%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP271-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 12:33:16 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.44s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 92
% Syntax : Number of formulae : 545 ( 15 unt; 47 def)
% Number of atoms : 2503 ( 612 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 3761 (1803 ~;1911 |; 0 &)
% ( 47 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 49 ( 47 usr; 48 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 95 ( 95 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c7) = sk_c6
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c6) = sk_c8
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c3) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c7) = sk_c6
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( inverse(sk_c6) = sk_c8
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( inverse(sk_c7) = sk_c6
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( inverse(sk_c6) = sk_c8
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
( inverse(sk_c3) = sk_c11
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f51,negated_conjecture,
( inverse(sk_c7) = sk_c6
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f52,negated_conjecture,
( inverse(sk_c6) = sk_c8
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f53,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/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
| inverse(X4) != sk_c10
| multiply(X4,sk_c10) != sk_c9
| multiply(sk_c11,sk_c9) != sk_c10
| inverse(X3) != sk_c11
| multiply(X3,sk_c11) != sk_c10 ),
file('/export/starexec/sandbox2/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
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f59,plain,
( inverse(sk_c3) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f60,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f61,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f62,plain,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f63,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f64,plain,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f65,plain,
( inverse(sk_c7) = sk_c6
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f66,plain,
( inverse(sk_c6) = sk_c8
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f68,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f69,plain,
( inverse(sk_c3) = sk_c11
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f70,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f71,plain,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f72,plain,
( multiply(sk_c5,sk_c8) = sk_c11
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f73,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f74,plain,
( multiply(sk_c8,sk_c10) = sk_c11
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f75,plain,
( inverse(sk_c7) = sk_c6
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f76,plain,
( inverse(sk_c6) = sk_c8
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f78,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f79,plain,
( inverse(sk_c3) = sk_c11
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f80,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f81,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f82,plain,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f83,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f84,plain,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f85,plain,
( inverse(sk_c7) = sk_c6
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f86,plain,
( inverse(sk_c6) = sk_c8
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f88,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f89,plain,
( inverse(sk_c3) = sk_c11
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f90,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f91,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f98,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f99,plain,
( inverse(sk_c3) = sk_c11
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f100,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f101,plain,
( inverse(sk_c4) = sk_c10
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f102,plain,
( multiply(sk_c5,sk_c8) = sk_c11
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f103,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f104,plain,
( multiply(sk_c8,sk_c10) = sk_c11
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f105,plain,
( inverse(sk_c7) = sk_c6
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f106,plain,
( inverse(sk_c6) = sk_c8
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f107,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c2) = 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] :
( inverse(X4) != sk_c10
| multiply(X4,sk_c10) != sk_c9
| multiply(sk_c11,sk_c9) != sk_c10
| ! [X3] :
( inverse(X3) != sk_c11
| multiply(X3,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
| inverse(X1) != sk_c10
| multiply(X1,sk_c10) != sk_c9
| multiply(sk_c11,sk_c9) != sk_c10
| inverse(X0) != sk_c11
| multiply(X0,sk_c11) != sk_c10 ),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f110,definition,
( sQ0_spl
<=> multiply(sk_c1,sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f111,plain,
( ~ sQ0_spl
| multiply(sk_c1,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(f153,definition,
( sQ11_spl
<=> inverse(sk_c1) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f154,plain,
( ~ sQ11_spl
| inverse(sk_c1) = 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(f162,plain,
( sQ7_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f74,f153,f137]) ).
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_c11,sk_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f167,plain,
( ~ sQ12_spl
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(component_clause,[status(thm)],[f166]) ).
fof(f168,plain,
( sQ12_spl
| multiply(sk_c11,sk_c9) != 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(f179,definition,
( sQ13_spl
<=> multiply(sk_c2,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f180,plain,
( ~ sQ13_spl
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(component_clause,[status(thm)],[f179]) ).
fof(f181,plain,
( sQ13_spl
| multiply(sk_c2,sk_c10) != sk_c9 ),
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(f192,definition,
( sQ14_spl
<=> inverse(sk_c2) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f193,plain,
( ~ sQ14_spl
| inverse(sk_c2) = 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] :
( sQ15_spl
<=> ( inverse(X0) != sk_c11
| multiply(X0,sk_c11) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f206,plain,
! [X0] :
( ~ sQ15_spl
| inverse(X0) != sk_c11
| multiply(X0,sk_c11) != sk_c10 ),
inference(component_clause,[status(thm)],[f205]) ).
fof(f208,definition,
! [X1] :
( sQ16_spl
<=> ( inverse(X1) != sk_c10
| multiply(X1,sk_c10) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f209,plain,
! [X0] :
( ~ sQ16_spl
| inverse(X0) != sk_c10
| multiply(X0,sk_c10) != sk_c9 ),
inference(component_clause,[status(thm)],[f208]) ).
fof(f211,definition,
! [X4,X5,X6,X7] :
( sQ17_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,[sQ17_spl])],[split_symbol_definition]) ).
fof(f212,plain,
! [X0,X1,X2,X3] :
( ~ sQ17_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)],[f211]) ).
fof(f214,plain,
( sQ17_spl
| sQ16_spl
| ~ sQ12_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f109,f205,f166,f208,f211]) ).
fof(f215,plain,
! [X0,X1] :
( ~ sQ17_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)],[f212]) ).
fof(f223,plain,
! [X0] :
( ~ sQ0_spl
| multiply(sk_c10,X0) = multiply(sk_c1,multiply(sk_c11,X0)) ),
inference(paramodulation,[status(thm)],[f111,f57]) ).
fof(f224,plain,
! [X0] :
( ~ sQ13_spl
| multiply(sk_c9,X0) = multiply(sk_c2,multiply(sk_c10,X0)) ),
inference(paramodulation,[status(thm)],[f180,f57]) ).
fof(f230,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ17_spl
| multiply(X0,sk_c8) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c5)
| multiply(inverse(sk_c5),sk_c10) != sk_c11
| multiply(sk_c5,inverse(sk_c5)) != sk_c11 ),
inference(paramodulation,[status(thm)],[f134,f215]) ).
fof(f255,definition,
( sQ24_spl
<=> multiply(sk_c5,inverse(sk_c5)) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f256,plain,
( ~ sQ24_spl
| multiply(sk_c5,inverse(sk_c5)) = sk_c11 ),
inference(component_clause,[status(thm)],[f255]) ).
fof(f257,plain,
( sQ24_spl
| multiply(sk_c5,inverse(sk_c5)) != sk_c11 ),
inference(component_clause,[status(thm)],[f255]) ).
fof(f258,definition,
( sQ25_spl
<=> multiply(inverse(sk_c5),sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f260,plain,
( sQ25_spl
| multiply(inverse(sk_c5),sk_c10) != sk_c11 ),
inference(component_clause,[status(thm)],[f258]) ).
fof(f261,definition,
! [X0] :
( sQ26_spl
<=> ( multiply(X0,sk_c8) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c5) ) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f264,plain,
( ~ sQ6_spl
| ~ sQ17_spl
| sQ26_spl
| ~ sQ25_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f230,f255,f258,f261,f211,f133]) ).
fof(f285,definition,
( sQ33_spl
<=> multiply(sk_c1,inverse(sk_c1)) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f286,plain,
( ~ sQ33_spl
| multiply(sk_c1,inverse(sk_c1)) = sk_c11 ),
inference(component_clause,[status(thm)],[f285]) ).
fof(f287,plain,
( sQ33_spl
| multiply(sk_c1,inverse(sk_c1)) != sk_c11 ),
inference(component_clause,[status(thm)],[f285]) ).
fof(f295,definition,
( sQ36_spl
<=> multiply(sk_c2,inverse(sk_c2)) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f297,plain,
( sQ36_spl
| multiply(sk_c2,inverse(sk_c2)) != sk_c11 ),
inference(component_clause,[status(thm)],[f295]) ).
fof(f307,plain,
( sQ36_spl
| ~ sQ14_spl
| multiply(sk_c2,sk_c10) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f193,f297]) ).
fof(f308,plain,
( sQ36_spl
| ~ sQ14_spl
| ~ sQ13_spl
| sk_c9 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f180,f307]) ).
fof(f311,plain,
( sQ33_spl
| ~ sQ11_spl
| multiply(sk_c1,sk_c11) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f154,f287]) ).
fof(f312,plain,
( sQ33_spl
| ~ sQ11_spl
| ~ sQ0_spl
| sk_c10 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f111,f311]) ).
fof(f313,plain,
( ~ sQ3_spl
| ~ sQ16_spl
| inverse(sk_c4) != sk_c10 ),
inference(resolution,[status(thm)],[f209,f122]) ).
fof(f314,plain,
( ~ sQ13_spl
| ~ sQ16_spl
| inverse(sk_c2) != sk_c10 ),
inference(resolution,[status(thm)],[f209,f180]) ).
fof(f319,plain,
( ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ14_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f193,f314]) ).
fof(f320,plain,
( ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ14_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f319]) ).
fof(f321,plain,
( ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f320]) ).
fof(f324,plain,
( ~ sQ8_spl
| multiply(sk_c6,sk_c7) = identity ),
inference(paramodulation,[status(thm)],[f142,f56]) ).
fof(f326,plain,
( ~ sQ4_spl
| multiply(sk_c10,sk_c4) = identity ),
inference(paramodulation,[status(thm)],[f126,f56]) ).
fof(f328,plain,
( ~ sQ14_spl
| multiply(sk_c10,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f193,f56]) ).
fof(f329,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f56,f57]) ).
fof(f330,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f55,f329]) ).
fof(f341,plain,
( ~ sQ1_spl
| ~ sQ15_spl
| inverse(sk_c3) != sk_c11 ),
inference(resolution,[status(thm)],[f206,f114]) ).
fof(f342,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| inverse(sk_c1) != sk_c11 ),
inference(resolution,[status(thm)],[f206,f111]) ).
fof(f348,plain,
( ~ sQ1_spl
| ~ sQ15_spl
| ~ sQ2_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f118,f341]) ).
fof(f349,plain,
( ~ sQ1_spl
| ~ sQ15_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f348]) ).
fof(f350,plain,
( ~ sQ1_spl
| ~ sQ15_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f349]) ).
fof(f352,plain,
( ~ sQ17_spl
| inverse(inverse(identity)) != inverse(identity)
| multiply(inverse(identity),sk_c10) != sk_c11
| multiply(identity,inverse(identity)) != sk_c11 ),
inference(resolution,[status(thm)],[f215,f55]) ).
fof(f362,definition,
( sQ39_spl
<=> multiply(identity,inverse(identity)) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f365,definition,
( sQ40_spl
<=> multiply(inverse(identity),sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f368,definition,
( sQ41_spl
<=> inverse(inverse(identity)) = inverse(identity) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f370,plain,
( sQ41_spl
| inverse(inverse(identity)) != inverse(identity) ),
inference(component_clause,[status(thm)],[f368]) ).
fof(f371,plain,
( ~ sQ17_spl
| ~ sQ41_spl
| ~ sQ40_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f352,f362,f365,f368,f211]) ).
fof(f394,plain,
( sQ25_spl
| ~ sQ6_spl
| multiply(sk_c8,sk_c10) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f134,f260]) ).
fof(f395,plain,
( sQ25_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f138,f394]) ).
fof(f396,plain,
( sQ25_spl
| ~ sQ6_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f395]) ).
fof(f397,plain,
( sQ25_spl
| ~ sQ6_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f396]) ).
fof(f399,plain,
( sQ24_spl
| ~ sQ6_spl
| multiply(sk_c5,sk_c8) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f134,f257]) ).
fof(f400,plain,
( sQ24_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f130,f399]) ).
fof(f401,plain,
( sQ24_spl
| ~ sQ6_spl
| ~ sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f400]) ).
fof(f402,plain,
( sQ24_spl
| ~ sQ6_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f401]) ).
fof(f413,plain,
( ~ sQ8_spl
| sk_c7 = multiply(inverse(sk_c6),identity) ),
inference(paramodulation,[status(thm)],[f324,f330]) ).
fof(f416,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f55,f330]) ).
fof(f419,plain,
( ~ sQ1_spl
| sk_c11 = multiply(inverse(sk_c3),sk_c10) ),
inference(paramodulation,[status(thm)],[f114,f330]) ).
fof(f420,plain,
( ~ sQ3_spl
| sk_c10 = multiply(inverse(sk_c4),sk_c9) ),
inference(paramodulation,[status(thm)],[f122,f330]) ).
fof(f421,plain,
( ~ sQ5_spl
| sk_c8 = multiply(inverse(sk_c5),sk_c11) ),
inference(paramodulation,[status(thm)],[f130,f330]) ).
fof(f425,plain,
( ~ sQ10_spl
| sk_c8 = multiply(inverse(sk_c7),sk_c6) ),
inference(paramodulation,[status(thm)],[f150,f330]) ).
fof(f427,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 = multiply(sk_c8,identity) ),
inference(forward_demodulation,[status(thm)],[f146,f413]) ).
fof(f429,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c11 = multiply(sk_c11,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f118,f419]) ).
fof(f430,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c10 = multiply(sk_c10,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f126,f420]) ).
fof(f431,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sk_c8 = multiply(sk_c8,sk_c11) ),
inference(forward_demodulation,[status(thm)],[f134,f421]) ).
fof(f432,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| sk_c8 = multiply(sk_c6,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f142,f425]) ).
fof(f441,plain,
! [X0] : X0 = multiply(inverse(inverse(identity)),X0),
inference(paramodulation,[status(thm)],[f416,f330]) ).
fof(f444,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c10 = multiply(inverse(sk_c11),sk_c11) ),
inference(paramodulation,[status(thm)],[f429,f330]) ).
fof(f447,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c10 = identity ),
inference(forward_demodulation,[status(thm)],[f56,f444]) ).
fof(f449,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c7 = multiply(sk_c8,sk_c10) ),
inference(backward_demodulation,[status(thm)],[f447,f427]) ).
fof(f450,plain,
( ~ sQ14_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c10,sk_c2) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f447,f328]) ).
fof(f456,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(inverse(X0),X0) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f447,f56]) ).
fof(f457,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c10,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f447,f55]) ).
fof(f458,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| sk_c7 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f138,f449]) ).
fof(f479,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c9,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f486,f457]) ).
fof(f481,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c9 = identity ),
inference(backward_demodulation,[status(thm)],[f486,f447]) ).
fof(f482,plain,
( sQ13_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c2,sk_c9) != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f486,f181]) ).
fof(f485,plain,
( ~ sQ14_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c2) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f486,f193]) ).
fof(f486,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c10 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f457,f430]) ).
fof(f491,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| X0 = multiply(sk_c9,multiply(sk_c2,X0)) ),
inference(paramodulation,[status(thm)],[f485,f330]) ).
fof(f492,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| X0 = multiply(sk_c2,X0) ),
inference(forward_demodulation,[status(thm)],[f479,f491]) ).
fof(f499,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| sk_c8 = multiply(sk_c8,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f458,f431]) ).
fof(f511,plain,
( ~ sQ14_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c9,sk_c2) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f486,f450]) ).
fof(f512,plain,
( ~ sQ14_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c2 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f479,f511]) ).
fof(f517,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ14_spl
| sk_c2 = identity ),
inference(backward_demodulation,[status(thm)],[f519,f481]) ).
fof(f518,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ14_spl
| sk_c10 = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f519,f486]) ).
fof(f519,plain,
( ~ sQ14_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c2 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f486,f512]) ).
fof(f584,plain,
( sQ13_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ14_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f492,f482]) ).
fof(f585,plain,
( sQ13_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ14_spl
| sk_c2 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f519,f584]) ).
fof(f586,plain,
( sQ13_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ14_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f519,f585]) ).
fof(f587,plain,
( sQ13_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ14_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f586]) ).
fof(f588,plain,
( sQ13_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f587]) ).
fof(f595,plain,
( ~ sQ0_spl
| sk_c11 = multiply(inverse(sk_c1),sk_c10) ),
inference(paramodulation,[status(thm)],[f111,f330]) ).
fof(f597,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| sk_c11 = multiply(sk_c11,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f154,f595]) ).
fof(f600,plain,
( ~ sQ13_spl
| sk_c10 = multiply(inverse(sk_c2),sk_c9) ),
inference(paramodulation,[status(thm)],[f180,f330]) ).
fof(f602,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| sk_c10 = multiply(sk_c10,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f193,f600]) ).
fof(f628,plain,
( ~ sQ17_spl
| inverse(inverse(inverse(identity))) != inverse(inverse(identity))
| multiply(inverse(inverse(identity)),sk_c10) != sk_c11
| multiply(inverse(identity),inverse(inverse(identity))) != sk_c11 ),
inference(resolution,[status(thm)],[f416,f215]) ).
fof(f634,definition,
( sQ42_spl
<=> multiply(inverse(identity),inverse(inverse(identity))) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f636,plain,
( sQ42_spl
| multiply(inverse(identity),inverse(inverse(identity))) != sk_c11 ),
inference(component_clause,[status(thm)],[f634]) ).
fof(f637,definition,
( sQ43_spl
<=> multiply(inverse(inverse(identity)),sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f639,plain,
( sQ43_spl
| multiply(inverse(inverse(identity)),sk_c10) != sk_c11 ),
inference(component_clause,[status(thm)],[f637]) ).
fof(f640,definition,
( sQ44_spl
<=> inverse(inverse(inverse(identity))) = inverse(inverse(identity)) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f642,plain,
( sQ44_spl
| inverse(inverse(inverse(identity))) != inverse(inverse(identity)) ),
inference(component_clause,[status(thm)],[f640]) ).
fof(f643,plain,
( ~ sQ17_spl
| ~ sQ44_spl
| ~ sQ43_spl
| ~ sQ42_spl ),
inference(split_clause,[status(thm)],[f628,f634,f637,f640,f211]) ).
fof(f644,plain,
( sQ42_spl
| inverse(inverse(identity)) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f416,f636]) ).
fof(f660,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c8,sk_c10) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f458,f138]) ).
fof(f668,plain,
( sQ12_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| multiply(sk_c7,sk_c9) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f458,f168]) ).
fof(f677,plain,
( ~ sQ14_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c2) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f518,f193]) ).
fof(f689,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ14_spl
| multiply(inverse(X0),X0) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f517,f56]) ).
fof(f720,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| sk_c7 = multiply(inverse(sk_c8),sk_c8) ),
inference(paramodulation,[status(thm)],[f499,f330]) ).
fof(f722,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ14_spl
| sk_c7 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f689,f720]) ).
fof(f730,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ14_spl
| sk_c2 = sk_c11 ),
inference(backward_demodulation,[status(thm)],[f722,f458]) ).
fof(f741,plain,
( sQ44_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ14_spl
| inverse(inverse(inverse(sk_c2))) != inverse(inverse(identity)) ),
inference(forward_demodulation,[status(thm)],[f517,f642]) ).
fof(f742,plain,
( sQ44_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ14_spl
| inverse(inverse(sk_c2)) != inverse(inverse(identity)) ),
inference(forward_demodulation,[status(thm)],[f677,f741]) ).
fof(f743,plain,
( sQ44_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ14_spl
| inverse(sk_c2) != inverse(inverse(identity)) ),
inference(forward_demodulation,[status(thm)],[f677,f742]) ).
fof(f744,plain,
( sQ44_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ14_spl
| sk_c2 != inverse(inverse(identity)) ),
inference(forward_demodulation,[status(thm)],[f677,f743]) ).
fof(f745,plain,
( sQ44_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ14_spl
| sk_c2 != inverse(inverse(sk_c2)) ),
inference(forward_demodulation,[status(thm)],[f517,f744]) ).
fof(f746,plain,
( sQ44_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ14_spl
| sk_c2 != inverse(sk_c2) ),
inference(forward_demodulation,[status(thm)],[f677,f745]) ).
fof(f747,plain,
( sQ44_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ14_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f677,f746]) ).
fof(f748,plain,
( sQ44_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ14_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f747]) ).
fof(f749,plain,
( sQ44_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f748]) ).
fof(f750,plain,
( sQ43_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ14_spl
| multiply(inverse(inverse(sk_c2)),sk_c10) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f517,f639]) ).
fof(f751,plain,
( sQ43_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ14_spl
| multiply(inverse(sk_c2),sk_c10) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f677,f750]) ).
fof(f752,plain,
( sQ43_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ14_spl
| multiply(sk_c2,sk_c10) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f677,f751]) ).
fof(f753,plain,
( sQ43_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ14_spl
| sk_c10 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f492,f752]) ).
fof(f754,plain,
( sQ43_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ14_spl
| sk_c2 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f518,f753]) ).
fof(f755,plain,
( sQ42_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ14_spl
| inverse(inverse(sk_c2)) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f517,f644]) ).
fof(f756,plain,
( sQ42_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ14_spl
| inverse(sk_c2) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f677,f755]) ).
fof(f757,plain,
( sQ42_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ14_spl
| sk_c2 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f677,f756]) ).
fof(f758,plain,
( sQ41_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ14_spl
| inverse(inverse(sk_c2)) != inverse(identity) ),
inference(forward_demodulation,[status(thm)],[f517,f370]) ).
fof(f759,plain,
( sQ41_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ14_spl
| inverse(sk_c2) != inverse(identity) ),
inference(forward_demodulation,[status(thm)],[f677,f758]) ).
fof(f760,plain,
( sQ41_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ14_spl
| sk_c2 != inverse(identity) ),
inference(forward_demodulation,[status(thm)],[f677,f759]) ).
fof(f761,plain,
( sQ41_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ14_spl
| sk_c2 != inverse(sk_c2) ),
inference(forward_demodulation,[status(thm)],[f517,f760]) ).
fof(f762,plain,
( sQ41_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ14_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f677,f761]) ).
fof(f763,plain,
( sQ41_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ14_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f762]) ).
fof(f764,plain,
( sQ41_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f763]) ).
fof(f858,plain,
( sQ43_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ14_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f730,f754]) ).
fof(f859,plain,
( sQ43_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ14_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f858]) ).
fof(f860,plain,
( sQ43_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ14_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f859]) ).
fof(f866,plain,
( sQ42_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ14_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f730,f757]) ).
fof(f867,plain,
( sQ42_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ14_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f866]) ).
fof(f868,plain,
( sQ42_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ14_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f867]) ).
fof(f869,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f342,f153,f205,f110]) ).
fof(f870,definition,
( sQ45_spl
<=> identity = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f871,plain,
( ~ sQ45_spl
| identity = sk_c10 ),
inference(component_clause,[status(thm)],[f870]) ).
fof(f872,plain,
( sQ45_spl
| identity != sk_c10 ),
inference(component_clause,[status(thm)],[f870]) ).
fof(f877,definition,
( sQ47_spl
<=> sk_c11 = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f878,plain,
( ~ sQ47_spl
| sk_c11 = sk_c10 ),
inference(component_clause,[status(thm)],[f877]) ).
fof(f879,plain,
( sQ47_spl
| sk_c11 != sk_c10 ),
inference(component_clause,[status(thm)],[f877]) ).
fof(f880,definition,
( sQ48_spl
<=> inverse(identity) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f882,plain,
( sQ48_spl
| inverse(identity) != sk_c11 ),
inference(component_clause,[status(thm)],[f880]) ).
fof(f884,definition,
( sQ49_spl
<=> sk_c10 = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f886,plain,
( sQ49_spl
| sk_c10 != sk_c10 ),
inference(component_clause,[status(thm)],[f884]) ).
fof(f888,plain,
( sQ49_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f886]) ).
fof(f889,plain,
sQ49_spl,
inference(contradiction_clause,[status(thm)],[f888]) ).
fof(f916,plain,
( ~ sQ11_spl
| multiply(sk_c11,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f154,f56]) ).
fof(f921,plain,
( ~ sQ13_spl
| sk_c10 = multiply(inverse(sk_c2),sk_c9) ),
inference(paramodulation,[status(thm)],[f180,f330]) ).
fof(f923,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| sk_c10 = multiply(sk_c10,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f193,f921]) ).
fof(f924,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| sk_c9 = multiply(inverse(sk_c10),sk_c10) ),
inference(paramodulation,[status(thm)],[f602,f330]) ).
fof(f926,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| sk_c9 = identity ),
inference(forward_demodulation,[status(thm)],[f56,f924]) ).
fof(f927,plain,
( sQ42_spl
| ~ sQ13_spl
| ~ sQ14_spl
| inverse(inverse(sk_c9)) != sk_c11 ),
inference(backward_demodulation,[status(thm)],[f926,f644]) ).
fof(f928,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ14_spl
| multiply(inverse(X0),X0) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f926,f56]) ).
fof(f929,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ14_spl
| multiply(sk_c9,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f926,f55]) ).
fof(f931,plain,
( sQ45_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sk_c9 != sk_c10 ),
inference(backward_demodulation,[status(thm)],[f926,f872]) ).
fof(f934,plain,
( ~ sQ17_spl
| ~ sQ13_spl
| ~ sQ14_spl
| inverse(inverse(sk_c9)) != inverse(sk_c9)
| multiply(inverse(sk_c9),sk_c10) != sk_c11
| multiply(sk_c9,inverse(sk_c9)) != sk_c11 ),
inference(resolution,[status(thm)],[f929,f215]) ).
fof(f936,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ14_spl
| X0 = multiply(inverse(sk_c9),X0) ),
inference(paramodulation,[status(thm)],[f929,f330]) ).
fof(f938,definition,
( sQ50_spl
<=> multiply(sk_c9,inverse(sk_c9)) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f939,plain,
( ~ sQ50_spl
| multiply(sk_c9,inverse(sk_c9)) = sk_c11 ),
inference(component_clause,[status(thm)],[f938]) ).
fof(f940,plain,
( sQ50_spl
| multiply(sk_c9,inverse(sk_c9)) != sk_c11 ),
inference(component_clause,[status(thm)],[f938]) ).
fof(f941,definition,
( sQ51_spl
<=> multiply(inverse(sk_c9),sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f944,definition,
( sQ52_spl
<=> inverse(inverse(sk_c9)) = inverse(sk_c9) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f947,plain,
( ~ sQ17_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ52_spl
| ~ sQ51_spl
| ~ sQ50_spl ),
inference(split_clause,[status(thm)],[f934,f938,f941,f944,f192,f179,f211]) ).
fof(f948,plain,
( sQ50_spl
| ~ sQ13_spl
| ~ sQ14_spl
| inverse(sk_c9) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f929,f940]) ).
fof(f951,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sk_c10 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f926,f447]) ).
fof(f952,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sQ45_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f951,f931]) ).
fof(f953,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sQ45_spl ),
inference(contradiction_clause,[status(thm)],[f952]) ).
fof(f954,definition,
( sQ53_spl
<=> sk_c9 = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f956,plain,
( sQ53_spl
| sk_c9 != sk_c9 ),
inference(component_clause,[status(thm)],[f954]) ).
fof(f958,plain,
( ~ sQ3_spl
| ~ sQ16_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f313,f125,f208,f121]) ).
fof(f959,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c11 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f138,f660]) ).
fof(f961,definition,
( sQ54_spl
<=> sk_c11 = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f962,plain,
( ~ sQ54_spl
| sk_c11 = sk_c9 ),
inference(component_clause,[status(thm)],[f961]) ).
fof(f963,plain,
( sQ54_spl
| sk_c11 != sk_c9 ),
inference(component_clause,[status(thm)],[f961]) ).
fof(f969,plain,
( sQ53_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f956]) ).
fof(f970,plain,
sQ53_spl,
inference(contradiction_clause,[status(thm)],[f969]) ).
fof(f971,plain,
( sQ47_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c7 != sk_c10 ),
inference(backward_demodulation,[status(thm)],[f959,f879]) ).
fof(f980,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c9 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f447,f481]) ).
fof(f981,plain,
( ~ sQ45_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| identity = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f980,f871]) ).
fof(f989,plain,
( sQ54_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c7 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f959,f963]) ).
fof(f990,plain,
( sQ47_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c7 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f980,f971]) ).
fof(f993,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c9,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f980,f457]) ).
fof(f997,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| inverse(sk_c4) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f980,f126]) ).
fof(f1008,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(inverse(X0),X0) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f980,f456]) ).
fof(f1011,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| multiply(sk_c9,sk_c4) = sk_c9 ),
inference(paramodulation,[status(thm)],[f997,f1008]) ).
fof(f1016,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c4 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f993,f1011]) ).
fof(f1026,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| inverse(sk_c9) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f1016,f997]) ).
fof(f1034,plain,
( ~ sQ8_spl
| ~ sQ45_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c6,sk_c7) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f981,f324]) ).
fof(f1073,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| multiply(sk_c9,sk_c4) = identity ),
inference(forward_demodulation,[status(thm)],[f980,f326]) ).
fof(f1074,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c4 = identity ),
inference(forward_demodulation,[status(thm)],[f993,f1073]) ).
fof(f1075,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c9 = identity ),
inference(forward_demodulation,[status(thm)],[f1016,f1074]) ).
fof(f1084,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 = multiply(sk_c8,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f959,f431]) ).
fof(f1085,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c7 = multiply(inverse(sk_c8),sk_c8) ),
inference(paramodulation,[status(thm)],[f1084,f330]) ).
fof(f1087,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c7 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1008,f1085]) ).
fof(f1088,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sQ54_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1087,f989]) ).
fof(f1089,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sQ54_spl ),
inference(contradiction_clause,[status(thm)],[f1088]) ).
fof(f1093,plain,
( ~ sQ8_spl
| ~ sQ45_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| multiply(sk_c6,sk_c7) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f1087,f1034]) ).
fof(f1094,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c9) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f1087,f1026]) ).
fof(f1099,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(inverse(X0),X0) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f1087,f1008]) ).
fof(f1103,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f1087,f980]) ).
fof(f1104,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c7) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f1087,f1094]) ).
fof(f1105,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c6 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f142,f1104]) ).
fof(f1109,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 = identity ),
inference(forward_demodulation,[status(thm)],[f1087,f1075]) ).
fof(f1114,plain,
( sQ47_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f1087,f990]) ).
fof(f1115,plain,
( sQ47_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1114]) ).
fof(f1116,plain,
( sQ47_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f1115]) ).
fof(f1117,plain,
( ~ sQ47_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c7 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f959,f878]) ).
fof(f1126,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f56,f57]) ).
fof(f1127,plain,
! [X0] : multiply(identity,X0) = X0,
inference(forward_demodulation,[status(thm)],[f330,f1126]) ).
fof(f1140,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c11 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f1105,f959]) ).
fof(f1146,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c6 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1105,f1103]) ).
fof(f1148,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f1105,f1109]) ).
fof(f1156,plain,
( sQ45_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c6 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1148,f872]) ).
fof(f1157,plain,
( sQ45_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f1146,f1156]) ).
fof(f1158,plain,
( sQ45_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1157]) ).
fof(f1159,plain,
( sQ45_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f1158]) ).
fof(f1162,plain,
( ~ sQ8_spl
| ~ sQ45_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| multiply(sk_c6,sk_c6) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f1105,f1093]) ).
fof(f1163,plain,
( ~ sQ8_spl
| ~ sQ45_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c8 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f432,f1162]) ).
fof(f1164,plain,
( ~ sQ8_spl
| ~ sQ45_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c8 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f1105,f1163]) ).
fof(f1170,plain,
( sQ33_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ47_spl ),
inference(split_clause,[status(thm)],[f312,f877,f110,f153,f285]) ).
fof(f1171,plain,
( sQ36_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f308,f961,f179,f192,f295]) ).
fof(f1172,plain,
( ~ sQ45_spl
| ~ sQ13_spl
| ~ sQ14_spl
| identity = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f1173,f871]) ).
fof(f1173,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ45_spl
| sk_c9 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f871,f926]) ).
fof(f1180,plain,
! [X0] :
( ~ sQ45_spl
| ~ sQ13_spl
| ~ sQ14_spl
| multiply(sk_c9,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f1172,f55]) ).
fof(f1184,plain,
( sQ48_spl
| ~ sQ45_spl
| ~ sQ13_spl
| ~ sQ14_spl
| inverse(sk_c9) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1172,f882]) ).
fof(f1188,plain,
( ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ45_spl
| inverse(sk_c2) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1173,f193]) ).
fof(f1189,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ45_spl
| X0 = multiply(sk_c9,multiply(sk_c2,X0)) ),
inference(paramodulation,[status(thm)],[f1188,f330]) ).
fof(f1190,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ45_spl
| X0 = multiply(sk_c2,X0) ),
inference(forward_demodulation,[status(thm)],[f1180,f1189]) ).
fof(f1191,plain,
! [X0] :
( ~ sQ45_spl
| ~ sQ13_spl
| ~ sQ14_spl
| multiply(inverse(X0),X0) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1172,f56]) ).
fof(f1192,plain,
( ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ45_spl
| multiply(sk_c9,sk_c2) = sk_c9 ),
inference(paramodulation,[status(thm)],[f1188,f1191]) ).
fof(f1196,plain,
( ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ45_spl
| sk_c2 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1180,f1192]) ).
fof(f1198,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ45_spl
| multiply(sk_c1,sk_c11) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1173,f111]) ).
fof(f1210,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ45_spl
| multiply(sk_c1,sk_c11) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f1196,f1198]) ).
fof(f1212,plain,
( ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ45_spl
| inverse(sk_c2) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f1196,f1188]) ).
fof(f1215,plain,
( sQ48_spl
| ~ sQ45_spl
| ~ sQ13_spl
| ~ sQ14_spl
| inverse(sk_c2) != sk_c11 ),
inference(backward_demodulation,[status(thm)],[f1196,f1184]) ).
fof(f1232,plain,
( sQ48_spl
| ~ sQ45_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sk_c2 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1212,f1215]) ).
fof(f1282,plain,
( sQ45_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sk_c9 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f926,f872]) ).
fof(f1291,plain,
( ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| multiply(sk_c11,sk_c1) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f926,f916]) ).
fof(f1316,plain,
( ~ sQ17_spl
| ~ sQ13_spl
| ~ sQ14_spl
| inverse(inverse(inverse(sk_c9))) != inverse(inverse(sk_c9))
| multiply(inverse(inverse(sk_c9)),sk_c10) != sk_c11
| multiply(inverse(sk_c9),inverse(inverse(sk_c9))) != sk_c11 ),
inference(resolution,[status(thm)],[f936,f215]) ).
fof(f1324,definition,
( sQ63_spl
<=> multiply(inverse(sk_c9),inverse(inverse(sk_c9))) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f1326,plain,
( sQ63_spl
| multiply(inverse(sk_c9),inverse(inverse(sk_c9))) != sk_c11 ),
inference(component_clause,[status(thm)],[f1324]) ).
fof(f1327,definition,
( sQ64_spl
<=> multiply(inverse(inverse(sk_c9)),sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f1330,definition,
( sQ65_spl
<=> inverse(inverse(inverse(sk_c9))) = inverse(inverse(sk_c9)) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f1333,plain,
( ~ sQ17_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ65_spl
| ~ sQ64_spl
| ~ sQ63_spl ),
inference(split_clause,[status(thm)],[f1316,f1324,f1327,f1330,f192,f179,f211]) ).
fof(f1334,plain,
( sQ63_spl
| ~ sQ13_spl
| ~ sQ14_spl
| inverse(inverse(sk_c9)) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f936,f1326]) ).
fof(f1375,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ14_spl
| X0 = multiply(inverse(inverse(sk_c9)),X0) ),
inference(forward_demodulation,[status(thm)],[f926,f441]) ).
fof(f1379,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| inverse(sk_c9) = sk_c9 ),
inference(paramodulation,[status(thm)],[f928,f1375]) ).
fof(f1399,plain,
( sQ42_spl
| ~ sQ13_spl
| ~ sQ14_spl
| inverse(sk_c9) != sk_c11 ),
inference(backward_demodulation,[status(thm)],[f1379,f927]) ).
fof(f1400,plain,
( sQ50_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sk_c9 != sk_c11 ),
inference(backward_demodulation,[status(thm)],[f1379,f948]) ).
fof(f1402,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ17_spl
| multiply(X0,sk_c9) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c9)
| multiply(inverse(sk_c9),sk_c10) != sk_c11
| multiply(sk_c9,inverse(sk_c9)) != sk_c11 ),
inference(paramodulation,[status(thm)],[f1379,f215]) ).
fof(f1406,plain,
( sQ42_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sk_c9 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1379,f1399]) ).
fof(f1407,definition,
! [X0] :
( sQ72_spl
<=> ( multiply(X0,sk_c9) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c9) ) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f1410,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ17_spl
| sQ72_spl
| ~ sQ51_spl
| ~ sQ50_spl ),
inference(split_clause,[status(thm)],[f1402,f938,f941,f1407,f211,f192,f179]) ).
fof(f1417,plain,
( ~ sQ24_spl
| ~ sQ17_spl
| sk_c11 != inverse(sk_c5)
| inverse(inverse(sk_c5)) != inverse(sk_c5)
| multiply(inverse(sk_c5),sk_c10) != sk_c11
| multiply(sk_c5,inverse(sk_c5)) != sk_c11 ),
inference(paramodulation,[status(thm)],[f256,f215]) ).
fof(f1420,definition,
( sQ73_spl
<=> inverse(inverse(sk_c5)) = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f1422,plain,
( sQ73_spl
| inverse(inverse(sk_c5)) != inverse(sk_c5) ),
inference(component_clause,[status(thm)],[f1420]) ).
fof(f1423,definition,
( sQ74_spl
<=> sk_c11 = inverse(sk_c5) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f1425,plain,
( sQ74_spl
| sk_c11 != inverse(sk_c5) ),
inference(component_clause,[status(thm)],[f1423]) ).
fof(f1426,plain,
( ~ sQ17_spl
| ~ sQ74_spl
| ~ sQ73_spl
| ~ sQ25_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f1417,f255,f258,f1420,f1423,f211]) ).
fof(f1427,plain,
( ~ sQ12_spl
| ~ sQ0_spl
| multiply(sk_c10,sk_c9) = multiply(sk_c1,sk_c10) ),
inference(paramodulation,[status(thm)],[f167,f223]) ).
fof(f1429,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| multiply(sk_c10,sk_c10) = multiply(sk_c1,sk_c11) ),
inference(paramodulation,[status(thm)],[f597,f223]) ).
fof(f1432,plain,
( ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sk_c10 = multiply(sk_c1,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f923,f1427]) ).
fof(f1433,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| multiply(sk_c10,sk_c10) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f111,f1429]) ).
fof(f1437,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ14_spl
| X0 = multiply(sk_c2,multiply(sk_c10,X0)) ),
inference(forward_demodulation,[status(thm)],[f929,f224]) ).
fof(f1443,plain,
( ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sk_c10 = multiply(inverse(sk_c1),sk_c10) ),
inference(paramodulation,[status(thm)],[f1432,f330]) ).
fof(f1445,plain,
( ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ11_spl
| sk_c10 = multiply(sk_c11,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f154,f1443]) ).
fof(f1446,plain,
( ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ11_spl
| sk_c10 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f597,f1445]) ).
fof(f1447,plain,
( ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ11_spl
| sQ47_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1446,f879]) ).
fof(f1448,plain,
( ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ11_spl
| sQ47_spl ),
inference(contradiction_clause,[status(thm)],[f1447]) ).
fof(f1449,plain,
( ~ sQ33_spl
| ~ sQ11_spl
| multiply(sk_c1,sk_c11) = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f154,f286]) ).
fof(f1450,plain,
( ~ sQ33_spl
| ~ sQ11_spl
| ~ sQ0_spl
| sk_c10 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f111,f1449]) ).
fof(f1460,plain,
! [X0,X1] :
( ~ sQ17_spl
| ~ sQ33_spl
| ~ sQ11_spl
| ~ sQ0_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c10) != sk_c10
| multiply(X0,inverse(X0)) != sk_c11 ),
inference(backward_demodulation,[status(thm)],[f1450,f215]) ).
fof(f1464,plain,
( ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ33_spl
| ~ sQ0_spl
| multiply(sk_c10,sk_c1) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f1450,f1291]) ).
fof(f1467,plain,
( ~ sQ11_spl
| ~ sQ33_spl
| ~ sQ0_spl
| inverse(sk_c1) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f1450,f154]) ).
fof(f1472,plain,
! [X0,X1] :
( ~ sQ17_spl
| ~ sQ33_spl
| ~ sQ11_spl
| ~ sQ0_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c10) != sk_c10
| multiply(X0,inverse(X0)) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1450,f1460]) ).
fof(f1479,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sk_c10 = multiply(sk_c2,sk_c10) ),
inference(paramodulation,[status(thm)],[f1433,f1437]) ).
fof(f1480,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| sk_c10 = multiply(inverse(sk_c10),sk_c10) ),
inference(paramodulation,[status(thm)],[f1433,f330]) ).
fof(f1482,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sk_c10 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f180,f1479]) ).
fof(f1483,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sQ45_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1482,f1282]) ).
fof(f1484,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sQ45_spl ),
inference(contradiction_clause,[status(thm)],[f1483]) ).
fof(f1485,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sk_c10 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f928,f1480]) ).
fof(f1494,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ45_spl
| ~ sQ33_spl
| ~ sQ11_spl
| multiply(sk_c1,sk_c10) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1450,f1210]) ).
fof(f1495,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ45_spl
| ~ sQ33_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sk_c10 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1432,f1494]) ).
fof(f1518,plain,
( ~ sQ11_spl
| ~ sQ33_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| inverse(sk_c1) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f1485,f1467]) ).
fof(f1521,plain,
( ~ sQ33_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sk_c9 = sk_c11 ),
inference(backward_demodulation,[status(thm)],[f1485,f1450]) ).
fof(f1529,plain,
( ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ13_spl
| inverse(sk_c2) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f1485,f193]) ).
fof(f1534,plain,
( ~ sQ33_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sQ54_spl ),
inference(split_clause,[status(thm)],[f1521,f961,f192,f179,f110,f153,f285]) ).
fof(f1539,plain,
( sQ50_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f1400,f961,f192,f179,f938]) ).
fof(f1540,plain,
( sQ42_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f1406,f961,f192,f179,f634]) ).
fof(f1542,plain,
( ~ sQ50_spl
| ~ sQ13_spl
| ~ sQ14_spl
| inverse(sk_c9) = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f929,f939]) ).
fof(f1543,plain,
( ~ sQ50_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sk_c9 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1379,f1542]) ).
fof(f1544,plain,
( sQ63_spl
| ~ sQ13_spl
| ~ sQ14_spl
| inverse(sk_c9) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1379,f1334]) ).
fof(f1545,plain,
( sQ63_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sk_c9 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1379,f1544]) ).
fof(f1552,plain,
( sQ43_spl
| ~ sQ13_spl
| ~ sQ14_spl
| multiply(inverse(inverse(sk_c9)),sk_c10) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f926,f639]) ).
fof(f1553,plain,
( sQ43_spl
| ~ sQ13_spl
| ~ sQ14_spl
| multiply(inverse(sk_c9),sk_c10) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1379,f1552]) ).
fof(f1554,plain,
( sQ43_spl
| ~ sQ13_spl
| ~ sQ14_spl
| multiply(sk_c9,sk_c10) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1379,f1553]) ).
fof(f1555,plain,
( sQ43_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sk_c10 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f929,f1554]) ).
fof(f1556,plain,
( sQ43_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ11_spl
| sk_c9 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1485,f1555]) ).
fof(f1567,plain,
! [X0,X1] :
( ~ sQ17_spl
| ~ sQ33_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ45_spl
| ~ sQ12_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c10) != sk_c10
| multiply(X0,inverse(X0)) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1495,f1472]) ).
fof(f1568,plain,
! [X0,X1] :
( ~ sQ17_spl
| ~ sQ33_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ45_spl
| ~ sQ12_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c2) != sk_c10
| multiply(X0,inverse(X0)) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1495,f1567]) ).
fof(f1569,plain,
! [X0,X1] :
( ~ sQ17_spl
| ~ sQ33_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ45_spl
| ~ sQ12_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c2) != sk_c2
| multiply(X0,inverse(X0)) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1495,f1568]) ).
fof(f1573,plain,
( ~ sQ54_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ45_spl
| sk_c11 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1196,f962]) ).
fof(f1574,plain,
( ~ sQ54_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ45_spl
| sQ48_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1573,f1232]) ).
fof(f1575,plain,
( ~ sQ54_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ45_spl
| sQ48_spl ),
inference(contradiction_clause,[status(thm)],[f1574]) ).
fof(f1576,plain,
( ~ sQ50_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ45_spl
| sk_c2 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1196,f1543]) ).
fof(f1577,plain,
( sQ63_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ45_spl
| sk_c2 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1196,f1545]) ).
fof(f1578,plain,
( sQ63_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ45_spl
| ~ sQ50_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1576,f1577]) ).
fof(f1579,plain,
( sQ63_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ45_spl
| ~ sQ50_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1578]) ).
fof(f1580,plain,
( sQ63_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ45_spl
| ~ sQ50_spl ),
inference(contradiction_clause,[status(thm)],[f1579]) ).
fof(f1585,plain,
( sQ43_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ45_spl
| sk_c2 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1196,f1556]) ).
fof(f1586,plain,
( sQ43_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ45_spl
| ~ sQ50_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1576,f1585]) ).
fof(f1587,plain,
( sQ43_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ45_spl
| ~ sQ50_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1586]) ).
fof(f1588,plain,
( sQ43_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ45_spl
| ~ sQ50_spl ),
inference(contradiction_clause,[status(thm)],[f1587]) ).
fof(f1608,plain,
( ~ sQ11_spl
| ~ sQ33_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ45_spl
| inverse(sk_c1) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1196,f1518]) ).
fof(f1610,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ33_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ45_spl
| X0 = multiply(sk_c2,multiply(sk_c1,X0)) ),
inference(paramodulation,[status(thm)],[f1608,f330]) ).
fof(f1611,definition,
( sQ77_spl
<=> multiply(sk_c1,inverse(sk_c1)) = sk_c2 ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f1613,plain,
( sQ77_spl
| multiply(sk_c1,inverse(sk_c1)) != sk_c2 ),
inference(component_clause,[status(thm)],[f1611]) ).
fof(f1614,definition,
( sQ78_spl
<=> multiply(inverse(sk_c1),sk_c2) = sk_c2 ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f1616,plain,
( sQ78_spl
| multiply(inverse(sk_c1),sk_c2) != sk_c2 ),
inference(component_clause,[status(thm)],[f1614]) ).
fof(f1621,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ33_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ45_spl
| X0 = multiply(sk_c1,X0) ),
inference(forward_demodulation,[status(thm)],[f1190,f1610]) ).
fof(f1623,plain,
( sQ78_spl
| ~ sQ11_spl
| ~ sQ33_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ45_spl
| multiply(sk_c2,sk_c2) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1608,f1616]) ).
fof(f1624,plain,
( sQ78_spl
| ~ sQ11_spl
| ~ sQ33_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ45_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1190,f1623]) ).
fof(f1625,plain,
( sQ78_spl
| ~ sQ11_spl
| ~ sQ33_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ45_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1624]) ).
fof(f1626,plain,
( sQ78_spl
| ~ sQ11_spl
| ~ sQ33_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ45_spl ),
inference(contradiction_clause,[status(thm)],[f1625]) ).
fof(f1627,plain,
( sQ77_spl
| ~ sQ11_spl
| ~ sQ33_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ45_spl
| multiply(sk_c1,sk_c2) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1608,f1613]) ).
fof(f1638,plain,
( ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ45_spl
| inverse(sk_c2) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1196,f1529]) ).
fof(f1649,plain,
( ~ sQ17_spl
| ~ sQ33_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ45_spl
| ~ sQ12_spl
| inverse(inverse(sk_c1)) != inverse(sk_c1)
| multiply(inverse(sk_c1),sk_c2) != sk_c2
| multiply(sk_c1,inverse(sk_c1)) != sk_c2 ),
inference(resolution,[status(thm)],[f1621,f1569]) ).
fof(f1653,definition,
( sQ80_spl
<=> inverse(inverse(sk_c1)) = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f1655,plain,
( sQ80_spl
| inverse(inverse(sk_c1)) != inverse(sk_c1) ),
inference(component_clause,[status(thm)],[f1653]) ).
fof(f1656,plain,
( ~ sQ17_spl
| ~ sQ33_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ45_spl
| ~ sQ12_spl
| ~ sQ80_spl
| ~ sQ78_spl
| ~ sQ77_spl ),
inference(split_clause,[status(thm)],[f1649,f1611,f1614,f1653,f166,f870,f192,f179,f110,f153,f285,f211]) ).
fof(f1662,plain,
( sQ80_spl
| ~ sQ11_spl
| ~ sQ33_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ45_spl
| inverse(sk_c2) != inverse(sk_c1) ),
inference(forward_demodulation,[status(thm)],[f1608,f1655]) ).
fof(f1663,plain,
( sQ80_spl
| ~ sQ11_spl
| ~ sQ33_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ45_spl
| sk_c2 != inverse(sk_c1) ),
inference(forward_demodulation,[status(thm)],[f1638,f1662]) ).
fof(f1664,plain,
( sQ80_spl
| ~ sQ11_spl
| ~ sQ33_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ45_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1608,f1663]) ).
fof(f1665,plain,
( sQ80_spl
| ~ sQ11_spl
| ~ sQ33_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ45_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1664]) ).
fof(f1666,plain,
( sQ80_spl
| ~ sQ11_spl
| ~ sQ33_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ45_spl ),
inference(contradiction_clause,[status(thm)],[f1665]) ).
fof(f1697,plain,
( ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ33_spl
| ~ sQ0_spl
| ~ sQ45_spl
| ~ sQ12_spl
| multiply(sk_c2,sk_c1) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1495,f1464]) ).
fof(f1698,plain,
( ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ33_spl
| ~ sQ0_spl
| ~ sQ45_spl
| ~ sQ12_spl
| sk_c1 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1190,f1697]) ).
fof(f1701,plain,
( ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ33_spl
| ~ sQ0_spl
| ~ sQ45_spl
| ~ sQ12_spl
| sk_c1 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1196,f1698]) ).
fof(f1722,plain,
( sQ77_spl
| ~ sQ11_spl
| ~ sQ33_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ45_spl
| ~ sQ12_spl
| multiply(sk_c2,sk_c2) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1701,f1627]) ).
fof(f1723,plain,
( sQ77_spl
| ~ sQ11_spl
| ~ sQ33_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ45_spl
| ~ sQ12_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1190,f1722]) ).
fof(f1724,plain,
( sQ77_spl
| ~ sQ11_spl
| ~ sQ33_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ45_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1723]) ).
fof(f1725,plain,
( sQ77_spl
| ~ sQ11_spl
| ~ sQ33_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ45_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f1724]) ).
fof(f1727,plain,
( ~ sQ47_spl
| ~ sQ54_spl
| sk_c9 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f962,f878]) ).
fof(f1738,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ47_spl
| ~ sQ54_spl
| sk_c6 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1727,f1146]) ).
fof(f1742,plain,
( ~ sQ47_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c6 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1105,f1117]) ).
fof(f1758,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c6,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f1148,f1127]) ).
fof(f1768,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ47_spl
| ~ sQ54_spl
| inverse(sk_c6) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1738,f1026]) ).
fof(f1769,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ47_spl
| ~ sQ54_spl
| inverse(sk_c6) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f1738,f1768]) ).
fof(f1788,plain,
( ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ45_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| inverse(sk_c5) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f1164,f134]) ).
fof(f1792,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(inverse(X0),X0) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f1105,f1099]) ).
fof(f1793,plain,
( ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ45_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c6,sk_c5) = sk_c6 ),
inference(paramodulation,[status(thm)],[f1788,f1792]) ).
fof(f1798,plain,
( ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ45_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c5 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f1758,f1793]) ).
fof(f1958,plain,
( sQ12_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c6,sk_c9) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1105,f668]) ).
fof(f1959,plain,
( sQ12_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c9 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1758,f1958]) ).
fof(f1960,plain,
( sQ12_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ47_spl
| ~ sQ54_spl
| sk_c6 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1738,f1959]) ).
fof(f1961,plain,
( sQ12_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ47_spl
| ~ sQ54_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f1742,f1960]) ).
fof(f1962,plain,
( sQ12_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ47_spl
| ~ sQ54_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1961]) ).
fof(f1963,plain,
( sQ12_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ47_spl
| ~ sQ54_spl ),
inference(contradiction_clause,[status(thm)],[f1962]) ).
fof(f1994,plain,
( sQ73_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ45_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| inverse(inverse(sk_c6)) != inverse(sk_c5) ),
inference(forward_demodulation,[status(thm)],[f1798,f1422]) ).
fof(f1995,plain,
( sQ73_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ45_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ47_spl
| ~ sQ54_spl
| inverse(sk_c6) != inverse(sk_c5) ),
inference(forward_demodulation,[status(thm)],[f1769,f1994]) ).
fof(f1996,plain,
( sQ73_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ45_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ47_spl
| ~ sQ54_spl
| sk_c6 != inverse(sk_c5) ),
inference(forward_demodulation,[status(thm)],[f1769,f1995]) ).
fof(f1997,plain,
( sQ73_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ45_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ47_spl
| ~ sQ54_spl
| sk_c6 != inverse(sk_c6) ),
inference(forward_demodulation,[status(thm)],[f1798,f1996]) ).
fof(f1998,plain,
( sQ73_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ45_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ47_spl
| ~ sQ54_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f1769,f1997]) ).
fof(f1999,plain,
( sQ73_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ45_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ47_spl
| ~ sQ54_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1998]) ).
fof(f2000,plain,
( sQ73_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ45_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ47_spl
| ~ sQ54_spl ),
inference(contradiction_clause,[status(thm)],[f1999]) ).
fof(f2026,plain,
( sQ74_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c6 != inverse(sk_c5) ),
inference(forward_demodulation,[status(thm)],[f1140,f1425]) ).
fof(f2027,plain,
( sQ74_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ45_spl
| ~ sQ10_spl
| sk_c6 != inverse(sk_c6) ),
inference(forward_demodulation,[status(thm)],[f1798,f2026]) ).
fof(f2028,plain,
( sQ74_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ45_spl
| ~ sQ10_spl
| ~ sQ47_spl
| ~ sQ54_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f1769,f2027]) ).
fof(f2029,plain,
( sQ74_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ45_spl
| ~ sQ10_spl
| ~ sQ47_spl
| ~ sQ54_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f2028]) ).
fof(f2030,plain,
( sQ74_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ45_spl
| ~ sQ10_spl
| ~ sQ47_spl
| ~ sQ54_spl ),
inference(contradiction_clause,[status(thm)],[f2029]) ).
fof(f2031,plain,
$false,
inference(sat_refutation,[status(thm)],[f116,f120,f124,f128,f132,f136,f140,f144,f148,f156,f157,f158,f159,f160,f161,f162,f163,f164,f169,f170,f171,f172,f173,f174,f175,f176,f177,f182,f183,f184,f185,f195,f196,f197,f198,f199,f200,f201,f202,f203,f204,f214,f264,f321,f350,f371,f397,f402,f588,f643,f749,f764,f860,f868,f869,f889,f947,f953,f958,f970,f1089,f1116,f1159,f1170,f1171,f1333,f1410,f1426,f1448,f1484,f1534,f1539,f1540,f1575,f1580,f1588,f1626,f1656,f1666,f1725,f1963,f2000,f2030]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP271-1 : 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 : n016.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
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 20:12:22 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.39 % Drodi V4.1.1
% 0.15/0.44 % Refutation found
% 0.15/0.44 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.46 % Elapsed time: 0.087924 seconds
% 0.15/0.46 % CPU time: 0.376846 seconds
% 0.15/0.46 % Total memory used: 108.053 MB
% 0.15/0.46 % Net memory used: 107.811 MB
%------------------------------------------------------------------------------