%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP350-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 12:33:29 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.45s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 123
% Syntax : Number of formulae : 533 ( 11 unt; 69 def)
% Number of atoms : 1644 ( 625 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 2078 ( 967 ~;1042 |; 0 &)
% ( 69 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 71 ( 69 usr; 70 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 112 ( 112 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c10,sk_c11) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c10,sk_c11) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c10,sk_c11) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c10,sk_c11) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c10,sk_c11) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c10,sk_c11) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c10,sk_c11) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c7) = sk_c6
| multiply(sk_c10,sk_c11) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c6) = sk_c8
| multiply(sk_c10,sk_c11) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c10,sk_c11) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c3) = sk_c11
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c7) = sk_c6
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( inverse(sk_c6) = sk_c8
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c9,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c9,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c9,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c9,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c9,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c9,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( inverse(sk_c3) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,negated_conjecture,
( inverse(sk_c7) = sk_c6
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,negated_conjecture,
( inverse(sk_c6) = sk_c8
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f56,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f57,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f63,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f64,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f65,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f66,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f67,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f73,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f74,negated_conjecture,
! [X3,X4,X1,X2,X5,X6,X7,X8] :
( multiply(X7,X6) != X8
| inverse(X8) != X6
| inverse(X7) != X8
| multiply(X6,sk_c10) != sk_c11
| inverse(X5) != X6
| multiply(X5,X6) != sk_c11
| inverse(X2) != sk_c10
| multiply(X2,sk_c10) != sk_c9
| inverse(X1) != sk_c11
| multiply(X1,sk_c11) != sk_c10
| multiply(X4,sk_c9) != sk_c10
| inverse(X4) != sk_c10
| multiply(X3,sk_c10) != sk_c11
| inverse(X3) != sk_c11
| multiply(sk_c9,sk_c11) != sk_c10
| inverse(sk_c10) != sk_c9
| multiply(sk_c10,sk_c11) != sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f75,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f76,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f77,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f78,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f79,plain,
( inverse(sk_c3) = sk_c11
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f80,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f81,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f82,plain,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f83,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f84,plain,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f85,plain,
( inverse(sk_c7) = sk_c6
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f86,plain,
( inverse(sk_c6) = sk_c8
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f87,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f88,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f89,plain,
( inverse(sk_c3) = sk_c11
| inverse(sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f90,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f91,plain,
( inverse(sk_c4) = sk_c10
| inverse(sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f92,plain,
( multiply(sk_c5,sk_c8) = sk_c11
| inverse(sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f93,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f94,plain,
( multiply(sk_c8,sk_c10) = sk_c11
| inverse(sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f95,plain,
( inverse(sk_c7) = sk_c6
| inverse(sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f96,plain,
( inverse(sk_c6) = sk_c8
| inverse(sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f97,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f98,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c9,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f99,plain,
( inverse(sk_c3) = sk_c11
| multiply(sk_c9,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f100,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c9,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f101,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c9,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f102,plain,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c9,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f103,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c9,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f108,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f109,plain,
( inverse(sk_c3) = sk_c11
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f110,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f111,plain,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f112,plain,
( multiply(sk_c5,sk_c8) = sk_c11
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f113,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f114,plain,
( multiply(sk_c8,sk_c10) = sk_c11
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f115,plain,
( inverse(sk_c7) = sk_c6
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f116,plain,
( inverse(sk_c6) = sk_c8
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f117,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f118,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f119,plain,
( inverse(sk_c3) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f120,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f121,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f122,plain,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f123,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f130,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f131,plain,
( inverse(sk_c4) = sk_c10
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f137,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f138,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f139,plain,
( inverse(sk_c3) = sk_c11
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f140,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f141,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f147,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f148,plain,
! [X6,X7,X8] :
( multiply(X7,X6) != X8
| inverse(X8) != X6
| inverse(X7) != X8
| multiply(X6,sk_c10) != sk_c11
| ! [X5] :
( inverse(X5) != X6
| multiply(X5,X6) != sk_c11
| ! [X2] :
( inverse(X2) != sk_c10
| multiply(X2,sk_c10) != sk_c9
| ! [X1] :
( inverse(X1) != sk_c11
| multiply(X1,sk_c11) != sk_c10
| ! [X4] :
( multiply(X4,sk_c9) != sk_c10
| inverse(X4) != sk_c10
| ! [X3] :
( multiply(X3,sk_c10) != sk_c11
| inverse(X3) != sk_c11
| multiply(sk_c9,sk_c11) != sk_c10
| inverse(sk_c10) != sk_c9
| multiply(sk_c10,sk_c11) != sk_c9 ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f74]) ).
fof(f149,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( multiply(X6,X5) != X7
| inverse(X7) != X5
| inverse(X6) != X7
| multiply(X5,sk_c10) != sk_c11
| inverse(X4) != X5
| multiply(X4,X5) != sk_c11
| inverse(X3) != sk_c10
| multiply(X3,sk_c10) != sk_c9
| inverse(X2) != sk_c11
| multiply(X2,sk_c11) != sk_c10
| multiply(X1,sk_c9) != sk_c10
| inverse(X1) != sk_c10
| multiply(X0,sk_c10) != sk_c11
| inverse(X0) != sk_c11
| multiply(sk_c9,sk_c11) != sk_c10
| inverse(sk_c10) != sk_c9
| multiply(sk_c10,sk_c11) != sk_c9 ),
inference(cnf_transformation,[status(thm)],[f148]) ).
fof(f150,definition,
( sQ0_spl
<=> multiply(sk_c10,sk_c11) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f151,plain,
( ~ sQ0_spl
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(component_clause,[status(thm)],[f150]) ).
fof(f152,plain,
( sQ0_spl
| multiply(sk_c10,sk_c11) != sk_c9 ),
inference(component_clause,[status(thm)],[f150]) ).
fof(f153,definition,
( sQ1_spl
<=> multiply(sk_c3,sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f154,plain,
( ~ sQ1_spl
| multiply(sk_c3,sk_c11) = sk_c10 ),
inference(component_clause,[status(thm)],[f153]) ).
fof(f156,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f78,f150,f153]) ).
fof(f157,definition,
( sQ2_spl
<=> inverse(sk_c3) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f158,plain,
( ~ sQ2_spl
| inverse(sk_c3) = sk_c11 ),
inference(component_clause,[status(thm)],[f157]) ).
fof(f160,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f79,f150,f157]) ).
fof(f161,definition,
( sQ3_spl
<=> multiply(sk_c4,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f162,plain,
( ~ sQ3_spl
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(component_clause,[status(thm)],[f161]) ).
fof(f164,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f80,f150,f161]) ).
fof(f165,definition,
( sQ4_spl
<=> inverse(sk_c4) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f166,plain,
( ~ sQ4_spl
| inverse(sk_c4) = sk_c10 ),
inference(component_clause,[status(thm)],[f165]) ).
fof(f168,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f81,f150,f165]) ).
fof(f169,definition,
( sQ5_spl
<=> multiply(sk_c5,sk_c8) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f170,plain,
( ~ sQ5_spl
| multiply(sk_c5,sk_c8) = sk_c11 ),
inference(component_clause,[status(thm)],[f169]) ).
fof(f172,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f82,f150,f169]) ).
fof(f173,definition,
( sQ6_spl
<=> inverse(sk_c5) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f174,plain,
( ~ sQ6_spl
| inverse(sk_c5) = sk_c8 ),
inference(component_clause,[status(thm)],[f173]) ).
fof(f176,plain,
( sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f83,f150,f173]) ).
fof(f177,definition,
( sQ7_spl
<=> multiply(sk_c8,sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f178,plain,
( ~ sQ7_spl
| multiply(sk_c8,sk_c10) = sk_c11 ),
inference(component_clause,[status(thm)],[f177]) ).
fof(f180,plain,
( sQ7_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f84,f150,f177]) ).
fof(f181,definition,
( sQ8_spl
<=> inverse(sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f182,plain,
( ~ sQ8_spl
| inverse(sk_c7) = sk_c6 ),
inference(component_clause,[status(thm)],[f181]) ).
fof(f184,plain,
( sQ8_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f85,f150,f181]) ).
fof(f185,definition,
( sQ9_spl
<=> inverse(sk_c6) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f186,plain,
( ~ sQ9_spl
| inverse(sk_c6) = sk_c8 ),
inference(component_clause,[status(thm)],[f185]) ).
fof(f188,plain,
( sQ9_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f86,f150,f185]) ).
fof(f189,definition,
( sQ10_spl
<=> multiply(sk_c7,sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f190,plain,
( ~ sQ10_spl
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(component_clause,[status(thm)],[f189]) ).
fof(f192,plain,
( sQ10_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f87,f150,f189]) ).
fof(f193,definition,
( sQ11_spl
<=> inverse(sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f194,plain,
( ~ sQ11_spl
| inverse(sk_c10) = sk_c9 ),
inference(component_clause,[status(thm)],[f193]) ).
fof(f195,plain,
( sQ11_spl
| inverse(sk_c10) != sk_c9 ),
inference(component_clause,[status(thm)],[f193]) ).
fof(f196,plain,
( sQ1_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f88,f193,f153]) ).
fof(f197,plain,
( sQ2_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f89,f193,f157]) ).
fof(f198,plain,
( sQ3_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f90,f193,f161]) ).
fof(f199,plain,
( sQ4_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f91,f193,f165]) ).
fof(f200,plain,
( sQ5_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f92,f193,f169]) ).
fof(f201,plain,
( sQ6_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f93,f193,f173]) ).
fof(f202,plain,
( sQ7_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f94,f193,f177]) ).
fof(f203,plain,
( sQ8_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f95,f193,f181]) ).
fof(f204,plain,
( sQ9_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f96,f193,f185]) ).
fof(f205,plain,
( sQ10_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f97,f193,f189]) ).
fof(f206,definition,
( sQ12_spl
<=> multiply(sk_c9,sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f207,plain,
( ~ sQ12_spl
| multiply(sk_c9,sk_c11) = sk_c10 ),
inference(component_clause,[status(thm)],[f206]) ).
fof(f208,plain,
( sQ12_spl
| multiply(sk_c9,sk_c11) != sk_c10 ),
inference(component_clause,[status(thm)],[f206]) ).
fof(f209,plain,
( sQ1_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f98,f206,f153]) ).
fof(f210,plain,
( sQ2_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f99,f206,f157]) ).
fof(f211,plain,
( sQ3_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f100,f206,f161]) ).
fof(f212,plain,
( sQ4_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f101,f206,f165]) ).
fof(f213,plain,
( sQ5_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f102,f206,f169]) ).
fof(f214,plain,
( sQ6_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f103,f206,f173]) ).
fof(f219,definition,
( sQ13_spl
<=> inverse(sk_c1) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f220,plain,
( ~ sQ13_spl
| inverse(sk_c1) = sk_c11 ),
inference(component_clause,[status(thm)],[f219]) ).
fof(f222,plain,
( sQ1_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f108,f219,f153]) ).
fof(f223,plain,
( sQ2_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f109,f219,f157]) ).
fof(f224,plain,
( sQ3_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f110,f219,f161]) ).
fof(f225,plain,
( sQ4_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f111,f219,f165]) ).
fof(f226,plain,
( sQ5_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f112,f219,f169]) ).
fof(f227,plain,
( sQ6_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f113,f219,f173]) ).
fof(f228,plain,
( sQ7_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f114,f219,f177]) ).
fof(f229,plain,
( sQ8_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f115,f219,f181]) ).
fof(f230,plain,
( sQ9_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f116,f219,f185]) ).
fof(f231,plain,
( sQ10_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f117,f219,f189]) ).
fof(f232,definition,
( sQ14_spl
<=> multiply(sk_c1,sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f233,plain,
( ~ sQ14_spl
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(component_clause,[status(thm)],[f232]) ).
fof(f235,plain,
( sQ1_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f118,f232,f153]) ).
fof(f236,plain,
( sQ2_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f119,f232,f157]) ).
fof(f237,plain,
( sQ3_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f120,f232,f161]) ).
fof(f238,plain,
( sQ4_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f121,f232,f165]) ).
fof(f239,plain,
( sQ5_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f122,f232,f169]) ).
fof(f240,plain,
( sQ6_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f123,f232,f173]) ).
fof(f245,definition,
( sQ15_spl
<=> inverse(sk_c2) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f246,plain,
( ~ sQ15_spl
| inverse(sk_c2) = sk_c10 ),
inference(component_clause,[status(thm)],[f245]) ).
fof(f250,plain,
( sQ3_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f130,f245,f161]) ).
fof(f251,plain,
( sQ4_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f131,f245,f165]) ).
fof(f257,plain,
( sQ10_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f137,f245,f189]) ).
fof(f258,definition,
( sQ16_spl
<=> multiply(sk_c2,sk_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f259,plain,
( ~ sQ16_spl
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(component_clause,[status(thm)],[f258]) ).
fof(f261,plain,
( sQ1_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f138,f258,f153]) ).
fof(f262,plain,
( sQ2_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f139,f258,f157]) ).
fof(f263,plain,
( sQ3_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f140,f258,f161]) ).
fof(f264,plain,
( sQ4_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f141,f258,f165]) ).
fof(f270,plain,
( sQ10_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f147,f258,f189]) ).
fof(f271,definition,
! [X0] :
( sQ17_spl
<=> ( multiply(X0,sk_c10) != sk_c11
| inverse(X0) != sk_c11 ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f272,plain,
! [X0] :
( ~ sQ17_spl
| multiply(X0,sk_c10) != sk_c11
| inverse(X0) != sk_c11 ),
inference(component_clause,[status(thm)],[f271]) ).
fof(f274,definition,
! [X1] :
( sQ18_spl
<=> ( multiply(X1,sk_c9) != sk_c10
| inverse(X1) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f275,plain,
! [X0] :
( ~ sQ18_spl
| multiply(X0,sk_c9) != sk_c10
| inverse(X0) != sk_c10 ),
inference(component_clause,[status(thm)],[f274]) ).
fof(f277,definition,
! [X2] :
( sQ19_spl
<=> ( inverse(X2) != sk_c11
| multiply(X2,sk_c11) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f278,plain,
! [X0] :
( ~ sQ19_spl
| inverse(X0) != sk_c11
| multiply(X0,sk_c11) != sk_c10 ),
inference(component_clause,[status(thm)],[f277]) ).
fof(f280,definition,
! [X3] :
( sQ20_spl
<=> ( inverse(X3) != sk_c10
| multiply(X3,sk_c10) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f281,plain,
! [X0] :
( ~ sQ20_spl
| inverse(X0) != sk_c10
| multiply(X0,sk_c10) != sk_c9 ),
inference(component_clause,[status(thm)],[f280]) ).
fof(f283,definition,
! [X4,X5,X6,X7] :
( sQ21_spl
<=> ( multiply(X6,X5) != X7
| inverse(X7) != X5
| inverse(X6) != X7
| multiply(X5,sk_c10) != sk_c11
| inverse(X4) != X5
| multiply(X4,X5) != sk_c11 ) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f284,plain,
! [X0,X1,X2,X3] :
( ~ sQ21_spl
| multiply(X2,X1) != X3
| inverse(X3) != X1
| inverse(X2) != X3
| multiply(X1,sk_c10) != sk_c11
| inverse(X0) != X1
| multiply(X0,X1) != sk_c11 ),
inference(component_clause,[status(thm)],[f283]) ).
fof(f286,plain,
( sQ21_spl
| sQ20_spl
| sQ19_spl
| sQ18_spl
| sQ17_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f149,f150,f193,f206,f271,f274,f277,f280,f283]) ).
fof(f294,plain,
( ~ sQ8_spl
| multiply(sk_c6,sk_c7) = identity ),
inference(paramodulation,[status(thm)],[f182,f76]) ).
fof(f295,plain,
( ~ sQ9_spl
| multiply(sk_c8,sk_c6) = identity ),
inference(paramodulation,[status(thm)],[f186,f76]) ).
fof(f296,plain,
( ~ sQ13_spl
| multiply(sk_c11,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f220,f76]) ).
fof(f298,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f76,f77]) ).
fof(f299,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f75,f298]) ).
fof(f300,plain,
! [X0] :
( ~ sQ10_spl
| multiply(sk_c6,X0) = multiply(sk_c7,multiply(sk_c8,X0)) ),
inference(paramodulation,[status(thm)],[f190,f77]) ).
fof(f301,plain,
! [X0] :
( ~ sQ7_spl
| multiply(sk_c11,X0) = multiply(sk_c8,multiply(sk_c10,X0)) ),
inference(paramodulation,[status(thm)],[f178,f77]) ).
fof(f302,plain,
( ~ sQ4_spl
| multiply(sk_c10,sk_c4) = identity ),
inference(paramodulation,[status(thm)],[f166,f76]) ).
fof(f303,plain,
! [X0] :
( ~ sQ5_spl
| multiply(sk_c11,X0) = multiply(sk_c5,multiply(sk_c8,X0)) ),
inference(paramodulation,[status(thm)],[f170,f77]) ).
fof(f307,plain,
! [X0] :
( ~ sQ1_spl
| multiply(sk_c10,X0) = multiply(sk_c3,multiply(sk_c11,X0)) ),
inference(paramodulation,[status(thm)],[f154,f77]) ).
fof(f308,plain,
! [X0] :
( ~ sQ12_spl
| multiply(sk_c10,X0) = multiply(sk_c9,multiply(sk_c11,X0)) ),
inference(paramodulation,[status(thm)],[f207,f77]) ).
fof(f317,plain,
! [X0,X1,X2] :
( ~ sQ21_spl
| multiply(X1,identity) != X2
| inverse(X2) != identity
| inverse(X1) != X2
| sk_c10 != sk_c11
| inverse(X0) != identity
| multiply(X0,identity) != sk_c11 ),
inference(paramodulation,[status(thm)],[f75,f284]) ).
fof(f319,plain,
! [X0,X1,X2,X3,X4] :
( ~ sQ21_spl
| multiply(X3,multiply(X1,X2)) != X4
| inverse(X4) != multiply(X1,X2)
| inverse(X3) != X4
| multiply(X1,multiply(X2,sk_c10)) != sk_c11
| inverse(X0) != multiply(X1,X2)
| multiply(X0,multiply(X1,X2)) != sk_c11 ),
inference(paramodulation,[status(thm)],[f77,f284]) ).
fof(f320,definition,
! [X0] :
( sQ22_spl
<=> ( inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c11 ) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f321,plain,
! [X0] :
( ~ sQ22_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c11 ),
inference(component_clause,[status(thm)],[f320]) ).
fof(f327,definition,
! [X0] :
( sQ24_spl
<=> ( inverse(X0) != sk_c1
| multiply(X0,sk_c1) != sk_c11 ) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f328,plain,
! [X0] :
( ~ sQ24_spl
| inverse(X0) != sk_c1
| multiply(X0,sk_c1) != sk_c11 ),
inference(component_clause,[status(thm)],[f327]) ).
fof(f334,definition,
! [X0] :
( sQ26_spl
<=> ( inverse(X0) != sk_c4
| multiply(X0,sk_c4) != sk_c11 ) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f335,plain,
! [X0] :
( ~ sQ26_spl
| inverse(X0) != sk_c4
| multiply(X0,sk_c4) != sk_c11 ),
inference(component_clause,[status(thm)],[f334]) ).
fof(f337,definition,
( sQ27_spl
<=> sk_c9 = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f339,plain,
( sQ27_spl
| sk_c9 != sk_c11 ),
inference(component_clause,[status(thm)],[f337]) ).
fof(f340,definition,
! [X1,X2] :
( sQ28_spl
<=> ( multiply(X1,sk_c4) != X2
| inverse(X2) != sk_c4
| inverse(X1) != X2 ) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f341,plain,
! [X0,X1] :
( ~ sQ28_spl
| multiply(X0,sk_c4) != X1
| inverse(X1) != sk_c4
| inverse(X0) != X1 ),
inference(component_clause,[status(thm)],[f340]) ).
fof(f344,definition,
( sQ29_spl
<=> sk_c11 = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f346,plain,
( sQ29_spl
| sk_c11 != sk_c11 ),
inference(component_clause,[status(thm)],[f344]) ).
fof(f348,definition,
! [X0] :
( sQ30_spl
<=> ( inverse(X0) != inverse(sk_c10)
| multiply(X0,inverse(sk_c10)) != sk_c11 ) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f349,plain,
! [X0] :
( ~ sQ30_spl
| inverse(X0) != inverse(sk_c10)
| multiply(X0,inverse(sk_c10)) != sk_c11 ),
inference(component_clause,[status(thm)],[f348]) ).
fof(f351,definition,
( sQ31_spl
<=> identity = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f353,plain,
( sQ31_spl
| identity != sk_c11 ),
inference(component_clause,[status(thm)],[f351]) ).
fof(f354,definition,
! [X1,X2] :
( sQ32_spl
<=> ( multiply(X1,inverse(sk_c10)) != X2
| inverse(X2) != inverse(sk_c10)
| inverse(X1) != X2 ) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f355,plain,
! [X0,X1] :
( ~ sQ32_spl
| multiply(X0,inverse(sk_c10)) != X1
| inverse(X1) != inverse(sk_c10)
| inverse(X0) != X1 ),
inference(component_clause,[status(thm)],[f354]) ).
fof(f358,definition,
! [X0] :
( sQ33_spl
<=> ( inverse(X0) != identity
| multiply(X0,identity) != sk_c11 ) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f359,plain,
! [X0] :
( ~ sQ33_spl
| inverse(X0) != identity
| multiply(X0,identity) != sk_c11 ),
inference(component_clause,[status(thm)],[f358]) ).
fof(f361,definition,
( sQ34_spl
<=> sk_c10 = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f362,plain,
( ~ sQ34_spl
| sk_c10 = sk_c11 ),
inference(component_clause,[status(thm)],[f361]) ).
fof(f363,plain,
( sQ34_spl
| sk_c10 != sk_c11 ),
inference(component_clause,[status(thm)],[f361]) ).
fof(f364,definition,
! [X1,X2] :
( sQ35_spl
<=> ( multiply(X1,identity) != X2
| inverse(X2) != identity
| inverse(X1) != X2 ) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f365,plain,
! [X0,X1] :
( ~ sQ35_spl
| multiply(X0,identity) != X1
| inverse(X1) != identity
| inverse(X0) != X1 ),
inference(component_clause,[status(thm)],[f364]) ).
fof(f367,plain,
( ~ sQ21_spl
| sQ35_spl
| ~ sQ34_spl
| sQ33_spl ),
inference(split_clause,[status(thm)],[f317,f358,f361,f364,f283]) ).
fof(f373,plain,
( ~ sQ20_spl
| inverse(inverse(sk_c10)) != sk_c10
| identity != sk_c9 ),
inference(paramodulation,[status(thm)],[f76,f281]) ).
fof(f374,plain,
( ~ sQ20_spl
| inverse(identity) != sk_c10
| sk_c10 != sk_c9 ),
inference(paramodulation,[status(thm)],[f75,f281]) ).
fof(f375,plain,
( ~ sQ14_spl
| ~ sQ20_spl
| inverse(sk_c1) != sk_c10
| sk_c11 != sk_c9 ),
inference(paramodulation,[status(thm)],[f233,f281]) ).
fof(f376,plain,
! [X0,X1] :
( ~ sQ20_spl
| inverse(multiply(X0,X1)) != sk_c10
| multiply(X0,multiply(X1,sk_c10)) != sk_c9 ),
inference(paramodulation,[status(thm)],[f77,f281]) ).
fof(f377,definition,
( sQ36_spl
<=> identity = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f378,plain,
( ~ sQ36_spl
| identity = sk_c9 ),
inference(component_clause,[status(thm)],[f377]) ).
fof(f379,plain,
( sQ36_spl
| identity != sk_c9 ),
inference(component_clause,[status(thm)],[f377]) ).
fof(f380,definition,
( sQ37_spl
<=> inverse(inverse(sk_c10)) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f383,plain,
( ~ sQ20_spl
| ~ sQ37_spl
| ~ sQ36_spl ),
inference(split_clause,[status(thm)],[f373,f377,f380,f280]) ).
fof(f384,definition,
( sQ38_spl
<=> sk_c10 = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f385,plain,
( ~ sQ38_spl
| sk_c10 = sk_c9 ),
inference(component_clause,[status(thm)],[f384]) ).
fof(f386,plain,
( sQ38_spl
| sk_c10 != sk_c9 ),
inference(component_clause,[status(thm)],[f384]) ).
fof(f387,definition,
( sQ39_spl
<=> inverse(identity) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f389,plain,
( sQ39_spl
| inverse(identity) != sk_c10 ),
inference(component_clause,[status(thm)],[f387]) ).
fof(f390,plain,
( ~ sQ20_spl
| ~ sQ39_spl
| ~ sQ38_spl ),
inference(split_clause,[status(thm)],[f374,f384,f387,f280]) ).
fof(f391,definition,
( sQ40_spl
<=> inverse(sk_c1) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f393,plain,
( sQ40_spl
| inverse(sk_c1) != sk_c10 ),
inference(component_clause,[status(thm)],[f391]) ).
fof(f394,plain,
( ~ sQ14_spl
| ~ sQ20_spl
| ~ sQ40_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f375,f337,f391,f280,f232]) ).
fof(f395,plain,
( sQ40_spl
| ~ sQ13_spl
| sk_c11 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f220,f393]) ).
fof(f398,plain,
( ~ sQ1_spl
| ~ sQ19_spl
| inverse(sk_c3) != sk_c11 ),
inference(resolution,[status(thm)],[f278,f154]) ).
fof(f399,plain,
( ~ sQ0_spl
| ~ sQ19_spl
| inverse(sk_c10) != sk_c11
| sk_c9 != sk_c10 ),
inference(paramodulation,[status(thm)],[f151,f278]) ).
fof(f403,plain,
( ~ sQ19_spl
| inverse(identity) != sk_c11
| sk_c11 != sk_c10 ),
inference(paramodulation,[status(thm)],[f75,f278]) ).
fof(f405,plain,
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ2_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f158,f398]) ).
fof(f406,plain,
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f405]) ).
fof(f407,plain,
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f406]) ).
fof(f408,plain,
( ~ sQ16_spl
| ~ sQ18_spl
| inverse(sk_c2) != sk_c10 ),
inference(resolution,[status(thm)],[f275,f259]) ).
fof(f409,plain,
( ~ sQ18_spl
| identity != sk_c10
| inverse(inverse(sk_c9)) != sk_c10 ),
inference(paramodulation,[status(thm)],[f76,f275]) ).
fof(f410,plain,
( ~ sQ18_spl
| sk_c9 != sk_c10
| inverse(identity) != sk_c10 ),
inference(paramodulation,[status(thm)],[f75,f275]) ).
fof(f413,plain,
( ~ sQ16_spl
| ~ sQ18_spl
| ~ sQ15_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f246,f408]) ).
fof(f414,plain,
( ~ sQ16_spl
| ~ sQ18_spl
| ~ sQ15_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f413]) ).
fof(f415,plain,
( ~ sQ16_spl
| ~ sQ18_spl
| ~ sQ15_spl ),
inference(contradiction_clause,[status(thm)],[f414]) ).
fof(f416,plain,
( ~ sQ17_spl
| identity != sk_c11
| inverse(inverse(sk_c10)) != sk_c11 ),
inference(paramodulation,[status(thm)],[f76,f272]) ).
fof(f417,plain,
( ~ sQ17_spl
| sk_c10 != sk_c11
| inverse(identity) != sk_c11 ),
inference(paramodulation,[status(thm)],[f75,f272]) ).
fof(f419,definition,
( sQ41_spl
<=> inverse(inverse(sk_c10)) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f422,plain,
( ~ sQ17_spl
| ~ sQ31_spl
| ~ sQ41_spl ),
inference(split_clause,[status(thm)],[f416,f419,f351,f271]) ).
fof(f423,definition,
( sQ42_spl
<=> inverse(identity) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f425,plain,
( sQ42_spl
| inverse(identity) != sk_c11 ),
inference(component_clause,[status(thm)],[f423]) ).
fof(f426,plain,
( ~ sQ17_spl
| ~ sQ34_spl
| ~ sQ42_spl ),
inference(split_clause,[status(thm)],[f417,f423,f361,f271]) ).
fof(f428,plain,
( ~ sQ3_spl
| ~ sQ17_spl
| sk_c9 != sk_c11
| inverse(sk_c4) != sk_c11 ),
inference(paramodulation,[status(thm)],[f162,f272]) ).
fof(f430,definition,
( sQ43_spl
<=> inverse(sk_c4) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f432,plain,
( sQ43_spl
| inverse(sk_c4) != sk_c11 ),
inference(component_clause,[status(thm)],[f430]) ).
fof(f433,plain,
( ~ sQ3_spl
| ~ sQ17_spl
| ~ sQ27_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f428,f430,f337,f271,f161]) ).
fof(f434,plain,
( sQ43_spl
| ~ sQ4_spl
| sk_c10 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f166,f432]) ).
fof(f437,plain,
( ~ sQ11_spl
| multiply(sk_c9,sk_c10) = identity ),
inference(paramodulation,[status(thm)],[f194,f76]) ).
fof(f444,plain,
( ~ sQ3_spl
| ~ sQ20_spl
| inverse(sk_c4) != sk_c10 ),
inference(resolution,[status(thm)],[f281,f162]) ).
fof(f451,plain,
( ~ sQ3_spl
| ~ sQ20_spl
| ~ sQ4_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f166,f444]) ).
fof(f452,plain,
( ~ sQ3_spl
| ~ sQ20_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f451]) ).
fof(f453,plain,
( ~ sQ3_spl
| ~ sQ20_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f452]) ).
fof(f454,plain,
( ~ sQ14_spl
| ~ sQ17_spl
| inverse(sk_c1) != sk_c11 ),
inference(resolution,[status(thm)],[f272,f233]) ).
fof(f462,plain,
( ~ sQ14_spl
| ~ sQ17_spl
| ~ sQ13_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f220,f454]) ).
fof(f463,plain,
( ~ sQ14_spl
| ~ sQ17_spl
| ~ sQ13_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f462]) ).
fof(f464,plain,
( ~ sQ14_spl
| ~ sQ17_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f463]) ).
fof(f472,plain,
( sQ29_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f346]) ).
fof(f473,plain,
sQ29_spl,
inference(contradiction_clause,[status(thm)],[f472]) ).
fof(f495,plain,
! [X0] :
( ~ sQ2_spl
| X0 = multiply(sk_c11,multiply(sk_c3,X0)) ),
inference(paramodulation,[status(thm)],[f158,f299]) ).
fof(f497,plain,
! [X0] :
( ~ sQ6_spl
| X0 = multiply(sk_c8,multiply(sk_c5,X0)) ),
inference(paramodulation,[status(thm)],[f174,f299]) ).
fof(f502,plain,
( ~ sQ8_spl
| sk_c7 = multiply(inverse(sk_c6),identity) ),
inference(paramodulation,[status(thm)],[f294,f299]) ).
fof(f504,plain,
( ~ sQ0_spl
| sk_c11 = multiply(inverse(sk_c10),sk_c9) ),
inference(paramodulation,[status(thm)],[f151,f299]) ).
fof(f506,plain,
( ~ sQ3_spl
| sk_c10 = multiply(inverse(sk_c4),sk_c9) ),
inference(paramodulation,[status(thm)],[f162,f299]) ).
fof(f507,plain,
( ~ sQ1_spl
| sk_c11 = multiply(inverse(sk_c3),sk_c10) ),
inference(paramodulation,[status(thm)],[f154,f299]) ).
fof(f512,plain,
( ~ sQ10_spl
| sk_c8 = multiply(inverse(sk_c7),sk_c6) ),
inference(paramodulation,[status(thm)],[f190,f299]) ).
fof(f520,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 = multiply(sk_c8,identity) ),
inference(forward_demodulation,[status(thm)],[f186,f502]) ).
fof(f522,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| sk_c11 = multiply(sk_c9,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f194,f504]) ).
fof(f523,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c10 = multiply(sk_c10,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f166,f506]) ).
fof(f524,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c11 = multiply(sk_c11,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f158,f507]) ).
fof(f526,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| sk_c8 = multiply(sk_c6,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f182,f512]) ).
fof(f561,plain,
( ~ sQ35_spl
| inverse(identity) != identity
| inverse(identity) != identity ),
inference(resolution,[status(thm)],[f365,f75]) ).
fof(f597,definition,
( sQ53_spl
<=> inverse(inverse(identity)) = identity ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f599,plain,
( sQ53_spl
| inverse(inverse(identity)) != identity ),
inference(component_clause,[status(thm)],[f597]) ).
fof(f600,definition,
( sQ54_spl
<=> inverse(identity) = identity ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f602,plain,
( sQ54_spl
| inverse(identity) != identity ),
inference(component_clause,[status(thm)],[f600]) ).
fof(f604,plain,
( ~ sQ35_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f561,f600,f364]) ).
fof(f621,plain,
( ~ sQ33_spl
| inverse(identity) != identity
| identity != sk_c11 ),
inference(paramodulation,[status(thm)],[f75,f359]) ).
fof(f624,plain,
( ~ sQ33_spl
| ~ sQ54_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f621,f351,f600,f358]) ).
fof(f639,plain,
( ~ sQ4_spl
| ~ sQ28_spl
| inverse(identity) != sk_c4
| inverse(sk_c10) != identity ),
inference(resolution,[status(thm)],[f341,f302]) ).
fof(f666,definition,
( sQ61_spl
<=> inverse(sk_c10) = identity ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f668,plain,
( sQ61_spl
| inverse(sk_c10) != identity ),
inference(component_clause,[status(thm)],[f666]) ).
fof(f669,definition,
( sQ62_spl
<=> inverse(identity) = sk_c4 ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f671,plain,
( sQ62_spl
| inverse(identity) != sk_c4 ),
inference(component_clause,[status(thm)],[f669]) ).
fof(f672,plain,
( ~ sQ4_spl
| ~ sQ28_spl
| ~ sQ62_spl
| ~ sQ61_spl ),
inference(split_clause,[status(thm)],[f639,f666,f669,f340,f165]) ).
fof(f676,definition,
( sQ64_spl
<=> inverse(multiply(sk_c3,multiply(sk_c11,sk_c4))) = sk_c4 ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f678,plain,
( sQ64_spl
| inverse(multiply(sk_c3,multiply(sk_c11,sk_c4))) != sk_c4 ),
inference(component_clause,[status(thm)],[f676]) ).
fof(f687,definition,
( sQ67_spl
<=> inverse(inverse(sk_c4)) = identity ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f689,plain,
( sQ67_spl
| inverse(inverse(sk_c4)) != identity ),
inference(component_clause,[status(thm)],[f687]) ).
fof(f691,definition,
( sQ68_spl
<=> inverse(sk_c4) = sk_c4 ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f693,plain,
( sQ68_spl
| inverse(sk_c4) != sk_c4 ),
inference(component_clause,[status(thm)],[f691]) ).
fof(f702,plain,
( sQ68_spl
| ~ sQ4_spl
| sk_c10 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f166,f693]) ).
fof(f710,plain,
( sQ64_spl
| ~ sQ1_spl
| inverse(multiply(sk_c10,sk_c4)) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f307,f678]) ).
fof(f711,plain,
( sQ64_spl
| ~ sQ1_spl
| ~ sQ4_spl
| inverse(identity) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f302,f710]) ).
fof(f721,plain,
( ~ sQ4_spl
| ~ sQ26_spl
| inverse(sk_c10) != sk_c4
| identity != sk_c11 ),
inference(paramodulation,[status(thm)],[f302,f335]) ).
fof(f722,plain,
( ~ sQ26_spl
| inverse(inverse(sk_c4)) != sk_c4
| identity != sk_c11 ),
inference(paramodulation,[status(thm)],[f76,f335]) ).
fof(f725,definition,
( sQ69_spl
<=> inverse(sk_c10) = sk_c4 ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f727,plain,
( sQ69_spl
| inverse(sk_c10) != sk_c4 ),
inference(component_clause,[status(thm)],[f725]) ).
fof(f728,plain,
( ~ sQ4_spl
| ~ sQ26_spl
| ~ sQ69_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f721,f351,f725,f334,f165]) ).
fof(f729,definition,
( sQ70_spl
<=> inverse(inverse(sk_c4)) = sk_c4 ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f731,plain,
( sQ70_spl
| inverse(inverse(sk_c4)) != sk_c4 ),
inference(component_clause,[status(thm)],[f729]) ).
fof(f732,plain,
( ~ sQ26_spl
| ~ sQ70_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f722,f351,f729,f334]) ).
fof(f818,plain,
( ~ sQ13_spl
| ~ sQ24_spl
| inverse(sk_c11) != sk_c1
| identity != sk_c11 ),
inference(paramodulation,[status(thm)],[f296,f328]) ).
fof(f819,plain,
( ~ sQ24_spl
| inverse(inverse(sk_c1)) != sk_c1
| identity != sk_c11 ),
inference(paramodulation,[status(thm)],[f76,f328]) ).
fof(f822,definition,
( sQ84_spl
<=> inverse(sk_c11) = sk_c1 ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f825,plain,
( ~ sQ13_spl
| ~ sQ24_spl
| ~ sQ84_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f818,f351,f822,f327,f219]) ).
fof(f826,definition,
( sQ85_spl
<=> inverse(inverse(sk_c1)) = sk_c1 ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f829,plain,
( ~ sQ24_spl
| ~ sQ85_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f819,f351,f826,f327]) ).
fof(f837,plain,
( ~ sQ14_spl
| sk_c10 = multiply(inverse(sk_c1),sk_c11) ),
inference(paramodulation,[status(thm)],[f233,f299]) ).
fof(f841,plain,
( ~ sQ14_spl
| ~ sQ13_spl
| sk_c10 = multiply(sk_c11,sk_c11) ),
inference(forward_demodulation,[status(thm)],[f220,f837]) ).
fof(f931,plain,
( ~ sQ5_spl
| ~ sQ22_spl
| inverse(sk_c5) != sk_c8 ),
inference(resolution,[status(thm)],[f321,f170]) ).
fof(f934,plain,
( ~ sQ22_spl
| inverse(inverse(sk_c8)) != sk_c8
| identity != sk_c11 ),
inference(paramodulation,[status(thm)],[f76,f321]) ).
fof(f937,plain,
( ~ sQ5_spl
| ~ sQ22_spl
| ~ sQ6_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f174,f931]) ).
fof(f938,plain,
( ~ sQ5_spl
| ~ sQ22_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f937]) ).
fof(f939,plain,
( ~ sQ5_spl
| ~ sQ22_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f938]) ).
fof(f940,plain,
( ~ sQ30_spl
| inverse(inverse(inverse(sk_c10))) != inverse(sk_c10)
| identity != sk_c11 ),
inference(paramodulation,[status(thm)],[f76,f349]) ).
fof(f941,plain,
( ~ sQ30_spl
| inverse(identity) != inverse(sk_c10)
| inverse(sk_c10) != sk_c11 ),
inference(paramodulation,[status(thm)],[f75,f349]) ).
fof(f943,definition,
( sQ100_spl
<=> inverse(inverse(inverse(sk_c10))) = inverse(sk_c10) ),
introduced(definition,[new_symbols(definition,[sQ100_spl])],[split_symbol_definition]) ).
fof(f946,plain,
( ~ sQ30_spl
| ~ sQ100_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f940,f351,f943,f348]) ).
fof(f947,definition,
( sQ101_spl
<=> inverse(sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ101_spl])],[split_symbol_definition]) ).
fof(f949,plain,
( sQ101_spl
| inverse(sk_c10) != sk_c11 ),
inference(component_clause,[status(thm)],[f947]) ).
fof(f950,definition,
( sQ102_spl
<=> inverse(identity) = inverse(sk_c10) ),
introduced(definition,[new_symbols(definition,[sQ102_spl])],[split_symbol_definition]) ).
fof(f952,plain,
( sQ102_spl
| inverse(identity) != inverse(sk_c10) ),
inference(component_clause,[status(thm)],[f950]) ).
fof(f953,plain,
( ~ sQ30_spl
| ~ sQ102_spl
| ~ sQ101_spl ),
inference(split_clause,[status(thm)],[f941,f947,f950,f348]) ).
fof(f958,plain,
( ~ sQ32_spl
| inverse(identity) != inverse(sk_c10)
| inverse(inverse(inverse(sk_c10))) != identity ),
inference(resolution,[status(thm)],[f355,f76]) ).
fof(f959,plain,
( ~ sQ32_spl
| inverse(inverse(sk_c10)) != inverse(sk_c10)
| inverse(identity) != inverse(sk_c10) ),
inference(resolution,[status(thm)],[f355,f75]) ).
fof(f995,definition,
( sQ111_spl
<=> inverse(inverse(inverse(sk_c10))) = identity ),
introduced(definition,[new_symbols(definition,[sQ111_spl])],[split_symbol_definition]) ).
fof(f998,plain,
( ~ sQ32_spl
| ~ sQ102_spl
| ~ sQ111_spl ),
inference(split_clause,[status(thm)],[f958,f995,f950,f354]) ).
fof(f999,definition,
( sQ112_spl
<=> inverse(inverse(sk_c10)) = inverse(sk_c10) ),
introduced(definition,[new_symbols(definition,[sQ112_spl])],[split_symbol_definition]) ).
fof(f1002,plain,
( ~ sQ32_spl
| ~ sQ112_spl
| ~ sQ102_spl ),
inference(split_clause,[status(thm)],[f959,f950,f999,f354]) ).
fof(f1090,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c9 = multiply(inverse(sk_c10),sk_c10) ),
inference(paramodulation,[status(thm)],[f523,f299]) ).
fof(f1094,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c9 = identity ),
inference(forward_demodulation,[status(thm)],[f76,f1090]) ).
fof(f1095,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sQ36_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1094,f379]) ).
fof(f1096,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sQ36_spl ),
inference(contradiction_clause,[status(thm)],[f1095]) ).
fof(f1102,plain,
( sQ11_spl
| ~ sQ3_spl
| ~ sQ4_spl
| inverse(sk_c10) != identity ),
inference(backward_demodulation,[status(thm)],[f1094,f195]) ).
fof(f1105,plain,
( ~ sQ12_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(identity,sk_c11) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f1094,f207]) ).
fof(f1108,plain,
( sQ27_spl
| ~ sQ3_spl
| ~ sQ4_spl
| identity != sk_c11 ),
inference(backward_demodulation,[status(thm)],[f1094,f339]) ).
fof(f1114,plain,
( ~ sQ12_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c11 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f75,f1105]) ).
fof(f1115,plain,
( ~ sQ12_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sQ34_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1114,f363]) ).
fof(f1116,plain,
( ~ sQ12_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sQ34_spl ),
inference(contradiction_clause,[status(thm)],[f1115]) ).
fof(f1117,plain,
( sQ12_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(identity,sk_c11) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1094,f208]) ).
fof(f1118,plain,
( sQ12_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c11 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f75,f1117]) ).
fof(f1134,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c10 = multiply(inverse(sk_c11),sk_c11) ),
inference(paramodulation,[status(thm)],[f524,f299]) ).
fof(f1137,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c10 = identity ),
inference(forward_demodulation,[status(thm)],[f76,f1134]) ).
fof(f1140,plain,
( sQ12_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c11 != identity ),
inference(backward_demodulation,[status(thm)],[f1137,f1118]) ).
fof(f1144,plain,
( sQ101_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(identity) != sk_c11 ),
inference(backward_demodulation,[status(thm)],[f1137,f949]) ).
fof(f1145,plain,
( sQ61_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(identity) != identity ),
inference(backward_demodulation,[status(thm)],[f1137,f668]) ).
fof(f1146,plain,
( sQ69_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(identity) != sk_c4 ),
inference(backward_demodulation,[status(thm)],[f1137,f727]) ).
fof(f1147,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c11,X0) = multiply(sk_c8,multiply(identity,X0)) ),
inference(backward_demodulation,[status(thm)],[f1137,f301]) ).
fof(f1148,plain,
( sQ68_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| identity != sk_c4 ),
inference(backward_demodulation,[status(thm)],[f1137,f702]) ).
fof(f1150,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(identity,sk_c4) = identity ),
inference(backward_demodulation,[status(thm)],[f1137,f302]) ).
fof(f1151,plain,
( ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c8,identity) = sk_c11 ),
inference(backward_demodulation,[status(thm)],[f1137,f178]) ).
fof(f1154,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c4) = identity ),
inference(backward_demodulation,[status(thm)],[f1137,f166]) ).
fof(f1157,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c11,X0) = multiply(sk_c8,X0) ),
inference(forward_demodulation,[status(thm)],[f75,f1147]) ).
fof(f1159,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c4 = identity ),
inference(forward_demodulation,[status(thm)],[f75,f1150]) ).
fof(f1168,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sQ68_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1159,f1148]) ).
fof(f1169,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sQ68_spl ),
inference(contradiction_clause,[status(thm)],[f1168]) ).
fof(f1171,plain,
( sQ62_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(identity) != identity ),
inference(backward_demodulation,[status(thm)],[f1159,f671]) ).
fof(f1172,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c7 = sk_c11 ),
inference(backward_demodulation,[status(thm)],[f1151,f520]) ).
fof(f1184,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c6,X0) = multiply(sk_c11,multiply(sk_c8,X0)) ),
inference(backward_demodulation,[status(thm)],[f1172,f300]) ).
fof(f1186,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c11,sk_c8) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f1172,f190]) ).
fof(f1187,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c11) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f1172,f182]) ).
fof(f1188,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(identity) = identity ),
inference(forward_demodulation,[status(thm)],[f1159,f1154]) ).
fof(f1189,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sQ54_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1188,f602]) ).
fof(f1190,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sQ54_spl ),
inference(contradiction_clause,[status(thm)],[f1189]) ).
fof(f1191,plain,
( sQ62_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f1171,f600,f157,f153,f165,f669]) ).
fof(f1201,plain,
( sQ101_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| identity != sk_c11 ),
inference(backward_demodulation,[status(thm)],[f1188,f1144]) ).
fof(f1217,plain,
( ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c11,identity) = sk_c11 ),
inference(backward_demodulation,[status(thm)],[f1157,f1151]) ).
fof(f1220,plain,
( ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c11,sk_c6) = identity ),
inference(backward_demodulation,[status(thm)],[f1157,f295]) ).
fof(f1222,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c11,X0) = multiply(sk_c5,multiply(sk_c11,X0)) ),
inference(backward_demodulation,[status(thm)],[f1157,f303]) ).
fof(f1239,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c6,X0) = multiply(sk_c11,multiply(sk_c11,X0)) ),
inference(forward_demodulation,[status(thm)],[f1157,f1184]) ).
fof(f1272,plain,
( sQ53_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(identity) != identity ),
inference(forward_demodulation,[status(thm)],[f1188,f599]) ).
fof(f1273,plain,
( sQ53_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f1188,f1272]) ).
fof(f1274,plain,
( sQ53_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1273]) ).
fof(f1275,plain,
( sQ53_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f1274]) ).
fof(f1277,plain,
( ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ10_spl
| ~ sQ8_spl
| multiply(sk_c6,sk_c6) = multiply(sk_c11,identity) ),
inference(paramodulation,[status(thm)],[f1220,f1239]) ).
fof(f1281,plain,
( ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c8 = multiply(sk_c11,identity) ),
inference(forward_demodulation,[status(thm)],[f526,f1277]) ).
fof(f1282,plain,
( ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c8 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1217,f1281]) ).
fof(f1300,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c11,sk_c11) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f1282,f1186]) ).
fof(f1327,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ1_spl
| multiply(sk_c11,multiply(sk_c3,X0)) = multiply(sk_c5,X0) ),
inference(paramodulation,[status(thm)],[f495,f1222]) ).
fof(f1336,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ1_spl
| X0 = multiply(sk_c5,X0) ),
inference(forward_demodulation,[status(thm)],[f495,f1327]) ).
fof(f1349,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ10_spl
| ~ sQ8_spl
| X0 = multiply(sk_c11,multiply(sk_c5,X0)) ),
inference(forward_demodulation,[status(thm)],[f1282,f497]) ).
fof(f1350,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sk_c11 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f1358,f1300]) ).
fof(f1353,plain,
( ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ5_spl
| identity = sk_c11 ),
inference(backward_demodulation,[status(thm)],[f1358,f1217]) ).
fof(f1358,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ5_spl
| X0 = multiply(sk_c11,X0) ),
inference(forward_demodulation,[status(thm)],[f1336,f1349]) ).
fof(f1366,plain,
( ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ5_spl
| sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1353,f353]) ).
fof(f1367,plain,
( ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ5_spl
| sQ31_spl ),
inference(contradiction_clause,[status(thm)],[f1366]) ).
fof(f1370,plain,
( sQ101_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f1201,f351,f165,f157,f153,f947]) ).
fof(f1371,plain,
( sQ27_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f1108,f351,f165,f161,f337]) ).
fof(f1372,definition,
( sQ113_spl
<=> inverse(inverse(sk_c9)) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ113_spl])],[split_symbol_definition]) ).
fof(f1375,definition,
( sQ114_spl
<=> identity = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ114_spl])],[split_symbol_definition]) ).
fof(f1377,plain,
( sQ114_spl
| identity != sk_c10 ),
inference(component_clause,[status(thm)],[f1375]) ).
fof(f1378,plain,
( ~ sQ18_spl
| ~ sQ114_spl
| ~ sQ113_spl ),
inference(split_clause,[status(thm)],[f409,f1372,f1375,f274]) ).
fof(f1379,plain,
( ~ sQ18_spl
| ~ sQ38_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f410,f387,f384,f274]) ).
fof(f1458,plain,
( sQ102_spl
| ~ sQ11_spl
| inverse(identity) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f194,f952]) ).
fof(f1478,plain,
! [X0] :
( ~ sQ20_spl
| inverse(multiply(inverse(multiply(X0,sk_c10)),X0)) != sk_c10
| identity != sk_c9 ),
inference(paramodulation,[status(thm)],[f76,f376]) ).
fof(f1489,definition,
( sQ117_spl
<=> inverse(multiply(sk_c2,sk_c9)) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ117_spl])],[split_symbol_definition]) ).
fof(f1491,plain,
( sQ117_spl
| inverse(multiply(sk_c2,sk_c9)) != sk_c10 ),
inference(component_clause,[status(thm)],[f1489]) ).
fof(f1500,definition,
( sQ120_spl
<=> inverse(multiply(sk_c3,sk_c11)) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ120_spl])],[split_symbol_definition]) ).
fof(f1502,plain,
( sQ120_spl
| inverse(multiply(sk_c3,sk_c11)) != sk_c10 ),
inference(component_clause,[status(thm)],[f1500]) ).
fof(f1508,definition,
( sQ122_spl
<=> multiply(sk_c9,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ122_spl])],[split_symbol_definition]) ).
fof(f1510,plain,
( sQ122_spl
| multiply(sk_c9,sk_c10) != sk_c9 ),
inference(component_clause,[status(thm)],[f1508]) ).
fof(f1519,definition,
! [X0] :
( sQ125_spl
<=> inverse(multiply(inverse(multiply(X0,sk_c10)),X0)) != sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ125_spl])],[split_symbol_definition]) ).
fof(f1522,plain,
( ~ sQ20_spl
| sQ125_spl
| ~ sQ36_spl ),
inference(split_clause,[status(thm)],[f1478,f377,f1519,f280]) ).
fof(f1528,plain,
( sQ122_spl
| ~ sQ11_spl
| identity != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f437,f1510]) ).
fof(f1531,plain,
( sQ120_spl
| ~ sQ1_spl
| inverse(sk_c10) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f154,f1502]) ).
fof(f1532,plain,
( sQ120_spl
| ~ sQ1_spl
| ~ sQ11_spl
| sk_c9 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f194,f1531]) ).
fof(f1534,plain,
( sQ117_spl
| ~ sQ16_spl
| inverse(sk_c10) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f259,f1491]) ).
fof(f1535,plain,
( sQ117_spl
| ~ sQ16_spl
| ~ sQ11_spl
| sk_c9 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f194,f1534]) ).
fof(f1537,definition,
( sQ126_spl
<=> inverse(inverse(sk_c8)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ126_spl])],[split_symbol_definition]) ).
fof(f1540,plain,
( ~ sQ22_spl
| ~ sQ126_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f934,f351,f1537,f320]) ).
fof(f1636,plain,
( ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| multiply(sk_c10,sk_c11) = multiply(sk_c9,sk_c10) ),
inference(paramodulation,[status(thm)],[f841,f308]) ).
fof(f1641,plain,
( ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ0_spl
| sk_c9 = multiply(sk_c9,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f151,f1636]) ).
fof(f1642,plain,
( ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ11_spl
| sk_c9 = identity ),
inference(forward_demodulation,[status(thm)],[f437,f1641]) ).
fof(f1646,plain,
( ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ11_spl
| sQ36_spl ),
inference(split_clause,[status(thm)],[f1642,f377,f193,f150,f206,f219,f232]) ).
fof(f1654,plain,
! [X0,X1,X2,X3] :
( ~ sQ21_spl
| multiply(X2,multiply(inverse(multiply(X1,sk_c10)),X1)) != X3
| inverse(X3) != multiply(inverse(multiply(X1,sk_c10)),X1)
| inverse(X2) != X3
| identity != sk_c11
| inverse(X0) != multiply(inverse(multiply(X1,sk_c10)),X1)
| multiply(X0,multiply(inverse(multiply(X1,sk_c10)),X1)) != sk_c11 ),
inference(paramodulation,[status(thm)],[f76,f319]) ).
fof(f1700,definition,
( sQ148_spl
<=> multiply(sk_c9,sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ148_spl])],[split_symbol_definition]) ).
fof(f1702,plain,
( sQ148_spl
| multiply(sk_c9,sk_c10) != sk_c11 ),
inference(component_clause,[status(thm)],[f1700]) ).
fof(f1715,definition,
! [X0,X1,X2,X3] :
( sQ151_spl
<=> ( multiply(X2,multiply(inverse(multiply(X1,sk_c10)),X1)) != X3
| inverse(X3) != multiply(inverse(multiply(X1,sk_c10)),X1)
| inverse(X2) != X3
| inverse(X0) != multiply(inverse(multiply(X1,sk_c10)),X1)
| multiply(X0,multiply(inverse(multiply(X1,sk_c10)),X1)) != sk_c11 ) ),
introduced(definition,[new_symbols(definition,[sQ151_spl])],[split_symbol_definition]) ).
fof(f1718,plain,
( ~ sQ21_spl
| ~ sQ31_spl
| sQ151_spl ),
inference(split_clause,[status(thm)],[f1654,f1715,f351,f283]) ).
fof(f1737,plain,
( sQ148_spl
| ~ sQ11_spl
| identity != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f437,f1702]) ).
fof(f1756,plain,
( ~ sQ36_spl
| sQ122_spl
| ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f378,f1528]) ).
fof(f1757,plain,
( ~ sQ36_spl
| sQ122_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f1756]) ).
fof(f1771,plain,
( sQ27_spl
| ~ sQ36_spl
| identity != sk_c11 ),
inference(backward_demodulation,[status(thm)],[f378,f339]) ).
fof(f1774,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ36_spl
| sk_c11 = multiply(sk_c9,identity) ),
inference(backward_demodulation,[status(thm)],[f378,f522]) ).
fof(f1775,plain,
( sQ102_spl
| ~ sQ11_spl
| ~ sQ36_spl
| inverse(identity) != identity ),
inference(backward_demodulation,[status(thm)],[f378,f1458]) ).
fof(f1781,plain,
( ~ sQ11_spl
| ~ sQ36_spl
| multiply(identity,sk_c10) = identity ),
inference(backward_demodulation,[status(thm)],[f378,f437]) ).
fof(f1783,plain,
( ~ sQ12_spl
| ~ sQ36_spl
| multiply(identity,sk_c11) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f378,f207]) ).
fof(f1786,plain,
( ~ sQ11_spl
| ~ sQ36_spl
| inverse(sk_c10) = identity ),
inference(backward_demodulation,[status(thm)],[f378,f194]) ).
fof(f1787,plain,
( sQ38_spl
| ~ sQ36_spl
| sk_c10 != identity ),
inference(backward_demodulation,[status(thm)],[f378,f386]) ).
fof(f1789,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ36_spl
| sk_c11 = multiply(identity,identity) ),
inference(forward_demodulation,[status(thm)],[f378,f1774]) ).
fof(f1790,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ36_spl
| sk_c11 = identity ),
inference(forward_demodulation,[status(thm)],[f75,f1789]) ).
fof(f1791,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ36_spl
| sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1790,f353]) ).
fof(f1792,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ36_spl
| sQ31_spl ),
inference(contradiction_clause,[status(thm)],[f1791]) ).
fof(f1795,plain,
( ~ sQ11_spl
| ~ sQ36_spl
| sk_c10 = identity ),
inference(forward_demodulation,[status(thm)],[f75,f1781]) ).
fof(f1796,plain,
( ~ sQ11_spl
| ~ sQ36_spl
| sQ114_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1795,f1377]) ).
fof(f1797,plain,
( ~ sQ11_spl
| ~ sQ36_spl
| sQ114_spl ),
inference(contradiction_clause,[status(thm)],[f1796]) ).
fof(f1798,plain,
( ~ sQ12_spl
| ~ sQ36_spl
| sk_c11 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f75,f1783]) ).
fof(f1799,plain,
( ~ sQ12_spl
| ~ sQ36_spl
| sQ40_spl
| ~ sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1798,f395]) ).
fof(f1800,plain,
( ~ sQ12_spl
| ~ sQ36_spl
| sQ40_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f1799]) ).
fof(f1801,plain,
( sQ38_spl
| ~ sQ36_spl
| ~ sQ114_spl ),
inference(split_clause,[status(thm)],[f1787,f1375,f377,f384]) ).
fof(f1802,plain,
( sQ27_spl
| ~ sQ36_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f1771,f351,f377,f337]) ).
fof(f1803,plain,
( sQ148_spl
| ~ sQ11_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f1737,f351,f193,f1700]) ).
fof(f1814,plain,
( ~ sQ12_spl
| ~ sQ36_spl
| sQ34_spl ),
inference(split_clause,[status(thm)],[f1798,f361,f377,f206]) ).
fof(f1815,plain,
( sQ117_spl
| ~ sQ16_spl
| ~ sQ11_spl
| ~ sQ38_spl ),
inference(split_clause,[status(thm)],[f1535,f384,f193,f258,f1489]) ).
fof(f1816,plain,
( sQ120_spl
| ~ sQ1_spl
| ~ sQ11_spl
| ~ sQ38_spl ),
inference(split_clause,[status(thm)],[f1532,f384,f193,f153,f1500]) ).
fof(f1818,plain,
( ~ sQ38_spl
| ~ sQ36_spl
| sk_c10 = identity ),
inference(forward_demodulation,[status(thm)],[f378,f385]) ).
fof(f1852,plain,
( sQ42_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ36_spl
| inverse(identity) != identity ),
inference(backward_demodulation,[status(thm)],[f1790,f425]) ).
fof(f1891,definition,
( sQ155_spl
<=> multiply(identity,sk_c10) = identity ),
introduced(definition,[new_symbols(definition,[sQ155_spl])],[split_symbol_definition]) ).
fof(f1893,plain,
( sQ155_spl
| multiply(identity,sk_c10) != identity ),
inference(component_clause,[status(thm)],[f1891]) ).
fof(f1931,plain,
( sQ155_spl
| sk_c10 != identity ),
inference(forward_demodulation,[status(thm)],[f75,f1893]) ).
fof(f1935,plain,
( ~ sQ11_spl
| ~ sQ36_spl
| inverse(identity) = identity ),
inference(backward_demodulation,[status(thm)],[f1795,f1786]) ).
fof(f1938,plain,
( sQ39_spl
| ~ sQ11_spl
| ~ sQ36_spl
| inverse(identity) != identity ),
inference(backward_demodulation,[status(thm)],[f1795,f389]) ).
fof(f1941,plain,
( ~ sQ11_spl
| ~ sQ36_spl
| sQ54_spl ),
inference(split_clause,[status(thm)],[f1935,f600,f377,f193]) ).
fof(f1943,plain,
( sQ39_spl
| ~ sQ11_spl
| ~ sQ36_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f1938,f600,f377,f193,f387]) ).
fof(f1944,plain,
( sQ42_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ36_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f1852,f600,f377,f193,f150,f423]) ).
fof(f1946,plain,
( sQ102_spl
| ~ sQ11_spl
| ~ sQ36_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f1775,f600,f377,f193,f950]) ).
fof(f1950,plain,
( ~ sQ0_spl
| ~ sQ19_spl
| ~ sQ101_spl
| ~ sQ38_spl ),
inference(split_clause,[status(thm)],[f399,f384,f947,f277,f150]) ).
fof(f1951,definition,
( sQ163_spl
<=> sk_c10 = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ163_spl])],[split_symbol_definition]) ).
fof(f1953,plain,
( sQ163_spl
| sk_c10 != sk_c10 ),
inference(component_clause,[status(thm)],[f1951]) ).
fof(f1963,plain,
( ~ sQ19_spl
| ~ sQ42_spl
| ~ sQ34_spl ),
inference(split_clause,[status(thm)],[f403,f361,f423,f277]) ).
fof(f1970,plain,
( sQ163_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1953]) ).
fof(f1971,plain,
sQ163_spl,
inference(contradiction_clause,[status(thm)],[f1970]) ).
fof(f1978,plain,
( sQ0_spl
| ~ sQ36_spl
| multiply(sk_c10,sk_c11) != identity ),
inference(forward_demodulation,[status(thm)],[f378,f152]) ).
fof(f1979,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sQ114_spl ),
inference(split_clause,[status(thm)],[f1137,f1375,f157,f153]) ).
fof(f1980,plain,
( sQ61_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f1145,f600,f157,f153,f666]) ).
fof(f1981,plain,
( sQ69_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ62_spl ),
inference(split_clause,[status(thm)],[f1146,f669,f157,f153,f725]) ).
fof(f1982,plain,
( sQ12_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f1140,f351,f157,f153,f165,f161,f206]) ).
fof(f1992,plain,
( sQ43_spl
| ~ sQ4_spl
| ~ sQ34_spl ),
inference(split_clause,[status(thm)],[f434,f361,f165,f430]) ).
fof(f1993,plain,
( sQ64_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ62_spl ),
inference(split_clause,[status(thm)],[f711,f669,f165,f153,f676]) ).
fof(f2037,plain,
( ~ sQ34_spl
| ~ sQ38_spl
| ~ sQ36_spl
| identity = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1818,f362]) ).
fof(f2044,plain,
( sQ11_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ38_spl
| ~ sQ36_spl
| inverse(identity) != identity ),
inference(forward_demodulation,[status(thm)],[f1818,f1102]) ).
fof(f2046,plain,
( sQ155_spl
| ~ sQ38_spl
| ~ sQ36_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f1818,f1931]) ).
fof(f2047,plain,
( sQ155_spl
| ~ sQ38_spl
| ~ sQ36_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f2046]) ).
fof(f2048,plain,
( sQ155_spl
| ~ sQ38_spl
| ~ sQ36_spl ),
inference(contradiction_clause,[status(thm)],[f2047]) ).
fof(f2050,plain,
( sQ0_spl
| ~ sQ36_spl
| ~ sQ38_spl
| multiply(identity,sk_c11) != identity ),
inference(forward_demodulation,[status(thm)],[f1818,f1978]) ).
fof(f2051,plain,
( sQ0_spl
| ~ sQ36_spl
| ~ sQ38_spl
| sk_c11 != identity ),
inference(forward_demodulation,[status(thm)],[f75,f2050]) ).
fof(f2052,plain,
( sQ0_spl
| ~ sQ36_spl
| ~ sQ38_spl
| ~ sQ34_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f2037,f2051]) ).
fof(f2053,plain,
( sQ0_spl
| ~ sQ36_spl
| ~ sQ38_spl
| ~ sQ34_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f2052]) ).
fof(f2054,plain,
( sQ0_spl
| ~ sQ36_spl
| ~ sQ38_spl
| ~ sQ34_spl ),
inference(contradiction_clause,[status(thm)],[f2053]) ).
fof(f2146,plain,
( sQ11_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ38_spl
| ~ sQ36_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ34_spl
| sk_c6 != identity ),
inference(backward_demodulation,[status(thm)],[f2149,f2044]) ).
fof(f2149,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ34_spl
| ~ sQ38_spl
| ~ sQ36_spl
| inverse(identity) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f2037,f1187]) ).
fof(f2168,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ34_spl
| ~ sQ38_spl
| ~ sQ36_spl
| identity = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f2037,f1350]) ).
fof(f2203,plain,
( sQ67_spl
| ~ sQ4_spl
| ~ sQ38_spl
| ~ sQ36_spl
| inverse(identity) != identity ),
inference(backward_demodulation,[status(thm)],[f2205,f689]) ).
fof(f2204,plain,
( sQ70_spl
| ~ sQ4_spl
| ~ sQ38_spl
| ~ sQ36_spl
| inverse(identity) != sk_c4 ),
inference(backward_demodulation,[status(thm)],[f2205,f731]) ).
fof(f2205,plain,
( ~ sQ4_spl
| ~ sQ38_spl
| ~ sQ36_spl
| inverse(sk_c4) = identity ),
inference(forward_demodulation,[status(thm)],[f1818,f166]) ).
fof(f2208,plain,
( sQ67_spl
| ~ sQ4_spl
| ~ sQ38_spl
| ~ sQ36_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f2203,f600,f377,f384,f165,f687]) ).
fof(f2209,plain,
( sQ70_spl
| ~ sQ4_spl
| ~ sQ38_spl
| ~ sQ36_spl
| ~ sQ62_spl ),
inference(split_clause,[status(thm)],[f2204,f669,f377,f384,f165,f729]) ).
fof(f2231,plain,
( sQ11_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ38_spl
| ~ sQ36_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ34_spl
| ~ sQ10_spl
| ~ sQ6_spl
| ~ sQ5_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f2168,f2146]) ).
fof(f2232,plain,
( sQ11_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ38_spl
| ~ sQ36_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ34_spl
| ~ sQ10_spl
| ~ sQ6_spl
| ~ sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f2231]) ).
fof(f2233,plain,
( sQ11_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ38_spl
| ~ sQ36_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ34_spl
| ~ sQ10_spl
| ~ sQ6_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f2232]) ).
fof(f2234,plain,
$false,
inference(sat_refutation,[status(thm)],[f156,f160,f164,f168,f172,f176,f180,f184,f188,f192,f196,f197,f198,f199,f200,f201,f202,f203,f204,f205,f209,f210,f211,f212,f213,f214,f222,f223,f224,f225,f226,f227,f228,f229,f230,f231,f235,f236,f237,f238,f239,f240,f250,f251,f257,f261,f262,f263,f264,f270,f286,f367,f383,f390,f394,f407,f415,f422,f426,f433,f453,f464,f473,f604,f624,f672,f728,f732,f825,f829,f939,f946,f953,f998,f1002,f1096,f1116,f1169,f1190,f1191,f1275,f1367,f1370,f1371,f1378,f1379,f1522,f1540,f1646,f1718,f1757,f1792,f1797,f1800,f1801,f1802,f1803,f1814,f1815,f1816,f1941,f1943,f1944,f1946,f1950,f1963,f1971,f1979,f1980,f1981,f1982,f1992,f1993,f2048,f2054,f2208,f2209,f2233]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP350-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n013.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 20:09:23 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 0.11/0.45 % Refutation found
% 0.11/0.45 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.48 % Elapsed time: 0.100114 seconds
% 0.11/0.48 % CPU time: 0.436901 seconds
% 0.11/0.48 % Total memory used: 112.585 MB
% 0.11/0.48 % Net memory used: 112.227 MB
%------------------------------------------------------------------------------