%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP312-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 12:33:23 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.47s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 135
% Syntax : Number of formulae : 686 ( 13 unt; 67 def)
% Number of atoms : 3170 ( 790 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 4738 (2254 ~;2417 |; 0 &)
% ( 67 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 69 ( 67 usr; 68 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 13 con; 0-2 aty)
% Number of variables : 126 ( 126 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c11
| multiply(sk_c11,sk_c12) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c4) = sk_c12
| multiply(sk_c11,sk_c12) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c5,sk_c11) = sk_c10
| multiply(sk_c11,sk_c12) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c5) = sk_c11
| multiply(sk_c11,sk_c12) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c12
| multiply(sk_c11,sk_c12) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c11,sk_c12) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c12
| multiply(sk_c11,sk_c12) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c11,sk_c12) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c7) = sk_c9
| multiply(sk_c11,sk_c12) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c11
| multiply(sk_c1,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c4) = sk_c12
| multiply(sk_c1,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c5,sk_c11) = sk_c10
| multiply(sk_c1,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c5) = sk_c11
| multiply(sk_c1,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c12
| multiply(sk_c1,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c1,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c12
| multiply(sk_c1,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c1,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( inverse(sk_c7) = sk_c9
| multiply(sk_c1,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| multiply(sk_c1,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c11
| inverse(sk_c1) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c4) = sk_c12
| inverse(sk_c1) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c5,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c5) = sk_c11
| inverse(sk_c1) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c12
| inverse(sk_c1) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c1) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c12
| inverse(sk_c1) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c1) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( inverse(sk_c7) = sk_c9
| inverse(sk_c1) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| inverse(sk_c1) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c11
| multiply(sk_c2,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( inverse(sk_c4) = sk_c12
| multiply(sk_c2,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
( multiply(sk_c5,sk_c11) = sk_c10
| multiply(sk_c2,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( inverse(sk_c5) = sk_c11
| multiply(sk_c2,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c12
| multiply(sk_c2,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c2,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,negated_conjecture,
( inverse(sk_c7) = sk_c9
| multiply(sk_c2,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c11
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
( inverse(sk_c4) = sk_c12
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,negated_conjecture,
( multiply(sk_c5,sk_c11) = sk_c10
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,negated_conjecture,
( inverse(sk_c5) = sk_c11
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c12
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f50,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c12
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f51,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f52,negated_conjecture,
( inverse(sk_c7) = sk_c9
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f53,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f55,negated_conjecture,
( inverse(sk_c4) = sk_c12
| multiply(sk_c3,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f56,negated_conjecture,
( multiply(sk_c5,sk_c11) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f57,negated_conjecture,
( inverse(sk_c5) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f58,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c12
| multiply(sk_c3,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f59,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c3,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f60,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c12
| multiply(sk_c3,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f61,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c3,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f62,negated_conjecture,
( inverse(sk_c7) = sk_c9
| multiply(sk_c3,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f64,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c11
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f65,negated_conjecture,
( inverse(sk_c4) = sk_c12
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f66,negated_conjecture,
( multiply(sk_c5,sk_c11) = sk_c10
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f67,negated_conjecture,
( inverse(sk_c5) = sk_c11
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f68,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c12
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f69,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f70,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c12
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f71,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f72,negated_conjecture,
( inverse(sk_c7) = sk_c9
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f74,negated_conjecture,
! [X4,X5,X6,X1,X2,X7,X3,X8,X9] :
( multiply(X8,X3) != X9
| inverse(X9) != X3
| inverse(X8) != X9
| multiply(X3,sk_c11) != sk_c12
| inverse(X7) != X3
| multiply(X7,X3) != sk_c12
| inverse(X2) != sk_c11
| multiply(X2,sk_c11) != sk_c10
| inverse(X1) != sk_c12
| multiply(X1,sk_c12) != sk_c11
| inverse(X6) != sk_c11
| multiply(X6,sk_c11) != sk_c12
| inverse(X5) != sk_c11
| multiply(X5,sk_c11) != sk_c10
| inverse(X4) != sk_c12
| multiply(X4,sk_c12) != sk_c11
| multiply(sk_c11,sk_c12) != sk_c10 ),
file('/export/starexec/sandbox/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_c4,sk_c12) = sk_c11
| multiply(sk_c11,sk_c12) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f79,plain,
( inverse(sk_c4) = sk_c12
| multiply(sk_c11,sk_c12) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f80,plain,
( multiply(sk_c5,sk_c11) = sk_c10
| multiply(sk_c11,sk_c12) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f81,plain,
( inverse(sk_c5) = sk_c11
| multiply(sk_c11,sk_c12) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f82,plain,
( multiply(sk_c6,sk_c9) = sk_c12
| multiply(sk_c11,sk_c12) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f83,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c11,sk_c12) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f84,plain,
( multiply(sk_c9,sk_c11) = sk_c12
| multiply(sk_c11,sk_c12) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f85,plain,
( inverse(sk_c8) = sk_c7
| multiply(sk_c11,sk_c12) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f86,plain,
( inverse(sk_c7) = sk_c9
| multiply(sk_c11,sk_c12) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f88,plain,
( multiply(sk_c4,sk_c12) = sk_c11
| multiply(sk_c1,sk_c12) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f89,plain,
( inverse(sk_c4) = sk_c12
| multiply(sk_c1,sk_c12) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f90,plain,
( multiply(sk_c5,sk_c11) = sk_c10
| multiply(sk_c1,sk_c12) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f91,plain,
( inverse(sk_c5) = sk_c11
| multiply(sk_c1,sk_c12) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f92,plain,
( multiply(sk_c6,sk_c9) = sk_c12
| multiply(sk_c1,sk_c12) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f93,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c1,sk_c12) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f94,plain,
( multiply(sk_c9,sk_c11) = sk_c12
| multiply(sk_c1,sk_c12) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f95,plain,
( inverse(sk_c8) = sk_c7
| multiply(sk_c1,sk_c12) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f96,plain,
( inverse(sk_c7) = sk_c9
| multiply(sk_c1,sk_c12) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f97,plain,
( multiply(sk_c8,sk_c9) = sk_c7
| multiply(sk_c1,sk_c12) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f98,plain,
( multiply(sk_c4,sk_c12) = sk_c11
| inverse(sk_c1) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f99,plain,
( inverse(sk_c4) = sk_c12
| inverse(sk_c1) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f100,plain,
( multiply(sk_c5,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f101,plain,
( inverse(sk_c5) = sk_c11
| inverse(sk_c1) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f102,plain,
( multiply(sk_c6,sk_c9) = sk_c12
| inverse(sk_c1) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f103,plain,
( inverse(sk_c6) = sk_c9
| inverse(sk_c1) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f104,plain,
( multiply(sk_c9,sk_c11) = sk_c12
| inverse(sk_c1) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f105,plain,
( inverse(sk_c8) = sk_c7
| inverse(sk_c1) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f106,plain,
( inverse(sk_c7) = sk_c9
| inverse(sk_c1) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f107,plain,
( multiply(sk_c8,sk_c9) = sk_c7
| inverse(sk_c1) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f108,plain,
( multiply(sk_c4,sk_c12) = sk_c11
| multiply(sk_c2,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f109,plain,
( inverse(sk_c4) = sk_c12
| multiply(sk_c2,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f110,plain,
( multiply(sk_c5,sk_c11) = sk_c10
| multiply(sk_c2,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f111,plain,
( inverse(sk_c5) = sk_c11
| multiply(sk_c2,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f114,plain,
( multiply(sk_c9,sk_c11) = sk_c12
| multiply(sk_c2,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f115,plain,
( inverse(sk_c8) = sk_c7
| multiply(sk_c2,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f116,plain,
( inverse(sk_c7) = sk_c9
| multiply(sk_c2,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f118,plain,
( multiply(sk_c4,sk_c12) = sk_c11
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f119,plain,
( inverse(sk_c4) = sk_c12
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f120,plain,
( multiply(sk_c5,sk_c11) = sk_c10
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f121,plain,
( inverse(sk_c5) = sk_c11
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f122,plain,
( multiply(sk_c6,sk_c9) = sk_c12
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f123,plain,
( inverse(sk_c6) = sk_c9
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f124,plain,
( multiply(sk_c9,sk_c11) = sk_c12
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f125,plain,
( inverse(sk_c8) = sk_c7
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f126,plain,
( inverse(sk_c7) = sk_c9
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f127,plain,
( multiply(sk_c8,sk_c9) = sk_c7
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f128,plain,
( multiply(sk_c4,sk_c12) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f129,plain,
( inverse(sk_c4) = sk_c12
| multiply(sk_c3,sk_c11) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f130,plain,
( multiply(sk_c5,sk_c11) = sk_c10
| multiply(sk_c3,sk_c11) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f131,plain,
( inverse(sk_c5) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f132,plain,
( multiply(sk_c6,sk_c9) = sk_c12
| multiply(sk_c3,sk_c11) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f133,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c3,sk_c11) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f134,plain,
( multiply(sk_c9,sk_c11) = sk_c12
| multiply(sk_c3,sk_c11) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f135,plain,
( inverse(sk_c8) = sk_c7
| multiply(sk_c3,sk_c11) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f136,plain,
( inverse(sk_c7) = sk_c9
| multiply(sk_c3,sk_c11) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f138,plain,
( multiply(sk_c4,sk_c12) = sk_c11
| inverse(sk_c3) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f139,plain,
( inverse(sk_c4) = sk_c12
| inverse(sk_c3) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f140,plain,
( multiply(sk_c5,sk_c11) = sk_c10
| inverse(sk_c3) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f141,plain,
( inverse(sk_c5) = sk_c11
| inverse(sk_c3) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f142,plain,
( multiply(sk_c6,sk_c9) = sk_c12
| inverse(sk_c3) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f143,plain,
( inverse(sk_c6) = sk_c9
| inverse(sk_c3) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f144,plain,
( multiply(sk_c9,sk_c11) = sk_c12
| inverse(sk_c3) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f145,plain,
( inverse(sk_c8) = sk_c7
| inverse(sk_c3) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f146,plain,
( inverse(sk_c7) = sk_c9
| inverse(sk_c3) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f148,plain,
! [X3,X8,X9] :
( multiply(X8,X3) != X9
| inverse(X9) != X3
| inverse(X8) != X9
| multiply(X3,sk_c11) != sk_c12
| ! [X7] :
( inverse(X7) != X3
| multiply(X7,X3) != sk_c12
| ! [X2] :
( inverse(X2) != sk_c11
| multiply(X2,sk_c11) != sk_c10
| ! [X1] :
( inverse(X1) != sk_c12
| multiply(X1,sk_c12) != sk_c11
| ! [X6] :
( inverse(X6) != sk_c11
| multiply(X6,sk_c11) != sk_c12
| ! [X5] :
( inverse(X5) != sk_c11
| multiply(X5,sk_c11) != sk_c10
| ! [X4] :
( inverse(X4) != sk_c12
| multiply(X4,sk_c12) != sk_c11
| multiply(sk_c11,sk_c12) != sk_c10 ) ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f74]) ).
fof(f149,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( multiply(X7,X6) != X8
| inverse(X8) != X6
| inverse(X7) != X8
| multiply(X6,sk_c11) != sk_c12
| inverse(X5) != X6
| multiply(X5,X6) != sk_c12
| inverse(X4) != sk_c11
| multiply(X4,sk_c11) != sk_c10
| inverse(X3) != sk_c12
| multiply(X3,sk_c12) != sk_c11
| inverse(X2) != sk_c11
| multiply(X2,sk_c11) != sk_c12
| inverse(X1) != sk_c11
| multiply(X1,sk_c11) != sk_c10
| inverse(X0) != sk_c12
| multiply(X0,sk_c12) != sk_c11
| multiply(sk_c11,sk_c12) != sk_c10 ),
inference(cnf_transformation,[status(thm)],[f148]) ).
fof(f150,definition,
( sQ0_spl
<=> multiply(sk_c11,sk_c12) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f151,plain,
( ~ sQ0_spl
| multiply(sk_c11,sk_c12) = sk_c10 ),
inference(component_clause,[status(thm)],[f150]) ).
fof(f152,plain,
( sQ0_spl
| multiply(sk_c11,sk_c12) != sk_c10 ),
inference(component_clause,[status(thm)],[f150]) ).
fof(f153,definition,
( sQ1_spl
<=> multiply(sk_c4,sk_c12) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f154,plain,
( ~ sQ1_spl
| multiply(sk_c4,sk_c12) = sk_c11 ),
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_c4) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f158,plain,
( ~ sQ2_spl
| inverse(sk_c4) = sk_c12 ),
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_c5,sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f162,plain,
( ~ sQ3_spl
| multiply(sk_c5,sk_c11) = sk_c10 ),
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_c5) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f166,plain,
( ~ sQ4_spl
| inverse(sk_c5) = sk_c11 ),
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_c6,sk_c9) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f170,plain,
( ~ sQ5_spl
| multiply(sk_c6,sk_c9) = sk_c12 ),
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_c6) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f174,plain,
( ~ sQ6_spl
| inverse(sk_c6) = sk_c9 ),
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_c9,sk_c11) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f178,plain,
( ~ sQ7_spl
| multiply(sk_c9,sk_c11) = sk_c12 ),
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_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f182,plain,
( ~ sQ8_spl
| inverse(sk_c8) = sk_c7 ),
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_c7) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f186,plain,
( ~ sQ9_spl
| inverse(sk_c7) = sk_c9 ),
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_c8,sk_c9) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f190,plain,
( ~ sQ10_spl
| multiply(sk_c8,sk_c9) = sk_c7 ),
inference(component_clause,[status(thm)],[f189]) ).
fof(f193,definition,
( sQ11_spl
<=> multiply(sk_c1,sk_c12) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f194,plain,
( ~ sQ11_spl
| multiply(sk_c1,sk_c12) = sk_c11 ),
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
<=> inverse(sk_c1) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f207,plain,
( ~ sQ12_spl
| inverse(sk_c1) = sk_c12 ),
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(f215,plain,
( sQ7_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f104,f206,f177]) ).
fof(f216,plain,
( sQ8_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f105,f206,f181]) ).
fof(f217,plain,
( sQ9_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f106,f206,f185]) ).
fof(f218,plain,
( sQ10_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f107,f206,f189]) ).
fof(f219,definition,
( sQ13_spl
<=> multiply(sk_c2,sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f220,plain,
( ~ sQ13_spl
| multiply(sk_c2,sk_c11) = sk_c10 ),
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(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(f232,definition,
( sQ14_spl
<=> inverse(sk_c2) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f233,plain,
( ~ sQ14_spl
| inverse(sk_c2) = 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(f241,plain,
( sQ7_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f124,f232,f177]) ).
fof(f242,plain,
( sQ8_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f125,f232,f181]) ).
fof(f243,plain,
( sQ9_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f126,f232,f185]) ).
fof(f244,plain,
( sQ10_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f127,f232,f189]) ).
fof(f245,definition,
( sQ15_spl
<=> multiply(sk_c3,sk_c11) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f246,plain,
( ~ sQ15_spl
| multiply(sk_c3,sk_c11) = sk_c12 ),
inference(component_clause,[status(thm)],[f245]) ).
fof(f248,plain,
( sQ1_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f128,f245,f153]) ).
fof(f249,plain,
( sQ2_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f129,f245,f157]) ).
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(f252,plain,
( sQ5_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f132,f245,f169]) ).
fof(f253,plain,
( sQ6_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f133,f245,f173]) ).
fof(f254,plain,
( sQ7_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f134,f245,f177]) ).
fof(f255,plain,
( sQ8_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f135,f245,f181]) ).
fof(f256,plain,
( sQ9_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f136,f245,f185]) ).
fof(f258,definition,
( sQ16_spl
<=> inverse(sk_c3) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f259,plain,
( ~ sQ16_spl
| inverse(sk_c3) = sk_c11 ),
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(f265,plain,
( sQ5_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f142,f258,f169]) ).
fof(f266,plain,
( sQ6_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f143,f258,f173]) ).
fof(f267,plain,
( sQ7_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f144,f258,f177]) ).
fof(f268,plain,
( sQ8_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f145,f258,f181]) ).
fof(f269,plain,
( sQ9_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f146,f258,f185]) ).
fof(f271,definition,
! [X0] :
( sQ17_spl
<=> ( inverse(X0) != sk_c12
| multiply(X0,sk_c12) != sk_c11 ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f272,plain,
! [X0] :
( ~ sQ17_spl
| inverse(X0) != sk_c12
| multiply(X0,sk_c12) != sk_c11 ),
inference(component_clause,[status(thm)],[f271]) ).
fof(f274,definition,
! [X1] :
( sQ18_spl
<=> ( inverse(X1) != sk_c11
| multiply(X1,sk_c11) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f275,plain,
! [X0] :
( ~ sQ18_spl
| inverse(X0) != sk_c11
| multiply(X0,sk_c11) != sk_c10 ),
inference(component_clause,[status(thm)],[f274]) ).
fof(f277,definition,
! [X2] :
( sQ19_spl
<=> ( inverse(X2) != sk_c11
| multiply(X2,sk_c11) != sk_c12 ) ),
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_c12 ),
inference(component_clause,[status(thm)],[f277]) ).
fof(f280,definition,
! [X5,X6,X7,X8] :
( sQ20_spl
<=> ( multiply(X7,X6) != X8
| inverse(X8) != X6
| inverse(X7) != X8
| multiply(X6,sk_c11) != sk_c12
| inverse(X5) != X6
| multiply(X5,X6) != sk_c12 ) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f281,plain,
! [X0,X1,X2,X3] :
( ~ sQ20_spl
| multiply(X2,X1) != X3
| inverse(X3) != X1
| inverse(X2) != X3
| multiply(X1,sk_c11) != sk_c12
| inverse(X0) != X1
| multiply(X0,X1) != sk_c12 ),
inference(component_clause,[status(thm)],[f280]) ).
fof(f283,plain,
( sQ20_spl
| sQ19_spl
| sQ18_spl
| sQ17_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f149,f150,f271,f274,f277,f280]) ).
fof(f284,plain,
! [X0,X1] :
( ~ sQ20_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c11) != sk_c12
| multiply(X0,inverse(X0)) != sk_c12 ),
inference(destructive_equality_resolution,[status(thm)],[f281]) ).
fof(f286,plain,
! [X0] :
( ~ sQ1_spl
| multiply(sk_c11,X0) = multiply(sk_c4,multiply(sk_c12,X0)) ),
inference(paramodulation,[status(thm)],[f154,f77]) ).
fof(f288,plain,
! [X0] :
( ~ sQ5_spl
| multiply(sk_c12,X0) = multiply(sk_c6,multiply(sk_c9,X0)) ),
inference(paramodulation,[status(thm)],[f170,f77]) ).
fof(f289,plain,
! [X0] :
( ~ sQ7_spl
| multiply(sk_c12,X0) = multiply(sk_c9,multiply(sk_c11,X0)) ),
inference(paramodulation,[status(thm)],[f178,f77]) ).
fof(f290,plain,
! [X0] :
( ~ sQ10_spl
| multiply(sk_c7,X0) = multiply(sk_c8,multiply(sk_c9,X0)) ),
inference(paramodulation,[status(thm)],[f190,f77]) ).
fof(f300,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ20_spl
| multiply(X0,sk_c7) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c8)
| multiply(inverse(sk_c8),sk_c11) != sk_c12
| multiply(sk_c8,inverse(sk_c8)) != sk_c12 ),
inference(paramodulation,[status(thm)],[f182,f284]) ).
fof(f301,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ20_spl
| multiply(X0,sk_c9) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c7)
| multiply(inverse(sk_c7),sk_c11) != sk_c12
| multiply(sk_c7,inverse(sk_c7)) != sk_c12 ),
inference(paramodulation,[status(thm)],[f186,f284]) ).
fof(f304,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ20_spl
| multiply(X0,sk_c11) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c3)
| multiply(inverse(sk_c3),sk_c11) != sk_c12
| multiply(sk_c3,inverse(sk_c3)) != sk_c12 ),
inference(paramodulation,[status(thm)],[f259,f284]) ).
fof(f335,definition,
( sQ30_spl
<=> multiply(sk_c8,inverse(sk_c8)) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f337,plain,
( sQ30_spl
| multiply(sk_c8,inverse(sk_c8)) != sk_c12 ),
inference(component_clause,[status(thm)],[f335]) ).
fof(f338,definition,
( sQ31_spl
<=> multiply(inverse(sk_c8),sk_c11) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f340,plain,
( sQ31_spl
| multiply(inverse(sk_c8),sk_c11) != sk_c12 ),
inference(component_clause,[status(thm)],[f338]) ).
fof(f341,definition,
! [X0] :
( sQ32_spl
<=> ( multiply(X0,sk_c7) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c8) ) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f344,plain,
( ~ sQ8_spl
| ~ sQ20_spl
| sQ32_spl
| ~ sQ31_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f300,f335,f338,f341,f280,f181]) ).
fof(f345,definition,
( sQ33_spl
<=> multiply(sk_c7,inverse(sk_c7)) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f347,plain,
( sQ33_spl
| multiply(sk_c7,inverse(sk_c7)) != sk_c12 ),
inference(component_clause,[status(thm)],[f345]) ).
fof(f348,definition,
( sQ34_spl
<=> multiply(inverse(sk_c7),sk_c11) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f350,plain,
( sQ34_spl
| multiply(inverse(sk_c7),sk_c11) != sk_c12 ),
inference(component_clause,[status(thm)],[f348]) ).
fof(f351,definition,
! [X0] :
( sQ35_spl
<=> ( multiply(X0,sk_c9) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c7) ) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f354,plain,
( ~ sQ9_spl
| ~ sQ20_spl
| sQ35_spl
| ~ sQ34_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f301,f345,f348,f351,f280,f185]) ).
fof(f375,definition,
( sQ42_spl
<=> multiply(sk_c3,inverse(sk_c3)) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f377,plain,
( sQ42_spl
| multiply(sk_c3,inverse(sk_c3)) != sk_c12 ),
inference(component_clause,[status(thm)],[f375]) ).
fof(f378,definition,
( sQ43_spl
<=> multiply(inverse(sk_c3),sk_c11) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f380,plain,
( sQ43_spl
| multiply(inverse(sk_c3),sk_c11) != sk_c12 ),
inference(component_clause,[status(thm)],[f378]) ).
fof(f381,definition,
! [X0] :
( sQ44_spl
<=> ( multiply(X0,sk_c11) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c3) ) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f384,plain,
( ~ sQ16_spl
| ~ sQ20_spl
| sQ44_spl
| ~ sQ43_spl
| ~ sQ42_spl ),
inference(split_clause,[status(thm)],[f304,f375,f378,f381,f280,f258]) ).
fof(f386,plain,
( sQ43_spl
| ~ sQ16_spl
| multiply(sk_c11,sk_c11) != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f259,f380]) ).
fof(f387,plain,
( sQ42_spl
| ~ sQ16_spl
| multiply(sk_c3,sk_c11) != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f259,f377]) ).
fof(f388,plain,
( sQ42_spl
| ~ sQ16_spl
| ~ sQ15_spl
| sk_c12 != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f246,f387]) ).
fof(f389,plain,
( sQ42_spl
| ~ sQ16_spl
| ~ sQ15_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f388]) ).
fof(f390,plain,
( sQ42_spl
| ~ sQ16_spl
| ~ sQ15_spl ),
inference(contradiction_clause,[status(thm)],[f389]) ).
fof(f393,plain,
( ~ sQ8_spl
| multiply(sk_c7,sk_c8) = identity ),
inference(paramodulation,[status(thm)],[f182,f76]) ).
fof(f398,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f76,f77]) ).
fof(f399,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f75,f398]) ).
fof(f413,plain,
( ~ sQ19_spl
| inverse(inverse(sk_c11)) != sk_c11
| identity != sk_c12 ),
inference(paramodulation,[status(thm)],[f76,f278]) ).
fof(f414,plain,
( ~ sQ19_spl
| inverse(identity) != sk_c11
| sk_c11 != sk_c12 ),
inference(paramodulation,[status(thm)],[f75,f278]) ).
fof(f416,plain,
( ~ sQ3_spl
| ~ sQ19_spl
| inverse(sk_c5) != sk_c11
| sk_c10 != sk_c12 ),
inference(paramodulation,[status(thm)],[f162,f278]) ).
fof(f417,plain,
( ~ sQ7_spl
| ~ sQ19_spl
| inverse(sk_c9) != sk_c11
| sk_c12 != sk_c12 ),
inference(paramodulation,[status(thm)],[f178,f278]) ).
fof(f418,plain,
( ~ sQ13_spl
| ~ sQ19_spl
| inverse(sk_c2) != sk_c11
| sk_c10 != sk_c12 ),
inference(paramodulation,[status(thm)],[f220,f278]) ).
fof(f419,definition,
( sQ45_spl
<=> identity = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f422,definition,
( sQ46_spl
<=> inverse(inverse(sk_c11)) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f424,plain,
( sQ46_spl
| inverse(inverse(sk_c11)) != sk_c11 ),
inference(component_clause,[status(thm)],[f422]) ).
fof(f425,plain,
( ~ sQ19_spl
| ~ sQ46_spl
| ~ sQ45_spl ),
inference(split_clause,[status(thm)],[f413,f419,f422,f277]) ).
fof(f426,definition,
( sQ47_spl
<=> sk_c11 = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f427,plain,
( ~ sQ47_spl
| sk_c11 = sk_c12 ),
inference(component_clause,[status(thm)],[f426]) ).
fof(f428,plain,
( sQ47_spl
| sk_c11 != sk_c12 ),
inference(component_clause,[status(thm)],[f426]) ).
fof(f429,definition,
( sQ48_spl
<=> inverse(identity) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f431,plain,
( sQ48_spl
| inverse(identity) != sk_c11 ),
inference(component_clause,[status(thm)],[f429]) ).
fof(f432,plain,
( ~ sQ19_spl
| ~ sQ48_spl
| ~ sQ47_spl ),
inference(split_clause,[status(thm)],[f414,f426,f429,f277]) ).
fof(f433,definition,
( sQ49_spl
<=> sk_c10 = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f436,plain,
( ~ sQ3_spl
| ~ sQ19_spl
| ~ sQ4_spl
| ~ sQ49_spl ),
inference(split_clause,[status(thm)],[f416,f433,f165,f277,f161]) ).
fof(f437,definition,
( sQ50_spl
<=> sk_c12 = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f439,plain,
( sQ50_spl
| sk_c12 != sk_c12 ),
inference(component_clause,[status(thm)],[f437]) ).
fof(f440,definition,
( sQ51_spl
<=> inverse(sk_c9) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f442,plain,
( sQ51_spl
| inverse(sk_c9) != sk_c11 ),
inference(component_clause,[status(thm)],[f440]) ).
fof(f443,plain,
( ~ sQ7_spl
| ~ sQ19_spl
| ~ sQ51_spl
| ~ sQ50_spl ),
inference(split_clause,[status(thm)],[f417,f437,f440,f277,f177]) ).
fof(f444,plain,
( ~ sQ13_spl
| ~ sQ19_spl
| ~ sQ14_spl
| ~ sQ49_spl ),
inference(split_clause,[status(thm)],[f418,f433,f232,f277,f219]) ).
fof(f445,plain,
( sQ50_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f439]) ).
fof(f446,plain,
sQ50_spl,
inference(contradiction_clause,[status(thm)],[f445]) ).
fof(f447,plain,
( ~ sQ3_spl
| ~ sQ18_spl
| inverse(sk_c5) != sk_c11 ),
inference(resolution,[status(thm)],[f275,f162]) ).
fof(f448,plain,
( ~ sQ18_spl
| inverse(inverse(sk_c11)) != sk_c11
| identity != sk_c10 ),
inference(paramodulation,[status(thm)],[f76,f275]) ).
fof(f453,plain,
( ~ sQ3_spl
| ~ sQ18_spl
| ~ sQ4_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f166,f447]) ).
fof(f454,plain,
( ~ sQ3_spl
| ~ sQ18_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f453]) ).
fof(f455,plain,
( ~ sQ3_spl
| ~ sQ18_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f454]) ).
fof(f456,plain,
( ~ sQ1_spl
| ~ sQ17_spl
| inverse(sk_c4) != sk_c12 ),
inference(resolution,[status(thm)],[f272,f154]) ).
fof(f459,plain,
( ~ sQ17_spl
| inverse(identity) != sk_c12
| sk_c12 != sk_c11 ),
inference(paramodulation,[status(thm)],[f75,f272]) ).
fof(f462,plain,
( ~ sQ11_spl
| ~ sQ17_spl
| inverse(sk_c1) != sk_c12
| sk_c11 != sk_c11 ),
inference(paramodulation,[status(thm)],[f194,f272]) ).
fof(f463,plain,
( ~ sQ1_spl
| ~ sQ17_spl
| ~ sQ2_spl
| sk_c12 != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f158,f456]) ).
fof(f464,plain,
( ~ sQ1_spl
| ~ sQ17_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f463]) ).
fof(f465,plain,
( ~ sQ1_spl
| ~ sQ17_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f464]) ).
fof(f466,plain,
( sQ34_spl
| ~ sQ9_spl
| multiply(sk_c9,sk_c11) != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f186,f350]) ).
fof(f467,plain,
( sQ34_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sk_c12 != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f178,f466]) ).
fof(f468,plain,
( sQ34_spl
| ~ sQ9_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f467]) ).
fof(f469,plain,
( sQ34_spl
| ~ sQ9_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f468]) ).
fof(f471,plain,
( sQ33_spl
| ~ sQ9_spl
| multiply(sk_c7,sk_c9) != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f186,f347]) ).
fof(f472,plain,
( sQ31_spl
| ~ sQ8_spl
| multiply(sk_c7,sk_c11) != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f182,f340]) ).
fof(f473,plain,
( sQ30_spl
| ~ sQ8_spl
| multiply(sk_c8,sk_c7) != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f182,f337]) ).
fof(f502,plain,
( ~ sQ8_spl
| sk_c8 = multiply(inverse(sk_c7),identity) ),
inference(paramodulation,[status(thm)],[f393,f399]) ).
fof(f505,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f75,f399]) ).
fof(f508,plain,
( ~ sQ1_spl
| sk_c12 = multiply(inverse(sk_c4),sk_c11) ),
inference(paramodulation,[status(thm)],[f154,f399]) ).
fof(f510,plain,
( ~ sQ3_spl
| sk_c11 = multiply(inverse(sk_c5),sk_c10) ),
inference(paramodulation,[status(thm)],[f162,f399]) ).
fof(f511,plain,
( ~ sQ5_spl
| sk_c9 = multiply(inverse(sk_c6),sk_c12) ),
inference(paramodulation,[status(thm)],[f170,f399]) ).
fof(f517,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c8 = multiply(sk_c9,identity) ),
inference(forward_demodulation,[status(thm)],[f186,f502]) ).
fof(f519,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c12 = multiply(sk_c12,sk_c11) ),
inference(forward_demodulation,[status(thm)],[f158,f508]) ).
fof(f521,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c11 = multiply(sk_c11,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f166,f510]) ).
fof(f522,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sk_c9 = multiply(sk_c9,sk_c12) ),
inference(forward_demodulation,[status(thm)],[f174,f511]) ).
fof(f535,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c11 = multiply(inverse(sk_c12),sk_c12) ),
inference(paramodulation,[status(thm)],[f519,f399]) ).
fof(f538,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c11 = identity ),
inference(forward_demodulation,[status(thm)],[f76,f535]) ).
fof(f540,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 = multiply(sk_c9,sk_c11) ),
inference(backward_demodulation,[status(thm)],[f538,f517]) ).
fof(f545,plain,
( ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c7,sk_c8) = sk_c11 ),
inference(backward_demodulation,[status(thm)],[f538,f393]) ).
fof(f547,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(inverse(X0),X0) = sk_c11 ),
inference(backward_demodulation,[status(thm)],[f538,f76]) ).
fof(f548,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c11,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f538,f75]) ).
fof(f549,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| sk_c8 = sk_c12 ),
inference(forward_demodulation,[status(thm)],[f178,f540]) ).
fof(f551,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ2_spl
| ~ sQ7_spl
| multiply(sk_c11,X0) = multiply(sk_c4,multiply(sk_c8,X0)) ),
inference(backward_demodulation,[status(thm)],[f549,f286]) ).
fof(f552,plain,
( sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| multiply(sk_c11,sk_c8) != sk_c10 ),
inference(backward_demodulation,[status(thm)],[f549,f152]) ).
fof(f554,plain,
( ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ7_spl
| inverse(sk_c4) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f549,f158]) ).
fof(f555,plain,
( ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ2_spl
| ~ sQ7_spl
| multiply(sk_c4,sk_c8) = sk_c11 ),
inference(backward_demodulation,[status(thm)],[f549,f154]) ).
fof(f556,plain,
( ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| multiply(sk_c6,sk_c9) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f549,f170]) ).
fof(f563,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c10,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f568,f548]) ).
fof(f564,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c10 = identity ),
inference(backward_demodulation,[status(thm)],[f568,f538]) ).
fof(f565,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c5) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f568,f166]) ).
fof(f567,plain,
( ~ sQ16_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c3) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f568,f259]) ).
fof(f568,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c11 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f548,f521]) ).
fof(f573,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| X0 = multiply(sk_c10,multiply(sk_c3,X0)) ),
inference(paramodulation,[status(thm)],[f567,f399]) ).
fof(f574,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| X0 = multiply(sk_c3,X0) ),
inference(forward_demodulation,[status(thm)],[f563,f573]) ).
fof(f578,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(inverse(X0),X0) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f568,f547]) ).
fof(f579,plain,
( ~ sQ16_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c10,sk_c3) = sk_c10 ),
inference(paramodulation,[status(thm)],[f567,f578]) ).
fof(f580,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c10,sk_c5) = sk_c10 ),
inference(paramodulation,[status(thm)],[f565,f578]) ).
fof(f587,plain,
( ~ sQ16_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c3 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f563,f579]) ).
fof(f588,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c5 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f563,f580]) ).
fof(f590,plain,
( sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c10,sk_c8) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f568,f552]) ).
fof(f591,plain,
( sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c8 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f563,f590]) ).
fof(f594,plain,
( sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ16_spl
| sk_c8 != sk_c3 ),
inference(backward_demodulation,[status(thm)],[f587,f591]) ).
fof(f596,plain,
( ~ sQ16_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c3) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f587,f567]) ).
fof(f599,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ16_spl
| sk_c3 = identity ),
inference(backward_demodulation,[status(thm)],[f587,f564]) ).
fof(f600,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ16_spl
| sk_c11 = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f587,f568]) ).
fof(f603,plain,
( ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ16_spl
| multiply(sk_c4,sk_c8) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f600,f555]) ).
fof(f612,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| sk_c9 = multiply(sk_c9,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f549,f522]) ).
fof(f643,plain,
( ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ16_spl
| multiply(sk_c7,sk_c8) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f600,f545]) ).
fof(f674,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| multiply(sk_c8,X0) = multiply(sk_c6,multiply(sk_c9,X0)) ),
inference(forward_demodulation,[status(thm)],[f549,f288]) ).
fof(f678,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| multiply(sk_c8,sk_c8) = multiply(sk_c6,sk_c9) ),
inference(paramodulation,[status(thm)],[f612,f674]) ).
fof(f682,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| multiply(sk_c8,sk_c8) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f556,f678]) ).
fof(f686,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c8,X0) = multiply(sk_c9,multiply(sk_c11,X0)) ),
inference(forward_demodulation,[status(thm)],[f549,f289]) ).
fof(f687,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ16_spl
| multiply(sk_c8,X0) = multiply(sk_c9,multiply(sk_c3,X0)) ),
inference(forward_demodulation,[status(thm)],[f600,f686]) ).
fof(f693,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ16_spl
| multiply(sk_c8,X0) = multiply(sk_c9,X0) ),
inference(forward_demodulation,[status(thm)],[f574,f687]) ).
fof(f697,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ16_spl
| multiply(sk_c7,X0) = multiply(sk_c8,multiply(sk_c8,X0)) ),
inference(forward_demodulation,[status(thm)],[f693,f290]) ).
fof(f719,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ16_spl
| multiply(sk_c3,X0) = multiply(sk_c4,multiply(sk_c8,X0)) ),
inference(forward_demodulation,[status(thm)],[f600,f551]) ).
fof(f720,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ16_spl
| X0 = multiply(sk_c4,multiply(sk_c8,X0)) ),
inference(forward_demodulation,[status(thm)],[f574,f719]) ).
fof(f728,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ16_spl
| sk_c8 = multiply(sk_c4,sk_c8) ),
inference(paramodulation,[status(thm)],[f682,f720]) ).
fof(f729,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ16_spl
| multiply(sk_c7,sk_c8) = multiply(sk_c8,sk_c8) ),
inference(paramodulation,[status(thm)],[f682,f697]) ).
fof(f732,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ16_spl
| sk_c8 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f603,f728]) ).
fof(f733,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ16_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f732,f594]) ).
fof(f734,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ16_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f733]) ).
fof(f735,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ16_spl
| sk_c3 = multiply(sk_c8,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f643,f729]) ).
fof(f736,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ16_spl
| sk_c3 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f682,f735]) ).
fof(f739,plain,
( ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| multiply(sk_c1,sk_c8) = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f549,f194]) ).
fof(f747,plain,
( sQ33_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| multiply(sk_c7,sk_c9) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f549,f471]) ).
fof(f749,plain,
( sQ48_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ16_spl
| inverse(sk_c3) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f599,f431]) ).
fof(f750,plain,
( sQ48_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ16_spl
| sk_c3 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f596,f749]) ).
fof(f751,plain,
( sQ48_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ16_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f600,f750]) ).
fof(f752,plain,
( sQ48_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ16_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f751]) ).
fof(f753,plain,
( sQ48_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ16_spl ),
inference(contradiction_clause,[status(thm)],[f752]) ).
fof(f756,plain,
( sQ46_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ16_spl
| inverse(inverse(sk_c3)) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f600,f424]) ).
fof(f757,plain,
( sQ46_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ16_spl
| inverse(sk_c3) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f596,f756]) ).
fof(f758,plain,
( sQ46_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ16_spl
| sk_c3 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f596,f757]) ).
fof(f759,plain,
( sQ46_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ16_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f600,f758]) ).
fof(f760,plain,
( sQ46_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ16_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f759]) ).
fof(f761,plain,
( sQ46_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ16_spl ),
inference(contradiction_clause,[status(thm)],[f760]) ).
fof(f766,plain,
( sQ43_spl
| ~ sQ16_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c3,sk_c11) != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f600,f386]) ).
fof(f767,plain,
( sQ43_spl
| ~ sQ16_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c11 != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f574,f766]) ).
fof(f768,plain,
( sQ43_spl
| ~ sQ16_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c3 != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f600,f767]) ).
fof(f769,plain,
( sQ43_spl
| ~ sQ16_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sk_c3 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f549,f768]) ).
fof(f783,plain,
( sQ30_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| multiply(sk_c8,sk_c7) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f549,f473]) ).
fof(f803,plain,
! [X0,X1] :
( ~ sQ20_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c11) != sk_c12
| multiply(X0,inverse(X0)) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f549,f284]) ).
fof(f853,plain,
( sQ43_spl
| ~ sQ16_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f736,f769]) ).
fof(f854,plain,
( sQ43_spl
| ~ sQ16_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f853]) ).
fof(f855,plain,
( sQ43_spl
| ~ sQ16_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f854]) ).
fof(f863,definition,
( sQ52_spl
<=> identity = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f865,plain,
( sQ52_spl
| identity != sk_c11 ),
inference(component_clause,[status(thm)],[f863]) ).
fof(f870,definition,
( sQ54_spl
<=> inverse(identity) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f872,plain,
( sQ54_spl
| inverse(identity) != sk_c12 ),
inference(component_clause,[status(thm)],[f870]) ).
fof(f873,plain,
( ~ sQ17_spl
| ~ sQ54_spl
| ~ sQ47_spl ),
inference(split_clause,[status(thm)],[f459,f426,f870,f271]) ).
fof(f874,definition,
( sQ55_spl
<=> sk_c11 = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f876,plain,
( sQ55_spl
| sk_c11 != sk_c11 ),
inference(component_clause,[status(thm)],[f874]) ).
fof(f878,plain,
( ~ sQ11_spl
| ~ sQ17_spl
| ~ sQ12_spl
| ~ sQ55_spl ),
inference(split_clause,[status(thm)],[f462,f874,f206,f271,f193]) ).
fof(f879,plain,
( sQ55_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f876]) ).
fof(f880,plain,
sQ55_spl,
inference(contradiction_clause,[status(thm)],[f879]) ).
fof(f887,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sQ52_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f538,f865]) ).
fof(f888,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sQ52_spl ),
inference(contradiction_clause,[status(thm)],[f887]) ).
fof(f890,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c11 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f588,f568]) ).
fof(f896,plain,
( ~ sQ47_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| sk_c11 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f549,f427]) ).
fof(f897,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ47_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sk_c8 = identity ),
inference(forward_demodulation,[status(thm)],[f896,f538]) ).
fof(f900,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ47_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| multiply(sk_c8,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f897,f75]) ).
fof(f903,plain,
( sQ54_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ47_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| inverse(sk_c8) != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f897,f872]) ).
fof(f904,plain,
( sQ54_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ47_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| inverse(sk_c8) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f549,f903]) ).
fof(f905,plain,
( ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ2_spl
| ~ sQ7_spl
| multiply(sk_c4,sk_c8) = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f549,f154]) ).
fof(f906,plain,
( ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ47_spl
| multiply(sk_c4,sk_c8) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f896,f905]) ).
fof(f911,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ47_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| multiply(inverse(X0),X0) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f897,f76]) ).
fof(f915,plain,
! [X0,X1] :
( ~ sQ20_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ47_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c8) != sk_c12
| multiply(X0,inverse(X0)) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f896,f803]) ).
fof(f916,plain,
! [X0,X1] :
( ~ sQ20_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ47_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c8) != sk_c8
| multiply(X0,inverse(X0)) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f549,f915]) ).
fof(f917,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ47_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ20_spl
| inverse(inverse(sk_c8)) != inverse(sk_c8)
| multiply(inverse(sk_c8),sk_c8) != sk_c8
| multiply(sk_c8,inverse(sk_c8)) != sk_c8 ),
inference(resolution,[status(thm)],[f916,f900]) ).
fof(f921,definition,
( sQ56_spl
<=> multiply(sk_c8,inverse(sk_c8)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f923,plain,
( sQ56_spl
| multiply(sk_c8,inverse(sk_c8)) != sk_c8 ),
inference(component_clause,[status(thm)],[f921]) ).
fof(f924,definition,
( sQ57_spl
<=> multiply(inverse(sk_c8),sk_c8) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f926,plain,
( sQ57_spl
| multiply(inverse(sk_c8),sk_c8) != sk_c8 ),
inference(component_clause,[status(thm)],[f924]) ).
fof(f927,definition,
( sQ58_spl
<=> inverse(inverse(sk_c8)) = inverse(sk_c8) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f930,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ47_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ20_spl
| ~ sQ58_spl
| ~ sQ57_spl
| ~ sQ56_spl ),
inference(split_clause,[status(thm)],[f917,f921,f924,f927,f280,f177,f185,f181,f426,f157,f153]) ).
fof(f931,plain,
( sQ57_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ47_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f911,f926]) ).
fof(f932,plain,
( sQ57_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ47_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f931]) ).
fof(f933,plain,
( sQ57_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ47_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f932]) ).
fof(f934,plain,
( sQ56_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ47_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| inverse(sk_c8) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f900,f923]) ).
fof(f935,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ20_spl
| ~ sQ47_spl
| multiply(X0,sk_c8) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c4)
| multiply(inverse(sk_c4),sk_c8) != sk_c8
| multiply(sk_c4,inverse(sk_c4)) != sk_c8 ),
inference(paramodulation,[status(thm)],[f554,f916]) ).
fof(f936,plain,
( ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ47_spl
| multiply(sk_c8,sk_c4) = sk_c8 ),
inference(paramodulation,[status(thm)],[f554,f911]) ).
fof(f938,definition,
( sQ59_spl
<=> multiply(sk_c4,inverse(sk_c4)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f940,plain,
( sQ59_spl
| multiply(sk_c4,inverse(sk_c4)) != sk_c8 ),
inference(component_clause,[status(thm)],[f938]) ).
fof(f941,definition,
( sQ60_spl
<=> multiply(inverse(sk_c4),sk_c8) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f943,plain,
( sQ60_spl
| multiply(inverse(sk_c4),sk_c8) != sk_c8 ),
inference(component_clause,[status(thm)],[f941]) ).
fof(f944,definition,
! [X0] :
( sQ61_spl
<=> ( multiply(X0,sk_c8) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c4) ) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f947,plain,
( ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ20_spl
| ~ sQ47_spl
| sQ61_spl
| ~ sQ60_spl
| ~ sQ59_spl ),
inference(split_clause,[status(thm)],[f935,f938,f941,f944,f426,f280,f177,f153,f185,f181,f157]) ).
fof(f948,plain,
( ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ47_spl
| sk_c4 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f900,f936]) ).
fof(f951,plain,
( sQ60_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ7_spl
| multiply(sk_c8,sk_c8) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f554,f943]) ).
fof(f952,plain,
( sQ60_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ47_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f900,f951]) ).
fof(f953,plain,
( sQ60_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ47_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f952]) ).
fof(f954,plain,
( sQ60_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ47_spl ),
inference(contradiction_clause,[status(thm)],[f953]) ).
fof(f955,plain,
( sQ59_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ7_spl
| multiply(sk_c4,sk_c8) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f554,f940]) ).
fof(f956,plain,
( sQ59_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ47_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f906,f955]) ).
fof(f957,plain,
( sQ59_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ47_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f956]) ).
fof(f958,plain,
( sQ59_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ47_spl ),
inference(contradiction_clause,[status(thm)],[f957]) ).
fof(f961,plain,
( ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ47_spl
| inverse(sk_c8) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f948,f554]) ).
fof(f963,plain,
( ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ47_spl
| sQ54_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f961,f904]) ).
fof(f964,plain,
( ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ47_spl
| sQ54_spl ),
inference(contradiction_clause,[status(thm)],[f963]) ).
fof(f976,plain,
! [X0] : multiply(identity,X0) = X0,
inference(paramodulation,[status(thm)],[f399,f505]) ).
fof(f992,plain,
( ~ sQ20_spl
| inverse(inverse(identity)) != inverse(identity)
| multiply(inverse(identity),sk_c11) != sk_c12
| multiply(identity,inverse(identity)) != sk_c12 ),
inference(resolution,[status(thm)],[f976,f284]) ).
fof(f996,definition,
( sQ65_spl
<=> multiply(identity,inverse(identity)) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f998,plain,
( sQ65_spl
| multiply(identity,inverse(identity)) != sk_c12 ),
inference(component_clause,[status(thm)],[f996]) ).
fof(f999,definition,
( sQ66_spl
<=> multiply(inverse(identity),sk_c11) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f1001,plain,
( sQ66_spl
| multiply(inverse(identity),sk_c11) != sk_c12 ),
inference(component_clause,[status(thm)],[f999]) ).
fof(f1002,definition,
( sQ67_spl
<=> inverse(inverse(identity)) = inverse(identity) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f1005,plain,
( ~ sQ20_spl
| ~ sQ67_spl
| ~ sQ66_spl
| ~ sQ65_spl ),
inference(split_clause,[status(thm)],[f992,f996,f999,f1002,f280]) ).
fof(f1006,plain,
( sQ66_spl
| sk_c11 != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f505,f1001]) ).
fof(f1007,plain,
( sQ65_spl
| inverse(identity) != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f976,f998]) ).
fof(f1016,plain,
( ~ sQ12_spl
| multiply(sk_c12,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f207,f76]) ).
fof(f1027,plain,
( ~ sQ15_spl
| sk_c11 = multiply(inverse(sk_c3),sk_c12) ),
inference(paramodulation,[status(thm)],[f246,f399]) ).
fof(f1029,plain,
( ~ sQ15_spl
| ~ sQ16_spl
| sk_c11 = multiply(sk_c11,sk_c12) ),
inference(forward_demodulation,[status(thm)],[f259,f1027]) ).
fof(f1030,plain,
( ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| sk_c11 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f151,f1029]) ).
fof(f1033,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| multiply(sk_c10,sk_c12) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f1030,f151]) ).
fof(f1034,plain,
( ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| multiply(sk_c1,sk_c12) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f1030,f194]) ).
fof(f1036,plain,
( ~ sQ16_spl
| ~ sQ15_spl
| ~ sQ0_spl
| inverse(sk_c3) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f1030,f259]) ).
fof(f1038,plain,
( ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| inverse(sk_c2) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f1030,f233]) ).
fof(f1039,plain,
! [X0,X1] :
( ~ sQ20_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c10) != sk_c12
| multiply(X0,inverse(X0)) != sk_c12 ),
inference(backward_demodulation,[status(thm)],[f1030,f284]) ).
fof(f1041,plain,
( sQ47_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| sk_c10 != sk_c12 ),
inference(backward_demodulation,[status(thm)],[f1030,f428]) ).
fof(f1054,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| sk_c12 = multiply(inverse(sk_c10),sk_c10) ),
inference(paramodulation,[status(thm)],[f1033,f399]) ).
fof(f1056,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| sk_c12 = identity ),
inference(forward_demodulation,[status(thm)],[f76,f1054]) ).
fof(f1058,plain,
( sQ65_spl
| ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| inverse(sk_c12) != sk_c12 ),
inference(backward_demodulation,[status(thm)],[f1056,f1007]) ).
fof(f1059,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| multiply(sk_c12,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f1056,f976]) ).
fof(f1069,plain,
( ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| sk_c12 = multiply(inverse(sk_c1),sk_c10) ),
inference(paramodulation,[status(thm)],[f1034,f399]) ).
fof(f1071,plain,
( ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ12_spl
| sk_c12 = multiply(sk_c12,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f207,f1069]) ).
fof(f1072,plain,
( ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ12_spl
| sk_c12 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1059,f1071]) ).
fof(f1073,plain,
( ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ12_spl
| sQ47_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1072,f1041]) ).
fof(f1074,plain,
( ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ12_spl
| sQ47_spl ),
inference(contradiction_clause,[status(thm)],[f1073]) ).
fof(f1076,plain,
( sQ66_spl
| ~ sQ47_spl ),
inference(split_clause,[status(thm)],[f1006,f426,f999]) ).
fof(f1080,plain,
( sQ47_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c5 != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f890,f428]) ).
fof(f1081,plain,
( sQ47_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sk_c5 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f549,f1080]) ).
fof(f1089,plain,
( ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c1,sk_c8) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f890,f739]) ).
fof(f1095,plain,
( ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ7_spl
| inverse(sk_c4) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f549,f158]) ).
fof(f1119,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(inverse(X0),X0) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f890,f547]) ).
fof(f1140,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| sk_c8 = multiply(inverse(sk_c8),sk_c8) ),
inference(paramodulation,[status(thm)],[f682,f399]) ).
fof(f1142,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c8 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f1119,f1140]) ).
fof(f1143,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sQ47_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1142,f1081]) ).
fof(f1144,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sQ47_spl ),
inference(contradiction_clause,[status(thm)],[f1143]) ).
fof(f1149,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sk_c10 = identity ),
inference(backward_demodulation,[status(thm)],[f1072,f1056]) ).
fof(f1150,plain,
( ~ sQ47_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| sk_c10 = sk_c12 ),
inference(forward_demodulation,[status(thm)],[f1030,f427]) ).
fof(f1151,plain,
( sQ65_spl
| ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ11_spl
| ~ sQ12_spl
| inverse(sk_c10) != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f1072,f1058]) ).
fof(f1152,plain,
( sQ65_spl
| ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ11_spl
| ~ sQ12_spl
| inverse(sk_c10) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1072,f1151]) ).
fof(f1156,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ11_spl
| ~ sQ12_spl
| multiply(sk_c10,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f1149,f976]) ).
fof(f1159,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| inverse(sk_c1) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1072,f207]) ).
fof(f1160,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| X0 = multiply(sk_c10,multiply(sk_c1,X0)) ),
inference(paramodulation,[status(thm)],[f1159,f399]) ).
fof(f1161,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| X0 = multiply(sk_c1,X0) ),
inference(forward_demodulation,[status(thm)],[f1156,f1160]) ).
fof(f1176,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| X0 = multiply(sk_c10,multiply(sk_c2,X0)) ),
inference(paramodulation,[status(thm)],[f1038,f399]) ).
fof(f1177,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| X0 = multiply(sk_c2,X0) ),
inference(forward_demodulation,[status(thm)],[f1156,f1176]) ).
fof(f1194,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ11_spl
| ~ sQ12_spl
| multiply(inverse(X0),X0) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1149,f76]) ).
fof(f1195,plain,
( ~ sQ16_spl
| ~ sQ15_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| multiply(sk_c10,sk_c3) = sk_c10 ),
inference(paramodulation,[status(thm)],[f1036,f1194]) ).
fof(f1200,plain,
( ~ sQ16_spl
| ~ sQ15_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sk_c3 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1156,f1195]) ).
fof(f1204,plain,
! [X0,X1] :
( ~ sQ20_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c10) != sk_c12
| multiply(X0,inverse(X0)) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1072,f1039]) ).
fof(f1205,plain,
! [X0,X1] :
( ~ sQ20_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c10) != sk_c10
| multiply(X0,inverse(X0)) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1072,f1204]) ).
fof(f1206,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ20_spl
| inverse(inverse(sk_c10)) != inverse(sk_c10)
| multiply(inverse(sk_c10),sk_c10) != sk_c10
| multiply(sk_c10,inverse(sk_c10)) != sk_c10 ),
inference(resolution,[status(thm)],[f1205,f1156]) ).
fof(f1207,plain,
( ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ20_spl
| inverse(inverse(sk_c2)) != inverse(sk_c2)
| multiply(inverse(sk_c2),sk_c10) != sk_c10
| multiply(sk_c2,inverse(sk_c2)) != sk_c10 ),
inference(resolution,[status(thm)],[f1205,f1177]) ).
fof(f1209,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ20_spl
| inverse(inverse(sk_c1)) != inverse(sk_c1)
| multiply(inverse(sk_c1),sk_c10) != sk_c10
| multiply(sk_c1,inverse(sk_c1)) != sk_c10 ),
inference(resolution,[status(thm)],[f1205,f1161]) ).
fof(f1216,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ15_spl
| ~ sQ0_spl
| ~ sQ20_spl
| ~ sQ11_spl
| ~ sQ12_spl
| multiply(X0,sk_c10) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c3)
| multiply(inverse(sk_c3),sk_c10) != sk_c10
| multiply(sk_c3,inverse(sk_c3)) != sk_c10 ),
inference(paramodulation,[status(thm)],[f1036,f1205]) ).
fof(f1218,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ20_spl
| multiply(X0,sk_c10) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c1)
| multiply(inverse(sk_c1),sk_c10) != sk_c10
| multiply(sk_c1,inverse(sk_c1)) != sk_c10 ),
inference(paramodulation,[status(thm)],[f1159,f1205]) ).
fof(f1219,definition,
( sQ68_spl
<=> multiply(sk_c10,inverse(sk_c10)) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f1221,plain,
( sQ68_spl
| multiply(sk_c10,inverse(sk_c10)) != sk_c10 ),
inference(component_clause,[status(thm)],[f1219]) ).
fof(f1222,definition,
( sQ69_spl
<=> multiply(inverse(sk_c10),sk_c10) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f1224,plain,
( sQ69_spl
| multiply(inverse(sk_c10),sk_c10) != sk_c10 ),
inference(component_clause,[status(thm)],[f1222]) ).
fof(f1225,definition,
( sQ70_spl
<=> inverse(inverse(sk_c10)) = inverse(sk_c10) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f1228,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ20_spl
| ~ sQ70_spl
| ~ sQ69_spl
| ~ sQ68_spl ),
inference(split_clause,[status(thm)],[f1206,f1219,f1222,f1225,f280,f206,f193,f258,f245,f150]) ).
fof(f1229,definition,
( sQ71_spl
<=> multiply(sk_c2,inverse(sk_c2)) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f1231,plain,
( sQ71_spl
| multiply(sk_c2,inverse(sk_c2)) != sk_c10 ),
inference(component_clause,[status(thm)],[f1229]) ).
fof(f1232,definition,
( sQ72_spl
<=> multiply(inverse(sk_c2),sk_c10) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f1234,plain,
( sQ72_spl
| multiply(inverse(sk_c2),sk_c10) != sk_c10 ),
inference(component_clause,[status(thm)],[f1232]) ).
fof(f1235,definition,
( sQ73_spl
<=> inverse(inverse(sk_c2)) = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f1237,plain,
( sQ73_spl
| inverse(inverse(sk_c2)) != inverse(sk_c2) ),
inference(component_clause,[status(thm)],[f1235]) ).
fof(f1238,plain,
( ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ20_spl
| ~ sQ73_spl
| ~ sQ72_spl
| ~ sQ71_spl ),
inference(split_clause,[status(thm)],[f1207,f1229,f1232,f1235,f280,f206,f193,f150,f258,f245,f232]) ).
fof(f1249,definition,
( sQ77_spl
<=> multiply(sk_c1,inverse(sk_c1)) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f1251,plain,
( sQ77_spl
| multiply(sk_c1,inverse(sk_c1)) != sk_c10 ),
inference(component_clause,[status(thm)],[f1249]) ).
fof(f1252,definition,
( sQ78_spl
<=> multiply(inverse(sk_c1),sk_c10) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f1254,plain,
( sQ78_spl
| multiply(inverse(sk_c1),sk_c10) != sk_c10 ),
inference(component_clause,[status(thm)],[f1252]) ).
fof(f1255,definition,
( sQ79_spl
<=> inverse(inverse(sk_c1)) = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f1258,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ20_spl
| ~ sQ79_spl
| ~ sQ78_spl
| ~ sQ77_spl ),
inference(split_clause,[status(thm)],[f1209,f1249,f1252,f1255,f280,f150,f258,f245,f193,f206]) ).
fof(f1263,definition,
( sQ80_spl
<=> multiply(sk_c3,inverse(sk_c3)) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f1266,definition,
( sQ81_spl
<=> multiply(inverse(sk_c3),sk_c10) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f1268,plain,
( sQ81_spl
| multiply(inverse(sk_c3),sk_c10) != sk_c10 ),
inference(component_clause,[status(thm)],[f1266]) ).
fof(f1269,definition,
! [X0] :
( sQ82_spl
<=> ( multiply(X0,sk_c10) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c3) ) ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f1272,plain,
( ~ sQ16_spl
| ~ sQ15_spl
| ~ sQ0_spl
| ~ sQ20_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sQ82_spl
| ~ sQ81_spl
| ~ sQ80_spl ),
inference(split_clause,[status(thm)],[f1216,f1263,f1266,f1269,f206,f193,f280,f150,f245,f258]) ).
fof(f1277,definition,
! [X0] :
( sQ84_spl
<=> ( multiply(X0,sk_c10) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c1) ) ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f1280,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ20_spl
| sQ84_spl
| ~ sQ78_spl
| ~ sQ77_spl ),
inference(split_clause,[status(thm)],[f1218,f1249,f1252,f1277,f280,f150,f258,f245,f193,f206]) ).
fof(f1281,plain,
( sQ78_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| multiply(sk_c10,sk_c10) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1159,f1254]) ).
fof(f1282,plain,
( sQ78_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1156,f1281]) ).
fof(f1283,plain,
( sQ78_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1282]) ).
fof(f1284,plain,
( sQ78_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f1283]) ).
fof(f1285,plain,
( sQ77_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| inverse(sk_c1) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1161,f1251]) ).
fof(f1286,plain,
( sQ77_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1159,f1285]) ).
fof(f1287,plain,
( sQ77_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1286]) ).
fof(f1288,plain,
( sQ77_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f1287]) ).
fof(f1289,plain,
( sQ72_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| multiply(sk_c10,sk_c10) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1038,f1234]) ).
fof(f1290,plain,
( sQ72_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1156,f1289]) ).
fof(f1291,plain,
( sQ72_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1290]) ).
fof(f1292,plain,
( sQ72_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f1291]) ).
fof(f1293,plain,
( sQ71_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| inverse(sk_c2) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1177,f1231]) ).
fof(f1294,plain,
( sQ71_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1038,f1293]) ).
fof(f1295,plain,
( sQ71_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1294]) ).
fof(f1296,plain,
( sQ71_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f1295]) ).
fof(f1300,plain,
( sQ81_spl
| ~ sQ16_spl
| ~ sQ15_spl
| ~ sQ0_spl
| multiply(sk_c10,sk_c10) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1036,f1268]) ).
fof(f1301,plain,
( sQ81_spl
| ~ sQ16_spl
| ~ sQ15_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1156,f1300]) ).
fof(f1302,plain,
( sQ81_spl
| ~ sQ16_spl
| ~ sQ15_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1301]) ).
fof(f1303,plain,
( sQ81_spl
| ~ sQ16_spl
| ~ sQ15_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f1302]) ).
fof(f1308,plain,
( sQ73_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| inverse(sk_c10) != inverse(sk_c2) ),
inference(forward_demodulation,[status(thm)],[f1038,f1237]) ).
fof(f1309,plain,
( sQ73_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| inverse(sk_c10) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1038,f1308]) ).
fof(f1310,plain,
( sQ69_spl
| ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1194,f1224]) ).
fof(f1311,plain,
( sQ69_spl
| ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ11_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1310]) ).
fof(f1312,plain,
( sQ69_spl
| ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ11_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f1311]) ).
fof(f1313,plain,
( sQ68_spl
| ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ11_spl
| ~ sQ12_spl
| inverse(sk_c10) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1156,f1221]) ).
fof(f1318,definition,
( sQ85_spl
<=> identity = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f1320,plain,
( sQ85_spl
| identity != sk_c10 ),
inference(component_clause,[status(thm)],[f1318]) ).
fof(f1321,plain,
( ~ sQ18_spl
| ~ sQ46_spl
| ~ sQ85_spl ),
inference(split_clause,[status(thm)],[f448,f1318,f422,f274]) ).
fof(f1322,definition,
( sQ86_spl
<=> sk_c11 = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f1324,plain,
( sQ86_spl
| sk_c11 != sk_c10 ),
inference(component_clause,[status(thm)],[f1322]) ).
fof(f1331,plain,
( sQ85_spl
| ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1149,f1320]) ).
fof(f1332,plain,
( sQ85_spl
| ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ11_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1331]) ).
fof(f1333,plain,
( sQ85_spl
| ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ11_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f1332]) ).
fof(f1334,plain,
( sQ86_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1030,f1324]) ).
fof(f1335,plain,
( sQ86_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1334]) ).
fof(f1336,plain,
( sQ86_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f1335]) ).
fof(f1362,plain,
( ~ sQ16_spl
| ~ sQ15_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| inverse(sk_c3) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f1200,f1036]) ).
fof(f1368,plain,
( sQ65_spl
| ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ11_spl
| ~ sQ12_spl
| inverse(sk_c10) != sk_c3 ),
inference(backward_demodulation,[status(thm)],[f1200,f1152]) ).
fof(f1371,plain,
( ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sk_c11 = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f1200,f1030]) ).
fof(f1372,plain,
( sQ65_spl
| ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ11_spl
| ~ sQ12_spl
| inverse(sk_c3) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f1200,f1368]) ).
fof(f1388,plain,
( sQ65_spl
| ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f1362,f1372]) ).
fof(f1389,plain,
( sQ65_spl
| ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ11_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1388]) ).
fof(f1390,plain,
( sQ65_spl
| ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ11_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f1389]) ).
fof(f1397,plain,
( sQ46_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| inverse(inverse(sk_c3)) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1371,f424]) ).
fof(f1398,plain,
( sQ46_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| inverse(sk_c3) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1362,f1397]) ).
fof(f1399,plain,
( sQ46_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sk_c3 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1362,f1398]) ).
fof(f1400,plain,
( sQ46_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f1371,f1399]) ).
fof(f1401,plain,
( sQ46_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1400]) ).
fof(f1402,plain,
( sQ46_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f1401]) ).
fof(f1403,plain,
( sQ68_spl
| ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ11_spl
| ~ sQ12_spl
| inverse(sk_c3) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1200,f1313]) ).
fof(f1404,plain,
( sQ68_spl
| ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sk_c3 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1362,f1403]) ).
fof(f1405,plain,
( sQ68_spl
| ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f1200,f1404]) ).
fof(f1406,plain,
( sQ68_spl
| ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ11_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1405]) ).
fof(f1407,plain,
( sQ68_spl
| ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ11_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f1406]) ).
fof(f1408,plain,
( sQ73_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| inverse(sk_c3) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1200,f1309]) ).
fof(f1409,plain,
( sQ73_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sk_c3 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1362,f1408]) ).
fof(f1410,plain,
( sQ73_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f1200,f1409]) ).
fof(f1411,plain,
( sQ73_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1410]) ).
fof(f1412,plain,
( sQ73_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f1411]) ).
fof(f1416,plain,
! [X0,X1] :
( ~ sQ20_spl
| ~ sQ47_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c12) != sk_c12
| multiply(X0,inverse(X0)) != sk_c12 ),
inference(backward_demodulation,[status(thm)],[f427,f284]) ).
fof(f1419,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sk_c8 = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f1142,f588]) ).
fof(f1424,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ47_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| multiply(inverse(X0),X0) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f897,f76]) ).
fof(f1426,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ47_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| multiply(sk_c8,X0) = multiply(inverse(X1),multiply(X1,X0)) ),
inference(paramodulation,[status(thm)],[f1424,f77]) ).
fof(f1427,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ47_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| multiply(sk_c8,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f399,f1426]) ).
fof(f1437,plain,
( ~ sQ12_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| inverse(sk_c1) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f549,f207]) ).
fof(f1440,plain,
( sQ51_spl
| ~ sQ47_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| inverse(sk_c9) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f896,f442]) ).
fof(f1451,plain,
( ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ47_spl
| inverse(sk_c8) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f948,f1095]) ).
fof(f1465,plain,
( sQ56_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ47_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f1451,f934]) ).
fof(f1466,plain,
( sQ56_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ47_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1465]) ).
fof(f1467,plain,
( sQ56_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ47_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f1466]) ).
fof(f1471,plain,
( ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ47_spl
| inverse(sk_c8) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f1484,f1451]) ).
fof(f1474,plain,
( sQ51_spl
| ~ sQ47_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| inverse(sk_c9) != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f1484,f1440]) ).
fof(f1475,plain,
( ~ sQ12_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ47_spl
| inverse(sk_c1) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f1484,f1437]) ).
fof(f1478,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ47_spl
| sk_c7 = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f1484,f1419]) ).
fof(f1480,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ47_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sk_c7 = identity ),
inference(backward_demodulation,[status(thm)],[f1484,f897]) ).
fof(f1481,plain,
( ~ sQ47_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| sk_c11 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f1484,f896]) ).
fof(f1482,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ47_spl
| sk_c7 = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f1484,f1142]) ).
fof(f1483,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ47_spl
| sk_c7 = sk_c12 ),
inference(backward_demodulation,[status(thm)],[f1484,f549]) ).
fof(f1484,plain,
( ~ sQ8_spl
| ~ sQ2_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ47_spl
| sk_c8 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f1451,f182]) ).
fof(f1485,plain,
( ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ47_spl
| inverse(sk_c7) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f1484,f1471]) ).
fof(f1486,plain,
( ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ47_spl
| sk_c9 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f186,f1485]) ).
fof(f1489,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ47_spl
| inverse(sk_c7) = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1482,f166]) ).
fof(f1490,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ47_spl
| inverse(sk_c7) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f1481,f1489]) ).
fof(f1510,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ47_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| multiply(sk_c7,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f1484,f1427]) ).
fof(f1514,plain,
( sQ51_spl
| ~ sQ47_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| inverse(sk_c7) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f1486,f1474]) ).
fof(f1515,plain,
( sQ51_spl
| ~ sQ47_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f1490,f1514]) ).
fof(f1516,plain,
( sQ51_spl
| ~ sQ47_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1515]) ).
fof(f1517,plain,
( sQ51_spl
| ~ sQ47_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f1516]) ).
fof(f1527,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ47_spl
| X0 = multiply(sk_c7,multiply(sk_c1,X0)) ),
inference(paramodulation,[status(thm)],[f1475,f399]) ).
fof(f1528,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ47_spl
| X0 = multiply(sk_c1,X0) ),
inference(forward_demodulation,[status(thm)],[f1510,f1527]) ).
fof(f1560,plain,
( ~ sQ12_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ47_spl
| multiply(sk_c7,sk_c1) = identity ),
inference(forward_demodulation,[status(thm)],[f1483,f1016]) ).
fof(f1561,plain,
( ~ sQ12_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ47_spl
| sk_c1 = identity ),
inference(forward_demodulation,[status(thm)],[f1510,f1560]) ).
fof(f1568,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ47_spl
| ~ sQ12_spl
| sk_c1 = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f1575,f1482]) ).
fof(f1573,plain,
( ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ47_spl
| ~ sQ12_spl
| sk_c9 = sk_c1 ),
inference(backward_demodulation,[status(thm)],[f1575,f1486]) ).
fof(f1575,plain,
( ~ sQ12_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ47_spl
| sk_c1 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f1480,f1561]) ).
fof(f1577,plain,
( ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ12_spl
| ~ sQ47_spl
| sk_c8 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f1528,f1089]) ).
fof(f1578,plain,
( ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ12_spl
| ~ sQ47_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c8 = sk_c1 ),
inference(forward_demodulation,[status(thm)],[f1568,f1577]) ).
fof(f1696,plain,
( sQ33_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ12_spl
| ~ sQ47_spl
| multiply(sk_c1,sk_c9) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f1575,f747]) ).
fof(f1697,plain,
( sQ33_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ12_spl
| ~ sQ47_spl
| sk_c9 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f1528,f1696]) ).
fof(f1698,plain,
( sQ33_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ12_spl
| ~ sQ47_spl
| sk_c1 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f1573,f1697]) ).
fof(f1699,plain,
( sQ33_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ12_spl
| ~ sQ47_spl
| ~ sQ11_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c1 != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f1578,f1698]) ).
fof(f1700,plain,
( sQ33_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ12_spl
| ~ sQ47_spl
| ~ sQ11_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1699]) ).
fof(f1701,plain,
( sQ33_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ12_spl
| ~ sQ47_spl
| ~ sQ11_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f1700]) ).
fof(f1751,plain,
( sQ30_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ47_spl
| multiply(sk_c7,sk_c7) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f1484,f783]) ).
fof(f1752,plain,
( sQ30_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ47_spl
| sk_c7 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f1510,f1751]) ).
fof(f1753,plain,
( sQ30_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ47_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f1484,f1752]) ).
fof(f1754,plain,
( sQ30_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ47_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1753]) ).
fof(f1755,plain,
( sQ30_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ47_spl ),
inference(contradiction_clause,[status(thm)],[f1754]) ).
fof(f1783,plain,
( sQ31_spl
| ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ47_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sk_c11 != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f1510,f472]) ).
fof(f1784,plain,
( sQ31_spl
| ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ47_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sk_c7 != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f1481,f1783]) ).
fof(f1785,plain,
( sQ31_spl
| ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ47_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f1483,f1784]) ).
fof(f1786,plain,
( sQ31_spl
| ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ47_spl
| ~ sQ9_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1785]) ).
fof(f1787,plain,
( sQ31_spl
| ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ47_spl
| ~ sQ9_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f1786]) ).
fof(f1814,plain,
! [X0,X1] :
( ~ sQ20_spl
| ~ sQ47_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c12) != sk_c12
| multiply(X0,inverse(X0)) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f1483,f1416]) ).
fof(f1815,plain,
! [X0,X1] :
( ~ sQ20_spl
| ~ sQ47_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c7) != sk_c12
| multiply(X0,inverse(X0)) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f1483,f1814]) ).
fof(f1816,plain,
! [X0,X1] :
( ~ sQ20_spl
| ~ sQ47_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c7) != sk_c7
| multiply(X0,inverse(X0)) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f1483,f1815]) ).
fof(f1817,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ47_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ20_spl
| inverse(inverse(sk_c7)) != inverse(sk_c7)
| multiply(inverse(sk_c7),sk_c7) != sk_c7
| multiply(sk_c7,inverse(sk_c7)) != sk_c7 ),
inference(resolution,[status(thm)],[f1816,f1510]) ).
fof(f1821,definition,
( sQ90_spl
<=> multiply(sk_c7,inverse(sk_c7)) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f1823,plain,
( sQ90_spl
| multiply(sk_c7,inverse(sk_c7)) != sk_c7 ),
inference(component_clause,[status(thm)],[f1821]) ).
fof(f1824,definition,
( sQ91_spl
<=> multiply(inverse(sk_c7),sk_c7) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ91_spl])],[split_symbol_definition]) ).
fof(f1826,plain,
( sQ91_spl
| multiply(inverse(sk_c7),sk_c7) != sk_c7 ),
inference(component_clause,[status(thm)],[f1824]) ).
fof(f1827,definition,
( sQ92_spl
<=> inverse(inverse(sk_c7)) = inverse(sk_c7) ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f1829,plain,
( sQ92_spl
| inverse(inverse(sk_c7)) != inverse(sk_c7) ),
inference(component_clause,[status(thm)],[f1827]) ).
fof(f1830,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ47_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ20_spl
| ~ sQ92_spl
| ~ sQ91_spl
| ~ sQ90_spl ),
inference(split_clause,[status(thm)],[f1817,f1821,f1824,f1827,f280,f177,f185,f181,f426,f157,f153]) ).
fof(f1839,plain,
( sQ91_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ47_spl
| multiply(sk_c7,sk_c7) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f1490,f1826]) ).
fof(f1840,plain,
( sQ91_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ47_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f1510,f1839]) ).
fof(f1841,plain,
( sQ91_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ47_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1840]) ).
fof(f1842,plain,
( sQ91_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ47_spl ),
inference(contradiction_clause,[status(thm)],[f1841]) ).
fof(f1843,plain,
( sQ90_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ47_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| inverse(sk_c7) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f1510,f1823]) ).
fof(f1844,plain,
( sQ90_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ47_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f1490,f1843]) ).
fof(f1845,plain,
( sQ90_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ47_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1844]) ).
fof(f1846,plain,
( sQ90_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ47_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f1845]) ).
fof(f1848,plain,
( sQ92_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ47_spl
| inverse(sk_c7) != inverse(sk_c7) ),
inference(forward_demodulation,[status(thm)],[f1490,f1829]) ).
fof(f1849,plain,
( sQ92_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ47_spl
| sk_c7 != inverse(sk_c7) ),
inference(forward_demodulation,[status(thm)],[f1490,f1848]) ).
fof(f1850,plain,
( sQ92_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ47_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f1490,f1849]) ).
fof(f1851,plain,
( sQ92_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ47_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1850]) ).
fof(f1852,plain,
( sQ92_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ47_spl ),
inference(contradiction_clause,[status(thm)],[f1851]) ).
fof(f1855,plain,
( sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ47_spl
| sk_c7 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1484,f591]) ).
fof(f1856,plain,
( sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ47_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f1478,f1855]) ).
fof(f1857,plain,
( sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ47_spl
| ~ sQ5_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1856]) ).
fof(f1858,plain,
( sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ47_spl
| ~ sQ5_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f1857]) ).
fof(f1859,plain,
( ~ sQ47_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ0_spl
| sQ49_spl ),
inference(split_clause,[status(thm)],[f1150,f433,f150,f258,f245,f426]) ).
fof(f1861,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| sQ45_spl ),
inference(split_clause,[status(thm)],[f1056,f419,f258,f245,f150]) ).
fof(f1862,plain,
$false,
inference(sat_refutation,[status(thm)],[f156,f160,f164,f168,f172,f176,f180,f184,f188,f196,f197,f198,f199,f200,f201,f202,f203,f204,f205,f209,f210,f211,f212,f213,f214,f215,f216,f217,f218,f222,f223,f224,f225,f228,f229,f230,f235,f236,f237,f238,f239,f240,f241,f242,f243,f244,f248,f249,f250,f251,f252,f253,f254,f255,f256,f261,f262,f263,f264,f265,f266,f267,f268,f269,f283,f344,f354,f384,f390,f425,f432,f436,f443,f444,f446,f455,f465,f469,f734,f753,f761,f855,f873,f878,f880,f888,f930,f933,f947,f954,f958,f964,f1005,f1074,f1076,f1144,f1228,f1238,f1258,f1272,f1280,f1284,f1288,f1292,f1296,f1303,f1312,f1321,f1333,f1336,f1390,f1402,f1407,f1412,f1467,f1517,f1701,f1755,f1787,f1830,f1842,f1846,f1852,f1858,f1859,f1861]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP312-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 20:12:20 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.10/0.47 % Refutation found
% 0.10/0.47 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.49 % Elapsed time: 0.113753 seconds
% 0.10/0.49 % CPU time: 0.615982 seconds
% 0.10/0.49 % Total memory used: 116.742 MB
% 0.10/0.49 % Net memory used: 116.276 MB
%------------------------------------------------------------------------------