%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP244-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 12:33:12 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.38s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 89
% Syntax : Number of formulae : 308 ( 11 unt; 31 def)
% Number of atoms : 774 ( 386 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 771 ( 305 ~; 435 |; 0 &)
% ( 31 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 33 ( 31 usr; 32 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 52 ( 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
( multiply(sk_c4,sk_c11) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c4) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c5,sk_c10) = sk_c9
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c5) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( inverse(sk_c6) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c7) = sk_c8
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c4,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( inverse(sk_c4) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( multiply(sk_c5,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( inverse(sk_c5) = sk_c10
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c6) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c10
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( inverse(sk_c7) = sk_c8
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c10
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c4,sk_c11) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( inverse(sk_c4) = sk_c11
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c5,sk_c10) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c5) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( inverse(sk_c6) = sk_c11
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( inverse(sk_c7) = sk_c8
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( multiply(sk_c4,sk_c11) = sk_c10
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( inverse(sk_c4) = sk_c11
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( multiply(sk_c5,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( inverse(sk_c5) = sk_c10
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( inverse(sk_c6) = sk_c11
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c10
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
( inverse(sk_c7) = sk_c8
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c10
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
( multiply(sk_c4,sk_c11) = sk_c10
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,negated_conjecture,
( inverse(sk_c4) = sk_c11
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,negated_conjecture,
( multiply(sk_c5,sk_c10) = sk_c9
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,negated_conjecture,
( inverse(sk_c5) = sk_c10
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
( inverse(sk_c6) = sk_c11
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c10
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,negated_conjecture,
( inverse(sk_c7) = sk_c8
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c10
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,negated_conjecture,
( multiply(sk_c4,sk_c11) = sk_c10
| multiply(sk_c3,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,negated_conjecture,
( inverse(sk_c4) = sk_c11
| multiply(sk_c3,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f51,negated_conjecture,
( multiply(sk_c5,sk_c10) = sk_c9
| multiply(sk_c3,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f52,negated_conjecture,
( inverse(sk_c5) = sk_c10
| multiply(sk_c3,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f53,negated_conjecture,
( inverse(sk_c6) = sk_c11
| multiply(sk_c3,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| multiply(sk_c3,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f55,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c10
| multiply(sk_c3,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f56,negated_conjecture,
( inverse(sk_c7) = sk_c8
| multiply(sk_c3,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f57,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c10
| multiply(sk_c3,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f58,negated_conjecture,
! [X4,X5,X6,X1,X2,X3,X7,X8] :
( multiply(X8,sk_c9) != sk_c10
| inverse(X7) != X8
| multiply(X7,X8) != sk_c10
| multiply(X3,sk_c10) != sk_c11
| inverse(X3) != sk_c11
| inverse(X2) != sk_c10
| multiply(X2,sk_c10) != sk_c9
| inverse(X1) != sk_c11
| multiply(X1,sk_c11) != sk_c10
| multiply(X6,sk_c10) != sk_c11
| inverse(X6) != sk_c11
| inverse(X5) != sk_c10
| multiply(X5,sk_c10) != sk_c9
| inverse(X4) != sk_c11
| multiply(X4,sk_c11) != sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f59,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f60,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f61,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f62,plain,
( multiply(sk_c4,sk_c11) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f63,plain,
( inverse(sk_c4) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f64,plain,
( multiply(sk_c5,sk_c10) = sk_c9
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f65,plain,
( inverse(sk_c5) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f66,plain,
( inverse(sk_c6) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f67,plain,
( multiply(sk_c6,sk_c10) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f68,plain,
( multiply(sk_c7,sk_c8) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f69,plain,
( inverse(sk_c7) = sk_c8
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f70,plain,
( multiply(sk_c8,sk_c9) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f71,plain,
( multiply(sk_c4,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f72,plain,
( inverse(sk_c4) = sk_c11
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f73,plain,
( multiply(sk_c5,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f74,plain,
( inverse(sk_c5) = sk_c10
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f75,plain,
( inverse(sk_c6) = sk_c11
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f76,plain,
( multiply(sk_c6,sk_c10) = sk_c11
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f77,plain,
( multiply(sk_c7,sk_c8) = sk_c10
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f78,plain,
( inverse(sk_c7) = sk_c8
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f79,plain,
( multiply(sk_c8,sk_c9) = sk_c10
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f80,plain,
( multiply(sk_c4,sk_c11) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f81,plain,
( inverse(sk_c4) = sk_c11
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f82,plain,
( multiply(sk_c5,sk_c10) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f83,plain,
( inverse(sk_c5) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f84,plain,
( inverse(sk_c6) = sk_c11
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f85,plain,
( multiply(sk_c6,sk_c10) = sk_c11
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f86,plain,
( multiply(sk_c7,sk_c8) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f87,plain,
( inverse(sk_c7) = sk_c8
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f88,plain,
( multiply(sk_c8,sk_c9) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f89,plain,
( multiply(sk_c4,sk_c11) = sk_c10
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f90,plain,
( inverse(sk_c4) = sk_c11
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f91,plain,
( multiply(sk_c5,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f92,plain,
( inverse(sk_c5) = sk_c10
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f93,plain,
( inverse(sk_c6) = sk_c11
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f94,plain,
( multiply(sk_c6,sk_c10) = sk_c11
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f95,plain,
( multiply(sk_c7,sk_c8) = sk_c10
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f96,plain,
( inverse(sk_c7) = sk_c8
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f97,plain,
( multiply(sk_c8,sk_c9) = sk_c10
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f98,plain,
( multiply(sk_c4,sk_c11) = sk_c10
| inverse(sk_c3) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f99,plain,
( inverse(sk_c4) = sk_c11
| inverse(sk_c3) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f100,plain,
( multiply(sk_c5,sk_c10) = sk_c9
| inverse(sk_c3) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f101,plain,
( inverse(sk_c5) = sk_c10
| inverse(sk_c3) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f102,plain,
( inverse(sk_c6) = sk_c11
| inverse(sk_c3) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f103,plain,
( multiply(sk_c6,sk_c10) = sk_c11
| inverse(sk_c3) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f104,plain,
( multiply(sk_c7,sk_c8) = sk_c10
| inverse(sk_c3) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f105,plain,
( inverse(sk_c7) = sk_c8
| inverse(sk_c3) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f106,plain,
( multiply(sk_c8,sk_c9) = sk_c10
| inverse(sk_c3) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f107,plain,
( multiply(sk_c4,sk_c11) = sk_c10
| multiply(sk_c3,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f108,plain,
( inverse(sk_c4) = sk_c11
| multiply(sk_c3,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f109,plain,
( multiply(sk_c5,sk_c10) = sk_c9
| multiply(sk_c3,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f110,plain,
( inverse(sk_c5) = sk_c10
| multiply(sk_c3,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f111,plain,
( inverse(sk_c6) = sk_c11
| multiply(sk_c3,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f112,plain,
( multiply(sk_c6,sk_c10) = sk_c11
| multiply(sk_c3,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f113,plain,
( multiply(sk_c7,sk_c8) = sk_c10
| multiply(sk_c3,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f114,plain,
( inverse(sk_c7) = sk_c8
| multiply(sk_c3,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f115,plain,
( multiply(sk_c8,sk_c9) = sk_c10
| multiply(sk_c3,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f116,plain,
! [X8] :
( multiply(X8,sk_c9) != sk_c10
| ! [X7] :
( inverse(X7) != X8
| multiply(X7,X8) != sk_c10
| ! [X3] :
( multiply(X3,sk_c10) != sk_c11
| inverse(X3) != sk_c11
| ! [X2] :
( inverse(X2) != sk_c10
| multiply(X2,sk_c10) != sk_c9
| ! [X1] :
( inverse(X1) != sk_c11
| multiply(X1,sk_c11) != sk_c10
| ! [X6] :
( multiply(X6,sk_c10) != sk_c11
| inverse(X6) != sk_c11
| ! [X5] :
( inverse(X5) != sk_c10
| multiply(X5,sk_c10) != sk_c9
| ! [X4] :
( inverse(X4) != sk_c11
| multiply(X4,sk_c11) != sk_c10 ) ) ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f58]) ).
fof(f117,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( multiply(X7,sk_c9) != sk_c10
| inverse(X6) != X7
| multiply(X6,X7) != sk_c10
| multiply(X5,sk_c10) != sk_c11
| inverse(X5) != sk_c11
| inverse(X4) != sk_c10
| multiply(X4,sk_c10) != sk_c9
| inverse(X3) != sk_c11
| multiply(X3,sk_c11) != sk_c10
| multiply(X2,sk_c10) != sk_c11
| inverse(X2) != sk_c11
| inverse(X1) != sk_c10
| multiply(X1,sk_c10) != sk_c9
| inverse(X0) != sk_c11
| multiply(X0,sk_c11) != sk_c10 ),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f118,definition,
( sQ0_spl
<=> multiply(sk_c1,sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f119,plain,
( ~ sQ0_spl
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(component_clause,[status(thm)],[f118]) ).
fof(f121,definition,
( sQ1_spl
<=> multiply(sk_c4,sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f122,plain,
( ~ sQ1_spl
| multiply(sk_c4,sk_c11) = sk_c10 ),
inference(component_clause,[status(thm)],[f121]) ).
fof(f124,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f62,f118,f121]) ).
fof(f125,definition,
( sQ2_spl
<=> inverse(sk_c4) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f126,plain,
( ~ sQ2_spl
| inverse(sk_c4) = sk_c11 ),
inference(component_clause,[status(thm)],[f125]) ).
fof(f128,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f63,f118,f125]) ).
fof(f129,definition,
( sQ3_spl
<=> multiply(sk_c5,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f130,plain,
( ~ sQ3_spl
| multiply(sk_c5,sk_c10) = sk_c9 ),
inference(component_clause,[status(thm)],[f129]) ).
fof(f132,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f64,f118,f129]) ).
fof(f133,definition,
( sQ4_spl
<=> inverse(sk_c5) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f134,plain,
( ~ sQ4_spl
| inverse(sk_c5) = sk_c10 ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f65,f118,f133]) ).
fof(f137,definition,
( sQ5_spl
<=> inverse(sk_c6) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f138,plain,
( ~ sQ5_spl
| inverse(sk_c6) = sk_c11 ),
inference(component_clause,[status(thm)],[f137]) ).
fof(f140,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f66,f118,f137]) ).
fof(f141,definition,
( sQ6_spl
<=> multiply(sk_c6,sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f142,plain,
( ~ sQ6_spl
| multiply(sk_c6,sk_c10) = sk_c11 ),
inference(component_clause,[status(thm)],[f141]) ).
fof(f144,plain,
( sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f67,f118,f141]) ).
fof(f145,definition,
( sQ7_spl
<=> multiply(sk_c7,sk_c8) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f146,plain,
( ~ sQ7_spl
| multiply(sk_c7,sk_c8) = sk_c10 ),
inference(component_clause,[status(thm)],[f145]) ).
fof(f148,plain,
( sQ7_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f68,f118,f145]) ).
fof(f149,definition,
( sQ8_spl
<=> inverse(sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f150,plain,
( ~ sQ8_spl
| inverse(sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f149]) ).
fof(f152,plain,
( sQ8_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f69,f118,f149]) ).
fof(f153,definition,
( sQ9_spl
<=> multiply(sk_c8,sk_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f156,plain,
( sQ9_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f70,f118,f153]) ).
fof(f157,definition,
( sQ10_spl
<=> inverse(sk_c1) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f158,plain,
( ~ sQ10_spl
| inverse(sk_c1) = sk_c11 ),
inference(component_clause,[status(thm)],[f157]) ).
fof(f160,plain,
( sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f71,f157,f121]) ).
fof(f161,plain,
( sQ2_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f72,f157,f125]) ).
fof(f162,plain,
( sQ3_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f73,f157,f129]) ).
fof(f163,plain,
( sQ4_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f74,f157,f133]) ).
fof(f164,plain,
( sQ5_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f75,f157,f137]) ).
fof(f165,plain,
( sQ6_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f76,f157,f141]) ).
fof(f166,plain,
( sQ7_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f77,f157,f145]) ).
fof(f167,plain,
( sQ8_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f78,f157,f149]) ).
fof(f168,plain,
( sQ9_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f79,f157,f153]) ).
fof(f169,definition,
( sQ11_spl
<=> multiply(sk_c2,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f170,plain,
( ~ sQ11_spl
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(component_clause,[status(thm)],[f169]) ).
fof(f172,plain,
( sQ1_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f80,f169,f121]) ).
fof(f173,plain,
( sQ2_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f81,f169,f125]) ).
fof(f174,plain,
( sQ3_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f82,f169,f129]) ).
fof(f175,plain,
( sQ4_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f83,f169,f133]) ).
fof(f176,plain,
( sQ5_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f84,f169,f137]) ).
fof(f177,plain,
( sQ6_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f85,f169,f141]) ).
fof(f178,plain,
( sQ7_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f86,f169,f145]) ).
fof(f179,plain,
( sQ8_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f87,f169,f149]) ).
fof(f180,plain,
( sQ9_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f88,f169,f153]) ).
fof(f181,definition,
( sQ12_spl
<=> inverse(sk_c2) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f182,plain,
( ~ sQ12_spl
| inverse(sk_c2) = sk_c10 ),
inference(component_clause,[status(thm)],[f181]) ).
fof(f184,plain,
( sQ1_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f89,f181,f121]) ).
fof(f185,plain,
( sQ2_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f90,f181,f125]) ).
fof(f186,plain,
( sQ3_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f91,f181,f129]) ).
fof(f187,plain,
( sQ4_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f92,f181,f133]) ).
fof(f188,plain,
( sQ5_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f93,f181,f137]) ).
fof(f189,plain,
( sQ6_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f94,f181,f141]) ).
fof(f190,plain,
( sQ7_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f95,f181,f145]) ).
fof(f191,plain,
( sQ8_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f96,f181,f149]) ).
fof(f192,plain,
( sQ9_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f97,f181,f153]) ).
fof(f193,definition,
( sQ13_spl
<=> inverse(sk_c3) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f194,plain,
( ~ sQ13_spl
| inverse(sk_c3) = sk_c11 ),
inference(component_clause,[status(thm)],[f193]) ).
fof(f196,plain,
( sQ1_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f98,f193,f121]) ).
fof(f197,plain,
( sQ2_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f99,f193,f125]) ).
fof(f198,plain,
( sQ3_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f100,f193,f129]) ).
fof(f199,plain,
( sQ4_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f101,f193,f133]) ).
fof(f200,plain,
( sQ5_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f102,f193,f137]) ).
fof(f201,plain,
( sQ6_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f103,f193,f141]) ).
fof(f202,plain,
( sQ7_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f104,f193,f145]) ).
fof(f203,plain,
( sQ8_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f105,f193,f149]) ).
fof(f204,plain,
( sQ9_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f106,f193,f153]) ).
fof(f205,definition,
( sQ14_spl
<=> multiply(sk_c3,sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f206,plain,
( ~ sQ14_spl
| multiply(sk_c3,sk_c10) = sk_c11 ),
inference(component_clause,[status(thm)],[f205]) ).
fof(f208,plain,
( sQ1_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f107,f205,f121]) ).
fof(f209,plain,
( sQ2_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f108,f205,f125]) ).
fof(f210,plain,
( sQ3_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f109,f205,f129]) ).
fof(f211,plain,
( sQ4_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f110,f205,f133]) ).
fof(f212,plain,
( sQ5_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f111,f205,f137]) ).
fof(f213,plain,
( sQ6_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f112,f205,f141]) ).
fof(f214,plain,
( sQ7_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f113,f205,f145]) ).
fof(f215,plain,
( sQ8_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f114,f205,f149]) ).
fof(f216,plain,
( sQ9_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f115,f205,f153]) ).
fof(f217,definition,
! [X0] :
( sQ15_spl
<=> ( inverse(X0) != sk_c11
| multiply(X0,sk_c11) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f218,plain,
! [X0] :
( ~ sQ15_spl
| inverse(X0) != sk_c11
| multiply(X0,sk_c11) != sk_c10 ),
inference(component_clause,[status(thm)],[f217]) ).
fof(f220,definition,
! [X1] :
( sQ16_spl
<=> ( inverse(X1) != sk_c10
| multiply(X1,sk_c10) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f221,plain,
! [X0] :
( ~ sQ16_spl
| inverse(X0) != sk_c10
| multiply(X0,sk_c10) != sk_c9 ),
inference(component_clause,[status(thm)],[f220]) ).
fof(f223,definition,
! [X2] :
( sQ17_spl
<=> ( multiply(X2,sk_c10) != sk_c11
| inverse(X2) != sk_c11 ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f224,plain,
! [X0] :
( ~ sQ17_spl
| multiply(X0,sk_c10) != sk_c11
| inverse(X0) != sk_c11 ),
inference(component_clause,[status(thm)],[f223]) ).
fof(f226,definition,
! [X6,X7] :
( sQ18_spl
<=> ( multiply(X7,sk_c9) != sk_c10
| inverse(X6) != X7
| multiply(X6,X7) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f227,plain,
! [X0,X1] :
( ~ sQ18_spl
| multiply(X1,sk_c9) != sk_c10
| inverse(X0) != X1
| multiply(X0,X1) != sk_c10 ),
inference(component_clause,[status(thm)],[f226]) ).
fof(f229,plain,
( sQ18_spl
| sQ17_spl
| sQ16_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f117,f217,f220,f223,f226]) ).
fof(f230,plain,
! [X0] :
( ~ sQ18_spl
| multiply(inverse(X0),sk_c9) != sk_c10
| multiply(X0,inverse(X0)) != sk_c10 ),
inference(destructive_equality_resolution,[status(thm)],[f227]) ).
fof(f242,plain,
( ~ sQ2_spl
| ~ sQ18_spl
| multiply(sk_c11,sk_c9) != sk_c10
| multiply(sk_c4,inverse(sk_c4)) != sk_c10 ),
inference(paramodulation,[status(thm)],[f126,f230]) ).
fof(f243,plain,
( ~ sQ4_spl
| ~ sQ18_spl
| multiply(sk_c10,sk_c9) != sk_c10
| multiply(sk_c5,inverse(sk_c5)) != sk_c10 ),
inference(paramodulation,[status(thm)],[f134,f230]) ).
fof(f245,plain,
( ~ sQ8_spl
| ~ sQ18_spl
| multiply(sk_c8,sk_c9) != sk_c10
| multiply(sk_c7,inverse(sk_c7)) != sk_c10 ),
inference(paramodulation,[status(thm)],[f150,f230]) ).
fof(f246,plain,
( ~ sQ10_spl
| ~ sQ18_spl
| multiply(sk_c11,sk_c9) != sk_c10
| multiply(sk_c1,inverse(sk_c1)) != sk_c10 ),
inference(paramodulation,[status(thm)],[f158,f230]) ).
fof(f247,plain,
( ~ sQ12_spl
| ~ sQ18_spl
| multiply(sk_c10,sk_c9) != sk_c10
| multiply(sk_c2,inverse(sk_c2)) != sk_c10 ),
inference(paramodulation,[status(thm)],[f182,f230]) ).
fof(f248,plain,
( ~ sQ13_spl
| ~ sQ18_spl
| multiply(sk_c11,sk_c9) != sk_c10
| multiply(sk_c3,inverse(sk_c3)) != sk_c10 ),
inference(paramodulation,[status(thm)],[f194,f230]) ).
fof(f249,definition,
( sQ19_spl
<=> multiply(sk_c4,inverse(sk_c4)) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f251,plain,
( sQ19_spl
| multiply(sk_c4,inverse(sk_c4)) != sk_c10 ),
inference(component_clause,[status(thm)],[f249]) ).
fof(f252,definition,
( sQ20_spl
<=> multiply(sk_c11,sk_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f255,plain,
( ~ sQ2_spl
| ~ sQ18_spl
| ~ sQ20_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f242,f249,f252,f226,f125]) ).
fof(f256,definition,
( sQ21_spl
<=> multiply(sk_c5,inverse(sk_c5)) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f259,definition,
( sQ22_spl
<=> multiply(sk_c10,sk_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f261,plain,
( sQ22_spl
| multiply(sk_c10,sk_c9) != sk_c10 ),
inference(component_clause,[status(thm)],[f259]) ).
fof(f262,plain,
( ~ sQ4_spl
| ~ sQ18_spl
| ~ sQ22_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f243,f256,f259,f226,f133]) ).
fof(f267,definition,
( sQ24_spl
<=> multiply(sk_c7,inverse(sk_c7)) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f269,plain,
( sQ24_spl
| multiply(sk_c7,inverse(sk_c7)) != sk_c10 ),
inference(component_clause,[status(thm)],[f267]) ).
fof(f270,plain,
( ~ sQ8_spl
| ~ sQ18_spl
| ~ sQ9_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f245,f267,f153,f226,f149]) ).
fof(f271,definition,
( sQ25_spl
<=> multiply(sk_c1,inverse(sk_c1)) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f273,plain,
( sQ25_spl
| multiply(sk_c1,inverse(sk_c1)) != sk_c10 ),
inference(component_clause,[status(thm)],[f271]) ).
fof(f274,plain,
( ~ sQ10_spl
| ~ sQ18_spl
| ~ sQ20_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f246,f271,f252,f226,f157]) ).
fof(f275,definition,
( sQ26_spl
<=> multiply(sk_c2,inverse(sk_c2)) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f277,plain,
( sQ26_spl
| multiply(sk_c2,inverse(sk_c2)) != sk_c10 ),
inference(component_clause,[status(thm)],[f275]) ).
fof(f278,plain,
( ~ sQ12_spl
| ~ sQ18_spl
| ~ sQ22_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f247,f275,f259,f226,f181]) ).
fof(f279,definition,
( sQ27_spl
<=> multiply(sk_c3,inverse(sk_c3)) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f282,plain,
( ~ sQ13_spl
| ~ sQ18_spl
| ~ sQ20_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f248,f279,f252,f226,f193]) ).
fof(f284,plain,
( sQ26_spl
| ~ sQ12_spl
| multiply(sk_c2,sk_c10) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f182,f277]) ).
fof(f285,plain,
( sQ26_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sk_c9 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f170,f284]) ).
fof(f286,plain,
( sQ25_spl
| ~ sQ10_spl
| multiply(sk_c1,sk_c11) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f158,f273]) ).
fof(f287,plain,
( sQ25_spl
| ~ sQ10_spl
| ~ sQ0_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f119,f286]) ).
fof(f288,plain,
( sQ25_spl
| ~ sQ10_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f287]) ).
fof(f289,plain,
( sQ25_spl
| ~ sQ10_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f288]) ).
fof(f290,plain,
( ~ sQ6_spl
| ~ sQ17_spl
| inverse(sk_c6) != sk_c11 ),
inference(resolution,[status(thm)],[f224,f142]) ).
fof(f291,plain,
( ~ sQ14_spl
| ~ sQ17_spl
| inverse(sk_c3) != sk_c11 ),
inference(resolution,[status(thm)],[f224,f206]) ).
fof(f297,plain,
( ~ sQ14_spl
| ~ sQ17_spl
| ~ sQ13_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f194,f291]) ).
fof(f298,plain,
( ~ sQ14_spl
| ~ sQ17_spl
| ~ sQ13_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f297]) ).
fof(f299,plain,
( ~ sQ14_spl
| ~ sQ17_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f298]) ).
fof(f306,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f60,f61]) ).
fof(f307,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f59,f306]) ).
fof(f314,plain,
( ~ sQ3_spl
| ~ sQ16_spl
| inverse(sk_c5) != sk_c10 ),
inference(resolution,[status(thm)],[f221,f130]) ).
fof(f315,plain,
( ~ sQ11_spl
| ~ sQ16_spl
| inverse(sk_c2) != sk_c10 ),
inference(resolution,[status(thm)],[f221,f170]) ).
fof(f323,plain,
( ~ sQ3_spl
| ~ sQ16_spl
| ~ sQ4_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f134,f314]) ).
fof(f324,plain,
( ~ sQ3_spl
| ~ sQ16_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f323]) ).
fof(f325,plain,
( ~ sQ3_spl
| ~ sQ16_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f324]) ).
fof(f326,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| inverse(sk_c1) != sk_c11 ),
inference(resolution,[status(thm)],[f218,f119]) ).
fof(f327,plain,
( ~ sQ1_spl
| ~ sQ15_spl
| inverse(sk_c4) != sk_c11 ),
inference(resolution,[status(thm)],[f218,f122]) ).
fof(f333,plain,
( ~ sQ1_spl
| ~ sQ15_spl
| ~ sQ2_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f126,f327]) ).
fof(f334,plain,
( ~ sQ1_spl
| ~ sQ15_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f333]) ).
fof(f335,plain,
( ~ sQ1_spl
| ~ sQ15_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f334]) ).
fof(f343,definition,
( sQ30_spl
<=> sk_c11 = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f345,plain,
( sQ30_spl
| sk_c11 != sk_c11 ),
inference(component_clause,[status(thm)],[f343]) ).
fof(f352,plain,
( ~ sQ6_spl
| ~ sQ17_spl
| ~ sQ5_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f138,f290]) ).
fof(f353,plain,
( ~ sQ6_spl
| ~ sQ17_spl
| ~ sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f352]) ).
fof(f354,plain,
( ~ sQ6_spl
| ~ sQ17_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f353]) ).
fof(f356,plain,
( sQ30_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f345]) ).
fof(f357,plain,
sQ30_spl,
inference(contradiction_clause,[status(thm)],[f356]) ).
fof(f359,plain,
( ~ sQ18_spl
| identity != sk_c10
| multiply(sk_c9,inverse(sk_c9)) != sk_c10 ),
inference(paramodulation,[status(thm)],[f60,f230]) ).
fof(f365,definition,
( sQ32_spl
<=> multiply(sk_c9,inverse(sk_c9)) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f368,definition,
( sQ33_spl
<=> identity = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f370,plain,
( sQ33_spl
| identity != sk_c10 ),
inference(component_clause,[status(thm)],[f368]) ).
fof(f371,plain,
( ~ sQ18_spl
| ~ sQ33_spl
| ~ sQ32_spl ),
inference(split_clause,[status(thm)],[f359,f365,f368,f226]) ).
fof(f388,plain,
( sQ24_spl
| ~ sQ8_spl
| multiply(sk_c7,sk_c8) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f150,f269]) ).
fof(f389,plain,
( sQ24_spl
| ~ sQ8_spl
| ~ sQ7_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f146,f388]) ).
fof(f390,plain,
( sQ24_spl
| ~ sQ8_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f389]) ).
fof(f391,plain,
( sQ24_spl
| ~ sQ8_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f390]) ).
fof(f392,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f326,f157,f217,f118]) ).
fof(f393,definition,
( sQ34_spl
<=> sk_c10 = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f395,plain,
( sQ34_spl
| sk_c10 != sk_c10 ),
inference(component_clause,[status(thm)],[f393]) ).
fof(f408,plain,
( sQ34_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f395]) ).
fof(f409,plain,
sQ34_spl,
inference(contradiction_clause,[status(thm)],[f408]) ).
fof(f427,plain,
( sQ19_spl
| ~ sQ2_spl
| multiply(sk_c4,sk_c11) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f126,f251]) ).
fof(f428,plain,
( sQ19_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f122,f427]) ).
fof(f429,plain,
( sQ19_spl
| ~ sQ2_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f428]) ).
fof(f430,plain,
( sQ19_spl
| ~ sQ2_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f429]) ).
fof(f439,plain,
( ~ sQ0_spl
| sk_c11 = multiply(inverse(sk_c1),sk_c10) ),
inference(paramodulation,[status(thm)],[f119,f307]) ).
fof(f447,plain,
( ~ sQ11_spl
| sk_c10 = multiply(inverse(sk_c2),sk_c9) ),
inference(paramodulation,[status(thm)],[f170,f307]) ).
fof(f450,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| sk_c11 = multiply(sk_c11,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f158,f439]) ).
fof(f451,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| sk_c10 = multiply(sk_c10,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f182,f447]) ).
fof(f452,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f451,f261]) ).
fof(f453,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f452]) ).
fof(f456,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| sk_c10 = multiply(inverse(sk_c11),sk_c11) ),
inference(paramodulation,[status(thm)],[f450,f307]) ).
fof(f458,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| sk_c10 = identity ),
inference(forward_demodulation,[status(thm)],[f60,f456]) ).
fof(f459,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| sQ33_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f458,f370]) ).
fof(f460,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| sQ33_spl ),
inference(contradiction_clause,[status(thm)],[f459]) ).
fof(f461,plain,
( ~ sQ11_spl
| ~ sQ16_spl
| ~ sQ12_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f182,f315]) ).
fof(f462,plain,
( ~ sQ11_spl
| ~ sQ16_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f461]) ).
fof(f463,plain,
( ~ sQ11_spl
| ~ sQ16_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f462]) ).
fof(f468,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ10_spl
| multiply(inverse(X0),X0) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f458,f60]) ).
fof(f469,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ10_spl
| multiply(sk_c10,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f458,f59]) ).
fof(f496,plain,
( ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ10_spl
| multiply(sk_c10,sk_c2) = sk_c10 ),
inference(paramodulation,[status(thm)],[f182,f468]) ).
fof(f501,plain,
( ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ10_spl
| sk_c2 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f469,f496]) ).
fof(f511,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ12_spl
| multiply(sk_c2,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f501,f469]) ).
fof(f523,plain,
( sQ26_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ10_spl
| sk_c9 != sk_c2 ),
inference(backward_demodulation,[status(thm)],[f501,f285]) ).
fof(f552,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ10_spl
| sk_c2 = multiply(sk_c10,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f501,f451]) ).
fof(f553,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ10_spl
| sk_c2 = multiply(sk_c2,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f501,f552]) ).
fof(f554,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ10_spl
| sk_c2 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f511,f553]) ).
fof(f555,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ10_spl
| sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f554,f523]) ).
fof(f556,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ10_spl
| sQ26_spl ),
inference(contradiction_clause,[status(thm)],[f555]) ).
fof(f557,plain,
$false,
inference(sat_refutation,[status(thm)],[f124,f128,f132,f136,f140,f144,f148,f152,f156,f160,f161,f162,f163,f164,f165,f166,f167,f168,f172,f173,f174,f175,f176,f177,f178,f179,f180,f184,f185,f186,f187,f188,f189,f190,f191,f192,f196,f197,f198,f199,f200,f201,f202,f203,f204,f208,f209,f210,f211,f212,f213,f214,f215,f216,f229,f255,f262,f270,f274,f278,f282,f289,f299,f325,f335,f354,f357,f371,f391,f392,f409,f430,f453,f460,f463,f556]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP244-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n001.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 20:12:27 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.38 % Refutation found
% 0.09/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.42 % Elapsed time: 0.046158 seconds
% 0.14/0.42 % CPU time: 0.096395 seconds
% 0.14/0.42 % Total memory used: 23.433 MB
% 0.14/0.42 % Net memory used: 23.422 MB
%------------------------------------------------------------------------------