%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP243-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:33:11 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 100
% Syntax : Number of formulae : 516 ( 16 unt; 42 def)
% Number of atoms : 2192 ( 599 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 3208 (1532 ~;1634 |; 0 &)
% ( 42 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 44 ( 42 usr; 43 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 13 con; 0-2 aty)
% Number of variables : 102 ( 102 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
( inverse(sk_c6) = sk_c12
| multiply(sk_c1,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( multiply(sk_c6,sk_c11) = sk_c12
| multiply(sk_c1,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( inverse(sk_c7) = sk_c11
| multiply(sk_c1,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c11
| multiply(sk_c1,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c11
| multiply(sk_c1,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c8) = sk_c9
| multiply(sk_c1,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| multiply(sk_c1,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c6) = sk_c12
| inverse(sk_c1) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( multiply(sk_c6,sk_c11) = sk_c12
| inverse(sk_c1) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( inverse(sk_c7) = sk_c11
| inverse(sk_c1) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c11
| inverse(sk_c1) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c11
| inverse(sk_c1) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( inverse(sk_c8) = sk_c9
| inverse(sk_c1) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| inverse(sk_c1) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( inverse(sk_c6) = sk_c12
| multiply(sk_c2,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c6,sk_c11) = sk_c12
| multiply(sk_c2,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( inverse(sk_c7) = sk_c11
| multiply(sk_c2,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c11
| multiply(sk_c2,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( inverse(sk_c8) = sk_c9
| multiply(sk_c2,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| multiply(sk_c2,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c6) = sk_c12
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c6,sk_c11) = sk_c12
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c7) = sk_c11
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c11
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( inverse(sk_c8) = sk_c9
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( inverse(sk_c6) = sk_c12
| inverse(sk_c3) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( multiply(sk_c6,sk_c11) = sk_c12
| inverse(sk_c3) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( inverse(sk_c7) = sk_c11
| inverse(sk_c3) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( inverse(sk_c8) = sk_c9
| inverse(sk_c3) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| inverse(sk_c3) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
( inverse(sk_c6) = sk_c12
| multiply(sk_c3,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
( multiply(sk_c6,sk_c11) = sk_c12
| multiply(sk_c3,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,negated_conjecture,
( inverse(sk_c7) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
( inverse(sk_c8) = sk_c9
| multiply(sk_c3,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,negated_conjecture,
( inverse(sk_c6) = sk_c12
| multiply(sk_c4,sk_c5) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,negated_conjecture,
( multiply(sk_c6,sk_c11) = sk_c12
| multiply(sk_c4,sk_c5) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,negated_conjecture,
( inverse(sk_c7) = sk_c11
| multiply(sk_c4,sk_c5) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c11
| multiply(sk_c4,sk_c5) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f51,negated_conjecture,
( inverse(sk_c8) = sk_c9
| multiply(sk_c4,sk_c5) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f52,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| multiply(sk_c4,sk_c5) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f53,negated_conjecture,
( inverse(sk_c6) = sk_c12
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
( multiply(sk_c6,sk_c11) = sk_c12
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f55,negated_conjecture,
( inverse(sk_c7) = sk_c11
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f56,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c11
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f58,negated_conjecture,
( inverse(sk_c8) = sk_c9
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f59,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| inverse(sk_c4) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f60,negated_conjecture,
( inverse(sk_c6) = sk_c12
| multiply(sk_c5,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f61,negated_conjecture,
( multiply(sk_c6,sk_c11) = sk_c12
| multiply(sk_c5,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f62,negated_conjecture,
( inverse(sk_c7) = sk_c11
| multiply(sk_c5,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f63,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c11
| multiply(sk_c5,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f65,negated_conjecture,
( inverse(sk_c8) = sk_c9
| multiply(sk_c5,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f66,negated_conjecture,
( multiply(sk_c9,sk_c10) = sk_c11
| multiply(sk_c5,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f67,negated_conjecture,
! [X5,X6,X7,X8,X9,X1,X2,X4,X3] :
( multiply(X3,sk_c10) != sk_c11
| inverse(X4) != X3
| multiply(X4,X3) != sk_c11
| multiply(X2,sk_c10) != sk_c11
| inverse(X2) != sk_c11
| multiply(X1,sk_c11) != sk_c12
| inverse(X1) != sk_c12
| multiply(X9,sk_c10) != sk_c11
| inverse(X8) != X9
| multiply(X8,X9) != sk_c11
| multiply(X7,sk_c11) != sk_c12
| inverse(X7) != sk_c12
| inverse(X6) != sk_c11
| multiply(X6,sk_c11) != sk_c10
| inverse(X5) != sk_c12
| multiply(X5,sk_c12) != sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f68,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f69,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f70,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f71,plain,
( inverse(sk_c6) = sk_c12
| multiply(sk_c1,sk_c12) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f72,plain,
( multiply(sk_c6,sk_c11) = sk_c12
| multiply(sk_c1,sk_c12) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f73,plain,
( inverse(sk_c7) = sk_c11
| multiply(sk_c1,sk_c12) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f74,plain,
( multiply(sk_c7,sk_c10) = sk_c11
| multiply(sk_c1,sk_c12) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f75,plain,
( multiply(sk_c8,sk_c9) = sk_c11
| multiply(sk_c1,sk_c12) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f76,plain,
( inverse(sk_c8) = sk_c9
| multiply(sk_c1,sk_c12) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f77,plain,
( multiply(sk_c9,sk_c10) = sk_c11
| multiply(sk_c1,sk_c12) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f78,plain,
( inverse(sk_c6) = sk_c12
| inverse(sk_c1) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f79,plain,
( multiply(sk_c6,sk_c11) = sk_c12
| inverse(sk_c1) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f80,plain,
( inverse(sk_c7) = sk_c11
| inverse(sk_c1) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f81,plain,
( multiply(sk_c7,sk_c10) = sk_c11
| inverse(sk_c1) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f82,plain,
( multiply(sk_c8,sk_c9) = sk_c11
| inverse(sk_c1) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f83,plain,
( inverse(sk_c8) = sk_c9
| inverse(sk_c1) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f84,plain,
( multiply(sk_c9,sk_c10) = sk_c11
| inverse(sk_c1) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f85,plain,
( inverse(sk_c6) = sk_c12
| multiply(sk_c2,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f86,plain,
( multiply(sk_c6,sk_c11) = sk_c12
| multiply(sk_c2,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f87,plain,
( inverse(sk_c7) = sk_c11
| multiply(sk_c2,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f88,plain,
( multiply(sk_c7,sk_c10) = sk_c11
| multiply(sk_c2,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f90,plain,
( inverse(sk_c8) = sk_c9
| multiply(sk_c2,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f91,plain,
( multiply(sk_c9,sk_c10) = sk_c11
| multiply(sk_c2,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f92,plain,
( inverse(sk_c6) = sk_c12
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f93,plain,
( multiply(sk_c6,sk_c11) = sk_c12
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f94,plain,
( inverse(sk_c7) = sk_c11
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f95,plain,
( multiply(sk_c7,sk_c10) = sk_c11
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f97,plain,
( inverse(sk_c8) = sk_c9
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f98,plain,
( multiply(sk_c9,sk_c10) = sk_c11
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f99,plain,
( inverse(sk_c6) = sk_c12
| inverse(sk_c3) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f100,plain,
( multiply(sk_c6,sk_c11) = sk_c12
| inverse(sk_c3) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f101,plain,
( inverse(sk_c7) = sk_c11
| inverse(sk_c3) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f104,plain,
( inverse(sk_c8) = sk_c9
| inverse(sk_c3) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f105,plain,
( multiply(sk_c9,sk_c10) = sk_c11
| inverse(sk_c3) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f106,plain,
( inverse(sk_c6) = sk_c12
| multiply(sk_c3,sk_c11) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f107,plain,
( multiply(sk_c6,sk_c11) = sk_c12
| multiply(sk_c3,sk_c11) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f108,plain,
( inverse(sk_c7) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f111,plain,
( inverse(sk_c8) = sk_c9
| multiply(sk_c3,sk_c11) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f112,plain,
( multiply(sk_c9,sk_c10) = sk_c11
| multiply(sk_c3,sk_c11) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f113,plain,
( inverse(sk_c6) = sk_c12
| multiply(sk_c4,sk_c5) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f114,plain,
( multiply(sk_c6,sk_c11) = sk_c12
| multiply(sk_c4,sk_c5) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f115,plain,
( inverse(sk_c7) = sk_c11
| multiply(sk_c4,sk_c5) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f116,plain,
( multiply(sk_c7,sk_c10) = sk_c11
| multiply(sk_c4,sk_c5) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f118,plain,
( inverse(sk_c8) = sk_c9
| multiply(sk_c4,sk_c5) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f119,plain,
( multiply(sk_c9,sk_c10) = sk_c11
| multiply(sk_c4,sk_c5) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f120,plain,
( inverse(sk_c6) = sk_c12
| inverse(sk_c4) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f121,plain,
( multiply(sk_c6,sk_c11) = sk_c12
| inverse(sk_c4) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f122,plain,
( inverse(sk_c7) = sk_c11
| inverse(sk_c4) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f123,plain,
( multiply(sk_c7,sk_c10) = sk_c11
| inverse(sk_c4) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f125,plain,
( inverse(sk_c8) = sk_c9
| inverse(sk_c4) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f126,plain,
( multiply(sk_c9,sk_c10) = sk_c11
| inverse(sk_c4) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f127,plain,
( inverse(sk_c6) = sk_c12
| multiply(sk_c5,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f128,plain,
( multiply(sk_c6,sk_c11) = sk_c12
| multiply(sk_c5,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f129,plain,
( inverse(sk_c7) = sk_c11
| multiply(sk_c5,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f130,plain,
( multiply(sk_c7,sk_c10) = sk_c11
| multiply(sk_c5,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f132,plain,
( inverse(sk_c8) = sk_c9
| multiply(sk_c5,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f133,plain,
( multiply(sk_c9,sk_c10) = sk_c11
| multiply(sk_c5,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f134,plain,
! [X3] :
( multiply(X3,sk_c10) != sk_c11
| ! [X4] :
( inverse(X4) != X3
| multiply(X4,X3) != sk_c11
| ! [X2] :
( multiply(X2,sk_c10) != sk_c11
| inverse(X2) != sk_c11
| ! [X1] :
( multiply(X1,sk_c11) != sk_c12
| inverse(X1) != sk_c12
| ! [X9] :
( multiply(X9,sk_c10) != sk_c11
| ! [X8] :
( inverse(X8) != X9
| multiply(X8,X9) != sk_c11
| ! [X7] :
( multiply(X7,sk_c11) != sk_c12
| inverse(X7) != sk_c12
| ! [X6] :
( inverse(X6) != sk_c11
| multiply(X6,sk_c11) != sk_c10
| ! [X5] :
( inverse(X5) != sk_c12
| multiply(X5,sk_c12) != sk_c11 ) ) ) ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f67]) ).
fof(f135,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( multiply(X8,sk_c10) != sk_c11
| inverse(X7) != X8
| multiply(X7,X8) != sk_c11
| multiply(X6,sk_c10) != sk_c11
| inverse(X6) != sk_c11
| multiply(X5,sk_c11) != sk_c12
| inverse(X5) != sk_c12
| multiply(X4,sk_c10) != sk_c11
| inverse(X3) != X4
| multiply(X3,X4) != sk_c11
| multiply(X2,sk_c11) != sk_c12
| inverse(X2) != sk_c12
| inverse(X1) != sk_c11
| multiply(X1,sk_c11) != sk_c10
| inverse(X0) != sk_c12
| multiply(X0,sk_c12) != sk_c11 ),
inference(cnf_transformation,[status(thm)],[f134]) ).
fof(f136,definition,
( sQ0_spl
<=> multiply(sk_c1,sk_c12) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f137,plain,
( ~ sQ0_spl
| multiply(sk_c1,sk_c12) = sk_c11 ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f139,definition,
( sQ1_spl
<=> inverse(sk_c6) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f140,plain,
( ~ sQ1_spl
| inverse(sk_c6) = sk_c12 ),
inference(component_clause,[status(thm)],[f139]) ).
fof(f142,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f71,f136,f139]) ).
fof(f143,definition,
( sQ2_spl
<=> multiply(sk_c6,sk_c11) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f144,plain,
( ~ sQ2_spl
| multiply(sk_c6,sk_c11) = sk_c12 ),
inference(component_clause,[status(thm)],[f143]) ).
fof(f146,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f72,f136,f143]) ).
fof(f147,definition,
( sQ3_spl
<=> inverse(sk_c7) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f148,plain,
( ~ sQ3_spl
| inverse(sk_c7) = sk_c11 ),
inference(component_clause,[status(thm)],[f147]) ).
fof(f149,plain,
( sQ3_spl
| inverse(sk_c7) != sk_c11 ),
inference(component_clause,[status(thm)],[f147]) ).
fof(f150,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f73,f136,f147]) ).
fof(f151,definition,
( sQ4_spl
<=> multiply(sk_c7,sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f152,plain,
( ~ sQ4_spl
| multiply(sk_c7,sk_c10) = sk_c11 ),
inference(component_clause,[status(thm)],[f151]) ).
fof(f153,plain,
( sQ4_spl
| multiply(sk_c7,sk_c10) != sk_c11 ),
inference(component_clause,[status(thm)],[f151]) ).
fof(f154,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f74,f136,f151]) ).
fof(f155,definition,
( sQ5_spl
<=> multiply(sk_c8,sk_c9) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f156,plain,
( ~ sQ5_spl
| multiply(sk_c8,sk_c9) = sk_c11 ),
inference(component_clause,[status(thm)],[f155]) ).
fof(f158,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f75,f136,f155]) ).
fof(f159,definition,
( sQ6_spl
<=> inverse(sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f160,plain,
( ~ sQ6_spl
| inverse(sk_c8) = sk_c9 ),
inference(component_clause,[status(thm)],[f159]) ).
fof(f162,plain,
( sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f76,f136,f159]) ).
fof(f163,definition,
( sQ7_spl
<=> multiply(sk_c9,sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f164,plain,
( ~ sQ7_spl
| multiply(sk_c9,sk_c10) = sk_c11 ),
inference(component_clause,[status(thm)],[f163]) ).
fof(f166,plain,
( sQ7_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f77,f136,f163]) ).
fof(f167,definition,
( sQ8_spl
<=> inverse(sk_c1) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f168,plain,
( ~ sQ8_spl
| inverse(sk_c1) = sk_c12 ),
inference(component_clause,[status(thm)],[f167]) ).
fof(f170,plain,
( sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f78,f167,f139]) ).
fof(f171,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f79,f167,f143]) ).
fof(f172,plain,
( sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f80,f167,f147]) ).
fof(f173,plain,
( sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f81,f167,f151]) ).
fof(f174,plain,
( sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f82,f167,f155]) ).
fof(f175,plain,
( sQ6_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f83,f167,f159]) ).
fof(f176,plain,
( sQ7_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f84,f167,f163]) ).
fof(f177,definition,
( sQ9_spl
<=> multiply(sk_c2,sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f178,plain,
( ~ sQ9_spl
| multiply(sk_c2,sk_c11) = sk_c10 ),
inference(component_clause,[status(thm)],[f177]) ).
fof(f180,plain,
( sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f85,f177,f139]) ).
fof(f181,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f86,f177,f143]) ).
fof(f182,plain,
( sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f87,f177,f147]) ).
fof(f183,plain,
( sQ4_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f88,f177,f151]) ).
fof(f185,plain,
( sQ6_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f90,f177,f159]) ).
fof(f186,plain,
( sQ7_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f91,f177,f163]) ).
fof(f187,definition,
( sQ10_spl
<=> inverse(sk_c2) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f188,plain,
( ~ sQ10_spl
| inverse(sk_c2) = sk_c11 ),
inference(component_clause,[status(thm)],[f187]) ).
fof(f189,plain,
( sQ10_spl
| inverse(sk_c2) != sk_c11 ),
inference(component_clause,[status(thm)],[f187]) ).
fof(f190,plain,
( sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f92,f187,f139]) ).
fof(f191,plain,
( sQ2_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f93,f187,f143]) ).
fof(f192,plain,
( sQ3_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f94,f187,f147]) ).
fof(f193,plain,
( sQ4_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f95,f187,f151]) ).
fof(f195,plain,
( sQ6_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f97,f187,f159]) ).
fof(f196,plain,
( sQ7_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f98,f187,f163]) ).
fof(f197,definition,
( sQ11_spl
<=> inverse(sk_c3) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f198,plain,
( ~ sQ11_spl
| inverse(sk_c3) = sk_c12 ),
inference(component_clause,[status(thm)],[f197]) ).
fof(f200,plain,
( sQ1_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f99,f197,f139]) ).
fof(f201,plain,
( sQ2_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f100,f197,f143]) ).
fof(f202,plain,
( sQ3_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f101,f197,f147]) ).
fof(f205,plain,
( sQ6_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f104,f197,f159]) ).
fof(f206,plain,
( sQ7_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f105,f197,f163]) ).
fof(f207,definition,
( sQ12_spl
<=> multiply(sk_c3,sk_c11) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f208,plain,
( ~ sQ12_spl
| multiply(sk_c3,sk_c11) = sk_c12 ),
inference(component_clause,[status(thm)],[f207]) ).
fof(f210,plain,
( sQ1_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f106,f207,f139]) ).
fof(f211,plain,
( sQ2_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f107,f207,f143]) ).
fof(f212,plain,
( sQ3_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f108,f207,f147]) ).
fof(f215,plain,
( sQ6_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f111,f207,f159]) ).
fof(f216,plain,
( sQ7_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f112,f207,f163]) ).
fof(f217,definition,
( sQ13_spl
<=> multiply(sk_c4,sk_c5) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f218,plain,
( ~ sQ13_spl
| multiply(sk_c4,sk_c5) = sk_c11 ),
inference(component_clause,[status(thm)],[f217]) ).
fof(f220,plain,
( sQ1_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f113,f217,f139]) ).
fof(f221,plain,
( sQ2_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f114,f217,f143]) ).
fof(f222,plain,
( sQ3_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f115,f217,f147]) ).
fof(f223,plain,
( sQ4_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f116,f217,f151]) ).
fof(f225,plain,
( sQ6_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f118,f217,f159]) ).
fof(f226,plain,
( sQ7_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f119,f217,f163]) ).
fof(f227,definition,
( sQ14_spl
<=> inverse(sk_c4) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f228,plain,
( ~ sQ14_spl
| inverse(sk_c4) = sk_c5 ),
inference(component_clause,[status(thm)],[f227]) ).
fof(f230,plain,
( sQ1_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f120,f227,f139]) ).
fof(f231,plain,
( sQ2_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f121,f227,f143]) ).
fof(f232,plain,
( sQ3_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f122,f227,f147]) ).
fof(f233,plain,
( sQ4_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f123,f227,f151]) ).
fof(f235,plain,
( sQ6_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f125,f227,f159]) ).
fof(f236,plain,
( sQ7_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f126,f227,f163]) ).
fof(f237,definition,
( sQ15_spl
<=> multiply(sk_c5,sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f238,plain,
( ~ sQ15_spl
| multiply(sk_c5,sk_c10) = sk_c11 ),
inference(component_clause,[status(thm)],[f237]) ).
fof(f240,plain,
( sQ1_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f127,f237,f139]) ).
fof(f241,plain,
( sQ2_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f128,f237,f143]) ).
fof(f242,plain,
( sQ3_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f129,f237,f147]) ).
fof(f243,plain,
( sQ4_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f130,f237,f151]) ).
fof(f245,plain,
( sQ6_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f132,f237,f159]) ).
fof(f246,plain,
( sQ7_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f133,f237,f163]) ).
fof(f247,definition,
! [X0] :
( sQ16_spl
<=> ( inverse(X0) != sk_c12
| multiply(X0,sk_c12) != sk_c11 ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f248,plain,
! [X0] :
( ~ sQ16_spl
| inverse(X0) != sk_c12
| multiply(X0,sk_c12) != sk_c11 ),
inference(component_clause,[status(thm)],[f247]) ).
fof(f250,definition,
! [X1] :
( sQ17_spl
<=> ( inverse(X1) != sk_c11
| multiply(X1,sk_c11) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f251,plain,
! [X0] :
( ~ sQ17_spl
| inverse(X0) != sk_c11
| multiply(X0,sk_c11) != sk_c10 ),
inference(component_clause,[status(thm)],[f250]) ).
fof(f253,definition,
! [X2] :
( sQ18_spl
<=> ( multiply(X2,sk_c11) != sk_c12
| inverse(X2) != sk_c12 ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f254,plain,
! [X0] :
( ~ sQ18_spl
| multiply(X0,sk_c11) != sk_c12
| inverse(X0) != sk_c12 ),
inference(component_clause,[status(thm)],[f253]) ).
fof(f256,definition,
! [X3,X4] :
( sQ19_spl
<=> ( multiply(X4,sk_c10) != sk_c11
| inverse(X3) != X4
| multiply(X3,X4) != sk_c11 ) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f257,plain,
! [X0,X1] :
( ~ sQ19_spl
| multiply(X1,sk_c10) != sk_c11
| inverse(X0) != X1
| multiply(X0,X1) != sk_c11 ),
inference(component_clause,[status(thm)],[f256]) ).
fof(f259,definition,
! [X6] :
( sQ20_spl
<=> ( multiply(X6,sk_c10) != sk_c11
| inverse(X6) != sk_c11 ) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f260,plain,
! [X0] :
( ~ sQ20_spl
| multiply(X0,sk_c10) != sk_c11
| inverse(X0) != sk_c11 ),
inference(component_clause,[status(thm)],[f259]) ).
fof(f262,plain,
( sQ20_spl
| sQ19_spl
| sQ18_spl
| sQ17_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f135,f247,f250,f253,f256,f259]) ).
fof(f271,plain,
! [X0] :
( ~ sQ5_spl
| multiply(sk_c11,X0) = multiply(sk_c8,multiply(sk_c9,X0)) ),
inference(paramodulation,[status(thm)],[f156,f70]) ).
fof(f275,plain,
( ~ sQ15_spl
| ~ sQ20_spl
| inverse(sk_c5) != sk_c11 ),
inference(resolution,[status(thm)],[f260,f238]) ).
fof(f276,plain,
( ~ sQ4_spl
| ~ sQ20_spl
| inverse(sk_c7) != sk_c11 ),
inference(resolution,[status(thm)],[f260,f152]) ).
fof(f282,plain,
( ~ sQ4_spl
| ~ sQ20_spl
| ~ sQ3_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f148,f276]) ).
fof(f283,plain,
( ~ sQ4_spl
| ~ sQ20_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f282]) ).
fof(f284,plain,
( ~ sQ4_spl
| ~ sQ20_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f283]) ).
fof(f285,plain,
! [X0] :
( ~ sQ19_spl
| multiply(inverse(X0),sk_c10) != sk_c11
| multiply(X0,inverse(X0)) != sk_c11 ),
inference(destructive_equality_resolution,[status(thm)],[f257]) ).
fof(f291,plain,
( ~ sQ1_spl
| multiply(sk_c12,sk_c6) = identity ),
inference(paramodulation,[status(thm)],[f140,f69]) ).
fof(f293,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f69,f70]) ).
fof(f294,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f68,f293]) ).
fof(f319,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f68,f294]) ).
fof(f321,plain,
( ~ sQ0_spl
| sk_c12 = multiply(inverse(sk_c1),sk_c11) ),
inference(paramodulation,[status(thm)],[f137,f294]) ).
fof(f322,plain,
( ~ sQ9_spl
| sk_c11 = multiply(inverse(sk_c2),sk_c10) ),
inference(paramodulation,[status(thm)],[f178,f294]) ).
fof(f324,plain,
( ~ sQ13_spl
| sk_c5 = multiply(inverse(sk_c4),sk_c11) ),
inference(paramodulation,[status(thm)],[f218,f294]) ).
fof(f327,plain,
( ~ sQ2_spl
| sk_c11 = multiply(inverse(sk_c6),sk_c12) ),
inference(paramodulation,[status(thm)],[f144,f294]) ).
fof(f329,plain,
( ~ sQ5_spl
| sk_c9 = multiply(inverse(sk_c8),sk_c11) ),
inference(paramodulation,[status(thm)],[f156,f294]) ).
fof(f333,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| sk_c12 = multiply(sk_c12,sk_c11) ),
inference(forward_demodulation,[status(thm)],[f168,f321]) ).
fof(f334,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| sk_c11 = multiply(sk_c11,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f188,f322]) ).
fof(f336,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| sk_c5 = multiply(sk_c5,sk_c11) ),
inference(forward_demodulation,[status(thm)],[f228,f324]) ).
fof(f338,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sk_c9 = multiply(sk_c9,sk_c11) ),
inference(forward_demodulation,[status(thm)],[f160,f329]) ).
fof(f344,plain,
! [X0] : X0 = multiply(inverse(inverse(identity)),X0),
inference(paramodulation,[status(thm)],[f319,f294]) ).
fof(f346,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| sk_c11 = multiply(inverse(sk_c12),sk_c12) ),
inference(paramodulation,[status(thm)],[f333,f294]) ).
fof(f348,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| sk_c11 = identity ),
inference(forward_demodulation,[status(thm)],[f69,f346]) ).
fof(f356,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| multiply(inverse(X0),X0) = sk_c11 ),
inference(backward_demodulation,[status(thm)],[f348,f69]) ).
fof(f357,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| multiply(sk_c11,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f348,f68]) ).
fof(f360,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c10,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f374,f357]) ).
fof(f363,plain,
( sQ3_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| inverse(sk_c7) != sk_c10 ),
inference(backward_demodulation,[status(thm)],[f374,f149]) ).
fof(f364,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| multiply(sk_c1,sk_c12) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f374,f137]) ).
fof(f366,plain,
( ~ sQ12_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| multiply(sk_c3,sk_c10) = sk_c12 ),
inference(backward_demodulation,[status(thm)],[f374,f208]) ).
fof(f367,plain,
( ~ sQ13_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| multiply(sk_c4,sk_c5) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f374,f218]) ).
fof(f368,plain,
( ~ sQ15_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| multiply(sk_c5,sk_c10) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f374,f238]) ).
fof(f370,plain,
( ~ sQ4_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| multiply(sk_c7,sk_c10) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f374,f152]) ).
fof(f372,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ8_spl
| inverse(sk_c2) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f374,f188]) ).
fof(f374,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sk_c11 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f357,f334]) ).
fof(f375,plain,
! [X0] :
( ~ sQ19_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| multiply(inverse(X0),sk_c10) != sk_c11
| multiply(X0,inverse(X0)) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f374,f285]) ).
fof(f376,plain,
! [X0] :
( ~ sQ19_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| multiply(inverse(X0),sk_c10) != sk_c10
| multiply(X0,inverse(X0)) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f374,f375]) ).
fof(f377,plain,
( ~ sQ8_spl
| ~ sQ19_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| multiply(sk_c12,sk_c10) != sk_c10
| multiply(sk_c1,inverse(sk_c1)) != sk_c10 ),
inference(paramodulation,[status(thm)],[f168,f376]) ).
fof(f378,plain,
( ~ sQ11_spl
| ~ sQ19_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| multiply(sk_c12,sk_c10) != sk_c10
| multiply(sk_c3,inverse(sk_c3)) != sk_c10 ),
inference(paramodulation,[status(thm)],[f198,f376]) ).
fof(f379,plain,
( ~ sQ14_spl
| ~ sQ19_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| multiply(sk_c5,sk_c10) != sk_c10
| multiply(sk_c4,inverse(sk_c4)) != sk_c10 ),
inference(paramodulation,[status(thm)],[f228,f376]) ).
fof(f380,plain,
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| multiply(sk_c12,sk_c10) != sk_c10
| multiply(sk_c6,inverse(sk_c6)) != sk_c10 ),
inference(paramodulation,[status(thm)],[f140,f376]) ).
fof(f382,definition,
( sQ21_spl
<=> multiply(sk_c1,inverse(sk_c1)) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f384,plain,
( sQ21_spl
| multiply(sk_c1,inverse(sk_c1)) != sk_c10 ),
inference(component_clause,[status(thm)],[f382]) ).
fof(f385,definition,
( sQ22_spl
<=> multiply(sk_c12,sk_c10) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f388,plain,
( ~ sQ8_spl
| ~ sQ19_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ22_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f377,f382,f385,f136,f187,f177,f256,f167]) ).
fof(f389,definition,
( sQ23_spl
<=> multiply(sk_c3,inverse(sk_c3)) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f392,plain,
( ~ sQ11_spl
| ~ sQ19_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ22_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f378,f389,f385,f167,f136,f187,f177,f256,f197]) ).
fof(f393,definition,
( sQ24_spl
<=> multiply(sk_c4,inverse(sk_c4)) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f395,plain,
( sQ24_spl
| multiply(sk_c4,inverse(sk_c4)) != sk_c10 ),
inference(component_clause,[status(thm)],[f393]) ).
fof(f396,definition,
( sQ25_spl
<=> multiply(sk_c5,sk_c10) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f398,plain,
( sQ25_spl
| multiply(sk_c5,sk_c10) != sk_c10 ),
inference(component_clause,[status(thm)],[f396]) ).
fof(f399,plain,
( ~ sQ14_spl
| ~ sQ19_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ25_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f379,f393,f396,f167,f136,f187,f177,f256,f227]) ).
fof(f400,definition,
( sQ26_spl
<=> multiply(sk_c6,inverse(sk_c6)) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f403,plain,
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ22_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f380,f400,f385,f167,f136,f187,f177,f256,f139]) ).
fof(f412,plain,
( sQ24_spl
| ~ sQ14_spl
| multiply(sk_c4,sk_c5) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f228,f395]) ).
fof(f414,plain,
( sQ21_spl
| ~ sQ8_spl
| multiply(sk_c1,sk_c12) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f168,f384]) ).
fof(f415,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| multiply(X0,sk_c10) != sk_c12
| inverse(X0) != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f374,f254]) ).
fof(f417,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(inverse(X0),X0) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f374,f356]) ).
fof(f423,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c10,X0) = multiply(inverse(X1),multiply(X1,X0)) ),
inference(paramodulation,[status(thm)],[f417,f70]) ).
fof(f424,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c10,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f294,f423]) ).
fof(f427,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ8_spl
| multiply(sk_c10,sk_c2) = sk_c10 ),
inference(paramodulation,[status(thm)],[f372,f417]) ).
fof(f429,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sk_c2 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f360,f427]) ).
fof(f431,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ8_spl
| inverse(sk_c2) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f429,f372]) ).
fof(f432,plain,
( sQ3_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| inverse(sk_c7) != sk_c2 ),
inference(backward_demodulation,[status(thm)],[f429,f363]) ).
fof(f435,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(inverse(X0),X0) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f429,f417]) ).
fof(f436,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sk_c11 = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f429,f374]) ).
fof(f437,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| multiply(sk_c1,sk_c12) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f429,f364]) ).
fof(f438,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c12 = multiply(inverse(sk_c1),sk_c2) ),
inference(paramodulation,[status(thm)],[f437,f294]) ).
fof(f440,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c12 = multiply(sk_c12,sk_c2) ),
inference(forward_demodulation,[status(thm)],[f168,f438]) ).
fof(f441,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c2,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f429,f424]) ).
fof(f450,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sk_c5 = multiply(sk_c5,sk_c2) ),
inference(forward_demodulation,[status(thm)],[f436,f336]) ).
fof(f458,plain,
( ~ sQ12_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| multiply(sk_c3,sk_c2) = sk_c12 ),
inference(forward_demodulation,[status(thm)],[f429,f366]) ).
fof(f486,plain,
( ~ sQ13_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| multiply(sk_c4,sk_c5) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f429,f367]) ).
fof(f491,plain,
( ~ sQ15_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| multiply(sk_c5,sk_c2) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f429,f368]) ).
fof(f492,plain,
( ~ sQ15_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sk_c5 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f450,f491]) ).
fof(f493,plain,
( ~ sQ13_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ15_spl
| ~ sQ14_spl
| multiply(sk_c4,sk_c5) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f510,f486]) ).
fof(f503,plain,
( sQ3_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ14_spl
| inverse(sk_c7) != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f510,f432]) ).
fof(f504,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ14_spl
| inverse(sk_c2) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f510,f431]) ).
fof(f505,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ14_spl
| multiply(sk_c5,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f510,f441]) ).
fof(f506,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sk_c11 = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f510,f436]) ).
fof(f507,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ14_spl
| multiply(sk_c1,sk_c12) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f510,f437]) ).
fof(f509,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sk_c5 = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f510,f429]) ).
fof(f510,plain,
( ~ sQ15_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sk_c5 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f429,f492]) ).
fof(f511,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ14_spl
| inverse(sk_c5) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f510,f504]) ).
fof(f520,plain,
( ~ sQ4_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ14_spl
| multiply(sk_c7,sk_c5) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f509,f370]) ).
fof(f521,plain,
( ~ sQ4_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ14_spl
| multiply(sk_c7,sk_c5) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f509,f520]) ).
fof(f523,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ14_spl
| multiply(sk_c5,X0) = multiply(sk_c7,multiply(sk_c5,X0)) ),
inference(paramodulation,[status(thm)],[f521,f70]) ).
fof(f524,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ14_spl
| X0 = multiply(sk_c7,multiply(sk_c5,X0)) ),
inference(forward_demodulation,[status(thm)],[f505,f523]) ).
fof(f525,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ14_spl
| X0 = multiply(sk_c7,X0) ),
inference(forward_demodulation,[status(thm)],[f505,f524]) ).
fof(f532,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ14_spl
| X0 = multiply(inverse(sk_c7),X0) ),
inference(paramodulation,[status(thm)],[f525,f294]) ).
fof(f568,definition,
( sQ32_spl
<=> sk_c12 = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f570,plain,
( sQ32_spl
| sk_c12 != sk_c12 ),
inference(component_clause,[status(thm)],[f568]) ).
fof(f577,plain,
( sQ32_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f570]) ).
fof(f578,plain,
sQ32_spl,
inference(contradiction_clause,[status(thm)],[f577]) ).
fof(f579,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ14_spl
| inverse(X0) != sk_c11
| multiply(X0,sk_c5) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f506,f251]) ).
fof(f580,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ14_spl
| inverse(X0) != sk_c11
| multiply(X0,sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f509,f579]) ).
fof(f581,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ14_spl
| inverse(X0) != sk_c5
| multiply(X0,sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f506,f580]) ).
fof(f592,plain,
( sQ25_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f505,f398]) ).
fof(f593,plain,
( sQ25_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sk_c5 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f509,f592]) ).
fof(f594,plain,
( sQ25_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f509,f593]) ).
fof(f595,plain,
( sQ25_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ14_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f594]) ).
fof(f596,plain,
( sQ25_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f595]) ).
fof(f597,plain,
( sQ24_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ15_spl
| ~ sQ13_spl
| multiply(sk_c4,sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f509,f412]) ).
fof(f599,plain,
( sQ21_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ14_spl
| multiply(sk_c1,sk_c12) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f509,f414]) ).
fof(f600,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ14_spl
| multiply(inverse(X0),X0) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f510,f435]) ).
fof(f611,plain,
( ~ sQ13_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ15_spl
| ~ sQ14_spl
| sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f493,f597]) ).
fof(f612,plain,
( ~ sQ13_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ15_spl
| ~ sQ14_spl
| sQ24_spl ),
inference(contradiction_clause,[status(thm)],[f611]) ).
fof(f649,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f507,f599]) ).
fof(f650,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sQ21_spl ),
inference(contradiction_clause,[status(thm)],[f649]) ).
fof(f653,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ17_spl
| inverse(inverse(sk_c5)) != sk_c5 ),
inference(resolution,[status(thm)],[f581,f600]) ).
fof(f662,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ17_spl
| inverse(sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f511,f653]) ).
fof(f663,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ17_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f511,f662]) ).
fof(f664,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ17_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f663]) ).
fof(f665,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f664]) ).
fof(f682,definition,
( sQ34_spl
<=> sk_c5 = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f684,plain,
( sQ34_spl
| sk_c5 != sk_c5 ),
inference(component_clause,[status(thm)],[f682]) ).
fof(f685,definition,
( sQ35_spl
<=> inverse(sk_c12) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f687,plain,
( sQ35_spl
| inverse(sk_c12) != sk_c12 ),
inference(component_clause,[status(thm)],[f685]) ).
fof(f695,plain,
( sQ34_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f684]) ).
fof(f696,plain,
sQ34_spl,
inference(contradiction_clause,[status(thm)],[f695]) ).
fof(f699,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ4_spl
| sk_c7 = sk_c5 ),
inference(paramodulation,[status(thm)],[f600,f532]) ).
fof(f706,plain,
( sQ3_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ4_spl
| inverse(sk_c5) != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f699,f503]) ).
fof(f708,plain,
( sQ3_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ4_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f511,f706]) ).
fof(f709,plain,
( sQ3_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f708]) ).
fof(f710,plain,
( sQ3_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f709]) ).
fof(f712,plain,
( ~ sQ3_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| inverse(sk_c7) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f436,f148]) ).
fof(f746,plain,
( ~ sQ3_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| multiply(sk_c2,sk_c7) = sk_c2 ),
inference(paramodulation,[status(thm)],[f712,f435]) ).
fof(f751,plain,
( ~ sQ3_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sk_c7 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f441,f746]) ).
fof(f755,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| multiply(X0,sk_c2) != sk_c12
| inverse(X0) != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f429,f415]) ).
fof(f757,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ18_spl
| sk_c12 != sk_c12
| inverse(sk_c12) != sk_c12 ),
inference(paramodulation,[status(thm)],[f440,f755]) ).
fof(f758,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ18_spl
| sk_c2 != sk_c12
| inverse(sk_c2) != sk_c12 ),
inference(paramodulation,[status(thm)],[f441,f755]) ).
fof(f759,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ18_spl
| sk_c2 != sk_c12
| inverse(inverse(sk_c2)) != sk_c12 ),
inference(paramodulation,[status(thm)],[f435,f755]) ).
fof(f761,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ18_spl
| ~ sQ32_spl
| ~ sQ35_spl ),
inference(split_clause,[status(thm)],[f757,f685,f568,f253,f167,f187,f177,f136]) ).
fof(f762,definition,
( sQ37_spl
<=> inverse(sk_c2) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f765,definition,
( sQ38_spl
<=> sk_c2 = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f768,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ18_spl
| ~ sQ38_spl
| ~ sQ37_spl ),
inference(split_clause,[status(thm)],[f758,f762,f765,f253,f187,f177,f167,f136]) ).
fof(f769,definition,
( sQ39_spl
<=> inverse(inverse(sk_c2)) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f772,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ18_spl
| ~ sQ38_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f759,f769,f765,f253,f187,f177,f167,f136]) ).
fof(f789,plain,
( sQ4_spl
| ~ sQ3_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| multiply(sk_c2,sk_c10) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f751,f153]) ).
fof(f790,plain,
( sQ4_spl
| ~ sQ3_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sk_c10 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f441,f789]) ).
fof(f791,plain,
( sQ4_spl
| ~ sQ3_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sk_c2 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f429,f790]) ).
fof(f792,plain,
( sQ4_spl
| ~ sQ3_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f436,f791]) ).
fof(f793,plain,
( sQ4_spl
| ~ sQ3_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f792]) ).
fof(f794,plain,
( sQ4_spl
| ~ sQ3_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f793]) ).
fof(f831,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sk_c11 = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f510,f436]) ).
fof(f833,plain,
( ~ sQ12_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ14_spl
| multiply(sk_c3,sk_c5) = sk_c12 ),
inference(forward_demodulation,[status(thm)],[f510,f458]) ).
fof(f890,definition,
( sQ41_spl
<=> sk_c11 = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f892,plain,
( sQ41_spl
| sk_c11 != sk_c11 ),
inference(component_clause,[status(thm)],[f890]) ).
fof(f894,plain,
( ~ sQ15_spl
| ~ sQ20_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sk_c5 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f511,f275]) ).
fof(f895,plain,
( ~ sQ15_spl
| ~ sQ20_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f831,f894]) ).
fof(f896,plain,
( ~ sQ15_spl
| ~ sQ20_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ13_spl
| ~ sQ14_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f895]) ).
fof(f897,plain,
( ~ sQ15_spl
| ~ sQ20_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ13_spl
| ~ sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f896]) ).
fof(f898,plain,
( sQ41_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f892]) ).
fof(f899,plain,
sQ41_spl,
inference(contradiction_clause,[status(thm)],[f898]) ).
fof(f986,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sk_c11 = multiply(sk_c12,sk_c12) ),
inference(forward_demodulation,[status(thm)],[f140,f327]) ).
fof(f998,plain,
( ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ8_spl
| multiply(sk_c11,sk_c7) = sk_c11 ),
inference(paramodulation,[status(thm)],[f148,f356]) ).
fof(f1004,plain,
( ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sk_c7 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f357,f998]) ).
fof(f1007,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ19_spl
| sk_c11 != sk_c11
| multiply(sk_c10,inverse(sk_c10)) != sk_c11 ),
inference(paramodulation,[status(thm)],[f356,f285]) ).
fof(f1008,plain,
( ~ sQ3_spl
| ~ sQ19_spl
| multiply(sk_c11,sk_c10) != sk_c11
| multiply(sk_c7,inverse(sk_c7)) != sk_c11 ),
inference(paramodulation,[status(thm)],[f148,f285]) ).
fof(f1009,plain,
( ~ sQ6_spl
| ~ sQ19_spl
| multiply(sk_c9,sk_c10) != sk_c11
| multiply(sk_c8,inverse(sk_c8)) != sk_c11 ),
inference(paramodulation,[status(thm)],[f160,f285]) ).
fof(f1010,plain,
( ~ sQ1_spl
| ~ sQ19_spl
| multiply(sk_c12,sk_c10) != sk_c11
| multiply(sk_c6,inverse(sk_c6)) != sk_c11 ),
inference(paramodulation,[status(thm)],[f140,f285]) ).
fof(f1011,plain,
( ~ sQ8_spl
| ~ sQ19_spl
| multiply(sk_c12,sk_c10) != sk_c11
| multiply(sk_c1,inverse(sk_c1)) != sk_c11 ),
inference(paramodulation,[status(thm)],[f168,f285]) ).
fof(f1012,definition,
( sQ42_spl
<=> multiply(sk_c10,inverse(sk_c10)) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f1014,plain,
( sQ42_spl
| multiply(sk_c10,inverse(sk_c10)) != sk_c11 ),
inference(component_clause,[status(thm)],[f1012]) ).
fof(f1015,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ19_spl
| ~ sQ41_spl
| ~ sQ42_spl ),
inference(split_clause,[status(thm)],[f1007,f1012,f890,f256,f167,f136]) ).
fof(f1016,definition,
( sQ43_spl
<=> multiply(sk_c7,inverse(sk_c7)) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f1019,definition,
( sQ44_spl
<=> multiply(sk_c11,sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f1021,plain,
( sQ44_spl
| multiply(sk_c11,sk_c10) != sk_c11 ),
inference(component_clause,[status(thm)],[f1019]) ).
fof(f1022,plain,
( ~ sQ3_spl
| ~ sQ19_spl
| ~ sQ44_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f1008,f1016,f1019,f256,f147]) ).
fof(f1023,definition,
( sQ45_spl
<=> multiply(sk_c8,inverse(sk_c8)) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f1025,plain,
( sQ45_spl
| multiply(sk_c8,inverse(sk_c8)) != sk_c11 ),
inference(component_clause,[status(thm)],[f1023]) ).
fof(f1026,plain,
( ~ sQ6_spl
| ~ sQ19_spl
| ~ sQ7_spl
| ~ sQ45_spl ),
inference(split_clause,[status(thm)],[f1009,f1023,f163,f256,f159]) ).
fof(f1027,definition,
( sQ46_spl
<=> multiply(sk_c6,inverse(sk_c6)) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f1030,definition,
( sQ47_spl
<=> multiply(sk_c12,sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f1033,plain,
( ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ47_spl
| ~ sQ46_spl ),
inference(split_clause,[status(thm)],[f1010,f1027,f1030,f256,f139]) ).
fof(f1034,definition,
( sQ48_spl
<=> multiply(sk_c1,inverse(sk_c1)) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f1037,plain,
( ~ sQ8_spl
| ~ sQ19_spl
| ~ sQ47_spl
| ~ sQ48_spl ),
inference(split_clause,[status(thm)],[f1011,f1034,f1030,f256,f167]) ).
fof(f1040,plain,
( sQ45_spl
| ~ sQ6_spl
| multiply(sk_c8,sk_c9) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f160,f1025]) ).
fof(f1041,plain,
( sQ44_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sk_c10 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f357,f1021]) ).
fof(f1048,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ3_spl
| multiply(inverse(X0),X0) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f1004,f356]) ).
fof(f1053,plain,
( sQ10_spl
| ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ8_spl
| inverse(sk_c2) != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f1004,f189]) ).
fof(f1054,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ3_spl
| multiply(sk_c7,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f1004,f357]) ).
fof(f1056,plain,
( ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ8_spl
| inverse(sk_c7) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f1004,f148]) ).
fof(f1059,plain,
( sQ44_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ3_spl
| sk_c10 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f1004,f1041]) ).
fof(f1060,plain,
( ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ8_spl
| multiply(sk_c2,sk_c7) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1004,f178]) ).
fof(f1087,plain,
( ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ3_spl
| sk_c10 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1054,f152]) ).
fof(f1088,plain,
( ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ3_spl
| sk_c10 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f1004,f1087]) ).
fof(f1089,plain,
( ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ3_spl
| sQ44_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1088,f1059]) ).
fof(f1090,plain,
( ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ3_spl
| sQ44_spl ),
inference(contradiction_clause,[status(thm)],[f1089]) ).
fof(f1099,plain,
( ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ4_spl
| inverse(sk_c7) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f1088,f1056]) ).
fof(f1100,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c10,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f1088,f1054]) ).
fof(f1101,plain,
( ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ4_spl
| multiply(sk_c2,sk_c10) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f1088,f1060]) ).
fof(f1102,plain,
( sQ10_spl
| ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ4_spl
| inverse(sk_c2) != sk_c10 ),
inference(backward_demodulation,[status(thm)],[f1088,f1053]) ).
fof(f1105,plain,
( ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ4_spl
| sk_c10 = sk_c11 ),
inference(backward_demodulation,[status(thm)],[f1088,f1004]) ).
fof(f1106,plain,
( ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ4_spl
| inverse(sk_c10) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1088,f1099]) ).
fof(f1124,plain,
( ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ4_spl
| multiply(sk_c9,sk_c10) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1105,f164]) ).
fof(f1126,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ4_spl
| multiply(sk_c10,X0) = multiply(sk_c9,multiply(sk_c10,X0)) ),
inference(paramodulation,[status(thm)],[f1124,f70]) ).
fof(f1127,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ4_spl
| X0 = multiply(sk_c9,multiply(sk_c10,X0)) ),
inference(forward_demodulation,[status(thm)],[f1100,f1126]) ).
fof(f1128,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ4_spl
| X0 = multiply(sk_c9,X0) ),
inference(forward_demodulation,[status(thm)],[f1100,f1127]) ).
fof(f1144,definition,
( sQ50_spl
<=> sk_c10 = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f1146,plain,
( sQ50_spl
| sk_c10 != sk_c10 ),
inference(component_clause,[status(thm)],[f1144]) ).
fof(f1153,plain,
( sQ50_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1146]) ).
fof(f1154,plain,
sQ50_spl,
inference(contradiction_clause,[status(thm)],[f1153]) ).
fof(f1161,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(inverse(X0),X0) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1088,f1048]) ).
fof(f1163,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c9,sk_c8) = sk_c10 ),
inference(paramodulation,[status(thm)],[f160,f1161]) ).
fof(f1168,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| sk_c8 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1128,f1163]) ).
fof(f1170,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(inverse(X0),X0) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f1168,f1161]) ).
fof(f1175,plain,
( sQ10_spl
| ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| inverse(sk_c2) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f1168,f1102]) ).
fof(f1177,plain,
( ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| inverse(sk_c10) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f1168,f1106]) ).
fof(f1178,plain,
( ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c8 = sk_c11 ),
inference(backward_demodulation,[status(thm)],[f1168,f1105]) ).
fof(f1181,plain,
( ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| inverse(sk_c8) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f1168,f1177]) ).
fof(f1182,plain,
( ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c9 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f160,f1181]) ).
fof(f1183,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| sk_c9 = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f1182,f1168]) ).
fof(f1184,plain,
( ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ4_spl
| ~ sQ7_spl
| inverse(sk_c9) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f1182,f160]) ).
fof(f1185,plain,
( ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c9 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1182,f1178]) ).
fof(f1192,plain,
( sQ10_spl
| ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| inverse(sk_c2) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1182,f1175]) ).
fof(f1215,plain,
( ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1183,f1101]) ).
fof(f1216,plain,
( ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(sk_c2,sk_c9) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1183,f1215]) ).
fof(f1218,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(sk_c9,X0) = multiply(sk_c2,multiply(sk_c9,X0)) ),
inference(paramodulation,[status(thm)],[f1216,f70]) ).
fof(f1219,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| X0 = multiply(sk_c2,multiply(sk_c9,X0)) ),
inference(forward_demodulation,[status(thm)],[f1128,f1218]) ).
fof(f1220,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| X0 = multiply(sk_c2,X0) ),
inference(forward_demodulation,[status(thm)],[f1128,f1219]) ).
fof(f1238,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| X0 = multiply(inverse(sk_c2),X0) ),
inference(paramodulation,[status(thm)],[f1220,f294]) ).
fof(f1249,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(inverse(X0),X0) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1182,f1170]) ).
fof(f1283,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| sk_c2 = sk_c9 ),
inference(paramodulation,[status(thm)],[f1249,f1238]) ).
fof(f1307,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| inverse(X0) != sk_c11
| multiply(X0,sk_c9) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1185,f251]) ).
fof(f1308,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| inverse(X0) != sk_c11
| multiply(X0,sk_c9) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1183,f1307]) ).
fof(f1309,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1185,f1308]) ).
fof(f1317,plain,
( ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ9_spl
| inverse(sk_c9) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f1283,f1184]) ).
fof(f1318,plain,
( sQ10_spl
| ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| inverse(sk_c2) != sk_c2 ),
inference(backward_demodulation,[status(thm)],[f1283,f1192]) ).
fof(f1325,plain,
( ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ9_spl
| inverse(sk_c2) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1283,f1317]) ).
fof(f1329,plain,
( sQ10_spl
| ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1325,f1318]) ).
fof(f1330,plain,
( sQ10_spl
| ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1329]) ).
fof(f1331,plain,
( sQ10_spl
| ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f1330]) ).
fof(f1426,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ14_spl
| multiply(X0,sk_c5) != sk_c12
| inverse(X0) != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f510,f755]) ).
fof(f1495,plain,
( ~ sQ18_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| inverse(sk_c3) != sk_c12 ),
inference(resolution,[status(thm)],[f833,f1426]) ).
fof(f1499,plain,
( ~ sQ18_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sk_c12 != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f198,f1495]) ).
fof(f1500,plain,
( ~ sQ18_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1499]) ).
fof(f1501,plain,
( ~ sQ18_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f1500]) ).
fof(f1510,plain,
( ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| inverse(sk_c9) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1183,f1106]) ).
fof(f1511,plain,
( ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| inverse(sk_c9) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1183,f1510]) ).
fof(f1513,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(sk_c9,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f1183,f1100]) ).
fof(f1525,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ17_spl
| inverse(sk_c9) != sk_c9 ),
inference(resolution,[status(thm)],[f1309,f1513]) ).
fof(f1528,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ17_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1511,f1525]) ).
fof(f1529,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ17_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1528]) ).
fof(f1530,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f1529]) ).
fof(f1534,plain,
( sQ42_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| multiply(sk_c9,inverse(sk_c10)) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1183,f1014]) ).
fof(f1535,plain,
( sQ42_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| inverse(sk_c10) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1513,f1534]) ).
fof(f1536,plain,
( sQ42_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| inverse(sk_c9) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1183,f1535]) ).
fof(f1537,plain,
( sQ42_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| sk_c9 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1511,f1536]) ).
fof(f1538,plain,
( sQ42_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1185,f1537]) ).
fof(f1539,plain,
( sQ42_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1538]) ).
fof(f1540,plain,
( sQ42_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f1539]) ).
fof(f1558,plain,
( ~ sQ5_spl
| sQ45_spl
| ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f156,f1040]) ).
fof(f1559,plain,
( ~ sQ5_spl
| sQ45_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f1558]) ).
fof(f1562,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ16_spl
| inverse(sk_c12) != sk_c12
| sk_c11 != sk_c11 ),
inference(paramodulation,[status(thm)],[f986,f248]) ).
fof(f1563,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sk_c12 = multiply(inverse(sk_c12),sk_c11) ),
inference(paramodulation,[status(thm)],[f986,f294]) ).
fof(f1565,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ16_spl
| ~ sQ35_spl
| ~ sQ41_spl ),
inference(split_clause,[status(thm)],[f1562,f890,f685,f247,f139,f143]) ).
fof(f1566,plain,
( ~ sQ4_spl
| sk_c10 = multiply(inverse(sk_c7),sk_c11) ),
inference(paramodulation,[status(thm)],[f152,f294]) ).
fof(f1568,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| sk_c10 = multiply(sk_c11,sk_c11) ),
inference(forward_demodulation,[status(thm)],[f148,f1566]) ).
fof(f1579,plain,
( ~ sQ1_spl
| sk_c6 = multiply(inverse(sk_c12),identity) ),
inference(paramodulation,[status(thm)],[f291,f294]) ).
fof(f1585,plain,
( ~ sQ2_spl
| ~ sQ18_spl
| inverse(sk_c6) != sk_c12 ),
inference(resolution,[status(thm)],[f254,f144]) ).
fof(f1590,plain,
( ~ sQ2_spl
| ~ sQ18_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f1585,f139,f253,f143]) ).
fof(f1615,plain,
( ~ sQ0_spl
| ~ sQ16_spl
| inverse(sk_c1) != sk_c12
| sk_c11 != sk_c11 ),
inference(paramodulation,[status(thm)],[f137,f248]) ).
fof(f1621,plain,
( ~ sQ0_spl
| ~ sQ16_spl
| ~ sQ8_spl
| ~ sQ41_spl ),
inference(split_clause,[status(thm)],[f1615,f890,f167,f247,f136]) ).
fof(f1638,plain,
inverse(identity) = identity,
inference(paramodulation,[status(thm)],[f344,f69]) ).
fof(f1682,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c11,sk_c11) = multiply(sk_c8,sk_c9) ),
inference(paramodulation,[status(thm)],[f338,f271]) ).
fof(f1686,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sk_c10 = multiply(sk_c8,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f1568,f1682]) ).
fof(f1687,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sk_c10 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f156,f1686]) ).
fof(f1715,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c10 = multiply(sk_c11,sk_c10) ),
inference(backward_demodulation,[status(thm)],[f1687,f1568]) ).
fof(f1718,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sk_c9 = multiply(sk_c9,sk_c10) ),
inference(backward_demodulation,[status(thm)],[f1687,f338]) ).
fof(f1723,plain,
( ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| multiply(sk_c9,sk_c10) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f1687,f164]) ).
fof(f1725,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c10 = multiply(sk_c10,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f1687,f1715]) ).
fof(f1732,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c10 = multiply(inverse(sk_c10),sk_c10) ),
inference(paramodulation,[status(thm)],[f1725,f294]) ).
fof(f1734,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c10 = identity ),
inference(forward_demodulation,[status(thm)],[f69,f1732]) ).
fof(f1745,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| inverse(identity) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f1734,f1638]) ).
fof(f1750,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c10,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f1734,f68]) ).
fof(f1751,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| inverse(sk_c10) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1734,f1745]) ).
fof(f1798,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(sk_c9,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f1805,f1750]) ).
fof(f1799,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| inverse(sk_c10) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f1805,f1751]) ).
fof(f1800,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c9 = identity ),
inference(backward_demodulation,[status(thm)],[f1805,f1734]) ).
fof(f1804,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ7_spl
| sk_c9 = sk_c11 ),
inference(backward_demodulation,[status(thm)],[f1805,f1687]) ).
fof(f1805,plain,
( ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sk_c9 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1718,f1723]) ).
fof(f1806,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| inverse(sk_c9) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1805,f1799]) ).
fof(f1927,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ7_spl
| inverse(X0) != sk_c11
| multiply(X0,sk_c9) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1804,f251]) ).
fof(f1928,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ7_spl
| inverse(X0) != sk_c11
| multiply(X0,sk_c9) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1805,f1927]) ).
fof(f1929,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ7_spl
| inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1804,f1928]) ).
fof(f1947,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ17_spl
| inverse(sk_c9) != sk_c9 ),
inference(resolution,[status(thm)],[f1929,f1798]) ).
fof(f1954,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ17_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1806,f1947]) ).
fof(f1955,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ17_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1954]) ).
fof(f1956,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f1955]) ).
fof(f1994,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ7_spl
| sk_c12 = multiply(inverse(sk_c12),sk_c9) ),
inference(forward_demodulation,[status(thm)],[f1804,f1563]) ).
fof(f2004,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c6 = multiply(inverse(sk_c12),sk_c9) ),
inference(forward_demodulation,[status(thm)],[f1800,f1579]) ).
fof(f2010,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ2_spl
| inverse(sk_c6) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f2015,f140]) ).
fof(f2011,plain,
( sQ35_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ2_spl
| inverse(sk_c12) != sk_c6 ),
inference(backward_demodulation,[status(thm)],[f2015,f687]) ).
fof(f2015,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ2_spl
| sk_c6 = sk_c12 ),
inference(forward_demodulation,[status(thm)],[f1994,f2004]) ).
fof(f2019,plain,
( sQ35_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ2_spl
| inverse(sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f2015,f2011]) ).
fof(f2023,plain,
( sQ35_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ2_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f2010,f2019]) ).
fof(f2024,plain,
( sQ35_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f2023]) ).
fof(f2025,plain,
( sQ35_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f2024]) ).
fof(f2026,plain,
$false,
inference(sat_refutation,[status(thm)],[f142,f146,f150,f154,f158,f162,f166,f170,f171,f172,f173,f174,f175,f176,f180,f181,f182,f183,f185,f186,f190,f191,f192,f193,f195,f196,f200,f201,f202,f205,f206,f210,f211,f212,f215,f216,f220,f221,f222,f223,f225,f226,f230,f231,f232,f233,f235,f236,f240,f241,f242,f243,f245,f246,f262,f284,f388,f392,f399,f403,f578,f596,f612,f650,f665,f696,f710,f761,f768,f772,f794,f897,f899,f1015,f1022,f1026,f1033,f1037,f1090,f1154,f1331,f1501,f1530,f1540,f1559,f1565,f1590,f1621,f1956,f2025]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP243-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.34 % Computer : n003.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8046.5625MB
% 0.10/0.34 % OS : Linux 6.8.0-71-generic
% 0.10/0.34 % CPULimit : 300
% 0.10/0.34 % WCLimit : 300
% 0.10/0.34 % DateTime : Sun Sep 20 20:08:29 UTC 2026
% 0.10/0.34 % CPUTime :
% 0.10/0.36 % Drodi V4.1.1
% 0.13/0.39 % Refutation found
% 0.13/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.42 % Elapsed time: 0.065717 seconds
% 0.13/0.42 % CPU time: 0.263072 seconds
% 0.13/0.42 % Total memory used: 108.233 MB
% 0.13/0.42 % Net memory used: 108.024 MB
%------------------------------------------------------------------------------