%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP386-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 12:33:35 PM UTC 2026
% Result : Unsatisfiable 0.16s 15.64s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 85
% Syntax : Number of formulae : 424 ( 14 unt; 31 def)
% Number of atoms : 1803 ( 525 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 2616 (1237 ~;1348 |; 0 &)
% ( 31 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 33 ( 31 usr; 32 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 98 ( 98 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c8
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c3) = sk_c9
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c10
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c4) = sk_c7
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c7,sk_c9) = sk_c10
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c6) = sk_c5
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c5) = sk_c7
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| multiply(sk_c9,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c9,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c8
| multiply(sk_c9,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c3) = sk_c9
| multiply(sk_c9,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c10
| multiply(sk_c9,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c9,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c7,sk_c9) = sk_c10
| multiply(sk_c9,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c6) = sk_c5
| multiply(sk_c9,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c9,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c9,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| multiply(sk_c10,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c10,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c8
| multiply(sk_c10,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c3) = sk_c9
| multiply(sk_c10,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c10
| multiply(sk_c10,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c10,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( multiply(sk_c7,sk_c9) = sk_c10
| multiply(sk_c10,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( inverse(sk_c6) = sk_c5
| multiply(sk_c10,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c10,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c10,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( inverse(sk_c2) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( inverse(sk_c3) = sk_c9
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
( inverse(sk_c4) = sk_c7
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
( multiply(sk_c7,sk_c9) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,negated_conjecture,
( inverse(sk_c6) = sk_c5
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,negated_conjecture,
( inverse(sk_c5) = sk_c7
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
( multiply(sk_c2,sk_c10) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
( inverse(sk_c2) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,negated_conjecture,
( inverse(sk_c3) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f50,negated_conjecture,
( multiply(sk_c7,sk_c9) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f51,negated_conjecture,
( inverse(sk_c6) = sk_c5
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f52,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f53,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
! [X2,X1,X3,X4,X5,X6,X7] :
( multiply(X6,X5) != X7
| inverse(X7) != X5
| inverse(X6) != X7
| multiply(X5,sk_c9) != sk_c10
| inverse(X4) != X5
| multiply(X4,X5) != sk_c10
| inverse(X3) != sk_c9
| multiply(X3,sk_c9) != sk_c8
| inverse(X1) != sk_c10
| multiply(X1,sk_c10) != sk_c9
| multiply(X2,sk_c9) != sk_c10
| inverse(X2) != sk_c10
| multiply(sk_c10,sk_c8) != sk_c9
| multiply(sk_c9,sk_c8) != sk_c10
| inverse(sk_c10) != sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f55,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f56,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f57,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f58,plain,
( multiply(sk_c2,sk_c10) = sk_c9
| inverse(sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f59,plain,
( inverse(sk_c2) = sk_c10
| inverse(sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f60,plain,
( multiply(sk_c3,sk_c9) = sk_c8
| inverse(sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f61,plain,
( inverse(sk_c3) = sk_c9
| inverse(sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f62,plain,
( multiply(sk_c4,sk_c7) = sk_c10
| inverse(sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f63,plain,
( inverse(sk_c4) = sk_c7
| inverse(sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f64,plain,
( multiply(sk_c7,sk_c9) = sk_c10
| inverse(sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f65,plain,
( inverse(sk_c6) = sk_c5
| inverse(sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f66,plain,
( inverse(sk_c5) = sk_c7
| inverse(sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f67,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f68,plain,
( multiply(sk_c2,sk_c10) = sk_c9
| multiply(sk_c9,sk_c8) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f69,plain,
( inverse(sk_c2) = sk_c10
| multiply(sk_c9,sk_c8) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f70,plain,
( multiply(sk_c3,sk_c9) = sk_c8
| multiply(sk_c9,sk_c8) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f71,plain,
( inverse(sk_c3) = sk_c9
| multiply(sk_c9,sk_c8) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f72,plain,
( multiply(sk_c4,sk_c7) = sk_c10
| multiply(sk_c9,sk_c8) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f73,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c9,sk_c8) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f74,plain,
( multiply(sk_c7,sk_c9) = sk_c10
| multiply(sk_c9,sk_c8) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f75,plain,
( inverse(sk_c6) = sk_c5
| multiply(sk_c9,sk_c8) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f76,plain,
( inverse(sk_c5) = sk_c7
| multiply(sk_c9,sk_c8) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f77,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c9,sk_c8) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f78,plain,
( multiply(sk_c2,sk_c10) = sk_c9
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f79,plain,
( inverse(sk_c2) = sk_c10
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f80,plain,
( multiply(sk_c3,sk_c9) = sk_c8
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f81,plain,
( inverse(sk_c3) = sk_c9
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f82,plain,
( multiply(sk_c4,sk_c7) = sk_c10
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f83,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f84,plain,
( multiply(sk_c7,sk_c9) = sk_c10
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f85,plain,
( inverse(sk_c6) = sk_c5
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f86,plain,
( inverse(sk_c5) = sk_c7
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f87,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f88,plain,
( multiply(sk_c2,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f89,plain,
( inverse(sk_c2) = sk_c10
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f90,plain,
( multiply(sk_c3,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f91,plain,
( inverse(sk_c3) = sk_c9
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f92,plain,
( multiply(sk_c4,sk_c7) = sk_c10
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f93,plain,
( inverse(sk_c4) = sk_c7
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f94,plain,
( multiply(sk_c7,sk_c9) = sk_c10
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f95,plain,
( inverse(sk_c6) = sk_c5
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f96,plain,
( inverse(sk_c5) = sk_c7
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f97,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f98,plain,
( multiply(sk_c2,sk_c10) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f99,plain,
( inverse(sk_c2) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f100,plain,
( multiply(sk_c3,sk_c9) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f101,plain,
( inverse(sk_c3) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f102,plain,
( multiply(sk_c4,sk_c7) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f103,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f104,plain,
( multiply(sk_c7,sk_c9) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f105,plain,
( inverse(sk_c6) = sk_c5
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f106,plain,
( inverse(sk_c5) = sk_c7
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f107,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f108,plain,
! [X5,X6,X7] :
( multiply(X6,X5) != X7
| inverse(X7) != X5
| inverse(X6) != X7
| multiply(X5,sk_c9) != sk_c10
| ! [X4] :
( inverse(X4) != X5
| multiply(X4,X5) != sk_c10
| ! [X3] :
( inverse(X3) != sk_c9
| multiply(X3,sk_c9) != sk_c8
| ! [X1] :
( inverse(X1) != sk_c10
| multiply(X1,sk_c10) != sk_c9
| ! [X2] :
( multiply(X2,sk_c9) != sk_c10
| inverse(X2) != sk_c10
| multiply(sk_c10,sk_c8) != sk_c9
| multiply(sk_c9,sk_c8) != sk_c10
| inverse(sk_c10) != sk_c9 ) ) ) ) ),
inference(miniscoping,[status(thm)],[f54]) ).
fof(f109,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( multiply(X5,X4) != X6
| inverse(X6) != X4
| inverse(X5) != X6
| multiply(X4,sk_c9) != sk_c10
| inverse(X3) != X4
| multiply(X3,X4) != sk_c10
| inverse(X2) != sk_c9
| multiply(X2,sk_c9) != sk_c8
| inverse(X1) != sk_c10
| multiply(X1,sk_c10) != sk_c9
| multiply(X0,sk_c9) != sk_c10
| inverse(X0) != sk_c10
| multiply(sk_c10,sk_c8) != sk_c9
| multiply(sk_c9,sk_c8) != sk_c10
| inverse(sk_c10) != sk_c9 ),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f110,definition,
( sQ0_spl
<=> inverse(sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f111,plain,
( ~ sQ0_spl
| inverse(sk_c10) = sk_c9 ),
inference(component_clause,[status(thm)],[f110]) ).
fof(f112,plain,
( sQ0_spl
| inverse(sk_c10) != sk_c9 ),
inference(component_clause,[status(thm)],[f110]) ).
fof(f113,definition,
( sQ1_spl
<=> multiply(sk_c2,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f114,plain,
( ~ sQ1_spl
| multiply(sk_c2,sk_c10) = sk_c9 ),
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_c2) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f118,plain,
( ~ sQ2_spl
| inverse(sk_c2) = sk_c10 ),
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_c3,sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f122,plain,
( ~ sQ3_spl
| multiply(sk_c3,sk_c9) = sk_c8 ),
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_c3) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f126,plain,
( ~ sQ4_spl
| inverse(sk_c3) = sk_c9 ),
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_c4,sk_c7) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f130,plain,
( ~ sQ5_spl
| multiply(sk_c4,sk_c7) = sk_c10 ),
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_c4) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f134,plain,
( ~ sQ6_spl
| inverse(sk_c4) = sk_c7 ),
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_c7,sk_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f138,plain,
( ~ sQ7_spl
| multiply(sk_c7,sk_c9) = sk_c10 ),
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_c6) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f142,plain,
( ~ sQ8_spl
| inverse(sk_c6) = sk_c5 ),
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_c5) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f146,plain,
( ~ sQ9_spl
| inverse(sk_c5) = sk_c7 ),
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_c6,sk_c7) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f150,plain,
( ~ sQ10_spl
| multiply(sk_c6,sk_c7) = sk_c5 ),
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_c9,sk_c8) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f154,plain,
( ~ sQ11_spl
| multiply(sk_c9,sk_c8) = sk_c10 ),
inference(component_clause,[status(thm)],[f153]) ).
fof(f155,plain,
( sQ11_spl
| multiply(sk_c9,sk_c8) != 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_c10,sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f167,plain,
( ~ sQ12_spl
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(component_clause,[status(thm)],[f166]) ).
fof(f168,plain,
( sQ12_spl
| multiply(sk_c10,sk_c8) != sk_c9 ),
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_c10 ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f180,plain,
( ~ sQ13_spl
| inverse(sk_c1) = sk_c10 ),
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_c1,sk_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f193,plain,
( ~ sQ14_spl
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(component_clause,[status(thm)],[f192]) ).
fof(f194,plain,
( sQ14_spl
| multiply(sk_c1,sk_c9) != sk_c10 ),
inference(component_clause,[status(thm)],[f192]) ).
fof(f195,plain,
( sQ1_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f98,f192,f113]) ).
fof(f196,plain,
( sQ2_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f99,f192,f117]) ).
fof(f197,plain,
( sQ3_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f100,f192,f121]) ).
fof(f198,plain,
( sQ4_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f101,f192,f125]) ).
fof(f199,plain,
( sQ5_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f102,f192,f129]) ).
fof(f200,plain,
( sQ6_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f103,f192,f133]) ).
fof(f201,plain,
( sQ7_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f104,f192,f137]) ).
fof(f202,plain,
( sQ8_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f105,f192,f141]) ).
fof(f203,plain,
( sQ9_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f106,f192,f145]) ).
fof(f204,plain,
( sQ10_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f107,f192,f149]) ).
fof(f205,definition,
! [X0] :
( sQ15_spl
<=> ( multiply(X0,sk_c9) != sk_c10
| inverse(X0) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f206,plain,
! [X0] :
( ~ sQ15_spl
| multiply(X0,sk_c9) != sk_c10
| inverse(X0) != sk_c10 ),
inference(component_clause,[status(thm)],[f205]) ).
fof(f208,definition,
! [X1] :
( sQ16_spl
<=> ( inverse(X1) != sk_c10
| multiply(X1,sk_c10) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f209,plain,
! [X0] :
( ~ sQ16_spl
| inverse(X0) != sk_c10
| multiply(X0,sk_c10) != sk_c9 ),
inference(component_clause,[status(thm)],[f208]) ).
fof(f211,definition,
! [X2] :
( sQ17_spl
<=> ( inverse(X2) != sk_c9
| multiply(X2,sk_c9) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f212,plain,
! [X0] :
( ~ sQ17_spl
| inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c8 ),
inference(component_clause,[status(thm)],[f211]) ).
fof(f214,definition,
! [X3,X4,X5,X6] :
( sQ18_spl
<=> ( multiply(X5,X4) != X6
| inverse(X6) != X4
| inverse(X5) != X6
| multiply(X4,sk_c9) != sk_c10
| inverse(X3) != X4
| multiply(X3,X4) != sk_c10 ) ),
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_c9) != sk_c10
| inverse(X0) != X1
| multiply(X0,X1) != sk_c10 ),
inference(component_clause,[status(thm)],[f214]) ).
fof(f217,plain,
( sQ18_spl
| sQ17_spl
| sQ16_spl
| sQ15_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f109,f110,f153,f166,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_c9) != sk_c10
| multiply(X0,inverse(X0)) != sk_c10 ),
inference(destructive_equality_resolution,[status(thm)],[f215]) ).
fof(f229,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ18_spl
| multiply(X0,inverse(sk_c2)) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c2)
| multiply(sk_c10,sk_c9) != sk_c10
| multiply(sk_c2,inverse(sk_c2)) != sk_c10 ),
inference(paramodulation,[status(thm)],[f118,f218]) ).
fof(f234,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ18_spl
| multiply(X0,inverse(sk_c1)) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c1)
| multiply(sk_c10,sk_c9) != sk_c10
| multiply(sk_c1,inverse(sk_c1)) != sk_c10 ),
inference(paramodulation,[status(thm)],[f180,f218]) ).
fof(f245,definition,
( sQ22_spl
<=> multiply(sk_c2,inverse(sk_c2)) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f247,plain,
( sQ22_spl
| multiply(sk_c2,inverse(sk_c2)) != sk_c10 ),
inference(component_clause,[status(thm)],[f245]) ).
fof(f248,definition,
( sQ23_spl
<=> multiply(sk_c10,sk_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f250,plain,
( sQ23_spl
| multiply(sk_c10,sk_c9) != sk_c10 ),
inference(component_clause,[status(thm)],[f248]) ).
fof(f251,definition,
! [X0] :
( sQ24_spl
<=> ( multiply(X0,inverse(sk_c2)) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c2) ) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f254,plain,
( ~ sQ2_spl
| ~ sQ18_spl
| sQ24_spl
| ~ sQ23_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f229,f245,f248,f251,f214,f117]) ).
fof(f286,definition,
( sQ34_spl
<=> multiply(sk_c1,inverse(sk_c1)) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f288,plain,
( sQ34_spl
| multiply(sk_c1,inverse(sk_c1)) != sk_c10 ),
inference(component_clause,[status(thm)],[f286]) ).
fof(f289,definition,
! [X0] :
( sQ35_spl
<=> ( multiply(X0,inverse(sk_c1)) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c1) ) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f290,plain,
! [X0] :
( ~ sQ35_spl
| multiply(X0,inverse(sk_c1)) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c1) ),
inference(component_clause,[status(thm)],[f289]) ).
fof(f292,plain,
( ~ sQ13_spl
| ~ sQ18_spl
| sQ35_spl
| ~ sQ23_spl
| ~ sQ34_spl ),
inference(split_clause,[status(thm)],[f234,f286,f248,f289,f214,f179]) ).
fof(f295,plain,
( sQ34_spl
| ~ sQ13_spl
| multiply(sk_c1,sk_c10) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f180,f288]) ).
fof(f302,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f56,f57]) ).
fof(f303,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f55,f302]) ).
fof(f311,plain,
( ~ sQ0_spl
| ~ sQ17_spl
| sk_c9 != sk_c9
| multiply(sk_c10,sk_c9) != sk_c8 ),
inference(paramodulation,[status(thm)],[f111,f212]) ).
fof(f312,plain,
( ~ sQ13_spl
| ~ sQ17_spl
| sk_c10 != sk_c9
| multiply(sk_c1,sk_c9) != sk_c8 ),
inference(paramodulation,[status(thm)],[f180,f212]) ).
fof(f313,definition,
( sQ36_spl
<=> multiply(sk_c10,sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f316,definition,
( sQ37_spl
<=> sk_c9 = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f318,plain,
( sQ37_spl
| sk_c9 != sk_c9 ),
inference(component_clause,[status(thm)],[f316]) ).
fof(f319,plain,
( ~ sQ0_spl
| ~ sQ17_spl
| ~ sQ37_spl
| ~ sQ36_spl ),
inference(split_clause,[status(thm)],[f311,f313,f316,f211,f110]) ).
fof(f320,definition,
( sQ38_spl
<=> multiply(sk_c1,sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f322,plain,
( sQ38_spl
| multiply(sk_c1,sk_c9) != sk_c8 ),
inference(component_clause,[status(thm)],[f320]) ).
fof(f323,definition,
( sQ39_spl
<=> sk_c10 = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f325,plain,
( sQ39_spl
| sk_c10 != sk_c9 ),
inference(component_clause,[status(thm)],[f323]) ).
fof(f326,plain,
( ~ sQ13_spl
| ~ sQ17_spl
| ~ sQ39_spl
| ~ sQ38_spl ),
inference(split_clause,[status(thm)],[f312,f320,f323,f211,f179]) ).
fof(f327,plain,
( sQ38_spl
| ~ sQ14_spl
| sk_c10 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f193,f322]) ).
fof(f328,plain,
( sQ37_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f318]) ).
fof(f329,plain,
sQ37_spl,
inference(contradiction_clause,[status(thm)],[f328]) ).
fof(f330,plain,
( ~ sQ13_spl
| ~ sQ16_spl
| multiply(sk_c1,sk_c10) != sk_c9 ),
inference(resolution,[status(thm)],[f209,f180]) ).
fof(f340,definition,
( sQ42_spl
<=> sk_c10 = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f342,plain,
( sQ42_spl
| sk_c10 != sk_c10 ),
inference(component_clause,[status(thm)],[f340]) ).
fof(f344,plain,
( sQ42_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f342]) ).
fof(f345,plain,
sQ42_spl,
inference(contradiction_clause,[status(thm)],[f344]) ).
fof(f346,plain,
( ~ sQ13_spl
| ~ sQ15_spl
| multiply(sk_c1,sk_c9) != sk_c10 ),
inference(resolution,[status(thm)],[f206,f180]) ).
fof(f347,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| multiply(sk_c10,sk_c9) != sk_c10
| sk_c9 != sk_c10 ),
inference(paramodulation,[status(thm)],[f111,f206]) ).
fof(f349,plain,
( ~ sQ13_spl
| ~ sQ15_spl
| ~ sQ14_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f193,f346]) ).
fof(f350,plain,
( ~ sQ13_spl
| ~ sQ15_spl
| ~ sQ14_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f349]) ).
fof(f351,plain,
( ~ sQ13_spl
| ~ sQ15_spl
| ~ sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f350]) ).
fof(f355,plain,
( ~ sQ8_spl
| multiply(sk_c5,sk_c6) = identity ),
inference(paramodulation,[status(thm)],[f142,f56]) ).
fof(f359,plain,
( ~ sQ3_spl
| ~ sQ17_spl
| inverse(sk_c3) != sk_c9 ),
inference(resolution,[status(thm)],[f212,f122]) ).
fof(f366,plain,
( ~ sQ3_spl
| ~ sQ17_spl
| ~ sQ4_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f126,f359]) ).
fof(f367,plain,
( ~ sQ3_spl
| ~ sQ17_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f366]) ).
fof(f368,plain,
( ~ sQ3_spl
| ~ sQ17_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f367]) ).
fof(f369,plain,
( ~ sQ1_spl
| ~ sQ16_spl
| inverse(sk_c2) != sk_c10 ),
inference(resolution,[status(thm)],[f209,f114]) ).
fof(f375,plain,
( ~ sQ1_spl
| ~ sQ16_spl
| ~ sQ2_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f118,f369]) ).
fof(f376,plain,
( ~ sQ1_spl
| ~ sQ16_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f375]) ).
fof(f377,plain,
( ~ sQ1_spl
| ~ sQ16_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f376]) ).
fof(f396,plain,
( sQ22_spl
| ~ sQ2_spl
| multiply(sk_c2,sk_c10) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f118,f247]) ).
fof(f397,plain,
( sQ22_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c9 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f114,f396]) ).
fof(f403,plain,
( ~ sQ8_spl
| sk_c6 = multiply(inverse(sk_c5),identity) ),
inference(paramodulation,[status(thm)],[f355,f303]) ).
fof(f411,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f303,f303]) ).
fof(f412,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f56,f303]) ).
fof(f413,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f55,f303]) ).
fof(f415,plain,
( ~ sQ1_spl
| sk_c10 = multiply(inverse(sk_c2),sk_c9) ),
inference(paramodulation,[status(thm)],[f114,f303]) ).
fof(f416,plain,
( ~ sQ3_spl
| sk_c9 = multiply(inverse(sk_c3),sk_c8) ),
inference(paramodulation,[status(thm)],[f122,f303]) ).
fof(f417,plain,
( ~ sQ5_spl
| sk_c7 = multiply(inverse(sk_c4),sk_c10) ),
inference(paramodulation,[status(thm)],[f130,f303]) ).
fof(f418,plain,
( ~ sQ10_spl
| sk_c7 = multiply(inverse(sk_c6),sk_c5) ),
inference(paramodulation,[status(thm)],[f150,f303]) ).
fof(f421,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c6 = multiply(sk_c7,identity) ),
inference(forward_demodulation,[status(thm)],[f146,f403]) ).
fof(f422,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c10 = multiply(sk_c10,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f118,f415]) ).
fof(f423,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f422,f250]) ).
fof(f424,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sQ23_spl ),
inference(contradiction_clause,[status(thm)],[f423]) ).
fof(f425,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c9 = multiply(sk_c9,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f126,f416]) ).
fof(f426,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ11_spl
| sk_c9 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f154,f425]) ).
fof(f427,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ11_spl
| sQ39_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f426,f325]) ).
fof(f428,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ11_spl
| sQ39_spl ),
inference(contradiction_clause,[status(thm)],[f427]) ).
fof(f429,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sk_c7 = multiply(sk_c7,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f134,f417]) ).
fof(f430,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| sk_c7 = multiply(sk_c5,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f142,f418]) ).
fof(f447,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sk_c10 = multiply(inverse(sk_c7),sk_c7) ),
inference(paramodulation,[status(thm)],[f429,f303]) ).
fof(f449,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sk_c10 = identity ),
inference(forward_demodulation,[status(thm)],[f56,f447]) ).
fof(f450,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c6 = multiply(sk_c7,sk_c10) ),
inference(backward_demodulation,[status(thm)],[f449,f421]) ).
fof(f456,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ6_spl
| multiply(inverse(X0),X0) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f449,f56]) ).
fof(f457,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c10,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f449,f55]) ).
fof(f458,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c6 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f429,f450]) ).
fof(f460,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c6,sk_c9) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f458,f138]) ).
fof(f461,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ5_spl
| ~ sQ6_spl
| inverse(sk_c5) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f458,f146]) ).
fof(f462,plain,
( ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| inverse(sk_c4) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f458,f134]) ).
fof(f463,plain,
( ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| multiply(sk_c4,sk_c6) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f458,f130]) ).
fof(f486,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c6 = multiply(sk_c5,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f458,f430]) ).
fof(f491,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c9,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f499,f457]) ).
fof(f492,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(inverse(X0),X0) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f499,f456]) ).
fof(f493,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c9 = identity ),
inference(backward_demodulation,[status(thm)],[f499,f449]) ).
fof(f494,plain,
( sQ11_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c9,sk_c8) != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f499,f155]) ).
fof(f499,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c10 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f457,f422]) ).
fof(f500,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c6,sk_c9) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f499,f460]) ).
fof(f504,plain,
( ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c4,sk_c6) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f499,f463]) ).
fof(f505,plain,
( ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c6 = multiply(inverse(sk_c4),sk_c9) ),
inference(paramodulation,[status(thm)],[f504,f303]) ).
fof(f507,plain,
( ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c6 = multiply(sk_c6,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f462,f505]) ).
fof(f508,plain,
( ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| sk_c6 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f500,f507]) ).
fof(f511,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sk_c6 = identity ),
inference(backward_demodulation,[status(thm)],[f508,f493]) ).
fof(f512,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sk_c10 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f508,f499]) ).
fof(f517,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| multiply(sk_c6,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f508,f491]) ).
fof(f518,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| X0 = multiply(inverse(sk_c6),X0) ),
inference(paramodulation,[status(thm)],[f517,f303]) ).
fof(f520,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| X0 = multiply(sk_c5,X0) ),
inference(forward_demodulation,[status(thm)],[f142,f518]) ).
fof(f527,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| sk_c6 = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f520,f486]) ).
fof(f535,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| sk_c10 = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f527,f512]) ).
fof(f536,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| sk_c5 = identity ),
inference(backward_demodulation,[status(thm)],[f527,f511]) ).
fof(f537,plain,
( ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ10_spl
| sk_c5 = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f527,f508]) ).
fof(f539,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| inverse(sk_c5) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f527,f461]) ).
fof(f544,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| multiply(inverse(X0),X0) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f537,f492]) ).
fof(f548,plain,
( sQ11_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| multiply(sk_c5,sk_c8) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f537,f494]) ).
fof(f549,plain,
( sQ11_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| sk_c8 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f520,f548]) ).
fof(f550,plain,
( sQ11_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| sk_c8 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f537,f549]) ).
fof(f589,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ10_spl
| sk_c5 = multiply(sk_c9,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f537,f425]) ).
fof(f590,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ10_spl
| sk_c5 = multiply(sk_c5,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f537,f589]) ).
fof(f591,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ10_spl
| sk_c5 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f520,f590]) ).
fof(f592,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ10_spl
| sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f591,f550]) ).
fof(f593,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ10_spl
| sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f592]) ).
fof(f651,plain,
( sQ22_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f397,f323,f113,f117,f245]) ).
fof(f686,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| inverse(sk_c5) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f535,f112]) ).
fof(f687,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| sk_c5 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f539,f686]) ).
fof(f688,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f537,f687]) ).
fof(f689,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f688]) ).
fof(f690,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f689]) ).
fof(f716,plain,
( sQ12_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| multiply(sk_c5,sk_c8) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f535,f168]) ).
fof(f717,plain,
( sQ12_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| sk_c8 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f520,f716]) ).
fof(f718,plain,
( sQ12_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| sk_c8 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f537,f717]) ).
fof(f727,plain,
( sQ12_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f591,f718]) ).
fof(f728,plain,
( sQ12_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ3_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f727]) ).
fof(f729,plain,
( sQ12_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ3_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f728]) ).
fof(f739,plain,
( ~ sQ12_spl
| sk_c8 = multiply(inverse(sk_c10),sk_c9) ),
inference(paramodulation,[status(thm)],[f167,f303]) ).
fof(f741,plain,
( ~ sQ12_spl
| ~ sQ0_spl
| sk_c8 = multiply(sk_c9,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f111,f739]) ).
fof(f752,plain,
( ~ sQ14_spl
| sk_c9 = multiply(inverse(sk_c1),sk_c10) ),
inference(paramodulation,[status(thm)],[f193,f303]) ).
fof(f754,plain,
( ~ sQ14_spl
| ~ sQ13_spl
| sk_c9 = multiply(sk_c10,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f180,f752]) ).
fof(f762,plain,
( ~ sQ13_spl
| multiply(sk_c10,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f180,f56]) ).
fof(f774,plain,
( ~ sQ14_spl
| ~ sQ13_spl
| sk_c10 = multiply(inverse(sk_c10),sk_c9) ),
inference(paramodulation,[status(thm)],[f754,f303]) ).
fof(f776,plain,
( ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ0_spl
| sk_c10 = multiply(sk_c9,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f111,f774]) ).
fof(f777,plain,
( ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ12_spl
| sk_c10 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f741,f776]) ).
fof(f778,plain,
( ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ12_spl
| sQ38_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f777,f327]) ).
fof(f779,plain,
( ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ12_spl
| sQ38_spl ),
inference(contradiction_clause,[status(thm)],[f778]) ).
fof(f787,plain,
( sQ34_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ12_spl
| multiply(sk_c1,sk_c10) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f777,f295]) ).
fof(f789,plain,
( ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ12_spl
| multiply(sk_c9,sk_c8) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f777,f154]) ).
fof(f791,plain,
( sQ39_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ12_spl
| sk_c8 != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f777,f325]) ).
fof(f793,plain,
( ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| inverse(sk_c8) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f777,f111]) ).
fof(f796,plain,
( sQ34_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ12_spl
| multiply(sk_c1,sk_c8) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f777,f787]) ).
fof(f807,plain,
( ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| multiply(sk_c9,sk_c8) = identity ),
inference(paramodulation,[status(thm)],[f793,f56]) ).
fof(f809,plain,
( ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sk_c8 = identity ),
inference(forward_demodulation,[status(thm)],[f789,f807]) ).
fof(f811,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl
| X0 = multiply(inverse(sk_c8),X0) ),
inference(backward_demodulation,[status(thm)],[f809,f413]) ).
fof(f812,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl
| multiply(sk_c8,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f809,f55]) ).
fof(f813,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl
| X0 = multiply(sk_c9,X0) ),
inference(forward_demodulation,[status(thm)],[f793,f811]) ).
fof(f815,plain,
( ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ11_spl
| sk_c8 = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f813,f741]) ).
fof(f818,plain,
( ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ11_spl
| sQ39_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f815,f791]) ).
fof(f819,plain,
( ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ11_spl
| sQ39_spl ),
inference(contradiction_clause,[status(thm)],[f818]) ).
fof(f822,plain,
( ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl
| inverse(sk_c8) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f815,f793]) ).
fof(f835,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ12_spl
| multiply(sk_c8,sk_c1) = identity ),
inference(forward_demodulation,[status(thm)],[f777,f762]) ).
fof(f836,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sk_c1 = identity ),
inference(forward_demodulation,[status(thm)],[f812,f835]) ).
fof(f837,plain,
( ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl
| inverse(sk_c8) = sk_c1 ),
inference(backward_demodulation,[status(thm)],[f844,f822]) ).
fof(f838,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl
| multiply(sk_c1,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f844,f812]) ).
fof(f839,plain,
( ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ11_spl
| sk_c1 = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f844,f815]) ).
fof(f843,plain,
( ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sk_c10 = sk_c1 ),
inference(backward_demodulation,[status(thm)],[f844,f777]) ).
fof(f844,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sk_c1 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f809,f836]) ).
fof(f845,plain,
( ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl
| inverse(sk_c1) = sk_c1 ),
inference(forward_demodulation,[status(thm)],[f844,f837]) ).
fof(f892,plain,
( sQ34_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f838,f796]) ).
fof(f893,plain,
( sQ34_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sk_c1 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f844,f892]) ).
fof(f894,plain,
( sQ34_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sk_c1 != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f844,f893]) ).
fof(f895,plain,
( sQ34_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f894]) ).
fof(f896,plain,
( sQ34_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f895]) ).
fof(f919,plain,
! [X0] :
( ~ sQ35_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl
| multiply(X0,inverse(sk_c1)) != inverse(X0)
| inverse(inverse(X0)) != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f845,f290]) ).
fof(f920,plain,
! [X0] :
( ~ sQ35_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl
| multiply(X0,sk_c1) != inverse(X0)
| inverse(inverse(X0)) != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f845,f919]) ).
fof(f921,plain,
( ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ35_spl
| multiply(sk_c1,sk_c1) != inverse(sk_c1)
| inverse(sk_c1) != sk_c1 ),
inference(paramodulation,[status(thm)],[f845,f920]) ).
fof(f922,definition,
( sQ46_spl
<=> inverse(sk_c1) = sk_c1 ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f924,plain,
( sQ46_spl
| inverse(sk_c1) != sk_c1 ),
inference(component_clause,[status(thm)],[f922]) ).
fof(f925,definition,
( sQ47_spl
<=> multiply(sk_c1,sk_c1) = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f927,plain,
( sQ47_spl
| multiply(sk_c1,sk_c1) != inverse(sk_c1) ),
inference(component_clause,[status(thm)],[f925]) ).
fof(f928,plain,
( ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ35_spl
| ~ sQ47_spl
| ~ sQ46_spl ),
inference(split_clause,[status(thm)],[f921,f922,f925,f289,f153,f166,f179,f192,f110]) ).
fof(f929,plain,
( sQ47_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sk_c1 != inverse(sk_c1) ),
inference(forward_demodulation,[status(thm)],[f838,f927]) ).
fof(f930,plain,
( sQ47_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sk_c1 != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f845,f929]) ).
fof(f931,plain,
( sQ47_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f930]) ).
fof(f932,plain,
( sQ47_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f931]) ).
fof(f933,plain,
( sQ46_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sk_c1 != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f845,f924]) ).
fof(f934,plain,
( sQ46_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f933]) ).
fof(f935,plain,
( sQ46_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f934]) ).
fof(f960,plain,
( ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sk_c10 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f838,f330]) ).
fof(f961,plain,
( ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sk_c1 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f843,f960]) ).
fof(f962,plain,
( ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sk_c1 != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f839,f961]) ).
fof(f963,plain,
( ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f962]) ).
fof(f964,plain,
( ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f963]) ).
fof(f1004,plain,
( sQ23_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| multiply(sk_c1,sk_c9) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f843,f250]) ).
fof(f1005,plain,
( sQ23_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sk_c9 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f838,f1004]) ).
fof(f1006,plain,
( sQ23_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sk_c1 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f839,f1005]) ).
fof(f1007,plain,
( sQ23_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sk_c1 != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f843,f1006]) ).
fof(f1008,plain,
( sQ23_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1007]) ).
fof(f1009,plain,
( sQ23_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f1008]) ).
fof(f1010,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ23_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f347,f323,f248,f205,f110]) ).
fof(f1027,plain,
! [X0,X1] :
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| multiply(sk_c5,X0) = multiply(inverse(X1),multiply(X1,X0)) ),
inference(paramodulation,[status(thm)],[f544,f57]) ).
fof(f1028,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| multiply(sk_c5,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f303,f1027]) ).
fof(f1071,plain,
( ~ sQ13_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| inverse(sk_c1) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f535,f180]) ).
fof(f1072,plain,
( ~ sQ13_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| multiply(sk_c5,sk_c1) = sk_c5 ),
inference(paramodulation,[status(thm)],[f1071,f544]) ).
fof(f1074,plain,
( ~ sQ13_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| sk_c1 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f520,f1072]) ).
fof(f1092,plain,
( ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ13_spl
| sk_c1 = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f1074,f537]) ).
fof(f1094,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ13_spl
| sk_c10 = sk_c1 ),
inference(backward_demodulation,[status(thm)],[f1074,f535]) ).
fof(f1101,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ13_spl
| multiply(sk_c1,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f1074,f1028]) ).
fof(f1224,plain,
( sQ14_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ13_spl
| sk_c9 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1101,f194]) ).
fof(f1225,plain,
( sQ14_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ13_spl
| sk_c1 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1092,f1224]) ).
fof(f1226,plain,
( sQ14_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ13_spl
| sk_c1 != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f1094,f1225]) ).
fof(f1227,plain,
( sQ14_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ13_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1226]) ).
fof(f1228,plain,
( sQ14_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f1227]) ).
fof(f1233,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ10_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c5) != sk_c10
| multiply(X0,inverse(X0)) != sk_c10 ),
inference(backward_demodulation,[status(thm)],[f537,f218]) ).
fof(f1270,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| multiply(inverse(X0),X0) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f535,f456]) ).
fof(f1369,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| X0 = multiply(inverse(inverse(X0)),sk_c5) ),
inference(forward_demodulation,[status(thm)],[f536,f412]) ).
fof(f1385,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ10_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c5) != sk_c10
| multiply(X0,inverse(X0)) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f535,f1233]) ).
fof(f1386,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ10_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c5) != sk_c5
| multiply(X0,inverse(X0)) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f535,f1385]) ).
fof(f1587,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| X0 = multiply(X0,sk_c5) ),
inference(backward_demodulation,[status(thm)],[f411,f1369]) ).
fof(f1589,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| multiply(X0,inverse(X0)) = sk_c5 ),
inference(paramodulation,[status(thm)],[f1270,f411]) ).
fof(f1602,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ10_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| inverse(X0) != sk_c5
| multiply(X0,inverse(X0)) != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f1587,f1386]) ).
fof(f1604,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| inverse(inverse(X0)) = multiply(X0,sk_c5) ),
inference(paramodulation,[status(thm)],[f411,f1587]) ).
fof(f1613,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| inverse(inverse(X0)) = X0 ),
inference(forward_demodulation,[status(thm)],[f1587,f1604]) ).
fof(f1625,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ10_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| X1 != inverse(X0)
| inverse(X0) != sk_c5
| multiply(X0,inverse(X0)) != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f1613,f1602]) ).
fof(f1631,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ10_spl
| multiply(inverse(X0),inverse(X0)) != inverse(inverse(X0))
| inverse(X0) != sk_c5
| multiply(X0,inverse(X0)) != sk_c5 ),
inference(destructive_equality_resolution,[status(thm)],[f1625]) ).
fof(f1670,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ10_spl
| multiply(inverse(X0),inverse(X0)) != inverse(inverse(X0))
| inverse(X0) != sk_c5
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f1589,f1631]) ).
fof(f1671,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ10_spl
| multiply(inverse(X0),inverse(X0)) != X0
| inverse(X0) != sk_c5
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f1613,f1670]) ).
fof(f1672,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ10_spl
| multiply(inverse(X0),inverse(X0)) != X0
| inverse(X0) != sk_c5 ),
inference(trivial_equality_resolution,[status(thm)],[f1671]) ).
fof(f1673,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ18_spl
| multiply(inverse(inverse(sk_c5)),inverse(inverse(sk_c5))) != inverse(sk_c5) ),
inference(resolution,[status(thm)],[f1672,f1613]) ).
fof(f1677,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ18_spl
| multiply(sk_c5,inverse(inverse(sk_c5))) != inverse(sk_c5) ),
inference(forward_demodulation,[status(thm)],[f1613,f1673]) ).
fof(f1678,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ18_spl
| inverse(inverse(sk_c5)) != inverse(sk_c5) ),
inference(forward_demodulation,[status(thm)],[f1028,f1677]) ).
fof(f1679,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ18_spl
| sk_c5 != inverse(sk_c5) ),
inference(forward_demodulation,[status(thm)],[f1613,f1678]) ).
fof(f1680,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ18_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f539,f1679]) ).
fof(f1681,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ18_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1680]) ).
fof(f1682,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f1681]) ).
fof(f1683,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,f254,f292,f319,f326,f329,f345,f351,f368,f377,f424,f428,f593,f651,f690,f729,f779,f819,f896,f928,f932,f935,f964,f1009,f1010,f1228,f1682]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP386-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/15.55 % Computer : n010.cluster.edu
% 0.11/15.55 % Model : x86_64 x86_64
% 0.11/15.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/15.55 % Memory : 8046.5625MB
% 0.11/15.55 % OS : Linux 6.8.0-71-generic
% 0.11/15.55 % CPULimit : 300
% 0.11/15.55 % WCLimit : 300
% 0.11/15.55 % DateTime : Sun Sep 20 20:11:25 UTC 2026
% 0.11/15.56 % CPUTime :
% 0.11/15.57 % Drodi V4.1.1
% 0.16/15.64 % Refutation found
% 0.16/15.64 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.16/15.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/15.68 % Elapsed time: 0.111027 seconds
% 0.16/15.68 % CPU time: 0.478183 seconds
% 0.16/15.68 % Total memory used: 107.102 MB
% 0.16/15.68 % Net memory used: 106.846 MB
%------------------------------------------------------------------------------