%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP318-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 12:33:24 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.42s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 98
% Syntax : Number of formulae : 498 ( 16 unt; 44 def)
% Number of atoms : 1942 ( 600 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 2750 (1306 ~;1400 |; 0 &)
% ( 44 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 46 ( 44 usr; 45 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 13 con; 0-2 aty)
% Number of variables : 115 ( 115 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c11
| multiply(sk_c11,sk_c12) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c4) = sk_c12
| multiply(sk_c11,sk_c12) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c5,sk_c11) = sk_c10
| multiply(sk_c11,sk_c12) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c5) = sk_c11
| multiply(sk_c11,sk_c12) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c12
| multiply(sk_c11,sk_c12) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c11,sk_c12) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c12
| multiply(sk_c11,sk_c12) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c11,sk_c12) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c7) = sk_c9
| multiply(sk_c11,sk_c12) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c4) = sk_c12
| multiply(sk_c1,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c5,sk_c11) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c5) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c12
| multiply(sk_c1,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c1,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c12
| multiply(sk_c1,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c1,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( inverse(sk_c7) = sk_c9
| multiply(sk_c1,sk_c11) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c4) = sk_c12
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c5) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c12
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c12
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( inverse(sk_c7) = sk_c9
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c11
| multiply(sk_c12,sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( inverse(sk_c4) = sk_c12
| multiply(sk_c12,sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( inverse(sk_c5) = sk_c11
| multiply(sk_c12,sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c12
| multiply(sk_c12,sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c12,sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c12
| multiply(sk_c12,sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c12,sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,negated_conjecture,
( inverse(sk_c7) = sk_c9
| multiply(sk_c12,sk_c3) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c11
| multiply(sk_c2,sk_c12) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
( inverse(sk_c4) = sk_c12
| multiply(sk_c2,sk_c12) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,negated_conjecture,
( inverse(sk_c5) = sk_c11
| multiply(sk_c2,sk_c12) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c12
| multiply(sk_c2,sk_c12) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c2,sk_c12) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c12
| multiply(sk_c2,sk_c12) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f51,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c2,sk_c12) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f52,negated_conjecture,
( inverse(sk_c7) = sk_c9
| multiply(sk_c2,sk_c12) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
( multiply(sk_c4,sk_c12) = sk_c11
| inverse(sk_c2) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f55,negated_conjecture,
( inverse(sk_c4) = sk_c12
| inverse(sk_c2) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f57,negated_conjecture,
( inverse(sk_c5) = sk_c11
| inverse(sk_c2) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f58,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c12
| inverse(sk_c2) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f59,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c2) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f60,negated_conjecture,
( multiply(sk_c9,sk_c11) = sk_c12
| inverse(sk_c2) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f61,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c2) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f62,negated_conjecture,
( inverse(sk_c7) = sk_c9
| inverse(sk_c2) = sk_c12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f64,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_c12
| multiply(X6,sk_c12) != X5
| multiply(sk_c12,X5) != sk_c11
| inverse(X4) != sk_c11
| multiply(X4,sk_c11) != sk_c12
| multiply(sk_c11,sk_c12) != sk_c10 ),
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_c4,sk_c12) = sk_c11
| multiply(sk_c11,sk_c12) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f69,plain,
( inverse(sk_c4) = sk_c12
| multiply(sk_c11,sk_c12) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f70,plain,
( multiply(sk_c5,sk_c11) = sk_c10
| multiply(sk_c11,sk_c12) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f71,plain,
( inverse(sk_c5) = sk_c11
| multiply(sk_c11,sk_c12) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f72,plain,
( multiply(sk_c6,sk_c9) = sk_c12
| multiply(sk_c11,sk_c12) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f73,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c11,sk_c12) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f74,plain,
( multiply(sk_c9,sk_c11) = sk_c12
| multiply(sk_c11,sk_c12) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f75,plain,
( inverse(sk_c8) = sk_c7
| multiply(sk_c11,sk_c12) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f76,plain,
( inverse(sk_c7) = sk_c9
| multiply(sk_c11,sk_c12) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f78,plain,
( multiply(sk_c4,sk_c12) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f79,plain,
( inverse(sk_c4) = sk_c12
| multiply(sk_c1,sk_c11) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f80,plain,
( multiply(sk_c5,sk_c11) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f81,plain,
( inverse(sk_c5) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f82,plain,
( multiply(sk_c6,sk_c9) = sk_c12
| multiply(sk_c1,sk_c11) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f83,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c1,sk_c11) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f84,plain,
( multiply(sk_c9,sk_c11) = sk_c12
| multiply(sk_c1,sk_c11) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f85,plain,
( inverse(sk_c8) = sk_c7
| multiply(sk_c1,sk_c11) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f86,plain,
( inverse(sk_c7) = sk_c9
| multiply(sk_c1,sk_c11) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f88,plain,
( multiply(sk_c4,sk_c12) = sk_c11
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f89,plain,
( inverse(sk_c4) = sk_c12
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f91,plain,
( inverse(sk_c5) = sk_c11
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f92,plain,
( multiply(sk_c6,sk_c9) = sk_c12
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f93,plain,
( inverse(sk_c6) = sk_c9
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f94,plain,
( multiply(sk_c9,sk_c11) = sk_c12
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f95,plain,
( inverse(sk_c8) = sk_c7
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f96,plain,
( inverse(sk_c7) = sk_c9
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f98,plain,
( multiply(sk_c4,sk_c12) = sk_c11
| multiply(sk_c12,sk_c3) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f99,plain,
( inverse(sk_c4) = sk_c12
| multiply(sk_c12,sk_c3) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f101,plain,
( inverse(sk_c5) = sk_c11
| multiply(sk_c12,sk_c3) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f102,plain,
( multiply(sk_c6,sk_c9) = sk_c12
| multiply(sk_c12,sk_c3) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f103,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c12,sk_c3) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f104,plain,
( multiply(sk_c9,sk_c11) = sk_c12
| multiply(sk_c12,sk_c3) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f105,plain,
( inverse(sk_c8) = sk_c7
| multiply(sk_c12,sk_c3) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f106,plain,
( inverse(sk_c7) = sk_c9
| multiply(sk_c12,sk_c3) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f108,plain,
( multiply(sk_c4,sk_c12) = sk_c11
| multiply(sk_c2,sk_c12) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f109,plain,
( inverse(sk_c4) = sk_c12
| multiply(sk_c2,sk_c12) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f111,plain,
( inverse(sk_c5) = sk_c11
| multiply(sk_c2,sk_c12) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f112,plain,
( multiply(sk_c6,sk_c9) = sk_c12
| multiply(sk_c2,sk_c12) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f113,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c2,sk_c12) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f114,plain,
( multiply(sk_c9,sk_c11) = sk_c12
| multiply(sk_c2,sk_c12) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f115,plain,
( inverse(sk_c8) = sk_c7
| multiply(sk_c2,sk_c12) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f116,plain,
( inverse(sk_c7) = sk_c9
| multiply(sk_c2,sk_c12) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f118,plain,
( multiply(sk_c4,sk_c12) = sk_c11
| inverse(sk_c2) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f119,plain,
( inverse(sk_c4) = sk_c12
| inverse(sk_c2) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f121,plain,
( inverse(sk_c5) = sk_c11
| inverse(sk_c2) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f122,plain,
( multiply(sk_c6,sk_c9) = sk_c12
| inverse(sk_c2) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f123,plain,
( inverse(sk_c6) = sk_c9
| inverse(sk_c2) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f124,plain,
( multiply(sk_c9,sk_c11) = sk_c12
| inverse(sk_c2) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f125,plain,
( inverse(sk_c8) = sk_c7
| inverse(sk_c2) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f126,plain,
( inverse(sk_c7) = sk_c9
| inverse(sk_c2) = sk_c12 ),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f128,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_c12
| ! [X5] :
( multiply(X6,sk_c12) != X5
| multiply(sk_c12,X5) != sk_c11
| ! [X4] :
( inverse(X4) != sk_c11
| multiply(X4,sk_c11) != sk_c12
| multiply(sk_c11,sk_c12) != sk_c10 ) ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f64]) ).
fof(f129,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_c12
| multiply(X2,sk_c12) != X1
| multiply(sk_c12,X1) != sk_c11
| inverse(X0) != sk_c11
| multiply(X0,sk_c11) != sk_c12
| multiply(sk_c11,sk_c12) != sk_c10 ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f130,definition,
( sQ0_spl
<=> multiply(sk_c11,sk_c12) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f131,plain,
( ~ sQ0_spl
| multiply(sk_c11,sk_c12) = sk_c10 ),
inference(component_clause,[status(thm)],[f130]) ).
fof(f132,plain,
( sQ0_spl
| multiply(sk_c11,sk_c12) != sk_c10 ),
inference(component_clause,[status(thm)],[f130]) ).
fof(f133,definition,
( sQ1_spl
<=> multiply(sk_c4,sk_c12) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f134,plain,
( ~ sQ1_spl
| multiply(sk_c4,sk_c12) = sk_c11 ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f135,plain,
( sQ1_spl
| multiply(sk_c4,sk_c12) != sk_c11 ),
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_c4) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f138,plain,
( ~ sQ2_spl
| inverse(sk_c4) = sk_c12 ),
inference(component_clause,[status(thm)],[f137]) ).
fof(f139,plain,
( sQ2_spl
| inverse(sk_c4) != sk_c12 ),
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_c5,sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f142,plain,
( ~ sQ3_spl
| multiply(sk_c5,sk_c11) = sk_c10 ),
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_c5) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f146,plain,
( ~ sQ4_spl
| inverse(sk_c5) = sk_c11 ),
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_c6,sk_c9) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f150,plain,
( ~ sQ5_spl
| multiply(sk_c6,sk_c9) = sk_c12 ),
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_c6) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f154,plain,
( ~ sQ6_spl
| inverse(sk_c6) = sk_c9 ),
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_c9,sk_c11) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f158,plain,
( ~ sQ7_spl
| multiply(sk_c9,sk_c11) = sk_c12 ),
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_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f162,plain,
( ~ sQ8_spl
| inverse(sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f161]) ).
fof(f164,plain,
( sQ8_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f75,f130,f161]) ).
fof(f165,definition,
( sQ9_spl
<=> inverse(sk_c7) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f166,plain,
( ~ sQ9_spl
| inverse(sk_c7) = sk_c9 ),
inference(component_clause,[status(thm)],[f165]) ).
fof(f168,plain,
( sQ9_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f76,f130,f165]) ).
fof(f173,definition,
( sQ11_spl
<=> multiply(sk_c1,sk_c11) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f174,plain,
( ~ sQ11_spl
| multiply(sk_c1,sk_c11) = sk_c12 ),
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(f186,definition,
( sQ12_spl
<=> inverse(sk_c1) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f187,plain,
( ~ sQ12_spl
| inverse(sk_c1) = sk_c11 ),
inference(component_clause,[status(thm)],[f186]) ).
fof(f188,plain,
( sQ12_spl
| inverse(sk_c1) != 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(f192,plain,
( sQ4_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f91,f186,f145]) ).
fof(f193,plain,
( sQ5_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f92,f186,f149]) ).
fof(f194,plain,
( sQ6_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f93,f186,f153]) ).
fof(f195,plain,
( sQ7_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f94,f186,f157]) ).
fof(f196,plain,
( sQ8_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f95,f186,f161]) ).
fof(f197,plain,
( sQ9_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f96,f186,f165]) ).
fof(f199,definition,
( sQ13_spl
<=> multiply(sk_c12,sk_c3) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f200,plain,
( ~ sQ13_spl
| multiply(sk_c12,sk_c3) = sk_c11 ),
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(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(f212,definition,
( sQ14_spl
<=> multiply(sk_c2,sk_c12) = sk_c3 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f213,plain,
( ~ sQ14_spl
| multiply(sk_c2,sk_c12) = sk_c3 ),
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(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(f225,definition,
( sQ15_spl
<=> inverse(sk_c2) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f226,plain,
( ~ sQ15_spl
| inverse(sk_c2) = sk_c12 ),
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(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(f238,definition,
! [X0] :
( sQ16_spl
<=> ( inverse(X0) != sk_c11
| multiply(X0,sk_c11) != sk_c12 ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f239,plain,
! [X0] :
( ~ sQ16_spl
| inverse(X0) != sk_c11
| multiply(X0,sk_c11) != sk_c12 ),
inference(component_clause,[status(thm)],[f238]) ).
fof(f241,definition,
! [X1,X2] :
( sQ17_spl
<=> ( inverse(X2) != sk_c12
| multiply(X2,sk_c12) != X1
| multiply(sk_c12,X1) != sk_c11 ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f242,plain,
! [X0,X1] :
( ~ sQ17_spl
| inverse(X1) != sk_c12
| multiply(X1,sk_c12) != X0
| multiply(sk_c12,X0) != sk_c11 ),
inference(component_clause,[status(thm)],[f241]) ).
fof(f244,definition,
! [X3] :
( sQ18_spl
<=> ( inverse(X3) != sk_c12
| multiply(X3,sk_c12) != sk_c11 ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f245,plain,
! [X0] :
( ~ sQ18_spl
| inverse(X0) != sk_c12
| multiply(X0,sk_c12) != sk_c11 ),
inference(component_clause,[status(thm)],[f244]) ).
fof(f247,definition,
! [X4] :
( sQ19_spl
<=> ( inverse(X4) != sk_c11
| multiply(X4,sk_c11) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f248,plain,
! [X0] :
( ~ sQ19_spl
| inverse(X0) != sk_c11
| multiply(X0,sk_c11) != sk_c10 ),
inference(component_clause,[status(thm)],[f247]) ).
fof(f250,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(f251,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)],[f250]) ).
fof(f253,plain,
( sQ20_spl
| sQ19_spl
| sQ18_spl
| sQ17_spl
| sQ16_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f129,f130,f238,f241,f244,f247,f250]) ).
fof(f254,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)],[f251]) ).
fof(f256,plain,
! [X0] :
( ~ sQ14_spl
| multiply(sk_c3,X0) = multiply(sk_c2,multiply(sk_c12,X0)) ),
inference(paramodulation,[status(thm)],[f213,f67]) ).
fof(f259,plain,
! [X0] :
( ~ sQ13_spl
| multiply(sk_c11,X0) = multiply(sk_c12,multiply(sk_c3,X0)) ),
inference(paramodulation,[status(thm)],[f200,f67]) ).
fof(f261,plain,
( ~ sQ2_spl
| multiply(sk_c12,sk_c4) = identity ),
inference(paramodulation,[status(thm)],[f138,f66]) ).
fof(f262,plain,
( ~ sQ4_spl
| multiply(sk_c11,sk_c5) = identity ),
inference(paramodulation,[status(thm)],[f146,f66]) ).
fof(f263,plain,
( ~ sQ6_spl
| multiply(sk_c9,sk_c6) = identity ),
inference(paramodulation,[status(thm)],[f154,f66]) ).
fof(f264,plain,
( ~ sQ8_spl
| multiply(sk_c7,sk_c8) = identity ),
inference(paramodulation,[status(thm)],[f162,f66]) ).
fof(f266,plain,
( ~ sQ12_spl
| multiply(sk_c11,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f187,f66]) ).
fof(f267,plain,
( ~ sQ15_spl
| multiply(sk_c12,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f226,f66]) ).
fof(f268,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f66,f67]) ).
fof(f269,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f65,f268]) ).
fof(f270,plain,
! [X0] :
( ~ sQ11_spl
| multiply(sk_c12,X0) = multiply(sk_c1,multiply(sk_c11,X0)) ),
inference(paramodulation,[status(thm)],[f174,f67]) ).
fof(f272,plain,
! [X0] :
( ~ sQ7_spl
| multiply(sk_c12,X0) = multiply(sk_c9,multiply(sk_c11,X0)) ),
inference(paramodulation,[status(thm)],[f158,f67]) ).
fof(f273,plain,
! [X0] :
( ~ sQ5_spl
| multiply(sk_c12,X0) = multiply(sk_c6,multiply(sk_c9,X0)) ),
inference(paramodulation,[status(thm)],[f150,f67]) ).
fof(f275,plain,
! [X0] :
( ~ sQ1_spl
| multiply(sk_c11,X0) = multiply(sk_c4,multiply(sk_c12,X0)) ),
inference(paramodulation,[status(thm)],[f134,f67]) ).
fof(f280,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)],[f138,f254]) ).
fof(f283,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ20_spl
| multiply(X0,inverse(sk_c8)) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c8)
| multiply(sk_c7,sk_c11) != sk_c12
| multiply(sk_c8,inverse(sk_c8)) != sk_c12 ),
inference(paramodulation,[status(thm)],[f162,f254]) ).
fof(f285,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ20_spl
| multiply(X0,inverse(sk_c1)) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c1)
| multiply(sk_c11,sk_c11) != sk_c12
| multiply(sk_c1,inverse(sk_c1)) != sk_c12 ),
inference(paramodulation,[status(thm)],[f187,f254]) ).
fof(f290,definition,
( sQ22_spl
<=> identity = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f291,plain,
( ~ sQ22_spl
| identity = sk_c12 ),
inference(component_clause,[status(thm)],[f290]) ).
fof(f292,plain,
( sQ22_spl
| identity != sk_c12 ),
inference(component_clause,[status(thm)],[f290]) ).
fof(f297,definition,
( sQ24_spl
<=> multiply(sk_c4,inverse(sk_c4)) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f299,plain,
( sQ24_spl
| multiply(sk_c4,inverse(sk_c4)) != sk_c12 ),
inference(component_clause,[status(thm)],[f297]) ).
fof(f300,definition,
( sQ25_spl
<=> multiply(sk_c12,sk_c11) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f302,plain,
( sQ25_spl
| multiply(sk_c12,sk_c11) != sk_c12 ),
inference(component_clause,[status(thm)],[f300]) ).
fof(f303,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(f306,plain,
( ~ sQ2_spl
| ~ sQ20_spl
| sQ26_spl
| ~ sQ25_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f280,f297,f300,f303,f250,f137]) ).
fof(f310,definition,
( sQ28_spl
<=> multiply(sk_c11,sk_c11) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f312,plain,
( sQ28_spl
| multiply(sk_c11,sk_c11) != sk_c12 ),
inference(component_clause,[status(thm)],[f310]) ).
fof(f324,definition,
( sQ32_spl
<=> multiply(sk_c8,inverse(sk_c8)) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f325,plain,
( ~ sQ32_spl
| multiply(sk_c8,inverse(sk_c8)) = sk_c12 ),
inference(component_clause,[status(thm)],[f324]) ).
fof(f326,plain,
( sQ32_spl
| multiply(sk_c8,inverse(sk_c8)) != sk_c12 ),
inference(component_clause,[status(thm)],[f324]) ).
fof(f327,definition,
( sQ33_spl
<=> multiply(sk_c7,sk_c11) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f329,plain,
( sQ33_spl
| multiply(sk_c7,sk_c11) != sk_c12 ),
inference(component_clause,[status(thm)],[f327]) ).
fof(f330,definition,
! [X0] :
( sQ34_spl
<=> ( multiply(X0,inverse(sk_c8)) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c8) ) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f331,plain,
! [X0] :
( ~ sQ34_spl
| multiply(X0,inverse(sk_c8)) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c8) ),
inference(component_clause,[status(thm)],[f330]) ).
fof(f333,plain,
( ~ sQ8_spl
| ~ sQ20_spl
| sQ34_spl
| ~ sQ33_spl
| ~ sQ32_spl ),
inference(split_clause,[status(thm)],[f283,f324,f327,f330,f250,f161]) ).
fof(f341,definition,
( sQ37_spl
<=> multiply(sk_c1,inverse(sk_c1)) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f343,plain,
( sQ37_spl
| multiply(sk_c1,inverse(sk_c1)) != sk_c12 ),
inference(component_clause,[status(thm)],[f341]) ).
fof(f344,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(f345,plain,
! [X0] :
( ~ sQ38_spl
| multiply(X0,inverse(sk_c1)) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c1) ),
inference(component_clause,[status(thm)],[f344]) ).
fof(f347,plain,
( ~ sQ12_spl
| ~ sQ20_spl
| sQ38_spl
| ~ sQ28_spl
| ~ sQ37_spl ),
inference(split_clause,[status(thm)],[f285,f341,f310,f344,f250,f186]) ).
fof(f359,plain,
! [X0] :
( ~ sQ38_spl
| ~ sQ12_spl
| multiply(X0,inverse(sk_c1)) != inverse(X0)
| inverse(inverse(X0)) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f187,f345]) ).
fof(f360,plain,
! [X0] :
( ~ sQ38_spl
| ~ sQ12_spl
| multiply(X0,sk_c11) != inverse(X0)
| inverse(inverse(X0)) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f187,f359]) ).
fof(f361,plain,
( sQ37_spl
| ~ sQ12_spl
| multiply(sk_c1,sk_c11) != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f187,f343]) ).
fof(f362,plain,
( sQ37_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sk_c12 != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f174,f361]) ).
fof(f363,plain,
( sQ37_spl
| ~ sQ12_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f362]) ).
fof(f364,plain,
( sQ37_spl
| ~ sQ12_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f363]) ).
fof(f372,plain,
! [X0] :
( ~ sQ34_spl
| ~ sQ8_spl
| multiply(X0,sk_c7) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c8) ),
inference(backward_demodulation,[status(thm)],[f162,f331]) ).
fof(f383,plain,
! [X0] :
( ~ sQ34_spl
| ~ sQ8_spl
| multiply(X0,sk_c7) != inverse(X0)
| inverse(inverse(X0)) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f162,f372]) ).
fof(f386,plain,
( ~ sQ12_spl
| ~ sQ19_spl
| multiply(sk_c1,sk_c11) != sk_c10 ),
inference(resolution,[status(thm)],[f248,f187]) ).
fof(f387,plain,
( ~ sQ12_spl
| ~ sQ19_spl
| sk_c11 != sk_c11
| multiply(sk_c1,sk_c11) != sk_c10 ),
inference(paramodulation,[status(thm)],[f187,f248]) ).
fof(f389,definition,
( sQ41_spl
<=> multiply(sk_c1,sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f392,definition,
( sQ42_spl
<=> sk_c11 = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f394,plain,
( sQ42_spl
| sk_c11 != sk_c11 ),
inference(component_clause,[status(thm)],[f392]) ).
fof(f395,plain,
( ~ sQ12_spl
| ~ sQ19_spl
| ~ sQ42_spl
| ~ sQ41_spl ),
inference(split_clause,[status(thm)],[f387,f389,f392,f247,f186]) ).
fof(f399,definition,
( sQ44_spl
<=> sk_c12 = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f400,plain,
( ~ sQ44_spl
| sk_c12 = sk_c11 ),
inference(component_clause,[status(thm)],[f399]) ).
fof(f403,plain,
( sQ42_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f394]) ).
fof(f404,plain,
sQ42_spl,
inference(contradiction_clause,[status(thm)],[f403]) ).
fof(f413,plain,
( ~ sQ1_spl
| ~ sQ18_spl
| inverse(sk_c4) != sk_c12 ),
inference(resolution,[status(thm)],[f245,f134]) ).
fof(f416,plain,
( ~ sQ18_spl
| inverse(identity) != sk_c12
| sk_c12 != sk_c11 ),
inference(paramodulation,[status(thm)],[f65,f245]) ).
fof(f418,plain,
( ~ sQ14_spl
| ~ sQ18_spl
| inverse(sk_c2) != sk_c12
| sk_c3 != sk_c11 ),
inference(paramodulation,[status(thm)],[f213,f245]) ).
fof(f419,plain,
( ~ sQ1_spl
| ~ sQ18_spl
| ~ sQ2_spl
| sk_c12 != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f138,f413]) ).
fof(f420,plain,
( ~ sQ1_spl
| ~ sQ18_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f419]) ).
fof(f421,plain,
( ~ sQ1_spl
| ~ sQ18_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f420]) ).
fof(f422,plain,
! [X0] :
( ~ sQ17_spl
| inverse(X0) != sk_c12
| multiply(sk_c12,multiply(X0,sk_c12)) != sk_c11 ),
inference(destructive_equality_resolution,[status(thm)],[f242]) ).
fof(f423,plain,
( ~ sQ1_spl
| ~ sQ17_spl
| inverse(sk_c4) != sk_c12
| multiply(sk_c12,sk_c11) != sk_c11 ),
inference(paramodulation,[status(thm)],[f134,f422]) ).
fof(f424,plain,
( ~ sQ17_spl
| inverse(inverse(sk_c12)) != sk_c12
| multiply(sk_c12,identity) != sk_c11 ),
inference(paramodulation,[status(thm)],[f66,f422]) ).
fof(f425,plain,
( ~ sQ17_spl
| inverse(identity) != sk_c12
| multiply(sk_c12,sk_c12) != sk_c11 ),
inference(paramodulation,[status(thm)],[f65,f422]) ).
fof(f427,plain,
( ~ sQ14_spl
| ~ sQ17_spl
| inverse(sk_c2) != sk_c12
| multiply(sk_c12,sk_c3) != sk_c11 ),
inference(paramodulation,[status(thm)],[f213,f422]) ).
fof(f428,definition,
( sQ45_spl
<=> multiply(sk_c12,sk_c11) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f431,plain,
( ~ sQ1_spl
| ~ sQ17_spl
| ~ sQ2_spl
| ~ sQ45_spl ),
inference(split_clause,[status(thm)],[f423,f428,f137,f241,f133]) ).
fof(f432,definition,
( sQ46_spl
<=> multiply(sk_c12,identity) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f433,plain,
( ~ sQ46_spl
| multiply(sk_c12,identity) = sk_c11 ),
inference(component_clause,[status(thm)],[f432]) ).
fof(f434,plain,
( sQ46_spl
| multiply(sk_c12,identity) != sk_c11 ),
inference(component_clause,[status(thm)],[f432]) ).
fof(f435,definition,
( sQ47_spl
<=> inverse(inverse(sk_c12)) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f437,plain,
( sQ47_spl
| inverse(inverse(sk_c12)) != sk_c12 ),
inference(component_clause,[status(thm)],[f435]) ).
fof(f438,plain,
( ~ sQ17_spl
| ~ sQ47_spl
| ~ sQ46_spl ),
inference(split_clause,[status(thm)],[f424,f432,f435,f241]) ).
fof(f439,definition,
( sQ48_spl
<=> multiply(sk_c12,sk_c12) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f442,definition,
( sQ49_spl
<=> inverse(identity) = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f445,plain,
( ~ sQ17_spl
| ~ sQ49_spl
| ~ sQ48_spl ),
inference(split_clause,[status(thm)],[f425,f439,f442,f241]) ).
fof(f446,plain,
( ~ sQ14_spl
| ~ sQ17_spl
| ~ sQ15_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f427,f199,f225,f241,f212]) ).
fof(f449,plain,
( ~ sQ7_spl
| ~ sQ16_spl
| inverse(sk_c9) != sk_c11
| sk_c12 != sk_c12 ),
inference(paramodulation,[status(thm)],[f158,f239]) ).
fof(f451,plain,
( ~ sQ16_spl
| inverse(inverse(sk_c11)) != sk_c11
| identity != sk_c12 ),
inference(paramodulation,[status(thm)],[f66,f239]) ).
fof(f452,plain,
( ~ sQ16_spl
| inverse(identity) != sk_c11
| sk_c11 != sk_c12 ),
inference(paramodulation,[status(thm)],[f65,f239]) ).
fof(f454,definition,
( sQ50_spl
<=> sk_c12 = sk_c12 ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f456,plain,
( sQ50_spl
| sk_c12 != sk_c12 ),
inference(component_clause,[status(thm)],[f454]) ).
fof(f457,definition,
( sQ51_spl
<=> inverse(sk_c9) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f460,plain,
( ~ sQ7_spl
| ~ sQ16_spl
| ~ sQ51_spl
| ~ sQ50_spl ),
inference(split_clause,[status(thm)],[f449,f454,f457,f238,f157]) ).
fof(f465,definition,
( sQ53_spl
<=> inverse(inverse(sk_c11)) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f467,plain,
( sQ53_spl
| inverse(inverse(sk_c11)) != sk_c11 ),
inference(component_clause,[status(thm)],[f465]) ).
fof(f468,plain,
( ~ sQ16_spl
| ~ sQ53_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f451,f290,f465,f238]) ).
fof(f469,definition,
( sQ54_spl
<=> inverse(identity) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f472,plain,
( ~ sQ16_spl
| ~ sQ54_spl
| ~ sQ44_spl ),
inference(split_clause,[status(thm)],[f452,f399,f469,f238]) ).
fof(f473,plain,
( sQ50_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f456]) ).
fof(f474,plain,
sQ50_spl,
inference(contradiction_clause,[status(thm)],[f473]) ).
fof(f484,plain,
! [X0] :
( ~ sQ8_spl
| multiply(identity,X0) = multiply(sk_c7,multiply(sk_c8,X0)) ),
inference(paramodulation,[status(thm)],[f264,f67]) ).
fof(f485,plain,
! [X0] :
( ~ sQ8_spl
| X0 = multiply(sk_c7,multiply(sk_c8,X0)) ),
inference(forward_demodulation,[status(thm)],[f65,f484]) ).
fof(f498,plain,
( ~ sQ8_spl
| sk_c8 = multiply(inverse(sk_c7),identity) ),
inference(paramodulation,[status(thm)],[f264,f269]) ).
fof(f499,plain,
( ~ sQ4_spl
| sk_c5 = multiply(inverse(sk_c11),identity) ),
inference(paramodulation,[status(thm)],[f262,f269]) ).
fof(f500,plain,
( ~ sQ11_spl
| sk_c11 = multiply(inverse(sk_c1),sk_c12) ),
inference(paramodulation,[status(thm)],[f174,f269]) ).
fof(f501,plain,
( ~ sQ2_spl
| sk_c4 = multiply(inverse(sk_c12),identity) ),
inference(paramodulation,[status(thm)],[f261,f269]) ).
fof(f502,plain,
( ~ sQ15_spl
| sk_c2 = multiply(inverse(sk_c12),identity) ),
inference(paramodulation,[status(thm)],[f267,f269]) ).
fof(f503,plain,
( ~ sQ6_spl
| sk_c6 = multiply(inverse(sk_c9),identity) ),
inference(paramodulation,[status(thm)],[f263,f269]) ).
fof(f505,plain,
( ~ sQ1_spl
| sk_c12 = multiply(inverse(sk_c4),sk_c11) ),
inference(paramodulation,[status(thm)],[f134,f269]) ).
fof(f506,plain,
( ~ sQ3_spl
| sk_c11 = multiply(inverse(sk_c5),sk_c10) ),
inference(paramodulation,[status(thm)],[f142,f269]) ).
fof(f507,plain,
( ~ sQ5_spl
| sk_c9 = multiply(inverse(sk_c6),sk_c12) ),
inference(paramodulation,[status(thm)],[f150,f269]) ).
fof(f509,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f269,f269]) ).
fof(f510,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f66,f269]) ).
fof(f513,plain,
! [X0] :
( ~ sQ14_spl
| multiply(sk_c12,X0) = multiply(inverse(sk_c2),multiply(sk_c3,X0)) ),
inference(paramodulation,[status(thm)],[f256,f269]) ).
fof(f514,plain,
( ~ sQ14_spl
| sk_c12 = multiply(inverse(sk_c2),sk_c3) ),
inference(paramodulation,[status(thm)],[f213,f269]) ).
fof(f516,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c8 = multiply(sk_c9,identity) ),
inference(forward_demodulation,[status(thm)],[f166,f498]) ).
fof(f525,plain,
( ~ sQ15_spl
| ~ sQ2_spl
| sk_c2 = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f501,f502]) ).
fof(f526,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c12 = multiply(sk_c12,sk_c11) ),
inference(forward_demodulation,[status(thm)],[f138,f505]) ).
fof(f527,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f526,f302]) ).
fof(f528,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sQ25_spl ),
inference(contradiction_clause,[status(thm)],[f527]) ).
fof(f529,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c11 = multiply(sk_c11,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f146,f506]) ).
fof(f530,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sk_c9 = multiply(sk_c9,sk_c12) ),
inference(forward_demodulation,[status(thm)],[f154,f507]) ).
fof(f532,plain,
( ~ sQ6_spl
| sk_c6 = inverse(sk_c9) ),
inference(backward_demodulation,[status(thm)],[f537,f503]) ).
fof(f533,plain,
( ~ sQ2_spl
| sk_c4 = inverse(sk_c12) ),
inference(backward_demodulation,[status(thm)],[f537,f501]) ).
fof(f534,plain,
( ~ sQ4_spl
| sk_c5 = inverse(sk_c11) ),
inference(backward_demodulation,[status(thm)],[f537,f499]) ).
fof(f535,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c8 = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f537,f516]) ).
fof(f536,plain,
( sQ46_spl
| sk_c12 != sk_c11 ),
inference(backward_demodulation,[status(thm)],[f537,f434]) ).
fof(f537,plain,
! [X0] : X0 = multiply(X0,identity),
inference(forward_demodulation,[status(thm)],[f509,f510]) ).
fof(f555,plain,
( sQ47_spl
| ~ sQ2_spl
| inverse(sk_c4) != sk_c12 ),
inference(backward_demodulation,[status(thm)],[f533,f437]) ).
fof(f556,plain,
( sQ53_spl
| ~ sQ4_spl
| inverse(sk_c5) != sk_c11 ),
inference(backward_demodulation,[status(thm)],[f534,f467]) ).
fof(f559,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c7,sk_c9) = identity ),
inference(backward_demodulation,[status(thm)],[f535,f264]) ).
fof(f560,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c9) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f535,f162]) ).
fof(f562,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| X0 = multiply(sk_c7,multiply(sk_c9,X0)) ),
inference(backward_demodulation,[status(thm)],[f535,f485]) ).
fof(f565,plain,
( sQ47_spl
| ~ sQ2_spl
| sk_c12 != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f138,f555]) ).
fof(f566,plain,
( sQ47_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f565]) ).
fof(f567,plain,
( sQ47_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f566]) ).
fof(f568,plain,
( sQ53_spl
| ~ sQ4_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f146,f556]) ).
fof(f569,plain,
( sQ53_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f568]) ).
fof(f570,plain,
( sQ53_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f569]) ).
fof(f573,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| sk_c11 = multiply(sk_c11,sk_c12) ),
inference(backward_demodulation,[status(thm)],[f187,f500]) ).
fof(f575,plain,
( ~ sQ12_spl
| ~ sQ19_spl
| ~ sQ11_spl
| sk_c12 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f174,f386]) ).
fof(f578,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ15_spl
| multiply(sk_c12,X0) = multiply(sk_c12,multiply(sk_c3,X0)) ),
inference(backward_demodulation,[status(thm)],[f226,f513]) ).
fof(f579,plain,
( ~ sQ14_spl
| ~ sQ15_spl
| sk_c12 = multiply(sk_c12,sk_c3) ),
inference(backward_demodulation,[status(thm)],[f226,f514]) ).
fof(f580,plain,
( ~ sQ15_spl
| sk_c2 = inverse(sk_c12) ),
inference(forward_demodulation,[status(thm)],[f537,f502]) ).
fof(f587,plain,
( ~ sQ12_spl
| ~ sQ19_spl
| ~ sQ11_spl
| ~ sQ0_spl
| sk_c12 != sk_c11 ),
inference(backward_demodulation,[status(thm)],[f591,f575]) ).
fof(f589,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| multiply(sk_c11,sk_c12) = sk_c11 ),
inference(backward_demodulation,[status(thm)],[f591,f131]) ).
fof(f591,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| sk_c11 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f131,f573]) ).
fof(f597,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ15_spl
| multiply(sk_c11,sk_c3) = sk_c11 ),
inference(backward_demodulation,[status(thm)],[f604,f200]) ).
fof(f600,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| multiply(sk_c11,X0) = multiply(sk_c1,multiply(sk_c11,X0)) ),
inference(backward_demodulation,[status(thm)],[f604,f270]) ).
fof(f604,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| multiply(sk_c12,X0) = multiply(sk_c11,X0) ),
inference(forward_demodulation,[status(thm)],[f259,f578]) ).
fof(f605,plain,
( ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| sk_c12 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f200,f579]) ).
fof(f606,plain,
( ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| sQ46_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f605,f536]) ).
fof(f607,plain,
( ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| sQ46_spl ),
inference(contradiction_clause,[status(thm)],[f606]) ).
fof(f611,plain,
( sQ33_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c6,sk_c11) != sk_c12 ),
inference(backward_demodulation,[status(thm)],[f624,f329]) ).
fof(f616,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| X0 = multiply(sk_c6,multiply(sk_c9,X0)) ),
inference(backward_demodulation,[status(thm)],[f624,f562]) ).
fof(f619,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| multiply(sk_c6,sk_c9) = identity ),
inference(backward_demodulation,[status(thm)],[f624,f559]) ).
fof(f622,plain,
! [X0] :
( ~ sQ34_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ9_spl
| multiply(X0,sk_c6) != inverse(X0)
| inverse(inverse(X0)) != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f624,f383]) ).
fof(f624,plain,
( ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c6 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f560,f532]) ).
fof(f633,plain,
( sQ24_spl
| ~ sQ2_spl
| multiply(sk_c4,sk_c12) != sk_c12 ),
inference(backward_demodulation,[status(thm)],[f138,f299]) ).
fof(f634,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c12 = multiply(sk_c12,sk_c11) ),
inference(backward_demodulation,[status(thm)],[f138,f505]) ).
fof(f641,plain,
( ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sk_c4 = identity ),
inference(backward_demodulation,[status(thm)],[f655,f261]) ).
fof(f651,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| multiply(sk_c11,X0) = multiply(sk_c4,X0) ),
inference(backward_demodulation,[status(thm)],[f655,f275]) ).
fof(f652,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| X0 = multiply(sk_c9,multiply(sk_c11,X0)) ),
inference(backward_demodulation,[status(thm)],[f655,f272]) ).
fof(f655,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| X0 = multiply(sk_c12,X0) ),
inference(forward_demodulation,[status(thm)],[f273,f616]) ).
fof(f658,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sk_c12 = identity ),
inference(forward_demodulation,[status(thm)],[f150,f619]) ).
fof(f659,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f658,f292]) ).
fof(f660,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f659]) ).
fof(f662,plain,
! [X0] :
( ~ sQ34_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ9_spl
| multiply(X0,sk_c6) != inverse(X0)
| inverse(inverse(X0)) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f624,f622]) ).
fof(f668,plain,
( sQ24_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c11 != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f134,f633]) ).
fof(f669,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sk_c12 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f655,f634]) ).
fof(f670,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sQ46_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f669,f536]) ).
fof(f671,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sQ46_spl ),
inference(contradiction_clause,[status(thm)],[f670]) ).
fof(f673,plain,
( ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| identity = inverse(sk_c12) ),
inference(backward_demodulation,[status(thm)],[f641,f533]) ).
fof(f679,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ2_spl
| multiply(sk_c11,X0) = multiply(identity,X0) ),
inference(forward_demodulation,[status(thm)],[f641,f651]) ).
fof(f680,plain,
( sQ28_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ2_spl
| sk_c11 != sk_c12 ),
inference(backward_demodulation,[status(thm)],[f686,f312]) ).
fof(f681,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ2_spl
| sk_c11 = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f686,f529]) ).
fof(f686,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ2_spl
| multiply(sk_c11,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f65,f679]) ).
fof(f688,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c9 = sk_c12 ),
inference(backward_demodulation,[status(thm)],[f692,f530]) ).
fof(f689,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c6 = identity ),
inference(backward_demodulation,[status(thm)],[f692,f263]) ).
fof(f692,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| X0 = multiply(sk_c9,X0) ),
inference(forward_demodulation,[status(thm)],[f686,f652]) ).
fof(f700,plain,
( ~ sQ11_spl
| ~ sQ22_spl
| sk_c11 = multiply(inverse(sk_c1),identity) ),
inference(backward_demodulation,[status(thm)],[f291,f500]) ).
fof(f704,plain,
( sQ12_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ22_spl
| inverse(sk_c1) != identity ),
inference(backward_demodulation,[status(thm)],[f706,f188]) ).
fof(f706,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ22_spl
| identity = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f291,f669]) ).
fof(f711,plain,
( ~ sQ46_spl
| sk_c12 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f537,f433]) ).
fof(f716,plain,
( ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ22_spl
| identity = inverse(identity) ),
inference(forward_demodulation,[status(thm)],[f291,f673]) ).
fof(f724,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ22_spl
| identity = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f706,f681]) ).
fof(f732,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ22_spl
| sk_c8 = identity ),
inference(backward_demodulation,[status(thm)],[f733,f535]) ).
fof(f733,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ22_spl
| sk_c9 = identity ),
inference(forward_demodulation,[status(thm)],[f291,f688]) ).
fof(f738,plain,
! [X0] :
( ~ sQ19_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ22_spl
| inverse(X0) != sk_c11
| multiply(X0,identity) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f706,f248]) ).
fof(f739,plain,
! [X0] :
( ~ sQ19_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ22_spl
| inverse(X0) != sk_c11
| X0 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f537,f738]) ).
fof(f740,plain,
! [X0] :
( ~ sQ19_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ22_spl
| ~ sQ3_spl
| ~ sQ4_spl
| inverse(X0) != sk_c11
| X0 != identity ),
inference(forward_demodulation,[status(thm)],[f724,f739]) ).
fof(f741,plain,
! [X0] :
( ~ sQ19_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ22_spl
| ~ sQ3_spl
| ~ sQ4_spl
| inverse(X0) != identity
| X0 != identity ),
inference(forward_demodulation,[status(thm)],[f706,f740]) ).
fof(f742,plain,
( ~ sQ19_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ22_spl
| ~ sQ3_spl
| ~ sQ4_spl
| inverse(identity) != identity ),
inference(destructive_equality_resolution,[status(thm)],[f741]) ).
fof(f743,plain,
( ~ sQ19_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ22_spl
| ~ sQ3_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f742,f716]) ).
fof(f744,plain,
( ~ sQ19_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ22_spl
| ~ sQ3_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f743]) ).
fof(f753,plain,
( ~ sQ11_spl
| ~ sQ22_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| identity = multiply(inverse(sk_c1),identity) ),
inference(forward_demodulation,[status(thm)],[f706,f700]) ).
fof(f754,plain,
( ~ sQ11_spl
| ~ sQ22_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| identity = inverse(sk_c1) ),
inference(forward_demodulation,[status(thm)],[f537,f753]) ).
fof(f757,plain,
( sQ12_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ22_spl
| ~ sQ11_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f754,f704]) ).
fof(f758,plain,
( sQ12_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ22_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f757]) ).
fof(f759,plain,
( sQ12_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ22_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f758]) ).
fof(f766,plain,
( sQ28_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ44_spl ),
inference(split_clause,[status(thm)],[f680,f399,f137,f149,f153,f165,f161,f133,f310]) ).
fof(f776,plain,
( sQ24_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ44_spl ),
inference(split_clause,[status(thm)],[f668,f399,f133,f137,f297]) ).
fof(f801,plain,
( ~ sQ46_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f711,f399,f432]) ).
fof(f804,plain,
( ~ sQ14_spl
| ~ sQ15_spl
| sk_c12 = multiply(sk_c12,sk_c3) ),
inference(backward_demodulation,[status(thm)],[f226,f514]) ).
fof(f813,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| multiply(sk_c11,X0) = multiply(sk_c12,X0) ),
inference(forward_demodulation,[status(thm)],[f270,f600]) ).
fof(f826,plain,
( ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ11_spl
| ~ sQ13_spl
| sk_c12 = multiply(sk_c11,sk_c3) ),
inference(forward_demodulation,[status(thm)],[f813,f804]) ).
fof(f829,plain,
( ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ13_spl
| sk_c2 = inverse(sk_c11) ),
inference(backward_demodulation,[status(thm)],[f842,f580]) ).
fof(f835,plain,
( sQ2_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ11_spl
| ~ sQ13_spl
| inverse(sk_c4) != sk_c11 ),
inference(backward_demodulation,[status(thm)],[f842,f139]) ).
fof(f837,plain,
( ~ sQ1_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ11_spl
| ~ sQ13_spl
| multiply(sk_c4,sk_c11) = sk_c11 ),
inference(backward_demodulation,[status(thm)],[f842,f134]) ).
fof(f839,plain,
( ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ11_spl
| ~ sQ13_spl
| multiply(sk_c2,sk_c11) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f842,f213]) ).
fof(f840,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| multiply(sk_c11,sk_c11) = sk_c11 ),
inference(backward_demodulation,[status(thm)],[f842,f589]) ).
fof(f842,plain,
( ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ11_spl
| ~ sQ13_spl
| sk_c12 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f597,f826]) ).
fof(f850,plain,
( sQ28_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ11_spl
| ~ sQ13_spl
| multiply(sk_c11,sk_c11) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f842,f312]) ).
fof(f857,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| sQ28_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f840,f850]) ).
fof(f858,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| sQ28_spl ),
inference(contradiction_clause,[status(thm)],[f857]) ).
fof(f861,plain,
( ~ sQ12_spl
| ~ sQ19_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ44_spl ),
inference(split_clause,[status(thm)],[f587,f399,f130,f173,f247,f186]) ).
fof(f875,plain,
( ~ sQ18_spl
| ~ sQ49_spl
| ~ sQ44_spl ),
inference(split_clause,[status(thm)],[f416,f399,f442,f244]) ).
fof(f878,definition,
( sQ56_spl
<=> sk_c3 = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f880,plain,
( sQ56_spl
| sk_c3 != sk_c11 ),
inference(component_clause,[status(thm)],[f878]) ).
fof(f881,plain,
( ~ sQ14_spl
| ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ56_spl ),
inference(split_clause,[status(thm)],[f418,f878,f225,f244,f212]) ).
fof(f885,plain,
inverse(identity) = identity,
inference(paramodulation,[status(thm)],[f66,f537]) ).
fof(f898,plain,
( ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ13_spl
| multiply(sk_c2,sk_c11) = identity ),
inference(paramodulation,[status(thm)],[f829,f66]) ).
fof(f907,plain,
( ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ13_spl
| sk_c3 = identity ),
inference(forward_demodulation,[status(thm)],[f839,f898]) ).
fof(f913,plain,
( ~ sQ12_spl
| sk_c1 = multiply(inverse(sk_c11),identity) ),
inference(paramodulation,[status(thm)],[f266,f269]) ).
fof(f915,plain,
( ~ sQ12_spl
| sk_c1 = inverse(sk_c11) ),
inference(forward_demodulation,[status(thm)],[f537,f913]) ).
fof(f920,plain,
( ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ13_spl
| sk_c1 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f829,f915]) ).
fof(f924,plain,
( ~ sQ1_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ11_spl
| ~ sQ13_spl
| sk_c11 = multiply(inverse(sk_c4),sk_c11) ),
inference(paramodulation,[status(thm)],[f837,f269]) ).
fof(f926,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| sk_c11 = multiply(inverse(sk_c11),sk_c11) ),
inference(paramodulation,[status(thm)],[f840,f269]) ).
fof(f928,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| sk_c11 = identity ),
inference(forward_demodulation,[status(thm)],[f66,f926]) ).
fof(f933,plain,
( ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| multiply(identity,sk_c1) = identity ),
inference(backward_demodulation,[status(thm)],[f928,f266]) ).
fof(f934,plain,
( sQ2_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ12_spl
| inverse(sk_c4) != identity ),
inference(backward_demodulation,[status(thm)],[f928,f835]) ).
fof(f939,plain,
( ~ sQ1_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ12_spl
| sk_c11 = multiply(inverse(sk_c4),identity) ),
inference(backward_demodulation,[status(thm)],[f928,f924]) ).
fof(f949,plain,
! [X0] :
( ~ sQ38_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| multiply(X0,identity) != inverse(X0)
| inverse(inverse(X0)) != sk_c11 ),
inference(backward_demodulation,[status(thm)],[f928,f360]) ).
fof(f955,plain,
( ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ0_spl
| identity = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f956,f920]) ).
fof(f956,plain,
( ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| sk_c1 = identity ),
inference(forward_demodulation,[status(thm)],[f65,f933]) ).
fof(f960,plain,
( ~ sQ1_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ12_spl
| identity = multiply(inverse(sk_c4),identity) ),
inference(forward_demodulation,[status(thm)],[f928,f939]) ).
fof(f961,plain,
( ~ sQ1_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ12_spl
| identity = inverse(sk_c4) ),
inference(forward_demodulation,[status(thm)],[f537,f960]) ).
fof(f962,plain,
( ~ sQ1_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ12_spl
| sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f961,f934]) ).
fof(f963,plain,
( ~ sQ1_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ12_spl
| sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f962]) ).
fof(f969,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ22_spl
| identity = sk_c12 ),
inference(forward_demodulation,[status(thm)],[f733,f688]) ).
fof(f1099,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ22_spl
| multiply(identity,sk_c12) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f706,f132]) ).
fof(f1100,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ22_spl
| sk_c12 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f65,f1099]) ).
fof(f1101,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ22_spl
| ~ sQ7_spl
| identity != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f969,f1100]) ).
fof(f1102,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ22_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f724,f1101]) ).
fof(f1103,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ22_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1102]) ).
fof(f1104,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ22_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f1103]) ).
fof(f1121,plain,
! [X0] :
( ~ sQ38_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| X0 != inverse(X0)
| inverse(inverse(X0)) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f537,f949]) ).
fof(f1148,plain,
( sQ32_spl
| ~ sQ44_spl
| multiply(sk_c8,inverse(sk_c8)) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f400,f326]) ).
fof(f1329,plain,
! [X0] :
( ~ sQ34_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(X0,sk_c6) != inverse(X0)
| inverse(inverse(X0)) != identity ),
inference(forward_demodulation,[status(thm)],[f689,f662]) ).
fof(f1330,plain,
! [X0] :
( ~ sQ34_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(X0,identity) != inverse(X0)
| inverse(inverse(X0)) != identity ),
inference(forward_demodulation,[status(thm)],[f689,f1329]) ).
fof(f1331,plain,
! [X0] :
( ~ sQ34_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| X0 != inverse(X0)
| inverse(inverse(X0)) != identity ),
inference(forward_demodulation,[status(thm)],[f537,f1330]) ).
fof(f1567,plain,
( ~ sQ34_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| identity != inverse(identity)
| inverse(identity) != identity ),
inference(paramodulation,[status(thm)],[f885,f1331]) ).
fof(f1568,definition,
( sQ57_spl
<=> inverse(identity) = identity ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f1570,plain,
( sQ57_spl
| inverse(identity) != identity ),
inference(component_clause,[status(thm)],[f1568]) ).
fof(f1571,plain,
( ~ sQ34_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ57_spl ),
inference(split_clause,[status(thm)],[f1567,f1568,f137,f133,f149,f157,f165,f153,f161,f330]) ).
fof(f1572,plain,
( sQ57_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f885,f1570]) ).
fof(f1573,plain,
( sQ57_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1572]) ).
fof(f1574,plain,
sQ57_spl,
inference(contradiction_clause,[status(thm)],[f1573]) ).
fof(f1575,plain,
( sQ32_spl
| ~ sQ44_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ22_spl
| multiply(identity,inverse(sk_c8)) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f732,f1148]) ).
fof(f1576,plain,
( sQ32_spl
| ~ sQ44_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ22_spl
| inverse(sk_c8) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f65,f1575]) ).
fof(f1577,plain,
( sQ32_spl
| ~ sQ44_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ22_spl
| inverse(identity) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f732,f1576]) ).
fof(f1578,plain,
( sQ32_spl
| ~ sQ44_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ22_spl
| identity != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f885,f1577]) ).
fof(f1579,plain,
( sQ32_spl
| ~ sQ44_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ22_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f706,f1578]) ).
fof(f1580,plain,
( sQ32_spl
| ~ sQ44_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ22_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1579]) ).
fof(f1581,plain,
( sQ32_spl
| ~ sQ44_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f1580]) ).
fof(f1585,plain,
( sQ33_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(identity,sk_c11) != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f689,f611]) ).
fof(f1586,plain,
( sQ33_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c11 != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f65,f1585]) ).
fof(f1587,plain,
( sQ33_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ22_spl
| identity != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f706,f1586]) ).
fof(f1588,plain,
( ~ sQ32_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ22_spl
| multiply(identity,inverse(sk_c8)) = sk_c12 ),
inference(forward_demodulation,[status(thm)],[f732,f325]) ).
fof(f1589,plain,
( ~ sQ32_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ22_spl
| inverse(sk_c8) = sk_c12 ),
inference(forward_demodulation,[status(thm)],[f65,f1588]) ).
fof(f1590,plain,
( ~ sQ32_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ22_spl
| inverse(identity) = sk_c12 ),
inference(forward_demodulation,[status(thm)],[f732,f1589]) ).
fof(f1591,plain,
( ~ sQ32_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ22_spl
| identity = sk_c12 ),
inference(forward_demodulation,[status(thm)],[f885,f1590]) ).
fof(f1592,plain,
( ~ sQ32_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ22_spl
| sQ33_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1591,f1587]) ).
fof(f1593,plain,
( ~ sQ32_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ22_spl
| sQ33_spl ),
inference(contradiction_clause,[status(thm)],[f1592]) ).
fof(f1612,plain,
( ~ sQ44_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| sk_c12 = identity ),
inference(backward_demodulation,[status(thm)],[f928,f400]) ).
fof(f1669,plain,
( ~ sQ15_spl
| ~ sQ2_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ0_spl
| identity = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f955,f525]) ).
fof(f1676,plain,
! [X0] :
( ~ sQ38_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| X0 != inverse(X0)
| inverse(inverse(X0)) != identity ),
inference(forward_demodulation,[status(thm)],[f928,f1121]) ).
fof(f1761,plain,
( sQ56_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ13_spl
| identity != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f907,f880]) ).
fof(f1762,plain,
( sQ56_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ12_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f928,f1761]) ).
fof(f1763,plain,
( sQ56_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1762]) ).
fof(f1764,plain,
( sQ56_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f1763]) ).
fof(f1786,plain,
( ~ sQ38_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| identity != inverse(identity)
| inverse(identity) != identity ),
inference(paramodulation,[status(thm)],[f885,f1676]) ).
fof(f1787,plain,
( ~ sQ38_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ57_spl ),
inference(split_clause,[status(thm)],[f1786,f1568,f199,f225,f212,f173,f130,f186,f344]) ).
fof(f1811,plain,
( sQ1_spl
| ~ sQ15_spl
| ~ sQ2_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ0_spl
| multiply(identity,sk_c12) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1669,f135]) ).
fof(f1812,plain,
( sQ1_spl
| ~ sQ15_spl
| ~ sQ2_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ0_spl
| sk_c12 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f65,f1811]) ).
fof(f1813,plain,
( sQ1_spl
| ~ sQ15_spl
| ~ sQ2_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ44_spl
| identity != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1612,f1812]) ).
fof(f1814,plain,
( sQ1_spl
| ~ sQ15_spl
| ~ sQ2_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ44_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f928,f1813]) ).
fof(f1815,plain,
( sQ1_spl
| ~ sQ15_spl
| ~ sQ2_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ44_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1814]) ).
fof(f1816,plain,
( sQ1_spl
| ~ sQ15_spl
| ~ sQ2_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ44_spl ),
inference(contradiction_clause,[status(thm)],[f1815]) ).
fof(f1820,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| inverse(X0) != sk_c11
| multiply(X0,identity) != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f928,f239]) ).
fof(f1821,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| inverse(X0) != sk_c11
| X0 != sk_c12 ),
inference(forward_demodulation,[status(thm)],[f537,f1820]) ).
fof(f1822,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ44_spl
| inverse(X0) != sk_c11
| X0 != identity ),
inference(forward_demodulation,[status(thm)],[f1612,f1821]) ).
fof(f1823,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ44_spl
| inverse(X0) != identity
| X0 != identity ),
inference(forward_demodulation,[status(thm)],[f928,f1822]) ).
fof(f1824,plain,
( ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ44_spl
| inverse(identity) != identity ),
inference(destructive_equality_resolution,[status(thm)],[f1823]) ).
fof(f1825,plain,
( ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ44_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1824,f885]) ).
fof(f1826,plain,
( ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ44_spl ),
inference(contradiction_clause,[status(thm)],[f1825]) ).
fof(f1827,plain,
$false,
inference(sat_refutation,[status(thm)],[f136,f140,f144,f148,f152,f156,f160,f164,f168,f176,f177,f178,f179,f180,f181,f182,f183,f184,f189,f190,f192,f193,f194,f195,f196,f197,f202,f203,f205,f206,f207,f208,f209,f210,f215,f216,f218,f219,f220,f221,f222,f223,f228,f229,f231,f232,f233,f234,f235,f236,f253,f306,f333,f347,f364,f395,f404,f421,f431,f438,f445,f446,f460,f468,f472,f474,f528,f567,f570,f607,f660,f671,f744,f759,f766,f776,f801,f858,f861,f875,f881,f963,f1104,f1571,f1574,f1581,f1593,f1764,f1787,f1816,f1826]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP318-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n019.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 20:09:20 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.10/0.42 % Refutation found
% 0.10/0.42 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.44 % Elapsed time: 0.075544 seconds
% 0.10/0.44 % CPU time: 0.416492 seconds
% 0.10/0.44 % Total memory used: 110.369 MB
% 0.10/0.44 % Net memory used: 110.029 MB
%------------------------------------------------------------------------------