%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP371-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 12:33:32 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.46s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 82
% Syntax : Number of formulae : 479 ( 10 unt; 40 def)
% Number of atoms : 2299 ( 556 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 3515 (1695 ~;1780 |; 0 &)
% ( 40 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 42 ( 40 usr; 41 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 107 ( 107 !; 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
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c3) = sk_c11
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c7) = sk_c6
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c6) = sk_c8
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c1,sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c1,sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c1,sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c1,sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c7) = sk_c6
| multiply(sk_c1,sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( inverse(sk_c6) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c3) = sk_c11
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( inverse(sk_c7) = sk_c6
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( inverse(sk_c6) = sk_c8
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c2,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c2,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,negated_conjecture,
( inverse(sk_c7) = sk_c6
| multiply(sk_c2,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,negated_conjecture,
( inverse(sk_c6) = sk_c8
| multiply(sk_c2,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c9,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c9,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c9,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c9,sk_c10) = sk_c11 ),
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
| multiply(sk_c9,sk_c10) != sk_c11
| multiply(X4,sk_c10) != sk_c11
| inverse(X3) != X4
| multiply(X3,X4) != sk_c11
| inverse(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
| 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_c1,sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f69,plain,
( inverse(sk_c3) = sk_c11
| multiply(sk_c1,sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f70,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c1,sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f71,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f73,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f74,plain,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c1,sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f75,plain,
( inverse(sk_c7) = sk_c6
| multiply(sk_c1,sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f76,plain,
( inverse(sk_c6) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f78,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f79,plain,
( inverse(sk_c3) = sk_c11
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f80,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f81,plain,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f83,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f84,plain,
( multiply(sk_c8,sk_c10) = sk_c11
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f85,plain,
( inverse(sk_c7) = sk_c6
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f86,plain,
( inverse(sk_c6) = sk_c8
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f88,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f89,plain,
( inverse(sk_c3) = sk_c11
| multiply(sk_c2,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f90,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f91,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f93,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f94,plain,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c2,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f95,plain,
( inverse(sk_c7) = sk_c6
| multiply(sk_c2,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f96,plain,
( inverse(sk_c6) = sk_c8
| multiply(sk_c2,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f98,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c9,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f99,plain,
( inverse(sk_c3) = sk_c11
| multiply(sk_c9,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f100,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c9,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f101,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c9,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f47]) ).
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
| multiply(sk_c9,sk_c10) != sk_c11
| ! [X4] :
( multiply(X4,sk_c10) != sk_c11
| ! [X3] :
( inverse(X3) != X4
| multiply(X3,X4) != 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(sk_c9,sk_c10) != sk_c11
| multiply(X1,sk_c10) != sk_c11
| inverse(X0) != X1
| multiply(X0,X1) != 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_c1,sk_c2) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f154,plain,
( ~ sQ11_spl
| multiply(sk_c1,sk_c2) = 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(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
<=> inverse(sk_c1) = sk_c2 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f167,plain,
( ~ sQ12_spl
| inverse(sk_c1) = sk_c2 ),
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(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_c11 ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f180,plain,
( ~ sQ13_spl
| multiply(sk_c2,sk_c10) = sk_c11 ),
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(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(f192,definition,
( sQ14_spl
<=> multiply(sk_c9,sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f193,plain,
( ~ sQ14_spl
| multiply(sk_c9,sk_c10) = sk_c11 ),
inference(component_clause,[status(thm)],[f192]) ).
fof(f194,plain,
( sQ14_spl
| multiply(sk_c9,sk_c10) != sk_c11 ),
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(f205,definition,
! [X0,X1] :
( sQ15_spl
<=> ( multiply(X1,sk_c10) != sk_c11
| inverse(X0) != X1
| multiply(X0,X1) != sk_c11 ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f206,plain,
! [X0,X1] :
( ~ sQ15_spl
| multiply(X1,sk_c10) != sk_c11
| inverse(X0) != X1
| multiply(X0,X1) != sk_c11 ),
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
| ~ sQ14_spl
| sQ15_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f109,f110,f205,f192,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(f230,plain,
( ~ sQ0_spl
| multiply(sk_c10,sk_c11) = identity ),
inference(paramodulation,[status(thm)],[f111,f56]) ).
fof(f231,plain,
( ~ sQ2_spl
| multiply(sk_c11,sk_c3) = identity ),
inference(paramodulation,[status(thm)],[f118,f56]) ).
fof(f233,plain,
( ~ sQ6_spl
| multiply(sk_c8,sk_c5) = identity ),
inference(paramodulation,[status(thm)],[f134,f56]) ).
fof(f234,plain,
( ~ sQ8_spl
| multiply(sk_c6,sk_c7) = identity ),
inference(paramodulation,[status(thm)],[f142,f56]) ).
fof(f237,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f56,f57]) ).
fof(f238,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f55,f237]) ).
fof(f262,plain,
( ~ sQ2_spl
| sk_c3 = multiply(inverse(sk_c11),identity) ),
inference(paramodulation,[status(thm)],[f231,f238]) ).
fof(f268,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f55,f238]) ).
fof(f269,plain,
( ~ sQ1_spl
| sk_c11 = multiply(inverse(sk_c3),sk_c10) ),
inference(paramodulation,[status(thm)],[f114,f238]) ).
fof(f271,plain,
( ~ sQ3_spl
| sk_c10 = multiply(inverse(sk_c4),sk_c9) ),
inference(paramodulation,[status(thm)],[f122,f238]) ).
fof(f272,plain,
( ~ sQ5_spl
| sk_c8 = multiply(inverse(sk_c5),sk_c11) ),
inference(paramodulation,[status(thm)],[f130,f238]) ).
fof(f277,plain,
( ~ sQ11_spl
| sk_c2 = multiply(inverse(sk_c1),sk_c11) ),
inference(paramodulation,[status(thm)],[f154,f238]) ).
fof(f282,plain,
( ~ sQ2_spl
| ~ sQ0_spl
| sk_c3 = multiply(sk_c10,identity) ),
inference(forward_demodulation,[status(thm)],[f111,f262]) ).
fof(f283,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c11 = multiply(sk_c11,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f118,f269]) ).
fof(f284,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c10 = multiply(sk_c10,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f126,f271]) ).
fof(f285,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sk_c8 = multiply(sk_c8,sk_c11) ),
inference(forward_demodulation,[status(thm)],[f134,f272]) ).
fof(f287,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| sk_c2 = multiply(sk_c2,sk_c11) ),
inference(forward_demodulation,[status(thm)],[f167,f277]) ).
fof(f292,plain,
! [X0] :
( ~ sQ18_spl
| multiply(X0,inverse(sk_c10)) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c10)
| identity != sk_c11
| multiply(sk_c10,inverse(sk_c10)) != sk_c11 ),
inference(paramodulation,[status(thm)],[f56,f218]) ).
fof(f298,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ18_spl
| multiply(X0,inverse(sk_c6)) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c6)
| multiply(sk_c8,sk_c10) != sk_c11
| multiply(sk_c6,inverse(sk_c6)) != sk_c11 ),
inference(paramodulation,[status(thm)],[f146,f218]) ).
fof(f300,definition,
( sQ19_spl
<=> multiply(sk_c10,inverse(sk_c10)) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f302,plain,
( sQ19_spl
| multiply(sk_c10,inverse(sk_c10)) != sk_c11 ),
inference(component_clause,[status(thm)],[f300]) ).
fof(f303,definition,
( sQ20_spl
<=> identity = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f304,plain,
( ~ sQ20_spl
| identity = sk_c11 ),
inference(component_clause,[status(thm)],[f303]) ).
fof(f305,plain,
( sQ20_spl
| identity != sk_c11 ),
inference(component_clause,[status(thm)],[f303]) ).
fof(f306,definition,
! [X0] :
( sQ21_spl
<=> ( multiply(X0,inverse(sk_c10)) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c10) ) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f307,plain,
! [X0] :
( ~ sQ21_spl
| multiply(X0,inverse(sk_c10)) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c10) ),
inference(component_clause,[status(thm)],[f306]) ).
fof(f309,plain,
( ~ sQ18_spl
| sQ21_spl
| ~ sQ20_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f292,f300,f303,f306,f214]) ).
fof(f313,definition,
( sQ23_spl
<=> multiply(sk_c10,sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f315,plain,
( sQ23_spl
| multiply(sk_c10,sk_c10) != sk_c11 ),
inference(component_clause,[status(thm)],[f313]) ).
fof(f323,definition,
( sQ26_spl
<=> multiply(sk_c11,sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f324,plain,
( ~ sQ26_spl
| multiply(sk_c11,sk_c10) = sk_c11 ),
inference(component_clause,[status(thm)],[f323]) ).
fof(f325,plain,
( sQ26_spl
| multiply(sk_c11,sk_c10) != sk_c11 ),
inference(component_clause,[status(thm)],[f323]) ).
fof(f354,definition,
( sQ35_spl
<=> multiply(sk_c6,inverse(sk_c6)) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f356,plain,
( sQ35_spl
| multiply(sk_c6,inverse(sk_c6)) != sk_c11 ),
inference(component_clause,[status(thm)],[f354]) ).
fof(f357,definition,
! [X0] :
( sQ36_spl
<=> ( multiply(X0,inverse(sk_c6)) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c6) ) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f358,plain,
! [X0] :
( ~ sQ36_spl
| multiply(X0,inverse(sk_c6)) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c6) ),
inference(component_clause,[status(thm)],[f357]) ).
fof(f360,plain,
( ~ sQ9_spl
| ~ sQ18_spl
| sQ36_spl
| ~ sQ7_spl
| ~ sQ35_spl ),
inference(split_clause,[status(thm)],[f298,f354,f137,f357,f214,f145]) ).
fof(f361,definition,
( sQ37_spl
<=> multiply(sk_c1,inverse(sk_c1)) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f363,plain,
( sQ37_spl
| multiply(sk_c1,inverse(sk_c1)) != sk_c11 ),
inference(component_clause,[status(thm)],[f361]) ).
fof(f370,plain,
( sQ37_spl
| ~ sQ12_spl
| multiply(sk_c1,sk_c2) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f167,f363]) ).
fof(f371,plain,
( sQ37_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f154,f370]) ).
fof(f372,plain,
( sQ37_spl
| ~ sQ12_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f371]) ).
fof(f373,plain,
( sQ37_spl
| ~ sQ12_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f372]) ).
fof(f374,plain,
( ~ sQ12_spl
| ~ sQ17_spl
| sk_c2 != sk_c10
| multiply(sk_c1,sk_c10) != sk_c9 ),
inference(paramodulation,[status(thm)],[f167,f212]) ).
fof(f375,definition,
( sQ39_spl
<=> multiply(sk_c1,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f377,plain,
( sQ39_spl
| multiply(sk_c1,sk_c10) != sk_c9 ),
inference(component_clause,[status(thm)],[f375]) ).
fof(f378,definition,
( sQ40_spl
<=> sk_c2 = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f380,plain,
( sQ40_spl
| sk_c2 != sk_c10 ),
inference(component_clause,[status(thm)],[f378]) ).
fof(f381,plain,
( ~ sQ12_spl
| ~ sQ17_spl
| ~ sQ40_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f374,f375,f378,f211,f166]) ).
fof(f401,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f283,f325]) ).
fof(f402,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sQ26_spl ),
inference(contradiction_clause,[status(thm)],[f401]) ).
fof(f405,plain,
( ~ sQ2_spl
| ~ sQ16_spl
| multiply(sk_c3,sk_c11) != sk_c10 ),
inference(resolution,[status(thm)],[f209,f118]) ).
fof(f412,plain,
( ~ sQ2_spl
| ~ sQ16_spl
| ~ sQ1_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f114,f405]) ).
fof(f413,plain,
( ~ sQ2_spl
| ~ sQ16_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f412]) ).
fof(f414,plain,
( ~ sQ2_spl
| ~ sQ16_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f413]) ).
fof(f415,plain,
! [X0] :
( ~ sQ15_spl
| multiply(inverse(X0),sk_c10) != sk_c11
| multiply(X0,inverse(X0)) != sk_c11 ),
inference(destructive_equality_resolution,[status(thm)],[f206]) ).
fof(f419,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c9 = multiply(inverse(sk_c10),sk_c10) ),
inference(paramodulation,[status(thm)],[f284,f238]) ).
fof(f421,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c9 = identity ),
inference(forward_demodulation,[status(thm)],[f56,f419]) ).
fof(f425,plain,
( sQ20_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c9 != sk_c11 ),
inference(backward_demodulation,[status(thm)],[f421,f305]) ).
fof(f428,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c9,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f421,f55]) ).
fof(f429,plain,
( ~ sQ14_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c10 = sk_c11 ),
inference(backward_demodulation,[status(thm)],[f428,f193]) ).
fof(f442,plain,
( ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c8,sk_c5) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f421,f233]) ).
fof(f449,plain,
( ~ sQ8_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c6,sk_c7) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f421,f234]) ).
fof(f450,plain,
( ~ sQ8_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c7 = multiply(inverse(sk_c6),sk_c9) ),
inference(paramodulation,[status(thm)],[f449,f238]) ).
fof(f452,plain,
( ~ sQ8_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ9_spl
| sk_c7 = multiply(sk_c8,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f146,f450]) ).
fof(f457,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(inverse(X0),sk_c10) != sk_c11
| multiply(X0,inverse(X0)) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f429,f415]) ).
fof(f458,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(inverse(X0),sk_c10) != sk_c10
| multiply(X0,inverse(X0)) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f429,f457]) ).
fof(f463,plain,
( ~ sQ4_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ3_spl
| multiply(sk_c10,sk_c10) != sk_c10
| multiply(sk_c4,inverse(sk_c4)) != sk_c10 ),
inference(paramodulation,[status(thm)],[f126,f458]) ).
fof(f468,definition,
( sQ42_spl
<=> multiply(sk_c10,sk_c10) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f470,plain,
( sQ42_spl
| multiply(sk_c10,sk_c10) != sk_c10 ),
inference(component_clause,[status(thm)],[f468]) ).
fof(f490,definition,
( sQ48_spl
<=> multiply(sk_c4,inverse(sk_c4)) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f492,plain,
( sQ48_spl
| multiply(sk_c4,inverse(sk_c4)) != sk_c10 ),
inference(component_clause,[status(thm)],[f490]) ).
fof(f493,plain,
( ~ sQ4_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ3_spl
| ~ sQ42_spl
| ~ sQ48_spl ),
inference(split_clause,[status(thm)],[f463,f490,f468,f121,f192,f205,f125]) ).
fof(f494,definition,
( sQ49_spl
<=> multiply(sk_c1,inverse(sk_c1)) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f495,plain,
( ~ sQ49_spl
| multiply(sk_c1,inverse(sk_c1)) = sk_c10 ),
inference(component_clause,[status(thm)],[f494]) ).
fof(f496,plain,
( sQ49_spl
| multiply(sk_c1,inverse(sk_c1)) != sk_c10 ),
inference(component_clause,[status(thm)],[f494]) ).
fof(f502,plain,
( sQ49_spl
| ~ sQ12_spl
| multiply(sk_c1,sk_c2) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f167,f496]) ).
fof(f503,plain,
( sQ48_spl
| ~ sQ4_spl
| multiply(sk_c4,sk_c10) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f126,f492]) ).
fof(f504,plain,
( sQ48_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sk_c9 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f122,f503]) ).
fof(f516,plain,
( ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c3 = multiply(sk_c10,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f421,f282]) ).
fof(f517,plain,
( ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c3 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f284,f516]) ).
fof(f547,plain,
( ~ sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| inverse(sk_c11) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f517,f111]) ).
fof(f550,plain,
( sQ48_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ0_spl
| sk_c9 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f517,f504]) ).
fof(f551,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| inverse(sk_c4) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f517,f126]) ).
fof(f553,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c3,sk_c11) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f517,f114]) ).
fof(f558,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c9,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f421,f55]) ).
fof(f567,plain,
( sQ42_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c3,sk_c10) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f517,f470]) ).
fof(f568,plain,
( sQ42_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c3,sk_c3) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f517,f567]) ).
fof(f569,plain,
( sQ42_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c3,sk_c3) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f517,f568]) ).
fof(f574,plain,
( ~ sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c3,sk_c11) = identity ),
inference(forward_demodulation,[status(thm)],[f517,f230]) ).
fof(f575,plain,
( ~ sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sk_c3 = identity ),
inference(forward_demodulation,[status(thm)],[f553,f574]) ).
fof(f576,plain,
( ~ sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sk_c3 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f421,f575]) ).
fof(f577,plain,
( ~ sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sQ48_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f576,f550]) ).
fof(f578,plain,
( ~ sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sQ48_spl ),
inference(contradiction_clause,[status(thm)],[f577]) ).
fof(f585,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| multiply(inverse(X0),X0) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f421,f56]) ).
fof(f598,plain,
( sQ42_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| multiply(sk_c3,sk_c3) != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f576,f569]) ).
fof(f600,plain,
( ~ sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| inverse(sk_c11) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f576,f547]) ).
fof(f602,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c3,sk_c11) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f576,f553]) ).
fof(f603,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ1_spl
| inverse(sk_c4) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f576,f551]) ).
fof(f605,plain,
( ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sk_c9 = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f576,f517]) ).
fof(f607,plain,
( sQ42_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| multiply(sk_c9,sk_c3) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f576,f598]) ).
fof(f608,plain,
( sQ42_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sk_c3 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f558,f607]) ).
fof(f609,plain,
( sQ42_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f576,f608]) ).
fof(f610,plain,
( sQ42_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f609]) ).
fof(f611,plain,
( sQ42_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f610]) ).
fof(f612,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c9,sk_c11) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f576,f602]) ).
fof(f613,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c11 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f558,f612]) ).
fof(f614,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f613,f425]) ).
fof(f615,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sQ20_spl ),
inference(contradiction_clause,[status(thm)],[f614]) ).
fof(f616,plain,
( ~ sQ20_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c9 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f421,f304]) ).
fof(f623,plain,
( ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| multiply(sk_c8,sk_c9) = sk_c11 ),
inference(backward_demodulation,[status(thm)],[f605,f138]) ).
fof(f630,plain,
( ~ sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ20_spl
| inverse(sk_c9) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f616,f600]) ).
fof(f640,plain,
( sQ14_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c10 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f558,f194]) ).
fof(f641,plain,
( sQ14_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ1_spl
| sk_c9 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f605,f640]) ).
fof(f642,plain,
( sQ14_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ20_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f616,f641]) ).
fof(f643,plain,
( sQ14_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ20_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f642]) ).
fof(f644,plain,
( sQ14_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ20_spl ),
inference(contradiction_clause,[status(thm)],[f643]) ).
fof(f655,plain,
( ~ sQ11_spl
| sk_c2 = multiply(inverse(sk_c1),sk_c11) ),
inference(paramodulation,[status(thm)],[f154,f238]) ).
fof(f657,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| sk_c2 = multiply(sk_c2,sk_c11) ),
inference(forward_demodulation,[status(thm)],[f167,f655]) ).
fof(f672,plain,
( sQ49_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sk_c11 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f154,f502]) ).
fof(f673,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| sk_c11 = multiply(inverse(sk_c2),sk_c2) ),
inference(paramodulation,[status(thm)],[f287,f238]) ).
fof(f675,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| sk_c11 = identity ),
inference(forward_demodulation,[status(thm)],[f56,f673]) ).
fof(f677,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ12_spl
| multiply(inverse(X0),X0) = sk_c11 ),
inference(backward_demodulation,[status(thm)],[f675,f56]) ).
fof(f678,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ12_spl
| X0 = multiply(inverse(sk_c11),X0) ),
inference(backward_demodulation,[status(thm)],[f675,f268]) ).
fof(f679,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ12_spl
| multiply(sk_c11,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f675,f55]) ).
fof(f680,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| X0 = multiply(sk_c10,X0) ),
inference(forward_demodulation,[status(thm)],[f111,f678]) ).
fof(f681,plain,
( sQ23_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| sk_c10 != sk_c11 ),
inference(backward_demodulation,[status(thm)],[f680,f315]) ).
fof(f692,plain,
! [X0] :
( ~ sQ14_spl
| multiply(sk_c11,X0) = multiply(sk_c9,multiply(sk_c10,X0)) ),
inference(paramodulation,[status(thm)],[f193,f57]) ).
fof(f693,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| X0 = multiply(sk_c9,multiply(sk_c10,X0)) ),
inference(forward_demodulation,[status(thm)],[f679,f692]) ).
fof(f694,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| X0 = multiply(sk_c9,X0) ),
inference(forward_demodulation,[status(thm)],[f680,f693]) ).
fof(f696,plain,
( ~ sQ0_spl
| ~ sQ16_spl
| sk_c10 != sk_c11
| multiply(sk_c11,sk_c11) != sk_c10 ),
inference(paramodulation,[status(thm)],[f111,f209]) ).
fof(f698,definition,
( sQ55_spl
<=> multiply(sk_c11,sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f700,plain,
( sQ55_spl
| multiply(sk_c11,sk_c11) != sk_c10 ),
inference(component_clause,[status(thm)],[f698]) ).
fof(f701,definition,
( sQ56_spl
<=> sk_c10 = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f703,plain,
( sQ56_spl
| sk_c10 != sk_c11 ),
inference(component_clause,[status(thm)],[f701]) ).
fof(f704,plain,
( ~ sQ0_spl
| ~ sQ16_spl
| ~ sQ56_spl
| ~ sQ55_spl ),
inference(split_clause,[status(thm)],[f696,f698,f701,f208,f110]) ).
fof(f705,plain,
( sQ55_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sk_c11 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f679,f700]) ).
fof(f706,plain,
( ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| sk_c10 = sk_c11 ),
inference(backward_demodulation,[status(thm)],[f694,f193]) ).
fof(f707,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| X0 = multiply(inverse(sk_c9),X0) ),
inference(paramodulation,[status(thm)],[f694,f238]) ).
fof(f709,plain,
( ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| sQ49_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f706,f672]) ).
fof(f710,plain,
( ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| sQ49_spl ),
inference(contradiction_clause,[status(thm)],[f709]) ).
fof(f711,plain,
( ~ sQ49_spl
| ~ sQ12_spl
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f167,f495]) ).
fof(f712,plain,
( ~ sQ49_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sk_c11 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f154,f711]) ).
fof(f716,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ0_spl
| sk_c10 = identity ),
inference(backward_demodulation,[status(thm)],[f706,f675]) ).
fof(f719,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| multiply(sk_c2,sk_c10) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f706,f180]) ).
fof(f728,plain,
( sQ55_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ0_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f706,f705]) ).
fof(f729,plain,
( sQ55_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f728]) ).
fof(f730,plain,
( sQ55_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f729]) ).
fof(f731,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| multiply(inverse(X0),sk_c10) != sk_c11
| multiply(X0,inverse(X0)) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f706,f415]) ).
fof(f732,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| multiply(inverse(X0),sk_c10) != sk_c10
| multiply(X0,inverse(X0)) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f706,f731]) ).
fof(f735,plain,
( sQ56_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f706,f703]) ).
fof(f736,plain,
( sQ56_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f735]) ).
fof(f737,plain,
( sQ56_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f736]) ).
fof(f738,plain,
( sQ23_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ14_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f706,f681]) ).
fof(f739,plain,
( sQ23_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ14_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f738]) ).
fof(f740,plain,
( sQ23_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f739]) ).
fof(f752,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(sk_c9,sk_c4) = sk_c9 ),
inference(paramodulation,[status(thm)],[f603,f585]) ).
fof(f754,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c4 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f558,f752]) ).
fof(f759,plain,
( ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ20_spl
| multiply(sk_c8,sk_c9) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f616,f623]) ).
fof(f761,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ20_spl
| multiply(sk_c9,X0) = multiply(sk_c8,multiply(sk_c9,X0)) ),
inference(paramodulation,[status(thm)],[f759,f57]) ).
fof(f762,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ20_spl
| X0 = multiply(sk_c8,multiply(sk_c9,X0)) ),
inference(forward_demodulation,[status(thm)],[f558,f761]) ).
fof(f763,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ20_spl
| X0 = multiply(sk_c8,X0) ),
inference(forward_demodulation,[status(thm)],[f558,f762]) ).
fof(f785,plain,
( ~ sQ8_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c6,sk_c7) = sk_c9 ),
inference(paramodulation,[status(thm)],[f142,f585]) ).
fof(f821,plain,
( ~ sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ20_spl
| ~ sQ6_spl
| ~ sQ7_spl
| inverse(sk_c9) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f830,f630]) ).
fof(f822,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ20_spl
| sk_c4 = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f830,f754]) ).
fof(f825,plain,
( ~ sQ20_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ1_spl
| sk_c5 = sk_c11 ),
inference(backward_demodulation,[status(thm)],[f830,f616]) ).
fof(f826,plain,
( ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ20_spl
| sk_c5 = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f830,f605]) ).
fof(f829,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ20_spl
| sk_c5 = identity ),
inference(backward_demodulation,[status(thm)],[f830,f421]) ).
fof(f830,plain,
( ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ20_spl
| sk_c5 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f763,f442]) ).
fof(f832,plain,
( ~ sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ20_spl
| ~ sQ6_spl
| ~ sQ7_spl
| inverse(sk_c5) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f830,f821]) ).
fof(f833,plain,
( ~ sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ20_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c8 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f134,f832]) ).
fof(f835,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ20_spl
| ~ sQ7_spl
| inverse(sk_c8) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f833,f134]) ).
fof(f836,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ20_spl
| sk_c4 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f833,f822]) ).
fof(f837,plain,
( ~ sQ20_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ1_spl
| sk_c8 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f833,f825]) ).
fof(f838,plain,
( ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ20_spl
| sk_c8 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f833,f826]) ).
fof(f840,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ20_spl
| multiply(sk_c8,sk_c10) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f836,f122]) ).
fof(f841,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ20_spl
| sk_c10 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f763,f840]) ).
fof(f842,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ20_spl
| sk_c8 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f838,f841]) ).
fof(f846,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ20_spl
| sk_c8 = identity ),
inference(forward_demodulation,[status(thm)],[f833,f829]) ).
fof(f850,plain,
( ~ sQ8_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ20_spl
| multiply(sk_c6,sk_c7) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f842,f449]) ).
fof(f851,plain,
( ~ sQ8_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ20_spl
| sk_c7 = multiply(inverse(sk_c6),sk_c8) ),
inference(paramodulation,[status(thm)],[f850,f238]) ).
fof(f853,plain,
( ~ sQ8_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ20_spl
| ~ sQ9_spl
| sk_c7 = multiply(sk_c8,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f146,f851]) ).
fof(f854,plain,
( ~ sQ8_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ20_spl
| ~ sQ9_spl
| sk_c7 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f763,f853]) ).
fof(f857,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ20_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c8) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f854,f835]) ).
fof(f858,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ20_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 = identity ),
inference(backward_demodulation,[status(thm)],[f854,f846]) ).
fof(f863,plain,
( ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ20_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f854,f838]) ).
fof(f864,plain,
( ~ sQ20_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 = sk_c11 ),
inference(backward_demodulation,[status(thm)],[f854,f837]) ).
fof(f870,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ20_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c7) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f854,f857]) ).
fof(f871,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ20_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c6 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f142,f870]) ).
fof(f875,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ20_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f871,f858]) ).
fof(f887,plain,
( ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ20_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c6 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f871,f863]) ).
fof(f888,plain,
( ~ sQ20_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c6 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f871,f864]) ).
fof(f1000,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ0_spl
| multiply(sk_c10,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f716,f55]) ).
fof(f1012,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ14_spl
| sk_c11 = identity ),
inference(forward_demodulation,[status(thm)],[f1000,f230]) ).
fof(f1014,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ0_spl
| multiply(inverse(X0),X0) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f716,f56]) ).
fof(f1038,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| multiply(sk_c10,X0) = multiply(sk_c2,multiply(sk_c10,X0)) ),
inference(paramodulation,[status(thm)],[f719,f57]) ).
fof(f1039,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| X0 = multiply(sk_c2,multiply(sk_c10,X0)) ),
inference(forward_demodulation,[status(thm)],[f1000,f1038]) ).
fof(f1040,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| X0 = multiply(sk_c2,X0) ),
inference(forward_demodulation,[status(thm)],[f1000,f1039]) ).
fof(f1049,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ0_spl
| sk_c2 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1040,f657]) ).
fof(f1050,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ49_spl
| sk_c2 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f712,f1049]) ).
fof(f1051,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ49_spl
| sQ40_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1050,f380]) ).
fof(f1052,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ49_spl
| sQ40_spl ),
inference(contradiction_clause,[status(thm)],[f1051]) ).
fof(f1056,plain,
( sQ39_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ49_spl
| multiply(sk_c1,sk_c2) != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f1050,f377]) ).
fof(f1058,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ49_spl
| multiply(inverse(X0),X0) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f1050,f1014]) ).
fof(f1065,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ49_spl
| sk_c2 = identity ),
inference(backward_demodulation,[status(thm)],[f1050,f716]) ).
fof(f1066,plain,
( ~ sQ49_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ0_spl
| sk_c11 = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f1050,f712]) ).
fof(f1069,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ49_spl
| multiply(inverse(X0),sk_c10) != sk_c10
| multiply(X0,inverse(X0)) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1050,f732]) ).
fof(f1070,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ49_spl
| multiply(inverse(X0),sk_c2) != sk_c10
| multiply(X0,inverse(X0)) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1050,f1069]) ).
fof(f1071,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ49_spl
| multiply(inverse(X0),sk_c2) != sk_c2
| multiply(X0,inverse(X0)) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1050,f1070]) ).
fof(f1072,plain,
( ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ49_spl
| multiply(sk_c2,sk_c2) != sk_c2
| multiply(sk_c1,inverse(sk_c1)) != sk_c2 ),
inference(paramodulation,[status(thm)],[f167,f1071]) ).
fof(f1073,definition,
( sQ57_spl
<=> multiply(sk_c1,inverse(sk_c1)) = sk_c2 ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f1075,plain,
( sQ57_spl
| multiply(sk_c1,inverse(sk_c1)) != sk_c2 ),
inference(component_clause,[status(thm)],[f1073]) ).
fof(f1076,definition,
( sQ58_spl
<=> multiply(sk_c2,sk_c2) = sk_c2 ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f1078,plain,
( sQ58_spl
| multiply(sk_c2,sk_c2) != sk_c2 ),
inference(component_clause,[status(thm)],[f1076]) ).
fof(f1079,plain,
( ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ49_spl
| ~ sQ58_spl
| ~ sQ57_spl ),
inference(split_clause,[status(thm)],[f1072,f1073,f1076,f494,f179,f110,f153,f192,f205,f166]) ).
fof(f1080,plain,
( sQ57_spl
| ~ sQ12_spl
| multiply(sk_c1,sk_c2) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f167,f1075]) ).
fof(f1081,plain,
( sQ58_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1040,f1078]) ).
fof(f1082,plain,
( sQ58_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1081]) ).
fof(f1083,plain,
( sQ58_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f1082]) ).
fof(f1085,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| multiply(sk_c2,sk_c1) = sk_c11 ),
inference(paramodulation,[status(thm)],[f167,f677]) ).
fof(f1088,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ0_spl
| sk_c1 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1040,f1085]) ).
fof(f1092,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ49_spl
| sk_c1 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1066,f1088]) ).
fof(f1140,plain,
( sQ39_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ49_spl
| multiply(sk_c2,sk_c2) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1092,f1056]) ).
fof(f1141,plain,
( sQ39_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ49_spl
| sk_c2 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1040,f1140]) ).
fof(f1143,plain,
( ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ49_spl
| sk_c9 = sk_c2 ),
inference(paramodulation,[status(thm)],[f707,f1058]) ).
fof(f1149,plain,
( ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ49_spl
| sQ39_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1143,f1141]) ).
fof(f1150,plain,
( ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ49_spl
| sQ39_spl ),
inference(contradiction_clause,[status(thm)],[f1149]) ).
fof(f1212,plain,
( sQ57_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ49_spl
| multiply(sk_c2,sk_c2) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1092,f1080]) ).
fof(f1213,plain,
( sQ57_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ49_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1040,f1212]) ).
fof(f1214,plain,
( sQ57_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ49_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1213]) ).
fof(f1215,plain,
( sQ57_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ49_spl ),
inference(contradiction_clause,[status(thm)],[f1214]) ).
fof(f1274,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ20_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c6 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f421,f875]) ).
fof(f1535,plain,
! [X0] :
( ~ sQ10_spl
| multiply(sk_c6,X0) = multiply(sk_c7,multiply(sk_c8,X0)) ),
inference(paramodulation,[status(thm)],[f150,f57]) ).
fof(f1594,plain,
( sQ19_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ49_spl
| multiply(sk_c2,inverse(sk_c10)) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1050,f302]) ).
fof(f1964,plain,
( ~ sQ0_spl
| ~ sQ20_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c6) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f888,f111]) ).
fof(f1965,plain,
( ~ sQ0_spl
| ~ sQ20_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c6) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f887,f1964]) ).
fof(f2043,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c9,X0) = multiply(inverse(X1),multiply(X1,X0)) ),
inference(paramodulation,[status(thm)],[f585,f57]) ).
fof(f2044,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c9,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f238,f2043]) ).
fof(f2348,plain,
( ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ20_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c6 = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f1274,f605]) ).
fof(f2349,plain,
( ~ sQ20_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c6 = sk_c11 ),
inference(backward_demodulation,[status(thm)],[f1274,f616]) ).
fof(f2350,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ20_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c4 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f1274,f754]) ).
fof(f2368,definition,
( sQ66_spl
<=> inverse(sk_c6) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f2370,plain,
( sQ66_spl
| inverse(sk_c6) != sk_c6 ),
inference(component_clause,[status(thm)],[f2368]) ).
fof(f2644,definition,
( sQ68_spl
<=> inverse(sk_c2) = sk_c2 ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f2646,plain,
( sQ68_spl
| inverse(sk_c2) != sk_c2 ),
inference(component_clause,[status(thm)],[f2644]) ).
fof(f2647,definition,
( sQ69_spl
<=> multiply(sk_c2,sk_c2) = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f2649,plain,
( sQ69_spl
| multiply(sk_c2,sk_c2) != inverse(sk_c2) ),
inference(component_clause,[status(thm)],[f2647]) ).
fof(f2651,plain,
( ~ sQ0_spl
| ~ sQ20_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sQ66_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1965,f2370]) ).
fof(f2652,plain,
( ~ sQ0_spl
| ~ sQ20_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sQ66_spl ),
inference(contradiction_clause,[status(thm)],[f2651]) ).
fof(f2775,plain,
( ~ sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sk_c10 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f111,f600]) ).
fof(f2777,plain,
( ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ20_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c6 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f2775,f2348]) ).
fof(f2794,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ20_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c6) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f2350,f126]) ).
fof(f2795,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ20_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c6) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f887,f2794]) ).
fof(f2802,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ20_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c6,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f2777,f2044]) ).
fof(f3075,plain,
! [X0] :
( ~ sQ36_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ20_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(X0,inverse(sk_c6)) != inverse(X0)
| inverse(inverse(X0)) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f2795,f358]) ).
fof(f3076,plain,
! [X0] :
( ~ sQ36_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ20_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(X0,sk_c6) != inverse(X0)
| inverse(inverse(X0)) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f2795,f3075]) ).
fof(f3077,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ20_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ36_spl
| multiply(sk_c6,sk_c6) != inverse(sk_c6)
| inverse(sk_c6) != sk_c6 ),
inference(paramodulation,[status(thm)],[f2795,f3076]) ).
fof(f3078,definition,
( sQ72_spl
<=> multiply(sk_c6,sk_c6) = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f3080,plain,
( sQ72_spl
| multiply(sk_c6,sk_c6) != inverse(sk_c6) ),
inference(component_clause,[status(thm)],[f3078]) ).
fof(f3081,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ20_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ36_spl
| ~ sQ72_spl
| ~ sQ66_spl ),
inference(split_clause,[status(thm)],[f3077,f2368,f3078,f357,f145,f141,f303,f137,f133,f113,f121,f110,f117,f125]) ).
fof(f3082,plain,
( sQ72_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ20_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c6 != inverse(sk_c6) ),
inference(forward_demodulation,[status(thm)],[f2802,f3080]) ).
fof(f3083,plain,
( sQ72_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ20_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f2795,f3082]) ).
fof(f3084,plain,
( sQ72_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ20_spl
| ~ sQ8_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f3083]) ).
fof(f3085,plain,
( sQ72_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ20_spl
| ~ sQ8_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f3084]) ).
fof(f3086,plain,
( sQ35_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ20_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c6) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f2802,f356]) ).
fof(f3087,plain,
( sQ35_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ20_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c6 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f2795,f3086]) ).
fof(f3088,plain,
( sQ35_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ20_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f2349,f3087]) ).
fof(f3089,plain,
( sQ35_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ20_spl
| ~ sQ8_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f3088]) ).
fof(f3090,plain,
( sQ35_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ20_spl
| ~ sQ8_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f3089]) ).
fof(f3092,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ20_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(X0) != sk_c10
| multiply(X0,sk_c6) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f887,f212]) ).
fof(f3093,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ20_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(X0) != sk_c10
| multiply(X0,sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f2777,f3092]) ).
fof(f3094,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ20_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f887,f3093]) ).
fof(f3119,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ20_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ17_spl
| multiply(sk_c6,sk_c6) != sk_c6 ),
inference(resolution,[status(thm)],[f3094,f2795]) ).
fof(f3121,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ20_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ17_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f2802,f3119]) ).
fof(f3122,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ20_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ17_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f3121]) ).
fof(f3123,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ20_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f3122]) ).
fof(f3125,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ14_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f1012,f303,f192,f166,f153,f110]) ).
fof(f3136,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ49_spl
| multiply(sk_c2,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f1065,f55]) ).
fof(f3139,plain,
( ~ sQ0_spl
| ~ sQ49_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| inverse(sk_c2) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1066,f111]) ).
fof(f3140,plain,
( ~ sQ0_spl
| ~ sQ49_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| inverse(sk_c2) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1050,f3139]) ).
fof(f3375,plain,
! [X0] :
( ~ sQ21_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ49_spl
| multiply(X0,inverse(sk_c10)) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c2) ),
inference(forward_demodulation,[status(thm)],[f1050,f307]) ).
fof(f3376,plain,
! [X0] :
( ~ sQ21_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ49_spl
| multiply(X0,inverse(sk_c10)) != inverse(X0)
| inverse(inverse(X0)) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f3140,f3375]) ).
fof(f3377,plain,
! [X0] :
( ~ sQ21_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ49_spl
| multiply(X0,inverse(sk_c2)) != inverse(X0)
| inverse(inverse(X0)) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1050,f3376]) ).
fof(f3378,plain,
! [X0] :
( ~ sQ21_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ49_spl
| multiply(X0,sk_c2) != inverse(X0)
| inverse(inverse(X0)) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f3140,f3377]) ).
fof(f3379,plain,
( ~ sQ0_spl
| ~ sQ49_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ21_spl
| multiply(sk_c2,sk_c2) != inverse(sk_c2)
| inverse(sk_c2) != sk_c2 ),
inference(paramodulation,[status(thm)],[f3140,f3378]) ).
fof(f3380,plain,
( ~ sQ0_spl
| ~ sQ49_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ21_spl
| ~ sQ69_spl
| ~ sQ68_spl ),
inference(split_clause,[status(thm)],[f3379,f2644,f2647,f306,f192,f179,f153,f166,f494,f110]) ).
fof(f3391,plain,
( sQ68_spl
| ~ sQ0_spl
| ~ sQ49_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f3140,f2646]) ).
fof(f3392,plain,
( sQ68_spl
| ~ sQ0_spl
| ~ sQ49_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f3391]) ).
fof(f3393,plain,
( sQ68_spl
| ~ sQ0_spl
| ~ sQ49_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f3392]) ).
fof(f3394,plain,
( sQ19_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ49_spl
| inverse(sk_c10) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f3136,f1594]) ).
fof(f3395,plain,
( sQ19_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ49_spl
| inverse(sk_c2) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1050,f3394]) ).
fof(f3396,plain,
( sQ19_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ49_spl
| sk_c2 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f3140,f3395]) ).
fof(f3397,plain,
( sQ19_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ49_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1066,f3396]) ).
fof(f3398,plain,
( sQ19_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ49_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f3397]) ).
fof(f3399,plain,
( sQ19_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ49_spl ),
inference(contradiction_clause,[status(thm)],[f3398]) ).
fof(f3401,plain,
( sQ69_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ49_spl
| sk_c2 != inverse(sk_c2) ),
inference(forward_demodulation,[status(thm)],[f3136,f2649]) ).
fof(f3402,plain,
( sQ69_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ49_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f3140,f3401]) ).
fof(f3403,plain,
( sQ69_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ49_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f3402]) ).
fof(f3404,plain,
( sQ69_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ49_spl ),
inference(contradiction_clause,[status(thm)],[f3403]) ).
fof(f3414,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| multiply(inverse(X0),X0) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f421,f56]) ).
fof(f3431,plain,
( ~ sQ26_spl
| sk_c10 = multiply(inverse(sk_c11),sk_c11) ),
inference(paramodulation,[status(thm)],[f324,f238]) ).
fof(f3433,plain,
( ~ sQ26_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c10 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f3414,f3431]) ).
fof(f3438,plain,
( sQ0_spl
| ~ sQ26_spl
| ~ sQ3_spl
| ~ sQ4_spl
| inverse(sk_c11) != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f3433,f112]) ).
fof(f3477,plain,
( ~ sQ7_spl
| ~ sQ26_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c8,sk_c9) = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f3433,f138]) ).
fof(f3482,plain,
( sQ0_spl
| ~ sQ26_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c7) != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f3486,f3438]) ).
fof(f3486,plain,
( ~ sQ7_spl
| ~ sQ26_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f452,f3477]) ).
fof(f3488,plain,
( sQ0_spl
| ~ sQ26_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c6 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f142,f3482]) ).
fof(f3525,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ26_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c8 = multiply(sk_c8,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f3486,f285]) ).
fof(f3526,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ26_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c6,sk_c7) = multiply(sk_c7,sk_c8) ),
inference(paramodulation,[status(thm)],[f3525,f1535]) ).
fof(f3529,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ26_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c9 = multiply(sk_c7,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f785,f3526]) ).
fof(f3530,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ26_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c9 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f150,f3529]) ).
fof(f3531,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ26_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3530,f3488]) ).
fof(f3532,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ26_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f3531]) ).
fof(f3533,plain,
$false,
inference(sat_refutation,[status(thm)],[f116,f120,f124,f128,f132,f136,f140,f144,f148,f152,f156,f157,f158,f159,f161,f162,f163,f164,f169,f170,f171,f172,f174,f175,f176,f177,f182,f183,f184,f185,f187,f188,f189,f190,f195,f196,f197,f198,f217,f309,f360,f373,f381,f402,f414,f493,f578,f611,f615,f644,f704,f710,f730,f737,f740,f1052,f1079,f1083,f1150,f1215,f2652,f3081,f3085,f3090,f3123,f3125,f3380,f3393,f3399,f3404,f3532]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP371-1 : 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 : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 20:13:21 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.14/0.46 % Refutation found
% 0.14/0.46 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.48 % Elapsed time: 0.105792 seconds
% 0.14/0.48 % CPU time: 0.636061 seconds
% 0.14/0.48 % Total memory used: 107.293 MB
% 0.14/0.48 % Net memory used: 106.654 MB
%------------------------------------------------------------------------------