%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP378-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 12:33:34 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 88
% Syntax : Number of formulae : 462 ( 11 unt; 34 def)
% Number of atoms : 2074 ( 562 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 3066 (1454 ~;1578 |; 0 &)
% ( 34 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 36 ( 34 usr; 35 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 115 ( 115 !; 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_c3,sk_c11) = sk_c10
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c3) = sk_c11
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c7) = sk_c6
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c6) = sk_c8
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c7) = sk_c6
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( inverse(sk_c6) = sk_c8
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c1,sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c1,sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c1,sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c1,sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c1,sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( inverse(sk_c7) = sk_c6
| multiply(sk_c1,sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( inverse(sk_c6) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c1,sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( inverse(sk_c3) = sk_c11
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,negated_conjecture,
( inverse(sk_c7) = sk_c6
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,negated_conjecture,
( inverse(sk_c6) = sk_c8
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c2,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c2,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c2,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f51,negated_conjecture,
( inverse(sk_c7) = sk_c6
| multiply(sk_c2,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f52,negated_conjecture,
( inverse(sk_c6) = sk_c8
| multiply(sk_c2,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f53,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c2,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
! [X3,X4,X1,X2,X5,X6,X7,X8] :
( multiply(X7,X6) != X8
| inverse(X8) != X6
| inverse(X7) != X8
| multiply(X6,sk_c10) != sk_c11
| inverse(X5) != X6
| multiply(X5,X6) != sk_c11
| inverse(X2) != sk_c10
| multiply(X2,sk_c10) != sk_c9
| inverse(X1) != sk_c11
| multiply(X1,sk_c11) != sk_c10
| multiply(X4,sk_c10) != sk_c11
| inverse(X3) != X4
| multiply(X3,X4) != sk_c11
| multiply(sk_c11,sk_c9) != sk_c10
| inverse(sk_c11) != sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f55,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f56,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f57,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f58,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f59,plain,
( inverse(sk_c3) = sk_c11
| inverse(sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f60,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f61,plain,
( inverse(sk_c4) = sk_c10
| inverse(sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f62,plain,
( multiply(sk_c5,sk_c8) = sk_c11
| inverse(sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f63,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f64,plain,
( multiply(sk_c8,sk_c10) = sk_c11
| inverse(sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f65,plain,
( inverse(sk_c7) = sk_c6
| inverse(sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f66,plain,
( inverse(sk_c6) = sk_c8
| inverse(sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f67,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f68,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f69,plain,
( inverse(sk_c3) = sk_c11
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f70,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f71,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f72,plain,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f73,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f74,plain,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f75,plain,
( inverse(sk_c7) = sk_c6
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f76,plain,
( inverse(sk_c6) = sk_c8
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f77,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f78,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c1,sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f79,plain,
( inverse(sk_c3) = sk_c11
| multiply(sk_c1,sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f80,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c1,sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f81,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f82,plain,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c1,sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f83,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f84,plain,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c1,sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f85,plain,
( inverse(sk_c7) = sk_c6
| multiply(sk_c1,sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f86,plain,
( inverse(sk_c6) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f87,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c1,sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f88,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f89,plain,
( inverse(sk_c3) = sk_c11
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f90,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f91,plain,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f92,plain,
( multiply(sk_c5,sk_c8) = sk_c11
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f93,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f94,plain,
( multiply(sk_c8,sk_c10) = sk_c11
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f95,plain,
( inverse(sk_c7) = sk_c6
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f96,plain,
( inverse(sk_c6) = sk_c8
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f97,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f98,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f99,plain,
( inverse(sk_c3) = sk_c11
| multiply(sk_c2,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f100,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f101,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f102,plain,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c2,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f103,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f104,plain,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c2,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f105,plain,
( inverse(sk_c7) = sk_c6
| multiply(sk_c2,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f106,plain,
( inverse(sk_c6) = sk_c8
| multiply(sk_c2,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f107,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c2,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f108,plain,
! [X6,X7,X8] :
( multiply(X7,X6) != X8
| inverse(X8) != X6
| inverse(X7) != X8
| multiply(X6,sk_c10) != sk_c11
| ! [X5] :
( inverse(X5) != X6
| multiply(X5,X6) != sk_c11
| ! [X2] :
( inverse(X2) != sk_c10
| multiply(X2,sk_c10) != sk_c9
| ! [X1] :
( inverse(X1) != sk_c11
| multiply(X1,sk_c11) != sk_c10
| ! [X4] :
( multiply(X4,sk_c10) != sk_c11
| ! [X3] :
( inverse(X3) != X4
| multiply(X3,X4) != sk_c11
| multiply(sk_c11,sk_c9) != sk_c10
| inverse(sk_c11) != sk_c10 ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f54]) ).
fof(f109,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( multiply(X6,X5) != X7
| inverse(X7) != X5
| inverse(X6) != X7
| multiply(X5,sk_c10) != sk_c11
| inverse(X4) != X5
| multiply(X4,X5) != sk_c11
| inverse(X3) != sk_c10
| multiply(X3,sk_c10) != sk_c9
| inverse(X2) != sk_c11
| multiply(X2,sk_c11) != sk_c10
| multiply(X1,sk_c10) != sk_c11
| inverse(X0) != X1
| multiply(X0,X1) != sk_c11
| multiply(sk_c11,sk_c9) != sk_c10
| inverse(sk_c11) != sk_c10 ),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f110,definition,
( sQ0_spl
<=> inverse(sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f111,plain,
( ~ sQ0_spl
| inverse(sk_c11) = sk_c10 ),
inference(component_clause,[status(thm)],[f110]) ).
fof(f112,plain,
( sQ0_spl
| inverse(sk_c11) != sk_c10 ),
inference(component_clause,[status(thm)],[f110]) ).
fof(f113,definition,
( sQ1_spl
<=> multiply(sk_c3,sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f114,plain,
( ~ sQ1_spl
| multiply(sk_c3,sk_c11) = sk_c10 ),
inference(component_clause,[status(thm)],[f113]) ).
fof(f116,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f58,f110,f113]) ).
fof(f117,definition,
( sQ2_spl
<=> inverse(sk_c3) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f118,plain,
( ~ sQ2_spl
| inverse(sk_c3) = sk_c11 ),
inference(component_clause,[status(thm)],[f117]) ).
fof(f119,plain,
( sQ2_spl
| inverse(sk_c3) != sk_c11 ),
inference(component_clause,[status(thm)],[f117]) ).
fof(f120,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f59,f110,f117]) ).
fof(f121,definition,
( sQ3_spl
<=> multiply(sk_c4,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f122,plain,
( ~ sQ3_spl
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(component_clause,[status(thm)],[f121]) ).
fof(f124,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f60,f110,f121]) ).
fof(f125,definition,
( sQ4_spl
<=> inverse(sk_c4) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f126,plain,
( ~ sQ4_spl
| inverse(sk_c4) = sk_c10 ),
inference(component_clause,[status(thm)],[f125]) ).
fof(f128,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f61,f110,f125]) ).
fof(f129,definition,
( sQ5_spl
<=> multiply(sk_c5,sk_c8) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f130,plain,
( ~ sQ5_spl
| multiply(sk_c5,sk_c8) = sk_c11 ),
inference(component_clause,[status(thm)],[f129]) ).
fof(f132,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f62,f110,f129]) ).
fof(f133,definition,
( sQ6_spl
<=> inverse(sk_c5) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f134,plain,
( ~ sQ6_spl
| inverse(sk_c5) = sk_c8 ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,plain,
( sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f63,f110,f133]) ).
fof(f137,definition,
( sQ7_spl
<=> multiply(sk_c8,sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f138,plain,
( ~ sQ7_spl
| multiply(sk_c8,sk_c10) = sk_c11 ),
inference(component_clause,[status(thm)],[f137]) ).
fof(f140,plain,
( sQ7_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f64,f110,f137]) ).
fof(f141,definition,
( sQ8_spl
<=> inverse(sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f142,plain,
( ~ sQ8_spl
| inverse(sk_c7) = sk_c6 ),
inference(component_clause,[status(thm)],[f141]) ).
fof(f144,plain,
( sQ8_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f65,f110,f141]) ).
fof(f145,definition,
( sQ9_spl
<=> inverse(sk_c6) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f146,plain,
( ~ sQ9_spl
| inverse(sk_c6) = sk_c8 ),
inference(component_clause,[status(thm)],[f145]) ).
fof(f148,plain,
( sQ9_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f66,f110,f145]) ).
fof(f149,definition,
( sQ10_spl
<=> multiply(sk_c7,sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f150,plain,
( ~ sQ10_spl
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(component_clause,[status(thm)],[f149]) ).
fof(f152,plain,
( sQ10_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f67,f110,f149]) ).
fof(f153,definition,
( sQ11_spl
<=> multiply(sk_c11,sk_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f154,plain,
( ~ sQ11_spl
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(component_clause,[status(thm)],[f153]) ).
fof(f155,plain,
( sQ11_spl
| multiply(sk_c11,sk_c9) != sk_c10 ),
inference(component_clause,[status(thm)],[f153]) ).
fof(f156,plain,
( sQ1_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f68,f153,f113]) ).
fof(f157,plain,
( sQ2_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f69,f153,f117]) ).
fof(f158,plain,
( sQ3_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f70,f153,f121]) ).
fof(f159,plain,
( sQ4_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f71,f153,f125]) ).
fof(f160,plain,
( sQ5_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f72,f153,f129]) ).
fof(f161,plain,
( sQ6_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f73,f153,f133]) ).
fof(f162,plain,
( sQ7_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f74,f153,f137]) ).
fof(f163,plain,
( sQ8_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f75,f153,f141]) ).
fof(f164,plain,
( sQ9_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f76,f153,f145]) ).
fof(f165,plain,
( sQ10_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f77,f153,f149]) ).
fof(f166,definition,
( sQ12_spl
<=> multiply(sk_c1,sk_c2) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f167,plain,
( ~ sQ12_spl
| multiply(sk_c1,sk_c2) = sk_c11 ),
inference(component_clause,[status(thm)],[f166]) ).
fof(f169,plain,
( sQ1_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f78,f166,f113]) ).
fof(f170,plain,
( sQ2_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f79,f166,f117]) ).
fof(f171,plain,
( sQ3_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f80,f166,f121]) ).
fof(f172,plain,
( sQ4_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f81,f166,f125]) ).
fof(f173,plain,
( sQ5_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f82,f166,f129]) ).
fof(f174,plain,
( sQ6_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f83,f166,f133]) ).
fof(f175,plain,
( sQ7_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f84,f166,f137]) ).
fof(f176,plain,
( sQ8_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f85,f166,f141]) ).
fof(f177,plain,
( sQ9_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f86,f166,f145]) ).
fof(f178,plain,
( sQ10_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f87,f166,f149]) ).
fof(f179,definition,
( sQ13_spl
<=> inverse(sk_c1) = sk_c2 ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f180,plain,
( ~ sQ13_spl
| inverse(sk_c1) = sk_c2 ),
inference(component_clause,[status(thm)],[f179]) ).
fof(f182,plain,
( sQ1_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f88,f179,f113]) ).
fof(f183,plain,
( sQ2_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f89,f179,f117]) ).
fof(f184,plain,
( sQ3_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f90,f179,f121]) ).
fof(f185,plain,
( sQ4_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f91,f179,f125]) ).
fof(f186,plain,
( sQ5_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f92,f179,f129]) ).
fof(f187,plain,
( sQ6_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f93,f179,f133]) ).
fof(f188,plain,
( sQ7_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f94,f179,f137]) ).
fof(f189,plain,
( sQ8_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f95,f179,f141]) ).
fof(f190,plain,
( sQ9_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f96,f179,f145]) ).
fof(f191,plain,
( sQ10_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f97,f179,f149]) ).
fof(f192,definition,
( sQ14_spl
<=> multiply(sk_c2,sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f193,plain,
( ~ sQ14_spl
| multiply(sk_c2,sk_c10) = sk_c11 ),
inference(component_clause,[status(thm)],[f192]) ).
fof(f195,plain,
( sQ1_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f98,f192,f113]) ).
fof(f196,plain,
( sQ2_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f99,f192,f117]) ).
fof(f197,plain,
( sQ3_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f100,f192,f121]) ).
fof(f198,plain,
( sQ4_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f101,f192,f125]) ).
fof(f199,plain,
( sQ5_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f102,f192,f129]) ).
fof(f200,plain,
( sQ6_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f103,f192,f133]) ).
fof(f201,plain,
( sQ7_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f104,f192,f137]) ).
fof(f202,plain,
( sQ8_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f105,f192,f141]) ).
fof(f203,plain,
( sQ9_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f106,f192,f145]) ).
fof(f204,plain,
( sQ10_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f107,f192,f149]) ).
fof(f205,definition,
! [X0,X1] :
( sQ15_spl
<=> ( multiply(X1,sk_c10) != sk_c11
| inverse(X0) != X1
| multiply(X0,X1) != sk_c11 ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f206,plain,
! [X0,X1] :
( ~ sQ15_spl
| multiply(X1,sk_c10) != sk_c11
| inverse(X0) != X1
| multiply(X0,X1) != sk_c11 ),
inference(component_clause,[status(thm)],[f205]) ).
fof(f208,definition,
! [X2] :
( sQ16_spl
<=> ( inverse(X2) != sk_c11
| multiply(X2,sk_c11) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f209,plain,
! [X0] :
( ~ sQ16_spl
| inverse(X0) != sk_c11
| multiply(X0,sk_c11) != sk_c10 ),
inference(component_clause,[status(thm)],[f208]) ).
fof(f211,definition,
! [X3] :
( sQ17_spl
<=> ( inverse(X3) != sk_c10
| multiply(X3,sk_c10) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f212,plain,
! [X0] :
( ~ sQ17_spl
| inverse(X0) != sk_c10
| multiply(X0,sk_c10) != sk_c9 ),
inference(component_clause,[status(thm)],[f211]) ).
fof(f214,definition,
! [X4,X5,X6,X7] :
( sQ18_spl
<=> ( multiply(X6,X5) != X7
| inverse(X7) != X5
| inverse(X6) != X7
| multiply(X5,sk_c10) != sk_c11
| inverse(X4) != X5
| multiply(X4,X5) != sk_c11 ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f215,plain,
! [X0,X1,X2,X3] :
( ~ sQ18_spl
| multiply(X2,X1) != X3
| inverse(X3) != X1
| inverse(X2) != X3
| multiply(X1,sk_c10) != sk_c11
| inverse(X0) != X1
| multiply(X0,X1) != sk_c11 ),
inference(component_clause,[status(thm)],[f214]) ).
fof(f217,plain,
( sQ18_spl
| sQ17_spl
| sQ16_spl
| sQ15_spl
| ~ sQ11_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f109,f110,f153,f205,f208,f211,f214]) ).
fof(f218,plain,
! [X0,X1] :
( ~ sQ18_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c10) != sk_c11
| multiply(X0,inverse(X0)) != sk_c11 ),
inference(destructive_equality_resolution,[status(thm)],[f215]) ).
fof(f220,plain,
! [X0] :
( ~ sQ11_spl
| multiply(sk_c10,X0) = multiply(sk_c11,multiply(sk_c9,X0)) ),
inference(paramodulation,[status(thm)],[f154,f57]) ).
fof(f221,plain,
! [X0] :
( ~ sQ1_spl
| multiply(sk_c10,X0) = multiply(sk_c3,multiply(sk_c11,X0)) ),
inference(paramodulation,[status(thm)],[f114,f57]) ).
fof(f224,plain,
! [X0] :
( ~ sQ7_spl
| multiply(sk_c11,X0) = multiply(sk_c8,multiply(sk_c10,X0)) ),
inference(paramodulation,[status(thm)],[f138,f57]) ).
fof(f225,plain,
! [X0] :
( ~ sQ10_spl
| multiply(sk_c6,X0) = multiply(sk_c7,multiply(sk_c8,X0)) ),
inference(paramodulation,[status(thm)],[f150,f57]) ).
fof(f268,definition,
( sQ28_spl
<=> multiply(sk_c5,inverse(sk_c5)) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f270,plain,
( sQ28_spl
| multiply(sk_c5,inverse(sk_c5)) != sk_c11 ),
inference(component_clause,[status(thm)],[f268]) ).
fof(f315,plain,
( ~ sQ3_spl
| ~ sQ17_spl
| inverse(sk_c4) != sk_c10
| sk_c9 != sk_c9 ),
inference(paramodulation,[status(thm)],[f122,f212]) ).
fof(f318,definition,
( sQ40_spl
<=> sk_c9 = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f320,plain,
( sQ40_spl
| sk_c9 != sk_c9 ),
inference(component_clause,[status(thm)],[f318]) ).
fof(f321,plain,
( ~ sQ3_spl
| ~ sQ17_spl
| ~ sQ4_spl
| ~ sQ40_spl ),
inference(split_clause,[status(thm)],[f315,f318,f125,f211,f121]) ).
fof(f333,plain,
( sQ40_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f320]) ).
fof(f334,plain,
sQ40_spl,
inference(contradiction_clause,[status(thm)],[f333]) ).
fof(f337,plain,
( ~ sQ8_spl
| multiply(sk_c6,sk_c7) = identity ),
inference(paramodulation,[status(thm)],[f142,f56]) ).
fof(f341,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f56,f57]) ).
fof(f342,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f55,f341]) ).
fof(f351,plain,
( ~ sQ1_spl
| ~ sQ16_spl
| inverse(sk_c3) != sk_c11 ),
inference(resolution,[status(thm)],[f209,f114]) ).
fof(f353,plain,
( ~ sQ16_spl
| inverse(identity) != sk_c11
| sk_c11 != sk_c10 ),
inference(paramodulation,[status(thm)],[f55,f209]) ).
fof(f356,plain,
( ~ sQ1_spl
| ~ sQ16_spl
| ~ sQ2_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f118,f351]) ).
fof(f357,plain,
( ~ sQ1_spl
| ~ sQ16_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f356]) ).
fof(f358,plain,
( ~ sQ1_spl
| ~ sQ16_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f357]) ).
fof(f359,plain,
! [X0] :
( ~ sQ15_spl
| multiply(inverse(X0),sk_c10) != sk_c11
| multiply(X0,inverse(X0)) != sk_c11 ),
inference(destructive_equality_resolution,[status(thm)],[f206]) ).
fof(f363,plain,
( ~ sQ6_spl
| ~ sQ15_spl
| multiply(sk_c8,sk_c10) != sk_c11
| multiply(sk_c5,inverse(sk_c5)) != sk_c11 ),
inference(paramodulation,[status(thm)],[f134,f359]) ).
fof(f378,plain,
( ~ sQ6_spl
| ~ sQ15_spl
| ~ sQ7_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f363,f268,f137,f205,f133]) ).
fof(f379,definition,
( sQ47_spl
<=> multiply(sk_c10,sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f381,plain,
( sQ47_spl
| multiply(sk_c10,sk_c10) != sk_c11 ),
inference(component_clause,[status(thm)],[f379]) ).
fof(f383,definition,
( sQ48_spl
<=> multiply(sk_c11,sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f385,plain,
( sQ48_spl
| multiply(sk_c11,sk_c10) != sk_c11 ),
inference(component_clause,[status(thm)],[f383]) ).
fof(f408,plain,
( sQ28_spl
| ~ sQ6_spl
| multiply(sk_c5,sk_c8) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f134,f270]) ).
fof(f409,plain,
( sQ28_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f130,f408]) ).
fof(f410,plain,
( sQ28_spl
| ~ sQ6_spl
| ~ sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f409]) ).
fof(f411,plain,
( sQ28_spl
| ~ sQ6_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f410]) ).
fof(f420,plain,
( ~ sQ8_spl
| sk_c7 = multiply(inverse(sk_c6),identity) ),
inference(paramodulation,[status(thm)],[f337,f342]) ).
fof(f423,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f55,f342]) ).
fof(f425,plain,
! [X0] :
( ~ sQ1_spl
| multiply(sk_c11,X0) = multiply(inverse(sk_c3),multiply(sk_c10,X0)) ),
inference(paramodulation,[status(thm)],[f221,f342]) ).
fof(f426,plain,
( ~ sQ1_spl
| sk_c11 = multiply(inverse(sk_c3),sk_c10) ),
inference(paramodulation,[status(thm)],[f114,f342]) ).
fof(f427,plain,
( ~ sQ3_spl
| sk_c10 = multiply(inverse(sk_c4),sk_c9) ),
inference(paramodulation,[status(thm)],[f122,f342]) ).
fof(f428,plain,
( ~ sQ5_spl
| sk_c8 = multiply(inverse(sk_c5),sk_c11) ),
inference(paramodulation,[status(thm)],[f130,f342]) ).
fof(f432,plain,
( ~ sQ10_spl
| sk_c8 = multiply(inverse(sk_c7),sk_c6) ),
inference(paramodulation,[status(thm)],[f150,f342]) ).
fof(f435,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 = multiply(sk_c8,identity) ),
inference(forward_demodulation,[status(thm)],[f146,f420]) ).
fof(f437,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c11 = multiply(sk_c11,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f118,f426]) ).
fof(f438,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c10 = multiply(sk_c10,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f126,f427]) ).
fof(f439,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sk_c8 = multiply(sk_c8,sk_c11) ),
inference(forward_demodulation,[status(thm)],[f134,f428]) ).
fof(f440,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| sk_c8 = multiply(sk_c6,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f142,f432]) ).
fof(f467,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c10 = multiply(inverse(sk_c11),sk_c11) ),
inference(paramodulation,[status(thm)],[f437,f342]) ).
fof(f470,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c10 = identity ),
inference(forward_demodulation,[status(thm)],[f56,f467]) ).
fof(f472,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c7 = multiply(sk_c8,sk_c10) ),
inference(backward_demodulation,[status(thm)],[f470,f435]) ).
fof(f476,plain,
( ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c6,sk_c7) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f470,f337]) ).
fof(f478,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(inverse(X0),X0) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f470,f56]) ).
fof(f479,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c10,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f470,f55]) ).
fof(f480,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| sk_c7 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f138,f472]) ).
fof(f481,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sk_c11 = multiply(sk_c7,sk_c10) ),
inference(backward_demodulation,[status(thm)],[f480,f437]) ).
fof(f483,plain,
( sQ11_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| multiply(sk_c7,sk_c9) != sk_c10 ),
inference(backward_demodulation,[status(thm)],[f480,f155]) ).
fof(f490,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sk_c7 = multiply(sk_c7,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f480,f481]) ).
fof(f495,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c9,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f499,f479]) ).
fof(f499,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c10 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f479,f438]) ).
fof(f507,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| sk_c8 = multiply(sk_c8,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f480,f439]) ).
fof(f514,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(inverse(X0),X0) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f499,f478]) ).
fof(f517,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c8,sk_c6) = sk_c9 ),
inference(paramodulation,[status(thm)],[f146,f514]) ).
fof(f524,plain,
( sQ11_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c7,sk_c9) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f499,f483]) ).
fof(f553,plain,
( ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c6,sk_c7) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f499,f476]) ).
fof(f562,plain,
( sQ11_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c7 != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f563,f524]) ).
fof(f563,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c7 = multiply(sk_c7,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f499,f490]) ).
fof(f578,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c7,X0) = multiply(sk_c8,multiply(sk_c10,X0)) ),
inference(forward_demodulation,[status(thm)],[f480,f224]) ).
fof(f579,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c7,X0) = multiply(sk_c8,multiply(sk_c9,X0)) ),
inference(forward_demodulation,[status(thm)],[f499,f578]) ).
fof(f583,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c8 = multiply(sk_c7,sk_c7) ),
inference(backward_demodulation,[status(thm)],[f584,f507]) ).
fof(f584,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c7,X0) = multiply(sk_c8,X0) ),
inference(forward_demodulation,[status(thm)],[f495,f579]) ).
fof(f588,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c6,X0) = multiply(sk_c7,multiply(sk_c7,X0)) ),
inference(forward_demodulation,[status(thm)],[f584,f225]) ).
fof(f600,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| multiply(sk_c7,sk_c6) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f584,f517]) ).
fof(f601,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ10_spl
| multiply(sk_c6,sk_c6) = multiply(sk_c7,sk_c9) ),
inference(paramodulation,[status(thm)],[f600,f588]) ).
fof(f604,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ10_spl
| sk_c8 = multiply(sk_c7,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f440,f601]) ).
fof(f605,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ10_spl
| sk_c8 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f563,f604]) ).
fof(f611,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ10_spl
| inverse(sk_c6) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f605,f146]) ).
fof(f613,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| multiply(sk_c7,sk_c7) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f605,f150]) ).
fof(f630,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ10_spl
| sk_c7 = multiply(sk_c7,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f605,f583]) ).
fof(f631,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ10_spl
| multiply(sk_c6,sk_c7) = multiply(sk_c7,sk_c7) ),
inference(paramodulation,[status(thm)],[f630,f588]) ).
fof(f632,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ10_spl
| sk_c7 = multiply(inverse(sk_c7),sk_c7) ),
inference(paramodulation,[status(thm)],[f630,f342]) ).
fof(f634,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ10_spl
| sk_c9 = multiply(sk_c7,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f553,f631]) ).
fof(f635,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ10_spl
| sk_c9 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f630,f634]) ).
fof(f636,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ10_spl
| sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f635,f562]) ).
fof(f637,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ10_spl
| sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f636]) ).
fof(f638,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ10_spl
| sk_c7 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f514,f632]) ).
fof(f640,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c9,X0) = multiply(sk_c11,multiply(sk_c9,X0)) ),
inference(forward_demodulation,[status(thm)],[f499,f220]) ).
fof(f641,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| X0 = multiply(sk_c11,multiply(sk_c9,X0)) ),
inference(forward_demodulation,[status(thm)],[f495,f640]) ).
fof(f642,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| X0 = multiply(sk_c7,multiply(sk_c9,X0)) ),
inference(forward_demodulation,[status(thm)],[f480,f641]) ).
fof(f643,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| X0 = multiply(sk_c7,X0) ),
inference(forward_demodulation,[status(thm)],[f495,f642]) ).
fof(f644,plain,
( ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| multiply(sk_c7,sk_c9) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f480,f154]) ).
fof(f645,plain,
( ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c7 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f563,f644]) ).
fof(f646,plain,
( ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c7 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f499,f645]) ).
fof(f654,plain,
( sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| inverse(sk_c7) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f480,f112]) ).
fof(f655,plain,
( sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| sk_c6 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f142,f654]) ).
fof(f656,plain,
( sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c6 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f499,f655]) ).
fof(f667,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| multiply(inverse(X0),X0) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f638,f514]) ).
fof(f670,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| sk_c10 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f638,f499]) ).
fof(f680,plain,
( ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ6_spl
| inverse(sk_c6) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f686,f611]) ).
fof(f684,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c6 = sk_c11 ),
inference(backward_demodulation,[status(thm)],[f686,f480]) ).
fof(f686,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c7 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f630,f613]) ).
fof(f691,plain,
( ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c6 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f686,f646]) ).
fof(f693,plain,
( sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f691,f656]) ).
fof(f694,plain,
( sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f693]) ).
fof(f695,plain,
( sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f694]) ).
fof(f705,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| sk_c10 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f686,f670]) ).
fof(f715,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ6_spl
| X0 = multiply(sk_c6,X0) ),
inference(forward_demodulation,[status(thm)],[f686,f643]) ).
fof(f728,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| multiply(inverse(X0),X0) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f686,f667]) ).
fof(f766,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c10) != sk_c11
| multiply(X0,inverse(X0)) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f684,f218]) ).
fof(f767,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c6) != sk_c11
| multiply(X0,inverse(X0)) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f705,f766]) ).
fof(f768,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c6) != sk_c6
| multiply(X0,inverse(X0)) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f684,f767]) ).
fof(f769,plain,
( ~ sQ11_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ18_spl
| inverse(inverse(sk_c6)) != inverse(sk_c6)
| multiply(inverse(sk_c6),sk_c6) != sk_c6
| multiply(sk_c6,inverse(sk_c6)) != sk_c6 ),
inference(resolution,[status(thm)],[f768,f715]) ).
fof(f774,definition,
( sQ49_spl
<=> multiply(sk_c6,inverse(sk_c6)) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f776,plain,
( sQ49_spl
| multiply(sk_c6,inverse(sk_c6)) != sk_c6 ),
inference(component_clause,[status(thm)],[f774]) ).
fof(f777,definition,
( sQ50_spl
<=> multiply(inverse(sk_c6),sk_c6) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f779,plain,
( sQ50_spl
| multiply(inverse(sk_c6),sk_c6) != sk_c6 ),
inference(component_clause,[status(thm)],[f777]) ).
fof(f780,definition,
( sQ51_spl
<=> inverse(inverse(sk_c6)) = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f782,plain,
( sQ51_spl
| inverse(inverse(sk_c6)) != inverse(sk_c6) ),
inference(component_clause,[status(thm)],[f780]) ).
fof(f783,plain,
( ~ sQ11_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ18_spl
| ~ sQ51_spl
| ~ sQ50_spl
| ~ sQ49_spl ),
inference(split_clause,[status(thm)],[f769,f774,f777,f780,f214,f133,f129,f149,f137,f145,f141,f117,f113,f125,f121,f153]) ).
fof(f792,plain,
( sQ50_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f728,f779]) ).
fof(f793,plain,
( sQ50_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f792]) ).
fof(f794,plain,
( sQ50_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f793]) ).
fof(f795,plain,
( sQ49_spl
| ~ sQ11_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ6_spl
| inverse(sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f715,f776]) ).
fof(f796,plain,
( sQ49_spl
| ~ sQ11_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f680,f795]) ).
fof(f797,plain,
( sQ49_spl
| ~ sQ11_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f796]) ).
fof(f798,plain,
( sQ49_spl
| ~ sQ11_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f797]) ).
fof(f800,plain,
( sQ51_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ6_spl
| inverse(sk_c6) != inverse(sk_c6) ),
inference(forward_demodulation,[status(thm)],[f680,f782]) ).
fof(f801,plain,
( sQ51_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c6 != inverse(sk_c6) ),
inference(forward_demodulation,[status(thm)],[f680,f800]) ).
fof(f802,plain,
( sQ51_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f680,f801]) ).
fof(f803,plain,
( sQ51_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f802]) ).
fof(f804,plain,
( sQ51_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f803]) ).
fof(f807,plain,
( ~ sQ12_spl
| sk_c2 = multiply(inverse(sk_c1),sk_c11) ),
inference(paramodulation,[status(thm)],[f167,f342]) ).
fof(f809,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| sk_c2 = multiply(sk_c2,sk_c11) ),
inference(forward_demodulation,[status(thm)],[f180,f807]) ).
fof(f828,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| sk_c11 = multiply(inverse(sk_c2),sk_c2) ),
inference(paramodulation,[status(thm)],[f809,f342]) ).
fof(f830,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| sk_c11 = identity ),
inference(forward_demodulation,[status(thm)],[f56,f828]) ).
fof(f831,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ13_spl
| multiply(inverse(X0),X0) = sk_c11 ),
inference(backward_demodulation,[status(thm)],[f830,f56]) ).
fof(f832,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ13_spl
| multiply(sk_c11,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f830,f55]) ).
fof(f833,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ13_spl
| X0 = multiply(inverse(sk_c11),X0) ),
inference(backward_demodulation,[status(thm)],[f830,f423]) ).
fof(f834,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| X0 = multiply(sk_c10,X0) ),
inference(forward_demodulation,[status(thm)],[f111,f833]) ).
fof(f835,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| sk_c9 = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f832,f154]) ).
fof(f836,plain,
( sQ48_spl
| ~ sQ12_spl
| ~ sQ13_spl
| sk_c10 != sk_c11 ),
inference(backward_demodulation,[status(thm)],[f832,f385]) ).
fof(f843,plain,
( ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| multiply(sk_c2,sk_c9) = sk_c11 ),
inference(backward_demodulation,[status(thm)],[f835,f193]) ).
fof(f845,plain,
( sQ47_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| multiply(sk_c10,sk_c9) != sk_c11 ),
inference(backward_demodulation,[status(thm)],[f835,f381]) ).
fof(f848,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| inverse(sk_c11) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f835,f111]) ).
fof(f849,plain,
( sQ47_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| multiply(sk_c9,sk_c9) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f835,f845]) ).
fof(f850,plain,
( sQ48_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| sk_c9 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f835,f836]) ).
fof(f851,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ11_spl
| X0 = multiply(sk_c9,X0) ),
inference(forward_demodulation,[status(thm)],[f835,f834]) ).
fof(f857,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| inverse(X0) != sk_c10
| multiply(X0,sk_c9) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f835,f212]) ).
fof(f858,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f835,f857]) ).
fof(f859,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ17_spl
| ~ sQ11_spl
| inverse(sk_c11) != sk_c9 ),
inference(resolution,[status(thm)],[f858,f832]) ).
fof(f864,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ17_spl
| ~ sQ11_spl
| ~ sQ0_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f848,f859]) ).
fof(f865,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ17_spl
| ~ sQ11_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f864]) ).
fof(f866,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ17_spl
| ~ sQ11_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f865]) ).
fof(f870,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| multiply(sk_c9,X0) = multiply(sk_c3,multiply(sk_c11,X0)) ),
inference(forward_demodulation,[status(thm)],[f835,f221]) ).
fof(f871,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| X0 = multiply(sk_c3,multiply(sk_c11,X0)) ),
inference(forward_demodulation,[status(thm)],[f851,f870]) ).
fof(f872,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| X0 = multiply(sk_c3,X0) ),
inference(forward_demodulation,[status(thm)],[f832,f871]) ).
fof(f873,plain,
( ~ sQ1_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| multiply(sk_c3,sk_c11) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f835,f114]) ).
fof(f875,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ12_spl
| ~ sQ13_spl
| X0 = multiply(inverse(sk_c3),multiply(sk_c10,X0)) ),
inference(forward_demodulation,[status(thm)],[f832,f425]) ).
fof(f876,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| X0 = multiply(inverse(sk_c3),multiply(sk_c9,X0)) ),
inference(forward_demodulation,[status(thm)],[f835,f875]) ).
fof(f877,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ0_spl
| X0 = multiply(inverse(sk_c3),X0) ),
inference(forward_demodulation,[status(thm)],[f851,f876]) ).
fof(f878,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| multiply(inverse(X0),sk_c9) != sk_c11
| multiply(X0,inverse(X0)) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f835,f359]) ).
fof(f880,plain,
( ~ sQ13_spl
| ~ sQ12_spl
| multiply(sk_c2,sk_c1) = sk_c11 ),
inference(paramodulation,[status(thm)],[f180,f831]) ).
fof(f895,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| multiply(sk_c11,X0) = multiply(sk_c2,multiply(sk_c9,X0)) ),
inference(paramodulation,[status(thm)],[f843,f57]) ).
fof(f896,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| X0 = multiply(sk_c2,multiply(sk_c9,X0)) ),
inference(forward_demodulation,[status(thm)],[f832,f895]) ).
fof(f897,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| X0 = multiply(sk_c2,X0) ),
inference(forward_demodulation,[status(thm)],[f851,f896]) ).
fof(f898,plain,
( ~ sQ1_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| sk_c11 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f872,f873]) ).
fof(f899,plain,
( ~ sQ1_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| sQ48_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f898,f850]) ).
fof(f900,plain,
( ~ sQ1_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| sQ48_spl ),
inference(contradiction_clause,[status(thm)],[f899]) ).
fof(f906,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ1_spl
| ~ sQ11_spl
| ~ sQ0_spl
| multiply(inverse(X0),X0) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f898,f831]) ).
fof(f907,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ1_spl
| inverse(sk_c9) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f898,f848]) ).
fof(f912,plain,
( sQ2_spl
| ~ sQ1_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| inverse(sk_c3) != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f898,f119]) ).
fof(f918,plain,
( sQ47_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| sk_c9 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f851,f849]) ).
fof(f919,plain,
( sQ47_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ1_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f898,f918]) ).
fof(f920,plain,
( sQ47_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f919]) ).
fof(f921,plain,
( sQ47_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f920]) ).
fof(f926,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ1_spl
| ~ sQ0_spl
| multiply(inverse(X0),sk_c9) != sk_c11
| multiply(X0,inverse(X0)) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f898,f878]) ).
fof(f927,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ1_spl
| ~ sQ0_spl
| multiply(inverse(X0),sk_c9) != sk_c9
| multiply(X0,inverse(X0)) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f898,f926]) ).
fof(f928,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ1_spl
| ~ sQ15_spl
| multiply(sk_c9,sk_c9) != sk_c9
| multiply(sk_c9,inverse(sk_c9)) != sk_c9 ),
inference(paramodulation,[status(thm)],[f907,f927]) ).
fof(f930,definition,
( sQ53_spl
<=> multiply(sk_c9,inverse(sk_c9)) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f932,plain,
( sQ53_spl
| multiply(sk_c9,inverse(sk_c9)) != sk_c9 ),
inference(component_clause,[status(thm)],[f930]) ).
fof(f933,definition,
( sQ54_spl
<=> multiply(sk_c9,sk_c9) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f935,plain,
( sQ54_spl
| multiply(sk_c9,sk_c9) != sk_c9 ),
inference(component_clause,[status(thm)],[f933]) ).
fof(f936,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ1_spl
| ~ sQ15_spl
| ~ sQ54_spl
| ~ sQ53_spl ),
inference(split_clause,[status(thm)],[f928,f930,f933,f205,f113,f179,f166,f153,f110]) ).
fof(f948,plain,
( sQ54_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ11_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f851,f935]) ).
fof(f949,plain,
( sQ54_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f948]) ).
fof(f950,plain,
( sQ54_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f949]) ).
fof(f951,plain,
( sQ53_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ11_spl
| inverse(sk_c9) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f851,f932]) ).
fof(f952,plain,
( sQ53_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ1_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f907,f951]) ).
fof(f953,plain,
( sQ53_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f952]) ).
fof(f954,plain,
( sQ53_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f953]) ).
fof(f966,plain,
( ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ0_spl
| sk_c1 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f897,f880]) ).
fof(f968,plain,
( sQ2_spl
| ~ sQ1_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ14_spl
| inverse(sk_c3) != sk_c1 ),
inference(backward_demodulation,[status(thm)],[f975,f912]) ).
fof(f969,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ1_spl
| ~ sQ14_spl
| inverse(sk_c9) = sk_c1 ),
inference(backward_demodulation,[status(thm)],[f975,f907]) ).
fof(f975,plain,
( ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ1_spl
| sk_c1 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f898,f966]) ).
fof(f977,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ1_spl
| ~ sQ14_spl
| inverse(sk_c1) = sk_c1 ),
inference(forward_demodulation,[status(thm)],[f975,f969]) ).
fof(f978,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ1_spl
| ~ sQ14_spl
| sk_c2 = sk_c1 ),
inference(forward_demodulation,[status(thm)],[f180,f977]) ).
fof(f979,plain,
( ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ1_spl
| sk_c2 = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f978,f975]) ).
fof(f980,plain,
( ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ1_spl
| ~ sQ14_spl
| inverse(sk_c2) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f978,f180]) ).
fof(f984,plain,
( sQ2_spl
| ~ sQ1_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ14_spl
| inverse(sk_c3) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f978,f968]) ).
fof(f996,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ1_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ14_spl
| multiply(inverse(X0),X0) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f979,f906]) ).
fof(f997,plain,
( ~ sQ1_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ14_spl
| sk_c3 = sk_c2 ),
inference(paramodulation,[status(thm)],[f877,f996]) ).
fof(f1005,plain,
( sQ2_spl
| ~ sQ1_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ14_spl
| inverse(sk_c2) != sk_c2 ),
inference(backward_demodulation,[status(thm)],[f997,f984]) ).
fof(f1008,plain,
( sQ2_spl
| ~ sQ1_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ14_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f980,f1005]) ).
fof(f1009,plain,
( sQ2_spl
| ~ sQ1_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ14_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1008]) ).
fof(f1010,plain,
( sQ2_spl
| ~ sQ1_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f1009]) ).
fof(f1093,definition,
( sQ60_spl
<=> multiply(sk_c2,inverse(sk_c2)) = sk_c2 ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f1095,plain,
( sQ60_spl
| multiply(sk_c2,inverse(sk_c2)) != sk_c2 ),
inference(component_clause,[status(thm)],[f1093]) ).
fof(f1096,definition,
( sQ61_spl
<=> multiply(inverse(sk_c2),sk_c2) = sk_c2 ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f1098,plain,
( sQ61_spl
| multiply(inverse(sk_c2),sk_c2) != sk_c2 ),
inference(component_clause,[status(thm)],[f1096]) ).
fof(f1099,definition,
( sQ62_spl
<=> inverse(inverse(sk_c2)) = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f1101,plain,
( sQ62_spl
| inverse(inverse(sk_c2)) != inverse(sk_c2) ),
inference(component_clause,[status(thm)],[f1099]) ).
fof(f1114,plain,
( sQ60_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| inverse(sk_c2) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f897,f1095]) ).
fof(f1124,plain,
( ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| sk_c9 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f897,f843]) ).
fof(f1126,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ0_spl
| sk_c2 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f897,f809]) ).
fof(f1127,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ0_spl
| sk_c1 = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f1128,f835]) ).
fof(f1128,plain,
( ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| sk_c9 = sk_c1 ),
inference(forward_demodulation,[status(thm)],[f966,f1124]) ).
fof(f1129,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ0_spl
| sk_c1 = identity ),
inference(forward_demodulation,[status(thm)],[f966,f830]) ).
fof(f1130,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ0_spl
| sk_c2 = identity ),
inference(backward_demodulation,[status(thm)],[f1133,f1129]) ).
fof(f1131,plain,
( ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| sk_c9 = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f1133,f1128]) ).
fof(f1132,plain,
( ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ0_spl
| sk_c2 = sk_c11 ),
inference(backward_demodulation,[status(thm)],[f1133,f966]) ).
fof(f1133,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ0_spl
| sk_c2 = sk_c1 ),
inference(forward_demodulation,[status(thm)],[f966,f1126]) ).
fof(f1134,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ0_spl
| sk_c2 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1133,f1127]) ).
fof(f1135,plain,
( ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ0_spl
| inverse(sk_c2) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1133,f180]) ).
fof(f1138,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ0_spl
| multiply(inverse(X0),sk_c9) != sk_c11
| multiply(X0,inverse(X0)) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1132,f878]) ).
fof(f1139,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ0_spl
| multiply(inverse(X0),sk_c2) != sk_c11
| multiply(X0,inverse(X0)) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1131,f1138]) ).
fof(f1140,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ0_spl
| multiply(inverse(X0),sk_c2) != sk_c2
| multiply(X0,inverse(X0)) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1132,f1139]) ).
fof(f1141,plain,
( ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ15_spl
| multiply(sk_c2,sk_c2) != sk_c2
| multiply(sk_c2,inverse(sk_c2)) != sk_c2 ),
inference(paramodulation,[status(thm)],[f1135,f1140]) ).
fof(f1142,definition,
( sQ64_spl
<=> multiply(sk_c2,sk_c2) = sk_c2 ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f1144,plain,
( sQ64_spl
| multiply(sk_c2,sk_c2) != sk_c2 ),
inference(component_clause,[status(thm)],[f1142]) ).
fof(f1145,plain,
( ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ64_spl
| ~ sQ60_spl ),
inference(split_clause,[status(thm)],[f1141,f1093,f1142,f205,f110,f153,f192,f166,f179]) ).
fof(f1146,plain,
( sQ64_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f897,f1144]) ).
fof(f1147,plain,
( sQ64_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1146]) ).
fof(f1148,plain,
( sQ64_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f1147]) ).
fof(f1149,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ0_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c10) != sk_c11
| multiply(X0,inverse(X0)) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1132,f218]) ).
fof(f1150,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ0_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c2) != sk_c11
| multiply(X0,inverse(X0)) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1134,f1149]) ).
fof(f1151,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ0_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c2) != sk_c2
| multiply(X0,inverse(X0)) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1132,f1150]) ).
fof(f1175,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ0_spl
| multiply(inverse(X0),X0) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1132,f831]) ).
fof(f1196,plain,
( ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ18_spl
| inverse(inverse(sk_c2)) != inverse(sk_c2)
| multiply(inverse(sk_c2),sk_c2) != sk_c2
| multiply(sk_c2,inverse(sk_c2)) != sk_c2 ),
inference(resolution,[status(thm)],[f1151,f897]) ).
fof(f1201,plain,
( ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ18_spl
| ~ sQ62_spl
| ~ sQ61_spl
| ~ sQ60_spl ),
inference(split_clause,[status(thm)],[f1196,f1093,f1096,f1099,f214,f110,f179,f166,f153,f192]) ).
fof(f1212,plain,
( sQ60_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1135,f1114]) ).
fof(f1213,plain,
( sQ60_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1212]) ).
fof(f1214,plain,
( sQ60_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f1213]) ).
fof(f1216,plain,
( sQ61_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ0_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1175,f1098]) ).
fof(f1217,plain,
( sQ61_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1216]) ).
fof(f1218,plain,
( sQ61_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f1217]) ).
fof(f1229,definition,
( sQ67_spl
<=> sk_c11 = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f1231,plain,
( sQ67_spl
| sk_c11 != sk_c10 ),
inference(component_clause,[status(thm)],[f1229]) ).
fof(f1232,definition,
( sQ68_spl
<=> inverse(identity) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f1234,plain,
( sQ68_spl
| inverse(identity) != sk_c11 ),
inference(component_clause,[status(thm)],[f1232]) ).
fof(f1235,plain,
( ~ sQ16_spl
| ~ sQ68_spl
| ~ sQ67_spl ),
inference(split_clause,[status(thm)],[f353,f1229,f1232,f208]) ).
fof(f1243,plain,
( sQ67_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ0_spl
| sk_c2 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1132,f1231]) ).
fof(f1244,plain,
( sQ67_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ0_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1134,f1243]) ).
fof(f1245,plain,
( sQ67_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1244]) ).
fof(f1246,plain,
( sQ67_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f1245]) ).
fof(f1247,plain,
( sQ68_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ0_spl
| inverse(sk_c2) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1130,f1234]) ).
fof(f1248,plain,
( sQ68_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ0_spl
| sk_c2 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1135,f1247]) ).
fof(f1249,plain,
( sQ68_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ0_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1132,f1248]) ).
fof(f1250,plain,
( sQ68_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1249]) ).
fof(f1251,plain,
( sQ68_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f1250]) ).
fof(f1258,plain,
( sQ62_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ0_spl
| inverse(sk_c2) != inverse(sk_c2) ),
inference(forward_demodulation,[status(thm)],[f1135,f1101]) ).
fof(f1259,plain,
( sQ62_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ0_spl
| sk_c2 != inverse(sk_c2) ),
inference(forward_demodulation,[status(thm)],[f1135,f1258]) ).
fof(f1260,plain,
( sQ62_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ0_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1135,f1259]) ).
fof(f1261,plain,
( sQ62_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1260]) ).
fof(f1262,plain,
( sQ62_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f1261]) ).
fof(f1263,plain,
$false,
inference(sat_refutation,[status(thm)],[f116,f120,f124,f128,f132,f136,f140,f144,f148,f152,f156,f157,f158,f159,f160,f161,f162,f163,f164,f165,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f182,f183,f184,f185,f186,f187,f188,f189,f190,f191,f195,f196,f197,f198,f199,f200,f201,f202,f203,f204,f217,f321,f334,f358,f378,f411,f637,f695,f783,f794,f798,f804,f866,f900,f921,f936,f950,f954,f1010,f1145,f1148,f1201,f1214,f1218,f1235,f1246,f1251,f1262]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP378-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 20:08:50 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.14/0.39 % Drodi V4.1.1
% 0.14/0.40 % Refutation found
% 0.14/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.43 % Elapsed time: 0.049758 seconds
% 0.14/0.43 % CPU time: 0.177381 seconds
% 0.14/0.43 % Total memory used: 32.721 MB
% 0.14/0.43 % Net memory used: 32.533 MB
%------------------------------------------------------------------------------