
inference(resolution,[status(thm)],[f44,f62]) ).
fof(f208,plain,
! [X0,X1] :
( ~ product2(X0,e_3,X1)
| ~ product2(X0,e_4,X1) ),
inference(resolution,[status(thm)],[f44,f60]) ).
fof(f209,plain,
! [X0,X1] :
( ~ product2(X0,X1,e_3)
| ~ product2(X0,X1,e_4) ),
inference(resolution,[status(thm)],[f44,f58]) ).
fof(f210,plain,
! [X0,X1] :
( ~ product1(e_3,X0,X1)
| ~ product1(e_4,X0,X1) ),
inference(resolution,[status(thm)],[f44,f54]) ).
fof(f211,plain,
! [X0,X1] :
( ~ product1(X0,e_3,X1)
| ~ product1(X0,e_4,X1) ),
inference(resolution,[status(thm)],[f44,f52]) ).
fof(f212,plain,
! [X0,X1] :
( ~ product1(X0,X1,e_3)
| ~ product1(X0,X1,e_4) ),
inference(resolution,[status(thm)],[f44,f50]) ).
fof(f231,plain,
~ product2(e_2,e_4,e_4),
inference(resolution,[status(thm)],[f189,f63]) ).
fof(f235,plain,
~ product2(e_4,e_2,e_4),
inference(resolution,[status(thm)],[f190,f63]) ).
fof(f236,plain,
! [X0] :
( ~ product2(X0,e_2,X0)
| ~ product1(X0,e_4,X0) ),
inference(resolution,[status(thm)],[f190,f66]) ).
fof(f238,plain,
~ product1(e_4,e_2,e_4),
inference(resolution,[status(thm)],[f235,f66]) ).
fof(f240,plain,
~ product2(e_4,e_4,e_2),
inference(resolution,[status(thm)],[f191,f63]) ).
fof(f244,plain,
~ product1(e_2,e_4,e_4),
inference(resolution,[status(thm)],[f192,f55]) ).
fof(f246,plain,
~ product1(e_4,e_4,e_2),
inference(resolution,[status(thm)],[f194,f55]) ).
fof(f247,plain,
~ product2(e_3,e_4,e_4),
inference(resolution,[status(thm)],[f207,f63]) ).
fof(f251,plain,
~ product2(e_4,e_3,e_4),
inference(resolution,[status(thm)],[f208,f63]) ).
fof(f252,plain,
! [X0] :
( ~ product2(X0,e_3,X0)
| ~ product1(X0,e_4,X0) ),
inference(resolution,[status(thm)],[f208,f66]) ).
fof(f254,plain,
~ product1(e_4,e_3,e_4),
inference(resolution,[status(thm)],[f251,f66]) ).
fof(f256,plain,
~ product2(e_4,e_4,e_3),
inference(resolution,[status(thm)],[f209,f63]) ).
fof(f259,plain,
! [X0] :
( ~ product1(e_3,e_4,X0)
| ~ product1(X0,e_3,e_4) ),
inference(resolution,[status(thm)],[f256,f65]) ).
fof(f260,plain,
~ product1(e_3,e_4,e_4),
inference(resolution,[status(thm)],[f210,f55]) ).
fof(f262,plain,
~ product1(e_4,e_4,e_3),
inference(resolution,[status(thm)],[f212,f55]) ).
fof(f281,plain,
! [X0] :
( ~ group_element(X0)
| product1(X0,e_4,e_1)
| product1(X0,e_4,e_2)
| product1(X0,e_4,e_3)
| product1(X0,e_4,e_4) ),
inference(resolution,[status(thm)],[f48,f35]) ).
fof(f282,plain,
! [X0] :
( ~ group_element(X0)
| product1(X0,e_3,e_1)
| product1(X0,e_3,e_2)
| product1(X0,e_3,e_3)
| product1(X0,e_3,e_4) ),
inference(resolution,[status(thm)],[f48,f34]) ).
fof(f285,plain,
! [X0] :
( ~ group_element(X0)
| product2(X0,e_4,e_1)
| product2(X0,e_4,e_2)
| product2(X0,e_4,e_3)
| product2(X0,e_4,e_4) ),
inference(resolution,[status(thm)],[f56,f35]) ).
fof(f289,plain,
( spl0_0
<=> product1(e_4,e_4,e_1) ),
introduced(split_symbol_definition) ).
fof(f290,plain,
( product1(e_4,e_4,e_1)
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f289]) ).
fof(f292,plain,
( spl0_1
<=> product1(e_4,e_4,e_2) ),
introduced(split_symbol_definition) ).
fof(f293,plain,
( product1(e_4,e_4,e_2)
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f292]) ).
fof(f295,plain,
( spl0_2
<=> product1(e_4,e_4,e_3) ),
introduced(split_symbol_definition) ).
fof(f296,plain,
( product1(e_4,e_4,e_3)
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f295]) ).
fof(f298,plain,
( spl0_3
<=> product1(e_4,e_4,e_4) ),
introduced(split_symbol_definition) ).
fof(f301,plain,
( product1(e_4,e_4,e_1)
| product1(e_4,e_4,e_2)
| product1(e_4,e_4,e_3)
| product1(e_4,e_4,e_4) ),
inference(resolution,[status(thm)],[f281,f35]) ).
fof(f302,plain,
( spl0_0
| spl0_1
| spl0_2
| spl0_3 ),
inference(split_clause,[status(thm)],[f301,f289,f292,f295,f298]) ).
fof(f303,plain,
( spl0_4
<=> product1(e_3,e_4,e_1) ),
introduced(split_symbol_definition) ).
fof(f304,plain,
( product1(e_3,e_4,e_1)
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f303]) ).
fof(f306,plain,
( spl0_5
<=> product1(e_3,e_4,e_2) ),
introduced(split_symbol_definition) ).
fof(f307,plain,
( product1(e_3,e_4,e_2)
| ~ spl0_5 ),
inference(component_clause,[status(thm)],[f306]) ).
fof(f309,plain,
( spl0_6
<=> product1(e_3,e_4,e_3) ),
introduced(split_symbol_definition) ).
fof(f310,plain,
( product1(e_3,e_4,e_3)
| ~ spl0_6 ),
inference(component_clause,[status(thm)],[f309]) ).
fof(f312,plain,
( spl0_7
<=> product1(e_3,e_4,e_4) ),
introduced(split_symbol_definition) ).
fof(f313,plain,
( product1(e_3,e_4,e_4)
| ~ spl0_7 ),
inference(component_clause,[status(thm)],[f312]) ).
fof(f315,plain,
( product1(e_3,e_4,e_1)
| product1(e_3,e_4,e_2)
| product1(e_3,e_4,e_3)
| product1(e_3,e_4,e_4) ),
inference(resolution,[status(thm)],[f281,f34]) ).
fof(f316,plain,
( spl0_4
| spl0_5
| spl0_6
| spl0_7 ),
inference(split_clause,[status(thm)],[f315,f303,f306,f309,f312]) ).
fof(f317,plain,
( spl0_8
<=> product1(e_2,e_4,e_1) ),
introduced(split_symbol_definition) ).
fof(f318,plain,
( product1(e_2,e_4,e_1)
| ~ spl0_8 ),
inference(component_clause,[status(thm)],[f317]) ).
fof(f320,plain,
( spl0_9
<=> product1(e_2,e_4,e_2) ),
introduced(split_symbol_definition) ).
fof(f321,plain,
( product1(e_2,e_4,e_2)
| ~ spl0_9 ),
inference(component_clause,[status(thm)],[f320]) ).
fof(f323,plain,
( spl0_10
<=> product1(e_2,e_4,e_3) ),
introduced(split_symbol_definition) ).
fof(f324,plain,
( product1(e_2,e_4,e_3)
| ~ spl0_10 ),
inference(component_clause,[status(thm)],[f323]) ).
fof(f326,plain,
( spl0_11
<=> product1(e_2,e_4,e_4) ),
introduced(split_symbol_definition) ).
fof(f327,plain,
( product1(e_2,e_4,e_4)
| ~ spl0_11 ),
inference(component_clause,[status(thm)],[f326]) ).
fof(f329,plain,
( product1(e_2,e_4,e_1)
| product1(e_2,e_4,e_2)
| product1(e_2,e_4,e_3)
| product1(e_2,e_4,e_4) ),
inference(resolution,[status(thm)],[f281,f33]) ).
fof(f330,plain,
( spl0_8
| spl0_9
| spl0_10
| spl0_11 ),
inference(split_clause,[status(thm)],[f329,f317,f320,f323,f326]) ).
fof(f331,plain,
( spl0_12
<=> product1(e_1,e_4,e_1) ),
introduced(split_symbol_definition) ).
fof(f332,plain,
( product1(e_1,e_4,e_1)
| ~ spl0_12 ),
inference(component_clause,[status(thm)],[f331]) ).
fof(f334,plain,
( spl0_13
<=> product1(e_1,e_4,e_2) ),
introduced(split_symbol_definition) ).
fof(f335,plain,
( product1(e_1,e_4,e_2)
| ~ spl0_13 ),
inference(component_clause,[status(thm)],[f334]) ).
fof(f337,plain,
( spl0_14
<=> product1(e_1,e_4,e_3) ),
introduced(split_symbol_definition) ).
fof(f338,plain,
( product1(e_1,e_4,e_3)
| ~ spl0_14 ),
inference(component_clause,[status(thm)],[f337]) ).
fof(f340,plain,
( spl0_15
<=> product1(e_1,e_4,e_4) ),
introduced(split_symbol_definition) ).
fof(f341,plain,
( product1(e_1,e_4,e_4)
| ~ spl0_15 ),
inference(component_clause,[status(thm)],[f340]) ).
fof(f343,plain,
( product1(e_1,e_4,e_1)
| product1(e_1,e_4,e_2)
| product1(e_1,e_4,e_3)
| product1(e_1,e_4,e_4) ),
inference(resolution,[status(thm)],[f281,f32]) ).
fof(f344,plain,
( spl0_12
| spl0_13
| spl0_14
| spl0_15 ),
inference(split_clause,[status(thm)],[f343,f331,f334,f337,f340]) ).
fof(f345,plain,
( $false
| ~ spl0_15 ),
inference(forward_subsumption_resolution,[status(thm)],[f341,f146]) ).
fof(f346,plain,
~ spl0_15,
inference(contradiction_clause,[status(thm)],[f345]) ).
fof(f347,plain,
( $false
| ~ spl0_11 ),
inference(forward_subsumption_resolution,[status(thm)],[f327,f244]) ).
fof(f348,plain,
~ spl0_11,
inference(contradiction_clause,[status(thm)],[f347]) ).
fof(f349,plain,
( $false
| ~ spl0_7 ),
inference(forward_subsumption_resolution,[status(thm)],[f313,f260]) ).
fof(f350,plain,
~ spl0_7,
inference(contradiction_clause,[status(thm)],[f349]) ).
fof(f357,plain,
( spl0_18
<=> product1(e_4,e_3,e_3) ),
introduced(split_symbol_definition) ).
fof(f358,plain,
( product1(e_4,e_3,e_3)
| ~ spl0_18 ),
inference(component_clause,[status(thm)],[f357]) ).
fof(f360,plain,
( spl0_19
<=> product1(e_4,e_3,e_4) ),
introduced(split_symbol_definition) ).
fof(f361,plain,
( product1(e_4,e_3,e_4)
| ~ spl0_19 ),
inference(component_clause,[status(thm)],[f360]) ).
fof(f365,plain,
( spl0_20
<=> product1(e_3,e_3,e_1) ),
introduced(split_symbol_definition) ).
fof(f366,plain,
( product1(e_3,e_3,e_1)
| ~ spl0_20 ),
inference(component_clause,[status(thm)],[f365]) ).
fof(f368,plain,
( spl0_21
<=> product1(e_3,e_3,e_2) ),
introduced(split_symbol_definition) ).
fof(f369,plain,
( product1(e_3,e_3,e_2)
| ~ spl0_21 ),
inference(component_clause,[status(thm)],[f368]) ).
fof(f379,plain,
( spl0_24
<=> product1(e_2,e_3,e_1) ),
introduced(split_symbol_definition) ).
fof(f380,plain,
( product1(e_2,e_3,e_1)
| ~ spl0_24 ),
inference(component_clause,[status(thm)],[f379]) ).
fof(f382,plain,
( spl0_25
<=> product1(e_2,e_3,e_2) ),
introduced(split_symbol_definition) ).
fof(f383,plain,
( product1(e_2,e_3,e_2)
| ~ spl0_25 ),
inference(component_clause,[status(thm)],[f382]) ).
fof(f385,plain,
( spl0_26
<=> product1(e_2,e_3,e_3) ),
introduced(split_symbol_definition) ).
fof(f386,plain,
( product1(e_2,e_3,e_3)
| ~ spl0_26 ),
inference(component_clause,[status(thm)],[f385]) ).
fof(f388,plain,
( spl0_27
<=> product1(e_2,e_3,e_4) ),
introduced(split_symbol_definition) ).
fof(f389,plain,
( product1(e_2,e_3,e_4)
| ~ spl0_27 ),
inference(component_clause,[status(thm)],[f388]) ).
fof(f391,plain,
( product1(e_2,e_3,e_1)
| product1(e_2,e_3,e_2)
| product1(e_2,e_3,e_3)
| product1(e_2,e_3,e_4) ),
inference(resolution,[status(thm)],[f282,f33]) ).
fof(f392,plain,
( spl0_24
| spl0_25
| spl0_26
| spl0_27 ),
inference(split_clause,[status(thm)],[f391,f379,f382,f385,f388]) ).
fof(f393,plain,
( spl0_28
<=> product1(e_1,e_3,e_1) ),
introduced(split_symbol_definition) ).
fof(f394,plain,
( product1(e_1,e_3,e_1)
| ~ spl0_28 ),
inference(component_clause,[status(thm)],[f393]) ).
fof(f396,plain,
( spl0_29
<=> product1(e_1,e_3,e_2) ),
introduced(split_symbol_definition) ).
fof(f397,plain,
( product1(e_1,e_3,e_2)
| ~ spl0_29 ),
inference(component_clause,[status(thm)],[f396]) ).
fof(f399,plain,
( spl0_30
<=> product1(e_1,e_3,e_3) ),
introduced(split_symbol_definition) ).
fof(f400,plain,
( product1(e_1,e_3,e_3)
| ~ spl0_30 ),
inference(component_clause,[status(thm)],[f399]) ).
fof(f402,plain,
( spl0_31
<=> product1(e_1,e_3,e_4) ),
introduced(split_symbol_definition) ).
fof(f403,plain,
( product1(e_1,e_3,e_4)
| ~ spl0_31 ),
inference(component_clause,[status(thm)],[f402]) ).
fof(f405,plain,
( product1(e_1,e_3,e_1)
| product1(e_1,e_3,e_2)
| product1(e_1,e_3,e_3)
| product1(e_1,e_3,e_4) ),
inference(resolution,[status(thm)],[f282,f32]) ).
fof(f406,plain,
( spl0_28
| spl0_29
| spl0_30
| spl0_31 ),
inference(split_clause,[status(thm)],[f405,f393,f396,f399,f402]) ).
fof(f407,plain,
( $false
| ~ spl0_30 ),
inference(forward_subsumption_resolution,[status(thm)],[f400,f123]) ).
fof(f408,plain,
~ spl0_30,
inference(contradiction_clause,[status(thm)],[f407]) ).
fof(f409,plain,
( $false
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[status(thm)],[f386,f181]) ).
fof(f410,plain,
~ spl0_26,
inference(contradiction_clause,[status(thm)],[f409]) ).
fof(f411,plain,
( $false
| ~ spl0_21 ),
inference(forward_subsumption_resolution,[status(thm)],[f369,f183]) ).
fof(f412,plain,
~ spl0_21,
inference(contradiction_clause,[status(thm)],[f411]) ).
fof(f413,plain,
( $false
| ~ spl0_20 ),
inference(forward_subsumption_resolution,[status(thm)],[f366,f126]) ).
fof(f414,plain,
~ spl0_20,
inference(contradiction_clause,[status(thm)],[f413]) ).
fof(f415,plain,
( $false
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[status(thm)],[f361,f254]) ).
fof(f416,plain,
~ spl0_19,
inference(contradiction_clause,[status(thm)],[f415]) ).
fof(f426,plain,
( spl0_35
<=> product1(e_4,e_2,e_4) ),
introduced(split_symbol_definition) ).
fof(f427,plain,
( product1(e_4,e_2,e_4)
| ~ spl0_35 ),
inference(component_clause,[status(thm)],[f426]) ).
fof(f437,plain,
( spl0_38
<=> product1(e_3,e_2,e_3) ),
introduced(split_symbol_definition) ).
fof(f438,plain,
( product1(e_3,e_2,e_3)
| ~ spl0_38 ),
inference(component_clause,[status(thm)],[f437]) ).
fof(f445,plain,
( spl0_40
<=> product1(e_2,e_2,e_1) ),
introduced(split_symbol_definition) ).
fof(f446,plain,
( product1(e_2,e_2,e_1)
| ~ spl0_40 ),
inference(component_clause,[status(thm)],[f445]) ).
fof(f462,plain,
( spl0_45
<=> product1(e_1,e_2,e_2) ),
introduced(split_symbol_definition) ).
fof(f463,plain,
( product1(e_1,e_2,e_2)
| ~ spl0_45 ),
inference(component_clause,[status(thm)],[f462]) ).
fof(f473,plain,
( $false
| ~ spl0_45 ),
inference(forward_subsumption_resolution,[status(thm)],[f463,f93]) ).
fof(f474,plain,
~ spl0_45,
inference(contradiction_clause,[status(thm)],[f473]) ).
fof(f475,plain,
( $false
| ~ spl0_40 ),
inference(forward_subsumption_resolution,[status(thm)],[f446,f95]) ).
fof(f476,plain,
~ spl0_40,
inference(contradiction_clause,[status(thm)],[f475]) ).
fof(f477,plain,
( $false
| ~ spl0_38 ),
inference(forward_subsumption_resolution,[status(thm)],[f438,f176]) ).
fof(f478,plain,
~ spl0_38,
inference(contradiction_clause,[status(thm)],[f477]) ).
fof(f479,plain,
( $false
| ~ spl0_35 ),
inference(forward_subsumption_resolution,[status(thm)],[f427,f238]) ).
fof(f480,plain,
~ spl0_35,
inference(contradiction_clause,[status(thm)],[f479]) ).
fof(f481,plain,
( spl0_48
<=> product1(e_4,e_1,e_1) ),
introduced(split_symbol_definition) ).
fof(f482,plain,
( product1(e_4,e_1,e_1)
| ~ spl0_48 ),
inference(component_clause,[status(thm)],[f481]) ).
fof(f490,plain,
( spl0_51
<=> product1(e_4,e_1,e_4) ),
introduced(split_symbol_definition) ).
fof(f491,plain,
( product1(e_4,e_1,e_4)
| ~ spl0_51 ),
inference(component_clause,[status(thm)],[f490]) ).
fof(f501,plain,
( spl0_54
<=> product1(e_3,e_1,e_3) ),
introduced(split_symbol_definition) ).
fof(f502,plain,
( product1(e_3,e_1,e_3)
| ~ spl0_54 ),
inference(component_clause,[status(thm)],[f501]) ).
fof(f512,plain,
( spl0_57
<=> product1(e_2,e_1,e_2) ),
introduced(split_symbol_definition) ).
fof(f513,plain,
( product1(e_2,e_1,e_2)
| ~ spl0_57 ),
inference(component_clause,[status(thm)],[f512]) ).
fof(f537,plain,
( $false
| ~ spl0_57 ),
inference(forward_subsumption_resolution,[status(thm)],[f513,f85]) ).
fof(f538,plain,
~ spl0_57,
inference(contradiction_clause,[status(thm)],[f537]) ).
fof(f539,plain,
( $false
| ~ spl0_54 ),
inference(forward_subsumption_resolution,[status(thm)],[f502,f115]) ).
fof(f540,plain,
~ spl0_54,
inference(contradiction_clause,[status(thm)],[f539]) ).
fof(f541,plain,
( $false
| ~ spl0_51 ),
inference(forward_subsumption_resolution,[status(thm)],[f491,f140]) ).
fof(f542,plain,
~ spl0_51,
inference(contradiction_clause,[status(thm)],[f541]) ).
fof(f543,plain,
( spl0_64
<=> product2(e_4,e_4,e_1) ),
introduced(split_symbol_definition) ).
fof(f544,plain,
( product2(e_4,e_4,e_1)
| ~ spl0_64 ),
inference(component_clause,[status(thm)],[f543]) ).
fof(f546,plain,
( spl0_65
<=> product2(e_4,e_4,e_2) ),
introduced(split_symbol_definition) ).
fof(f547,plain,
( product2(e_4,e_4,e_2)
| ~ spl0_65 ),
inference(component_clause,[status(thm)],[f546]) ).
fof(f549,plain,
( spl0_66
<=> product2(e_4,e_4,e_3) ),
introduced(split_symbol_definition) ).
fof(f550,plain,
( product2(e_4,e_4,e_3)
| ~ spl0_66 ),
inference(component_clause,[status(thm)],[f549]) ).
fof(f552,plain,
( spl0_67
<=> product2(e_4,e_4,e_4) ),
introduced(split_symbol_definition) ).
fof(f555,plain,
( product2(e_4,e_4,e_1)
| product2(e_4,e_4,e_2)
| product2(e_4,e_4,e_3)
| product2(e_4,e_4,e_4) ),
inference(resolution,[status(thm)],[f285,f35]) ).
fof(f556,plain,
( spl0_64
| spl0_65
| spl0_66
| spl0_67 ),
inference(split_clause,[status(thm)],[f555,f543,f546,f549,f552]) ).
fof(f566,plain,
( spl0_71
<=> product2(e_3,e_4,e_4) ),
introduced(split_symbol_definition) ).
fof(f567,plain,
( product2(e_3,e_4,e_4)
| ~ spl0_71 ),
inference(component_clause,[status(thm)],[f566]) ).
fof(f574,plain,
( spl0_73
<=> product2(e_2,e_4,e_2) ),
introduced(split_symbol_definition) ).
fof(f575,plain,
( product2(e_2,e_4,e_2)
| ~ spl0_73 ),
inference(component_clause,[status(thm)],[f574]) ).
fof(f580,plain,
( spl0_75
<=> product2(e_2,e_4,e_4) ),
introduced(split_symbol_definition) ).
fof(f581,plain,
( product2(e_2,e_4,e_4)
| ~ spl0_75 ),
inference(component_clause,[status(thm)],[f580]) ).
fof(f585,plain,
( spl0_76
<=> product2(e_1,e_4,e_1) ),
introduced(split_symbol_definition) ).
fof(f586,plain,
( product2(e_1,e_4,e_1)
| ~ spl0_76 ),
inference(component_clause,[status(thm)],[f585]) ).
fof(f594,plain,
( spl0_79
<=> product2(e_1,e_4,e_4) ),
introduced(split_symbol_definition) ).
fof(f595,plain,
( product2(e_1,e_4,e_4)
| ~ spl0_79 ),
inference(component_clause,[status(thm)],[f594]) ).
fof(f599,plain,
( $false
| ~ spl0_79 ),
inference(forward_subsumption_resolution,[status(thm)],[f595,f133]) ).
fof(f600,plain,
~ spl0_79,
inference(contradiction_clause,[status(thm)],[f599]) ).
fof(f601,plain,
( $false
| ~ spl0_75 ),
inference(forward_subsumption_resolution,[status(thm)],[f581,f231]) ).
fof(f602,plain,
~ spl0_75,
inference(contradiction_clause,[status(thm)],[f601]) ).
fof(f603,plain,
( $false
| ~ spl0_71 ),
inference(forward_subsumption_resolution,[status(thm)],[f567,f247]) ).
fof(f604,plain,
~ spl0_71,
inference(contradiction_clause,[status(thm)],[f603]) ).
fof(f605,plain,
( $false
| ~ spl0_66 ),
inference(forward_subsumption_resolution,[status(thm)],[f550,f256]) ).
fof(f606,plain,
~ spl0_66,
inference(contradiction_clause,[status(thm)],[f605]) ).
fof(f607,plain,
( $false
| ~ spl0_65 ),
inference(forward_subsumption_resolution,[status(thm)],[f547,f240]) ).
fof(f608,plain,
~ spl0_65,
inference(contradiction_clause,[status(thm)],[f607]) ).
fof(f609,plain,
( $false
| ~ spl0_64 ),
inference(forward_subsumption_resolution,[status(thm)],[f544,f142]) ).
fof(f610,plain,
~ spl0_64,
inference(contradiction_clause,[status(thm)],[f609]) ).
fof(f617,plain,
( spl0_82
<=> product2(e_4,e_3,e_3) ),
introduced(split_symbol_definition) ).
fof(f618,plain,
( product2(e_4,e_3,e_3)
| ~ spl0_82 ),
inference(component_clause,[status(thm)],[f617]) ).
fof(f620,plain,
( spl0_83
<=> product2(e_4,e_3,e_4) ),
introduced(split_symbol_definition) ).
fof(f621,plain,
( product2(e_4,e_3,e_4)
| ~ spl0_83 ),
inference(component_clause,[status(thm)],[f620]) ).
fof(f625,plain,
( spl0_84
<=> product2(e_3,e_3,e_1) ),
introduced(split_symbol_definition) ).
fof(f626,plain,
( product2(e_3,e_3,e_1)
| ~ spl0_84 ),
inference(component_clause,[status(thm)],[f625]) ).
fof(f628,plain,
( spl0_85
<=> product2(e_3,e_3,e_2) ),
introduced(split_symbol_definition) ).
fof(f629,plain,
( product2(e_3,e_3,e_2)
| ~ spl0_85 ),
inference(component_clause,[status(thm)],[f628]) ).
fof(f645,plain,
( spl0_90
<=> product2(e_2,e_3,e_3) ),
introduced(split_symbol_definition) ).
fof(f646,plain,
( product2(e_2,e_3,e_3)
| ~ spl0_90 ),
inference(component_clause,[status(thm)],[f645]) ).
fof(f659,plain,
( spl0_94
<=> product2(e_1,e_3,e_3) ),
introduced(split_symbol_definition) ).
fof(f660,plain,
( product2(e_1,e_3,e_3)
| ~ spl0_94 ),
inference(component_clause,[status(thm)],[f659]) ).
fof(f667,plain,
( $false
| ~ spl0_94 ),
inference(forward_subsumption_resolution,[status(thm)],[f660,f103]) ).
fof(f668,plain,
~ spl0_94,
inference(contradiction_clause,[status(thm)],[f667]) ).
fof(f669,plain,
( $false
| ~ spl0_90 ),
inference(forward_subsumption_resolution,[status(thm)],[f646,f169]) ).
fof(f670,plain,
~ spl0_90,
inference(contradiction_clause,[status(thm)],[f669]) ).
fof(f671,plain,
( $false
| ~ spl0_85 ),
inference(forward_subsumption_resolution,[status(thm)],[f629,f178]) ).
fof(f672,plain,
~ spl0_85,
inference(contradiction_clause,[status(thm)],[f671]) ).
fof(f673,plain,
( $false
| ~ spl0_84 ),
inference(forward_subsumption_resolution,[status(thm)],[f626,f117]) ).
fof(f674,plain,
~ spl0_84,
inference(contradiction_clause,[status(thm)],[f673]) ).
fof(f675,plain,
( $false
| ~ spl0_83 ),
inference(forward_subsumption_resolution,[status(thm)],[f621,f251]) ).
fof(f676,plain,
~ spl0_83,
inference(contradiction_clause,[status(thm)],[f675]) ).
fof(f686,plain,
( spl0_99
<=> product2(e_4,e_2,e_4) ),
introduced(split_symbol_definition) ).
fof(f687,plain,
( product2(e_4,e_2,e_4)
| ~ spl0_99 ),
inference(component_clause,[status(thm)],[f686]) ).
fof(f697,plain,
( spl0_102
<=> product2(e_3,e_2,e_3) ),
introduced(split_symbol_definition) ).
fof(f698,plain,
( product2(e_3,e_2,e_3)
| ~ spl0_102 ),
inference(component_clause,[status(thm)],[f697]) ).
fof(f705,plain,
( spl0_104
<=> product2(e_2,e_2,e_1) ),
introduced(split_symbol_definition) ).
fof(f706,plain,
( product2(e_2,e_2,e_1)
| ~ spl0_104 ),
inference(component_clause,[status(thm)],[f705]) ).
fof(f722,plain,
( spl0_109
<=> product2(e_1,e_2,e_2) ),
introduced(split_symbol_definition) ).
fof(f723,plain,
( product2(e_1,e_2,e_2)
| ~ spl0_109 ),
inference(component_clause,[status(thm)],[f722]) ).
fof(f733,plain,
( $false
| ~ spl0_109 ),
inference(forward_subsumption_resolution,[status(thm)],[f723,f73]) ).
fof(f734,plain,
~ spl0_109,
inference(contradiction_clause,[status(thm)],[f733]) ).
fof(f735,plain,
( $false
| ~ spl0_104 ),
inference(forward_subsumption_resolution,[status(thm)],[f706,f87]) ).
fof(f736,plain,
~ spl0_104,
inference(contradiction_clause,[status(thm)],[f735]) ).
fof(f737,plain,
( $false
| ~ spl0_102 ),
inference(forward_subsumption_resolution,[status(thm)],[f698,f173]) ).
fof(f738,plain,
~ spl0_102,
inference(contradiction_clause,[status(thm)],[f737]) ).
fof(f739,plain,
( $false
| ~ spl0_99 ),
inference(forward_subsumption_resolution,[status(thm)],[f687,f235]) ).
fof(f740,plain,
~ spl0_99,
inference(contradiction_clause,[status(thm)],[f739]) ).
fof(f750,plain,
( spl0_115
<=> product2(e_4,e_1,e_4) ),
introduced(split_symbol_definition) ).
fof(f751,plain,
( product2(e_4,e_1,e_4)
| ~ spl0_115 ),
inference(component_clause,[status(thm)],[f750]) ).
fof(f761,plain,
( spl0_118
<=> product2(e_3,e_1,e_3) ),
introduced(split_symbol_definition) ).
fof(f762,plain,
( product2(e_3,e_1,e_3)
| ~ spl0_118 ),
inference(component_clause,[status(thm)],[f761]) ).
fof(f772,plain,
( spl0_121
<=> product2(e_2,e_1,e_2) ),
introduced(split_symbol_definition) ).
fof(f773,plain,
( product2(e_2,e_1,e_2)
| ~ spl0_121 ),
inference(component_clause,[status(thm)],[f772]) ).
fof(f797,plain,
( $false
| ~ spl0_121 ),
inference(forward_subsumption_resolution,[status(thm)],[f773,f79]) ).
fof(f798,plain,
~ spl0_121,
inference(contradiction_clause,[status(thm)],[f797]) ).
fof(f799,plain,
( $false
| ~ spl0_118 ),
inference(forward_subsumption_resolution,[status(thm)],[f762,f109]) ).
fof(f800,plain,
~ spl0_118,
inference(contradiction_clause,[status(thm)],[f799]) ).
fof(f801,plain,
( $false
| ~ spl0_115 ),
inference(forward_subsumption_resolution,[status(thm)],[f751,f137]) ).
fof(f802,plain,
~ spl0_115,
inference(contradiction_clause,[status(thm)],[f801]) ).
fof(f825,plain,
( ~ product1(e_1,e_3,e_2)
| ~ spl0_13 ),
inference(resolution,[status(thm)],[f335,f211]) ).
fof(f826,plain,
( $false
| ~ spl0_29
| ~ spl0_13 ),
inference(forward_subsumption_resolution,[status(thm)],[f825,f397]) ).
fof(f827,plain,
( ~ spl0_29
| ~ spl0_13 ),
inference(contradiction_clause,[status(thm)],[f826]) ).
fof(f856,plain,
( ~ product1(e_2,e_3,e_1)
| ~ spl0_8 ),
inference(resolution,[status(thm)],[f318,f211]) ).
fof(f857,plain,
( $false
| ~ spl0_24
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[status(thm)],[f856,f380]) ).
fof(f858,plain,
( ~ spl0_24
| ~ spl0_8 ),
inference(contradiction_clause,[status(thm)],[f857]) ).
fof(f874,plain,
( ~ product2(e_2,e_2,e_2)
| ~ spl0_9 ),
inference(resolution,[status(thm)],[f321,f236]) ).
fof(f875,plain,
( $false
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[status(thm)],[f874,f63]) ).
fof(f876,plain,
~ spl0_9,
inference(contradiction_clause,[status(thm)],[f875]) ).
fof(f885,plain,
( ~ product1(e_2,e_3,e_4)
| ~ spl0_5 ),
inference(resolution,[status(thm)],[f307,f259]) ).
fof(f886,plain,
( $false
| ~ spl0_27
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[status(thm)],[f885,f389]) ).
fof(f887,plain,
( ~ spl0_27
| ~ spl0_5 ),
inference(contradiction_clause,[status(thm)],[f886]) ).
fof(f888,plain,
( ~ product1(e_1,e_3,e_4)
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f304,f259]) ).
fof(f889,plain,
( $false
| ~ spl0_31
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f888,f403]) ).
fof(f890,plain,
( ~ spl0_31
| ~ spl0_4 ),
inference(contradiction_clause,[status(thm)],[f889]) ).
fof(f892,plain,
( ~ product1(e_2,e_4,e_1)
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f304,f166]) ).
fof(f893,plain,
( ~ spl0_8
| ~ spl0_4 ),
inference(split_clause,[status(thm)],[f892,f317,f303]) ).
fof(f904,plain,
( ~ product1(e_1,e_4,e_2)
| ~ spl0_5 ),
inference(resolution,[status(thm)],[f307,f100]) ).
fof(f905,plain,
( ~ spl0_13
| ~ spl0_5 ),
inference(split_clause,[status(thm)],[f904,f334,f306]) ).
fof(f922,plain,
( ~ product2(e_1,e_1,e_1)
| ~ spl0_12 ),
inference(resolution,[status(thm)],[f332,f138]) ).
fof(f923,plain,
( $false
| ~ spl0_12 ),
inference(forward_subsumption_resolution,[status(thm)],[f922,f63]) ).
fof(f924,plain,
~ spl0_12,
inference(contradiction_clause,[status(thm)],[f923]) ).
fof(f931,plain,
( ~ product1(e_1,e_4,e_3)
| ~ spl0_10 ),
inference(resolution,[status(thm)],[f324,f70]) ).
fof(f952,plain,
( ~ product2(e_2,e_2,e_2)
| ~ spl0_25 ),
inference(resolution,[status(thm)],[f383,f174]) ).
fof(f953,plain,
( $false
| ~ spl0_25 ),
inference(forward_subsumption_resolution,[status(thm)],[f952,f63]) ).
fof(f954,plain,
~ spl0_25,
inference(contradiction_clause,[status(thm)],[f953]) ).
fof(f958,plain,
( ~ product1(e_3,e_3,e_3)
| ~ spl0_18 ),
inference(resolution,[status(thm)],[f358,f210]) ).
fof(f959,plain,
( $false
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[status(thm)],[f958,f55]) ).
fof(f960,plain,
~ spl0_18,
inference(contradiction_clause,[status(thm)],[f959]) ).
fof(f1022,plain,
( ~ product1(e_1,e_1,e_1)
| ~ spl0_48 ),
inference(resolution,[status(thm)],[f482,f130]) ).
fof(f1023,plain,
( $false
| ~ spl0_48 ),
inference(forward_subsumption_resolution,[status(thm)],[f1022,f55]) ).
fof(f1024,plain,
~ spl0_48,
inference(contradiction_clause,[status(thm)],[f1023]) ).
fof(f1036,plain,
( ~ product2(e_1,e_1,e_1)
| ~ spl0_76 ),
inference(resolution,[status(thm)],[f586,f128]) ).
fof(f1037,plain,
( $false
| ~ spl0_76 ),
inference(forward_subsumption_resolution,[status(thm)],[f1036,f63]) ).
fof(f1038,plain,
~ spl0_76,
inference(contradiction_clause,[status(thm)],[f1037]) ).
fof(f1057,plain,
( ~ product2(e_2,e_2,e_2)
| ~ spl0_73 ),
inference(resolution,[status(thm)],[f575,f190]) ).
fof(f1058,plain,
( $false
| ~ spl0_73 ),
inference(forward_subsumption_resolution,[status(thm)],[f1057,f63]) ).
fof(f1059,plain,
~ spl0_73,
inference(contradiction_clause,[status(thm)],[f1058]) ).
fof(f1097,plain,
( ~ product2(e_3,e_3,e_3)
| ~ spl0_82 ),
inference(resolution,[status(thm)],[f618,f207]) ).
fof(f1098,plain,
( $false
| ~ spl0_82 ),
inference(forward_subsumption_resolution,[status(thm)],[f1097,f63]) ).
fof(f1099,plain,
~ spl0_82,
inference(contradiction_clause,[status(thm)],[f1098]) ).
fof(f1156,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[status(thm)],[f296,f262]) ).
fof(f1157,plain,
~ spl0_2,
inference(contradiction_clause,[status(thm)],[f1156]) ).
fof(f1158,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f293,f246]) ).
fof(f1159,plain,
~ spl0_1,
inference(contradiction_clause,[status(thm)],[f1158]) ).
fof(f1160,plain,
( $false
| ~ spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f290,f148]) ).
fof(f1161,plain,
~ spl0_0,
inference(contradiction_clause,[status(thm)],[f1160]) ).
fof(f1200,plain,
( ~ product1(e_1,e_1,e_1)
| ~ spl0_28 ),
inference(resolution,[status(thm)],[f394,f101]) ).
fof(f1201,plain,
( $false
| ~ spl0_28 ),
inference(forward_subsumption_resolution,[status(thm)],[f1200,f55]) ).
fof(f1202,plain,
~ spl0_28,
inference(contradiction_clause,[status(thm)],[f1201]) ).
fof(f1219,plain,
( ~ product2(e_3,e_3,e_3)
| ~ spl0_6 ),
inference(resolution,[status(thm)],[f310,f252]) ).
fof(f1220,plain,
( $false
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[status(thm)],[f1219,f63]) ).
fof(f1221,plain,
~ spl0_6,
inference(contradiction_clause,[status(thm)],[f1220]) ).
fof(f1234,plain,
( $false
| ~ spl0_10
| ~ spl0_14 ),
inference(forward_subsumption_resolution,[status(thm)],[f338,f931]) ).
fof(f1235,plain,
( ~ spl0_10
| ~ spl0_14 ),
inference(contradiction_clause,[status(thm)],[f1234]) ).
fof(f1236,plain,
$false,
inference(sat_refutation,[status(thm)],[f302,f316,f330,f344,f346,f348,f350,f392,f406,f408,f410,f412,f414,f416,f474,f476,f478,f480,f538,f540,f542,f556,f600,f602,f604,f606,f608,f610,f668,f670,f672,f674,f676,f734,f736,f738,f740,f798,f800,f802,f827,f858,f876,f887,f890,f893,f905,f924,f954,f960,f1024,f1038,f1059,f1099,f1157,f1159,f1161,f1202,f1221,f1235]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP124-9.004 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue May 30 11:29:25 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Drodi V3.5.1
% 0.20/0.41 % Refutation found
% 0.20/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.20/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.42 % Elapsed time: 0.070564 seconds
% 0.20/0.42 % CPU time: 0.434972 seconds
% 0.20/0.42 % Memory used: 7.768 MB
%------------------------------------------------------------------------------