%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP380-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:33:34 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 90
% Syntax : Number of formulae : 438 ( 16 unt; 38 def)
% Number of atoms : 1558 ( 511 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 2068 ( 948 ~;1082 |; 0 &)
% ( 38 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 40 ( 38 usr; 39 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 98 ( 98 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c3) = sk_c11
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c7) = sk_c6
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c6) = sk_c8
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c10,sk_c9) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c10,sk_c9) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c10,sk_c9) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c10,sk_c9) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c10,sk_c9) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c10,sk_c9) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c7) = sk_c6
| multiply(sk_c10,sk_c9) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( inverse(sk_c6) = sk_c8
| multiply(sk_c10,sk_c9) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( inverse(sk_c7) = sk_c6
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( inverse(sk_c6) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( inverse(sk_c3) = sk_c11
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,negated_conjecture,
( inverse(sk_c7) = sk_c6
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,negated_conjecture,
( inverse(sk_c6) = sk_c8
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f50,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f51,negated_conjecture,
( inverse(sk_c7) = sk_c6
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f52,negated_conjecture,
( inverse(sk_c6) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f53,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f54,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
| multiply(X4,sk_c9) != sk_c10
| inverse(X3) != X4
| multiply(X3,X4) != sk_c10
| multiply(sk_c10,sk_c9) != sk_c11
| inverse(sk_c11) != sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f55,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f56,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f57,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f58,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f59,plain,
( inverse(sk_c3) = sk_c11
| inverse(sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f60,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f61,plain,
( inverse(sk_c4) = sk_c10
| inverse(sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f62,plain,
( multiply(sk_c5,sk_c8) = sk_c11
| inverse(sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f63,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f64,plain,
( multiply(sk_c8,sk_c10) = sk_c11
| inverse(sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f65,plain,
( inverse(sk_c7) = sk_c6
| inverse(sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f66,plain,
( inverse(sk_c6) = sk_c8
| inverse(sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f67,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f68,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f69,plain,
( inverse(sk_c3) = sk_c11
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f70,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f71,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f72,plain,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f73,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f75,plain,
( inverse(sk_c7) = sk_c6
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f76,plain,
( inverse(sk_c6) = sk_c8
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f78,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f79,plain,
( inverse(sk_c3) = sk_c11
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f80,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f81,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f82,plain,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f83,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f84,plain,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f85,plain,
( inverse(sk_c7) = sk_c6
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f86,plain,
( inverse(sk_c6) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f87,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f88,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f89,plain,
( inverse(sk_c3) = sk_c11
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f90,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f91,plain,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f92,plain,
( multiply(sk_c5,sk_c8) = sk_c11
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f93,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f94,plain,
( multiply(sk_c8,sk_c10) = sk_c11
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f95,plain,
( inverse(sk_c7) = sk_c6
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f96,plain,
( inverse(sk_c6) = sk_c8
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f97,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f98,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f99,plain,
( inverse(sk_c3) = sk_c11
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f100,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f101,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f102,plain,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f103,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f104,plain,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f105,plain,
( inverse(sk_c7) = sk_c6
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f106,plain,
( inverse(sk_c6) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f107,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f108,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] :
( multiply(X4,sk_c9) != sk_c10
| ! [X3] :
( inverse(X3) != X4
| multiply(X3,X4) != sk_c10
| multiply(sk_c10,sk_c9) != sk_c11
| inverse(sk_c11) != sk_c10 ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f54]) ).
fof(f109,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
| multiply(X1,sk_c9) != sk_c10
| inverse(X0) != X1
| multiply(X0,X1) != sk_c10
| multiply(sk_c10,sk_c9) != sk_c11
| inverse(sk_c11) != sk_c10 ),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f110,definition,
( sQ0_spl
<=> inverse(sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f111,plain,
( ~ sQ0_spl
| inverse(sk_c11) = sk_c10 ),
inference(component_clause,[status(thm)],[f110]) ).
fof(f112,plain,
( sQ0_spl
| inverse(sk_c11) != sk_c10 ),
inference(component_clause,[status(thm)],[f110]) ).
fof(f113,definition,
( sQ1_spl
<=> multiply(sk_c3,sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f114,plain,
( ~ sQ1_spl
| multiply(sk_c3,sk_c11) = sk_c10 ),
inference(component_clause,[status(thm)],[f113]) ).
fof(f116,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f58,f110,f113]) ).
fof(f117,definition,
( sQ2_spl
<=> inverse(sk_c3) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f118,plain,
( ~ sQ2_spl
| inverse(sk_c3) = sk_c11 ),
inference(component_clause,[status(thm)],[f117]) ).
fof(f120,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f59,f110,f117]) ).
fof(f121,definition,
( sQ3_spl
<=> multiply(sk_c4,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f122,plain,
( ~ sQ3_spl
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(component_clause,[status(thm)],[f121]) ).
fof(f124,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f60,f110,f121]) ).
fof(f125,definition,
( sQ4_spl
<=> inverse(sk_c4) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f126,plain,
( ~ sQ4_spl
| inverse(sk_c4) = sk_c10 ),
inference(component_clause,[status(thm)],[f125]) ).
fof(f128,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f61,f110,f125]) ).
fof(f129,definition,
( sQ5_spl
<=> multiply(sk_c5,sk_c8) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f130,plain,
( ~ sQ5_spl
| multiply(sk_c5,sk_c8) = sk_c11 ),
inference(component_clause,[status(thm)],[f129]) ).
fof(f132,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f62,f110,f129]) ).
fof(f133,definition,
( sQ6_spl
<=> inverse(sk_c5) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f134,plain,
( ~ sQ6_spl
| inverse(sk_c5) = sk_c8 ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,plain,
( sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f63,f110,f133]) ).
fof(f137,definition,
( sQ7_spl
<=> multiply(sk_c8,sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f138,plain,
( ~ sQ7_spl
| multiply(sk_c8,sk_c10) = sk_c11 ),
inference(component_clause,[status(thm)],[f137]) ).
fof(f140,plain,
( sQ7_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f64,f110,f137]) ).
fof(f141,definition,
( sQ8_spl
<=> inverse(sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f142,plain,
( ~ sQ8_spl
| inverse(sk_c7) = sk_c6 ),
inference(component_clause,[status(thm)],[f141]) ).
fof(f144,plain,
( sQ8_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f65,f110,f141]) ).
fof(f145,definition,
( sQ9_spl
<=> inverse(sk_c6) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f146,plain,
( ~ sQ9_spl
| inverse(sk_c6) = sk_c8 ),
inference(component_clause,[status(thm)],[f145]) ).
fof(f148,plain,
( sQ9_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f66,f110,f145]) ).
fof(f149,definition,
( sQ10_spl
<=> multiply(sk_c7,sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f150,plain,
( ~ sQ10_spl
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(component_clause,[status(thm)],[f149]) ).
fof(f152,plain,
( sQ10_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f67,f110,f149]) ).
fof(f153,definition,
( sQ11_spl
<=> multiply(sk_c10,sk_c9) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f154,plain,
( ~ sQ11_spl
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(component_clause,[status(thm)],[f153]) ).
fof(f155,plain,
( sQ11_spl
| multiply(sk_c10,sk_c9) != sk_c11 ),
inference(component_clause,[status(thm)],[f153]) ).
fof(f156,plain,
( sQ1_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f68,f153,f113]) ).
fof(f157,plain,
( sQ2_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f69,f153,f117]) ).
fof(f158,plain,
( sQ3_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f70,f153,f121]) ).
fof(f159,plain,
( sQ4_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f71,f153,f125]) ).
fof(f160,plain,
( sQ5_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f72,f153,f129]) ).
fof(f161,plain,
( sQ6_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f73,f153,f133]) ).
fof(f163,plain,
( sQ8_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f75,f153,f141]) ).
fof(f164,plain,
( sQ9_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f76,f153,f145]) ).
fof(f166,definition,
( sQ12_spl
<=> multiply(sk_c1,sk_c2) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f167,plain,
( ~ sQ12_spl
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(component_clause,[status(thm)],[f166]) ).
fof(f169,plain,
( sQ1_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f78,f166,f113]) ).
fof(f170,plain,
( sQ2_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f79,f166,f117]) ).
fof(f171,plain,
( sQ3_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f80,f166,f121]) ).
fof(f172,plain,
( sQ4_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f81,f166,f125]) ).
fof(f173,plain,
( sQ5_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f82,f166,f129]) ).
fof(f174,plain,
( sQ6_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f83,f166,f133]) ).
fof(f175,plain,
( sQ7_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f84,f166,f137]) ).
fof(f176,plain,
( sQ8_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f85,f166,f141]) ).
fof(f177,plain,
( sQ9_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f86,f166,f145]) ).
fof(f178,plain,
( sQ10_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f87,f166,f149]) ).
fof(f179,definition,
( sQ13_spl
<=> inverse(sk_c1) = sk_c2 ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f180,plain,
( ~ sQ13_spl
| inverse(sk_c1) = sk_c2 ),
inference(component_clause,[status(thm)],[f179]) ).
fof(f182,plain,
( sQ1_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f88,f179,f113]) ).
fof(f183,plain,
( sQ2_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f89,f179,f117]) ).
fof(f184,plain,
( sQ3_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f90,f179,f121]) ).
fof(f185,plain,
( sQ4_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f91,f179,f125]) ).
fof(f186,plain,
( sQ5_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f92,f179,f129]) ).
fof(f187,plain,
( sQ6_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f93,f179,f133]) ).
fof(f188,plain,
( sQ7_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f94,f179,f137]) ).
fof(f189,plain,
( sQ8_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f95,f179,f141]) ).
fof(f190,plain,
( sQ9_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f96,f179,f145]) ).
fof(f191,plain,
( sQ10_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f97,f179,f149]) ).
fof(f192,definition,
( sQ14_spl
<=> multiply(sk_c2,sk_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f193,plain,
( ~ sQ14_spl
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(component_clause,[status(thm)],[f192]) ).
fof(f195,plain,
( sQ1_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f98,f192,f113]) ).
fof(f196,plain,
( sQ2_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f99,f192,f117]) ).
fof(f197,plain,
( sQ3_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f100,f192,f121]) ).
fof(f198,plain,
( sQ4_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f101,f192,f125]) ).
fof(f199,plain,
( sQ5_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f102,f192,f129]) ).
fof(f200,plain,
( sQ6_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f103,f192,f133]) ).
fof(f201,plain,
( sQ7_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f104,f192,f137]) ).
fof(f202,plain,
( sQ8_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f105,f192,f141]) ).
fof(f203,plain,
( sQ9_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f106,f192,f145]) ).
fof(f204,plain,
( sQ10_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f107,f192,f149]) ).
fof(f205,definition,
! [X0,X1] :
( sQ15_spl
<=> ( multiply(X1,sk_c9) != sk_c10
| inverse(X0) != X1
| multiply(X0,X1) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f206,plain,
! [X0,X1] :
( ~ sQ15_spl
| multiply(X1,sk_c9) != sk_c10
| inverse(X0) != X1
| multiply(X0,X1) != sk_c10 ),
inference(component_clause,[status(thm)],[f205]) ).
fof(f208,definition,
! [X2] :
( sQ16_spl
<=> ( inverse(X2) != sk_c11
| multiply(X2,sk_c11) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f209,plain,
! [X0] :
( ~ sQ16_spl
| inverse(X0) != sk_c11
| multiply(X0,sk_c11) != sk_c10 ),
inference(component_clause,[status(thm)],[f208]) ).
fof(f211,definition,
! [X3] :
( sQ17_spl
<=> ( inverse(X3) != sk_c10
| multiply(X3,sk_c10) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f212,plain,
! [X0] :
( ~ sQ17_spl
| inverse(X0) != sk_c10
| multiply(X0,sk_c10) != sk_c9 ),
inference(component_clause,[status(thm)],[f211]) ).
fof(f214,definition,
! [X4,X5,X6,X7] :
( sQ18_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,[sQ18_spl])],[split_symbol_definition]) ).
fof(f215,plain,
! [X0,X1,X2,X3] :
( ~ sQ18_spl
| multiply(X2,X1) != X3
| inverse(X3) != X1
| inverse(X2) != X3
| multiply(X1,sk_c10) != sk_c11
| inverse(X0) != X1
| multiply(X0,X1) != sk_c11 ),
inference(component_clause,[status(thm)],[f214]) ).
fof(f217,plain,
( sQ18_spl
| sQ17_spl
| sQ16_spl
| sQ15_spl
| ~ sQ11_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f109,f110,f153,f205,f208,f211,f214]) ).
fof(f218,plain,
! [X0,X1] :
( ~ sQ18_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c10) != sk_c11
| multiply(X0,inverse(X0)) != sk_c11 ),
inference(destructive_equality_resolution,[status(thm)],[f215]) ).
fof(f220,plain,
! [X0] :
( ~ sQ14_spl
| multiply(sk_c10,X0) = multiply(sk_c2,multiply(sk_c9,X0)) ),
inference(paramodulation,[status(thm)],[f193,f57]) ).
fof(f223,plain,
! [X0] :
( ~ sQ12_spl
| multiply(sk_c10,X0) = multiply(sk_c1,multiply(sk_c2,X0)) ),
inference(paramodulation,[status(thm)],[f167,f57]) ).
fof(f226,plain,
( ~ sQ6_spl
| multiply(sk_c8,sk_c5) = identity ),
inference(paramodulation,[status(thm)],[f134,f56]) ).
fof(f227,plain,
( ~ sQ8_spl
| multiply(sk_c6,sk_c7) = identity ),
inference(paramodulation,[status(thm)],[f142,f56]) ).
fof(f228,plain,
( ~ sQ9_spl
| multiply(sk_c8,sk_c6) = identity ),
inference(paramodulation,[status(thm)],[f146,f56]) ).
fof(f229,plain,
( ~ sQ13_spl
| multiply(sk_c2,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f180,f56]) ).
fof(f230,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f56,f57]) ).
fof(f231,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f55,f230]) ).
fof(f233,plain,
! [X0] :
( ~ sQ7_spl
| multiply(sk_c11,X0) = multiply(sk_c8,multiply(sk_c10,X0)) ),
inference(paramodulation,[status(thm)],[f138,f57]) ).
fof(f234,plain,
( ~ sQ2_spl
| multiply(sk_c11,sk_c3) = identity ),
inference(paramodulation,[status(thm)],[f118,f56]) ).
fof(f235,plain,
( ~ sQ0_spl
| multiply(sk_c10,sk_c11) = identity ),
inference(paramodulation,[status(thm)],[f111,f56]) ).
fof(f236,plain,
! [X0] :
( ~ sQ5_spl
| multiply(sk_c11,X0) = multiply(sk_c5,multiply(sk_c8,X0)) ),
inference(paramodulation,[status(thm)],[f130,f57]) ).
fof(f238,plain,
! [X0] :
( ~ sQ1_spl
| multiply(sk_c10,X0) = multiply(sk_c3,multiply(sk_c11,X0)) ),
inference(paramodulation,[status(thm)],[f114,f57]) ).
fof(f240,plain,
! [X0] :
( ~ sQ18_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)],[f55,f218]) ).
fof(f252,definition,
( sQ20_spl
<=> multiply(inverse(identity),sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f254,plain,
( sQ20_spl
| multiply(inverse(identity),sk_c10) != sk_c11 ),
inference(component_clause,[status(thm)],[f252]) ).
fof(f255,definition,
( sQ21_spl
<=> inverse(inverse(identity)) = inverse(identity) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f257,plain,
( sQ21_spl
| inverse(inverse(identity)) != inverse(identity) ),
inference(component_clause,[status(thm)],[f255]) ).
fof(f259,definition,
( sQ22_spl
<=> inverse(identity) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f261,plain,
( sQ22_spl
| inverse(identity) != sk_c11 ),
inference(component_clause,[status(thm)],[f259]) ).
fof(f262,definition,
! [X0] :
( sQ23_spl
<=> ( multiply(X0,inverse(identity)) != inverse(X0)
| inverse(inverse(X0)) != inverse(identity) ) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f263,plain,
! [X0] :
( ~ sQ23_spl
| multiply(X0,inverse(identity)) != inverse(X0)
| inverse(inverse(X0)) != inverse(identity) ),
inference(component_clause,[status(thm)],[f262]) ).
fof(f265,plain,
( ~ sQ18_spl
| sQ23_spl
| ~ sQ20_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f240,f259,f252,f262,f214]) ).
fof(f343,plain,
! [X0] :
( ~ sQ11_spl
| multiply(sk_c11,X0) = multiply(sk_c10,multiply(sk_c9,X0)) ),
inference(paramodulation,[status(thm)],[f154,f57]) ).
fof(f345,plain,
( ~ sQ3_spl
| ~ sQ17_spl
| inverse(sk_c4) != sk_c10
| sk_c9 != sk_c9 ),
inference(paramodulation,[status(thm)],[f122,f212]) ).
fof(f350,definition,
( sQ44_spl
<=> sk_c9 = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f352,plain,
( sQ44_spl
| sk_c9 != sk_c9 ),
inference(component_clause,[status(thm)],[f350]) ).
fof(f353,plain,
( ~ sQ3_spl
| ~ sQ17_spl
| ~ sQ4_spl
| ~ sQ44_spl ),
inference(split_clause,[status(thm)],[f345,f350,f125,f211,f121]) ).
fof(f354,definition,
( sQ45_spl
<=> sk_c11 = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f356,plain,
( sQ45_spl
| sk_c11 != sk_c9 ),
inference(component_clause,[status(thm)],[f354]) ).
fof(f364,definition,
( sQ48_spl
<=> inverse(inverse(sk_c10)) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f366,plain,
( sQ48_spl
| inverse(inverse(sk_c10)) != sk_c10 ),
inference(component_clause,[status(thm)],[f364]) ).
fof(f371,definition,
( sQ50_spl
<=> inverse(identity) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f373,plain,
( sQ50_spl
| inverse(identity) != sk_c10 ),
inference(component_clause,[status(thm)],[f371]) ).
fof(f375,plain,
( sQ44_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f352]) ).
fof(f376,plain,
sQ44_spl,
inference(contradiction_clause,[status(thm)],[f375]) ).
fof(f377,plain,
! [X0] :
( ~ sQ15_spl
| multiply(inverse(X0),sk_c9) != sk_c10
| multiply(X0,inverse(X0)) != sk_c10 ),
inference(destructive_equality_resolution,[status(thm)],[f206]) ).
fof(f380,plain,
( ~ sQ1_spl
| ~ sQ16_spl
| inverse(sk_c3) != sk_c11
| sk_c10 != sk_c10 ),
inference(paramodulation,[status(thm)],[f114,f209]) ).
fof(f381,plain,
( ~ sQ16_spl
| inverse(inverse(sk_c11)) != sk_c11
| identity != sk_c10 ),
inference(paramodulation,[status(thm)],[f56,f209]) ).
fof(f384,definition,
( sQ51_spl
<=> sk_c10 = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f386,plain,
( sQ51_spl
| sk_c10 != sk_c10 ),
inference(component_clause,[status(thm)],[f384]) ).
fof(f387,plain,
( ~ sQ1_spl
| ~ sQ16_spl
| ~ sQ2_spl
| ~ sQ51_spl ),
inference(split_clause,[status(thm)],[f380,f384,f117,f208,f113]) ).
fof(f388,definition,
( sQ52_spl
<=> identity = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f390,plain,
( sQ52_spl
| identity != sk_c10 ),
inference(component_clause,[status(thm)],[f388]) ).
fof(f391,definition,
( sQ53_spl
<=> inverse(inverse(sk_c11)) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f392,plain,
( ~ sQ53_spl
| inverse(inverse(sk_c11)) = sk_c11 ),
inference(component_clause,[status(thm)],[f391]) ).
fof(f393,plain,
( sQ53_spl
| inverse(inverse(sk_c11)) != sk_c11 ),
inference(component_clause,[status(thm)],[f391]) ).
fof(f394,plain,
( ~ sQ16_spl
| ~ sQ53_spl
| ~ sQ52_spl ),
inference(split_clause,[status(thm)],[f381,f388,f391,f208]) ).
fof(f399,plain,
( sQ53_spl
| ~ sQ0_spl
| inverse(sk_c10) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f111,f393]) ).
fof(f400,plain,
( sQ51_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f386]) ).
fof(f401,plain,
sQ51_spl,
inference(contradiction_clause,[status(thm)],[f400]) ).
fof(f404,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| multiply(inverse(sk_c11),sk_c9) != sk_c10
| multiply(sk_c11,sk_c10) != sk_c10 ),
inference(paramodulation,[status(thm)],[f111,f377]) ).
fof(f405,plain,
( ~ sQ13_spl
| ~ sQ15_spl
| multiply(inverse(sk_c1),sk_c9) != sk_c10
| multiply(sk_c1,sk_c2) != sk_c10 ),
inference(paramodulation,[status(thm)],[f180,f377]) ).
fof(f410,definition,
( sQ56_spl
<=> multiply(sk_c11,sk_c10) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f412,plain,
( sQ56_spl
| multiply(sk_c11,sk_c10) != sk_c10 ),
inference(component_clause,[status(thm)],[f410]) ).
fof(f413,definition,
( sQ57_spl
<=> multiply(inverse(sk_c11),sk_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f415,plain,
( sQ57_spl
| multiply(inverse(sk_c11),sk_c9) != sk_c10 ),
inference(component_clause,[status(thm)],[f413]) ).
fof(f416,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ57_spl
| ~ sQ56_spl ),
inference(split_clause,[status(thm)],[f404,f410,f413,f205,f110]) ).
fof(f417,definition,
( sQ58_spl
<=> multiply(inverse(sk_c1),sk_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f419,plain,
( sQ58_spl
| multiply(inverse(sk_c1),sk_c9) != sk_c10 ),
inference(component_clause,[status(thm)],[f417]) ).
fof(f420,plain,
( ~ sQ13_spl
| ~ sQ15_spl
| ~ sQ58_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f405,f166,f417,f205,f179]) ).
fof(f421,plain,
( sQ58_spl
| ~ sQ13_spl
| multiply(sk_c2,sk_c9) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f180,f419]) ).
fof(f422,plain,
( sQ58_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f193,f421]) ).
fof(f423,plain,
( sQ58_spl
| ~ sQ13_spl
| ~ sQ14_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f422]) ).
fof(f424,plain,
( sQ58_spl
| ~ sQ13_spl
| ~ sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f423]) ).
fof(f462,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ12_spl
| multiply(sk_c10,multiply(sk_c9,X0)) = multiply(sk_c1,multiply(sk_c10,X0)) ),
inference(paramodulation,[status(thm)],[f220,f223]) ).
fof(f463,plain,
( ~ sQ14_spl
| ~ sQ12_spl
| multiply(sk_c10,sk_c9) = multiply(sk_c1,sk_c10) ),
inference(paramodulation,[status(thm)],[f193,f223]) ).
fof(f465,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| multiply(sk_c11,X0) = multiply(sk_c1,multiply(sk_c10,X0)) ),
inference(forward_demodulation,[status(thm)],[f343,f462]) ).
fof(f466,plain,
( ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sk_c11 = multiply(sk_c1,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f154,f463]) ).
fof(f478,plain,
( ~ sQ23_spl
| identity != inverse(inverse(inverse(identity)))
| inverse(inverse(inverse(inverse(identity)))) != inverse(identity) ),
inference(paramodulation,[status(thm)],[f56,f263]) ).
fof(f479,plain,
( ~ sQ23_spl
| inverse(identity) != inverse(identity)
| inverse(inverse(identity)) != inverse(identity) ),
inference(paramodulation,[status(thm)],[f55,f263]) ).
fof(f481,definition,
( sQ59_spl
<=> inverse(inverse(inverse(inverse(identity)))) = inverse(identity) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f484,definition,
( sQ60_spl
<=> identity = inverse(inverse(inverse(identity))) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f486,plain,
( sQ60_spl
| identity != inverse(inverse(inverse(identity))) ),
inference(component_clause,[status(thm)],[f484]) ).
fof(f487,plain,
( ~ sQ23_spl
| ~ sQ60_spl
| ~ sQ59_spl ),
inference(split_clause,[status(thm)],[f478,f481,f484,f262]) ).
fof(f488,definition,
( sQ61_spl
<=> inverse(identity) = inverse(identity) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f490,plain,
( sQ61_spl
| inverse(identity) != inverse(identity) ),
inference(component_clause,[status(thm)],[f488]) ).
fof(f491,plain,
( ~ sQ23_spl
| ~ sQ61_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f479,f255,f488,f262]) ).
fof(f492,plain,
( sQ61_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f490]) ).
fof(f493,plain,
sQ61_spl,
inference(contradiction_clause,[status(thm)],[f492]) ).
fof(f514,plain,
! [X0] :
( ~ sQ8_spl
| multiply(identity,X0) = multiply(sk_c6,multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f227,f57]) ).
fof(f515,plain,
! [X0] :
( ~ sQ8_spl
| X0 = multiply(sk_c6,multiply(sk_c7,X0)) ),
inference(forward_demodulation,[status(thm)],[f55,f514]) ).
fof(f530,plain,
( ~ sQ2_spl
| sk_c3 = multiply(inverse(sk_c11),identity) ),
inference(paramodulation,[status(thm)],[f234,f231]) ).
fof(f531,plain,
( ~ sQ8_spl
| sk_c7 = multiply(inverse(sk_c6),identity) ),
inference(paramodulation,[status(thm)],[f227,f231]) ).
fof(f532,plain,
( ~ sQ9_spl
| sk_c6 = multiply(inverse(sk_c8),identity) ),
inference(paramodulation,[status(thm)],[f228,f231]) ).
fof(f533,plain,
( ~ sQ6_spl
| sk_c5 = multiply(inverse(sk_c8),identity) ),
inference(paramodulation,[status(thm)],[f226,f231]) ).
fof(f534,plain,
( ~ sQ7_spl
| sk_c10 = multiply(inverse(sk_c8),sk_c11) ),
inference(paramodulation,[status(thm)],[f138,f231]) ).
fof(f536,plain,
( ~ sQ3_spl
| sk_c10 = multiply(inverse(sk_c4),sk_c9) ),
inference(paramodulation,[status(thm)],[f122,f231]) ).
fof(f539,plain,
! [X0] :
( ~ sQ1_spl
| multiply(sk_c11,X0) = multiply(inverse(sk_c3),multiply(sk_c10,X0)) ),
inference(paramodulation,[status(thm)],[f238,f231]) ).
fof(f540,plain,
( ~ sQ1_spl
| sk_c11 = multiply(inverse(sk_c3),sk_c10) ),
inference(paramodulation,[status(thm)],[f114,f231]) ).
fof(f543,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f231,f231]) ).
fof(f544,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f56,f231]) ).
fof(f545,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f55,f231]) ).
fof(f547,plain,
( ~ sQ12_spl
| sk_c2 = multiply(inverse(sk_c1),sk_c10) ),
inference(paramodulation,[status(thm)],[f167,f231]) ).
fof(f549,plain,
! [X0] :
( ~ sQ14_spl
| multiply(sk_c9,X0) = multiply(inverse(sk_c2),multiply(sk_c10,X0)) ),
inference(paramodulation,[status(thm)],[f220,f231]) ).
fof(f550,plain,
( ~ sQ14_spl
| sk_c9 = multiply(inverse(sk_c2),sk_c10) ),
inference(paramodulation,[status(thm)],[f193,f231]) ).
fof(f552,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 = multiply(sk_c8,identity) ),
inference(forward_demodulation,[status(thm)],[f146,f531]) ).
fof(f555,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ9_spl
| multiply(sk_c6,sk_c8) = sk_c11 ),
inference(backward_demodulation,[status(thm)],[f559,f130]) ).
fof(f558,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ9_spl
| multiply(sk_c11,X0) = multiply(sk_c6,multiply(sk_c8,X0)) ),
inference(backward_demodulation,[status(thm)],[f559,f236]) ).
fof(f559,plain,
( ~ sQ6_spl
| ~ sQ9_spl
| sk_c5 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f532,f533]) ).
fof(f561,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c10 = multiply(sk_c10,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f126,f536]) ).
fof(f562,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ11_spl
| sk_c10 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f154,f561]) ).
fof(f565,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c11,X0) = multiply(sk_c11,multiply(sk_c10,X0)) ),
inference(forward_demodulation,[status(thm)],[f118,f539]) ).
fof(f566,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c11 = multiply(sk_c11,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f118,f540]) ).
fof(f571,plain,
( ~ sQ9_spl
| sk_c6 = inverse(sk_c8) ),
inference(backward_demodulation,[status(thm)],[f575,f532]) ).
fof(f572,plain,
( ~ sQ2_spl
| sk_c3 = inverse(sk_c11) ),
inference(backward_demodulation,[status(thm)],[f575,f530]) ).
fof(f574,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f575,f552]) ).
fof(f575,plain,
! [X0] : X0 = multiply(X0,identity),
inference(forward_demodulation,[status(thm)],[f543,f544]) ).
fof(f577,plain,
( sQ20_spl
| sk_c10 != sk_c11 ),
inference(backward_demodulation,[status(thm)],[f545,f254]) ).
fof(f592,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ11_spl
| inverse(sk_c10) != sk_c10 ),
inference(backward_demodulation,[status(thm)],[f562,f112]) ).
fof(f593,plain,
( sQ22_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ11_spl
| inverse(identity) != sk_c10 ),
inference(backward_demodulation,[status(thm)],[f562,f261]) ).
fof(f613,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c6,sk_c8) = identity ),
inference(backward_demodulation,[status(thm)],[f574,f227]) ).
fof(f616,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c8,sk_c8) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f574,f150]) ).
fof(f617,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| X0 = multiply(sk_c6,multiply(sk_c8,X0)) ),
inference(backward_demodulation,[status(thm)],[f574,f515]) ).
fof(f618,plain,
( sQ57_spl
| ~ sQ2_spl
| multiply(sk_c3,sk_c9) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f572,f415]) ).
fof(f619,plain,
( ~ sQ7_spl
| ~ sQ9_spl
| sk_c10 = multiply(sk_c6,sk_c11) ),
inference(forward_demodulation,[status(thm)],[f571,f534]) ).
fof(f622,plain,
( sQ11_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c10 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f561,f155]) ).
fof(f624,plain,
( sQ21_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| inverse(inverse(identity)) != inverse(sk_c11) ),
inference(backward_demodulation,[status(thm)],[f638,f257]) ).
fof(f625,plain,
( sQ50_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| inverse(sk_c11) != sk_c10 ),
inference(backward_demodulation,[status(thm)],[f638,f373]) ).
fof(f630,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| X0 = multiply(inverse(sk_c11),X0) ),
inference(backward_demodulation,[status(thm)],[f638,f545]) ).
fof(f631,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| X0 = multiply(X0,sk_c11) ),
inference(backward_demodulation,[status(thm)],[f638,f575]) ).
fof(f638,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c11 = identity ),
inference(forward_demodulation,[status(thm)],[f555,f613]) ).
fof(f640,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c11,X0) = multiply(sk_c10,X0) ),
inference(backward_demodulation,[status(thm)],[f645,f565]) ).
fof(f641,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c11 = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f645,f566]) ).
fof(f642,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| X0 = multiply(sk_c8,multiply(sk_c10,X0)) ),
inference(backward_demodulation,[status(thm)],[f645,f233]) ).
fof(f645,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| X0 = multiply(sk_c11,X0) ),
inference(forward_demodulation,[status(thm)],[f558,f617]) ).
fof(f647,plain,
( sQ21_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| inverse(inverse(sk_c11)) != inverse(sk_c11) ),
inference(forward_demodulation,[status(thm)],[f638,f624]) ).
fof(f648,plain,
( sQ21_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ2_spl
| inverse(sk_c3) != inverse(sk_c11) ),
inference(forward_demodulation,[status(thm)],[f572,f647]) ).
fof(f649,plain,
( sQ21_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ2_spl
| sk_c11 != inverse(sk_c11) ),
inference(forward_demodulation,[status(thm)],[f118,f648]) ).
fof(f650,plain,
( sQ21_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ2_spl
| sk_c11 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f572,f649]) ).
fof(f651,plain,
( sQ50_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ2_spl
| sk_c3 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f572,f625]) ).
fof(f655,plain,
( ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ2_spl
| sk_c11 = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f657,f114]) ).
fof(f656,plain,
( sQ57_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c9 != sk_c10 ),
inference(backward_demodulation,[status(thm)],[f657,f618]) ).
fof(f657,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ2_spl
| X0 = multiply(sk_c3,X0) ),
inference(forward_demodulation,[status(thm)],[f572,f630]) ).
fof(f658,plain,
( ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c10 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f631,f619]) ).
fof(f675,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c10 = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f680,f561]) ).
fof(f680,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| X0 = multiply(sk_c10,X0) ),
inference(forward_demodulation,[status(thm)],[f645,f640]) ).
fof(f681,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f641,f577]) ).
fof(f682,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sQ20_spl ),
inference(contradiction_clause,[status(thm)],[f681]) ).
fof(f683,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f688,f616]) ).
fof(f688,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| X0 = multiply(sk_c8,X0) ),
inference(forward_demodulation,[status(thm)],[f680,f642]) ).
fof(f696,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| X0 = multiply(X0,sk_c10) ),
inference(backward_demodulation,[status(thm)],[f655,f631]) ).
fof(f697,plain,
( sQ21_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c10 != sk_c3 ),
inference(backward_demodulation,[status(thm)],[f655,f650]) ).
fof(f701,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c3 = inverse(sk_c10) ),
inference(backward_demodulation,[status(thm)],[f655,f572]) ).
fof(f702,plain,
( ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ5_spl
| ~ sQ6_spl
| inverse(sk_c10) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f658,f146]) ).
fof(f704,plain,
( ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c10 = inverse(sk_c8) ),
inference(backward_demodulation,[status(thm)],[f658,f571]) ).
fof(f706,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sQ57_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f675,f656]) ).
fof(f707,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sQ57_spl ),
inference(contradiction_clause,[status(thm)],[f706]) ).
fof(f713,plain,
( sQ11_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ2_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f655,f622]) ).
fof(f714,plain,
( sQ11_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f713]) ).
fof(f715,plain,
( sQ11_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f714]) ).
fof(f719,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f658,f683]) ).
fof(f729,plain,
( ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c3 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f701,f702]) ).
fof(f730,plain,
( ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ10_spl
| sk_c3 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f719,f729]) ).
fof(f731,plain,
( ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ10_spl
| sQ50_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f730,f651]) ).
fof(f732,plain,
( ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ10_spl
| sQ50_spl ),
inference(contradiction_clause,[status(thm)],[f731]) ).
fof(f733,plain,
( ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c10 = inverse(sk_c10) ),
inference(forward_demodulation,[status(thm)],[f719,f704]) ).
fof(f738,plain,
( ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c10 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f701,f733]) ).
fof(f752,plain,
( sQ22_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ11_spl
| ~ sQ50_spl ),
inference(split_clause,[status(thm)],[f593,f371,f153,f125,f121,f259]) ).
fof(f785,plain,
( sQ56_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c11 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f696,f412]) ).
fof(f786,plain,
( sQ56_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f655,f785]) ).
fof(f787,plain,
( sQ56_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f786]) ).
fof(f788,plain,
( sQ56_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f787]) ).
fof(f789,plain,
( sQ21_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ10_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f738,f697]) ).
fof(f790,plain,
( sQ21_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f789]) ).
fof(f791,plain,
( sQ21_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f790]) ).
fof(f793,plain,
( ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| multiply(sk_c10,sk_c9) = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f466,f463]) ).
fof(f794,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| multiply(sk_c10,multiply(sk_c9,X0)) = multiply(sk_c11,X0) ),
inference(forward_demodulation,[status(thm)],[f465,f462]) ).
fof(f795,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| sk_c2 = multiply(sk_c2,sk_c10) ),
inference(backward_demodulation,[status(thm)],[f180,f547]) ).
fof(f812,plain,
! [X0] :
( ~ sQ0_spl
| X0 = multiply(sk_c10,multiply(sk_c11,X0)) ),
inference(paramodulation,[status(thm)],[f111,f231]) ).
fof(f817,plain,
( ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sk_c10 = multiply(inverse(sk_c1),sk_c11) ),
inference(paramodulation,[status(thm)],[f466,f231]) ).
fof(f819,plain,
( ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| sk_c10 = multiply(sk_c2,sk_c11) ),
inference(forward_demodulation,[status(thm)],[f180,f817]) ).
fof(f822,plain,
( ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ17_spl
| inverse(sk_c1) != sk_c10
| sk_c11 != sk_c9 ),
inference(paramodulation,[status(thm)],[f466,f212]) ).
fof(f824,definition,
( sQ66_spl
<=> inverse(sk_c1) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f826,plain,
( sQ66_spl
| inverse(sk_c1) != sk_c10 ),
inference(component_clause,[status(thm)],[f824]) ).
fof(f827,plain,
( ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ17_spl
| ~ sQ66_spl
| ~ sQ45_spl ),
inference(split_clause,[status(thm)],[f822,f354,f824,f211,f153,f166,f192]) ).
fof(f828,plain,
( sQ66_spl
| ~ sQ13_spl
| sk_c2 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f180,f826]) ).
fof(f831,definition,
( sQ67_spl
<=> inverse(sk_c10) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f833,plain,
( sQ67_spl
| inverse(sk_c10) != sk_c10 ),
inference(component_clause,[status(thm)],[f831]) ).
fof(f856,plain,
( ~ sQ13_spl
| sk_c1 = multiply(inverse(sk_c2),identity) ),
inference(paramodulation,[status(thm)],[f229,f231]) ).
fof(f862,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ13_spl
| multiply(sk_c9,X0) = multiply(sk_c1,multiply(sk_c10,X0)) ),
inference(backward_demodulation,[status(thm)],[f864,f549]) ).
fof(f863,plain,
( ~ sQ14_spl
| ~ sQ13_spl
| sk_c9 = multiply(sk_c1,sk_c10) ),
inference(backward_demodulation,[status(thm)],[f864,f550]) ).
fof(f864,plain,
( ~ sQ13_spl
| sk_c1 = inverse(sk_c2) ),
inference(forward_demodulation,[status(thm)],[f575,f856]) ).
fof(f870,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl
| multiply(sk_c10,X0) = multiply(sk_c2,multiply(sk_c11,X0)) ),
inference(backward_demodulation,[status(thm)],[f872,f220]) ).
fof(f871,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| multiply(sk_c10,multiply(sk_c11,X0)) = multiply(sk_c11,X0) ),
inference(backward_demodulation,[status(thm)],[f872,f794]) ).
fof(f872,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl
| multiply(sk_c9,X0) = multiply(sk_c11,X0) ),
inference(forward_demodulation,[status(thm)],[f465,f862]) ).
fof(f873,plain,
( ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sk_c9 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f466,f863]) ).
fof(f874,plain,
( ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sQ45_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f873,f356]) ).
fof(f875,plain,
( ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sQ45_spl ),
inference(contradiction_clause,[status(thm)],[f874]) ).
fof(f877,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ0_spl
| multiply(sk_c10,X0) = multiply(sk_c2,X0) ),
inference(backward_demodulation,[status(thm)],[f882,f870]) ).
fof(f880,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| X0 = multiply(sk_c10,X0) ),
inference(backward_demodulation,[status(thm)],[f882,f812]) ).
fof(f882,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ0_spl
| X0 = multiply(sk_c11,X0) ),
inference(forward_demodulation,[status(thm)],[f812,f871]) ).
fof(f883,plain,
( ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| multiply(sk_c10,sk_c11) = sk_c11 ),
inference(backward_demodulation,[status(thm)],[f873,f793]) ).
fof(f890,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ0_spl
| multiply(sk_c10,sk_c1) = identity ),
inference(backward_demodulation,[status(thm)],[f877,f229]) ).
fof(f892,plain,
( ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ0_spl
| sk_c10 = multiply(sk_c10,sk_c11) ),
inference(backward_demodulation,[status(thm)],[f877,f819]) ).
fof(f895,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ0_spl
| sk_c2 = multiply(sk_c10,sk_c10) ),
inference(backward_demodulation,[status(thm)],[f877,f795]) ).
fof(f905,plain,
( sQ52_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ0_spl
| sk_c11 != sk_c10 ),
inference(backward_demodulation,[status(thm)],[f916,f390]) ).
fof(f908,plain,
( sQ60_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ0_spl
| identity != inverse(inverse(inverse(sk_c11))) ),
inference(backward_demodulation,[status(thm)],[f916,f486]) ).
fof(f915,plain,
( sQ21_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ0_spl
| inverse(inverse(identity)) != inverse(sk_c11) ),
inference(backward_demodulation,[status(thm)],[f916,f257]) ).
fof(f916,plain,
( ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ0_spl
| identity = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f235,f883]) ).
fof(f920,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ0_spl
| sk_c1 = identity ),
inference(forward_demodulation,[status(thm)],[f880,f890]) ).
fof(f921,plain,
( ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ0_spl
| sk_c11 = multiply(sk_c11,sk_c10) ),
inference(backward_demodulation,[status(thm)],[f927,f466]) ).
fof(f923,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ0_spl
| multiply(sk_c11,sk_c2) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f927,f167]) ).
fof(f926,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ0_spl
| sk_c11 = inverse(sk_c2) ),
inference(backward_demodulation,[status(thm)],[f927,f864]) ).
fof(f927,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ0_spl
| sk_c1 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f916,f920]) ).
fof(f931,plain,
( ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ0_spl
| sk_c10 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f880,f892]) ).
fof(f932,plain,
( ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ0_spl
| sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f931,f577]) ).
fof(f933,plain,
( ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ0_spl
| sQ20_spl ),
inference(contradiction_clause,[status(thm)],[f932]) ).
fof(f938,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ0_spl
| sk_c2 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f880,f895]) ).
fof(f939,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ0_spl
| sQ66_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f938,f828]) ).
fof(f940,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ0_spl
| sQ66_spl ),
inference(contradiction_clause,[status(thm)],[f939]) ).
fof(f943,plain,
( sQ60_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ0_spl
| sk_c11 != inverse(inverse(inverse(sk_c11))) ),
inference(forward_demodulation,[status(thm)],[f916,f908]) ).
fof(f944,plain,
( sQ60_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ0_spl
| sk_c11 != inverse(inverse(sk_c10)) ),
inference(forward_demodulation,[status(thm)],[f111,f943]) ).
fof(f951,plain,
( sQ21_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ0_spl
| inverse(inverse(sk_c11)) != inverse(sk_c11) ),
inference(forward_demodulation,[status(thm)],[f916,f915]) ).
fof(f952,plain,
( sQ21_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ0_spl
| inverse(sk_c10) != inverse(sk_c11) ),
inference(forward_demodulation,[status(thm)],[f111,f951]) ).
fof(f953,plain,
( sQ21_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ0_spl
| inverse(sk_c10) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f111,f952]) ).
fof(f956,plain,
( ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ0_spl
| sk_c11 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f882,f921]) ).
fof(f965,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ0_spl
| sk_c2 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f882,f923]) ).
fof(f967,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ0_spl
| sk_c11 = inverse(sk_c10) ),
inference(forward_demodulation,[status(thm)],[f965,f926]) ).
fof(f968,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ0_spl
| sQ53_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f967,f399]) ).
fof(f969,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ0_spl
| sQ53_spl ),
inference(contradiction_clause,[status(thm)],[f968]) ).
fof(f970,plain,
( sQ22_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ0_spl
| inverse(sk_c11) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f916,f261]) ).
fof(f971,plain,
( sQ22_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ0_spl
| sk_c10 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f111,f970]) ).
fof(f987,plain,
( sQ60_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ0_spl
| sk_c10 != inverse(inverse(sk_c10)) ),
inference(backward_demodulation,[status(thm)],[f956,f944]) ).
fof(f998,plain,
( sQ52_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ0_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f956,f905]) ).
fof(f999,plain,
( sQ52_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f998]) ).
fof(f1000,plain,
( sQ52_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f999]) ).
fof(f1009,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ0_spl
| sk_c10 = inverse(sk_c10) ),
inference(forward_demodulation,[status(thm)],[f956,f967]) ).
fof(f1010,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ0_spl
| sQ67_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1009,f833]) ).
fof(f1011,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ0_spl
| sQ67_spl ),
inference(contradiction_clause,[status(thm)],[f1010]) ).
fof(f1012,plain,
( ~ sQ53_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ0_spl
| inverse(inverse(sk_c10)) = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f956,f392]) ).
fof(f1013,plain,
( ~ sQ53_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ0_spl
| inverse(inverse(sk_c10)) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f956,f1012]) ).
fof(f1014,plain,
( ~ sQ53_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ0_spl
| sQ48_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1013,f366]) ).
fof(f1015,plain,
( ~ sQ53_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ0_spl
| sQ48_spl ),
inference(contradiction_clause,[status(thm)],[f1014]) ).
fof(f1016,plain,
( sQ22_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ0_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f956,f971]) ).
fof(f1017,plain,
( sQ22_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1016]) ).
fof(f1018,plain,
( sQ22_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f1017]) ).
fof(f1027,plain,
( sQ60_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ48_spl ),
inference(split_clause,[status(thm)],[f987,f364,f110,f179,f153,f166,f192,f484]) ).
fof(f1070,plain,
( sQ21_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ67_spl ),
inference(split_clause,[status(thm)],[f953,f831,f110,f179,f153,f166,f192,f255]) ).
fof(f1113,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ10_spl
| sk_c10 = inverse(sk_c10) ),
inference(forward_demodulation,[status(thm)],[f738,f701]) ).
fof(f1114,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ10_spl
| sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1113,f592]) ).
fof(f1115,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ10_spl
| sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f1114]) ).
fof(f1116,plain,
$false,
inference(sat_refutation,[status(thm)],[f116,f120,f124,f128,f132,f136,f140,f144,f148,f152,f156,f157,f158,f159,f160,f161,f163,f164,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f182,f183,f184,f185,f186,f187,f188,f189,f190,f191,f195,f196,f197,f198,f199,f200,f201,f202,f203,f204,f217,f265,f353,f376,f387,f394,f401,f416,f420,f424,f487,f491,f493,f682,f707,f715,f732,f752,f788,f791,f827,f875,f933,f940,f969,f1000,f1011,f1015,f1018,f1027,f1070,f1115]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP380-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n010.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 20:10:56 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 0.13/0.41 % Refutation found
% 0.13/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.44 % Elapsed time: 0.069733 seconds
% 0.13/0.44 % CPU time: 0.306775 seconds
% 0.13/0.44 % Total memory used: 92.816 MB
% 0.13/0.44 % Net memory used: 92.557 MB
%------------------------------------------------------------------------------