%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP242-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 12:33:11 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.43s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 88
% Syntax : Number of formulae : 438 ( 19 unt; 25 def)
% Number of atoms : 1867 ( 589 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 2724 (1295 ~;1404 |; 0 &)
% ( 25 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 27 ( 25 usr; 26 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 122 ( 122 !; 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_c10,sk_c9) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c10) = sk_c9
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c8,sk_c11) = sk_c9
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c8) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c10) = sk_c9
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( inverse(sk_c7) = sk_c10
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c8,sk_c11) = sk_c9
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c8) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c10) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c11
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c8,sk_c11) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c8) = sk_c11
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( inverse(sk_c10) = sk_c9
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c11
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c7) = sk_c10
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c8,sk_c11) = sk_c9
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c8) = sk_c11
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c3,sk_c6) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( inverse(sk_c10) = sk_c9
| multiply(sk_c3,sk_c6) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c11
| multiply(sk_c3,sk_c6) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c3,sk_c6) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( multiply(sk_c8,sk_c11) = sk_c9
| multiply(sk_c3,sk_c6) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( inverse(sk_c8) = sk_c11
| multiply(sk_c3,sk_c6) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( inverse(sk_c10) = sk_c9
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c11
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( inverse(sk_c7) = sk_c10
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
( multiply(sk_c8,sk_c11) = sk_c9
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
( inverse(sk_c8) = sk_c11
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c6,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,negated_conjecture,
( inverse(sk_c10) = sk_c9
| multiply(sk_c6,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c11
| multiply(sk_c6,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c6,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
( multiply(sk_c8,sk_c11) = sk_c9
| multiply(sk_c6,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
( inverse(sk_c8) = sk_c11
| multiply(sk_c6,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| inverse(sk_c5) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,negated_conjecture,
( inverse(sk_c10) = sk_c9
| inverse(sk_c5) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c11
| inverse(sk_c5) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,negated_conjecture,
( inverse(sk_c7) = sk_c10
| inverse(sk_c5) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f50,negated_conjecture,
( multiply(sk_c8,sk_c11) = sk_c9
| inverse(sk_c5) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f51,negated_conjecture,
( inverse(sk_c8) = sk_c11
| inverse(sk_c5) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f52,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f53,negated_conjecture,
( inverse(sk_c10) = sk_c9
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c11
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f55,negated_conjecture,
( inverse(sk_c7) = sk_c10
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f56,negated_conjecture,
( multiply(sk_c8,sk_c11) = sk_c9
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f57,negated_conjecture,
( inverse(sk_c8) = sk_c11
| inverse(sk_c4) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f58,negated_conjecture,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c5,sk_c6) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f59,negated_conjecture,
( inverse(sk_c10) = sk_c9
| multiply(sk_c5,sk_c6) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f60,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c11
| multiply(sk_c5,sk_c6) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f62,negated_conjecture,
( multiply(sk_c8,sk_c11) = sk_c9
| multiply(sk_c5,sk_c6) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f63,negated_conjecture,
( inverse(sk_c8) = sk_c11
| multiply(sk_c5,sk_c6) = sk_c4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f64,negated_conjecture,
! [X3,X4,X5,X6,X7,X8,X1,X2] :
( inverse(X2) != sk_c11
| multiply(X2,sk_c11) != sk_c9
| inverse(X1) != sk_c10
| multiply(X1,sk_c10) != sk_c11
| inverse(sk_c10) != sk_c9
| multiply(sk_c10,sk_c9) != sk_c11
| multiply(X7,X6) != X8
| inverse(X8) != X6
| inverse(X7) != X8
| multiply(X6,sk_c10) != sk_c11
| inverse(X5) != X6
| multiply(X5,X6) != sk_c11
| inverse(X4) != sk_c10
| multiply(X4,sk_c10) != sk_c9
| inverse(X3) != sk_c11
| multiply(X3,sk_c11) != sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f65,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f66,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f67,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f68,plain,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f69,plain,
( inverse(sk_c10) = sk_c9
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f70,plain,
( multiply(sk_c7,sk_c10) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f71,plain,
( inverse(sk_c7) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f72,plain,
( multiply(sk_c8,sk_c11) = sk_c9
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f73,plain,
( inverse(sk_c8) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f74,plain,
( multiply(sk_c10,sk_c9) = sk_c11
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f75,plain,
( inverse(sk_c10) = sk_c9
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f76,plain,
( multiply(sk_c7,sk_c10) = sk_c11
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f77,plain,
( inverse(sk_c7) = sk_c10
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f78,plain,
( multiply(sk_c8,sk_c11) = sk_c9
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f79,plain,
( inverse(sk_c8) = sk_c11
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f80,plain,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f81,plain,
( inverse(sk_c10) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f82,plain,
( multiply(sk_c7,sk_c10) = sk_c11
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f83,plain,
( inverse(sk_c7) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f84,plain,
( multiply(sk_c8,sk_c11) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f85,plain,
( inverse(sk_c8) = sk_c11
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f86,plain,
( multiply(sk_c10,sk_c9) = sk_c11
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f87,plain,
( inverse(sk_c10) = sk_c9
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f88,plain,
( multiply(sk_c7,sk_c10) = sk_c11
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f89,plain,
( inverse(sk_c7) = sk_c10
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f90,plain,
( multiply(sk_c8,sk_c11) = sk_c9
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f91,plain,
( inverse(sk_c8) = sk_c11
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f92,plain,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c3,sk_c6) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f93,plain,
( inverse(sk_c10) = sk_c9
| multiply(sk_c3,sk_c6) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f94,plain,
( multiply(sk_c7,sk_c10) = sk_c11
| multiply(sk_c3,sk_c6) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f95,plain,
( inverse(sk_c7) = sk_c10
| multiply(sk_c3,sk_c6) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f96,plain,
( multiply(sk_c8,sk_c11) = sk_c9
| multiply(sk_c3,sk_c6) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f97,plain,
( inverse(sk_c8) = sk_c11
| multiply(sk_c3,sk_c6) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f98,plain,
( multiply(sk_c10,sk_c9) = sk_c11
| inverse(sk_c3) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f99,plain,
( inverse(sk_c10) = sk_c9
| inverse(sk_c3) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f100,plain,
( multiply(sk_c7,sk_c10) = sk_c11
| inverse(sk_c3) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f101,plain,
( inverse(sk_c7) = sk_c10
| inverse(sk_c3) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f102,plain,
( multiply(sk_c8,sk_c11) = sk_c9
| inverse(sk_c3) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f103,plain,
( inverse(sk_c8) = sk_c11
| inverse(sk_c3) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f104,plain,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c6,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f105,plain,
( inverse(sk_c10) = sk_c9
| multiply(sk_c6,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f106,plain,
( multiply(sk_c7,sk_c10) = sk_c11
| multiply(sk_c6,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f107,plain,
( inverse(sk_c7) = sk_c10
| multiply(sk_c6,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f108,plain,
( multiply(sk_c8,sk_c11) = sk_c9
| multiply(sk_c6,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f109,plain,
( inverse(sk_c8) = sk_c11
| multiply(sk_c6,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f110,plain,
( multiply(sk_c10,sk_c9) = sk_c11
| inverse(sk_c5) = sk_c4 ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f111,plain,
( inverse(sk_c10) = sk_c9
| inverse(sk_c5) = sk_c4 ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f112,plain,
( multiply(sk_c7,sk_c10) = sk_c11
| inverse(sk_c5) = sk_c4 ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f113,plain,
( inverse(sk_c7) = sk_c10
| inverse(sk_c5) = sk_c4 ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f114,plain,
( multiply(sk_c8,sk_c11) = sk_c9
| inverse(sk_c5) = sk_c4 ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f115,plain,
( inverse(sk_c8) = sk_c11
| inverse(sk_c5) = sk_c4 ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f116,plain,
( multiply(sk_c10,sk_c9) = sk_c11
| inverse(sk_c4) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f117,plain,
( inverse(sk_c10) = sk_c9
| inverse(sk_c4) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f118,plain,
( multiply(sk_c7,sk_c10) = sk_c11
| inverse(sk_c4) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f119,plain,
( inverse(sk_c7) = sk_c10
| inverse(sk_c4) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f120,plain,
( multiply(sk_c8,sk_c11) = sk_c9
| inverse(sk_c4) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f121,plain,
( inverse(sk_c8) = sk_c11
| inverse(sk_c4) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f122,plain,
( multiply(sk_c10,sk_c9) = sk_c11
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f123,plain,
( inverse(sk_c10) = sk_c9
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f124,plain,
( multiply(sk_c7,sk_c10) = sk_c11
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f126,plain,
( multiply(sk_c8,sk_c11) = sk_c9
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f127,plain,
( inverse(sk_c8) = sk_c11
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f128,plain,
! [X2] :
( inverse(X2) != sk_c11
| multiply(X2,sk_c11) != sk_c9
| ! [X1] :
( inverse(X1) != sk_c10
| multiply(X1,sk_c10) != sk_c11
| inverse(sk_c10) != sk_c9
| multiply(sk_c10,sk_c9) != sk_c11
| ! [X6,X7,X8] :
( multiply(X7,X6) != X8
| inverse(X8) != X6
| inverse(X7) != X8
| multiply(X6,sk_c10) != sk_c11
| ! [X5] :
( inverse(X5) != X6
| multiply(X5,X6) != sk_c11
| ! [X4] :
( inverse(X4) != sk_c10
| multiply(X4,sk_c10) != sk_c9
| ! [X3] :
( inverse(X3) != sk_c11
| multiply(X3,sk_c11) != sk_c10 ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f64]) ).
fof(f129,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( inverse(X7) != sk_c11
| multiply(X7,sk_c11) != sk_c9
| inverse(X6) != sk_c10
| multiply(X6,sk_c10) != sk_c11
| inverse(sk_c10) != sk_c9
| multiply(sk_c10,sk_c9) != sk_c11
| multiply(X4,X3) != X5
| inverse(X5) != X3
| inverse(X4) != X5
| multiply(X3,sk_c10) != sk_c11
| inverse(X2) != X3
| multiply(X2,X3) != sk_c11
| inverse(X1) != sk_c10
| multiply(X1,sk_c10) != sk_c9
| inverse(X0) != sk_c11
| multiply(X0,sk_c11) != sk_c10 ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f130,definition,
( sQ0_spl
<=> multiply(sk_c1,sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f131,plain,
( ~ sQ0_spl
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(component_clause,[status(thm)],[f130]) ).
fof(f133,definition,
( sQ1_spl
<=> multiply(sk_c10,sk_c9) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f134,plain,
( ~ sQ1_spl
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f135,plain,
( sQ1_spl
| multiply(sk_c10,sk_c9) != sk_c11 ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f68,f130,f133]) ).
fof(f137,definition,
( sQ2_spl
<=> inverse(sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f138,plain,
( ~ sQ2_spl
| inverse(sk_c10) = sk_c9 ),
inference(component_clause,[status(thm)],[f137]) ).
fof(f139,plain,
( sQ2_spl
| inverse(sk_c10) != sk_c9 ),
inference(component_clause,[status(thm)],[f137]) ).
fof(f140,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f69,f130,f137]) ).
fof(f141,definition,
( sQ3_spl
<=> multiply(sk_c7,sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f142,plain,
( ~ sQ3_spl
| multiply(sk_c7,sk_c10) = sk_c11 ),
inference(component_clause,[status(thm)],[f141]) ).
fof(f144,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f70,f130,f141]) ).
fof(f145,definition,
( sQ4_spl
<=> inverse(sk_c7) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f146,plain,
( ~ sQ4_spl
| inverse(sk_c7) = sk_c10 ),
inference(component_clause,[status(thm)],[f145]) ).
fof(f147,plain,
( sQ4_spl
| inverse(sk_c7) != sk_c10 ),
inference(component_clause,[status(thm)],[f145]) ).
fof(f148,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f71,f130,f145]) ).
fof(f149,definition,
( sQ5_spl
<=> multiply(sk_c8,sk_c11) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f150,plain,
( ~ sQ5_spl
| multiply(sk_c8,sk_c11) = sk_c9 ),
inference(component_clause,[status(thm)],[f149]) ).
fof(f151,plain,
( sQ5_spl
| multiply(sk_c8,sk_c11) != sk_c9 ),
inference(component_clause,[status(thm)],[f149]) ).
fof(f152,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f72,f130,f149]) ).
fof(f153,definition,
( sQ6_spl
<=> inverse(sk_c8) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f154,plain,
( ~ sQ6_spl
| inverse(sk_c8) = sk_c11 ),
inference(component_clause,[status(thm)],[f153]) ).
fof(f156,plain,
( sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f73,f130,f153]) ).
fof(f157,definition,
( sQ7_spl
<=> inverse(sk_c1) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f158,plain,
( ~ sQ7_spl
| inverse(sk_c1) = sk_c11 ),
inference(component_clause,[status(thm)],[f157]) ).
fof(f160,plain,
( sQ1_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f74,f157,f133]) ).
fof(f161,plain,
( sQ2_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f75,f157,f137]) ).
fof(f162,plain,
( sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f76,f157,f141]) ).
fof(f163,plain,
( sQ4_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f77,f157,f145]) ).
fof(f164,plain,
( sQ5_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f78,f157,f149]) ).
fof(f165,plain,
( sQ6_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f79,f157,f153]) ).
fof(f166,definition,
( sQ8_spl
<=> multiply(sk_c2,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f167,plain,
( ~ sQ8_spl
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(component_clause,[status(thm)],[f166]) ).
fof(f169,plain,
( sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f80,f166,f133]) ).
fof(f170,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f81,f166,f137]) ).
fof(f171,plain,
( sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f82,f166,f141]) ).
fof(f172,plain,
( sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f83,f166,f145]) ).
fof(f173,plain,
( sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f84,f166,f149]) ).
fof(f174,plain,
( sQ6_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f85,f166,f153]) ).
fof(f175,definition,
( sQ9_spl
<=> inverse(sk_c2) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f176,plain,
( ~ sQ9_spl
| inverse(sk_c2) = sk_c10 ),
inference(component_clause,[status(thm)],[f175]) ).
fof(f178,plain,
( sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f86,f175,f133]) ).
fof(f179,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f87,f175,f137]) ).
fof(f180,plain,
( sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f88,f175,f141]) ).
fof(f181,plain,
( sQ4_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f89,f175,f145]) ).
fof(f182,plain,
( sQ5_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f90,f175,f149]) ).
fof(f183,plain,
( sQ6_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f91,f175,f153]) ).
fof(f184,definition,
( sQ10_spl
<=> multiply(sk_c3,sk_c6) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f185,plain,
( ~ sQ10_spl
| multiply(sk_c3,sk_c6) = sk_c11 ),
inference(component_clause,[status(thm)],[f184]) ).
fof(f187,plain,
( sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f92,f184,f133]) ).
fof(f188,plain,
( sQ2_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f93,f184,f137]) ).
fof(f189,plain,
( sQ3_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f94,f184,f141]) ).
fof(f190,plain,
( sQ4_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f95,f184,f145]) ).
fof(f191,plain,
( sQ5_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f96,f184,f149]) ).
fof(f192,plain,
( sQ6_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f97,f184,f153]) ).
fof(f193,definition,
( sQ11_spl
<=> inverse(sk_c3) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f194,plain,
( ~ sQ11_spl
| inverse(sk_c3) = sk_c6 ),
inference(component_clause,[status(thm)],[f193]) ).
fof(f196,plain,
( sQ1_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f98,f193,f133]) ).
fof(f197,plain,
( sQ2_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f99,f193,f137]) ).
fof(f198,plain,
( sQ3_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f100,f193,f141]) ).
fof(f199,plain,
( sQ4_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f101,f193,f145]) ).
fof(f200,plain,
( sQ5_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f102,f193,f149]) ).
fof(f201,plain,
( sQ6_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f103,f193,f153]) ).
fof(f202,definition,
( sQ12_spl
<=> multiply(sk_c6,sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f203,plain,
( ~ sQ12_spl
| multiply(sk_c6,sk_c10) = sk_c11 ),
inference(component_clause,[status(thm)],[f202]) ).
fof(f205,plain,
( sQ1_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f104,f202,f133]) ).
fof(f206,plain,
( sQ2_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f105,f202,f137]) ).
fof(f207,plain,
( sQ3_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f106,f202,f141]) ).
fof(f208,plain,
( sQ4_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f107,f202,f145]) ).
fof(f209,plain,
( sQ5_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f108,f202,f149]) ).
fof(f210,plain,
( sQ6_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f109,f202,f153]) ).
fof(f211,definition,
( sQ13_spl
<=> inverse(sk_c5) = sk_c4 ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f212,plain,
( ~ sQ13_spl
| inverse(sk_c5) = sk_c4 ),
inference(component_clause,[status(thm)],[f211]) ).
fof(f214,plain,
( sQ1_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f110,f211,f133]) ).
fof(f215,plain,
( sQ2_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f111,f211,f137]) ).
fof(f216,plain,
( sQ3_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f112,f211,f141]) ).
fof(f217,plain,
( sQ4_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f113,f211,f145]) ).
fof(f218,plain,
( sQ5_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f114,f211,f149]) ).
fof(f219,plain,
( sQ6_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f115,f211,f153]) ).
fof(f220,definition,
( sQ14_spl
<=> inverse(sk_c4) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f221,plain,
( ~ sQ14_spl
| inverse(sk_c4) = sk_c6 ),
inference(component_clause,[status(thm)],[f220]) ).
fof(f223,plain,
( sQ1_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f116,f220,f133]) ).
fof(f224,plain,
( sQ2_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f117,f220,f137]) ).
fof(f225,plain,
( sQ3_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f118,f220,f141]) ).
fof(f226,plain,
( sQ4_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f119,f220,f145]) ).
fof(f227,plain,
( sQ5_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f120,f220,f149]) ).
fof(f228,plain,
( sQ6_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f121,f220,f153]) ).
fof(f229,definition,
( sQ15_spl
<=> multiply(sk_c5,sk_c6) = sk_c4 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f230,plain,
( ~ sQ15_spl
| multiply(sk_c5,sk_c6) = sk_c4 ),
inference(component_clause,[status(thm)],[f229]) ).
fof(f232,plain,
( sQ1_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f122,f229,f133]) ).
fof(f233,plain,
( sQ2_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f123,f229,f137]) ).
fof(f234,plain,
( sQ3_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f124,f229,f141]) ).
fof(f236,plain,
( sQ5_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f126,f229,f149]) ).
fof(f237,plain,
( sQ6_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f127,f229,f153]) ).
fof(f238,definition,
! [X0] :
( sQ16_spl
<=> ( inverse(X0) != sk_c11
| multiply(X0,sk_c11) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f239,plain,
! [X0] :
( ~ sQ16_spl
| inverse(X0) != sk_c11
| multiply(X0,sk_c11) != sk_c10 ),
inference(component_clause,[status(thm)],[f238]) ).
fof(f241,definition,
! [X1] :
( sQ17_spl
<=> ( inverse(X1) != sk_c10
| multiply(X1,sk_c10) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f242,plain,
! [X0] :
( ~ sQ17_spl
| inverse(X0) != sk_c10
| multiply(X0,sk_c10) != sk_c9 ),
inference(component_clause,[status(thm)],[f241]) ).
fof(f244,definition,
! [X2,X3,X4,X5] :
( sQ18_spl
<=> ( multiply(X4,X3) != X5
| inverse(X5) != X3
| inverse(X4) != X5
| multiply(X3,sk_c10) != sk_c11
| inverse(X2) != X3
| multiply(X2,X3) != sk_c11 ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f245,plain,
! [X0,X1,X2,X3] :
( ~ sQ18_spl
| multiply(X2,X1) != X3
| inverse(X3) != X1
| inverse(X2) != X3
| multiply(X1,sk_c10) != sk_c11
| inverse(X0) != X1
| multiply(X0,X1) != sk_c11 ),
inference(component_clause,[status(thm)],[f244]) ).
fof(f247,definition,
! [X6] :
( sQ19_spl
<=> ( inverse(X6) != sk_c10
| multiply(X6,sk_c10) != sk_c11 ) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f248,plain,
! [X0] :
( ~ sQ19_spl
| inverse(X0) != sk_c10
| multiply(X0,sk_c10) != sk_c11 ),
inference(component_clause,[status(thm)],[f247]) ).
fof(f250,definition,
! [X7] :
( sQ20_spl
<=> ( inverse(X7) != sk_c11
| multiply(X7,sk_c11) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f251,plain,
! [X0] :
( ~ sQ20_spl
| inverse(X0) != sk_c11
| multiply(X0,sk_c11) != sk_c9 ),
inference(component_clause,[status(thm)],[f250]) ).
fof(f253,plain,
( sQ20_spl
| sQ19_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sQ18_spl
| sQ17_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f129,f238,f241,f244,f133,f137,f247,f250]) ).
fof(f255,plain,
! [X0] :
( ~ sQ5_spl
| multiply(sk_c9,X0) = multiply(sk_c8,multiply(sk_c11,X0)) ),
inference(paramodulation,[status(thm)],[f150,f67]) ).
fof(f260,plain,
( ~ sQ2_spl
| multiply(sk_c9,sk_c10) = identity ),
inference(paramodulation,[status(thm)],[f138,f66]) ).
fof(f261,plain,
( ~ sQ7_spl
| multiply(sk_c11,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f158,f66]) ).
fof(f262,plain,
( ~ sQ9_spl
| multiply(sk_c10,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f176,f66]) ).
fof(f263,plain,
( ~ sQ11_spl
| multiply(sk_c6,sk_c3) = identity ),
inference(paramodulation,[status(thm)],[f194,f66]) ).
fof(f264,plain,
( ~ sQ13_spl
| multiply(sk_c4,sk_c5) = identity ),
inference(paramodulation,[status(thm)],[f212,f66]) ).
fof(f265,plain,
( ~ sQ14_spl
| multiply(sk_c6,sk_c4) = identity ),
inference(paramodulation,[status(thm)],[f221,f66]) ).
fof(f267,plain,
( ~ sQ6_spl
| multiply(sk_c11,sk_c8) = identity ),
inference(paramodulation,[status(thm)],[f154,f66]) ).
fof(f268,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f66,f67]) ).
fof(f269,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f65,f268]) ).
fof(f272,plain,
! [X0] :
( ~ sQ10_spl
| multiply(sk_c11,X0) = multiply(sk_c3,multiply(sk_c6,X0)) ),
inference(paramodulation,[status(thm)],[f185,f67]) ).
fof(f278,plain,
( ~ sQ5_spl
| ~ sQ20_spl
| inverse(sk_c8) != sk_c11 ),
inference(resolution,[status(thm)],[f251,f150]) ).
fof(f279,plain,
( ~ sQ0_spl
| ~ sQ20_spl
| inverse(sk_c1) != sk_c11
| sk_c10 != sk_c9 ),
inference(paramodulation,[status(thm)],[f131,f251]) ).
fof(f284,plain,
( ~ sQ5_spl
| ~ sQ20_spl
| ~ sQ6_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f154,f278]) ).
fof(f285,plain,
( ~ sQ5_spl
| ~ sQ20_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f284]) ).
fof(f286,plain,
( ~ sQ5_spl
| ~ sQ20_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f285]) ).
fof(f293,plain,
! [X0] :
( ~ sQ13_spl
| multiply(identity,X0) = multiply(sk_c4,multiply(sk_c5,X0)) ),
inference(paramodulation,[status(thm)],[f264,f67]) ).
fof(f294,plain,
! [X0] :
( ~ sQ13_spl
| X0 = multiply(sk_c4,multiply(sk_c5,X0)) ),
inference(forward_demodulation,[status(thm)],[f65,f293]) ).
fof(f296,plain,
( ~ sQ3_spl
| ~ sQ19_spl
| inverse(sk_c7) != sk_c10 ),
inference(resolution,[status(thm)],[f248,f142]) ).
fof(f303,plain,
( ~ sQ3_spl
| ~ sQ19_spl
| ~ sQ4_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f146,f296]) ).
fof(f304,plain,
( ~ sQ3_spl
| ~ sQ19_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f303]) ).
fof(f305,plain,
( ~ sQ3_spl
| ~ sQ19_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f304]) ).
fof(f306,plain,
! [X0,X1] :
( ~ sQ18_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c10) != sk_c11
| multiply(X0,inverse(X0)) != sk_c11 ),
inference(destructive_equality_resolution,[status(thm)],[f245]) ).
fof(f317,plain,
( ~ sQ13_spl
| sk_c5 = multiply(inverse(sk_c4),identity) ),
inference(paramodulation,[status(thm)],[f264,f269]) ).
fof(f319,plain,
( ~ sQ6_spl
| sk_c8 = multiply(inverse(sk_c11),identity) ),
inference(paramodulation,[status(thm)],[f267,f269]) ).
fof(f320,plain,
( ~ sQ7_spl
| sk_c1 = multiply(inverse(sk_c11),identity) ),
inference(paramodulation,[status(thm)],[f261,f269]) ).
fof(f321,plain,
( ~ sQ0_spl
| sk_c11 = multiply(inverse(sk_c1),sk_c10) ),
inference(paramodulation,[status(thm)],[f131,f269]) ).
fof(f322,plain,
( ~ sQ8_spl
| sk_c10 = multiply(inverse(sk_c2),sk_c9) ),
inference(paramodulation,[status(thm)],[f167,f269]) ).
fof(f324,plain,
( ~ sQ14_spl
| sk_c4 = multiply(inverse(sk_c6),identity) ),
inference(paramodulation,[status(thm)],[f265,f269]) ).
fof(f325,plain,
( ~ sQ11_spl
| sk_c3 = multiply(inverse(sk_c6),identity) ),
inference(paramodulation,[status(thm)],[f263,f269]) ).
fof(f326,plain,
( ~ sQ12_spl
| sk_c10 = multiply(inverse(sk_c6),sk_c11) ),
inference(paramodulation,[status(thm)],[f203,f269]) ).
fof(f327,plain,
( ~ sQ15_spl
| sk_c6 = multiply(inverse(sk_c5),sk_c4) ),
inference(paramodulation,[status(thm)],[f230,f269]) ).
fof(f328,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f269,f269]) ).
fof(f329,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f66,f269]) ).
fof(f331,plain,
( ~ sQ3_spl
| sk_c10 = multiply(inverse(sk_c7),sk_c11) ),
inference(paramodulation,[status(thm)],[f142,f269]) ).
fof(f334,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| sk_c5 = multiply(sk_c6,identity) ),
inference(forward_demodulation,[status(thm)],[f221,f317]) ).
fof(f336,plain,
( sQ5_spl
| ~ sQ7_spl
| ~ sQ6_spl
| multiply(sk_c1,sk_c11) != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f340,f151]) ).
fof(f340,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| sk_c1 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f319,f320]) ).
fof(f341,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| sk_c11 = multiply(sk_c11,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f158,f321]) ).
fof(f342,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c10 = multiply(sk_c10,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f176,f322]) ).
fof(f345,plain,
( ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| multiply(sk_c3,sk_c5) = identity ),
inference(backward_demodulation,[status(thm)],[f353,f264]) ).
fof(f351,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| X0 = multiply(sk_c3,multiply(sk_c5,X0)) ),
inference(backward_demodulation,[status(thm)],[f353,f294]) ).
fof(f353,plain,
( ~ sQ11_spl
| ~ sQ14_spl
| sk_c3 = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f324,f325]) ).
fof(f354,plain,
( ~ sQ15_spl
| ~ sQ13_spl
| sk_c6 = multiply(sk_c4,sk_c4) ),
inference(forward_demodulation,[status(thm)],[f212,f327]) ).
fof(f355,plain,
( ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| sk_c6 = multiply(sk_c3,sk_c4) ),
inference(forward_demodulation,[status(thm)],[f353,f354]) ).
fof(f356,plain,
( ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| sk_c6 = multiply(sk_c3,sk_c3) ),
inference(forward_demodulation,[status(thm)],[f353,f355]) ).
fof(f358,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| sk_c5 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f359,f334]) ).
fof(f359,plain,
! [X0] : X0 = multiply(X0,identity),
inference(forward_demodulation,[status(thm)],[f328,f329]) ).
fof(f361,plain,
( sQ5_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| sk_c10 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f131,f336]) ).
fof(f367,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| X0 = multiply(sk_c3,multiply(sk_c6,X0)) ),
inference(backward_demodulation,[status(thm)],[f358,f351]) ).
fof(f368,plain,
( ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| multiply(sk_c3,sk_c6) = identity ),
inference(backward_demodulation,[status(thm)],[f358,f345]) ).
fof(f370,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| sk_c11 = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f376,f341]) ).
fof(f376,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| X0 = multiply(sk_c11,X0) ),
inference(forward_demodulation,[status(thm)],[f272,f367]) ).
fof(f383,plain,
( ~ sQ3_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| sk_c10 = multiply(inverse(sk_c7),identity) ),
inference(backward_demodulation,[status(thm)],[f388,f331]) ).
fof(f384,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| sk_c10 = multiply(inverse(sk_c6),identity) ),
inference(backward_demodulation,[status(thm)],[f388,f326]) ).
fof(f388,plain,
( ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| sk_c11 = identity ),
inference(forward_demodulation,[status(thm)],[f185,f368]) ).
fof(f390,plain,
( sQ4_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| inverse(sk_c7) != identity ),
inference(backward_demodulation,[status(thm)],[f400,f147]) ).
fof(f391,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| multiply(identity,sk_c2) = identity ),
inference(backward_demodulation,[status(thm)],[f400,f262]) ).
fof(f392,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| multiply(sk_c2,identity) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f400,f167]) ).
fof(f395,plain,
( sQ5_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| identity != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f400,f361]) ).
fof(f400,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| identity = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f388,f370]) ).
fof(f414,plain,
( ~ sQ3_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| identity = multiply(inverse(sk_c7),identity) ),
inference(forward_demodulation,[status(thm)],[f400,f383]) ).
fof(f415,plain,
( ~ sQ3_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| identity = inverse(sk_c7) ),
inference(forward_demodulation,[status(thm)],[f359,f414]) ).
fof(f416,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| identity = multiply(inverse(sk_c6),identity) ),
inference(forward_demodulation,[status(thm)],[f400,f384]) ).
fof(f417,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| identity = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f324,f416]) ).
fof(f418,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| multiply(sk_c6,identity) = identity ),
inference(backward_demodulation,[status(thm)],[f423,f263]) ).
fof(f420,plain,
( ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sk_c6 = multiply(sk_c3,identity) ),
inference(backward_demodulation,[status(thm)],[f423,f356]) ).
fof(f423,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| identity = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f353,f417]) ).
fof(f433,plain,
( sQ4_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ3_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f415,f390]) ).
fof(f434,plain,
( sQ4_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f433]) ).
fof(f435,plain,
( sQ4_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f434]) ).
fof(f436,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| sk_c2 = identity ),
inference(forward_demodulation,[status(thm)],[f65,f391]) ).
fof(f437,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| sk_c2 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f359,f392]) ).
fof(f438,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ9_spl
| identity = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f436,f437]) ).
fof(f442,plain,
( sQ5_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ9_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f438,f395]) ).
fof(f443,plain,
( sQ5_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f442]) ).
fof(f444,plain,
( sQ5_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f443]) ).
fof(f445,plain,
( ~ sQ6_spl
| sk_c8 = inverse(sk_c11) ),
inference(forward_demodulation,[status(thm)],[f359,f319]) ).
fof(f447,plain,
inverse(identity) = identity,
inference(paramodulation,[status(thm)],[f66,f359]) ).
fof(f461,plain,
( ~ sQ1_spl
| sk_c9 = multiply(inverse(sk_c10),sk_c11) ),
inference(paramodulation,[status(thm)],[f134,f269]) ).
fof(f463,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c9 = multiply(sk_c9,sk_c11) ),
inference(forward_demodulation,[status(thm)],[f138,f461]) ).
fof(f468,plain,
! [X0] :
( ~ sQ6_spl
| X0 = multiply(sk_c8,multiply(sk_c11,X0)) ),
inference(paramodulation,[status(thm)],[f445,f269]) ).
fof(f469,plain,
( ~ sQ6_spl
| multiply(sk_c8,sk_c11) = identity ),
inference(paramodulation,[status(thm)],[f445,f66]) ).
fof(f470,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sk_c9 = sk_c11 ),
inference(backward_demodulation,[status(thm)],[f475,f463]) ).
fof(f472,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sk_c10 = identity ),
inference(backward_demodulation,[status(thm)],[f475,f260]) ).
fof(f475,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ5_spl
| X0 = multiply(sk_c9,X0) ),
inference(forward_demodulation,[status(thm)],[f255,f468]) ).
fof(f481,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| sk_c9 = identity ),
inference(forward_demodulation,[status(thm)],[f150,f469]) ).
fof(f484,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c10) != identity
| multiply(X0,inverse(X0)) != sk_c11 ),
inference(backward_demodulation,[status(thm)],[f493,f306]) ).
fof(f493,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| identity = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f481,f470]) ).
fof(f509,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c10) != identity
| multiply(X0,inverse(X0)) != identity ),
inference(forward_demodulation,[status(thm)],[f493,f484]) ).
fof(f510,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),identity) != identity
| multiply(X0,inverse(X0)) != identity ),
inference(forward_demodulation,[status(thm)],[f472,f509]) ).
fof(f511,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| inverse(X0) != identity
| multiply(X0,inverse(X0)) != identity ),
inference(forward_demodulation,[status(thm)],[f359,f510]) ).
fof(f537,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| multiply(X0,inverse(identity)) != inverse(X0)
| inverse(inverse(X0)) != inverse(identity)
| multiply(identity,inverse(identity)) != identity ),
inference(resolution,[status(thm)],[f447,f511]) ).
fof(f541,definition,
( sQ21_spl
<=> multiply(identity,inverse(identity)) = identity ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f543,plain,
( sQ21_spl
| multiply(identity,inverse(identity)) != identity ),
inference(component_clause,[status(thm)],[f541]) ).
fof(f544,definition,
! [X0] :
( sQ22_spl
<=> ( multiply(X0,inverse(identity)) != inverse(X0)
| inverse(inverse(X0)) != inverse(identity) ) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f545,plain,
! [X0] :
( ~ sQ22_spl
| multiply(X0,inverse(identity)) != inverse(X0)
| inverse(inverse(X0)) != inverse(identity) ),
inference(component_clause,[status(thm)],[f544]) ).
fof(f547,plain,
( ~ sQ18_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sQ22_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f537,f541,f544,f149,f153,f137,f133,f244]) ).
fof(f548,definition,
( sQ23_spl
<=> identity = identity ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f550,plain,
( sQ23_spl
| identity != identity ),
inference(component_clause,[status(thm)],[f548]) ).
fof(f553,plain,
! [X0] :
( ~ sQ22_spl
| multiply(X0,inverse(identity)) != inverse(X0)
| inverse(inverse(X0)) != identity ),
inference(forward_demodulation,[status(thm)],[f447,f545]) ).
fof(f554,plain,
! [X0] :
( ~ sQ22_spl
| multiply(X0,identity) != inverse(X0)
| inverse(inverse(X0)) != identity ),
inference(forward_demodulation,[status(thm)],[f447,f553]) ).
fof(f555,plain,
! [X0] :
( ~ sQ22_spl
| X0 != inverse(X0)
| inverse(inverse(X0)) != identity ),
inference(forward_demodulation,[status(thm)],[f359,f554]) ).
fof(f556,plain,
( sQ21_spl
| inverse(identity) != identity ),
inference(forward_demodulation,[status(thm)],[f65,f543]) ).
fof(f557,plain,
( sQ21_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f447,f556]) ).
fof(f558,plain,
( sQ21_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f557]) ).
fof(f559,plain,
sQ21_spl,
inference(contradiction_clause,[status(thm)],[f558]) ).
fof(f560,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| inverse(X0) != sk_c10
| multiply(X0,identity) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f472,f242]) ).
fof(f561,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| inverse(X0) != sk_c10
| X0 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f359,f560]) ).
fof(f562,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| inverse(X0) != sk_c10
| X0 != identity ),
inference(forward_demodulation,[status(thm)],[f481,f561]) ).
fof(f563,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| inverse(X0) != identity
| X0 != identity ),
inference(forward_demodulation,[status(thm)],[f472,f562]) ).
fof(f564,plain,
( ~ sQ17_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| inverse(identity) != identity ),
inference(destructive_equality_resolution,[status(thm)],[f563]) ).
fof(f565,plain,
( ~ sQ17_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f564,f447]) ).
fof(f566,plain,
( ~ sQ17_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f565]) ).
fof(f610,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f359,f418]) ).
fof(f612,plain,
( ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| identity = multiply(sk_c3,identity) ),
inference(forward_demodulation,[status(thm)],[f610,f420]) ).
fof(f613,plain,
( ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| identity = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f359,f612]) ).
fof(f647,plain,
( ~ sQ10_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ7_spl
| multiply(identity,sk_c6) = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f613,f185]) ).
fof(f648,plain,
( ~ sQ10_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sk_c6 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f65,f647]) ).
fof(f649,plain,
( ~ sQ10_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ7_spl
| identity = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f610,f648]) ).
fof(f706,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| inverse(X0) != sk_c11
| multiply(X0,sk_c11) != identity ),
inference(backward_demodulation,[status(thm)],[f472,f239]) ).
fof(f742,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ1_spl
| inverse(X0) != sk_c11
| multiply(X0,identity) != identity ),
inference(forward_demodulation,[status(thm)],[f493,f706]) ).
fof(f743,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ1_spl
| inverse(X0) != sk_c11
| X0 != identity ),
inference(forward_demodulation,[status(thm)],[f359,f742]) ).
fof(f744,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ1_spl
| inverse(X0) != identity
| X0 != identity ),
inference(forward_demodulation,[status(thm)],[f493,f743]) ).
fof(f745,plain,
( ~ sQ16_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ1_spl
| inverse(identity) != identity ),
inference(destructive_equality_resolution,[status(thm)],[f744]) ).
fof(f746,plain,
( ~ sQ16_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f745,f447]) ).
fof(f747,plain,
( ~ sQ16_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f746]) ).
fof(f872,plain,
! [X0] : multiply(X0,inverse(X0)) = identity,
inference(paramodulation,[status(thm)],[f66,f328]) ).
fof(f873,plain,
! [X0] : multiply(X0,identity) = inverse(inverse(X0)),
inference(paramodulation,[status(thm)],[f359,f328]) ).
fof(f882,plain,
! [X0] :
( ~ sQ22_spl
| X0 != inverse(X0)
| X0 != identity ),
inference(backward_demodulation,[status(thm)],[f883,f555]) ).
fof(f883,plain,
! [X0] : X0 = inverse(inverse(X0)),
inference(forward_demodulation,[status(thm)],[f359,f873]) ).
fof(f893,plain,
( ~ sQ22_spl
| identity != inverse(identity) ),
inference(destructive_equality_resolution,[status(thm)],[f882]) ).
fof(f894,plain,
( ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f893,f447]) ).
fof(f895,plain,
~ sQ22_spl,
inference(contradiction_clause,[status(thm)],[f894]) ).
fof(f896,plain,
( ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sk_c6 = multiply(identity,sk_c3) ),
inference(forward_demodulation,[status(thm)],[f613,f356]) ).
fof(f897,plain,
( ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sk_c6 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f65,f896]) ).
fof(f898,plain,
( ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f613,f897]) ).
fof(f923,plain,
( sQ23_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f550]) ).
fof(f924,plain,
sQ23_spl,
inference(contradiction_clause,[status(thm)],[f923]) ).
fof(f928,plain,
( ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| multiply(identity,sk_c10) = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f898,f203]) ).
fof(f929,plain,
( ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sk_c10 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f65,f928]) ).
fof(f930,plain,
( ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sk_c10 = identity ),
inference(forward_demodulation,[status(thm)],[f649,f929]) ).
fof(f937,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| identity = multiply(sk_c10,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f930,f342]) ).
fof(f938,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| identity = multiply(identity,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f930,f937]) ).
fof(f940,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| identity = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f65,f938]) ).
fof(f941,plain,
( ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| multiply(sk_c2,identity) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f930,f167]) ).
fof(f942,plain,
( ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sk_c2 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f359,f941]) ).
fof(f943,plain,
( ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ9_spl
| sk_c2 = identity ),
inference(forward_demodulation,[status(thm)],[f940,f942]) ).
fof(f951,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| inverse(identity) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f943,f176]) ).
fof(f952,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| inverse(identity) = identity ),
inference(forward_demodulation,[status(thm)],[f930,f951]) ).
fof(f973,definition,
( sQ25_spl
<=> sk_c10 = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f975,plain,
( sQ25_spl
| sk_c10 != sk_c9 ),
inference(component_clause,[status(thm)],[f973]) ).
fof(f976,plain,
( ~ sQ0_spl
| ~ sQ20_spl
| ~ sQ7_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f279,f973,f157,f250,f130]) ).
fof(f1122,plain,
( sQ25_spl
| ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| identity != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f930,f975]) ).
fof(f1123,plain,
( sQ25_spl
| ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f940,f1122]) ).
fof(f1124,plain,
( sQ25_spl
| ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1123]) ).
fof(f1125,plain,
( sQ25_spl
| ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f1124]) ).
fof(f1126,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ10_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ7_spl
| inverse(X0) != sk_c11
| multiply(X0,identity) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f649,f239]) ).
fof(f1127,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ10_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ7_spl
| inverse(X0) != sk_c11
| X0 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f359,f1126]) ).
fof(f1128,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ10_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ7_spl
| inverse(X0) != sk_c11
| X0 != identity ),
inference(forward_demodulation,[status(thm)],[f930,f1127]) ).
fof(f1129,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ10_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ7_spl
| inverse(X0) != identity
| X0 != identity ),
inference(forward_demodulation,[status(thm)],[f649,f1128]) ).
fof(f1130,plain,
( ~ sQ16_spl
| ~ sQ10_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ7_spl
| inverse(identity) != identity ),
inference(destructive_equality_resolution,[status(thm)],[f1129]) ).
fof(f1131,plain,
( ~ sQ16_spl
| ~ sQ10_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1130,f952]) ).
fof(f1132,plain,
( ~ sQ16_spl
| ~ sQ10_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f1131]) ).
fof(f1138,plain,
! [X0,X1] :
( ~ sQ18_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c10) != sk_c11
| identity != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f872,f306]) ).
fof(f1139,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ sQ10_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ7_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c10) != sk_c11
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f649,f1138]) ).
fof(f1140,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ sQ10_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ7_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),identity) != sk_c11
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f930,f1139]) ).
fof(f1141,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ sQ10_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ7_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| inverse(X0) != sk_c11
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f359,f1140]) ).
fof(f1142,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ sQ10_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ7_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| inverse(X0) != identity
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f649,f1141]) ).
fof(f1143,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ sQ10_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ7_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| X1 != inverse(X0)
| inverse(X0) != identity
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f883,f1142]) ).
fof(f1144,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ sQ10_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ7_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| X1 != inverse(X0)
| inverse(X0) != identity ),
inference(trivial_equality_resolution,[status(thm)],[f1143]) ).
fof(f1145,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ10_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ7_spl
| multiply(inverse(X0),inverse(X0)) != inverse(inverse(X0))
| inverse(X0) != identity ),
inference(destructive_equality_resolution,[status(thm)],[f1144]) ).
fof(f1190,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ18_spl
| multiply(inverse(identity),inverse(identity)) != inverse(inverse(identity)) ),
inference(resolution,[status(thm)],[f1145,f952]) ).
fof(f1194,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ18_spl
| multiply(identity,inverse(identity)) != inverse(inverse(identity)) ),
inference(forward_demodulation,[status(thm)],[f952,f1190]) ).
fof(f1195,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ18_spl
| inverse(identity) != inverse(inverse(identity)) ),
inference(forward_demodulation,[status(thm)],[f65,f1194]) ).
fof(f1196,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ18_spl
| identity != inverse(inverse(identity)) ),
inference(forward_demodulation,[status(thm)],[f952,f1195]) ).
fof(f1197,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ18_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f883,f1196]) ).
fof(f1198,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ18_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1197]) ).
fof(f1199,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f1198]) ).
fof(f1200,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| inverse(X0) != sk_c10
| multiply(X0,identity) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f930,f242]) ).
fof(f1201,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| inverse(X0) != sk_c10
| X0 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f359,f1200]) ).
fof(f1202,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(X0) != sk_c10
| X0 != identity ),
inference(forward_demodulation,[status(thm)],[f940,f1201]) ).
fof(f1203,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(X0) != identity
| X0 != identity ),
inference(forward_demodulation,[status(thm)],[f930,f1202]) ).
fof(f1204,plain,
( ~ sQ17_spl
| ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(identity) != identity ),
inference(destructive_equality_resolution,[status(thm)],[f1203]) ).
fof(f1205,plain,
( ~ sQ17_spl
| ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1204,f952]) ).
fof(f1206,plain,
( ~ sQ17_spl
| ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f1205]) ).
fof(f1252,plain,
! [X0] :
( ~ sQ19_spl
| ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| inverse(X0) != sk_c10
| multiply(X0,identity) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f930,f248]) ).
fof(f1253,plain,
! [X0] :
( ~ sQ19_spl
| ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| inverse(X0) != sk_c10
| X0 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f359,f1252]) ).
fof(f1254,plain,
! [X0] :
( ~ sQ19_spl
| ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| inverse(X0) != sk_c10
| X0 != identity ),
inference(forward_demodulation,[status(thm)],[f649,f1253]) ).
fof(f1255,plain,
! [X0] :
( ~ sQ19_spl
| ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| inverse(X0) != identity
| X0 != identity ),
inference(forward_demodulation,[status(thm)],[f930,f1254]) ).
fof(f1256,plain,
( ~ sQ19_spl
| ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| inverse(identity) != identity ),
inference(destructive_equality_resolution,[status(thm)],[f1255]) ).
fof(f1257,plain,
( ~ sQ19_spl
| ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1256,f952]) ).
fof(f1258,plain,
( ~ sQ19_spl
| ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f1257]) ).
fof(f1259,plain,
( sQ2_spl
| ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| inverse(identity) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f930,f139]) ).
fof(f1260,plain,
( sQ2_spl
| ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ8_spl
| identity != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f952,f1259]) ).
fof(f1261,plain,
( sQ2_spl
| ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ8_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f940,f1260]) ).
fof(f1262,plain,
( sQ2_spl
| ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1261]) ).
fof(f1263,plain,
( sQ2_spl
| ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f1262]) ).
fof(f1264,plain,
( sQ1_spl
| ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| multiply(identity,sk_c9) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f930,f135]) ).
fof(f1265,plain,
( sQ1_spl
| ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sk_c9 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f65,f1264]) ).
fof(f1266,plain,
( sQ1_spl
| ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| identity != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f940,f1265]) ).
fof(f1267,plain,
( sQ1_spl
| ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f649,f1266]) ).
fof(f1268,plain,
( sQ1_spl
| ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1267]) ).
fof(f1269,plain,
( sQ1_spl
| ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f1268]) ).
fof(f1270,plain,
$false,
inference(sat_refutation,[status(thm)],[f136,f140,f144,f148,f152,f156,f160,f161,f162,f163,f164,f165,f169,f170,f171,f172,f173,f174,f178,f179,f180,f181,f182,f183,f187,f188,f189,f190,f191,f192,f196,f197,f198,f199,f200,f201,f205,f206,f207,f208,f209,f210,f214,f215,f216,f217,f218,f219,f223,f224,f225,f226,f227,f228,f232,f233,f234,f236,f237,f253,f286,f305,f435,f444,f547,f559,f566,f747,f895,f924,f976,f1125,f1132,f1199,f1206,f1258,f1263,f1269]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP242-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n011.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 20:07:12 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.43 % Refutation found
% 0.09/0.43 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.45 % Elapsed time: 0.070284 seconds
% 0.09/0.45 % CPU time: 0.331433 seconds
% 0.09/0.45 % Total memory used: 110.386 MB
% 0.09/0.45 % Net memory used: 110.128 MB
%------------------------------------------------------------------------------