%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP258-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:33:14 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.48s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 91
% Syntax : Number of formulae : 516 ( 16 unt; 36 def)
% Number of atoms : 2430 ( 655 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 3697 (1783 ~;1878 |; 0 &)
% ( 36 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 38 ( 36 usr; 37 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 13 con; 0-2 aty)
% Number of variables : 144 ( 144 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c11
| multiply(sk_c1,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c4) = sk_c12
| multiply(sk_c1,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c5,sk_c11) = sk_c10
| multiply(sk_c1,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c5) = sk_c11
| multiply(sk_c1,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c12
| multiply(sk_c1,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c1,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c12
| multiply(sk_c1,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c1,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c7) = sk_c9
| multiply(sk_c1,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c11
| inverse(sk_c1) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c4) = sk_c12
| inverse(sk_c1) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c5,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c5) = sk_c11
| inverse(sk_c1) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c12
| inverse(sk_c1) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c1) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c12
| inverse(sk_c1) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c1) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( inverse(sk_c7) = sk_c9
| inverse(sk_c1) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c11
| multiply(sk_c2,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c5,sk_c11) = sk_c10
| multiply(sk_c2,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c11
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( inverse(sk_c4) = sk_c12
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
( multiply(sk_c5,sk_c11) = sk_c10
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( inverse(sk_c5) = sk_c11
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c12
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c11
| multiply(sk_c10,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
( inverse(sk_c4) = sk_c12
| multiply(sk_c10,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,negated_conjecture,
( multiply(sk_c5,sk_c11) = sk_c10
| multiply(sk_c10,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,negated_conjecture,
( inverse(sk_c5) = sk_c11
| multiply(sk_c10,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c12
| multiply(sk_c10,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c10,sk_c12) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c11
| multiply(sk_c3,sk_c10) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f55,negated_conjecture,
( inverse(sk_c4) = sk_c12
| multiply(sk_c3,sk_c10) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f56,negated_conjecture,
( multiply(sk_c5,sk_c11) = sk_c10
| multiply(sk_c3,sk_c10) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f57,negated_conjecture,
( inverse(sk_c5) = sk_c11
| multiply(sk_c3,sk_c10) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f58,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c12
| multiply(sk_c3,sk_c10) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f59,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c3,sk_c10) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f60,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c12
| multiply(sk_c3,sk_c10) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f61,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c3,sk_c10) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f62,negated_conjecture,
( inverse(sk_c7) = sk_c9
| multiply(sk_c3,sk_c10) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f64,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c11
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f65,negated_conjecture,
( inverse(sk_c4) = sk_c12
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f66,negated_conjecture,
( multiply(sk_c5,sk_c11) = sk_c10
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f67,negated_conjecture,
( inverse(sk_c5) = sk_c11
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f68,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c12
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f69,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f70,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c12
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f71,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f72,negated_conjecture,
( inverse(sk_c7) = sk_c9
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f73,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c7
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f74,negated_conjecture,
! [X4,X5,X6,X1,X2,X7,X3,X8,X9] :
( multiply(X8,X3) != X9
| inverse(X9) != X3
| inverse(X8) != X9
| multiply(X3,sk_c11) != sk_c12
| inverse(X7) != X3
| multiply(X7,X3) != sk_c12
| inverse(X2) != sk_c11
| multiply(X2,sk_c11) != sk_c10
| inverse(X1) != sk_c12
| multiply(X1,sk_c12) != sk_c11
| inverse(X6) != sk_c10
| multiply(X6,sk_c10) != sk_c12
| multiply(sk_c10,sk_c12) != sk_c11
| inverse(X5) != sk_c11
| multiply(X5,sk_c11) != sk_c10
| inverse(X4) != sk_c12
| multiply(X4,sk_c12) != sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f75,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f76,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f77,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f78,plain,
( multiply(sk_c4,sk_c12) = sk_c11
| multiply(sk_c1,sk_c12) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f79,plain,
( inverse(sk_c4) = sk_c12
| multiply(sk_c1,sk_c12) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f80,plain,
( multiply(sk_c5,sk_c11) = sk_c10
| multiply(sk_c1,sk_c12) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f81,plain,
( inverse(sk_c5) = sk_c11
| multiply(sk_c1,sk_c12) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f82,plain,
( multiply(sk_c6,sk_c9) = sk_c12
| multiply(sk_c1,sk_c12) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f83,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c1,sk_c12) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f84,plain,
( multiply(sk_c9,sk_c11) = sk_c12
| multiply(sk_c1,sk_c12) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f85,plain,
( inverse(sk_c8) = sk_c7
| multiply(sk_c1,sk_c12) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f86,plain,
( inverse(sk_c7) = sk_c9
| multiply(sk_c1,sk_c12) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f88,plain,
( multiply(sk_c4,sk_c12) = sk_c11
| inverse(sk_c1) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f89,plain,
( inverse(sk_c4) = sk_c12
| inverse(sk_c1) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f90,plain,
( multiply(sk_c5,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f91,plain,
( inverse(sk_c5) = sk_c11
| inverse(sk_c1) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f92,plain,
( multiply(sk_c6,sk_c9) = sk_c12
| inverse(sk_c1) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f93,plain,
( inverse(sk_c6) = sk_c9
| inverse(sk_c1) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f94,plain,
( multiply(sk_c9,sk_c11) = sk_c12
| inverse(sk_c1) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f95,plain,
( inverse(sk_c8) = sk_c7
| inverse(sk_c1) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f96,plain,
( inverse(sk_c7) = sk_c9
| inverse(sk_c1) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f98,plain,
( multiply(sk_c4,sk_c12) = sk_c11
| multiply(sk_c2,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f100,plain,
( multiply(sk_c5,sk_c11) = sk_c10
| multiply(sk_c2,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f108,plain,
( multiply(sk_c4,sk_c12) = sk_c11
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f109,plain,
( inverse(sk_c4) = sk_c12
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f110,plain,
( multiply(sk_c5,sk_c11) = sk_c10
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f111,plain,
( inverse(sk_c5) = sk_c11
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f112,plain,
( multiply(sk_c6,sk_c9) = sk_c12
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f113,plain,
( inverse(sk_c6) = sk_c9
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f118,plain,
( multiply(sk_c4,sk_c12) = sk_c11
| multiply(sk_c10,sk_c12) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f119,plain,
( inverse(sk_c4) = sk_c12
| multiply(sk_c10,sk_c12) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f120,plain,
( multiply(sk_c5,sk_c11) = sk_c10
| multiply(sk_c10,sk_c12) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f121,plain,
( inverse(sk_c5) = sk_c11
| multiply(sk_c10,sk_c12) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f122,plain,
( multiply(sk_c6,sk_c9) = sk_c12
| multiply(sk_c10,sk_c12) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f123,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c10,sk_c12) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f128,plain,
( multiply(sk_c4,sk_c12) = sk_c11
| multiply(sk_c3,sk_c10) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f129,plain,
( inverse(sk_c4) = sk_c12
| multiply(sk_c3,sk_c10) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f130,plain,
( multiply(sk_c5,sk_c11) = sk_c10
| multiply(sk_c3,sk_c10) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f131,plain,
( inverse(sk_c5) = sk_c11
| multiply(sk_c3,sk_c10) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f132,plain,
( multiply(sk_c6,sk_c9) = sk_c12
| multiply(sk_c3,sk_c10) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f133,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c3,sk_c10) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f134,plain,
( multiply(sk_c9,sk_c11) = sk_c12
| multiply(sk_c3,sk_c10) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f135,plain,
( inverse(sk_c8) = sk_c7
| multiply(sk_c3,sk_c10) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f136,plain,
( inverse(sk_c7) = sk_c9
| multiply(sk_c3,sk_c10) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f138,plain,
( multiply(sk_c4,sk_c12) = sk_c11
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f139,plain,
( inverse(sk_c4) = sk_c12
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f140,plain,
( multiply(sk_c5,sk_c11) = sk_c10
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f141,plain,
( inverse(sk_c5) = sk_c11
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f142,plain,
( multiply(sk_c6,sk_c9) = sk_c12
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f143,plain,
( inverse(sk_c6) = sk_c9
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f144,plain,
( multiply(sk_c9,sk_c11) = sk_c12
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f145,plain,
( inverse(sk_c8) = sk_c7
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f146,plain,
( inverse(sk_c7) = sk_c9
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f147,plain,
( multiply(sk_c8,sk_c9) = sk_c7
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f148,plain,
! [X3,X8,X9] :
( multiply(X8,X3) != X9
| inverse(X9) != X3
| inverse(X8) != X9
| multiply(X3,sk_c11) != sk_c12
| ! [X7] :
( inverse(X7) != X3
| multiply(X7,X3) != sk_c12
| ! [X2] :
( inverse(X2) != sk_c11
| multiply(X2,sk_c11) != sk_c10
| ! [X1] :
( inverse(X1) != sk_c12
| multiply(X1,sk_c12) != sk_c11
| ! [X6] :
( inverse(X6) != sk_c10
| multiply(X6,sk_c10) != sk_c12
| multiply(sk_c10,sk_c12) != sk_c11
| ! [X5] :
( inverse(X5) != sk_c11
| multiply(X5,sk_c11) != sk_c10
| ! [X4] :
( inverse(X4) != sk_c12
| multiply(X4,sk_c12) != sk_c11 ) ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f74]) ).
fof(f149,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7,X8] :
( multiply(X7,X6) != X8
| inverse(X8) != X6
| inverse(X7) != X8
| multiply(X6,sk_c11) != sk_c12
| inverse(X5) != X6
| multiply(X5,X6) != sk_c12
| inverse(X4) != sk_c11
| multiply(X4,sk_c11) != sk_c10
| inverse(X3) != sk_c12
| multiply(X3,sk_c12) != sk_c11
| inverse(X2) != sk_c10
| multiply(X2,sk_c10) != sk_c12
| multiply(sk_c10,sk_c12) != sk_c11
| 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)],[f148]) ).
fof(f150,definition,
( sQ0_spl
<=> multiply(sk_c1,sk_c12) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f151,plain,
( ~ sQ0_spl
| multiply(sk_c1,sk_c12) = sk_c11 ),
inference(component_clause,[status(thm)],[f150]) ).
fof(f153,definition,
( sQ1_spl
<=> multiply(sk_c4,sk_c12) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f154,plain,
( ~ sQ1_spl
| multiply(sk_c4,sk_c12) = sk_c11 ),
inference(component_clause,[status(thm)],[f153]) ).
fof(f156,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f78,f150,f153]) ).
fof(f157,definition,
( sQ2_spl
<=> inverse(sk_c4) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f158,plain,
( ~ sQ2_spl
| inverse(sk_c4) = sk_c12 ),
inference(component_clause,[status(thm)],[f157]) ).
fof(f159,plain,
( sQ2_spl
| inverse(sk_c4) != sk_c12 ),
inference(component_clause,[status(thm)],[f157]) ).
fof(f160,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f79,f150,f157]) ).
fof(f161,definition,
( sQ3_spl
<=> multiply(sk_c5,sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f162,plain,
( ~ sQ3_spl
| multiply(sk_c5,sk_c11) = sk_c10 ),
inference(component_clause,[status(thm)],[f161]) ).
fof(f164,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f80,f150,f161]) ).
fof(f165,definition,
( sQ4_spl
<=> inverse(sk_c5) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f166,plain,
( ~ sQ4_spl
| inverse(sk_c5) = sk_c11 ),
inference(component_clause,[status(thm)],[f165]) ).
fof(f167,plain,
( sQ4_spl
| inverse(sk_c5) != sk_c11 ),
inference(component_clause,[status(thm)],[f165]) ).
fof(f168,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f81,f150,f165]) ).
fof(f169,definition,
( sQ5_spl
<=> multiply(sk_c6,sk_c9) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f170,plain,
( ~ sQ5_spl
| multiply(sk_c6,sk_c9) = sk_c12 ),
inference(component_clause,[status(thm)],[f169]) ).
fof(f172,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f82,f150,f169]) ).
fof(f173,definition,
( sQ6_spl
<=> inverse(sk_c6) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f174,plain,
( ~ sQ6_spl
| inverse(sk_c6) = sk_c9 ),
inference(component_clause,[status(thm)],[f173]) ).
fof(f176,plain,
( sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f83,f150,f173]) ).
fof(f177,definition,
( sQ7_spl
<=> multiply(sk_c9,sk_c11) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f178,plain,
( ~ sQ7_spl
| multiply(sk_c9,sk_c11) = sk_c12 ),
inference(component_clause,[status(thm)],[f177]) ).
fof(f180,plain,
( sQ7_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f84,f150,f177]) ).
fof(f181,definition,
( sQ8_spl
<=> inverse(sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f182,plain,
( ~ sQ8_spl
| inverse(sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f181]) ).
fof(f184,plain,
( sQ8_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f85,f150,f181]) ).
fof(f185,definition,
( sQ9_spl
<=> inverse(sk_c7) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f186,plain,
( ~ sQ9_spl
| inverse(sk_c7) = sk_c9 ),
inference(component_clause,[status(thm)],[f185]) ).
fof(f188,plain,
( sQ9_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f86,f150,f185]) ).
fof(f189,definition,
( sQ10_spl
<=> multiply(sk_c8,sk_c9) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f190,plain,
( ~ sQ10_spl
| multiply(sk_c8,sk_c9) = sk_c7 ),
inference(component_clause,[status(thm)],[f189]) ).
fof(f193,definition,
( sQ11_spl
<=> inverse(sk_c1) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f194,plain,
( ~ sQ11_spl
| inverse(sk_c1) = sk_c12 ),
inference(component_clause,[status(thm)],[f193]) ).
fof(f196,plain,
( sQ1_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f88,f193,f153]) ).
fof(f197,plain,
( sQ2_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f89,f193,f157]) ).
fof(f198,plain,
( sQ3_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f90,f193,f161]) ).
fof(f199,plain,
( sQ4_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f91,f193,f165]) ).
fof(f200,plain,
( sQ5_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f92,f193,f169]) ).
fof(f201,plain,
( sQ6_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f93,f193,f173]) ).
fof(f202,plain,
( sQ7_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f94,f193,f177]) ).
fof(f203,plain,
( sQ8_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f95,f193,f181]) ).
fof(f204,plain,
( sQ9_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f96,f193,f185]) ).
fof(f206,definition,
( sQ12_spl
<=> multiply(sk_c2,sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f207,plain,
( ~ sQ12_spl
| multiply(sk_c2,sk_c11) = sk_c10 ),
inference(component_clause,[status(thm)],[f206]) ).
fof(f209,plain,
( sQ1_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f98,f206,f153]) ).
fof(f211,plain,
( sQ3_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f100,f206,f161]) ).
fof(f219,definition,
( sQ13_spl
<=> inverse(sk_c2) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f220,plain,
( ~ sQ13_spl
| inverse(sk_c2) = sk_c11 ),
inference(component_clause,[status(thm)],[f219]) ).
fof(f222,plain,
( sQ1_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f108,f219,f153]) ).
fof(f223,plain,
( sQ2_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f109,f219,f157]) ).
fof(f224,plain,
( sQ3_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f110,f219,f161]) ).
fof(f225,plain,
( sQ4_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f111,f219,f165]) ).
fof(f226,plain,
( sQ5_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f112,f219,f169]) ).
fof(f227,plain,
( sQ6_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f113,f219,f173]) ).
fof(f232,definition,
( sQ14_spl
<=> multiply(sk_c10,sk_c12) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f233,plain,
( ~ sQ14_spl
| multiply(sk_c10,sk_c12) = sk_c11 ),
inference(component_clause,[status(thm)],[f232]) ).
fof(f234,plain,
( sQ14_spl
| multiply(sk_c10,sk_c12) != sk_c11 ),
inference(component_clause,[status(thm)],[f232]) ).
fof(f235,plain,
( sQ1_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f118,f232,f153]) ).
fof(f236,plain,
( sQ2_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f119,f232,f157]) ).
fof(f237,plain,
( sQ3_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f120,f232,f161]) ).
fof(f238,plain,
( sQ4_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f121,f232,f165]) ).
fof(f239,plain,
( sQ5_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f122,f232,f169]) ).
fof(f240,plain,
( sQ6_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f123,f232,f173]) ).
fof(f245,definition,
( sQ15_spl
<=> multiply(sk_c3,sk_c10) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f246,plain,
( ~ sQ15_spl
| multiply(sk_c3,sk_c10) = sk_c12 ),
inference(component_clause,[status(thm)],[f245]) ).
fof(f248,plain,
( sQ1_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f128,f245,f153]) ).
fof(f249,plain,
( sQ2_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f129,f245,f157]) ).
fof(f250,plain,
( sQ3_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f130,f245,f161]) ).
fof(f251,plain,
( sQ4_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f131,f245,f165]) ).
fof(f252,plain,
( sQ5_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f132,f245,f169]) ).
fof(f253,plain,
( sQ6_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f133,f245,f173]) ).
fof(f254,plain,
( sQ7_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f134,f245,f177]) ).
fof(f255,plain,
( sQ8_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f135,f245,f181]) ).
fof(f256,plain,
( sQ9_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f136,f245,f185]) ).
fof(f258,definition,
( sQ16_spl
<=> inverse(sk_c3) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f259,plain,
( ~ sQ16_spl
| inverse(sk_c3) = sk_c10 ),
inference(component_clause,[status(thm)],[f258]) ).
fof(f261,plain,
( sQ1_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f138,f258,f153]) ).
fof(f262,plain,
( sQ2_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f139,f258,f157]) ).
fof(f263,plain,
( sQ3_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f140,f258,f161]) ).
fof(f264,plain,
( sQ4_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f141,f258,f165]) ).
fof(f265,plain,
( sQ5_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f142,f258,f169]) ).
fof(f266,plain,
( sQ6_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f143,f258,f173]) ).
fof(f267,plain,
( sQ7_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f144,f258,f177]) ).
fof(f268,plain,
( sQ8_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f145,f258,f181]) ).
fof(f269,plain,
( sQ9_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f146,f258,f185]) ).
fof(f270,plain,
( sQ10_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f147,f258,f189]) ).
fof(f271,definition,
! [X0] :
( sQ17_spl
<=> ( inverse(X0) != sk_c12
| multiply(X0,sk_c12) != sk_c11 ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f272,plain,
! [X0] :
( ~ sQ17_spl
| inverse(X0) != sk_c12
| multiply(X0,sk_c12) != sk_c11 ),
inference(component_clause,[status(thm)],[f271]) ).
fof(f274,definition,
! [X1] :
( sQ18_spl
<=> ( inverse(X1) != sk_c11
| multiply(X1,sk_c11) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f275,plain,
! [X0] :
( ~ sQ18_spl
| inverse(X0) != sk_c11
| multiply(X0,sk_c11) != sk_c10 ),
inference(component_clause,[status(thm)],[f274]) ).
fof(f277,definition,
! [X2] :
( sQ19_spl
<=> ( inverse(X2) != sk_c10
| multiply(X2,sk_c10) != sk_c12 ) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f278,plain,
! [X0] :
( ~ sQ19_spl
| inverse(X0) != sk_c10
| multiply(X0,sk_c10) != sk_c12 ),
inference(component_clause,[status(thm)],[f277]) ).
fof(f280,definition,
! [X5,X6,X7,X8] :
( sQ20_spl
<=> ( multiply(X7,X6) != X8
| inverse(X8) != X6
| inverse(X7) != X8
| multiply(X6,sk_c11) != sk_c12
| inverse(X5) != X6
| multiply(X5,X6) != sk_c12 ) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f281,plain,
! [X0,X1,X2,X3] :
( ~ sQ20_spl
| multiply(X2,X1) != X3
| inverse(X3) != X1
| inverse(X2) != X3
| multiply(X1,sk_c11) != sk_c12
| inverse(X0) != X1
| multiply(X0,X1) != sk_c12 ),
inference(component_clause,[status(thm)],[f280]) ).
fof(f283,plain,
( sQ20_spl
| sQ19_spl
| ~ sQ14_spl
| sQ18_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f149,f271,f274,f232,f277,f280]) ).
fof(f284,plain,
! [X0,X1] :
( ~ sQ20_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c11) != sk_c12
| multiply(X0,inverse(X0)) != sk_c12 ),
inference(destructive_equality_resolution,[status(thm)],[f281]) ).
fof(f298,plain,
( ~ sQ8_spl
| multiply(sk_c7,sk_c8) = identity ),
inference(paramodulation,[status(thm)],[f182,f76]) ).
fof(f300,plain,
( ~ sQ11_spl
| multiply(sk_c12,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f194,f76]) ).
fof(f301,plain,
( ~ sQ13_spl
| multiply(sk_c11,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f220,f76]) ).
fof(f302,plain,
( ~ sQ16_spl
| multiply(sk_c10,sk_c3) = identity ),
inference(paramodulation,[status(thm)],[f259,f76]) ).
fof(f303,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f76,f77]) ).
fof(f304,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f75,f303]) ).
fof(f305,plain,
! [X0] :
( ~ sQ3_spl
| multiply(sk_c10,X0) = multiply(sk_c5,multiply(sk_c11,X0)) ),
inference(paramodulation,[status(thm)],[f162,f77]) ).
fof(f323,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ20_spl
| multiply(X0,inverse(sk_c4)) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c4)
| multiply(sk_c12,sk_c11) != sk_c12
| multiply(sk_c4,inverse(sk_c4)) != sk_c12 ),
inference(paramodulation,[status(thm)],[f158,f284]) ).
fof(f328,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ20_spl
| multiply(X0,inverse(sk_c1)) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c1)
| multiply(sk_c12,sk_c11) != sk_c12
| multiply(sk_c1,inverse(sk_c1)) != sk_c12 ),
inference(paramodulation,[status(thm)],[f194,f284]) ).
fof(f330,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ20_spl
| multiply(X0,inverse(sk_c3)) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c3)
| multiply(sk_c10,sk_c11) != sk_c12
| multiply(sk_c3,inverse(sk_c3)) != sk_c12 ),
inference(paramodulation,[status(thm)],[f259,f284]) ).
fof(f341,definition,
( sQ24_spl
<=> multiply(sk_c4,inverse(sk_c4)) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f344,definition,
( sQ25_spl
<=> multiply(sk_c12,sk_c11) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f346,plain,
( sQ25_spl
| multiply(sk_c12,sk_c11) != sk_c12 ),
inference(component_clause,[status(thm)],[f344]) ).
fof(f347,definition,
! [X0] :
( sQ26_spl
<=> ( multiply(X0,inverse(sk_c4)) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c4) ) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f350,plain,
( ~ sQ2_spl
| ~ sQ20_spl
| sQ26_spl
| ~ sQ25_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f323,f341,f344,f347,f280,f157]) ).
fof(f385,definition,
( sQ37_spl
<=> multiply(sk_c1,inverse(sk_c1)) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f388,definition,
! [X0] :
( sQ38_spl
<=> ( multiply(X0,inverse(sk_c1)) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c1) ) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f391,plain,
( ~ sQ11_spl
| ~ sQ20_spl
| sQ38_spl
| ~ sQ25_spl
| ~ sQ37_spl ),
inference(split_clause,[status(thm)],[f328,f385,f344,f388,f280,f193]) ).
fof(f399,definition,
( sQ41_spl
<=> multiply(sk_c3,inverse(sk_c3)) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f401,plain,
( sQ41_spl
| multiply(sk_c3,inverse(sk_c3)) != sk_c12 ),
inference(component_clause,[status(thm)],[f399]) ).
fof(f402,definition,
( sQ42_spl
<=> multiply(sk_c10,sk_c11) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f403,plain,
( ~ sQ42_spl
| multiply(sk_c10,sk_c11) = sk_c12 ),
inference(component_clause,[status(thm)],[f402]) ).
fof(f404,plain,
( sQ42_spl
| multiply(sk_c10,sk_c11) != sk_c12 ),
inference(component_clause,[status(thm)],[f402]) ).
fof(f405,definition,
! [X0] :
( sQ43_spl
<=> ( multiply(X0,inverse(sk_c3)) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c3) ) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f406,plain,
! [X0] :
( ~ sQ43_spl
| multiply(X0,inverse(sk_c3)) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c3) ),
inference(component_clause,[status(thm)],[f405]) ).
fof(f408,plain,
( ~ sQ16_spl
| ~ sQ20_spl
| sQ43_spl
| ~ sQ42_spl
| ~ sQ41_spl ),
inference(split_clause,[status(thm)],[f330,f399,f402,f405,f280,f258]) ).
fof(f409,plain,
! [X0] :
( ~ sQ43_spl
| ~ sQ16_spl
| multiply(X0,inverse(sk_c3)) != inverse(X0)
| inverse(inverse(X0)) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f259,f406]) ).
fof(f410,plain,
! [X0] :
( ~ sQ43_spl
| ~ sQ16_spl
| multiply(X0,sk_c10) != inverse(X0)
| inverse(inverse(X0)) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f259,f409]) ).
fof(f411,plain,
( sQ41_spl
| ~ sQ16_spl
| multiply(sk_c3,sk_c10) != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f259,f401]) ).
fof(f412,plain,
( sQ41_spl
| ~ sQ16_spl
| ~ sQ15_spl
| sk_c12 != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f246,f411]) ).
fof(f413,plain,
( sQ41_spl
| ~ sQ16_spl
| ~ sQ15_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f412]) ).
fof(f414,plain,
( sQ41_spl
| ~ sQ16_spl
| ~ sQ15_spl ),
inference(contradiction_clause,[status(thm)],[f413]) ).
fof(f416,plain,
( ~ sQ16_spl
| ~ sQ19_spl
| sk_c10 != sk_c10
| multiply(sk_c3,sk_c10) != sk_c12 ),
inference(paramodulation,[status(thm)],[f259,f278]) ).
fof(f417,definition,
( sQ44_spl
<=> sk_c10 = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f419,plain,
( sQ44_spl
| sk_c10 != sk_c10 ),
inference(component_clause,[status(thm)],[f417]) ).
fof(f420,plain,
( ~ sQ16_spl
| ~ sQ19_spl
| ~ sQ44_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f416,f245,f417,f277,f258]) ).
fof(f421,plain,
( sQ44_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f419]) ).
fof(f422,plain,
sQ44_spl,
inference(contradiction_clause,[status(thm)],[f421]) ).
fof(f435,plain,
( ~ sQ3_spl
| ~ sQ18_spl
| inverse(sk_c5) != sk_c11 ),
inference(resolution,[status(thm)],[f275,f162]) ).
fof(f436,plain,
( ~ sQ12_spl
| ~ sQ18_spl
| inverse(sk_c2) != sk_c11 ),
inference(resolution,[status(thm)],[f275,f207]) ).
fof(f443,plain,
( ~ sQ3_spl
| ~ sQ18_spl
| ~ sQ4_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f166,f435]) ).
fof(f444,plain,
( ~ sQ3_spl
| ~ sQ18_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f443]) ).
fof(f445,plain,
( ~ sQ3_spl
| ~ sQ18_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f444]) ).
fof(f458,plain,
( ~ sQ8_spl
| sk_c8 = multiply(inverse(sk_c7),identity) ),
inference(paramodulation,[status(thm)],[f298,f304]) ).
fof(f465,plain,
( ~ sQ1_spl
| sk_c12 = multiply(inverse(sk_c4),sk_c11) ),
inference(paramodulation,[status(thm)],[f154,f304]) ).
fof(f466,plain,
( ~ sQ3_spl
| sk_c11 = multiply(inverse(sk_c5),sk_c10) ),
inference(paramodulation,[status(thm)],[f162,f304]) ).
fof(f467,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f304,f304]) ).
fof(f468,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f76,f304]) ).
fof(f470,plain,
( ~ sQ5_spl
| sk_c9 = multiply(inverse(sk_c6),sk_c12) ),
inference(paramodulation,[status(thm)],[f170,f304]) ).
fof(f472,plain,
( ~ sQ10_spl
| sk_c9 = multiply(inverse(sk_c8),sk_c7) ),
inference(paramodulation,[status(thm)],[f190,f304]) ).
fof(f476,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c8 = multiply(sk_c9,identity) ),
inference(forward_demodulation,[status(thm)],[f186,f458]) ).
fof(f477,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c12 = multiply(sk_c12,sk_c11) ),
inference(forward_demodulation,[status(thm)],[f158,f465]) ).
fof(f478,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f477,f346]) ).
fof(f479,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sQ25_spl ),
inference(contradiction_clause,[status(thm)],[f478]) ).
fof(f480,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c11 = multiply(sk_c11,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f166,f466]) ).
fof(f481,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sk_c9 = multiply(sk_c9,sk_c12) ),
inference(forward_demodulation,[status(thm)],[f174,f470]) ).
fof(f487,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c10 = multiply(inverse(sk_c11),sk_c11) ),
inference(paramodulation,[status(thm)],[f480,f304]) ).
fof(f489,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c10 = identity ),
inference(forward_demodulation,[status(thm)],[f76,f487]) ).
fof(f490,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c8 = multiply(sk_c9,sk_c10) ),
inference(backward_demodulation,[status(thm)],[f489,f476]) ).
fof(f496,plain,
( ~ sQ16_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c10,sk_c3) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f489,f302]) ).
fof(f498,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| multiply(inverse(X0),X0) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f489,f76]) ).
fof(f499,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c10,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f489,f75]) ).
fof(f500,plain,
( ~ sQ2_spl
| ~ sQ17_spl
| multiply(sk_c4,sk_c12) != sk_c11 ),
inference(resolution,[status(thm)],[f272,f158]) ).
fof(f507,plain,
( ~ sQ2_spl
| ~ sQ17_spl
| ~ sQ1_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f154,f500]) ).
fof(f508,plain,
( ~ sQ2_spl
| ~ sQ17_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f507]) ).
fof(f509,plain,
( ~ sQ2_spl
| ~ sQ17_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f508]) ).
fof(f511,plain,
( ~ sQ8_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c7,sk_c8) = sk_c10 ),
inference(paramodulation,[status(thm)],[f182,f498]) ).
fof(f519,plain,
( sQ42_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c11 != sk_c12 ),
inference(backward_demodulation,[status(thm)],[f499,f404]) ).
fof(f522,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sk_c12 = multiply(inverse(sk_c9),sk_c9) ),
inference(paramodulation,[status(thm)],[f481,f304]) ).
fof(f524,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c12 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f498,f522]) ).
fof(f528,plain,
( ~ sQ14_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c12 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f499,f233]) ).
fof(f529,plain,
( ~ sQ14_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sQ42_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f528,f519]) ).
fof(f530,plain,
( ~ sQ14_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sQ42_spl ),
inference(contradiction_clause,[status(thm)],[f529]) ).
fof(f531,plain,
( sQ14_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c12 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f499,f234]) ).
fof(f533,plain,
( ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c9,sk_c11) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f524,f178]) ).
fof(f539,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c6,sk_c9) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f524,f170]) ).
fof(f541,plain,
( sQ14_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c10 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f524,f531]) ).
fof(f559,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c10 = multiply(sk_c12,sk_c11) ),
inference(forward_demodulation,[status(thm)],[f524,f477]) ).
fof(f560,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c10 = multiply(sk_c10,sk_c11) ),
inference(forward_demodulation,[status(thm)],[f524,f559]) ).
fof(f561,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c10 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f499,f560]) ).
fof(f562,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f561,f541]) ).
fof(f563,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f562]) ).
fof(f569,plain,
! [X0,X1] :
( ~ sQ20_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c11) != sk_c12
| multiply(X0,inverse(X0)) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f524,f284]) ).
fof(f570,plain,
! [X0,X1] :
( ~ sQ20_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c11) != sk_c10
| multiply(X0,inverse(X0)) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f524,f569]) ).
fof(f571,plain,
( ~ sQ42_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c11 = sk_c12 ),
inference(forward_demodulation,[status(thm)],[f499,f403]) ).
fof(f572,plain,
( ~ sQ42_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c11 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f524,f571]) ).
fof(f573,plain,
( ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c9,sk_c10) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f561,f533]) ).
fof(f575,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| inverse(sk_c5) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f561,f166]) ).
fof(f580,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| multiply(sk_c10,sk_c5) = sk_c10 ),
inference(paramodulation,[status(thm)],[f575,f498]) ).
fof(f582,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| sk_c5 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f499,f580]) ).
fof(f597,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c9 = multiply(inverse(sk_c6),sk_c10) ),
inference(paramodulation,[status(thm)],[f539,f304]) ).
fof(f599,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c9 = multiply(sk_c9,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f174,f597]) ).
fof(f600,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c9 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f490,f599]) ).
fof(f607,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c6,sk_c8) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f600,f539]) ).
fof(f611,plain,
( ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| inverse(sk_c7) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f600,f186]) ).
fof(f612,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c6) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f600,f174]) ).
fof(f621,plain,
! [X0,X1] :
( ~ sQ20_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c10) != sk_c10
| multiply(X0,inverse(X0)) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f561,f570]) ).
fof(f670,plain,
! [X0] :
( ~ sQ19_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| inverse(X0) != sk_c10
| multiply(X0,sk_c10) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f524,f278]) ).
fof(f697,plain,
( ~ sQ16_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c3 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f499,f496]) ).
fof(f700,plain,
( ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c8,sk_c10) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f600,f573]) ).
fof(f701,plain,
( ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ16_spl
| multiply(sk_c8,sk_c3) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f697,f700]) ).
fof(f702,plain,
( ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ16_spl
| multiply(sk_c8,sk_c3) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f697,f701]) ).
fof(f722,plain,
( ~ sQ8_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ16_spl
| multiply(sk_c7,sk_c8) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f697,f511]) ).
fof(f723,plain,
( ~ sQ8_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ16_spl
| sk_c8 = multiply(inverse(sk_c7),sk_c3) ),
inference(paramodulation,[status(thm)],[f722,f304]) ).
fof(f725,plain,
( ~ sQ8_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ16_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c8 = multiply(sk_c8,sk_c3) ),
inference(forward_demodulation,[status(thm)],[f611,f723]) ).
fof(f726,plain,
( ~ sQ8_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ16_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f702,f725]) ).
fof(f731,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ16_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c6) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f726,f612]) ).
fof(f739,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ16_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c6,sk_c3) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f726,f607]) ).
fof(f740,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ16_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c6,sk_c3) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f697,f739]) ).
fof(f749,plain,
! [X0] :
( ~ sQ19_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ16_spl
| inverse(X0) != sk_c10
| multiply(X0,sk_c3) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f697,f670]) ).
fof(f750,plain,
! [X0] :
( ~ sQ19_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ16_spl
| inverse(X0) != sk_c10
| multiply(X0,sk_c3) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f697,f749]) ).
fof(f751,plain,
! [X0] :
( ~ sQ19_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ16_spl
| inverse(X0) != sk_c3
| multiply(X0,sk_c3) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f697,f750]) ).
fof(f752,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ16_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ19_spl
| multiply(sk_c6,sk_c3) != sk_c3 ),
inference(resolution,[status(thm)],[f751,f731]) ).
fof(f756,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ16_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ19_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f740,f752]) ).
fof(f757,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ16_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ19_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f756]) ).
fof(f758,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ16_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ19_spl ),
inference(contradiction_clause,[status(thm)],[f757]) ).
fof(f809,plain,
( ~ sQ42_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c10 = sk_c12 ),
inference(forward_demodulation,[status(thm)],[f572,f571]) ).
fof(f817,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c10,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f489,f75]) ).
fof(f832,plain,
( ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c8,sk_c8) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f600,f190]) ).
fof(f833,plain,
( ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c8 = multiply(inverse(sk_c8),sk_c7) ),
inference(paramodulation,[status(thm)],[f832,f304]) ).
fof(f1103,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f76,f304]) ).
fof(f1115,plain,
( ~ sQ0_spl
| sk_c12 = multiply(inverse(sk_c1),sk_c11) ),
inference(paramodulation,[status(thm)],[f151,f304]) ).
fof(f1117,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| sk_c12 = multiply(sk_c12,sk_c11) ),
inference(forward_demodulation,[status(thm)],[f194,f1115]) ).
fof(f1128,plain,
( ~ sQ15_spl
| sk_c10 = multiply(inverse(sk_c3),sk_c12) ),
inference(paramodulation,[status(thm)],[f246,f304]) ).
fof(f1130,plain,
( ~ sQ15_spl
| ~ sQ16_spl
| sk_c10 = multiply(sk_c10,sk_c12) ),
inference(forward_demodulation,[status(thm)],[f259,f1128]) ).
fof(f1131,plain,
( ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| sk_c10 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f233,f1130]) ).
fof(f1133,plain,
( ~ sQ1_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| multiply(sk_c4,sk_c12) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f1131,f154]) ).
fof(f1134,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| multiply(sk_c1,sk_c12) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f1131,f151]) ).
fof(f1135,plain,
( ~ sQ13_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| multiply(sk_c10,sk_c2) = identity ),
inference(backward_demodulation,[status(thm)],[f1131,f301]) ).
fof(f1138,plain,
( sQ4_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| inverse(sk_c5) != sk_c10 ),
inference(backward_demodulation,[status(thm)],[f1131,f167]) ).
fof(f1140,plain,
( ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ16_spl
| multiply(sk_c10,sk_c12) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f1131,f233]) ).
fof(f1141,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| inverse(X0) != sk_c12
| multiply(X0,sk_c12) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1131,f272]) ).
fof(f1144,plain,
( ~ sQ11_spl
| ~ sQ17_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| sk_c12 != sk_c12
| multiply(sk_c1,sk_c12) != sk_c10 ),
inference(paramodulation,[status(thm)],[f194,f1141]) ).
fof(f1149,definition,
( sQ57_spl
<=> multiply(sk_c1,sk_c12) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f1151,plain,
( sQ57_spl
| multiply(sk_c1,sk_c12) != sk_c10 ),
inference(component_clause,[status(thm)],[f1149]) ).
fof(f1152,definition,
( sQ58_spl
<=> sk_c12 = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f1154,plain,
( sQ58_spl
| sk_c12 != sk_c12 ),
inference(component_clause,[status(thm)],[f1152]) ).
fof(f1155,plain,
( ~ sQ11_spl
| ~ sQ17_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ58_spl
| ~ sQ57_spl ),
inference(split_clause,[status(thm)],[f1144,f1149,f1152,f232,f258,f245,f271,f193]) ).
fof(f1156,plain,
( sQ58_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1154]) ).
fof(f1157,plain,
sQ58_spl,
inference(contradiction_clause,[status(thm)],[f1156]) ).
fof(f1158,plain,
! [X0,X1] :
( ~ sQ20_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c10) != sk_c12
| multiply(X0,inverse(X0)) != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f1131,f284]) ).
fof(f1169,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| sk_c12 = multiply(sk_c12,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f1131,f1117]) ).
fof(f1170,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| sk_c10 = multiply(inverse(sk_c12),sk_c12) ),
inference(paramodulation,[status(thm)],[f1169,f304]) ).
fof(f1172,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| sk_c10 = identity ),
inference(forward_demodulation,[status(thm)],[f76,f1170]) ).
fof(f1180,plain,
( ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| multiply(sk_c12,sk_c1) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f1172,f300]) ).
fof(f1182,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| multiply(inverse(X0),X0) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f1172,f76]) ).
fof(f1183,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| multiply(sk_c10,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f1172,f75]) ).
fof(f1192,plain,
( ~ sQ13_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ11_spl
| sk_c2 = identity ),
inference(forward_demodulation,[status(thm)],[f1183,f1135]) ).
fof(f1193,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ11_spl
| multiply(sk_c1,sk_c12) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f1205,f1134]) ).
fof(f1194,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| multiply(sk_c2,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f1205,f1183]) ).
fof(f1195,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| sk_c2 = identity ),
inference(backward_demodulation,[status(thm)],[f1205,f1172]) ).
fof(f1196,plain,
( ~ sQ1_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ11_spl
| multiply(sk_c4,sk_c12) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f1205,f1133]) ).
fof(f1200,plain,
( sQ4_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ11_spl
| inverse(sk_c5) != sk_c2 ),
inference(backward_demodulation,[status(thm)],[f1205,f1138]) ).
fof(f1201,plain,
( ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ11_spl
| sk_c2 = sk_c11 ),
inference(backward_demodulation,[status(thm)],[f1205,f1131]) ).
fof(f1204,plain,
( ~ sQ16_spl
| ~ sQ13_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ11_spl
| inverse(sk_c3) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f1205,f259]) ).
fof(f1205,plain,
( ~ sQ13_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ11_spl
| sk_c2 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1172,f1192]) ).
fof(f1212,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ13_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ11_spl
| X0 = multiply(sk_c2,multiply(sk_c3,X0)) ),
inference(paramodulation,[status(thm)],[f1204,f304]) ).
fof(f1213,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ13_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ11_spl
| X0 = multiply(sk_c3,X0) ),
inference(forward_demodulation,[status(thm)],[f1194,f1212]) ).
fof(f1217,plain,
( ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ11_spl
| multiply(sk_c2,sk_c12) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1205,f1140]) ).
fof(f1218,plain,
( ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ11_spl
| sk_c12 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1194,f1217]) ).
fof(f1219,plain,
( sQ2_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ11_spl
| inverse(sk_c4) != sk_c2 ),
inference(backward_demodulation,[status(thm)],[f1221,f159]) ).
fof(f1221,plain,
( ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ11_spl
| sk_c12 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1205,f1218]) ).
fof(f1281,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| multiply(inverse(X0),X0) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1205,f1182]) ).
fof(f1282,plain,
( ~ sQ16_spl
| ~ sQ13_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ11_spl
| multiply(sk_c2,sk_c3) = sk_c2 ),
inference(paramodulation,[status(thm)],[f1204,f1281]) ).
fof(f1286,plain,
( ~ sQ16_spl
| ~ sQ13_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ11_spl
| sk_c3 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1194,f1282]) ).
fof(f1288,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| multiply(inverse(X0),X0) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f1286,f1281]) ).
fof(f1289,plain,
( ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ11_spl
| sk_c12 = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f1286,f1221]) ).
fof(f1290,plain,
( ~ sQ16_spl
| ~ sQ13_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ11_spl
| inverse(sk_c3) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f1286,f1204]) ).
fof(f1291,plain,
( sQ4_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ11_spl
| inverse(sk_c5) != sk_c3 ),
inference(backward_demodulation,[status(thm)],[f1286,f1200]) ).
fof(f1294,plain,
( ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ11_spl
| sk_c3 = sk_c11 ),
inference(backward_demodulation,[status(thm)],[f1286,f1201]) ).
fof(f1295,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| sk_c3 = identity ),
inference(backward_demodulation,[status(thm)],[f1286,f1195]) ).
fof(f1296,plain,
( ~ sQ13_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ11_spl
| sk_c3 = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f1286,f1205]) ).
fof(f1298,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ11_spl
| multiply(sk_c1,sk_c3) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1289,f1193]) ).
fof(f1299,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ11_spl
| multiply(sk_c1,sk_c3) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f1286,f1298]) ).
fof(f1301,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ11_spl
| multiply(sk_c3,X0) = multiply(sk_c1,multiply(sk_c3,X0)) ),
inference(paramodulation,[status(thm)],[f1299,f77]) ).
fof(f1302,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ11_spl
| X0 = multiply(sk_c1,multiply(sk_c3,X0)) ),
inference(forward_demodulation,[status(thm)],[f1213,f1301]) ).
fof(f1303,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ11_spl
| X0 = multiply(sk_c1,X0) ),
inference(forward_demodulation,[status(thm)],[f1213,f1302]) ).
fof(f1304,plain,
( sQ2_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ11_spl
| inverse(sk_c4) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f1286,f1219]) ).
fof(f1314,plain,
( ~ sQ1_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ11_spl
| multiply(sk_c4,sk_c3) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1289,f1196]) ).
fof(f1315,plain,
( ~ sQ1_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ11_spl
| multiply(sk_c4,sk_c3) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f1286,f1314]) ).
fof(f1317,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ11_spl
| multiply(sk_c3,X0) = multiply(sk_c4,multiply(sk_c3,X0)) ),
inference(paramodulation,[status(thm)],[f1315,f77]) ).
fof(f1318,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ11_spl
| X0 = multiply(sk_c4,multiply(sk_c3,X0)) ),
inference(forward_demodulation,[status(thm)],[f1213,f1317]) ).
fof(f1319,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ11_spl
| X0 = multiply(sk_c4,X0) ),
inference(forward_demodulation,[status(thm)],[f1213,f1318]) ).
fof(f1322,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ11_spl
| X0 = multiply(inverse(sk_c4),X0) ),
inference(paramodulation,[status(thm)],[f1319,f304]) ).
fof(f1324,plain,
( sQ57_spl
| ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ11_spl
| sk_c12 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1303,f1151]) ).
fof(f1325,plain,
( sQ57_spl
| ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ11_spl
| sk_c3 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1289,f1324]) ).
fof(f1326,plain,
( sQ57_spl
| ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ11_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f1296,f1325]) ).
fof(f1327,plain,
( sQ57_spl
| ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1326]) ).
fof(f1328,plain,
( sQ57_spl
| ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f1327]) ).
fof(f1349,plain,
( ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| multiply(sk_c3,sk_c1) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1289,f1180]) ).
fof(f1350,plain,
( ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| sk_c1 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1213,f1349]) ).
fof(f1353,plain,
( ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| sk_c1 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f1296,f1350]) ).
fof(f1385,plain,
( ~ sQ12_spl
| ~ sQ18_spl
| ~ sQ16_spl
| ~ sQ13_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ11_spl
| inverse(sk_c3) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1286,f436]) ).
fof(f1386,plain,
( ~ sQ12_spl
| ~ sQ18_spl
| ~ sQ16_spl
| ~ sQ13_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ11_spl
| sk_c3 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1290,f1385]) ).
fof(f1387,plain,
( ~ sQ12_spl
| ~ sQ18_spl
| ~ sQ16_spl
| ~ sQ13_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ11_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f1294,f1386]) ).
fof(f1388,plain,
( ~ sQ12_spl
| ~ sQ18_spl
| ~ sQ16_spl
| ~ sQ13_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1387]) ).
fof(f1389,plain,
( ~ sQ12_spl
| ~ sQ18_spl
| ~ sQ16_spl
| ~ sQ13_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f1388]) ).
fof(f1430,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ1_spl
| sk_c4 = sk_c3 ),
inference(paramodulation,[status(thm)],[f1288,f1322]) ).
fof(f1437,plain,
( sQ2_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ1_spl
| inverse(sk_c3) != sk_c3 ),
inference(backward_demodulation,[status(thm)],[f1430,f1304]) ).
fof(f1439,plain,
( sQ2_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ1_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f1290,f1437]) ).
fof(f1440,plain,
( sQ2_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1439]) ).
fof(f1441,plain,
( sQ2_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f1440]) ).
fof(f1442,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ13_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ11_spl
| multiply(sk_c3,X0) = multiply(sk_c5,multiply(sk_c11,X0)) ),
inference(forward_demodulation,[status(thm)],[f1296,f305]) ).
fof(f1443,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ13_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ11_spl
| X0 = multiply(sk_c5,multiply(sk_c11,X0)) ),
inference(forward_demodulation,[status(thm)],[f1213,f1442]) ).
fof(f1444,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ13_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ11_spl
| X0 = multiply(sk_c5,multiply(sk_c3,X0)) ),
inference(forward_demodulation,[status(thm)],[f1294,f1443]) ).
fof(f1445,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ13_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ11_spl
| X0 = multiply(sk_c5,X0) ),
inference(forward_demodulation,[status(thm)],[f1213,f1444]) ).
fof(f1483,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ13_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ11_spl
| X0 = multiply(inverse(sk_c5),X0) ),
inference(paramodulation,[status(thm)],[f1445,f304]) ).
fof(f1487,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ3_spl
| sk_c5 = sk_c3 ),
inference(paramodulation,[status(thm)],[f1288,f1483]) ).
fof(f1501,plain,
( sQ4_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ3_spl
| inverse(sk_c3) != sk_c3 ),
inference(backward_demodulation,[status(thm)],[f1487,f1291]) ).
fof(f1503,plain,
( sQ4_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ3_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f1290,f1501]) ).
fof(f1504,plain,
( sQ4_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1503]) ).
fof(f1505,plain,
( sQ4_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f1504]) ).
fof(f1571,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ11_spl
| sk_c9 = multiply(inverse(sk_c6),sk_c3) ),
inference(forward_demodulation,[status(thm)],[f1289,f470]) ).
fof(f1582,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| X0 = multiply(inverse(inverse(X0)),sk_c3) ),
inference(forward_demodulation,[status(thm)],[f1295,f468]) ).
fof(f1780,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| X0 = multiply(X0,sk_c3) ),
inference(backward_demodulation,[status(thm)],[f467,f1582]) ).
fof(f1793,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ11_spl
| sk_c9 = inverse(sk_c6) ),
inference(backward_demodulation,[status(thm)],[f1780,f1571]) ).
fof(f1801,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| multiply(X0,sk_c3) = inverse(inverse(X0)) ),
inference(paramodulation,[status(thm)],[f1780,f467]) ).
fof(f1806,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ11_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f1793,f173,f193,f150,f219,f258,f245,f232,f169]) ).
fof(f1808,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| X0 = inverse(inverse(X0)) ),
inference(forward_demodulation,[status(thm)],[f1780,f1801]) ).
fof(f1810,plain,
! [X0] : X0 = multiply(X0,identity),
inference(forward_demodulation,[status(thm)],[f467,f1103]) ).
fof(f1811,plain,
! [X0] : X0 = multiply(X0,identity),
inference(forward_demodulation,[status(thm)],[f467,f468]) ).
fof(f1813,plain,
( ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c8 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f472,f833]) ).
fof(f1819,plain,
( ~ sQ42_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c10 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f571,f809]) ).
fof(f1825,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| inverse(sk_c10) = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f582,f166]) ).
fof(f1826,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ42_spl
| inverse(sk_c10) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1819,f1825]) ).
fof(f1844,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| X0 = multiply(X0,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f489,f1810]) ).
fof(f1846,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| inverse(inverse(X0)) = multiply(X0,sk_c10) ),
inference(paramodulation,[status(thm)],[f467,f1844]) ).
fof(f1855,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| inverse(inverse(X0)) = X0 ),
inference(forward_demodulation,[status(thm)],[f1844,f1846]) ).
fof(f1886,definition,
( sQ70_spl
<=> inverse(sk_c10) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f1888,plain,
( sQ70_spl
| inverse(sk_c10) != sk_c10 ),
inference(component_clause,[status(thm)],[f1886]) ).
fof(f1905,plain,
( sQ70_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ42_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1826,f1888]) ).
fof(f1906,plain,
( sQ70_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ42_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1905]) ).
fof(f1907,plain,
( sQ70_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ42_spl ),
inference(contradiction_clause,[status(thm)],[f1906]) ).
fof(f1935,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c8) = sk_c6 ),
inference(paramodulation,[status(thm)],[f612,f1855]) ).
fof(f1941,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f182,f1935]) ).
fof(f1969,plain,
( ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c8 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1844,f700]) ).
fof(f1973,plain,
! [X0,X1] :
( ~ sQ20_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| inverse(X0) != sk_c10
| multiply(X0,inverse(X0)) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1844,f621]) ).
fof(f1974,plain,
! [X0,X1] :
( ~ sQ20_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| X1 != inverse(X0)
| inverse(X0) != sk_c10
| multiply(X0,inverse(X0)) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1855,f1973]) ).
fof(f1975,plain,
! [X0] :
( ~ sQ20_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(inverse(X0),inverse(X0)) != inverse(inverse(X0))
| inverse(X0) != sk_c10
| multiply(X0,inverse(X0)) != sk_c10 ),
inference(destructive_equality_resolution,[status(thm)],[f1974]) ).
fof(f1976,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ20_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(inverse(sk_c10),inverse(sk_c10)) != inverse(inverse(sk_c10))
| inverse(sk_c10) != sk_c10
| inverse(sk_c10) != sk_c10 ),
inference(paramodulation,[status(thm)],[f817,f1975]) ).
fof(f1982,definition,
( sQ77_spl
<=> multiply(inverse(sk_c10),inverse(sk_c10)) = inverse(inverse(sk_c10)) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f1984,plain,
( sQ77_spl
| multiply(inverse(sk_c10),inverse(sk_c10)) != inverse(inverse(sk_c10)) ),
inference(component_clause,[status(thm)],[f1982]) ).
fof(f1985,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ20_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ77_spl
| ~ sQ70_spl ),
inference(split_clause,[status(thm)],[f1976,f1886,f1982,f157,f153,f173,f169,f280,f165,f161]) ).
fof(f2003,plain,
( sQ77_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ42_spl
| multiply(sk_c10,inverse(sk_c10)) != inverse(inverse(sk_c10)) ),
inference(forward_demodulation,[status(thm)],[f1826,f1984]) ).
fof(f2004,plain,
( sQ77_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ42_spl
| inverse(sk_c10) != inverse(inverse(sk_c10)) ),
inference(forward_demodulation,[status(thm)],[f817,f2003]) ).
fof(f2005,plain,
( sQ77_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ42_spl
| sk_c10 != inverse(inverse(sk_c10)) ),
inference(forward_demodulation,[status(thm)],[f1826,f2004]) ).
fof(f2006,plain,
( sQ77_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ42_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1855,f2005]) ).
fof(f2007,plain,
( sQ77_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ42_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f2006]) ).
fof(f2008,plain,
( sQ77_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ42_spl ),
inference(contradiction_clause,[status(thm)],[f2007]) ).
fof(f2012,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c3 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f489,f1295]) ).
fof(f2056,plain,
! [X0] :
( ~ sQ43_spl
| ~ sQ16_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(X0,sk_c10) != inverse(X0)
| X0 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1855,f410]) ).
fof(f2057,plain,
! [X0] :
( ~ sQ43_spl
| ~ sQ16_spl
| ~ sQ3_spl
| ~ sQ4_spl
| X0 != inverse(X0)
| X0 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1844,f2056]) ).
fof(f2058,plain,
( ~ sQ43_spl
| ~ sQ16_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c10 != inverse(sk_c10) ),
inference(destructive_equality_resolution,[status(thm)],[f2057]) ).
fof(f2063,plain,
( ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c12 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f817,f1140]) ).
fof(f2103,plain,
( ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ13_spl
| sk_c12 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f2012,f2063]) ).
fof(f2107,plain,
( ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| inverse(sk_c3) = sk_c12 ),
inference(forward_demodulation,[status(thm)],[f1353,f194]) ).
fof(f2108,plain,
( ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ3_spl
| ~ sQ4_spl
| inverse(sk_c3) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f2103,f2107]) ).
fof(f2141,plain,
( ~ sQ43_spl
| ~ sQ16_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ13_spl
| sk_c3 != inverse(sk_c10) ),
inference(forward_demodulation,[status(thm)],[f2012,f2058]) ).
fof(f2142,plain,
( ~ sQ43_spl
| ~ sQ16_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ13_spl
| sk_c3 != inverse(sk_c3) ),
inference(forward_demodulation,[status(thm)],[f2012,f2141]) ).
fof(f2143,plain,
( ~ sQ43_spl
| ~ sQ16_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ13_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f2108,f2142]) ).
fof(f2144,plain,
( ~ sQ43_spl
| ~ sQ16_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ13_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f2143]) ).
fof(f2145,plain,
( ~ sQ43_spl
| ~ sQ16_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f2144]) ).
fof(f2183,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(inverse(X0),X0) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f1969,f498]) ).
fof(f2185,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| X0 = multiply(inverse(inverse(X0)),sk_c8) ),
inference(paramodulation,[status(thm)],[f2183,f304]) ).
fof(f2187,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| X0 = multiply(X0,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f1855,f2185]) ).
fof(f2204,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c8,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f1969,f817]) ).
fof(f2214,plain,
( ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c8,sk_c7) = sk_c8 ),
inference(paramodulation,[status(thm)],[f611,f2183]) ).
fof(f2217,plain,
( ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c7 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f2204,f2214]) ).
fof(f2233,plain,
( ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f2217,f1969]) ).
fof(f2234,plain,
( ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c7 = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f2217,f1813]) ).
fof(f2250,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c7) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1941,f174]) ).
fof(f2251,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c7) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f2234,f2250]) ).
fof(f2278,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| X0 = multiply(X0,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f2217,f2187]) ).
fof(f2362,plain,
! [X0] :
( ~ sQ19_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(X0) != sk_c10
| multiply(X0,sk_c7) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f2233,f670]) ).
fof(f2363,plain,
! [X0] :
( ~ sQ19_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(X0) != sk_c10
| X0 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f2278,f2362]) ).
fof(f2364,plain,
! [X0] :
( ~ sQ19_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(X0) != sk_c10
| X0 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f2233,f2363]) ).
fof(f2365,plain,
! [X0] :
( ~ sQ19_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(X0) != sk_c7
| X0 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f2233,f2364]) ).
fof(f2366,plain,
( ~ sQ19_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c7) != sk_c7 ),
inference(destructive_equality_resolution,[status(thm)],[f2365]) ).
fof(f2367,plain,
( ~ sQ19_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2366,f2251]) ).
fof(f2368,plain,
( ~ sQ19_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f2367]) ).
fof(f2372,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| sk_c3 = identity ),
inference(forward_demodulation,[status(thm)],[f1296,f1172]) ).
fof(f2380,plain,
( ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| inverse(sk_c3) = sk_c12 ),
inference(forward_demodulation,[status(thm)],[f1353,f194]) ).
fof(f2381,plain,
( ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| inverse(sk_c3) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f1289,f2380]) ).
fof(f2387,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| multiply(sk_c3,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f1296,f1183]) ).
fof(f2395,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| X0 = multiply(X0,sk_c3) ),
inference(forward_demodulation,[status(thm)],[f2372,f1811]) ).
fof(f2444,plain,
! [X0,X1] :
( ~ sQ20_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ11_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c10) != sk_c12
| multiply(X0,inverse(X0)) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f1289,f1158]) ).
fof(f2445,plain,
! [X0,X1] :
( ~ sQ20_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ11_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c3) != sk_c12
| multiply(X0,inverse(X0)) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f1296,f2444]) ).
fof(f2446,plain,
! [X0,X1] :
( ~ sQ20_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ11_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| inverse(X0) != sk_c12
| multiply(X0,inverse(X0)) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f2395,f2445]) ).
fof(f2447,plain,
! [X0,X1] :
( ~ sQ20_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ11_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| inverse(X0) != sk_c3
| multiply(X0,inverse(X0)) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f1289,f2446]) ).
fof(f2448,plain,
! [X0,X1] :
( ~ sQ20_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ11_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| X1 != inverse(X0)
| inverse(X0) != sk_c3
| multiply(X0,inverse(X0)) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f1808,f2447]) ).
fof(f2449,plain,
! [X0] :
( ~ sQ20_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ11_spl
| multiply(inverse(X0),inverse(X0)) != inverse(inverse(X0))
| inverse(X0) != sk_c3
| multiply(X0,inverse(X0)) != sk_c3 ),
inference(destructive_equality_resolution,[status(thm)],[f2448]) ).
fof(f2450,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ20_spl
| multiply(inverse(sk_c3),inverse(sk_c3)) != inverse(inverse(sk_c3))
| inverse(sk_c3) != sk_c3
| inverse(sk_c3) != sk_c3 ),
inference(paramodulation,[status(thm)],[f2387,f2449]) ).
fof(f2454,definition,
( sQ80_spl
<=> inverse(sk_c3) = sk_c3 ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f2456,plain,
( sQ80_spl
| inverse(sk_c3) != sk_c3 ),
inference(component_clause,[status(thm)],[f2454]) ).
fof(f2457,definition,
( sQ81_spl
<=> multiply(inverse(sk_c3),inverse(sk_c3)) = inverse(inverse(sk_c3)) ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f2459,plain,
( sQ81_spl
| multiply(inverse(sk_c3),inverse(sk_c3)) != inverse(inverse(sk_c3)) ),
inference(component_clause,[status(thm)],[f2457]) ).
fof(f2460,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ20_spl
| ~ sQ81_spl
| ~ sQ80_spl ),
inference(split_clause,[status(thm)],[f2450,f2454,f2457,f280,f219,f232,f258,f245,f193,f150]) ).
fof(f2468,plain,
( sQ80_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f2381,f2456]) ).
fof(f2469,plain,
( sQ80_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f2468]) ).
fof(f2470,plain,
( sQ80_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f2469]) ).
fof(f2471,plain,
( sQ81_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| multiply(sk_c3,inverse(sk_c3)) != inverse(inverse(sk_c3)) ),
inference(forward_demodulation,[status(thm)],[f2381,f2459]) ).
fof(f2472,plain,
( sQ81_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| inverse(sk_c3) != inverse(inverse(sk_c3)) ),
inference(forward_demodulation,[status(thm)],[f2387,f2471]) ).
fof(f2473,plain,
( sQ81_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| sk_c3 != inverse(inverse(sk_c3)) ),
inference(forward_demodulation,[status(thm)],[f2381,f2472]) ).
fof(f2474,plain,
( sQ81_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f1808,f2473]) ).
fof(f2475,plain,
( sQ81_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f2474]) ).
fof(f2476,plain,
( sQ81_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f2475]) ).
fof(f2477,plain,
$false,
inference(sat_refutation,[status(thm)],[f156,f160,f164,f168,f172,f176,f180,f184,f188,f196,f197,f198,f199,f200,f201,f202,f203,f204,f209,f211,f222,f223,f224,f225,f226,f227,f235,f236,f237,f238,f239,f240,f248,f249,f250,f251,f252,f253,f254,f255,f256,f261,f262,f263,f264,f265,f266,f267,f268,f269,f270,f283,f350,f391,f408,f414,f420,f422,f445,f479,f509,f530,f563,f758,f1155,f1157,f1328,f1389,f1441,f1505,f1806,f1907,f1985,f2008,f2145,f2368,f2460,f2470,f2476]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP258-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 20:06:06 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.14/0.48 % Refutation found
% 0.14/0.48 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.50 % Elapsed time: 0.120353 seconds
% 0.14/0.50 % CPU time: 0.708891 seconds
% 0.14/0.50 % Total memory used: 120.983 MB
% 0.14/0.50 % Net memory used: 120.251 MB
%------------------------------------------------------------------------------