%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP254-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 12:33:13 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.43s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 98
% Syntax : Number of formulae : 416 ( 10 unt; 40 def)
% Number of atoms : 1402 ( 515 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 1802 ( 816 ~; 946 |; 0 &)
% ( 40 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 42 ( 40 usr; 41 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 13 con; 0-2 aty)
% Number of variables : 79 ( 79 !; 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_c12) = sk_c11
| multiply(sk_c1,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c4) = sk_c12
| multiply(sk_c1,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c5,sk_c11) = sk_c10
| multiply(sk_c1,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c5) = sk_c11
| multiply(sk_c1,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c12
| multiply(sk_c1,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c1,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c12
| multiply(sk_c1,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c1,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c7) = sk_c9
| multiply(sk_c1,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c11
| inverse(sk_c1) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c4) = sk_c12
| inverse(sk_c1) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c5,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c5) = sk_c11
| inverse(sk_c1) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c12
| inverse(sk_c1) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c1) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c12
| inverse(sk_c1) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c1) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( inverse(sk_c7) = sk_c9
| inverse(sk_c1) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c11
| multiply(sk_c2,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c4) = sk_c12
| multiply(sk_c2,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c5,sk_c11) = sk_c10
| multiply(sk_c2,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c5) = sk_c11
| multiply(sk_c2,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c12
| multiply(sk_c2,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c2,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c12
| multiply(sk_c2,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c2,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( inverse(sk_c7) = sk_c9
| multiply(sk_c2,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c11
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( inverse(sk_c4) = sk_c12
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
( multiply(sk_c5,sk_c11) = sk_c10
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( inverse(sk_c5) = sk_c11
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c12
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c12
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,negated_conjecture,
( inverse(sk_c7) = sk_c9
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c11
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
( inverse(sk_c4) = sk_c12
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,negated_conjecture,
( multiply(sk_c5,sk_c11) = sk_c10
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,negated_conjecture,
( inverse(sk_c5) = sk_c11
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c12
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c12
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f51,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f52,negated_conjecture,
( inverse(sk_c7) = sk_c9
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c11
| multiply(sk_c3,sk_c12) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f55,negated_conjecture,
( inverse(sk_c4) = sk_c12
| multiply(sk_c3,sk_c12) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f56,negated_conjecture,
( multiply(sk_c5,sk_c11) = sk_c10
| multiply(sk_c3,sk_c12) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f57,negated_conjecture,
( inverse(sk_c5) = sk_c11
| multiply(sk_c3,sk_c12) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f58,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c12
| multiply(sk_c3,sk_c12) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f59,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c3,sk_c12) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f60,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c12
| multiply(sk_c3,sk_c12) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f61,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c3,sk_c12) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f62,negated_conjecture,
( inverse(sk_c7) = sk_c9
| multiply(sk_c3,sk_c12) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f64,negated_conjecture,
! [X4,X5,X6,X1,X2,X7,X3,X8,X9] :
( multiply(X8,X3) != X9
| inverse(X9) != X3
| inverse(X8) != X9
| multiply(X3,sk_c11) != sk_c12
| inverse(X7) != X3
| multiply(X7,X3) != sk_c12
| inverse(X2) != sk_c11
| multiply(X2,sk_c11) != sk_c10
| inverse(X1) != sk_c12
| multiply(X1,sk_c12) != sk_c11
| multiply(X6,sk_c12) != sk_c10
| inverse(X6) != sk_c10
| inverse(X5) != sk_c11
| multiply(X5,sk_c11) != sk_c10
| inverse(X4) != sk_c12
| multiply(X4,sk_c12) != sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f65,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f66,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f67,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f68,plain,
( multiply(sk_c4,sk_c12) = sk_c11
| multiply(sk_c1,sk_c12) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f69,plain,
( inverse(sk_c4) = sk_c12
| multiply(sk_c1,sk_c12) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f70,plain,
( multiply(sk_c5,sk_c11) = sk_c10
| multiply(sk_c1,sk_c12) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f71,plain,
( inverse(sk_c5) = sk_c11
| multiply(sk_c1,sk_c12) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f72,plain,
( multiply(sk_c6,sk_c9) = sk_c12
| multiply(sk_c1,sk_c12) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f73,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c1,sk_c12) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f74,plain,
( multiply(sk_c9,sk_c11) = sk_c12
| multiply(sk_c1,sk_c12) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f75,plain,
( inverse(sk_c8) = sk_c7
| multiply(sk_c1,sk_c12) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f76,plain,
( inverse(sk_c7) = sk_c9
| multiply(sk_c1,sk_c12) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f78,plain,
( multiply(sk_c4,sk_c12) = sk_c11
| inverse(sk_c1) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f79,plain,
( inverse(sk_c4) = sk_c12
| inverse(sk_c1) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f80,plain,
( multiply(sk_c5,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f81,plain,
( inverse(sk_c5) = sk_c11
| inverse(sk_c1) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f82,plain,
( multiply(sk_c6,sk_c9) = sk_c12
| inverse(sk_c1) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f83,plain,
( inverse(sk_c6) = sk_c9
| inverse(sk_c1) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f84,plain,
( multiply(sk_c9,sk_c11) = sk_c12
| inverse(sk_c1) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f85,plain,
( inverse(sk_c8) = sk_c7
| inverse(sk_c1) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f86,plain,
( inverse(sk_c7) = sk_c9
| inverse(sk_c1) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f88,plain,
( multiply(sk_c4,sk_c12) = sk_c11
| multiply(sk_c2,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f89,plain,
( inverse(sk_c4) = sk_c12
| multiply(sk_c2,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f90,plain,
( multiply(sk_c5,sk_c11) = sk_c10
| multiply(sk_c2,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f91,plain,
( inverse(sk_c5) = sk_c11
| multiply(sk_c2,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f92,plain,
( multiply(sk_c6,sk_c9) = sk_c12
| multiply(sk_c2,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f93,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c2,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f94,plain,
( multiply(sk_c9,sk_c11) = sk_c12
| multiply(sk_c2,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f95,plain,
( inverse(sk_c8) = sk_c7
| multiply(sk_c2,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f96,plain,
( inverse(sk_c7) = sk_c9
| multiply(sk_c2,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f98,plain,
( multiply(sk_c4,sk_c12) = sk_c11
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f99,plain,
( inverse(sk_c4) = sk_c12
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f100,plain,
( multiply(sk_c5,sk_c11) = sk_c10
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f101,plain,
( inverse(sk_c5) = sk_c11
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f102,plain,
( multiply(sk_c6,sk_c9) = sk_c12
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f103,plain,
( inverse(sk_c6) = sk_c9
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f104,plain,
( multiply(sk_c9,sk_c11) = sk_c12
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f105,plain,
( inverse(sk_c8) = sk_c7
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f106,plain,
( inverse(sk_c7) = sk_c9
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f108,plain,
( multiply(sk_c4,sk_c12) = sk_c11
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f109,plain,
( inverse(sk_c4) = sk_c12
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f110,plain,
( multiply(sk_c5,sk_c11) = sk_c10
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f111,plain,
( inverse(sk_c5) = sk_c11
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f112,plain,
( multiply(sk_c6,sk_c9) = sk_c12
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f113,plain,
( inverse(sk_c6) = sk_c9
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f114,plain,
( multiply(sk_c9,sk_c11) = sk_c12
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f115,plain,
( inverse(sk_c8) = sk_c7
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f116,plain,
( inverse(sk_c7) = sk_c9
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f118,plain,
( multiply(sk_c4,sk_c12) = sk_c11
| multiply(sk_c3,sk_c12) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f119,plain,
( inverse(sk_c4) = sk_c12
| multiply(sk_c3,sk_c12) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f120,plain,
( multiply(sk_c5,sk_c11) = sk_c10
| multiply(sk_c3,sk_c12) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f121,plain,
( inverse(sk_c5) = sk_c11
| multiply(sk_c3,sk_c12) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f122,plain,
( multiply(sk_c6,sk_c9) = sk_c12
| multiply(sk_c3,sk_c12) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f123,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c3,sk_c12) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f124,plain,
( multiply(sk_c9,sk_c11) = sk_c12
| multiply(sk_c3,sk_c12) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f125,plain,
( inverse(sk_c8) = sk_c7
| multiply(sk_c3,sk_c12) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f126,plain,
( inverse(sk_c7) = sk_c9
| multiply(sk_c3,sk_c12) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f128,plain,
! [X3,X8,X9] :
( multiply(X8,X3) != X9
| inverse(X9) != X3
| inverse(X8) != X9
| multiply(X3,sk_c11) != sk_c12
| ! [X7] :
( inverse(X7) != X3
| multiply(X7,X3) != sk_c12
| ! [X2] :
( inverse(X2) != sk_c11
| multiply(X2,sk_c11) != sk_c10
| ! [X1] :
( inverse(X1) != sk_c12
| multiply(X1,sk_c12) != sk_c11
| ! [X6] :
( multiply(X6,sk_c12) != sk_c10
| inverse(X6) != sk_c10
| ! [X5] :
( inverse(X5) != sk_c11
| multiply(X5,sk_c11) != sk_c10
| ! [X4] :
( inverse(X4) != sk_c12
| multiply(X4,sk_c12) != sk_c11 ) ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f64]) ).
fof(f129,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( multiply(X7,X6) != X8
| inverse(X8) != X6
| inverse(X7) != X8
| multiply(X6,sk_c11) != sk_c12
| inverse(X5) != X6
| multiply(X5,X6) != sk_c12
| inverse(X4) != sk_c11
| multiply(X4,sk_c11) != sk_c10
| inverse(X3) != sk_c12
| multiply(X3,sk_c12) != sk_c11
| multiply(X2,sk_c12) != sk_c10
| inverse(X2) != sk_c10
| inverse(X1) != sk_c11
| multiply(X1,sk_c11) != sk_c10
| inverse(X0) != sk_c12
| multiply(X0,sk_c12) != sk_c11 ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f130,definition,
( sQ0_spl
<=> multiply(sk_c1,sk_c12) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f131,plain,
( ~ sQ0_spl
| multiply(sk_c1,sk_c12) = sk_c11 ),
inference(component_clause,[status(thm)],[f130]) ).
fof(f133,definition,
( sQ1_spl
<=> multiply(sk_c4,sk_c12) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f134,plain,
( ~ sQ1_spl
| multiply(sk_c4,sk_c12) = sk_c11 ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f68,f130,f133]) ).
fof(f137,definition,
( sQ2_spl
<=> inverse(sk_c4) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f138,plain,
( ~ sQ2_spl
| inverse(sk_c4) = sk_c12 ),
inference(component_clause,[status(thm)],[f137]) ).
fof(f140,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f69,f130,f137]) ).
fof(f141,definition,
( sQ3_spl
<=> multiply(sk_c5,sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f142,plain,
( ~ sQ3_spl
| multiply(sk_c5,sk_c11) = sk_c10 ),
inference(component_clause,[status(thm)],[f141]) ).
fof(f144,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f70,f130,f141]) ).
fof(f145,definition,
( sQ4_spl
<=> inverse(sk_c5) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f146,plain,
( ~ sQ4_spl
| inverse(sk_c5) = sk_c11 ),
inference(component_clause,[status(thm)],[f145]) ).
fof(f148,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f71,f130,f145]) ).
fof(f149,definition,
( sQ5_spl
<=> multiply(sk_c6,sk_c9) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f150,plain,
( ~ sQ5_spl
| multiply(sk_c6,sk_c9) = sk_c12 ),
inference(component_clause,[status(thm)],[f149]) ).
fof(f152,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f72,f130,f149]) ).
fof(f153,definition,
( sQ6_spl
<=> inverse(sk_c6) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f154,plain,
( ~ sQ6_spl
| inverse(sk_c6) = sk_c9 ),
inference(component_clause,[status(thm)],[f153]) ).
fof(f156,plain,
( sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f73,f130,f153]) ).
fof(f157,definition,
( sQ7_spl
<=> multiply(sk_c9,sk_c11) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f158,plain,
( ~ sQ7_spl
| multiply(sk_c9,sk_c11) = sk_c12 ),
inference(component_clause,[status(thm)],[f157]) ).
fof(f160,plain,
( sQ7_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f74,f130,f157]) ).
fof(f161,definition,
( sQ8_spl
<=> inverse(sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f162,plain,
( ~ sQ8_spl
| inverse(sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f161]) ).
fof(f164,plain,
( sQ8_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f75,f130,f161]) ).
fof(f165,definition,
( sQ9_spl
<=> inverse(sk_c7) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f166,plain,
( ~ sQ9_spl
| inverse(sk_c7) = sk_c9 ),
inference(component_clause,[status(thm)],[f165]) ).
fof(f168,plain,
( sQ9_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f76,f130,f165]) ).
fof(f173,definition,
( sQ11_spl
<=> inverse(sk_c1) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f174,plain,
( ~ sQ11_spl
| inverse(sk_c1) = sk_c12 ),
inference(component_clause,[status(thm)],[f173]) ).
fof(f176,plain,
( sQ1_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f78,f173,f133]) ).
fof(f177,plain,
( sQ2_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f79,f173,f137]) ).
fof(f178,plain,
( sQ3_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f80,f173,f141]) ).
fof(f179,plain,
( sQ4_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f81,f173,f145]) ).
fof(f180,plain,
( sQ5_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f82,f173,f149]) ).
fof(f181,plain,
( sQ6_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f83,f173,f153]) ).
fof(f182,plain,
( sQ7_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f84,f173,f157]) ).
fof(f183,plain,
( sQ8_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f85,f173,f161]) ).
fof(f184,plain,
( sQ9_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f86,f173,f165]) ).
fof(f186,definition,
( sQ12_spl
<=> multiply(sk_c2,sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f187,plain,
( ~ sQ12_spl
| multiply(sk_c2,sk_c11) = sk_c10 ),
inference(component_clause,[status(thm)],[f186]) ).
fof(f189,plain,
( sQ1_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f88,f186,f133]) ).
fof(f190,plain,
( sQ2_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f89,f186,f137]) ).
fof(f191,plain,
( sQ3_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f90,f186,f141]) ).
fof(f192,plain,
( sQ4_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f91,f186,f145]) ).
fof(f193,plain,
( sQ5_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f92,f186,f149]) ).
fof(f194,plain,
( sQ6_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f93,f186,f153]) ).
fof(f195,plain,
( sQ7_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f94,f186,f157]) ).
fof(f196,plain,
( sQ8_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f95,f186,f161]) ).
fof(f197,plain,
( sQ9_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f96,f186,f165]) ).
fof(f199,definition,
( sQ13_spl
<=> inverse(sk_c2) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f200,plain,
( ~ sQ13_spl
| inverse(sk_c2) = sk_c11 ),
inference(component_clause,[status(thm)],[f199]) ).
fof(f202,plain,
( sQ1_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f98,f199,f133]) ).
fof(f203,plain,
( sQ2_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f99,f199,f137]) ).
fof(f204,plain,
( sQ3_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f100,f199,f141]) ).
fof(f205,plain,
( sQ4_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f101,f199,f145]) ).
fof(f206,plain,
( sQ5_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f102,f199,f149]) ).
fof(f207,plain,
( sQ6_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f103,f199,f153]) ).
fof(f208,plain,
( sQ7_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f104,f199,f157]) ).
fof(f209,plain,
( sQ8_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f105,f199,f161]) ).
fof(f210,plain,
( sQ9_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f106,f199,f165]) ).
fof(f212,definition,
( sQ14_spl
<=> inverse(sk_c3) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f213,plain,
( ~ sQ14_spl
| inverse(sk_c3) = sk_c10 ),
inference(component_clause,[status(thm)],[f212]) ).
fof(f215,plain,
( sQ1_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f108,f212,f133]) ).
fof(f216,plain,
( sQ2_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f109,f212,f137]) ).
fof(f217,plain,
( sQ3_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f110,f212,f141]) ).
fof(f218,plain,
( sQ4_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f111,f212,f145]) ).
fof(f219,plain,
( sQ5_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f112,f212,f149]) ).
fof(f220,plain,
( sQ6_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f113,f212,f153]) ).
fof(f221,plain,
( sQ7_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f114,f212,f157]) ).
fof(f222,plain,
( sQ8_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f115,f212,f161]) ).
fof(f223,plain,
( sQ9_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f116,f212,f165]) ).
fof(f225,definition,
( sQ15_spl
<=> multiply(sk_c3,sk_c12) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f226,plain,
( ~ sQ15_spl
| multiply(sk_c3,sk_c12) = sk_c10 ),
inference(component_clause,[status(thm)],[f225]) ).
fof(f228,plain,
( sQ1_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f118,f225,f133]) ).
fof(f229,plain,
( sQ2_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f119,f225,f137]) ).
fof(f230,plain,
( sQ3_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f120,f225,f141]) ).
fof(f231,plain,
( sQ4_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f121,f225,f145]) ).
fof(f232,plain,
( sQ5_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f122,f225,f149]) ).
fof(f233,plain,
( sQ6_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f123,f225,f153]) ).
fof(f234,plain,
( sQ7_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f124,f225,f157]) ).
fof(f235,plain,
( sQ8_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f125,f225,f161]) ).
fof(f236,plain,
( sQ9_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f126,f225,f165]) ).
fof(f238,definition,
! [X0] :
( sQ16_spl
<=> ( inverse(X0) != sk_c12
| multiply(X0,sk_c12) != sk_c11 ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f239,plain,
! [X0] :
( ~ sQ16_spl
| inverse(X0) != sk_c12
| multiply(X0,sk_c12) != sk_c11 ),
inference(component_clause,[status(thm)],[f238]) ).
fof(f241,definition,
! [X1] :
( sQ17_spl
<=> ( inverse(X1) != sk_c11
| multiply(X1,sk_c11) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f242,plain,
! [X0] :
( ~ sQ17_spl
| inverse(X0) != sk_c11
| multiply(X0,sk_c11) != sk_c10 ),
inference(component_clause,[status(thm)],[f241]) ).
fof(f244,definition,
! [X2] :
( sQ18_spl
<=> ( multiply(X2,sk_c12) != sk_c10
| inverse(X2) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f245,plain,
! [X0] :
( ~ sQ18_spl
| multiply(X0,sk_c12) != sk_c10
| inverse(X0) != sk_c10 ),
inference(component_clause,[status(thm)],[f244]) ).
fof(f247,definition,
! [X5,X6,X7,X8] :
( sQ19_spl
<=> ( multiply(X7,X6) != X8
| inverse(X8) != X6
| inverse(X7) != X8
| multiply(X6,sk_c11) != sk_c12
| inverse(X5) != X6
| multiply(X5,X6) != sk_c12 ) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f248,plain,
! [X0,X1,X2,X3] :
( ~ sQ19_spl
| multiply(X2,X1) != X3
| inverse(X3) != X1
| inverse(X2) != X3
| multiply(X1,sk_c11) != sk_c12
| inverse(X0) != X1
| multiply(X0,X1) != sk_c12 ),
inference(component_clause,[status(thm)],[f247]) ).
fof(f250,plain,
( sQ19_spl
| sQ18_spl
| sQ17_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f129,f238,f241,f244,f247]) ).
fof(f251,plain,
! [X0,X1] :
( ~ sQ19_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c11) != sk_c12
| multiply(X0,inverse(X0)) != sk_c12 ),
inference(destructive_equality_resolution,[status(thm)],[f248]) ).
fof(f266,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ19_spl
| multiply(X0,sk_c9) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c6)
| multiply(inverse(sk_c6),sk_c11) != sk_c12
| multiply(sk_c6,inverse(sk_c6)) != sk_c12 ),
inference(paramodulation,[status(thm)],[f154,f251]) ).
fof(f292,definition,
( sQ26_spl
<=> multiply(sk_c6,inverse(sk_c6)) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f294,plain,
( sQ26_spl
| multiply(sk_c6,inverse(sk_c6)) != sk_c12 ),
inference(component_clause,[status(thm)],[f292]) ).
fof(f295,definition,
( sQ27_spl
<=> multiply(inverse(sk_c6),sk_c11) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f297,plain,
( sQ27_spl
| multiply(inverse(sk_c6),sk_c11) != sk_c12 ),
inference(component_clause,[status(thm)],[f295]) ).
fof(f298,definition,
! [X0] :
( sQ28_spl
<=> ( multiply(X0,sk_c9) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c6) ) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f301,plain,
( ~ sQ6_spl
| ~ sQ19_spl
| sQ28_spl
| ~ sQ27_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f266,f292,f295,f298,f247,f153]) ).
fof(f367,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f66,f67]) ).
fof(f368,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f65,f367]) ).
fof(f375,plain,
( ~ sQ15_spl
| ~ sQ18_spl
| inverse(sk_c3) != sk_c10 ),
inference(resolution,[status(thm)],[f245,f226]) ).
fof(f376,plain,
( ~ sQ18_spl
| identity != sk_c10
| inverse(inverse(sk_c12)) != sk_c10 ),
inference(paramodulation,[status(thm)],[f66,f245]) ).
fof(f379,plain,
( ~ sQ1_spl
| ~ sQ18_spl
| sk_c11 != sk_c10
| inverse(sk_c4) != sk_c10 ),
inference(paramodulation,[status(thm)],[f134,f245]) ).
fof(f382,plain,
( ~ sQ15_spl
| ~ sQ18_spl
| ~ sQ14_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f213,f375]) ).
fof(f383,plain,
( ~ sQ15_spl
| ~ sQ18_spl
| ~ sQ14_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f382]) ).
fof(f384,plain,
( ~ sQ15_spl
| ~ sQ18_spl
| ~ sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f383]) ).
fof(f387,plain,
( ~ sQ17_spl
| inverse(inverse(sk_c11)) != sk_c11
| identity != sk_c10 ),
inference(paramodulation,[status(thm)],[f66,f242]) ).
fof(f388,plain,
( ~ sQ17_spl
| inverse(identity) != sk_c11
| sk_c11 != sk_c10 ),
inference(paramodulation,[status(thm)],[f65,f242]) ).
fof(f390,plain,
( ~ sQ3_spl
| ~ sQ17_spl
| inverse(sk_c5) != sk_c11
| sk_c10 != sk_c10 ),
inference(paramodulation,[status(thm)],[f142,f242]) ).
fof(f392,plain,
( ~ sQ12_spl
| ~ sQ17_spl
| inverse(sk_c2) != sk_c11
| sk_c10 != sk_c10 ),
inference(paramodulation,[status(thm)],[f187,f242]) ).
fof(f393,definition,
( sQ44_spl
<=> identity = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f395,plain,
( sQ44_spl
| identity != sk_c10 ),
inference(component_clause,[status(thm)],[f393]) ).
fof(f396,definition,
( sQ45_spl
<=> inverse(inverse(sk_c11)) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f399,plain,
( ~ sQ17_spl
| ~ sQ45_spl
| ~ sQ44_spl ),
inference(split_clause,[status(thm)],[f387,f393,f396,f241]) ).
fof(f400,definition,
( sQ46_spl
<=> sk_c11 = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f402,plain,
( sQ46_spl
| sk_c11 != sk_c10 ),
inference(component_clause,[status(thm)],[f400]) ).
fof(f403,definition,
( sQ47_spl
<=> inverse(identity) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f405,plain,
( sQ47_spl
| inverse(identity) != sk_c11 ),
inference(component_clause,[status(thm)],[f403]) ).
fof(f406,plain,
( ~ sQ17_spl
| ~ sQ47_spl
| ~ sQ46_spl ),
inference(split_clause,[status(thm)],[f388,f400,f403,f241]) ).
fof(f407,definition,
( sQ48_spl
<=> sk_c10 = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f409,plain,
( sQ48_spl
| sk_c10 != sk_c10 ),
inference(component_clause,[status(thm)],[f407]) ).
fof(f410,plain,
( ~ sQ3_spl
| ~ sQ17_spl
| ~ sQ4_spl
| ~ sQ48_spl ),
inference(split_clause,[status(thm)],[f390,f407,f145,f241,f141]) ).
fof(f418,plain,
( ~ sQ12_spl
| ~ sQ17_spl
| ~ sQ13_spl
| ~ sQ48_spl ),
inference(split_clause,[status(thm)],[f392,f407,f199,f241,f186]) ).
fof(f419,plain,
( sQ48_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f409]) ).
fof(f420,plain,
sQ48_spl,
inference(contradiction_clause,[status(thm)],[f419]) ).
fof(f422,plain,
( ~ sQ4_spl
| multiply(sk_c11,sk_c5) = identity ),
inference(paramodulation,[status(thm)],[f146,f66]) ).
fof(f426,plain,
( ~ sQ8_spl
| multiply(sk_c7,sk_c8) = identity ),
inference(paramodulation,[status(thm)],[f162,f66]) ).
fof(f440,plain,
( ~ sQ1_spl
| ~ sQ16_spl
| inverse(sk_c4) != sk_c12 ),
inference(resolution,[status(thm)],[f239,f134]) ).
fof(f441,plain,
( ~ sQ0_spl
| ~ sQ16_spl
| inverse(sk_c1) != sk_c12 ),
inference(resolution,[status(thm)],[f239,f131]) ).
fof(f448,plain,
( ~ sQ1_spl
| ~ sQ16_spl
| ~ sQ2_spl
| sk_c12 != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f138,f440]) ).
fof(f449,plain,
( ~ sQ1_spl
| ~ sQ16_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f448]) ).
fof(f450,plain,
( ~ sQ1_spl
| ~ sQ16_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f449]) ).
fof(f451,plain,
( ~ sQ19_spl
| inverse(inverse(identity)) != inverse(identity)
| multiply(inverse(identity),sk_c11) != sk_c12
| multiply(identity,inverse(identity)) != sk_c12 ),
inference(resolution,[status(thm)],[f251,f65]) ).
fof(f460,definition,
( sQ51_spl
<=> multiply(identity,inverse(identity)) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f462,plain,
( sQ51_spl
| multiply(identity,inverse(identity)) != sk_c12 ),
inference(component_clause,[status(thm)],[f460]) ).
fof(f463,definition,
( sQ52_spl
<=> multiply(inverse(identity),sk_c11) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f465,plain,
( sQ52_spl
| multiply(inverse(identity),sk_c11) != sk_c12 ),
inference(component_clause,[status(thm)],[f463]) ).
fof(f466,definition,
( sQ53_spl
<=> inverse(inverse(identity)) = inverse(identity) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f468,plain,
( sQ53_spl
| inverse(inverse(identity)) != inverse(identity) ),
inference(component_clause,[status(thm)],[f466]) ).
fof(f469,plain,
( ~ sQ19_spl
| ~ sQ53_spl
| ~ sQ52_spl
| ~ sQ51_spl ),
inference(split_clause,[status(thm)],[f451,f460,f463,f466,f247]) ).
fof(f475,plain,
( sQ51_spl
| inverse(identity) != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f65,f462]) ).
fof(f480,plain,
( sQ27_spl
| ~ sQ6_spl
| multiply(sk_c9,sk_c11) != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f154,f297]) ).
fof(f481,plain,
( sQ27_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c12 != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f158,f480]) ).
fof(f482,plain,
( sQ27_spl
| ~ sQ6_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f481]) ).
fof(f483,plain,
( sQ27_spl
| ~ sQ6_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f482]) ).
fof(f485,plain,
( sQ26_spl
| ~ sQ6_spl
| multiply(sk_c6,sk_c9) != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f154,f294]) ).
fof(f486,plain,
( sQ26_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sk_c12 != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f150,f485]) ).
fof(f487,plain,
( sQ26_spl
| ~ sQ6_spl
| ~ sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f486]) ).
fof(f488,plain,
( sQ26_spl
| ~ sQ6_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f487]) ).
fof(f490,definition,
( sQ54_spl
<=> inverse(inverse(sk_c12)) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f493,plain,
( ~ sQ18_spl
| ~ sQ44_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f376,f490,f393,f244]) ).
fof(f494,definition,
( sQ55_spl
<=> inverse(identity) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f496,plain,
( sQ55_spl
| inverse(identity) != sk_c10 ),
inference(component_clause,[status(thm)],[f494]) ).
fof(f498,definition,
( sQ56_spl
<=> inverse(sk_c4) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f501,plain,
( ~ sQ1_spl
| ~ sQ18_spl
| ~ sQ46_spl
| ~ sQ56_spl ),
inference(split_clause,[status(thm)],[f379,f498,f400,f244,f133]) ).
fof(f508,plain,
( ~ sQ8_spl
| sk_c8 = multiply(inverse(sk_c7),identity) ),
inference(paramodulation,[status(thm)],[f426,f368]) ).
fof(f515,plain,
( ~ sQ1_spl
| sk_c12 = multiply(inverse(sk_c4),sk_c11) ),
inference(paramodulation,[status(thm)],[f134,f368]) ).
fof(f516,plain,
( ~ sQ3_spl
| sk_c11 = multiply(inverse(sk_c5),sk_c10) ),
inference(paramodulation,[status(thm)],[f142,f368]) ).
fof(f524,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c8 = multiply(sk_c9,identity) ),
inference(forward_demodulation,[status(thm)],[f166,f508]) ).
fof(f525,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c12 = multiply(sk_c12,sk_c11) ),
inference(forward_demodulation,[status(thm)],[f138,f515]) ).
fof(f526,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c11 = multiply(sk_c11,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f146,f516]) ).
fof(f539,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c11 = multiply(inverse(sk_c12),sk_c12) ),
inference(paramodulation,[status(thm)],[f525,f368]) ).
fof(f541,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c11 = identity ),
inference(forward_demodulation,[status(thm)],[f66,f539]) ).
fof(f543,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 = multiply(sk_c9,sk_c11) ),
inference(backward_demodulation,[status(thm)],[f541,f524]) ).
fof(f544,plain,
( sQ44_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c11 != sk_c10 ),
inference(backward_demodulation,[status(thm)],[f541,f395]) ).
fof(f548,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c11,sk_c5) = sk_c11 ),
inference(backward_demodulation,[status(thm)],[f541,f422]) ).
fof(f550,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(inverse(X0),X0) = sk_c11 ),
inference(backward_demodulation,[status(thm)],[f541,f66]) ).
fof(f551,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c11,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f541,f65]) ).
fof(f552,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| sk_c8 = sk_c12 ),
inference(forward_demodulation,[status(thm)],[f158,f543]) ).
fof(f557,plain,
( ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| multiply(sk_c6,sk_c9) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f552,f150]) ).
fof(f561,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| multiply(X0,sk_c8) != sk_c10
| inverse(X0) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f552,f245]) ).
fof(f575,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ18_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sk_c8 != sk_c10
| inverse(sk_c11) != sk_c10 ),
inference(paramodulation,[status(thm)],[f551,f561]) ).
fof(f578,definition,
( sQ58_spl
<=> inverse(sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f580,plain,
( sQ58_spl
| inverse(sk_c11) != sk_c10 ),
inference(component_clause,[status(thm)],[f578]) ).
fof(f581,definition,
( sQ59_spl
<=> sk_c8 = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f583,plain,
( sQ59_spl
| sk_c8 != sk_c10 ),
inference(component_clause,[status(thm)],[f581]) ).
fof(f584,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ18_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ59_spl
| ~ sQ58_spl ),
inference(split_clause,[status(thm)],[f575,f578,f581,f157,f165,f161,f244,f137,f133]) ).
fof(f587,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c11 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f551,f526]) ).
fof(f588,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sQ46_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f587,f402]) ).
fof(f589,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sQ46_spl ),
inference(contradiction_clause,[status(thm)],[f588]) ).
fof(f598,plain,
( sQ55_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c11) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f541,f496]) ).
fof(f604,plain,
( sQ52_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(inverse(sk_c11),sk_c11) != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f541,f465]) ).
fof(f605,plain,
( sQ52_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c11 != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f550,f604]) ).
fof(f607,plain,
( sQ51_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c11) != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f541,f475]) ).
fof(f608,plain,
( sQ51_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| inverse(sk_c11) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f552,f607]) ).
fof(f609,plain,
( sQ47_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c11) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f541,f405]) ).
fof(f643,plain,
( sQ44_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ46_spl ),
inference(split_clause,[status(thm)],[f544,f400,f137,f133,f393]) ).
fof(f651,plain,
( sQ58_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c10) != sk_c10 ),
inference(backward_demodulation,[status(thm)],[f587,f580]) ).
fof(f652,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c10,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f587,f551]) ).
fof(f654,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c10 = identity ),
inference(backward_demodulation,[status(thm)],[f587,f541]) ).
fof(f655,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c5) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f587,f146]) ).
fof(f657,plain,
( sQ51_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| inverse(sk_c10) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f587,f608]) ).
fof(f659,plain,
( ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| sk_c9 = multiply(inverse(sk_c6),sk_c8) ),
inference(paramodulation,[status(thm)],[f557,f368]) ).
fof(f661,plain,
( ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ6_spl
| sk_c9 = multiply(sk_c9,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f154,f659]) ).
fof(f665,plain,
( sQ47_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| inverse(sk_c10) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f587,f609]) ).
fof(f666,plain,
( sQ47_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| inverse(sk_c10) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f587,f665]) ).
fof(f698,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| multiply(sk_c10,sk_c5) = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f587,f548]) ).
fof(f699,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c5 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f652,f698]) ).
fof(f701,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c10) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f702,f655]) ).
fof(f702,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c5 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f587,f699]) ).
fof(f703,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sQ47_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f701,f666]) ).
fof(f704,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sQ47_spl ),
inference(contradiction_clause,[status(thm)],[f703]) ).
fof(f708,plain,
( sQ51_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c10 != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f701,f657]) ).
fof(f711,plain,
( sQ58_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f701,f651]) ).
fof(f712,plain,
( sQ58_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f711]) ).
fof(f713,plain,
( sQ58_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f712]) ).
fof(f714,plain,
( sQ55_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ58_spl ),
inference(split_clause,[status(thm)],[f598,f578,f137,f133,f494]) ).
fof(f733,definition,
( sQ60_spl
<=> multiply(sk_c10,inverse(sk_c10)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f735,plain,
( sQ60_spl
| multiply(sk_c10,inverse(sk_c10)) != sk_c8 ),
inference(component_clause,[status(thm)],[f733]) ).
fof(f736,definition,
( sQ61_spl
<=> multiply(inverse(sk_c10),sk_c10) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f738,plain,
( sQ61_spl
| multiply(inverse(sk_c10),sk_c10) != sk_c8 ),
inference(component_clause,[status(thm)],[f736]) ).
fof(f782,plain,
( sQ61_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c10,sk_c10) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f701,f738]) ).
fof(f783,plain,
( sQ61_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c10 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f652,f782]) ).
fof(f784,plain,
( sQ60_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| inverse(sk_c10) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f652,f735]) ).
fof(f785,plain,
( sQ60_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c10 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f701,f784]) ).
fof(f800,plain,
( ~ sQ0_spl
| sk_c12 = multiply(inverse(sk_c1),sk_c11) ),
inference(paramodulation,[status(thm)],[f131,f368]) ).
fof(f802,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| sk_c12 = multiply(sk_c12,sk_c11) ),
inference(forward_demodulation,[status(thm)],[f174,f800]) ).
fof(f812,plain,
( ~ sQ15_spl
| sk_c12 = multiply(inverse(sk_c3),sk_c10) ),
inference(paramodulation,[status(thm)],[f226,f368]) ).
fof(f814,plain,
( ~ sQ15_spl
| ~ sQ14_spl
| sk_c12 = multiply(sk_c10,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f213,f812]) ).
fof(f845,plain,
( ~ sQ12_spl
| sk_c11 = multiply(inverse(sk_c2),sk_c10) ),
inference(paramodulation,[status(thm)],[f187,f368]) ).
fof(f847,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| sk_c11 = multiply(sk_c11,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f200,f845]) ).
fof(f869,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| sk_c10 = multiply(inverse(sk_c11),sk_c11) ),
inference(paramodulation,[status(thm)],[f847,f368]) ).
fof(f871,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| sk_c10 = identity ),
inference(forward_demodulation,[status(thm)],[f66,f869]) ).
fof(f876,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ13_spl
| multiply(inverse(X0),X0) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f871,f66]) ).
fof(f878,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ13_spl
| multiply(sk_c10,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f871,f65]) ).
fof(f879,plain,
( sQ51_spl
| ~ sQ12_spl
| ~ sQ13_spl
| inverse(sk_c10) != sk_c12 ),
inference(backward_demodulation,[status(thm)],[f871,f475]) ).
fof(f880,plain,
( ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| sk_c12 = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f878,f814]) ).
fof(f910,plain,
( ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| inverse(sk_c1) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f880,f174]) ).
fof(f912,plain,
! [X0,X1] :
( ~ sQ19_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c11) != sk_c10
| multiply(X0,inverse(X0)) != sk_c12 ),
inference(backward_demodulation,[status(thm)],[f880,f251]) ).
fof(f916,plain,
! [X0,X1] :
( ~ sQ19_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c11) != sk_c10
| multiply(X0,inverse(X0)) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f880,f912]) ).
fof(f917,plain,
( ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| multiply(sk_c10,sk_c3) = sk_c10 ),
inference(paramodulation,[status(thm)],[f213,f876]) ).
fof(f921,plain,
( ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| sk_c3 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f878,f917]) ).
fof(f926,plain,
( ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| sk_c12 = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f921,f880]) ).
fof(f927,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| multiply(sk_c3,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f921,f878]) ).
fof(f928,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sk_c3 = identity ),
inference(backward_demodulation,[status(thm)],[f921,f871]) ).
fof(f933,plain,
( ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| inverse(sk_c3) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f921,f213]) ).
fof(f936,plain,
( sQ51_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| inverse(sk_c3) != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f921,f879]) ).
fof(f937,plain,
( sQ51_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ15_spl
| inverse(sk_c3) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f926,f936]) ).
fof(f940,plain,
( ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| inverse(sk_c1) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f921,f910]) ).
fof(f944,plain,
( ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| sQ51_spl
| ~ sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f933,f937]) ).
fof(f945,plain,
( ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| sQ51_spl
| ~ sQ15_spl ),
inference(contradiction_clause,[status(thm)],[f944]) ).
fof(f967,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| sk_c3 = multiply(sk_c12,sk_c11) ),
inference(forward_demodulation,[status(thm)],[f926,f802]) ).
fof(f968,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| sk_c3 = multiply(sk_c3,sk_c11) ),
inference(forward_demodulation,[status(thm)],[f926,f967]) ).
fof(f969,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| sk_c3 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f927,f968]) ).
fof(f977,plain,
( ~ sQ0_spl
| ~ sQ16_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| sk_c3 != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f940,f441]) ).
fof(f978,plain,
( ~ sQ0_spl
| ~ sQ16_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f926,f977]) ).
fof(f979,plain,
( ~ sQ0_spl
| ~ sQ16_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f978]) ).
fof(f980,plain,
( ~ sQ0_spl
| ~ sQ16_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f979]) ).
fof(f1027,plain,
! [X0,X1] :
( ~ sQ19_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c11) != sk_c10
| multiply(X0,inverse(X0)) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f921,f916]) ).
fof(f1028,plain,
! [X0,X1] :
( ~ sQ19_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c11) != sk_c3
| multiply(X0,inverse(X0)) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f921,f1027]) ).
fof(f1192,plain,
( sQ52_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| sk_c3 != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f969,f605]) ).
fof(f1193,plain,
( sQ52_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f926,f1192]) ).
fof(f1194,plain,
( sQ52_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1193]) ).
fof(f1195,plain,
( sQ52_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f1194]) ).
fof(f1206,plain,
( sQ52_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c10 != sk_c12 ),
inference(backward_demodulation,[status(thm)],[f587,f605]) ).
fof(f1223,plain,
( sQ52_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sk_c10 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f552,f1206]) ).
fof(f1254,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(inverse(X0),X0) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f654,f66]) ).
fof(f1352,plain,
( ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ6_spl
| sk_c8 = multiply(inverse(sk_c9),sk_c9) ),
inference(paramodulation,[status(thm)],[f661,f368]) ).
fof(f1354,plain,
( ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c8 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1254,f1352]) ).
fof(f1355,plain,
( ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sQ59_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1354,f583]) ).
fof(f1356,plain,
( ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sQ59_spl ),
inference(contradiction_clause,[status(thm)],[f1355]) ).
fof(f1360,plain,
( sQ52_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ59_spl ),
inference(split_clause,[status(thm)],[f1223,f581,f157,f165,f161,f145,f141,f137,f133,f463]) ).
fof(f1368,plain,
( sQ61_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ59_spl ),
inference(split_clause,[status(thm)],[f783,f581,f137,f133,f141,f145,f736]) ).
fof(f1369,plain,
( sQ60_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ59_spl ),
inference(split_clause,[status(thm)],[f785,f581,f145,f141,f137,f133,f733]) ).
fof(f1393,plain,
( sQ51_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ59_spl ),
inference(split_clause,[status(thm)],[f708,f581,f145,f141,f157,f165,f161,f137,f133,f460]) ).
fof(f1404,plain,
( sQ53_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| inverse(inverse(sk_c10)) != inverse(identity) ),
inference(forward_demodulation,[status(thm)],[f654,f468]) ).
fof(f1405,plain,
( sQ53_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| inverse(sk_c10) != inverse(identity) ),
inference(forward_demodulation,[status(thm)],[f701,f1404]) ).
fof(f1406,plain,
( sQ53_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c10 != inverse(identity) ),
inference(forward_demodulation,[status(thm)],[f701,f1405]) ).
fof(f1407,plain,
( sQ53_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c10 != inverse(sk_c10) ),
inference(forward_demodulation,[status(thm)],[f654,f1406]) ).
fof(f1408,plain,
( sQ53_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f701,f1407]) ).
fof(f1409,plain,
( sQ53_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1408]) ).
fof(f1410,plain,
( sQ53_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f1409]) ).
fof(f1437,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| multiply(sk_c3,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f928,f65]) ).
fof(f1444,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| multiply(inverse(X0),X0) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f928,f66]) ).
fof(f1497,plain,
! [X0,X1] :
( ~ sQ19_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ11_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c3) != sk_c3
| multiply(X0,inverse(X0)) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f969,f1028]) ).
fof(f1498,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ19_spl
| ~ sQ15_spl
| ~ sQ0_spl
| ~ sQ11_spl
| inverse(inverse(sk_c3)) != inverse(sk_c3)
| multiply(inverse(sk_c3),sk_c3) != sk_c3
| multiply(sk_c3,inverse(sk_c3)) != sk_c3 ),
inference(resolution,[status(thm)],[f1497,f1437]) ).
fof(f1503,definition,
( sQ84_spl
<=> multiply(sk_c3,inverse(sk_c3)) = sk_c3 ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f1505,plain,
( sQ84_spl
| multiply(sk_c3,inverse(sk_c3)) != sk_c3 ),
inference(component_clause,[status(thm)],[f1503]) ).
fof(f1506,definition,
( sQ85_spl
<=> multiply(inverse(sk_c3),sk_c3) = sk_c3 ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f1508,plain,
( sQ85_spl
| multiply(inverse(sk_c3),sk_c3) != sk_c3 ),
inference(component_clause,[status(thm)],[f1506]) ).
fof(f1509,definition,
( sQ86_spl
<=> inverse(inverse(sk_c3)) = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f1511,plain,
( sQ86_spl
| inverse(inverse(sk_c3)) != inverse(sk_c3) ),
inference(component_clause,[status(thm)],[f1509]) ).
fof(f1512,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ19_spl
| ~ sQ15_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ86_spl
| ~ sQ85_spl
| ~ sQ84_spl ),
inference(split_clause,[status(thm)],[f1498,f1503,f1506,f1509,f173,f130,f225,f247,f212,f199,f186]) ).
fof(f1521,plain,
( sQ85_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f1444,f1508]) ).
fof(f1522,plain,
( sQ85_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1521]) ).
fof(f1523,plain,
( sQ85_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f1522]) ).
fof(f1524,plain,
( sQ84_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| inverse(sk_c3) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f1437,f1505]) ).
fof(f1525,plain,
( sQ84_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f933,f1524]) ).
fof(f1526,plain,
( sQ84_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1525]) ).
fof(f1527,plain,
( sQ84_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f1526]) ).
fof(f1529,plain,
( sQ86_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| inverse(sk_c3) != inverse(sk_c3) ),
inference(forward_demodulation,[status(thm)],[f933,f1511]) ).
fof(f1530,plain,
( sQ86_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| sk_c3 != inverse(sk_c3) ),
inference(forward_demodulation,[status(thm)],[f933,f1529]) ).
fof(f1531,plain,
( sQ86_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f933,f1530]) ).
fof(f1532,plain,
( sQ86_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1531]) ).
fof(f1533,plain,
( sQ86_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f1532]) ).
fof(f1534,plain,
$false,
inference(sat_refutation,[status(thm)],[f136,f140,f144,f148,f152,f156,f160,f164,f168,f176,f177,f178,f179,f180,f181,f182,f183,f184,f189,f190,f191,f192,f193,f194,f195,f196,f197,f202,f203,f204,f205,f206,f207,f208,f209,f210,f215,f216,f217,f218,f219,f220,f221,f222,f223,f228,f229,f230,f231,f232,f233,f234,f235,f236,f250,f301,f384,f399,f406,f410,f418,f420,f450,f469,f483,f488,f493,f501,f584,f589,f643,f704,f713,f714,f945,f980,f1195,f1356,f1360,f1368,f1369,f1393,f1410,f1512,f1523,f1527,f1533]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP254-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n013.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 20:07:05 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.43 % Refutation found
% 0.10/0.43 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.46 % Elapsed time: 0.082531 seconds
% 0.10/0.46 % CPU time: 0.338422 seconds
% 0.10/0.46 % Total memory used: 106.092 MB
% 0.10/0.46 % Net memory used: 105.922 MB
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