%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP224-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 12:33:08 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.42s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 102
% Syntax : Number of formulae : 411 ( 12 unt; 48 def)
% Number of atoms : 1259 ( 489 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 1546 ( 698 ~; 800 |; 0 &)
% ( 48 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 50 ( 48 usr; 49 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 78 ( 78 !; 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_c5) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c4) = sk_c5
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c5,sk_c10) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c6) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c10
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( inverse(sk_c7) = sk_c8
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c8,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c9) = sk_c10
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c5,sk_c10) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c6) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( inverse(sk_c7) = sk_c8
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( multiply(sk_c8,sk_c11) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( inverse(sk_c9) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c11
| multiply(sk_c11,sk_c3) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c11,sk_c3) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c5,sk_c10) = sk_c11
| multiply(sk_c11,sk_c3) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c6) = sk_c11
| multiply(sk_c11,sk_c3) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| multiply(sk_c11,sk_c3) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c10
| multiply(sk_c11,sk_c3) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( inverse(sk_c7) = sk_c8
| multiply(sk_c11,sk_c3) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( multiply(sk_c8,sk_c11) = sk_c10
| multiply(sk_c11,sk_c3) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( inverse(sk_c9) = sk_c10
| multiply(sk_c11,sk_c3) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| multiply(sk_c11,sk_c3) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c11
| multiply(sk_c2,sk_c11) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c2,sk_c11) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
( multiply(sk_c5,sk_c10) = sk_c11
| multiply(sk_c2,sk_c11) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( inverse(sk_c6) = sk_c11
| multiply(sk_c2,sk_c11) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| multiply(sk_c2,sk_c11) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c10
| multiply(sk_c2,sk_c11) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
( inverse(sk_c7) = sk_c8
| multiply(sk_c2,sk_c11) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,negated_conjecture,
( multiply(sk_c8,sk_c11) = sk_c10
| multiply(sk_c2,sk_c11) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,negated_conjecture,
( inverse(sk_c9) = sk_c10
| multiply(sk_c2,sk_c11) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| multiply(sk_c2,sk_c11) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c11
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
( inverse(sk_c4) = sk_c5
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,negated_conjecture,
( multiply(sk_c5,sk_c10) = sk_c11
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,negated_conjecture,
( inverse(sk_c6) = sk_c11
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c10
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f50,negated_conjecture,
( inverse(sk_c7) = sk_c8
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f51,negated_conjecture,
( multiply(sk_c8,sk_c11) = sk_c10
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f52,negated_conjecture,
( inverse(sk_c9) = sk_c10
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f53,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c10
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
! [X4,X5,X6,X2,X1,X3,X7,X8,X9] :
( multiply(X9,sk_c11) != sk_c10
| inverse(X9) != sk_c10
| multiply(X8,sk_c11) != sk_c10
| inverse(X7) != X8
| multiply(X7,X8) != sk_c10
| multiply(X3,sk_c10) != sk_c11
| inverse(X3) != sk_c11
| multiply(X1,sk_c10) != sk_c11
| inverse(X2) != X1
| multiply(X2,X1) != sk_c11
| inverse(X6) != sk_c11
| multiply(X6,sk_c11) != X5
| multiply(sk_c11,X5) != sk_c10
| multiply(X4,sk_c10) != sk_c11
| inverse(X4) != sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f55,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f56,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f57,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f58,plain,
( multiply(sk_c4,sk_c5) = sk_c11
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f59,plain,
( inverse(sk_c4) = sk_c5
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f60,plain,
( multiply(sk_c5,sk_c10) = sk_c11
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f61,plain,
( inverse(sk_c6) = sk_c11
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f62,plain,
( multiply(sk_c6,sk_c10) = sk_c11
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f63,plain,
( multiply(sk_c7,sk_c8) = sk_c10
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f64,plain,
( inverse(sk_c7) = sk_c8
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f65,plain,
( multiply(sk_c8,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f66,plain,
( inverse(sk_c9) = sk_c10
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f67,plain,
( multiply(sk_c9,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f68,plain,
( multiply(sk_c4,sk_c5) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f69,plain,
( inverse(sk_c4) = sk_c5
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f70,plain,
( multiply(sk_c5,sk_c10) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f71,plain,
( inverse(sk_c6) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f72,plain,
( multiply(sk_c6,sk_c10) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f73,plain,
( multiply(sk_c7,sk_c8) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f74,plain,
( inverse(sk_c7) = sk_c8
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f75,plain,
( multiply(sk_c8,sk_c11) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f76,plain,
( inverse(sk_c9) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f77,plain,
( multiply(sk_c9,sk_c11) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f78,plain,
( multiply(sk_c4,sk_c5) = sk_c11
| multiply(sk_c11,sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f79,plain,
( inverse(sk_c4) = sk_c5
| multiply(sk_c11,sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f80,plain,
( multiply(sk_c5,sk_c10) = sk_c11
| multiply(sk_c11,sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f81,plain,
( inverse(sk_c6) = sk_c11
| multiply(sk_c11,sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f82,plain,
( multiply(sk_c6,sk_c10) = sk_c11
| multiply(sk_c11,sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f83,plain,
( multiply(sk_c7,sk_c8) = sk_c10
| multiply(sk_c11,sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f84,plain,
( inverse(sk_c7) = sk_c8
| multiply(sk_c11,sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f85,plain,
( multiply(sk_c8,sk_c11) = sk_c10
| multiply(sk_c11,sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f86,plain,
( inverse(sk_c9) = sk_c10
| multiply(sk_c11,sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f87,plain,
( multiply(sk_c9,sk_c11) = sk_c10
| multiply(sk_c11,sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f88,plain,
( multiply(sk_c4,sk_c5) = sk_c11
| multiply(sk_c2,sk_c11) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f89,plain,
( inverse(sk_c4) = sk_c5
| multiply(sk_c2,sk_c11) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f90,plain,
( multiply(sk_c5,sk_c10) = sk_c11
| multiply(sk_c2,sk_c11) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f91,plain,
( inverse(sk_c6) = sk_c11
| multiply(sk_c2,sk_c11) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f92,plain,
( multiply(sk_c6,sk_c10) = sk_c11
| multiply(sk_c2,sk_c11) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f93,plain,
( multiply(sk_c7,sk_c8) = sk_c10
| multiply(sk_c2,sk_c11) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f94,plain,
( inverse(sk_c7) = sk_c8
| multiply(sk_c2,sk_c11) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f95,plain,
( multiply(sk_c8,sk_c11) = sk_c10
| multiply(sk_c2,sk_c11) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f96,plain,
( inverse(sk_c9) = sk_c10
| multiply(sk_c2,sk_c11) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f97,plain,
( multiply(sk_c9,sk_c11) = sk_c10
| multiply(sk_c2,sk_c11) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f98,plain,
( multiply(sk_c4,sk_c5) = sk_c11
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f99,plain,
( inverse(sk_c4) = sk_c5
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f100,plain,
( multiply(sk_c5,sk_c10) = sk_c11
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f101,plain,
( inverse(sk_c6) = sk_c11
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f102,plain,
( multiply(sk_c6,sk_c10) = sk_c11
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f103,plain,
( multiply(sk_c7,sk_c8) = sk_c10
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f104,plain,
( inverse(sk_c7) = sk_c8
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f105,plain,
( multiply(sk_c8,sk_c11) = sk_c10
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f106,plain,
( inverse(sk_c9) = sk_c10
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f107,plain,
( multiply(sk_c9,sk_c11) = sk_c10
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f108,plain,
! [X9] :
( multiply(X9,sk_c11) != sk_c10
| inverse(X9) != sk_c10
| ! [X8] :
( multiply(X8,sk_c11) != sk_c10
| ! [X7] :
( inverse(X7) != X8
| multiply(X7,X8) != sk_c10
| ! [X3] :
( multiply(X3,sk_c10) != sk_c11
| inverse(X3) != sk_c11
| ! [X1] :
( multiply(X1,sk_c10) != sk_c11
| ! [X2] :
( inverse(X2) != X1
| multiply(X2,X1) != sk_c11
| ! [X6] :
( inverse(X6) != sk_c11
| ! [X5] :
( multiply(X6,sk_c11) != X5
| multiply(sk_c11,X5) != sk_c10
| ! [X4] :
( multiply(X4,sk_c10) != sk_c11
| inverse(X4) != sk_c11 ) ) ) ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f54]) ).
fof(f109,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( multiply(X8,sk_c11) != sk_c10
| inverse(X8) != sk_c10
| multiply(X7,sk_c11) != sk_c10
| inverse(X6) != X7
| multiply(X6,X7) != sk_c10
| multiply(X5,sk_c10) != sk_c11
| inverse(X5) != sk_c11
| multiply(X4,sk_c10) != sk_c11
| inverse(X3) != X4
| multiply(X3,X4) != sk_c11
| inverse(X2) != sk_c11
| multiply(X2,sk_c11) != X1
| multiply(sk_c11,X1) != sk_c10
| multiply(X0,sk_c10) != sk_c11
| inverse(X0) != sk_c11 ),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f110,definition,
( sQ0_spl
<=> inverse(sk_c1) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f111,plain,
( ~ sQ0_spl
| inverse(sk_c1) = sk_c11 ),
inference(component_clause,[status(thm)],[f110]) ).
fof(f113,definition,
( sQ1_spl
<=> multiply(sk_c4,sk_c5) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f114,plain,
( ~ sQ1_spl
| multiply(sk_c4,sk_c5) = sk_c11 ),
inference(component_clause,[status(thm)],[f113]) ).
fof(f116,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f58,f110,f113]) ).
fof(f117,definition,
( sQ2_spl
<=> inverse(sk_c4) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f118,plain,
( ~ sQ2_spl
| inverse(sk_c4) = sk_c5 ),
inference(component_clause,[status(thm)],[f117]) ).
fof(f120,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f59,f110,f117]) ).
fof(f121,definition,
( sQ3_spl
<=> multiply(sk_c5,sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f122,plain,
( ~ sQ3_spl
| multiply(sk_c5,sk_c10) = sk_c11 ),
inference(component_clause,[status(thm)],[f121]) ).
fof(f124,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f60,f110,f121]) ).
fof(f125,definition,
( sQ4_spl
<=> inverse(sk_c6) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f126,plain,
( ~ sQ4_spl
| inverse(sk_c6) = sk_c11 ),
inference(component_clause,[status(thm)],[f125]) ).
fof(f128,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f61,f110,f125]) ).
fof(f129,definition,
( sQ5_spl
<=> multiply(sk_c6,sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f130,plain,
( ~ sQ5_spl
| multiply(sk_c6,sk_c10) = sk_c11 ),
inference(component_clause,[status(thm)],[f129]) ).
fof(f132,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f62,f110,f129]) ).
fof(f133,definition,
( sQ6_spl
<=> multiply(sk_c7,sk_c8) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f134,plain,
( ~ sQ6_spl
| multiply(sk_c7,sk_c8) = sk_c10 ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,plain,
( sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f63,f110,f133]) ).
fof(f137,definition,
( sQ7_spl
<=> inverse(sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f138,plain,
( ~ sQ7_spl
| inverse(sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f137]) ).
fof(f140,plain,
( sQ7_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f64,f110,f137]) ).
fof(f141,definition,
( sQ8_spl
<=> multiply(sk_c8,sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f142,plain,
( ~ sQ8_spl
| multiply(sk_c8,sk_c11) = sk_c10 ),
inference(component_clause,[status(thm)],[f141]) ).
fof(f144,plain,
( sQ8_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f65,f110,f141]) ).
fof(f145,definition,
( sQ9_spl
<=> inverse(sk_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f146,plain,
( ~ sQ9_spl
| inverse(sk_c9) = sk_c10 ),
inference(component_clause,[status(thm)],[f145]) ).
fof(f148,plain,
( sQ9_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f66,f110,f145]) ).
fof(f149,definition,
( sQ10_spl
<=> multiply(sk_c9,sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f150,plain,
( ~ sQ10_spl
| multiply(sk_c9,sk_c11) = sk_c10 ),
inference(component_clause,[status(thm)],[f149]) ).
fof(f152,plain,
( sQ10_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f67,f110,f149]) ).
fof(f153,definition,
( sQ11_spl
<=> multiply(sk_c1,sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f154,plain,
( ~ sQ11_spl
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(component_clause,[status(thm)],[f153]) ).
fof(f156,plain,
( sQ1_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f68,f153,f113]) ).
fof(f157,plain,
( sQ2_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f69,f153,f117]) ).
fof(f158,plain,
( sQ3_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f70,f153,f121]) ).
fof(f159,plain,
( sQ4_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f71,f153,f125]) ).
fof(f160,plain,
( sQ5_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f72,f153,f129]) ).
fof(f161,plain,
( sQ6_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f73,f153,f133]) ).
fof(f162,plain,
( sQ7_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f74,f153,f137]) ).
fof(f163,plain,
( sQ8_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f75,f153,f141]) ).
fof(f164,plain,
( sQ9_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f76,f153,f145]) ).
fof(f165,plain,
( sQ10_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f77,f153,f149]) ).
fof(f166,definition,
( sQ12_spl
<=> multiply(sk_c11,sk_c3) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f167,plain,
( ~ sQ12_spl
| multiply(sk_c11,sk_c3) = sk_c10 ),
inference(component_clause,[status(thm)],[f166]) ).
fof(f169,plain,
( sQ1_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f78,f166,f113]) ).
fof(f170,plain,
( sQ2_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f79,f166,f117]) ).
fof(f171,plain,
( sQ3_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f80,f166,f121]) ).
fof(f172,plain,
( sQ4_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f81,f166,f125]) ).
fof(f173,plain,
( sQ5_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f82,f166,f129]) ).
fof(f174,plain,
( sQ6_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f83,f166,f133]) ).
fof(f175,plain,
( sQ7_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f84,f166,f137]) ).
fof(f176,plain,
( sQ8_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f85,f166,f141]) ).
fof(f177,plain,
( sQ9_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f86,f166,f145]) ).
fof(f178,plain,
( sQ10_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f87,f166,f149]) ).
fof(f179,definition,
( sQ13_spl
<=> multiply(sk_c2,sk_c11) = sk_c3 ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f180,plain,
( ~ sQ13_spl
| multiply(sk_c2,sk_c11) = sk_c3 ),
inference(component_clause,[status(thm)],[f179]) ).
fof(f182,plain,
( sQ1_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f88,f179,f113]) ).
fof(f183,plain,
( sQ2_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f89,f179,f117]) ).
fof(f184,plain,
( sQ3_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f90,f179,f121]) ).
fof(f185,plain,
( sQ4_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f91,f179,f125]) ).
fof(f186,plain,
( sQ5_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f92,f179,f129]) ).
fof(f187,plain,
( sQ6_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f93,f179,f133]) ).
fof(f188,plain,
( sQ7_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f94,f179,f137]) ).
fof(f189,plain,
( sQ8_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f95,f179,f141]) ).
fof(f190,plain,
( sQ9_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f96,f179,f145]) ).
fof(f191,plain,
( sQ10_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f97,f179,f149]) ).
fof(f192,definition,
( sQ14_spl
<=> inverse(sk_c2) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f193,plain,
( ~ sQ14_spl
| inverse(sk_c2) = sk_c11 ),
inference(component_clause,[status(thm)],[f192]) ).
fof(f195,plain,
( sQ1_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f98,f192,f113]) ).
fof(f196,plain,
( sQ2_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f99,f192,f117]) ).
fof(f197,plain,
( sQ3_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f100,f192,f121]) ).
fof(f198,plain,
( sQ4_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f101,f192,f125]) ).
fof(f199,plain,
( sQ5_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f102,f192,f129]) ).
fof(f200,plain,
( sQ6_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f103,f192,f133]) ).
fof(f201,plain,
( sQ7_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f104,f192,f137]) ).
fof(f202,plain,
( sQ8_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f105,f192,f141]) ).
fof(f203,plain,
( sQ9_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f106,f192,f145]) ).
fof(f204,plain,
( sQ10_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f107,f192,f149]) ).
fof(f205,definition,
! [X0] :
( sQ15_spl
<=> ( multiply(X0,sk_c10) != sk_c11
| inverse(X0) != sk_c11 ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f206,plain,
! [X0] :
( ~ sQ15_spl
| multiply(X0,sk_c10) != sk_c11
| inverse(X0) != sk_c11 ),
inference(component_clause,[status(thm)],[f205]) ).
fof(f208,definition,
! [X1,X2] :
( sQ16_spl
<=> ( inverse(X2) != sk_c11
| multiply(X2,sk_c11) != X1
| multiply(sk_c11,X1) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f209,plain,
! [X0,X1] :
( ~ sQ16_spl
| inverse(X1) != sk_c11
| multiply(X1,sk_c11) != X0
| multiply(sk_c11,X0) != sk_c10 ),
inference(component_clause,[status(thm)],[f208]) ).
fof(f211,definition,
! [X3,X4] :
( sQ17_spl
<=> ( multiply(X4,sk_c10) != sk_c11
| inverse(X3) != X4
| multiply(X3,X4) != sk_c11 ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f212,plain,
! [X0,X1] :
( ~ sQ17_spl
| multiply(X1,sk_c10) != sk_c11
| inverse(X0) != X1
| multiply(X0,X1) != sk_c11 ),
inference(component_clause,[status(thm)],[f211]) ).
fof(f214,definition,
! [X6,X7] :
( sQ18_spl
<=> ( multiply(X7,sk_c11) != sk_c10
| inverse(X6) != X7
| multiply(X6,X7) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f215,plain,
! [X0,X1] :
( ~ sQ18_spl
| multiply(X1,sk_c11) != sk_c10
| inverse(X0) != X1
| multiply(X0,X1) != sk_c10 ),
inference(component_clause,[status(thm)],[f214]) ).
fof(f217,definition,
! [X8] :
( sQ19_spl
<=> ( multiply(X8,sk_c11) != sk_c10
| inverse(X8) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f218,plain,
! [X0] :
( ~ sQ19_spl
| multiply(X0,sk_c11) != sk_c10
| inverse(X0) != sk_c10 ),
inference(component_clause,[status(thm)],[f217]) ).
fof(f220,plain,
( sQ19_spl
| sQ18_spl
| sQ17_spl
| sQ16_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f109,f205,f208,f211,f214,f217]) ).
fof(f222,plain,
( ~ sQ10_spl
| ~ sQ19_spl
| inverse(sk_c9) != sk_c10 ),
inference(resolution,[status(thm)],[f218,f150]) ).
fof(f225,plain,
( ~ sQ13_spl
| ~ sQ19_spl
| sk_c3 != sk_c10
| inverse(sk_c2) != sk_c10 ),
inference(paramodulation,[status(thm)],[f180,f218]) ).
fof(f226,plain,
( ~ sQ10_spl
| ~ sQ19_spl
| ~ sQ9_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f146,f222]) ).
fof(f227,plain,
( ~ sQ10_spl
| ~ sQ19_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f226]) ).
fof(f228,plain,
( ~ sQ10_spl
| ~ sQ19_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f227]) ).
fof(f229,plain,
! [X0] :
( ~ sQ18_spl
| multiply(inverse(X0),sk_c11) != sk_c10
| multiply(X0,inverse(X0)) != sk_c10 ),
inference(destructive_equality_resolution,[status(thm)],[f215]) ).
fof(f230,plain,
! [X0] :
( ~ sQ17_spl
| multiply(inverse(X0),sk_c10) != sk_c11
| multiply(X0,inverse(X0)) != sk_c11 ),
inference(destructive_equality_resolution,[status(thm)],[f212]) ).
fof(f231,plain,
! [X0] :
( ~ sQ16_spl
| inverse(X0) != sk_c11
| multiply(sk_c11,multiply(X0,sk_c11)) != sk_c10 ),
inference(destructive_equality_resolution,[status(thm)],[f209]) ).
fof(f233,plain,
! [X0] :
( ~ sQ1_spl
| multiply(sk_c11,X0) = multiply(sk_c4,multiply(sk_c5,X0)) ),
inference(paramodulation,[status(thm)],[f114,f57]) ).
fof(f244,plain,
( ~ sQ2_spl
| ~ sQ18_spl
| multiply(sk_c5,sk_c11) != sk_c10
| multiply(sk_c4,inverse(sk_c4)) != sk_c10 ),
inference(paramodulation,[status(thm)],[f118,f229]) ).
fof(f245,plain,
( ~ sQ4_spl
| ~ sQ18_spl
| multiply(sk_c11,sk_c11) != sk_c10
| multiply(sk_c6,inverse(sk_c6)) != sk_c10 ),
inference(paramodulation,[status(thm)],[f126,f229]) ).
fof(f246,plain,
( ~ sQ7_spl
| ~ sQ18_spl
| multiply(sk_c8,sk_c11) != sk_c10
| multiply(sk_c7,inverse(sk_c7)) != sk_c10 ),
inference(paramodulation,[status(thm)],[f138,f229]) ).
fof(f247,plain,
( ~ sQ0_spl
| ~ sQ18_spl
| multiply(sk_c11,sk_c11) != sk_c10
| multiply(sk_c1,inverse(sk_c1)) != sk_c10 ),
inference(paramodulation,[status(thm)],[f111,f229]) ).
fof(f249,definition,
( sQ20_spl
<=> multiply(sk_c4,inverse(sk_c4)) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f252,definition,
( sQ21_spl
<=> multiply(sk_c5,sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f255,plain,
( ~ sQ2_spl
| ~ sQ18_spl
| ~ sQ21_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f244,f249,f252,f214,f117]) ).
fof(f256,definition,
( sQ22_spl
<=> multiply(sk_c6,inverse(sk_c6)) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f259,definition,
( sQ23_spl
<=> multiply(sk_c11,sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f260,plain,
( ~ sQ23_spl
| multiply(sk_c11,sk_c11) = sk_c10 ),
inference(component_clause,[status(thm)],[f259]) ).
fof(f261,plain,
( sQ23_spl
| multiply(sk_c11,sk_c11) != sk_c10 ),
inference(component_clause,[status(thm)],[f259]) ).
fof(f262,plain,
( ~ sQ4_spl
| ~ sQ18_spl
| ~ sQ23_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f245,f256,f259,f214,f125]) ).
fof(f263,definition,
( sQ24_spl
<=> multiply(sk_c7,inverse(sk_c7)) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f265,plain,
( sQ24_spl
| multiply(sk_c7,inverse(sk_c7)) != sk_c10 ),
inference(component_clause,[status(thm)],[f263]) ).
fof(f266,plain,
( ~ sQ7_spl
| ~ sQ18_spl
| ~ sQ8_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f246,f263,f141,f214,f137]) ).
fof(f267,definition,
( sQ25_spl
<=> multiply(sk_c1,inverse(sk_c1)) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f269,plain,
( sQ25_spl
| multiply(sk_c1,inverse(sk_c1)) != sk_c10 ),
inference(component_clause,[status(thm)],[f267]) ).
fof(f270,plain,
( ~ sQ0_spl
| ~ sQ18_spl
| ~ sQ23_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f247,f267,f259,f214,f110]) ).
fof(f277,plain,
( sQ25_spl
| ~ sQ0_spl
| multiply(sk_c1,sk_c11) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f111,f269]) ).
fof(f278,plain,
( sQ24_spl
| ~ sQ7_spl
| multiply(sk_c7,sk_c8) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f138,f265]) ).
fof(f279,plain,
( sQ24_spl
| ~ sQ7_spl
| ~ sQ6_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f134,f278]) ).
fof(f280,plain,
( sQ24_spl
| ~ sQ7_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f279]) ).
fof(f281,plain,
( sQ24_spl
| ~ sQ7_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f280]) ).
fof(f290,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f56,f57]) ).
fof(f291,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f55,f290]) ).
fof(f308,plain,
( ~ sQ1_spl
| sk_c5 = multiply(inverse(sk_c4),sk_c11) ),
inference(paramodulation,[status(thm)],[f114,f291]) ).
fof(f311,plain,
( ~ sQ5_spl
| sk_c10 = multiply(inverse(sk_c6),sk_c11) ),
inference(paramodulation,[status(thm)],[f130,f291]) ).
fof(f315,plain,
( ~ sQ11_spl
| sk_c10 = multiply(inverse(sk_c1),sk_c11) ),
inference(paramodulation,[status(thm)],[f154,f291]) ).
fof(f320,plain,
( ~ sQ13_spl
| sk_c11 = multiply(inverse(sk_c2),sk_c3) ),
inference(paramodulation,[status(thm)],[f180,f291]) ).
fof(f322,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c5 = multiply(sk_c5,sk_c11) ),
inference(forward_demodulation,[status(thm)],[f118,f308]) ).
fof(f323,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| sk_c10 = multiply(sk_c11,sk_c11) ),
inference(forward_demodulation,[status(thm)],[f126,f311]) ).
fof(f324,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f323,f261]) ).
fof(f325,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| sQ23_spl ),
inference(contradiction_clause,[status(thm)],[f324]) ).
fof(f326,plain,
( ~ sQ11_spl
| ~ sQ0_spl
| sk_c10 = multiply(sk_c11,sk_c11) ),
inference(forward_demodulation,[status(thm)],[f111,f315]) ).
fof(f327,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| sk_c11 = multiply(sk_c11,sk_c3) ),
inference(forward_demodulation,[status(thm)],[f193,f320]) ).
fof(f338,definition,
( sQ28_spl
<=> identity = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f340,plain,
( sQ28_spl
| identity != sk_c11 ),
inference(component_clause,[status(thm)],[f338]) ).
fof(f342,definition,
( sQ29_spl
<=> multiply(sk_c1,inverse(sk_c1)) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f344,plain,
( sQ29_spl
| multiply(sk_c1,inverse(sk_c1)) != sk_c11 ),
inference(component_clause,[status(thm)],[f342]) ).
fof(f345,definition,
( sQ30_spl
<=> multiply(sk_c11,sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f347,plain,
( sQ30_spl
| multiply(sk_c11,sk_c10) != sk_c11 ),
inference(component_clause,[status(thm)],[f345]) ).
fof(f355,plain,
( sQ29_spl
| ~ sQ0_spl
| multiply(sk_c1,sk_c11) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f111,f344]) ).
fof(f356,plain,
( ~ sQ16_spl
| inverse(inverse(sk_c11)) != sk_c11
| multiply(sk_c11,identity) != sk_c10 ),
inference(paramodulation,[status(thm)],[f56,f231]) ).
fof(f357,plain,
( ~ sQ16_spl
| inverse(identity) != sk_c11
| multiply(sk_c11,sk_c11) != sk_c10 ),
inference(paramodulation,[status(thm)],[f55,f231]) ).
fof(f359,plain,
( ~ sQ8_spl
| ~ sQ16_spl
| inverse(sk_c8) != sk_c11
| multiply(sk_c11,sk_c10) != sk_c10 ),
inference(paramodulation,[status(thm)],[f142,f231]) ).
fof(f360,plain,
( ~ sQ10_spl
| ~ sQ16_spl
| inverse(sk_c9) != sk_c11
| multiply(sk_c11,sk_c10) != sk_c10 ),
inference(paramodulation,[status(thm)],[f150,f231]) ).
fof(f361,plain,
( ~ sQ13_spl
| ~ sQ16_spl
| inverse(sk_c2) != sk_c11
| multiply(sk_c11,sk_c3) != sk_c10 ),
inference(paramodulation,[status(thm)],[f180,f231]) ).
fof(f362,definition,
( sQ32_spl
<=> multiply(sk_c11,identity) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f364,plain,
( sQ32_spl
| multiply(sk_c11,identity) != sk_c10 ),
inference(component_clause,[status(thm)],[f362]) ).
fof(f365,definition,
( sQ33_spl
<=> inverse(inverse(sk_c11)) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f368,plain,
( ~ sQ16_spl
| ~ sQ33_spl
| ~ sQ32_spl ),
inference(split_clause,[status(thm)],[f356,f362,f365,f208]) ).
fof(f369,definition,
( sQ34_spl
<=> inverse(identity) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f372,plain,
( ~ sQ16_spl
| ~ sQ34_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f357,f259,f369,f208]) ).
fof(f373,definition,
( sQ35_spl
<=> multiply(sk_c11,sk_c10) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f375,plain,
( sQ35_spl
| multiply(sk_c11,sk_c10) != sk_c10 ),
inference(component_clause,[status(thm)],[f373]) ).
fof(f376,definition,
( sQ36_spl
<=> inverse(sk_c8) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f379,plain,
( ~ sQ8_spl
| ~ sQ16_spl
| ~ sQ36_spl
| ~ sQ35_spl ),
inference(split_clause,[status(thm)],[f359,f373,f376,f208,f141]) ).
fof(f380,definition,
( sQ37_spl
<=> inverse(sk_c9) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f382,plain,
( sQ37_spl
| inverse(sk_c9) != sk_c11 ),
inference(component_clause,[status(thm)],[f380]) ).
fof(f383,plain,
( ~ sQ10_spl
| ~ sQ16_spl
| ~ sQ37_spl
| ~ sQ35_spl ),
inference(split_clause,[status(thm)],[f360,f373,f380,f208,f149]) ).
fof(f384,plain,
( ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f361,f166,f192,f208,f179]) ).
fof(f396,plain,
( ~ sQ2_spl
| ~ sQ17_spl
| multiply(sk_c5,sk_c10) != sk_c11
| multiply(sk_c4,inverse(sk_c4)) != sk_c11 ),
inference(paramodulation,[status(thm)],[f118,f230]) ).
fof(f411,definition,
( sQ41_spl
<=> multiply(sk_c4,inverse(sk_c4)) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f413,plain,
( sQ41_spl
| multiply(sk_c4,inverse(sk_c4)) != sk_c11 ),
inference(component_clause,[status(thm)],[f411]) ).
fof(f414,plain,
( ~ sQ2_spl
| ~ sQ17_spl
| ~ sQ3_spl
| ~ sQ41_spl ),
inference(split_clause,[status(thm)],[f396,f411,f121,f211,f117]) ).
fof(f418,definition,
( sQ43_spl
<=> multiply(sk_c10,sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f420,plain,
( sQ43_spl
| multiply(sk_c10,sk_c10) != sk_c11 ),
inference(component_clause,[status(thm)],[f418]) ).
fof(f423,plain,
( sQ41_spl
| ~ sQ2_spl
| multiply(sk_c4,sk_c5) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f118,f413]) ).
fof(f424,plain,
( sQ41_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f114,f423]) ).
fof(f425,plain,
( sQ41_spl
| ~ sQ2_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f424]) ).
fof(f426,plain,
( sQ41_spl
| ~ sQ2_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f425]) ).
fof(f435,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| sk_c3 = multiply(inverse(sk_c11),sk_c11) ),
inference(paramodulation,[status(thm)],[f327,f291]) ).
fof(f437,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| sk_c3 = identity ),
inference(forward_demodulation,[status(thm)],[f56,f435]) ).
fof(f468,definition,
( sQ46_spl
<=> inverse(sk_c5) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f485,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ16_spl
| inverse(sk_c11) != sk_c11
| multiply(sk_c11,sk_c10) != sk_c10 ),
inference(paramodulation,[status(thm)],[f323,f231]) ).
fof(f488,definition,
( sQ47_spl
<=> inverse(sk_c11) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f491,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ16_spl
| ~ sQ47_spl
| ~ sQ35_spl ),
inference(split_clause,[status(thm)],[f485,f373,f488,f208,f125,f129]) ).
fof(f502,plain,
( sQ32_spl
| ~ sQ13_spl
| ~ sQ14_spl
| multiply(sk_c11,sk_c3) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f437,f364]) ).
fof(f503,plain,
( sQ32_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sk_c11 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f327,f502]) ).
fof(f518,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c11,sk_c11) = multiply(sk_c4,sk_c5) ),
inference(paramodulation,[status(thm)],[f322,f233]) ).
fof(f523,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c10 = multiply(sk_c4,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f323,f518]) ).
fof(f524,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c10 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f114,f523]) ).
fof(f529,plain,
( ~ sQ11_spl
| ~ sQ0_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f326,f259,f110,f153]) ).
fof(f531,plain,
( sQ37_spl
| ~ sQ9_spl
| sk_c10 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f146,f382]) ).
fof(f533,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sk_c11 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f327,f167]) ).
fof(f547,plain,
( ~ sQ3_spl
| ~ sQ15_spl
| sk_c11 != sk_c11
| inverse(sk_c5) != sk_c11 ),
inference(paramodulation,[status(thm)],[f122,f206]) ).
fof(f548,definition,
( sQ49_spl
<=> sk_c10 = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f549,plain,
( ~ sQ49_spl
| sk_c10 = sk_c11 ),
inference(component_clause,[status(thm)],[f548]) ).
fof(f550,plain,
( sQ49_spl
| sk_c10 != sk_c11 ),
inference(component_clause,[status(thm)],[f548]) ).
fof(f560,definition,
( sQ52_spl
<=> sk_c11 = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f562,plain,
( sQ52_spl
| sk_c11 != sk_c11 ),
inference(component_clause,[status(thm)],[f560]) ).
fof(f563,plain,
( ~ sQ3_spl
| ~ sQ15_spl
| ~ sQ52_spl
| ~ sQ46_spl ),
inference(split_clause,[status(thm)],[f547,f468,f560,f205,f121]) ).
fof(f564,plain,
( sQ52_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f562]) ).
fof(f565,plain,
sQ52_spl,
inference(contradiction_clause,[status(thm)],[f564]) ).
fof(f567,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sQ49_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f524,f550]) ).
fof(f568,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sQ49_spl ),
inference(contradiction_clause,[status(thm)],[f567]) ).
fof(f569,plain,
( sQ37_spl
| ~ sQ9_spl
| ~ sQ49_spl ),
inference(split_clause,[status(thm)],[f531,f548,f145,f380]) ).
fof(f572,plain,
( sQ28_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| identity != sk_c10 ),
inference(backward_demodulation,[status(thm)],[f524,f340]) ).
fof(f585,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(X0) != sk_c11
| multiply(sk_c10,multiply(X0,sk_c11)) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f524,f231]) ).
fof(f586,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(X0) != sk_c11
| multiply(sk_c10,multiply(X0,sk_c10)) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f524,f585]) ).
fof(f587,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(X0) != sk_c10
| multiply(sk_c10,multiply(X0,sk_c10)) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f524,f586]) ).
fof(f593,definition,
( sQ53_spl
<=> multiply(sk_c10,sk_c10) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f595,plain,
( sQ53_spl
| multiply(sk_c10,sk_c10) != sk_c10 ),
inference(component_clause,[status(thm)],[f593]) ).
fof(f599,plain,
( ~ sQ16_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(identity) != sk_c10
| multiply(sk_c10,sk_c10) != sk_c10 ),
inference(paramodulation,[status(thm)],[f55,f587]) ).
fof(f602,definition,
( sQ54_spl
<=> inverse(identity) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f605,plain,
( ~ sQ16_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ54_spl
| ~ sQ53_spl ),
inference(split_clause,[status(thm)],[f599,f593,f602,f125,f129,f117,f113,f208]) ).
fof(f607,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| inverse(sk_c6) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f524,f126]) ).
fof(f610,plain,
( ~ sQ23_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c10,sk_c11) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f524,f260]) ).
fof(f611,plain,
( ~ sQ23_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c10,sk_c10) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f524,f610]) ).
fof(f612,plain,
( ~ sQ23_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ16_spl
| inverse(sk_c10) != sk_c10
| multiply(sk_c10,sk_c10) != sk_c10 ),
inference(paramodulation,[status(thm)],[f611,f587]) ).
fof(f615,definition,
( sQ55_spl
<=> inverse(sk_c10) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f618,plain,
( ~ sQ23_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ16_spl
| ~ sQ55_spl
| ~ sQ53_spl ),
inference(split_clause,[status(thm)],[f612,f593,f615,f208,f125,f129,f117,f113,f259]) ).
fof(f619,plain,
( sQ35_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c10,sk_c10) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f524,f375]) ).
fof(f620,plain,
( sQ35_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ23_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f611,f619]) ).
fof(f621,plain,
( sQ35_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ23_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f620]) ).
fof(f622,plain,
( sQ35_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ23_spl ),
inference(contradiction_clause,[status(thm)],[f621]) ).
fof(f623,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(X0,sk_c10) != sk_c11
| inverse(X0) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f524,f206]) ).
fof(f624,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(X0,sk_c10) != sk_c10
| inverse(X0) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f524,f623]) ).
fof(f633,plain,
( sQ30_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c10,sk_c10) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f524,f347]) ).
fof(f634,plain,
( sQ30_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ23_spl
| sk_c10 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f611,f633]) ).
fof(f635,plain,
( sQ30_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ23_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f524,f634]) ).
fof(f636,plain,
( sQ30_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ23_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f635]) ).
fof(f637,plain,
( sQ30_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ23_spl ),
inference(contradiction_clause,[status(thm)],[f636]) ).
fof(f649,plain,
( sQ43_spl
| ~ sQ23_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c10 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f611,f420]) ).
fof(f650,plain,
( sQ43_spl
| ~ sQ23_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f524,f649]) ).
fof(f651,plain,
( sQ43_spl
| ~ sQ23_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f650]) ).
fof(f652,plain,
( sQ43_spl
| ~ sQ23_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f651]) ).
fof(f657,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| multiply(sk_c6,sk_c10) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f524,f130]) ).
fof(f665,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| multiply(sk_c10,sk_c6) = identity ),
inference(paramodulation,[status(thm)],[f607,f56]) ).
fof(f705,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 = multiply(sk_c5,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f524,f322]) ).
fof(f706,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c10 = multiply(inverse(sk_c5),sk_c5) ),
inference(paramodulation,[status(thm)],[f705,f291]) ).
fof(f708,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c10 = identity ),
inference(forward_demodulation,[status(thm)],[f56,f706]) ).
fof(f709,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sQ28_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f708,f572]) ).
fof(f710,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sQ28_spl ),
inference(contradiction_clause,[status(thm)],[f709]) ).
fof(f712,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sQ49_spl ),
inference(split_clause,[status(thm)],[f533,f548,f192,f179,f166]) ).
fof(f719,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ14_spl
| multiply(inverse(X0),X0) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f437,f56]) ).
fof(f721,plain,
( ~ sQ49_spl
| sQ32_spl
| ~ sQ13_spl
| ~ sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f549,f503]) ).
fof(f722,plain,
( ~ sQ49_spl
| sQ32_spl
| ~ sQ13_spl
| ~ sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f721]) ).
fof(f735,plain,
( ~ sQ0_spl
| ~ sQ49_spl
| inverse(sk_c1) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f549,f111]) ).
fof(f741,plain,
( ~ sQ14_spl
| ~ sQ49_spl
| inverse(sk_c2) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f549,f193]) ).
fof(f746,plain,
( ~ sQ11_spl
| ~ sQ49_spl
| multiply(sk_c1,sk_c10) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f549,f154]) ).
fof(f747,plain,
( ~ sQ11_spl
| ~ sQ49_spl
| sk_c10 = multiply(inverse(sk_c1),sk_c10) ),
inference(paramodulation,[status(thm)],[f746,f291]) ).
fof(f749,plain,
( ~ sQ11_spl
| ~ sQ49_spl
| ~ sQ0_spl
| sk_c10 = multiply(sk_c10,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f735,f747]) ).
fof(f761,plain,
( sQ25_spl
| ~ sQ0_spl
| ~ sQ49_spl
| multiply(sk_c1,sk_c10) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f549,f277]) ).
fof(f762,plain,
( sQ25_spl
| ~ sQ0_spl
| ~ sQ49_spl
| ~ sQ11_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f746,f761]) ).
fof(f763,plain,
( sQ25_spl
| ~ sQ0_spl
| ~ sQ49_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f762]) ).
fof(f764,plain,
( sQ25_spl
| ~ sQ0_spl
| ~ sQ49_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f763]) ).
fof(f766,plain,
( sQ29_spl
| ~ sQ0_spl
| ~ sQ49_spl
| multiply(sk_c1,sk_c10) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f549,f355]) ).
fof(f767,plain,
( sQ29_spl
| ~ sQ0_spl
| ~ sQ49_spl
| ~ sQ11_spl
| sk_c10 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f746,f766]) ).
fof(f768,plain,
( sQ29_spl
| ~ sQ0_spl
| ~ sQ49_spl
| ~ sQ11_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f549,f767]) ).
fof(f769,plain,
( sQ29_spl
| ~ sQ0_spl
| ~ sQ49_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f768]) ).
fof(f770,plain,
( sQ29_spl
| ~ sQ0_spl
| ~ sQ49_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f769]) ).
fof(f773,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ49_spl
| multiply(X0,sk_c10) != sk_c11
| inverse(X0) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f549,f206]) ).
fof(f774,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ49_spl
| multiply(X0,sk_c10) != sk_c10
| inverse(X0) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f549,f773]) ).
fof(f792,plain,
( ~ sQ23_spl
| ~ sQ49_spl
| multiply(sk_c10,sk_c11) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f549,f260]) ).
fof(f793,plain,
( ~ sQ23_spl
| ~ sQ49_spl
| multiply(sk_c10,sk_c10) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f549,f792]) ).
fof(f794,plain,
( ~ sQ23_spl
| ~ sQ49_spl
| sQ53_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f793,f595]) ).
fof(f795,plain,
( ~ sQ23_spl
| ~ sQ49_spl
| sQ53_spl ),
inference(contradiction_clause,[status(thm)],[f794]) ).
fof(f815,plain,
( ~ sQ11_spl
| ~ sQ49_spl
| ~ sQ15_spl
| inverse(sk_c1) != sk_c10 ),
inference(resolution,[status(thm)],[f774,f746]) ).
fof(f824,plain,
( ~ sQ11_spl
| ~ sQ49_spl
| ~ sQ15_spl
| ~ sQ0_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f735,f815]) ).
fof(f825,plain,
( ~ sQ11_spl
| ~ sQ49_spl
| ~ sQ15_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f824]) ).
fof(f826,plain,
( ~ sQ11_spl
| ~ sQ49_spl
| ~ sQ15_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f825]) ).
fof(f827,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ49_spl
| multiply(inverse(X0),sk_c10) != sk_c11
| multiply(X0,inverse(X0)) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f549,f230]) ).
fof(f828,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ49_spl
| multiply(inverse(X0),sk_c10) != sk_c10
| multiply(X0,inverse(X0)) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f549,f827]) ).
fof(f835,plain,
( ~ sQ0_spl
| ~ sQ49_spl
| ~ sQ17_spl
| multiply(sk_c10,sk_c10) != sk_c10
| multiply(sk_c1,inverse(sk_c1)) != sk_c10 ),
inference(paramodulation,[status(thm)],[f735,f828]) ).
fof(f840,definition,
( sQ57_spl
<=> sk_c10 = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f842,plain,
( sQ57_spl
| sk_c10 != sk_c10 ),
inference(component_clause,[status(thm)],[f840]) ).
fof(f847,definition,
( sQ59_spl
<=> sk_c3 = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f849,plain,
( sQ59_spl
| sk_c3 != sk_c10 ),
inference(component_clause,[status(thm)],[f847]) ).
fof(f852,plain,
( ~ sQ0_spl
| ~ sQ49_spl
| ~ sQ17_spl
| ~ sQ53_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f835,f267,f593,f211,f548,f110]) ).
fof(f853,plain,
( sQ57_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f842]) ).
fof(f854,plain,
sQ57_spl,
inference(contradiction_clause,[status(thm)],[f853]) ).
fof(f858,definition,
( sQ60_spl
<=> inverse(sk_c2) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f860,plain,
( sQ60_spl
| inverse(sk_c2) != sk_c10 ),
inference(component_clause,[status(thm)],[f858]) ).
fof(f861,plain,
( ~ sQ13_spl
| ~ sQ19_spl
| ~ sQ59_spl
| ~ sQ60_spl ),
inference(split_clause,[status(thm)],[f225,f858,f847,f217,f179]) ).
fof(f862,plain,
( sQ60_spl
| ~ sQ14_spl
| ~ sQ49_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f741,f860]) ).
fof(f863,plain,
( sQ60_spl
| ~ sQ14_spl
| ~ sQ49_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f862]) ).
fof(f864,plain,
( sQ60_spl
| ~ sQ14_spl
| ~ sQ49_spl ),
inference(contradiction_clause,[status(thm)],[f863]) ).
fof(f865,plain,
( ~ sQ11_spl
| ~ sQ49_spl
| ~ sQ0_spl
| sk_c10 = multiply(inverse(sk_c10),sk_c10) ),
inference(paramodulation,[status(thm)],[f749,f291]) ).
fof(f867,plain,
( ~ sQ11_spl
| ~ sQ49_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sk_c10 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f719,f865]) ).
fof(f910,plain,
( sQ59_spl
| ~ sQ11_spl
| ~ sQ49_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f867,f849]) ).
fof(f911,plain,
( sQ59_spl
| ~ sQ11_spl
| ~ sQ49_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f910]) ).
fof(f912,plain,
( sQ59_spl
| ~ sQ11_spl
| ~ sQ49_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f911]) ).
fof(f925,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c10,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f708,f55]) ).
fof(f937,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| multiply(sk_c10,X0) = multiply(sk_c6,multiply(sk_c10,X0)) ),
inference(paramodulation,[status(thm)],[f657,f57]) ).
fof(f939,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| X0 = multiply(sk_c6,multiply(sk_c10,X0)) ),
inference(forward_demodulation,[status(thm)],[f925,f937]) ).
fof(f940,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| X0 = multiply(sk_c6,X0) ),
inference(forward_demodulation,[status(thm)],[f925,f939]) ).
fof(f945,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f925,f665]) ).
fof(f951,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| inverse(sk_c6) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f956,f607]) ).
fof(f956,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| sk_c6 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f708,f945]) ).
fof(f959,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(X0,sk_c10) != sk_c10
| inverse(X0) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f956,f624]) ).
fof(f960,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(X0,sk_c6) != sk_c10
| inverse(X0) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f956,f959]) ).
fof(f961,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(X0,sk_c6) != sk_c6
| inverse(X0) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f956,f960]) ).
fof(f962,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ15_spl
| inverse(sk_c6) != sk_c6 ),
inference(resolution,[status(thm)],[f961,f940]) ).
fof(f970,definition,
( sQ62_spl
<=> sk_c6 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f972,plain,
( sQ62_spl
| sk_c6 != sk_c6 ),
inference(component_clause,[status(thm)],[f970]) ).
fof(f978,plain,
( sQ62_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f972]) ).
fof(f979,plain,
sQ62_spl,
inference(contradiction_clause,[status(thm)],[f978]) ).
fof(f996,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ15_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f951,f962]) ).
fof(f997,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ15_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f996]) ).
fof(f998,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ15_spl ),
inference(contradiction_clause,[status(thm)],[f997]) ).
fof(f999,plain,
$false,
inference(sat_refutation,[status(thm)],[f116,f120,f124,f128,f132,f136,f140,f144,f148,f152,f156,f157,f158,f159,f160,f161,f162,f163,f164,f165,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f182,f183,f184,f185,f186,f187,f188,f189,f190,f191,f195,f196,f197,f198,f199,f200,f201,f202,f203,f204,f220,f228,f255,f262,f266,f270,f281,f325,f368,f372,f379,f383,f384,f414,f426,f491,f529,f563,f565,f568,f569,f605,f618,f622,f637,f652,f710,f712,f722,f764,f770,f795,f826,f852,f854,f861,f864,f912,f979,f998]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP224-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n018.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Sun Sep 20 20:08:57 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 0.13/0.42 % Refutation found
% 0.13/0.42 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.45 % Elapsed time: 0.091668 seconds
% 0.13/0.45 % CPU time: 0.445765 seconds
% 0.13/0.45 % Total memory used: 111.502 MB
% 0.13/0.45 % Net memory used: 111.197 MB
%------------------------------------------------------------------------------