%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP240-1 : 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 12:33:11 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.41s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 94
% Syntax : Number of formulae : 376 ( 12 unt; 34 def)
% Number of atoms : 1369 ( 464 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 1822 ( 829 ~; 959 |; 0 &)
% ( 34 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 36 ( 34 usr; 35 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 62 ( 62 !; 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,
( inverse(sk_c4) = sk_c10
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c10
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c9
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c9
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c7) = sk_c10
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c10
| inverse(sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c9
| inverse(sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c9
| inverse(sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| inverse(sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c7) = sk_c10
| inverse(sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c10
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( inverse(sk_c7) = sk_c10
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c10,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c10
| multiply(sk_c10,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c9
| multiply(sk_c10,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c10,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c9
| multiply(sk_c10,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c10,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c10,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c10,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c2,sk_c10) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f50,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c2,sk_c10) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f51,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f52,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f53,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c10
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c9
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f55,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f56,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f57,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f58,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f59,negated_conjecture,
( inverse(sk_c7) = sk_c10
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f60,negated_conjecture,
! [X4,X5,X6,X1,X3,X2,X7,X8] :
( inverse(X8) != sk_c10
| multiply(X8,sk_c10) != X7
| multiply(sk_c10,X7) != sk_c9
| multiply(X2,sk_c10) != sk_c9
| inverse(X3) != X2
| multiply(X3,X2) != sk_c9
| multiply(X1,sk_c9) != sk_c10
| inverse(X1) != sk_c10
| inverse(X6) != sk_c10
| multiply(X6,sk_c10) != X5
| multiply(sk_c10,X5) != sk_c9
| inverse(X4) != sk_c9
| multiply(X4,sk_c9) != sk_c10
| inverse(sk_c9) != sk_c10
| inverse(sk_c10) != sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f61,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f62,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f63,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f64,plain,
( inverse(sk_c4) = sk_c10
| inverse(sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f65,plain,
( multiply(sk_c4,sk_c9) = sk_c10
| inverse(sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f66,plain,
( multiply(sk_c5,sk_c6) = sk_c9
| inverse(sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f67,plain,
( inverse(sk_c5) = sk_c6
| inverse(sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f68,plain,
( multiply(sk_c6,sk_c10) = sk_c9
| inverse(sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f69,plain,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f70,plain,
( multiply(sk_c7,sk_c10) = sk_c8
| inverse(sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f71,plain,
( inverse(sk_c7) = sk_c10
| inverse(sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f72,plain,
( inverse(sk_c4) = sk_c10
| inverse(sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f73,plain,
( multiply(sk_c4,sk_c9) = sk_c10
| inverse(sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f74,plain,
( multiply(sk_c5,sk_c6) = sk_c9
| inverse(sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f75,plain,
( inverse(sk_c5) = sk_c6
| inverse(sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f76,plain,
( multiply(sk_c6,sk_c10) = sk_c9
| inverse(sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f77,plain,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f78,plain,
( multiply(sk_c7,sk_c10) = sk_c8
| inverse(sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f79,plain,
( inverse(sk_c7) = sk_c10
| inverse(sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f80,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f81,plain,
( multiply(sk_c4,sk_c9) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f82,plain,
( multiply(sk_c5,sk_c6) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f83,plain,
( inverse(sk_c5) = sk_c6
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f84,plain,
( multiply(sk_c6,sk_c10) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f85,plain,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f86,plain,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f87,plain,
( inverse(sk_c7) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f88,plain,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f89,plain,
( multiply(sk_c4,sk_c9) = sk_c10
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f90,plain,
( multiply(sk_c5,sk_c6) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f91,plain,
( inverse(sk_c5) = sk_c6
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f92,plain,
( multiply(sk_c6,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f93,plain,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f94,plain,
( multiply(sk_c7,sk_c10) = sk_c8
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f95,plain,
( inverse(sk_c7) = sk_c10
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f96,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c10,sk_c3) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f97,plain,
( multiply(sk_c4,sk_c9) = sk_c10
| multiply(sk_c10,sk_c3) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f98,plain,
( multiply(sk_c5,sk_c6) = sk_c9
| multiply(sk_c10,sk_c3) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f99,plain,
( inverse(sk_c5) = sk_c6
| multiply(sk_c10,sk_c3) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f100,plain,
( multiply(sk_c6,sk_c10) = sk_c9
| multiply(sk_c10,sk_c3) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f101,plain,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c10,sk_c3) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f102,plain,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c10,sk_c3) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f103,plain,
( inverse(sk_c7) = sk_c10
| multiply(sk_c10,sk_c3) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f104,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f105,plain,
( multiply(sk_c4,sk_c9) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f106,plain,
( multiply(sk_c5,sk_c6) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f107,plain,
( inverse(sk_c5) = sk_c6
| multiply(sk_c2,sk_c10) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f108,plain,
( multiply(sk_c6,sk_c10) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f109,plain,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f110,plain,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c2,sk_c10) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f111,plain,
( inverse(sk_c7) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f112,plain,
( inverse(sk_c4) = sk_c10
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f113,plain,
( multiply(sk_c4,sk_c9) = sk_c10
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f114,plain,
( multiply(sk_c5,sk_c6) = sk_c9
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f115,plain,
( inverse(sk_c5) = sk_c6
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f116,plain,
( multiply(sk_c6,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f117,plain,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f118,plain,
( multiply(sk_c7,sk_c10) = sk_c8
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f119,plain,
( inverse(sk_c7) = sk_c10
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f120,plain,
! [X8] :
( inverse(X8) != sk_c10
| ! [X7] :
( multiply(X8,sk_c10) != X7
| multiply(sk_c10,X7) != sk_c9
| ! [X2] :
( multiply(X2,sk_c10) != sk_c9
| ! [X3] :
( inverse(X3) != X2
| multiply(X3,X2) != sk_c9
| ! [X1] :
( multiply(X1,sk_c9) != sk_c10
| inverse(X1) != sk_c10
| ! [X6] :
( inverse(X6) != sk_c10
| ! [X5] :
( multiply(X6,sk_c10) != X5
| multiply(sk_c10,X5) != sk_c9
| ! [X4] :
( inverse(X4) != sk_c9
| multiply(X4,sk_c9) != sk_c10
| inverse(sk_c9) != sk_c10
| inverse(sk_c10) != sk_c9 ) ) ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f60]) ).
fof(f121,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( inverse(X7) != sk_c10
| multiply(X7,sk_c10) != X6
| multiply(sk_c10,X6) != sk_c9
| multiply(X5,sk_c10) != sk_c9
| inverse(X4) != X5
| multiply(X4,X5) != sk_c9
| multiply(X3,sk_c9) != sk_c10
| inverse(X3) != sk_c10
| inverse(X2) != sk_c10
| multiply(X2,sk_c10) != X1
| multiply(sk_c10,X1) != sk_c9
| inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c10
| inverse(sk_c9) != sk_c10
| inverse(sk_c10) != sk_c9 ),
inference(cnf_transformation,[status(thm)],[f120]) ).
fof(f122,definition,
( sQ0_spl
<=> inverse(sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f123,plain,
( ~ sQ0_spl
| inverse(sk_c10) = sk_c9 ),
inference(component_clause,[status(thm)],[f122]) ).
fof(f124,plain,
( sQ0_spl
| inverse(sk_c10) != sk_c9 ),
inference(component_clause,[status(thm)],[f122]) ).
fof(f125,definition,
( sQ1_spl
<=> inverse(sk_c4) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f126,plain,
( ~ sQ1_spl
| inverse(sk_c4) = sk_c10 ),
inference(component_clause,[status(thm)],[f125]) ).
fof(f128,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f64,f122,f125]) ).
fof(f129,definition,
( sQ2_spl
<=> multiply(sk_c4,sk_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f130,plain,
( ~ sQ2_spl
| multiply(sk_c4,sk_c9) = sk_c10 ),
inference(component_clause,[status(thm)],[f129]) ).
fof(f132,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f65,f122,f129]) ).
fof(f133,definition,
( sQ3_spl
<=> multiply(sk_c5,sk_c6) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f134,plain,
( ~ sQ3_spl
| multiply(sk_c5,sk_c6) = sk_c9 ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f66,f122,f133]) ).
fof(f137,definition,
( sQ4_spl
<=> inverse(sk_c5) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f138,plain,
( ~ sQ4_spl
| inverse(sk_c5) = sk_c6 ),
inference(component_clause,[status(thm)],[f137]) ).
fof(f140,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f67,f122,f137]) ).
fof(f141,definition,
( sQ5_spl
<=> multiply(sk_c6,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f142,plain,
( ~ sQ5_spl
| multiply(sk_c6,sk_c10) = sk_c9 ),
inference(component_clause,[status(thm)],[f141]) ).
fof(f144,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f68,f122,f141]) ).
fof(f145,definition,
( sQ6_spl
<=> multiply(sk_c10,sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f146,plain,
( ~ sQ6_spl
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(component_clause,[status(thm)],[f145]) ).
fof(f148,plain,
( sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f69,f122,f145]) ).
fof(f149,definition,
( sQ7_spl
<=> multiply(sk_c7,sk_c10) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f150,plain,
( ~ sQ7_spl
| multiply(sk_c7,sk_c10) = sk_c8 ),
inference(component_clause,[status(thm)],[f149]) ).
fof(f152,plain,
( sQ7_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f70,f122,f149]) ).
fof(f153,definition,
( sQ8_spl
<=> inverse(sk_c7) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f154,plain,
( ~ sQ8_spl
| inverse(sk_c7) = sk_c10 ),
inference(component_clause,[status(thm)],[f153]) ).
fof(f156,plain,
( sQ8_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f71,f122,f153]) ).
fof(f157,definition,
( sQ9_spl
<=> inverse(sk_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f158,plain,
( ~ sQ9_spl
| inverse(sk_c9) = sk_c10 ),
inference(component_clause,[status(thm)],[f157]) ).
fof(f159,plain,
( sQ9_spl
| inverse(sk_c9) != sk_c10 ),
inference(component_clause,[status(thm)],[f157]) ).
fof(f160,plain,
( sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f72,f157,f125]) ).
fof(f161,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f73,f157,f129]) ).
fof(f162,plain,
( sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f74,f157,f133]) ).
fof(f163,plain,
( sQ4_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f75,f157,f137]) ).
fof(f164,plain,
( sQ5_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f76,f157,f141]) ).
fof(f165,plain,
( sQ6_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f77,f157,f145]) ).
fof(f166,plain,
( sQ7_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f78,f157,f149]) ).
fof(f167,plain,
( sQ8_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f79,f157,f153]) ).
fof(f168,definition,
( sQ10_spl
<=> multiply(sk_c1,sk_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f169,plain,
( ~ sQ10_spl
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(component_clause,[status(thm)],[f168]) ).
fof(f171,plain,
( sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f80,f168,f125]) ).
fof(f172,plain,
( sQ2_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f81,f168,f129]) ).
fof(f173,plain,
( sQ3_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f82,f168,f133]) ).
fof(f174,plain,
( sQ4_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f83,f168,f137]) ).
fof(f175,plain,
( sQ5_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f84,f168,f141]) ).
fof(f176,plain,
( sQ6_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f85,f168,f145]) ).
fof(f177,plain,
( sQ7_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f86,f168,f149]) ).
fof(f178,plain,
( sQ8_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f87,f168,f153]) ).
fof(f179,definition,
( sQ11_spl
<=> inverse(sk_c1) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f180,plain,
( ~ sQ11_spl
| inverse(sk_c1) = sk_c9 ),
inference(component_clause,[status(thm)],[f179]) ).
fof(f182,plain,
( sQ1_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f88,f179,f125]) ).
fof(f183,plain,
( sQ2_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f89,f179,f129]) ).
fof(f184,plain,
( sQ3_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f90,f179,f133]) ).
fof(f185,plain,
( sQ4_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f91,f179,f137]) ).
fof(f186,plain,
( sQ5_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f92,f179,f141]) ).
fof(f187,plain,
( sQ6_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f93,f179,f145]) ).
fof(f188,plain,
( sQ7_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f94,f179,f149]) ).
fof(f189,plain,
( sQ8_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f95,f179,f153]) ).
fof(f190,definition,
( sQ12_spl
<=> multiply(sk_c10,sk_c3) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f191,plain,
( ~ sQ12_spl
| multiply(sk_c10,sk_c3) = sk_c9 ),
inference(component_clause,[status(thm)],[f190]) ).
fof(f193,plain,
( sQ1_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f96,f190,f125]) ).
fof(f194,plain,
( sQ2_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f97,f190,f129]) ).
fof(f195,plain,
( sQ3_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f98,f190,f133]) ).
fof(f196,plain,
( sQ4_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f99,f190,f137]) ).
fof(f197,plain,
( sQ5_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f100,f190,f141]) ).
fof(f198,plain,
( sQ6_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f101,f190,f145]) ).
fof(f199,plain,
( sQ7_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f102,f190,f149]) ).
fof(f200,plain,
( sQ8_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f103,f190,f153]) ).
fof(f201,definition,
( sQ13_spl
<=> multiply(sk_c2,sk_c10) = sk_c3 ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f202,plain,
( ~ sQ13_spl
| multiply(sk_c2,sk_c10) = sk_c3 ),
inference(component_clause,[status(thm)],[f201]) ).
fof(f204,plain,
( sQ1_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f104,f201,f125]) ).
fof(f205,plain,
( sQ2_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f105,f201,f129]) ).
fof(f206,plain,
( sQ3_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f106,f201,f133]) ).
fof(f207,plain,
( sQ4_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f107,f201,f137]) ).
fof(f208,plain,
( sQ5_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f108,f201,f141]) ).
fof(f209,plain,
( sQ6_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f109,f201,f145]) ).
fof(f210,plain,
( sQ7_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f110,f201,f149]) ).
fof(f211,plain,
( sQ8_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f111,f201,f153]) ).
fof(f212,definition,
( sQ14_spl
<=> inverse(sk_c2) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f213,plain,
( ~ sQ14_spl
| inverse(sk_c2) = sk_c10 ),
inference(component_clause,[status(thm)],[f212]) ).
fof(f215,plain,
( sQ1_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f112,f212,f125]) ).
fof(f216,plain,
( sQ2_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f113,f212,f129]) ).
fof(f217,plain,
( sQ3_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f114,f212,f133]) ).
fof(f218,plain,
( sQ4_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f115,f212,f137]) ).
fof(f219,plain,
( sQ5_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f116,f212,f141]) ).
fof(f220,plain,
( sQ6_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f117,f212,f145]) ).
fof(f221,plain,
( sQ7_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f118,f212,f149]) ).
fof(f222,plain,
( sQ8_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f119,f212,f153]) ).
fof(f223,definition,
! [X0] :
( sQ15_spl
<=> ( inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f224,plain,
! [X0] :
( ~ sQ15_spl
| inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c10 ),
inference(component_clause,[status(thm)],[f223]) ).
fof(f226,definition,
! [X1,X2] :
( sQ16_spl
<=> ( inverse(X2) != sk_c10
| multiply(X2,sk_c10) != X1
| multiply(sk_c10,X1) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f227,plain,
! [X0,X1] :
( ~ sQ16_spl
| inverse(X1) != sk_c10
| multiply(X1,sk_c10) != X0
| multiply(sk_c10,X0) != sk_c9 ),
inference(component_clause,[status(thm)],[f226]) ).
fof(f229,definition,
! [X3] :
( sQ17_spl
<=> ( multiply(X3,sk_c9) != sk_c10
| inverse(X3) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f230,plain,
! [X0] :
( ~ sQ17_spl
| multiply(X0,sk_c9) != sk_c10
| inverse(X0) != sk_c10 ),
inference(component_clause,[status(thm)],[f229]) ).
fof(f232,definition,
! [X4,X5] :
( sQ18_spl
<=> ( multiply(X5,sk_c10) != sk_c9
| inverse(X4) != X5
| multiply(X4,X5) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f233,plain,
! [X0,X1] :
( ~ sQ18_spl
| multiply(X1,sk_c10) != sk_c9
| inverse(X0) != X1
| multiply(X0,X1) != sk_c9 ),
inference(component_clause,[status(thm)],[f232]) ).
fof(f235,plain,
( sQ18_spl
| sQ17_spl
| sQ16_spl
| sQ15_spl
| ~ sQ9_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f121,f122,f157,f223,f226,f229,f232]) ).
fof(f236,plain,
! [X0] :
( ~ sQ18_spl
| multiply(inverse(X0),sk_c10) != sk_c9
| multiply(X0,inverse(X0)) != sk_c9 ),
inference(destructive_equality_resolution,[status(thm)],[f233]) ).
fof(f249,plain,
( ~ sQ9_spl
| ~ sQ18_spl
| multiply(sk_c10,sk_c10) != sk_c9
| multiply(sk_c9,inverse(sk_c9)) != sk_c9 ),
inference(paramodulation,[status(thm)],[f158,f236]) ).
fof(f250,plain,
( ~ sQ1_spl
| ~ sQ18_spl
| multiply(sk_c10,sk_c10) != sk_c9
| multiply(sk_c4,inverse(sk_c4)) != sk_c9 ),
inference(paramodulation,[status(thm)],[f126,f236]) ).
fof(f251,plain,
( ~ sQ4_spl
| ~ sQ18_spl
| multiply(sk_c6,sk_c10) != sk_c9
| multiply(sk_c5,inverse(sk_c5)) != sk_c9 ),
inference(paramodulation,[status(thm)],[f138,f236]) ).
fof(f262,definition,
( sQ21_spl
<=> multiply(sk_c9,inverse(sk_c9)) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f264,plain,
( sQ21_spl
| multiply(sk_c9,inverse(sk_c9)) != sk_c9 ),
inference(component_clause,[status(thm)],[f262]) ).
fof(f265,definition,
( sQ22_spl
<=> multiply(sk_c10,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f268,plain,
( ~ sQ9_spl
| ~ sQ18_spl
| ~ sQ22_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f249,f262,f265,f232,f157]) ).
fof(f269,definition,
( sQ23_spl
<=> multiply(sk_c4,inverse(sk_c4)) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f272,plain,
( ~ sQ1_spl
| ~ sQ18_spl
| ~ sQ22_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f250,f269,f265,f232,f125]) ).
fof(f273,definition,
( sQ24_spl
<=> multiply(sk_c5,inverse(sk_c5)) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f276,plain,
( ~ sQ4_spl
| ~ sQ18_spl
| ~ sQ5_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f251,f273,f141,f232,f137]) ).
fof(f298,plain,
( ~ sQ2_spl
| ~ sQ17_spl
| sk_c10 != sk_c10
| inverse(sk_c4) != sk_c10 ),
inference(paramodulation,[status(thm)],[f130,f230]) ).
fof(f299,plain,
( ~ sQ10_spl
| ~ sQ17_spl
| sk_c10 != sk_c10
| inverse(sk_c1) != sk_c10 ),
inference(paramodulation,[status(thm)],[f169,f230]) ).
fof(f301,definition,
( sQ28_spl
<=> sk_c10 = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f303,plain,
( sQ28_spl
| sk_c10 != sk_c10 ),
inference(component_clause,[status(thm)],[f301]) ).
fof(f304,plain,
( ~ sQ2_spl
| ~ sQ17_spl
| ~ sQ28_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f298,f125,f301,f229,f129]) ).
fof(f305,definition,
( sQ29_spl
<=> inverse(sk_c1) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f307,plain,
( sQ29_spl
| inverse(sk_c1) != sk_c10 ),
inference(component_clause,[status(thm)],[f305]) ).
fof(f308,plain,
( ~ sQ10_spl
| ~ sQ17_spl
| ~ sQ28_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f299,f305,f301,f229,f168]) ).
fof(f309,plain,
( sQ28_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f303]) ).
fof(f310,plain,
sQ28_spl,
inference(contradiction_clause,[status(thm)],[f309]) ).
fof(f311,plain,
( sQ29_spl
| ~ sQ11_spl
| sk_c9 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f180,f307]) ).
fof(f312,plain,
! [X0] :
( ~ sQ16_spl
| inverse(X0) != sk_c10
| multiply(sk_c10,multiply(X0,sk_c10)) != sk_c9 ),
inference(destructive_equality_resolution,[status(thm)],[f227]) ).
fof(f314,plain,
( ~ sQ0_spl
| multiply(sk_c9,sk_c10) = identity ),
inference(paramodulation,[status(thm)],[f123,f62]) ).
fof(f315,plain,
( ~ sQ9_spl
| multiply(sk_c10,sk_c9) = identity ),
inference(paramodulation,[status(thm)],[f158,f62]) ).
fof(f318,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f62,f63]) ).
fof(f319,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f61,f318]) ).
fof(f329,plain,
( ~ sQ0_spl
| ~ sQ16_spl
| inverse(sk_c9) != sk_c10
| multiply(sk_c10,identity) != sk_c9 ),
inference(paramodulation,[status(thm)],[f314,f312]) ).
fof(f330,plain,
( ~ sQ16_spl
| inverse(inverse(sk_c10)) != sk_c10
| multiply(sk_c10,identity) != sk_c9 ),
inference(paramodulation,[status(thm)],[f62,f312]) ).
fof(f331,plain,
( ~ sQ16_spl
| inverse(identity) != sk_c10
| multiply(sk_c10,sk_c10) != sk_c9 ),
inference(paramodulation,[status(thm)],[f61,f312]) ).
fof(f333,plain,
( ~ sQ7_spl
| ~ sQ16_spl
| inverse(sk_c7) != sk_c10
| multiply(sk_c10,sk_c8) != sk_c9 ),
inference(paramodulation,[status(thm)],[f150,f312]) ).
fof(f334,plain,
( ~ sQ13_spl
| ~ sQ16_spl
| inverse(sk_c2) != sk_c10
| multiply(sk_c10,sk_c3) != sk_c9 ),
inference(paramodulation,[status(thm)],[f202,f312]) ).
fof(f335,definition,
( sQ30_spl
<=> multiply(sk_c10,identity) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f338,plain,
( ~ sQ0_spl
| ~ sQ16_spl
| ~ sQ9_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f329,f335,f157,f226,f122]) ).
fof(f339,definition,
( sQ31_spl
<=> inverse(inverse(sk_c10)) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f342,plain,
( ~ sQ16_spl
| ~ sQ31_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f330,f335,f339,f226]) ).
fof(f343,definition,
( sQ32_spl
<=> inverse(identity) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f346,plain,
( ~ sQ16_spl
| ~ sQ32_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f331,f265,f343,f226]) ).
fof(f347,plain,
( ~ sQ7_spl
| ~ sQ16_spl
| ~ sQ8_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f333,f145,f153,f226,f149]) ).
fof(f348,plain,
( ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f334,f190,f212,f226,f201]) ).
fof(f349,plain,
( ~ sQ2_spl
| ~ sQ15_spl
| inverse(sk_c4) != sk_c9 ),
inference(resolution,[status(thm)],[f224,f130]) ).
fof(f350,plain,
( ~ sQ2_spl
| ~ sQ15_spl
| inverse(sk_c4) != sk_c9
| sk_c10 != sk_c10 ),
inference(paramodulation,[status(thm)],[f130,f224]) ).
fof(f351,plain,
( ~ sQ15_spl
| inverse(inverse(sk_c9)) != sk_c9
| identity != sk_c10 ),
inference(paramodulation,[status(thm)],[f62,f224]) ).
fof(f352,plain,
( ~ sQ15_spl
| inverse(identity) != sk_c9
| sk_c9 != sk_c10 ),
inference(paramodulation,[status(thm)],[f61,f224]) ).
fof(f354,definition,
( sQ33_spl
<=> inverse(sk_c4) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f357,plain,
( ~ sQ2_spl
| ~ sQ15_spl
| ~ sQ33_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f350,f301,f354,f223,f129]) ).
fof(f358,definition,
( sQ34_spl
<=> identity = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f360,plain,
( sQ34_spl
| identity != sk_c10 ),
inference(component_clause,[status(thm)],[f358]) ).
fof(f361,definition,
( sQ35_spl
<=> inverse(inverse(sk_c9)) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f364,plain,
( ~ sQ15_spl
| ~ sQ35_spl
| ~ sQ34_spl ),
inference(split_clause,[status(thm)],[f351,f358,f361,f223]) ).
fof(f365,definition,
( sQ36_spl
<=> sk_c9 = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f367,plain,
( sQ36_spl
| sk_c9 != sk_c10 ),
inference(component_clause,[status(thm)],[f365]) ).
fof(f368,definition,
( sQ37_spl
<=> inverse(identity) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f370,plain,
( sQ37_spl
| inverse(identity) != sk_c9 ),
inference(component_clause,[status(thm)],[f368]) ).
fof(f371,plain,
( ~ sQ15_spl
| ~ sQ37_spl
| ~ sQ36_spl ),
inference(split_clause,[status(thm)],[f352,f365,f368,f223]) ).
fof(f390,plain,
( ~ sQ2_spl
| sk_c9 = multiply(inverse(sk_c4),sk_c10) ),
inference(paramodulation,[status(thm)],[f130,f319]) ).
fof(f393,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f61,f319]) ).
fof(f395,plain,
( ~ sQ3_spl
| sk_c6 = multiply(inverse(sk_c5),sk_c9) ),
inference(paramodulation,[status(thm)],[f134,f319]) ).
fof(f396,plain,
( ~ sQ7_spl
| sk_c10 = multiply(inverse(sk_c7),sk_c8) ),
inference(paramodulation,[status(thm)],[f150,f319]) ).
fof(f401,plain,
( ~ sQ13_spl
| sk_c10 = multiply(inverse(sk_c2),sk_c3) ),
inference(paramodulation,[status(thm)],[f202,f319]) ).
fof(f403,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sk_c9 = multiply(sk_c10,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f126,f390]) ).
fof(f404,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c6 = multiply(sk_c6,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f138,f395]) ).
fof(f405,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| sk_c10 = multiply(sk_c10,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f154,f396]) ).
fof(f406,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| sk_c10 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f146,f405]) ).
fof(f407,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| sk_c10 = multiply(sk_c10,sk_c3) ),
inference(forward_demodulation,[status(thm)],[f213,f401]) ).
fof(f411,plain,
( ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| multiply(sk_c6,sk_c9) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f406,f142]) ).
fof(f414,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| inverse(sk_c7) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f406,f154]) ).
fof(f415,plain,
( ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| inverse(sk_c4) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f406,f126]) ).
fof(f418,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| multiply(sk_c9,sk_c8) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f406,f146]) ).
fof(f428,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| sk_c9 = multiply(sk_c9,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f406,f403]) ).
fof(f429,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| sk_c9 = multiply(sk_c9,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f406,f428]) ).
fof(f430,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| sk_c9 = multiply(inverse(sk_c9),sk_c9) ),
inference(paramodulation,[status(thm)],[f429,f319]) ).
fof(f432,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| sk_c9 = identity ),
inference(forward_demodulation,[status(thm)],[f62,f430]) ).
fof(f437,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| multiply(sk_c9,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f432,f61]) ).
fof(f449,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| multiply(sk_c6,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f458,f437]) ).
fof(f450,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sk_c6 = identity ),
inference(backward_demodulation,[status(thm)],[f458,f432]) ).
fof(f454,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| inverse(sk_c7) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f458,f414]) ).
fof(f456,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sk_c10 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f458,f406]) ).
fof(f458,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| sk_c6 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f411,f404]) ).
fof(f467,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| X0 = multiply(sk_c6,multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f454,f319]) ).
fof(f468,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ1_spl
| X0 = multiply(sk_c7,X0) ),
inference(forward_demodulation,[status(thm)],[f449,f467]) ).
fof(f475,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| multiply(sk_c6,sk_c8) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f458,f418]) ).
fof(f476,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c8 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f449,f475]) ).
fof(f478,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ1_spl
| inverse(sk_c7) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f487,f454]) ).
fof(f482,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c10 = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f487,f456]) ).
fof(f483,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sk_c8 = identity ),
inference(backward_demodulation,[status(thm)],[f487,f450]) ).
fof(f485,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c8 = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f487,f458]) ).
fof(f487,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c8 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f458,f476]) ).
fof(f512,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| sk_c10 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f191,f407]) ).
fof(f513,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| sQ29_spl
| ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f512,f311]) ).
fof(f514,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| sQ29_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f513]) ).
fof(f539,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| multiply(inverse(X0),X0) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f483,f62]) ).
fof(f709,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| sQ36_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f512,f367]) ).
fof(f710,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| sQ36_spl ),
inference(contradiction_clause,[status(thm)],[f709]) ).
fof(f711,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f403,f265,f125,f129]) ).
fof(f713,plain,
( ~ sQ9_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| inverse(sk_c9) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f512,f158]) ).
fof(f721,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| multiply(inverse(X0),sk_c9) != sk_c9
| multiply(X0,inverse(X0)) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f512,f236]) ).
fof(f736,plain,
( ~ sQ10_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| multiply(sk_c1,sk_c9) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f512,f169]) ).
fof(f737,plain,
( ~ sQ10_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| sk_c9 = multiply(inverse(sk_c1),sk_c9) ),
inference(paramodulation,[status(thm)],[f736,f319]) ).
fof(f739,plain,
( ~ sQ10_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sk_c9 = multiply(sk_c9,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f180,f737]) ).
fof(f759,plain,
( ~ sQ18_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| multiply(identity,inverse(identity)) != sk_c9 ),
inference(resolution,[status(thm)],[f393,f721]) ).
fof(f765,plain,
( ~ sQ18_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| inverse(identity) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f61,f759]) ).
fof(f769,definition,
( sQ40_spl
<=> sk_c9 = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f771,plain,
( sQ40_spl
| sk_c9 != sk_c9 ),
inference(component_clause,[status(thm)],[f769]) ).
fof(f774,plain,
( sQ40_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f771]) ).
fof(f775,plain,
sQ40_spl,
inference(contradiction_clause,[status(thm)],[f774]) ).
fof(f777,plain,
( ~ sQ9_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| multiply(sk_c9,sk_c9) = identity ),
inference(forward_demodulation,[status(thm)],[f512,f315]) ).
fof(f817,plain,
( ~ sQ10_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sk_c9 = identity ),
inference(forward_demodulation,[status(thm)],[f777,f739]) ).
fof(f827,plain,
( ~ sQ18_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| inverse(sk_c9) != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f817,f765]) ).
fof(f832,plain,
( ~ sQ18_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f713,f827]) ).
fof(f833,plain,
( ~ sQ18_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f832]) ).
fof(f834,plain,
( ~ sQ18_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f833]) ).
fof(f836,plain,
( sQ37_spl
| ~ sQ10_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ9_spl
| inverse(sk_c9) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f817,f370]) ).
fof(f837,plain,
( sQ37_spl
| ~ sQ10_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f713,f836]) ).
fof(f838,plain,
( sQ37_spl
| ~ sQ10_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f837]) ).
fof(f839,plain,
( sQ37_spl
| ~ sQ10_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f838]) ).
fof(f840,plain,
( sQ34_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ1_spl
| identity != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f482,f360]) ).
fof(f844,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| multiply(inverse(X0),X0) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f483,f62]) ).
fof(f849,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| multiply(sk_c8,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f483,f61]) ).
fof(f865,plain,
( sQ34_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f483,f840]) ).
fof(f866,plain,
( sQ34_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f865]) ).
fof(f867,plain,
( sQ34_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f866]) ).
fof(f872,plain,
( sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ1_spl
| inverse(sk_c8) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f482,f124]) ).
fof(f873,plain,
( sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ1_spl
| inverse(sk_c8) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f485,f872]) ).
fof(f914,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ1_spl
| multiply(sk_c8,sk_c7) = sk_c8 ),
inference(paramodulation,[status(thm)],[f478,f844]) ).
fof(f916,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c7 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f849,f914]) ).
fof(f923,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c7 = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f916,f485]) ).
fof(f927,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c7 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f916,f487]) ).
fof(f930,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c10 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f916,f482]) ).
fof(f933,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ1_spl
| inverse(sk_c7) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f927,f454]) ).
fof(f936,plain,
( ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| inverse(sk_c4) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f923,f415]) ).
fof(f953,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| multiply(inverse(X0),X0) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f916,f539]) ).
fof(f954,plain,
( ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| multiply(sk_c7,sk_c4) = sk_c7 ),
inference(paramodulation,[status(thm)],[f936,f953]) ).
fof(f958,plain,
( ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| sk_c4 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f468,f954]) ).
fof(f964,plain,
( sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ1_spl
| inverse(sk_c7) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f916,f873]) ).
fof(f965,plain,
( sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c7 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f933,f964]) ).
fof(f966,plain,
( sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f916,f965]) ).
fof(f967,plain,
( sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f966]) ).
fof(f968,plain,
( sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f967]) ).
fof(f980,plain,
( sQ9_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ1_spl
| inverse(sk_c7) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f923,f159]) ).
fof(f981,plain,
( sQ9_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c7 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f933,f980]) ).
fof(f982,plain,
( sQ9_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f930,f981]) ).
fof(f983,plain,
( sQ9_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f982]) ).
fof(f984,plain,
( sQ9_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f983]) ).
fof(f993,plain,
( ~ sQ2_spl
| ~ sQ15_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| inverse(sk_c7) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f958,f349]) ).
fof(f994,plain,
( ~ sQ2_spl
| ~ sQ15_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sk_c7 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f933,f993]) ).
fof(f995,plain,
( ~ sQ2_spl
| ~ sQ15_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f923,f994]) ).
fof(f996,plain,
( ~ sQ2_spl
| ~ sQ15_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f995]) ).
fof(f997,plain,
( ~ sQ2_spl
| ~ sQ15_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f996]) ).
fof(f1001,plain,
( sQ21_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ1_spl
| multiply(sk_c7,inverse(sk_c9)) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f923,f264]) ).
fof(f1002,plain,
( sQ21_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ1_spl
| inverse(sk_c9) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f468,f1001]) ).
fof(f1003,plain,
( sQ21_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ1_spl
| inverse(sk_c7) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f923,f1002]) ).
fof(f1004,plain,
( sQ21_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c7 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f933,f1003]) ).
fof(f1005,plain,
( sQ21_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f923,f1004]) ).
fof(f1006,plain,
( sQ21_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1005]) ).
fof(f1007,plain,
( sQ21_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f1006]) ).
fof(f1008,plain,
$false,
inference(sat_refutation,[status(thm)],[f128,f132,f136,f140,f144,f148,f152,f156,f160,f161,f162,f163,f164,f165,f166,f167,f171,f172,f173,f174,f175,f176,f177,f178,f182,f183,f184,f185,f186,f187,f188,f189,f193,f194,f195,f196,f197,f198,f199,f200,f204,f205,f206,f207,f208,f209,f210,f211,f215,f216,f217,f218,f219,f220,f221,f222,f235,f268,f272,f276,f304,f308,f310,f338,f342,f346,f347,f348,f357,f364,f371,f514,f710,f711,f775,f834,f839,f867,f968,f984,f997,f1007]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP240-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n018.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 20:09:13 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.41 % Refutation found
% 0.09/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.44 % Elapsed time: 0.072172 seconds
% 0.09/0.44 % CPU time: 0.247120 seconds
% 0.09/0.44 % Total memory used: 106.711 MB
% 0.09/0.44 % Net memory used: 106.523 MB
%------------------------------------------------------------------------------