%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP307-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:33:22 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.45s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 98
% Syntax : Number of formulae : 564 ( 11 unt; 45 def)
% Number of atoms : 2338 ( 647 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 3379 (1605 ~;1729 |; 0 &)
% ( 45 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 47 ( 45 usr; 46 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 116 ( 116 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c11,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c11,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c11,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c11,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c11,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c11,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c11,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c11) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c3) = sk_c11
| inverse(sk_c11) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c11) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c11) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| inverse(sk_c11) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c11) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| inverse(sk_c11) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c7) = sk_c6
| inverse(sk_c11) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( inverse(sk_c6) = sk_c8
| inverse(sk_c11) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c11) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c9,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c9,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c11,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c11,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c11,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c11,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c11,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c11,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c11,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,negated_conjecture,
( inverse(sk_c7) = sk_c6
| multiply(sk_c11,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,negated_conjecture,
( inverse(sk_c6) = sk_c8
| multiply(sk_c11,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c11,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c1,sk_c11) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c11) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f51,negated_conjecture,
( inverse(sk_c7) = sk_c6
| multiply(sk_c1,sk_c11) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f52,negated_conjecture,
( inverse(sk_c6) = sk_c8
| multiply(sk_c1,sk_c11) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f53,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c1,sk_c11) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f55,negated_conjecture,
( inverse(sk_c3) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f56,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f57,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f58,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f59,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f60,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f61,negated_conjecture,
( inverse(sk_c7) = sk_c6
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f62,negated_conjecture,
( inverse(sk_c6) = sk_c8
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f63,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f64,negated_conjecture,
! [X3,X4,X1,X2,X5,X6,X7,X8] :
( multiply(X7,X6) != X8
| inverse(X8) != X6
| inverse(X7) != X8
| multiply(X6,sk_c10) != sk_c11
| inverse(X5) != X6
| multiply(X5,X6) != sk_c11
| inverse(X2) != sk_c10
| multiply(X2,sk_c10) != sk_c9
| inverse(X1) != sk_c11
| multiply(X1,sk_c11) != sk_c10
| inverse(X4) != sk_c11
| multiply(X4,sk_c11) != X3
| multiply(sk_c11,X3) != sk_c10
| multiply(sk_c9,sk_c10) != sk_c11
| inverse(sk_c11) != sk_c9
| multiply(sk_c11,sk_c10) != sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f65,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f66,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f67,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f68,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c11,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f69,plain,
( inverse(sk_c3) = sk_c11
| multiply(sk_c11,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f70,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c11,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f71,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c11,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f72,plain,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c11,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f73,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c11,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f74,plain,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c11,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f78,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c11) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f79,plain,
( inverse(sk_c3) = sk_c11
| inverse(sk_c11) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f80,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c11) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f81,plain,
( inverse(sk_c4) = sk_c10
| inverse(sk_c11) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f82,plain,
( multiply(sk_c5,sk_c8) = sk_c11
| inverse(sk_c11) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f83,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c11) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f84,plain,
( multiply(sk_c8,sk_c10) = sk_c11
| inverse(sk_c11) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f85,plain,
( inverse(sk_c7) = sk_c6
| inverse(sk_c11) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f86,plain,
( inverse(sk_c6) = sk_c8
| inverse(sk_c11) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f87,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c11) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f88,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c9,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f89,plain,
( inverse(sk_c3) = sk_c11
| multiply(sk_c9,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f98,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c11,sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f99,plain,
( inverse(sk_c3) = sk_c11
| multiply(sk_c11,sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f100,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c11,sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f101,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c11,sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f102,plain,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c11,sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f103,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c11,sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f104,plain,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c11,sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f105,plain,
( inverse(sk_c7) = sk_c6
| multiply(sk_c11,sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f106,plain,
( inverse(sk_c6) = sk_c8
| multiply(sk_c11,sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f107,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c11,sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f108,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f109,plain,
( inverse(sk_c3) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f110,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c1,sk_c11) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f111,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f112,plain,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f113,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c11) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f114,plain,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f115,plain,
( inverse(sk_c7) = sk_c6
| multiply(sk_c1,sk_c11) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f116,plain,
( inverse(sk_c6) = sk_c8
| multiply(sk_c1,sk_c11) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f117,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c1,sk_c11) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f118,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f119,plain,
( inverse(sk_c3) = sk_c11
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f120,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f121,plain,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f122,plain,
( multiply(sk_c5,sk_c8) = sk_c11
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f123,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f124,plain,
( multiply(sk_c8,sk_c10) = sk_c11
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f125,plain,
( inverse(sk_c7) = sk_c6
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f126,plain,
( inverse(sk_c6) = sk_c8
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f127,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f63]) ).
fof(f128,plain,
! [X6,X7,X8] :
( multiply(X7,X6) != X8
| inverse(X8) != X6
| inverse(X7) != X8
| multiply(X6,sk_c10) != sk_c11
| ! [X5] :
( inverse(X5) != X6
| multiply(X5,X6) != sk_c11
| ! [X2] :
( inverse(X2) != sk_c10
| multiply(X2,sk_c10) != sk_c9
| ! [X1] :
( inverse(X1) != sk_c11
| multiply(X1,sk_c11) != sk_c10
| ! [X4] :
( inverse(X4) != sk_c11
| ! [X3] :
( multiply(X4,sk_c11) != X3
| multiply(sk_c11,X3) != sk_c10
| multiply(sk_c9,sk_c10) != sk_c11
| inverse(sk_c11) != sk_c9
| multiply(sk_c11,sk_c10) != sk_c9 ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f64]) ).
fof(f129,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( multiply(X6,X5) != X7
| inverse(X7) != X5
| inverse(X6) != X7
| multiply(X5,sk_c10) != sk_c11
| inverse(X4) != X5
| multiply(X4,X5) != sk_c11
| inverse(X3) != sk_c10
| multiply(X3,sk_c10) != sk_c9
| inverse(X2) != sk_c11
| multiply(X2,sk_c11) != sk_c10
| inverse(X1) != sk_c11
| multiply(X1,sk_c11) != X0
| multiply(sk_c11,X0) != sk_c10
| multiply(sk_c9,sk_c10) != sk_c11
| inverse(sk_c11) != sk_c9
| multiply(sk_c11,sk_c10) != sk_c9 ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f130,definition,
( sQ0_spl
<=> multiply(sk_c11,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f131,plain,
( ~ sQ0_spl
| multiply(sk_c11,sk_c10) = sk_c9 ),
inference(component_clause,[status(thm)],[f130]) ).
fof(f132,plain,
( sQ0_spl
| multiply(sk_c11,sk_c10) != sk_c9 ),
inference(component_clause,[status(thm)],[f130]) ).
fof(f133,definition,
( sQ1_spl
<=> multiply(sk_c3,sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f134,plain,
( ~ sQ1_spl
| multiply(sk_c3,sk_c11) = sk_c10 ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f68,f130,f133]) ).
fof(f137,definition,
( sQ2_spl
<=> inverse(sk_c3) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f138,plain,
( ~ sQ2_spl
| inverse(sk_c3) = sk_c11 ),
inference(component_clause,[status(thm)],[f137]) ).
fof(f140,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f69,f130,f137]) ).
fof(f141,definition,
( sQ3_spl
<=> multiply(sk_c4,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f142,plain,
( ~ sQ3_spl
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(component_clause,[status(thm)],[f141]) ).
fof(f144,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f70,f130,f141]) ).
fof(f145,definition,
( sQ4_spl
<=> inverse(sk_c4) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f146,plain,
( ~ sQ4_spl
| inverse(sk_c4) = sk_c10 ),
inference(component_clause,[status(thm)],[f145]) ).
fof(f148,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f71,f130,f145]) ).
fof(f149,definition,
( sQ5_spl
<=> multiply(sk_c5,sk_c8) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f150,plain,
( ~ sQ5_spl
| multiply(sk_c5,sk_c8) = sk_c11 ),
inference(component_clause,[status(thm)],[f149]) ).
fof(f152,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f72,f130,f149]) ).
fof(f153,definition,
( sQ6_spl
<=> inverse(sk_c5) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f154,plain,
( ~ sQ6_spl
| inverse(sk_c5) = sk_c8 ),
inference(component_clause,[status(thm)],[f153]) ).
fof(f156,plain,
( sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f73,f130,f153]) ).
fof(f157,definition,
( sQ7_spl
<=> multiply(sk_c8,sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f158,plain,
( ~ sQ7_spl
| multiply(sk_c8,sk_c10) = sk_c11 ),
inference(component_clause,[status(thm)],[f157]) ).
fof(f160,plain,
( sQ7_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f74,f130,f157]) ).
fof(f161,definition,
( sQ8_spl
<=> inverse(sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f162,plain,
( ~ sQ8_spl
| inverse(sk_c7) = sk_c6 ),
inference(component_clause,[status(thm)],[f161]) ).
fof(f165,definition,
( sQ9_spl
<=> inverse(sk_c6) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f166,plain,
( ~ sQ9_spl
| inverse(sk_c6) = sk_c8 ),
inference(component_clause,[status(thm)],[f165]) ).
fof(f169,definition,
( sQ10_spl
<=> multiply(sk_c7,sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f170,plain,
( ~ sQ10_spl
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(component_clause,[status(thm)],[f169]) ).
fof(f173,definition,
( sQ11_spl
<=> inverse(sk_c11) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f174,plain,
( ~ sQ11_spl
| inverse(sk_c11) = sk_c9 ),
inference(component_clause,[status(thm)],[f173]) ).
fof(f175,plain,
( sQ11_spl
| inverse(sk_c11) != sk_c9 ),
inference(component_clause,[status(thm)],[f173]) ).
fof(f176,plain,
( sQ1_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f78,f173,f133]) ).
fof(f177,plain,
( sQ2_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f79,f173,f137]) ).
fof(f178,plain,
( sQ3_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f80,f173,f141]) ).
fof(f179,plain,
( sQ4_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f81,f173,f145]) ).
fof(f180,plain,
( sQ5_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f82,f173,f149]) ).
fof(f181,plain,
( sQ6_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f83,f173,f153]) ).
fof(f182,plain,
( sQ7_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f84,f173,f157]) ).
fof(f183,plain,
( sQ8_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f85,f173,f161]) ).
fof(f184,plain,
( sQ9_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f86,f173,f165]) ).
fof(f185,plain,
( sQ10_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f87,f173,f169]) ).
fof(f186,definition,
( sQ12_spl
<=> multiply(sk_c9,sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f187,plain,
( ~ sQ12_spl
| multiply(sk_c9,sk_c10) = sk_c11 ),
inference(component_clause,[status(thm)],[f186]) ).
fof(f189,plain,
( sQ1_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f88,f186,f133]) ).
fof(f190,plain,
( sQ2_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f89,f186,f137]) ).
fof(f199,definition,
( sQ13_spl
<=> multiply(sk_c11,sk_c2) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f200,plain,
( ~ sQ13_spl
| multiply(sk_c11,sk_c2) = sk_c10 ),
inference(component_clause,[status(thm)],[f199]) ).
fof(f202,plain,
( sQ1_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f98,f199,f133]) ).
fof(f203,plain,
( sQ2_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f99,f199,f137]) ).
fof(f204,plain,
( sQ3_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f100,f199,f141]) ).
fof(f205,plain,
( sQ4_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f101,f199,f145]) ).
fof(f206,plain,
( sQ5_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f102,f199,f149]) ).
fof(f207,plain,
( sQ6_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f103,f199,f153]) ).
fof(f208,plain,
( sQ7_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f104,f199,f157]) ).
fof(f209,plain,
( sQ8_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f105,f199,f161]) ).
fof(f210,plain,
( sQ9_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f106,f199,f165]) ).
fof(f211,plain,
( sQ10_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f107,f199,f169]) ).
fof(f212,definition,
( sQ14_spl
<=> multiply(sk_c1,sk_c11) = sk_c2 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f213,plain,
( ~ sQ14_spl
| multiply(sk_c1,sk_c11) = sk_c2 ),
inference(component_clause,[status(thm)],[f212]) ).
fof(f215,plain,
( sQ1_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f108,f212,f133]) ).
fof(f216,plain,
( sQ2_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f109,f212,f137]) ).
fof(f217,plain,
( sQ3_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f110,f212,f141]) ).
fof(f218,plain,
( sQ4_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f111,f212,f145]) ).
fof(f219,plain,
( sQ5_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f112,f212,f149]) ).
fof(f220,plain,
( sQ6_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f113,f212,f153]) ).
fof(f221,plain,
( sQ7_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f114,f212,f157]) ).
fof(f222,plain,
( sQ8_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f115,f212,f161]) ).
fof(f223,plain,
( sQ9_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f116,f212,f165]) ).
fof(f224,plain,
( sQ10_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f117,f212,f169]) ).
fof(f225,definition,
( sQ15_spl
<=> inverse(sk_c1) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f226,plain,
( ~ sQ15_spl
| inverse(sk_c1) = sk_c11 ),
inference(component_clause,[status(thm)],[f225]) ).
fof(f228,plain,
( sQ1_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f118,f225,f133]) ).
fof(f229,plain,
( sQ2_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f119,f225,f137]) ).
fof(f230,plain,
( sQ3_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f120,f225,f141]) ).
fof(f231,plain,
( sQ4_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f121,f225,f145]) ).
fof(f232,plain,
( sQ5_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f122,f225,f149]) ).
fof(f233,plain,
( sQ6_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f123,f225,f153]) ).
fof(f234,plain,
( sQ7_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f124,f225,f157]) ).
fof(f235,plain,
( sQ8_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f125,f225,f161]) ).
fof(f236,plain,
( sQ9_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f126,f225,f165]) ).
fof(f237,plain,
( sQ10_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f127,f225,f169]) ).
fof(f238,definition,
! [X0,X1] :
( sQ16_spl
<=> ( inverse(X1) != sk_c11
| multiply(X1,sk_c11) != X0
| multiply(sk_c11,X0) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f239,plain,
! [X0,X1] :
( ~ sQ16_spl
| inverse(X1) != sk_c11
| multiply(X1,sk_c11) != X0
| multiply(sk_c11,X0) != sk_c10 ),
inference(component_clause,[status(thm)],[f238]) ).
fof(f241,definition,
! [X2] :
( sQ17_spl
<=> ( inverse(X2) != sk_c11
| multiply(X2,sk_c11) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f242,plain,
! [X0] :
( ~ sQ17_spl
| inverse(X0) != sk_c11
| multiply(X0,sk_c11) != sk_c10 ),
inference(component_clause,[status(thm)],[f241]) ).
fof(f244,definition,
! [X3] :
( sQ18_spl
<=> ( inverse(X3) != sk_c10
| multiply(X3,sk_c10) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f245,plain,
! [X0] :
( ~ sQ18_spl
| inverse(X0) != sk_c10
| multiply(X0,sk_c10) != sk_c9 ),
inference(component_clause,[status(thm)],[f244]) ).
fof(f247,definition,
! [X4,X5,X6,X7] :
( sQ19_spl
<=> ( multiply(X6,X5) != X7
| inverse(X7) != X5
| inverse(X6) != X7
| multiply(X5,sk_c10) != sk_c11
| inverse(X4) != X5
| multiply(X4,X5) != sk_c11 ) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f248,plain,
! [X0,X1,X2,X3] :
( ~ sQ19_spl
| multiply(X2,X1) != X3
| inverse(X3) != X1
| inverse(X2) != X3
| multiply(X1,sk_c10) != sk_c11
| inverse(X0) != X1
| multiply(X0,X1) != sk_c11 ),
inference(component_clause,[status(thm)],[f247]) ).
fof(f250,plain,
( sQ19_spl
| sQ18_spl
| sQ17_spl
| sQ16_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f129,f130,f173,f186,f238,f241,f244,f247]) ).
fof(f251,plain,
! [X0,X1] :
( ~ sQ19_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c10) != sk_c11
| multiply(X0,inverse(X0)) != sk_c11 ),
inference(destructive_equality_resolution,[status(thm)],[f248]) ).
fof(f253,plain,
! [X0] :
( ~ sQ14_spl
| multiply(sk_c2,X0) = multiply(sk_c1,multiply(sk_c11,X0)) ),
inference(paramodulation,[status(thm)],[f213,f67]) ).
fof(f256,plain,
! [X0] :
( ~ sQ13_spl
| multiply(sk_c10,X0) = multiply(sk_c11,multiply(sk_c2,X0)) ),
inference(paramodulation,[status(thm)],[f200,f67]) ).
fof(f258,plain,
( ~ sQ4_spl
| multiply(sk_c10,sk_c4) = identity ),
inference(paramodulation,[status(thm)],[f146,f66]) ).
fof(f259,plain,
( ~ sQ6_spl
| multiply(sk_c8,sk_c5) = identity ),
inference(paramodulation,[status(thm)],[f154,f66]) ).
fof(f261,plain,
( ~ sQ9_spl
| multiply(sk_c8,sk_c6) = identity ),
inference(paramodulation,[status(thm)],[f166,f66]) ).
fof(f262,plain,
( ~ sQ15_spl
| multiply(sk_c11,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f226,f66]) ).
fof(f263,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f66,f67]) ).
fof(f264,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f65,f263]) ).
fof(f265,plain,
! [X0] :
( ~ sQ10_spl
| multiply(sk_c6,X0) = multiply(sk_c7,multiply(sk_c8,X0)) ),
inference(paramodulation,[status(thm)],[f170,f67]) ).
fof(f266,plain,
! [X0] :
( ~ sQ7_spl
| multiply(sk_c11,X0) = multiply(sk_c8,multiply(sk_c10,X0)) ),
inference(paramodulation,[status(thm)],[f158,f67]) ).
fof(f267,plain,
( ~ sQ2_spl
| multiply(sk_c11,sk_c3) = identity ),
inference(paramodulation,[status(thm)],[f138,f66]) ).
fof(f268,plain,
( ~ sQ11_spl
| multiply(sk_c9,sk_c11) = identity ),
inference(paramodulation,[status(thm)],[f174,f66]) ).
fof(f269,plain,
! [X0] :
( ~ sQ5_spl
| multiply(sk_c11,X0) = multiply(sk_c5,multiply(sk_c8,X0)) ),
inference(paramodulation,[status(thm)],[f150,f67]) ).
fof(f270,plain,
! [X0] :
( ~ sQ3_spl
| multiply(sk_c9,X0) = multiply(sk_c4,multiply(sk_c10,X0)) ),
inference(paramodulation,[status(thm)],[f142,f67]) ).
fof(f271,plain,
! [X0] :
( ~ sQ1_spl
| multiply(sk_c10,X0) = multiply(sk_c3,multiply(sk_c11,X0)) ),
inference(paramodulation,[status(thm)],[f134,f67]) ).
fof(f272,plain,
( ~ sQ19_spl
| inverse(inverse(identity)) != inverse(identity)
| multiply(inverse(identity),sk_c10) != sk_c11
| multiply(identity,inverse(identity)) != sk_c11 ),
inference(resolution,[status(thm)],[f251,f65]) ).
fof(f273,plain,
! [X0] :
( ~ sQ19_spl
| multiply(X0,inverse(identity)) != inverse(X0)
| inverse(inverse(X0)) != inverse(identity)
| multiply(inverse(identity),sk_c10) != sk_c11
| inverse(identity) != sk_c11 ),
inference(paramodulation,[status(thm)],[f65,f251]) ).
fof(f275,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ19_spl
| multiply(X0,inverse(sk_c11)) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c11)
| multiply(inverse(sk_c11),sk_c10) != sk_c11
| multiply(sk_c11,sk_c9) != sk_c11 ),
inference(paramodulation,[status(thm)],[f174,f251]) ).
fof(f276,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ19_spl
| multiply(X0,inverse(sk_c3)) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c3)
| multiply(inverse(sk_c3),sk_c10) != sk_c11
| multiply(sk_c3,sk_c11) != sk_c11 ),
inference(paramodulation,[status(thm)],[f138,f251]) ).
fof(f277,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ19_spl
| multiply(X0,inverse(sk_c4)) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c4)
| multiply(inverse(sk_c4),sk_c10) != sk_c11
| multiply(sk_c4,sk_c10) != sk_c11 ),
inference(paramodulation,[status(thm)],[f146,f251]) ).
fof(f278,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ19_spl
| multiply(X0,inverse(sk_c5)) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c5)
| multiply(inverse(sk_c5),sk_c10) != sk_c11
| multiply(sk_c5,sk_c8) != sk_c11 ),
inference(paramodulation,[status(thm)],[f154,f251]) ).
fof(f282,definition,
( sQ20_spl
<=> multiply(identity,inverse(identity)) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f284,plain,
( sQ20_spl
| multiply(identity,inverse(identity)) != sk_c11 ),
inference(component_clause,[status(thm)],[f282]) ).
fof(f285,definition,
( sQ21_spl
<=> multiply(inverse(identity),sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f287,plain,
( sQ21_spl
| multiply(inverse(identity),sk_c10) != sk_c11 ),
inference(component_clause,[status(thm)],[f285]) ).
fof(f288,definition,
( sQ22_spl
<=> inverse(inverse(identity)) = inverse(identity) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f290,plain,
( sQ22_spl
| inverse(inverse(identity)) != inverse(identity) ),
inference(component_clause,[status(thm)],[f288]) ).
fof(f291,plain,
( ~ sQ19_spl
| ~ sQ22_spl
| ~ sQ21_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f272,f282,f285,f288,f247]) ).
fof(f292,definition,
( sQ23_spl
<=> inverse(identity) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f294,plain,
( sQ23_spl
| inverse(identity) != sk_c11 ),
inference(component_clause,[status(thm)],[f292]) ).
fof(f295,definition,
! [X0] :
( sQ24_spl
<=> ( multiply(X0,inverse(identity)) != inverse(X0)
| inverse(inverse(X0)) != inverse(identity) ) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f298,plain,
( ~ sQ19_spl
| sQ24_spl
| ~ sQ21_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f273,f292,f285,f295,f247]) ).
fof(f299,definition,
( sQ25_spl
<=> multiply(sk_c11,sk_c9) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f301,plain,
( sQ25_spl
| multiply(sk_c11,sk_c9) != sk_c11 ),
inference(component_clause,[status(thm)],[f299]) ).
fof(f302,definition,
( sQ26_spl
<=> multiply(inverse(sk_c11),sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f303,plain,
( ~ sQ26_spl
| multiply(inverse(sk_c11),sk_c10) = sk_c11 ),
inference(component_clause,[status(thm)],[f302]) ).
fof(f304,plain,
( sQ26_spl
| multiply(inverse(sk_c11),sk_c10) != sk_c11 ),
inference(component_clause,[status(thm)],[f302]) ).
fof(f305,definition,
! [X0] :
( sQ27_spl
<=> ( multiply(X0,inverse(sk_c11)) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c11) ) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f308,plain,
( ~ sQ11_spl
| ~ sQ19_spl
| sQ27_spl
| ~ sQ26_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f275,f299,f302,f305,f247,f173]) ).
fof(f309,definition,
( sQ28_spl
<=> multiply(sk_c3,sk_c11) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f311,plain,
( sQ28_spl
| multiply(sk_c3,sk_c11) != sk_c11 ),
inference(component_clause,[status(thm)],[f309]) ).
fof(f312,definition,
( sQ29_spl
<=> multiply(inverse(sk_c3),sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f313,plain,
( ~ sQ29_spl
| multiply(inverse(sk_c3),sk_c10) = sk_c11 ),
inference(component_clause,[status(thm)],[f312]) ).
fof(f314,plain,
( sQ29_spl
| multiply(inverse(sk_c3),sk_c10) != sk_c11 ),
inference(component_clause,[status(thm)],[f312]) ).
fof(f315,definition,
! [X0] :
( sQ30_spl
<=> ( multiply(X0,inverse(sk_c3)) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c3) ) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f316,plain,
! [X0] :
( ~ sQ30_spl
| multiply(X0,inverse(sk_c3)) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c3) ),
inference(component_clause,[status(thm)],[f315]) ).
fof(f318,plain,
( ~ sQ2_spl
| ~ sQ19_spl
| sQ30_spl
| ~ sQ29_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f276,f309,f312,f315,f247,f137]) ).
fof(f319,definition,
( sQ31_spl
<=> multiply(sk_c4,sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f322,definition,
( sQ32_spl
<=> multiply(inverse(sk_c4),sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f324,plain,
( sQ32_spl
| multiply(inverse(sk_c4),sk_c10) != sk_c11 ),
inference(component_clause,[status(thm)],[f322]) ).
fof(f325,definition,
! [X0] :
( sQ33_spl
<=> ( multiply(X0,inverse(sk_c4)) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c4) ) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f328,plain,
( ~ sQ4_spl
| ~ sQ19_spl
| sQ33_spl
| ~ sQ32_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f277,f319,f322,f325,f247,f145]) ).
fof(f329,definition,
( sQ34_spl
<=> multiply(inverse(sk_c5),sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f331,plain,
( sQ34_spl
| multiply(inverse(sk_c5),sk_c10) != sk_c11 ),
inference(component_clause,[status(thm)],[f329]) ).
fof(f332,definition,
! [X0] :
( sQ35_spl
<=> ( multiply(X0,inverse(sk_c5)) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c5) ) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f335,plain,
( ~ sQ6_spl
| ~ sQ19_spl
| sQ35_spl
| ~ sQ34_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f278,f149,f329,f332,f247,f153]) ).
fof(f372,plain,
( sQ28_spl
| ~ sQ1_spl
| sk_c10 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f134,f311]) ).
fof(f375,plain,
( sQ26_spl
| ~ sQ11_spl
| multiply(sk_c9,sk_c10) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f174,f304]) ).
fof(f376,plain,
( sQ26_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f187,f375]) ).
fof(f377,plain,
( sQ26_spl
| ~ sQ11_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f376]) ).
fof(f378,plain,
( sQ26_spl
| ~ sQ11_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f377]) ).
fof(f379,plain,
! [X0] :
( ~ sQ30_spl
| ~ sQ2_spl
| multiply(X0,sk_c11) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c3) ),
inference(backward_demodulation,[status(thm)],[f138,f316]) ).
fof(f380,plain,
( sQ32_spl
| ~ sQ4_spl
| multiply(sk_c10,sk_c10) != sk_c11 ),
inference(backward_demodulation,[status(thm)],[f146,f324]) ).
fof(f382,plain,
( sQ34_spl
| ~ sQ6_spl
| multiply(sk_c8,sk_c10) != sk_c11 ),
inference(backward_demodulation,[status(thm)],[f154,f331]) ).
fof(f388,plain,
! [X0] :
( ~ sQ30_spl
| ~ sQ2_spl
| multiply(X0,sk_c11) != inverse(X0)
| inverse(inverse(X0)) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f138,f379]) ).
fof(f390,plain,
( sQ34_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f158,f382]) ).
fof(f391,plain,
( sQ34_spl
| ~ sQ6_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f390]) ).
fof(f392,plain,
( sQ34_spl
| ~ sQ6_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f391]) ).
fof(f394,plain,
! [X0] :
( ~ sQ12_spl
| multiply(sk_c11,X0) = multiply(sk_c9,multiply(sk_c10,X0)) ),
inference(paramodulation,[status(thm)],[f187,f67]) ).
fof(f400,plain,
! [X0] :
( ~ sQ15_spl
| multiply(identity,X0) = multiply(sk_c11,multiply(sk_c1,X0)) ),
inference(paramodulation,[status(thm)],[f262,f67]) ).
fof(f401,plain,
! [X0] :
( ~ sQ15_spl
| X0 = multiply(sk_c11,multiply(sk_c1,X0)) ),
inference(forward_demodulation,[status(thm)],[f65,f400]) ).
fof(f402,plain,
! [X0] :
( ~ sQ2_spl
| multiply(identity,X0) = multiply(sk_c11,multiply(sk_c3,X0)) ),
inference(paramodulation,[status(thm)],[f267,f67]) ).
fof(f403,plain,
! [X0] :
( ~ sQ2_spl
| X0 = multiply(sk_c11,multiply(sk_c3,X0)) ),
inference(forward_demodulation,[status(thm)],[f65,f402]) ).
fof(f408,plain,
( ~ sQ15_spl
| ~ sQ14_spl
| multiply(sk_c2,sk_c1) = multiply(sk_c1,identity) ),
inference(paramodulation,[status(thm)],[f262,f253]) ).
fof(f420,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| multiply(sk_c6,sk_c10) = multiply(sk_c7,sk_c11) ),
inference(paramodulation,[status(thm)],[f158,f265]) ).
fof(f424,plain,
( ~ sQ4_spl
| ~ sQ7_spl
| multiply(sk_c11,sk_c4) = multiply(sk_c8,identity) ),
inference(paramodulation,[status(thm)],[f258,f266]) ).
fof(f429,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| multiply(sk_c9,sk_c4) = multiply(sk_c4,identity) ),
inference(paramodulation,[status(thm)],[f258,f270]) ).
fof(f434,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| multiply(sk_c10,sk_c3) = multiply(sk_c3,identity) ),
inference(paramodulation,[status(thm)],[f267,f271]) ).
fof(f444,plain,
( ~ sQ7_spl
| ~ sQ5_spl
| multiply(sk_c11,sk_c10) = multiply(sk_c5,sk_c11) ),
inference(paramodulation,[status(thm)],[f158,f269]) ).
fof(f448,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| multiply(sk_c11,sk_c5) = multiply(sk_c5,identity) ),
inference(paramodulation,[status(thm)],[f259,f269]) ).
fof(f449,plain,
( ~ sQ6_spl
| ~ sQ10_spl
| multiply(sk_c6,sk_c5) = multiply(sk_c7,identity) ),
inference(paramodulation,[status(thm)],[f259,f265]) ).
fof(f454,plain,
( ~ sQ9_spl
| ~ sQ5_spl
| multiply(sk_c11,sk_c6) = multiply(sk_c5,identity) ),
inference(paramodulation,[status(thm)],[f261,f269]) ).
fof(f455,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c6,sk_c6) = multiply(sk_c7,identity) ),
inference(paramodulation,[status(thm)],[f261,f265]) ).
fof(f458,plain,
( ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c11,sk_c6) = multiply(sk_c11,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f448,f454]) ).
fof(f460,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ6_spl
| multiply(sk_c6,sk_c6) = multiply(sk_c6,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f449,f455]) ).
fof(f464,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ15_spl
| multiply(sk_c11,X0) = multiply(sk_c11,multiply(sk_c2,X0)) ),
inference(paramodulation,[status(thm)],[f253,f401]) ).
fof(f465,plain,
( ~ sQ14_spl
| ~ sQ15_spl
| sk_c11 = multiply(sk_c11,sk_c2) ),
inference(paramodulation,[status(thm)],[f213,f401]) ).
fof(f481,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| multiply(sk_c11,X0) = multiply(sk_c9,multiply(sk_c11,X0)) ),
inference(backward_demodulation,[status(thm)],[f482,f394]) ).
fof(f482,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| multiply(sk_c11,X0) = multiply(sk_c10,X0) ),
inference(forward_demodulation,[status(thm)],[f256,f464]) ).
fof(f493,plain,
( ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| sk_c11 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f200,f465]) ).
fof(f602,plain,
( sQ21_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| multiply(inverse(identity),sk_c11) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f493,f287]) ).
fof(f613,plain,
( sQ28_spl
| ~ sQ1_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f493,f372]) ).
fof(f614,plain,
( sQ28_spl
| ~ sQ1_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f613]) ).
fof(f615,plain,
( sQ28_spl
| ~ sQ1_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f614]) ).
fof(f626,plain,
( ~ sQ26_spl
| ~ sQ11_spl
| multiply(sk_c9,sk_c10) = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f174,f303]) ).
fof(f627,plain,
( ~ sQ26_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| multiply(sk_c9,sk_c11) = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f493,f626]) ).
fof(f630,plain,
( sQ22_spl
| ~ sQ26_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| inverse(inverse(identity)) != inverse(sk_c11) ),
inference(backward_demodulation,[status(thm)],[f634,f290]) ).
fof(f631,plain,
( sQ23_spl
| ~ sQ26_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| inverse(sk_c11) != sk_c11 ),
inference(backward_demodulation,[status(thm)],[f634,f294]) ).
fof(f633,plain,
( sQ21_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ26_spl
| ~ sQ11_spl
| multiply(inverse(sk_c11),sk_c11) != sk_c11 ),
inference(backward_demodulation,[status(thm)],[f634,f602]) ).
fof(f634,plain,
( ~ sQ26_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| identity = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f268,f627]) ).
fof(f635,plain,
( ~ sQ15_spl
| ~ sQ26_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ13_spl
| multiply(sk_c11,sk_c1) = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f634,f262]) ).
fof(f638,plain,
! [X0] :
( ~ sQ26_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| multiply(inverse(X0),X0) = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f634,f66]) ).
fof(f640,plain,
( ~ sQ15_spl
| ~ sQ26_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ13_spl
| sk_c1 = sk_c11 ),
inference(backward_demodulation,[status(thm)],[f651,f635]) ).
fof(f644,plain,
( sQ25_spl
| ~ sQ26_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| sk_c9 != sk_c11 ),
inference(backward_demodulation,[status(thm)],[f651,f301]) ).
fof(f648,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ26_spl
| ~ sQ11_spl
| multiply(sk_c11,X0) = multiply(sk_c9,X0) ),
inference(backward_demodulation,[status(thm)],[f651,f481]) ).
fof(f649,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ26_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ13_spl
| multiply(sk_c2,X0) = multiply(sk_c1,X0) ),
inference(backward_demodulation,[status(thm)],[f651,f253]) ).
fof(f651,plain,
! [X0] :
( ~ sQ26_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| multiply(sk_c11,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f634,f65]) ).
fof(f656,plain,
( ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ26_spl
| ~ sQ11_spl
| ~ sQ13_spl
| multiply(sk_c2,sk_c1) = multiply(sk_c1,sk_c11) ),
inference(forward_demodulation,[status(thm)],[f634,f408]) ).
fof(f657,plain,
( ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ26_spl
| ~ sQ11_spl
| ~ sQ13_spl
| multiply(sk_c2,sk_c1) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f213,f656]) ).
fof(f664,plain,
( sQ22_spl
| ~ sQ26_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| inverse(inverse(sk_c11)) != inverse(sk_c11) ),
inference(forward_demodulation,[status(thm)],[f634,f630]) ).
fof(f665,plain,
( sQ22_spl
| ~ sQ26_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| inverse(sk_c9) != inverse(sk_c11) ),
inference(forward_demodulation,[status(thm)],[f174,f664]) ).
fof(f666,plain,
( sQ22_spl
| ~ sQ26_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| inverse(sk_c9) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f174,f665]) ).
fof(f667,plain,
( sQ23_spl
| ~ sQ26_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| sk_c9 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f174,f631]) ).
fof(f671,plain,
( sQ21_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ26_spl
| ~ sQ11_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f638,f633]) ).
fof(f672,plain,
( sQ21_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ26_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f671]) ).
fof(f673,plain,
( sQ21_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ26_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f672]) ).
fof(f675,plain,
( ~ sQ15_spl
| ~ sQ26_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ13_spl
| inverse(sk_c11) = sk_c11 ),
inference(backward_demodulation,[status(thm)],[f640,f226]) ).
fof(f676,plain,
( ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ26_spl
| ~ sQ11_spl
| ~ sQ13_spl
| multiply(sk_c2,sk_c11) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f640,f657]) ).
fof(f686,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ26_spl
| ~ sQ11_spl
| X0 = multiply(sk_c9,X0) ),
inference(forward_demodulation,[status(thm)],[f651,f648]) ).
fof(f687,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ26_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ13_spl
| multiply(sk_c2,X0) = multiply(sk_c11,X0) ),
inference(forward_demodulation,[status(thm)],[f640,f649]) ).
fof(f690,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ26_spl
| ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ13_spl
| multiply(sk_c2,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f651,f687]) ).
fof(f696,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ26_spl
| ~ sQ11_spl
| X0 = multiply(sk_c11,X0) ),
inference(backward_demodulation,[status(thm)],[f701,f686]) ).
fof(f697,plain,
( sQ22_spl
| ~ sQ26_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| inverse(sk_c9) != sk_c11 ),
inference(backward_demodulation,[status(thm)],[f701,f666]) ).
fof(f701,plain,
( ~ sQ15_spl
| ~ sQ26_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ13_spl
| sk_c9 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f174,f675]) ).
fof(f702,plain,
( ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ26_spl
| ~ sQ11_spl
| ~ sQ13_spl
| sk_c11 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f690,f676]) ).
fof(f708,plain,
( sQ25_spl
| ~ sQ26_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f701,f644]) ).
fof(f709,plain,
( sQ25_spl
| ~ sQ26_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f708]) ).
fof(f710,plain,
( sQ25_spl
| ~ sQ26_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f709]) ).
fof(f711,plain,
( sQ23_spl
| ~ sQ26_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f701,f667]) ).
fof(f712,plain,
( sQ23_spl
| ~ sQ26_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f711]) ).
fof(f713,plain,
( sQ23_spl
| ~ sQ26_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f712]) ).
fof(f719,plain,
( ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| multiply(sk_c6,sk_c6) = multiply(sk_c7,identity) ),
inference(forward_demodulation,[status(thm)],[f460,f449]) ).
fof(f720,plain,
( sQ20_spl
| inverse(identity) != sk_c11 ),
inference(backward_demodulation,[status(thm)],[f65,f284]) ).
fof(f722,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ9_spl
| multiply(sk_c11,sk_c6) = multiply(sk_c5,identity) ),
inference(backward_demodulation,[status(thm)],[f458,f448]) ).
fof(f728,plain,
! [X0] :
( ~ sQ16_spl
| inverse(X0) != sk_c11
| multiply(sk_c11,multiply(X0,sk_c11)) != sk_c10 ),
inference(destructive_equality_resolution,[status(thm)],[f239]) ).
fof(f729,plain,
( sQ29_spl
| ~ sQ2_spl
| multiply(sk_c11,sk_c10) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f138,f314]) ).
fof(f730,plain,
( sQ29_spl
| ~ sQ2_spl
| ~ sQ0_spl
| sk_c9 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f131,f729]) ).
fof(f746,plain,
( ~ sQ14_spl
| ~ sQ16_spl
| inverse(sk_c1) != sk_c11
| multiply(sk_c11,sk_c2) != sk_c10 ),
inference(paramodulation,[status(thm)],[f213,f728]) ).
fof(f748,plain,
( ~ sQ14_spl
| ~ sQ16_spl
| ~ sQ15_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f746,f199,f225,f238,f212]) ).
fof(f749,plain,
( ~ sQ14_spl
| ~ sQ17_spl
| inverse(sk_c1) != sk_c11
| sk_c2 != sk_c10 ),
inference(paramodulation,[status(thm)],[f213,f242]) ).
fof(f751,definition,
( sQ45_spl
<=> sk_c2 = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f753,plain,
( sQ45_spl
| sk_c2 != sk_c10 ),
inference(component_clause,[status(thm)],[f751]) ).
fof(f754,plain,
( ~ sQ14_spl
| ~ sQ17_spl
| ~ sQ15_spl
| ~ sQ45_spl ),
inference(split_clause,[status(thm)],[f749,f751,f225,f241,f212]) ).
fof(f756,plain,
( ~ sQ0_spl
| ~ sQ18_spl
| inverse(sk_c11) != sk_c10
| sk_c9 != sk_c9 ),
inference(paramodulation,[status(thm)],[f131,f245]) ).
fof(f759,definition,
( sQ46_spl
<=> sk_c9 = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f761,plain,
( sQ46_spl
| sk_c9 != sk_c9 ),
inference(component_clause,[status(thm)],[f759]) ).
fof(f762,definition,
( sQ47_spl
<=> inverse(sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f763,plain,
( ~ sQ47_spl
| inverse(sk_c11) = sk_c10 ),
inference(component_clause,[status(thm)],[f762]) ).
fof(f764,plain,
( sQ47_spl
| inverse(sk_c11) != sk_c10 ),
inference(component_clause,[status(thm)],[f762]) ).
fof(f765,plain,
( ~ sQ0_spl
| ~ sQ18_spl
| ~ sQ47_spl
| ~ sQ46_spl ),
inference(split_clause,[status(thm)],[f756,f759,f762,f244,f130]) ).
fof(f766,plain,
( sQ47_spl
| ~ sQ11_spl
| sk_c9 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f174,f764]) ).
fof(f767,plain,
( sQ46_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f761]) ).
fof(f768,plain,
sQ46_spl,
inference(contradiction_clause,[status(thm)],[f767]) ).
fof(f771,plain,
( ~ sQ4_spl
| ~ sQ30_spl
| ~ sQ2_spl
| multiply(sk_c4,sk_c11) != inverse(sk_c4)
| inverse(sk_c10) != sk_c11 ),
inference(paramodulation,[status(thm)],[f146,f388]) ).
fof(f773,plain,
( ~ sQ11_spl
| ~ sQ30_spl
| ~ sQ2_spl
| multiply(sk_c11,sk_c11) != inverse(sk_c11)
| inverse(sk_c9) != sk_c11 ),
inference(paramodulation,[status(thm)],[f174,f388]) ).
fof(f776,plain,
( ~ sQ2_spl
| ~ sQ30_spl
| multiply(sk_c3,sk_c11) != inverse(sk_c3)
| inverse(sk_c11) != sk_c11 ),
inference(paramodulation,[status(thm)],[f138,f388]) ).
fof(f777,definition,
( sQ48_spl
<=> inverse(sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f779,plain,
( sQ48_spl
| inverse(sk_c10) != sk_c11 ),
inference(component_clause,[status(thm)],[f777]) ).
fof(f780,definition,
( sQ49_spl
<=> multiply(sk_c4,sk_c11) = inverse(sk_c4) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f782,plain,
( sQ49_spl
| multiply(sk_c4,sk_c11) != inverse(sk_c4) ),
inference(component_clause,[status(thm)],[f780]) ).
fof(f783,plain,
( ~ sQ4_spl
| ~ sQ30_spl
| ~ sQ2_spl
| ~ sQ49_spl
| ~ sQ48_spl ),
inference(split_clause,[status(thm)],[f771,f777,f780,f137,f315,f145]) ).
fof(f791,definition,
( sQ52_spl
<=> inverse(sk_c9) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f793,plain,
( sQ52_spl
| inverse(sk_c9) != sk_c11 ),
inference(component_clause,[status(thm)],[f791]) ).
fof(f794,definition,
( sQ53_spl
<=> multiply(sk_c11,sk_c11) = inverse(sk_c11) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f797,plain,
( ~ sQ11_spl
| ~ sQ30_spl
| ~ sQ2_spl
| ~ sQ53_spl
| ~ sQ52_spl ),
inference(split_clause,[status(thm)],[f773,f791,f794,f137,f315,f173]) ).
fof(f809,definition,
( sQ57_spl
<=> inverse(sk_c11) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f812,definition,
( sQ58_spl
<=> multiply(sk_c3,sk_c11) = inverse(sk_c3) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f814,plain,
( sQ58_spl
| multiply(sk_c3,sk_c11) != inverse(sk_c3) ),
inference(component_clause,[status(thm)],[f812]) ).
fof(f815,plain,
( ~ sQ2_spl
| ~ sQ30_spl
| ~ sQ58_spl
| ~ sQ57_spl ),
inference(split_clause,[status(thm)],[f776,f809,f812,f315,f137]) ).
fof(f816,plain,
( sQ58_spl
| ~ sQ1_spl
| sk_c10 != inverse(sk_c3) ),
inference(forward_demodulation,[status(thm)],[f134,f814]) ).
fof(f817,plain,
( sQ58_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c10 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f138,f816]) ).
fof(f826,plain,
( sQ49_spl
| ~ sQ4_spl
| multiply(sk_c4,sk_c11) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f146,f782]) ).
fof(f835,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f264,f264]) ).
fof(f836,plain,
( ~ sQ3_spl
| sk_c10 = multiply(inverse(sk_c4),sk_c9) ),
inference(paramodulation,[status(thm)],[f142,f264]) ).
fof(f837,plain,
( ~ sQ1_spl
| sk_c11 = multiply(inverse(sk_c3),sk_c10) ),
inference(paramodulation,[status(thm)],[f134,f264]) ).
fof(f838,plain,
( ~ sQ2_spl
| sk_c3 = multiply(inverse(sk_c11),identity) ),
inference(paramodulation,[status(thm)],[f267,f264]) ).
fof(f839,plain,
( ~ sQ0_spl
| sk_c10 = multiply(inverse(sk_c11),sk_c9) ),
inference(paramodulation,[status(thm)],[f131,f264]) ).
fof(f840,plain,
( ~ sQ10_spl
| sk_c8 = multiply(inverse(sk_c7),sk_c6) ),
inference(paramodulation,[status(thm)],[f170,f264]) ).
fof(f841,plain,
( ~ sQ5_spl
| sk_c8 = multiply(inverse(sk_c5),sk_c11) ),
inference(paramodulation,[status(thm)],[f150,f264]) ).
fof(f844,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c10 = multiply(sk_c10,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f146,f836]) ).
fof(f845,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c11 = multiply(sk_c11,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f138,f837]) ).
fof(f846,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| sk_c11 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f131,f845]) ).
fof(f847,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f846,f730]) ).
fof(f848,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| sQ29_spl ),
inference(contradiction_clause,[status(thm)],[f847]) ).
fof(f849,plain,
( ~ sQ2_spl
| ~ sQ11_spl
| sk_c3 = multiply(sk_c9,identity) ),
inference(forward_demodulation,[status(thm)],[f174,f838]) ).
fof(f850,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| sk_c10 = multiply(sk_c9,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f174,f839]) ).
fof(f851,plain,
( ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| sk_c8 = multiply(sk_c7,identity) ),
inference(backward_demodulation,[status(thm)],[f853,f719]) ).
fof(f853,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| sk_c8 = multiply(sk_c6,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f162,f840]) ).
fof(f854,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sk_c8 = multiply(sk_c8,sk_c11) ),
inference(forward_demodulation,[status(thm)],[f154,f841]) ).
fof(f858,plain,
( ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c11,sk_c10) = sk_c11 ),
inference(backward_demodulation,[status(thm)],[f846,f131]) ).
fof(f860,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c10 = multiply(sk_c9,sk_c11) ),
inference(backward_demodulation,[status(thm)],[f846,f850]) ).
fof(f861,plain,
( ~ sQ2_spl
| ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ0_spl
| sk_c3 = multiply(sk_c11,identity) ),
inference(backward_demodulation,[status(thm)],[f846,f849]) ).
fof(f862,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| sk_c10 = multiply(sk_c10,sk_c11) ),
inference(backward_demodulation,[status(thm)],[f846,f844]) ).
fof(f864,plain,
( sQ52_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| inverse(sk_c11) != sk_c11 ),
inference(backward_demodulation,[status(thm)],[f846,f793]) ).
fof(f871,plain,
( ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| multiply(sk_c11,sk_c11) = identity ),
inference(backward_demodulation,[status(thm)],[f846,f268]) ).
fof(f873,plain,
( sQ26_spl
| ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| multiply(sk_c11,sk_c10) != sk_c11 ),
inference(backward_demodulation,[status(thm)],[f846,f375]) ).
fof(f877,plain,
( ~ sQ29_spl
| ~ sQ2_spl
| multiply(sk_c11,sk_c10) = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f138,f313]) ).
fof(f878,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c10 = multiply(sk_c11,sk_c11) ),
inference(forward_demodulation,[status(thm)],[f846,f860]) ).
fof(f879,plain,
( sQ52_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ57_spl ),
inference(split_clause,[status(thm)],[f864,f809,f130,f137,f133,f791]) ).
fof(f883,plain,
( ~ sQ2_spl
| ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ0_spl
| sk_c3 = multiply(sk_c11,sk_c10) ),
inference(backward_demodulation,[status(thm)],[f897,f861]) ).
fof(f887,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ11_spl
| ~ sQ0_spl
| multiply(sk_c10,sk_c3) = multiply(sk_c3,sk_c10) ),
inference(backward_demodulation,[status(thm)],[f897,f434]) ).
fof(f897,plain,
( ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| sk_c10 = identity ),
inference(forward_demodulation,[status(thm)],[f878,f871]) ).
fof(f899,plain,
( sQ26_spl
| ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ29_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f877,f873]) ).
fof(f900,plain,
( sQ26_spl
| ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ29_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f899]) ).
fof(f901,plain,
( sQ26_spl
| ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ29_spl ),
inference(contradiction_clause,[status(thm)],[f900]) ).
fof(f906,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ26_spl
| ~ sQ11_spl
| X0 = multiply(sk_c9,multiply(sk_c11,X0)) ),
inference(forward_demodulation,[status(thm)],[f696,f481]) ).
fof(f907,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ26_spl
| ~ sQ11_spl
| X0 = multiply(sk_c9,X0) ),
inference(forward_demodulation,[status(thm)],[f696,f906]) ).
fof(f912,plain,
( sQ45_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ26_spl
| ~ sQ11_spl
| sk_c2 != sk_c11 ),
inference(backward_demodulation,[status(thm)],[f922,f753]) ).
fof(f922,plain,
( ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ26_spl
| ~ sQ11_spl
| sk_c10 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f907,f187]) ).
fof(f923,plain,
( sQ20_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f720,f292,f282]) ).
fof(f936,plain,
( sQ47_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ26_spl
| sk_c9 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f922,f766]) ).
fof(f937,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ26_spl
| ~ sQ11_spl
| sk_c10 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f696,f131]) ).
fof(f938,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ26_spl
| ~ sQ11_spl
| sk_c11 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f922,f937]) ).
fof(f939,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ26_spl
| ~ sQ11_spl
| sQ47_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f938,f936]) ).
fof(f940,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ26_spl
| ~ sQ11_spl
| sQ47_spl ),
inference(contradiction_clause,[status(thm)],[f939]) ).
fof(f941,plain,
( ~ sQ26_spl
| ~ sQ11_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f626,f186,f173,f302]) ).
fof(f943,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c11 = multiply(sk_c11,sk_c10) ),
inference(backward_demodulation,[status(thm)],[f138,f837]) ).
fof(f954,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c10 = multiply(sk_c9,sk_c11) ),
inference(backward_demodulation,[status(thm)],[f846,f850]) ).
fof(f962,plain,
( ~ sQ2_spl
| ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ0_spl
| sk_c3 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f131,f883]) ).
fof(f964,plain,
( ~ sQ2_spl
| ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ0_spl
| inverse(sk_c11) = sk_c11 ),
inference(backward_demodulation,[status(thm)],[f968,f138]) ).
fof(f965,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ0_spl
| X0 = multiply(sk_c11,multiply(sk_c11,X0)) ),
inference(backward_demodulation,[status(thm)],[f968,f403]) ).
fof(f967,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ11_spl
| ~ sQ0_spl
| multiply(sk_c10,X0) = multiply(sk_c11,multiply(sk_c11,X0)) ),
inference(backward_demodulation,[status(thm)],[f968,f271]) ).
fof(f968,plain,
( ~ sQ2_spl
| ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ0_spl
| sk_c3 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f846,f962]) ).
fof(f969,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ11_spl
| ~ sQ0_spl
| multiply(sk_c10,sk_c11) = multiply(sk_c3,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f968,f887]) ).
fof(f970,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c10 = multiply(sk_c3,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f862,f969]) ).
fof(f971,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c10 = multiply(sk_c11,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f968,f970]) ).
fof(f972,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c10 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f131,f971]) ).
fof(f973,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c10 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f846,f972]) ).
fof(f974,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sQ58_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f973,f817]) ).
fof(f975,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sQ58_spl ),
inference(contradiction_clause,[status(thm)],[f974]) ).
fof(f979,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| multiply(sk_c11,sk_c4) = multiply(sk_c4,identity) ),
inference(forward_demodulation,[status(thm)],[f846,f429]) ).
fof(f995,plain,
( ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c10 = multiply(inverse(sk_c11),sk_c11) ),
inference(forward_demodulation,[status(thm)],[f846,f839]) ).
fof(f996,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl
| multiply(sk_c10,sk_c3) = multiply(sk_c3,sk_c10) ),
inference(backward_demodulation,[status(thm)],[f1011,f434]) ).
fof(f998,plain,
( ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c11,sk_c4) = multiply(sk_c8,sk_c10) ),
inference(backward_demodulation,[status(thm)],[f1011,f424]) ).
fof(f1004,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| multiply(sk_c11,sk_c4) = multiply(sk_c4,sk_c10) ),
inference(backward_demodulation,[status(thm)],[f1011,f979]) ).
fof(f1007,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(inverse(X0),X0) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f1011,f66]) ).
fof(f1011,plain,
( ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c10 = identity ),
inference(forward_demodulation,[status(thm)],[f66,f995]) ).
fof(f1012,plain,
( ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ1_spl
| sk_c3 = multiply(inverse(sk_c11),sk_c10) ),
inference(forward_demodulation,[status(thm)],[f1011,f838]) ).
fof(f1017,plain,
( ~ sQ2_spl
| ~ sQ26_spl
| ~ sQ0_spl
| ~ sQ1_spl
| inverse(sk_c11) = sk_c11 ),
inference(backward_demodulation,[status(thm)],[f1018,f138]) ).
fof(f1018,plain,
( ~ sQ26_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ1_spl
| sk_c3 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1012,f303]) ).
fof(f1022,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl
| ~ sQ26_spl
| multiply(sk_c10,sk_c11) = multiply(sk_c3,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f1018,f996]) ).
fof(f1023,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl
| ~ sQ26_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c10 = multiply(sk_c3,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f862,f1022]) ).
fof(f1024,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl
| ~ sQ26_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c10 = multiply(sk_c11,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f1018,f1023]) ).
fof(f1036,plain,
( sQ49_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl
| ~ sQ26_spl
| ~ sQ3_spl
| multiply(sk_c4,sk_c11) != sk_c11 ),
inference(backward_demodulation,[status(thm)],[f1045,f826]) ).
fof(f1045,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl
| ~ sQ26_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c10 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f858,f1024]) ).
fof(f1047,plain,
( ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c11,sk_c4) = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f158,f998]) ).
fof(f1059,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sk_c11 = multiply(sk_c4,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f1047,f1004]) ).
fof(f1060,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ26_spl
| sk_c11 = multiply(sk_c4,sk_c11) ),
inference(forward_demodulation,[status(thm)],[f1045,f1059]) ).
fof(f1078,plain,
( ~ sQ2_spl
| ~ sQ26_spl
| ~ sQ0_spl
| ~ sQ1_spl
| sQ57_spl ),
inference(split_clause,[status(thm)],[f1017,f809,f133,f130,f302,f137]) ).
fof(f1088,plain,
( sQ49_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl
| ~ sQ26_spl
| ~ sQ3_spl
| ~ sQ7_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1060,f1036]) ).
fof(f1089,plain,
( sQ49_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl
| ~ sQ26_spl
| ~ sQ3_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1088]) ).
fof(f1090,plain,
( sQ49_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl
| ~ sQ26_spl
| ~ sQ3_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f1089]) ).
fof(f1093,plain,
( ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c11 = multiply(sk_c5,sk_c11) ),
inference(forward_demodulation,[status(thm)],[f943,f444]) ).
fof(f1094,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c11 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f943,f132]) ).
fof(f1110,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sk_c11 = multiply(inverse(sk_c8),sk_c8) ),
inference(paramodulation,[status(thm)],[f854,f264]) ).
fof(f1112,plain,
( sQ23_spl
| ~ sQ5_spl
| ~ sQ6_spl
| inverse(sk_c11) != sk_c11 ),
inference(backward_demodulation,[status(thm)],[f1128,f294]) ).
fof(f1114,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c3 = multiply(inverse(sk_c11),sk_c11) ),
inference(backward_demodulation,[status(thm)],[f1128,f838]) ).
fof(f1115,plain,
( sQ22_spl
| ~ sQ5_spl
| ~ sQ6_spl
| inverse(inverse(identity)) != inverse(sk_c11) ),
inference(backward_demodulation,[status(thm)],[f1128,f290]) ).
fof(f1117,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c11,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f1128,f65]) ).
fof(f1121,plain,
( ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ5_spl
| sk_c8 = multiply(sk_c7,sk_c11) ),
inference(backward_demodulation,[status(thm)],[f1128,f851]) ).
fof(f1122,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ9_spl
| multiply(sk_c11,sk_c6) = multiply(sk_c5,sk_c11) ),
inference(backward_demodulation,[status(thm)],[f1128,f722]) ).
fof(f1125,plain,
( ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c11,sk_c4) = multiply(sk_c8,sk_c11) ),
inference(backward_demodulation,[status(thm)],[f1128,f424]) ).
fof(f1128,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sk_c11 = identity ),
inference(forward_demodulation,[status(thm)],[f66,f1110]) ).
fof(f1129,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c3 = identity ),
inference(forward_demodulation,[status(thm)],[f66,f1114]) ).
fof(f1130,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| inverse(sk_c11) = sk_c11 ),
inference(backward_demodulation,[status(thm)],[f1134,f138]) ).
fof(f1131,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c11,sk_c11) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f1134,f134]) ).
fof(f1134,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c3 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1128,f1129]) ).
fof(f1135,plain,
( sQ22_spl
| ~ sQ5_spl
| ~ sQ6_spl
| inverse(inverse(sk_c11)) != inverse(sk_c11) ),
inference(forward_demodulation,[status(thm)],[f1128,f1115]) ).
fof(f1143,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| X0 = multiply(sk_c8,multiply(sk_c10,X0)) ),
inference(backward_demodulation,[status(thm)],[f1117,f266]) ).
fof(f1151,plain,
( ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ5_spl
| ~ sQ7_spl
| sk_c8 = multiply(sk_c6,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f420,f1121]) ).
fof(f1152,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ9_spl
| sk_c6 = multiply(sk_c5,sk_c11) ),
inference(forward_demodulation,[status(thm)],[f1117,f1122]) ).
fof(f1154,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c11) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f1167,f166]) ).
fof(f1159,plain,
( ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 = multiply(sk_c11,sk_c10) ),
inference(backward_demodulation,[status(thm)],[f1167,f1151]) ).
fof(f1167,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c6 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1093,f1152]) ).
fof(f1170,plain,
( ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c4 = multiply(sk_c8,sk_c11) ),
inference(forward_demodulation,[status(thm)],[f1117,f1125]) ).
fof(f1171,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c8,sk_c10) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f1176,f142]) ).
fof(f1172,plain,
( ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| inverse(sk_c8) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f1176,f146]) ).
fof(f1176,plain,
( ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c4 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f854,f1170]) ).
fof(f1180,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1130,f1112]) ).
fof(f1181,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sQ23_spl ),
inference(contradiction_clause,[status(thm)],[f1180]) ).
fof(f1184,plain,
( sQ48_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| inverse(sk_c11) != sk_c11 ),
inference(backward_demodulation,[status(thm)],[f1192,f779]) ).
fof(f1188,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c10 = multiply(sk_c11,sk_c9) ),
inference(backward_demodulation,[status(thm)],[f1192,f844]) ).
fof(f1189,plain,
( sQ26_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(inverse(sk_c11),sk_c11) != sk_c11 ),
inference(backward_demodulation,[status(thm)],[f1192,f304]) ).
fof(f1190,plain,
( sQ32_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c10,sk_c11) != sk_c11 ),
inference(backward_demodulation,[status(thm)],[f1192,f380]) ).
fof(f1192,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c11 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1117,f1131]) ).
fof(f1211,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| X0 = multiply(sk_c8,multiply(sk_c11,X0)) ),
inference(forward_demodulation,[status(thm)],[f1192,f1143]) ).
fof(f1213,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| X0 = multiply(sk_c8,X0) ),
inference(forward_demodulation,[status(thm)],[f1117,f1211]) ).
fof(f1224,plain,
( sQ11_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f1154,f175]) ).
fof(f1226,plain,
( sQ22_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(inverse(sk_c11)) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f1154,f1135]) ).
fof(f1235,plain,
( ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1117,f1159]) ).
fof(f1241,plain,
( ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1192,f1235]) ).
fof(f1253,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c10 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1213,f1171]) ).
fof(f1254,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c11 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1192,f1253]) ).
fof(f1255,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1254,f1094]) ).
fof(f1256,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f1255]) ).
fof(f1257,plain,
( ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c11) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1241,f1172]) ).
fof(f1258,plain,
( ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c11) = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1192,f1257]) ).
fof(f1275,plain,
( sQ48_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1258,f1184]) ).
fof(f1276,plain,
( sQ48_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1275]) ).
fof(f1277,plain,
( sQ48_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f1276]) ).
fof(f1281,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c11 = multiply(sk_c11,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f1192,f1188]) ).
fof(f1283,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c11 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1117,f1281]) ).
fof(f1284,plain,
( sQ26_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| multiply(sk_c11,sk_c11) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1258,f1189]) ).
fof(f1285,plain,
( sQ26_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1117,f1284]) ).
fof(f1286,plain,
( sQ26_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1285]) ).
fof(f1287,plain,
( sQ26_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f1286]) ).
fof(f1288,plain,
( sQ32_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c11,sk_c11) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1192,f1190]) ).
fof(f1289,plain,
( sQ32_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1117,f1288]) ).
fof(f1290,plain,
( sQ32_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1289]) ).
fof(f1291,plain,
( sQ32_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f1290]) ).
fof(f1306,plain,
( sQ11_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c11 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1241,f1224]) ).
fof(f1307,plain,
( sQ11_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1283,f1306]) ).
fof(f1308,plain,
( sQ11_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ3_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1307]) ).
fof(f1309,plain,
( sQ11_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ3_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f1308]) ).
fof(f1313,plain,
( sQ22_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ10_spl
| ~ sQ8_spl
| inverse(sk_c11) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f1258,f1226]) ).
fof(f1314,plain,
( sQ22_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c11 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f1258,f1313]) ).
fof(f1315,plain,
( sQ22_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1241,f1314]) ).
fof(f1316,plain,
( sQ22_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ10_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1315]) ).
fof(f1317,plain,
( sQ22_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ10_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f1316]) ).
fof(f1340,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(inverse(X0),X0) = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1192,f1007]) ).
fof(f1378,plain,
( sQ47_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c11 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1258,f764]) ).
fof(f1379,plain,
( sQ47_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1192,f1378]) ).
fof(f1380,plain,
( sQ47_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1379]) ).
fof(f1381,plain,
( sQ47_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f1380]) ).
fof(f1493,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ5_spl
| ~ sQ6_spl
| inverse(X0) != sk_c11
| multiply(X0,sk_c11) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1117,f728]) ).
fof(f1494,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(X0) != sk_c11
| multiply(X0,sk_c11) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1192,f1493]) ).
fof(f1503,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| X0 = multiply(inverse(inverse(X0)),sk_c11) ),
inference(paramodulation,[status(thm)],[f1340,f264]) ).
fof(f1506,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| inverse(X0) != sk_c11
| X0 != sk_c11 ),
inference(backward_demodulation,[status(thm)],[f1508,f1494]) ).
fof(f1508,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| X0 = multiply(X0,sk_c11) ),
inference(forward_demodulation,[status(thm)],[f835,f1503]) ).
fof(f1510,plain,
( ~ sQ16_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| inverse(sk_c11) != sk_c11 ),
inference(destructive_equality_resolution,[status(thm)],[f1506]) ).
fof(f1511,plain,
( ~ sQ16_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1510,f1258]) ).
fof(f1512,plain,
( ~ sQ16_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f1511]) ).
fof(f1514,plain,
( ~ sQ11_spl
| ~ sQ47_spl
| sk_c10 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f763,f174]) ).
fof(f1516,plain,
( ~ sQ11_spl
| ~ sQ47_spl
| multiply(sk_c10,sk_c11) = identity ),
inference(forward_demodulation,[status(thm)],[f1514,f268]) ).
fof(f1522,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ0_spl
| X0 = multiply(sk_c10,X0) ),
inference(forward_demodulation,[status(thm)],[f967,f965]) ).
fof(f1527,plain,
( ~ sQ47_spl
| ~ sQ2_spl
| ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ0_spl
| inverse(sk_c11) = sk_c11 ),
inference(backward_demodulation,[status(thm)],[f1528,f763]) ).
fof(f1528,plain,
( ~ sQ2_spl
| ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ0_spl
| ~ sQ47_spl
| sk_c10 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f763,f964]) ).
fof(f1533,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ47_spl
| sk_c11 = multiply(sk_c9,sk_c11) ),
inference(forward_demodulation,[status(thm)],[f1528,f954]) ).
fof(f1534,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ47_spl
| sk_c11 = multiply(sk_c10,sk_c11) ),
inference(forward_demodulation,[status(thm)],[f1514,f1533]) ).
fof(f1535,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ47_spl
| sk_c11 = identity ),
inference(forward_demodulation,[status(thm)],[f1516,f1534]) ).
fof(f1583,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ47_spl
| multiply(sk_c11,X0) = multiply(sk_c10,multiply(sk_c10,X0)) ),
inference(forward_demodulation,[status(thm)],[f1514,f394]) ).
fof(f1584,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ47_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl
| multiply(sk_c11,X0) = multiply(sk_c10,X0) ),
inference(forward_demodulation,[status(thm)],[f1522,f1583]) ).
fof(f1586,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ47_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl
| multiply(sk_c11,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f1522,f1584]) ).
fof(f1670,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ2_spl
| ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ0_spl
| ~ sQ47_spl
| inverse(X0) != sk_c11
| multiply(X0,sk_c11) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1528,f242]) ).
fof(f1698,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ2_spl
| ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ0_spl
| ~ sQ47_spl
| ~ sQ5_spl
| ~ sQ6_spl
| inverse(X0) != sk_c11
| X0 != sk_c11 ),
inference(backward_demodulation,[status(thm)],[f1508,f1670]) ).
fof(f2030,plain,
( ~ sQ17_spl
| ~ sQ2_spl
| ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ0_spl
| ~ sQ47_spl
| ~ sQ5_spl
| ~ sQ6_spl
| inverse(sk_c11) != sk_c11 ),
inference(destructive_equality_resolution,[status(thm)],[f1698]) ).
fof(f2031,plain,
( ~ sQ17_spl
| ~ sQ2_spl
| ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ0_spl
| ~ sQ47_spl
| ~ sQ5_spl
| ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2030,f1527]) ).
fof(f2032,plain,
( ~ sQ17_spl
| ~ sQ2_spl
| ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ0_spl
| ~ sQ47_spl
| ~ sQ5_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f2031]) ).
fof(f2087,plain,
( sQ21_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ47_spl
| multiply(inverse(sk_c11),sk_c10) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1535,f287]) ).
fof(f2088,plain,
( sQ21_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ47_spl
| multiply(sk_c11,sk_c10) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1527,f2087]) ).
fof(f2089,plain,
( sQ21_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ47_spl
| ~ sQ12_spl
| sk_c10 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1586,f2088]) ).
fof(f2090,plain,
( sQ21_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ47_spl
| ~ sQ12_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1528,f2089]) ).
fof(f2091,plain,
( sQ21_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ47_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f2090]) ).
fof(f2092,plain,
( sQ21_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ47_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f2091]) ).
fof(f2160,plain,
( sQ22_spl
| ~ sQ26_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ52_spl ),
inference(split_clause,[status(thm)],[f697,f791,f199,f225,f212,f173,f302,f288]) ).
fof(f2197,plain,
( ~ sQ15_spl
| ~ sQ26_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ13_spl
| inverse(sk_c11) = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f640,f226]) ).
fof(f2295,plain,
( sQ52_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ26_spl
| ~ sQ11_spl
| inverse(sk_c11) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f938,f793]) ).
fof(f2296,plain,
( sQ52_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ26_spl
| ~ sQ11_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f2197,f2295]) ).
fof(f2297,plain,
( sQ52_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ26_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f2296]) ).
fof(f2298,plain,
( sQ52_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ26_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f2297]) ).
fof(f2313,plain,
( sQ45_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ26_spl
| ~ sQ11_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f702,f912]) ).
fof(f2314,plain,
( sQ45_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ26_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f2313]) ).
fof(f2315,plain,
( sQ45_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ26_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f2314]) ).
fof(f2316,plain,
$false,
inference(sat_refutation,[status(thm)],[f136,f140,f144,f148,f152,f156,f160,f176,f177,f178,f179,f180,f181,f182,f183,f184,f185,f189,f190,f202,f203,f204,f205,f206,f207,f208,f209,f210,f211,f215,f216,f217,f218,f219,f220,f221,f222,f223,f224,f228,f229,f230,f231,f232,f233,f234,f235,f236,f237,f250,f291,f298,f308,f318,f328,f335,f378,f392,f615,f673,f710,f713,f748,f754,f765,f768,f783,f797,f815,f848,f879,f901,f923,f940,f941,f975,f1078,f1090,f1181,f1256,f1277,f1287,f1291,f1309,f1317,f1381,f1512,f2032,f2092,f2160,f2298,f2315]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP307-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.34 % Computer : n013.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 20:08:21 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.36 % Drodi V4.1.1
% 0.13/0.45 % Refutation found
% 0.13/0.45 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.48 % Elapsed time: 0.121265 seconds
% 0.13/0.48 % CPU time: 0.748511 seconds
% 0.13/0.48 % Total memory used: 121.952 MB
% 0.13/0.48 % Net memory used: 120.996 MB
%------------------------------------------------------------------------------