%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP246-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 12:33:12 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.41s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 65
% Syntax : Number of formulae : 284 ( 12 unt; 27 def)
% Number of atoms : 831 ( 337 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 988 ( 441 ~; 520 |; 0 &)
% ( 27 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 29 ( 27 usr; 28 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 62 ( 62 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
( multiply(sk_c4,sk_c11) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c4) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c5) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( inverse(sk_c6) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c4,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( inverse(sk_c4) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( inverse(sk_c5) = sk_c10
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c6) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c4,sk_c11) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( inverse(sk_c4) = sk_c11
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c5,sk_c10) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c5) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( inverse(sk_c6) = sk_c11
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( multiply(sk_c4,sk_c11) = sk_c10
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( inverse(sk_c4) = sk_c11
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( multiply(sk_c5,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( inverse(sk_c5) = sk_c10
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( inverse(sk_c6) = sk_c11
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
( multiply(sk_c4,sk_c11) = sk_c10
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,negated_conjecture,
( inverse(sk_c4) = sk_c11
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,negated_conjecture,
( multiply(sk_c5,sk_c10) = sk_c9
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,negated_conjecture,
( inverse(sk_c5) = sk_c10
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
( inverse(sk_c6) = sk_c11
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| inverse(sk_c3) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,negated_conjecture,
( multiply(sk_c4,sk_c11) = sk_c10
| multiply(sk_c3,sk_c9) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f50,negated_conjecture,
( inverse(sk_c4) = sk_c11
| multiply(sk_c3,sk_c9) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f51,negated_conjecture,
( multiply(sk_c5,sk_c10) = sk_c9
| multiply(sk_c3,sk_c9) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f52,negated_conjecture,
( inverse(sk_c5) = sk_c10
| multiply(sk_c3,sk_c9) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f53,negated_conjecture,
( inverse(sk_c6) = sk_c11
| multiply(sk_c3,sk_c9) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| multiply(sk_c3,sk_c9) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f58,negated_conjecture,
! [X4,X5,X6,X1,X2,X3,X7,X8] :
( multiply(X8,sk_c9) != sk_c10
| inverse(X7) != X8
| multiply(X7,X8) != sk_c10
| multiply(X3,sk_c10) != sk_c11
| inverse(X3) != sk_c11
| inverse(X2) != sk_c10
| multiply(X2,sk_c10) != sk_c9
| inverse(X1) != sk_c11
| multiply(X1,sk_c11) != sk_c10
| multiply(X6,sk_c9) != sk_c11
| inverse(X6) != sk_c11
| inverse(X5) != sk_c10
| multiply(X5,sk_c10) != sk_c9
| inverse(X4) != sk_c11
| multiply(X4,sk_c11) != sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f59,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f60,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f61,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f62,plain,
( multiply(sk_c4,sk_c11) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f63,plain,
( inverse(sk_c4) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f65,plain,
( inverse(sk_c5) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f66,plain,
( inverse(sk_c6) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f67,plain,
( multiply(sk_c6,sk_c10) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f71,plain,
( multiply(sk_c4,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f72,plain,
( inverse(sk_c4) = sk_c11
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f74,plain,
( inverse(sk_c5) = sk_c10
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f75,plain,
( inverse(sk_c6) = sk_c11
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f76,plain,
( multiply(sk_c6,sk_c10) = sk_c11
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f80,plain,
( multiply(sk_c4,sk_c11) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f81,plain,
( inverse(sk_c4) = sk_c11
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f82,plain,
( multiply(sk_c5,sk_c10) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f83,plain,
( inverse(sk_c5) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f84,plain,
( inverse(sk_c6) = sk_c11
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f85,plain,
( multiply(sk_c6,sk_c10) = sk_c11
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f89,plain,
( multiply(sk_c4,sk_c11) = sk_c10
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f90,plain,
( inverse(sk_c4) = sk_c11
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f91,plain,
( multiply(sk_c5,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f92,plain,
( inverse(sk_c5) = sk_c10
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f93,plain,
( inverse(sk_c6) = sk_c11
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f94,plain,
( multiply(sk_c6,sk_c10) = sk_c11
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f98,plain,
( multiply(sk_c4,sk_c11) = sk_c10
| inverse(sk_c3) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f99,plain,
( inverse(sk_c4) = sk_c11
| inverse(sk_c3) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f100,plain,
( multiply(sk_c5,sk_c10) = sk_c9
| inverse(sk_c3) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f101,plain,
( inverse(sk_c5) = sk_c10
| inverse(sk_c3) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f102,plain,
( inverse(sk_c6) = sk_c11
| inverse(sk_c3) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f103,plain,
( multiply(sk_c6,sk_c10) = sk_c11
| inverse(sk_c3) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f107,plain,
( multiply(sk_c4,sk_c11) = sk_c10
| multiply(sk_c3,sk_c9) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f108,plain,
( inverse(sk_c4) = sk_c11
| multiply(sk_c3,sk_c9) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f109,plain,
( multiply(sk_c5,sk_c10) = sk_c9
| multiply(sk_c3,sk_c9) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f110,plain,
( inverse(sk_c5) = sk_c10
| multiply(sk_c3,sk_c9) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f111,plain,
( inverse(sk_c6) = sk_c11
| multiply(sk_c3,sk_c9) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f112,plain,
( multiply(sk_c6,sk_c10) = sk_c11
| multiply(sk_c3,sk_c9) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f116,plain,
! [X8] :
( multiply(X8,sk_c9) != sk_c10
| ! [X7] :
( inverse(X7) != X8
| multiply(X7,X8) != sk_c10
| ! [X3] :
( multiply(X3,sk_c10) != sk_c11
| inverse(X3) != sk_c11
| ! [X2] :
( inverse(X2) != sk_c10
| multiply(X2,sk_c10) != sk_c9
| ! [X1] :
( inverse(X1) != sk_c11
| multiply(X1,sk_c11) != sk_c10
| ! [X6] :
( multiply(X6,sk_c9) != sk_c11
| inverse(X6) != sk_c11
| ! [X5] :
( inverse(X5) != sk_c10
| multiply(X5,sk_c10) != sk_c9
| ! [X4] :
( inverse(X4) != sk_c11
| multiply(X4,sk_c11) != sk_c10 ) ) ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f58]) ).
fof(f117,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( multiply(X7,sk_c9) != sk_c10
| inverse(X6) != X7
| multiply(X6,X7) != sk_c10
| multiply(X5,sk_c10) != sk_c11
| inverse(X5) != sk_c11
| inverse(X4) != sk_c10
| multiply(X4,sk_c10) != sk_c9
| inverse(X3) != sk_c11
| multiply(X3,sk_c11) != sk_c10
| multiply(X2,sk_c9) != sk_c11
| inverse(X2) != sk_c11
| inverse(X1) != sk_c10
| multiply(X1,sk_c10) != sk_c9
| inverse(X0) != sk_c11
| multiply(X0,sk_c11) != sk_c10 ),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f118,definition,
( sQ0_spl
<=> multiply(sk_c1,sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f119,plain,
( ~ sQ0_spl
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(component_clause,[status(thm)],[f118]) ).
fof(f121,definition,
( sQ1_spl
<=> multiply(sk_c4,sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f122,plain,
( ~ sQ1_spl
| multiply(sk_c4,sk_c11) = sk_c10 ),
inference(component_clause,[status(thm)],[f121]) ).
fof(f124,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f62,f118,f121]) ).
fof(f125,definition,
( sQ2_spl
<=> inverse(sk_c4) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f126,plain,
( ~ sQ2_spl
| inverse(sk_c4) = sk_c11 ),
inference(component_clause,[status(thm)],[f125]) ).
fof(f128,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f63,f118,f125]) ).
fof(f129,definition,
( sQ3_spl
<=> multiply(sk_c5,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f130,plain,
( ~ sQ3_spl
| multiply(sk_c5,sk_c10) = sk_c9 ),
inference(component_clause,[status(thm)],[f129]) ).
fof(f131,plain,
( sQ3_spl
| multiply(sk_c5,sk_c10) != sk_c9 ),
inference(component_clause,[status(thm)],[f129]) ).
fof(f133,definition,
( sQ4_spl
<=> inverse(sk_c5) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f134,plain,
( ~ sQ4_spl
| inverse(sk_c5) = sk_c10 ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f65,f118,f133]) ).
fof(f137,definition,
( sQ5_spl
<=> inverse(sk_c6) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f140,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f66,f118,f137]) ).
fof(f141,definition,
( sQ6_spl
<=> multiply(sk_c6,sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f142,plain,
( ~ sQ6_spl
| multiply(sk_c6,sk_c10) = sk_c11 ),
inference(component_clause,[status(thm)],[f141]) ).
fof(f144,plain,
( sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f67,f118,f141]) ).
fof(f157,definition,
( sQ10_spl
<=> inverse(sk_c1) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f158,plain,
( ~ sQ10_spl
| inverse(sk_c1) = sk_c11 ),
inference(component_clause,[status(thm)],[f157]) ).
fof(f160,plain,
( sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f71,f157,f121]) ).
fof(f161,plain,
( sQ2_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f72,f157,f125]) ).
fof(f163,plain,
( sQ4_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f74,f157,f133]) ).
fof(f164,plain,
( sQ5_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f75,f157,f137]) ).
fof(f165,plain,
( sQ6_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f76,f157,f141]) ).
fof(f169,definition,
( sQ11_spl
<=> multiply(sk_c2,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f170,plain,
( ~ sQ11_spl
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(component_clause,[status(thm)],[f169]) ).
fof(f172,plain,
( sQ1_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f80,f169,f121]) ).
fof(f173,plain,
( sQ2_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f81,f169,f125]) ).
fof(f174,plain,
( sQ3_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f82,f169,f129]) ).
fof(f175,plain,
( sQ4_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f83,f169,f133]) ).
fof(f176,plain,
( sQ5_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f84,f169,f137]) ).
fof(f177,plain,
( sQ6_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f85,f169,f141]) ).
fof(f181,definition,
( sQ12_spl
<=> inverse(sk_c2) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f182,plain,
( ~ sQ12_spl
| inverse(sk_c2) = sk_c10 ),
inference(component_clause,[status(thm)],[f181]) ).
fof(f184,plain,
( sQ1_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f89,f181,f121]) ).
fof(f185,plain,
( sQ2_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f90,f181,f125]) ).
fof(f186,plain,
( sQ3_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f91,f181,f129]) ).
fof(f187,plain,
( sQ4_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f92,f181,f133]) ).
fof(f188,plain,
( sQ5_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f93,f181,f137]) ).
fof(f189,plain,
( sQ6_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f94,f181,f141]) ).
fof(f193,definition,
( sQ13_spl
<=> inverse(sk_c3) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f194,plain,
( ~ sQ13_spl
| inverse(sk_c3) = sk_c11 ),
inference(component_clause,[status(thm)],[f193]) ).
fof(f196,plain,
( sQ1_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f98,f193,f121]) ).
fof(f197,plain,
( sQ2_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f99,f193,f125]) ).
fof(f198,plain,
( sQ3_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f100,f193,f129]) ).
fof(f199,plain,
( sQ4_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f101,f193,f133]) ).
fof(f200,plain,
( sQ5_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f102,f193,f137]) ).
fof(f201,plain,
( sQ6_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f103,f193,f141]) ).
fof(f205,definition,
( sQ14_spl
<=> multiply(sk_c3,sk_c9) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f206,plain,
( ~ sQ14_spl
| multiply(sk_c3,sk_c9) = sk_c11 ),
inference(component_clause,[status(thm)],[f205]) ).
fof(f208,plain,
( sQ1_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f107,f205,f121]) ).
fof(f209,plain,
( sQ2_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f108,f205,f125]) ).
fof(f210,plain,
( sQ3_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f109,f205,f129]) ).
fof(f211,plain,
( sQ4_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f110,f205,f133]) ).
fof(f212,plain,
( sQ5_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f111,f205,f137]) ).
fof(f213,plain,
( sQ6_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f112,f205,f141]) ).
fof(f217,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(f218,plain,
! [X0] :
( ~ sQ15_spl
| inverse(X0) != sk_c11
| multiply(X0,sk_c11) != sk_c10 ),
inference(component_clause,[status(thm)],[f217]) ).
fof(f220,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(f221,plain,
! [X0] :
( ~ sQ16_spl
| inverse(X0) != sk_c10
| multiply(X0,sk_c10) != sk_c9 ),
inference(component_clause,[status(thm)],[f220]) ).
fof(f223,definition,
! [X2] :
( sQ17_spl
<=> ( multiply(X2,sk_c9) != sk_c11
| inverse(X2) != sk_c11 ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f224,plain,
! [X0] :
( ~ sQ17_spl
| multiply(X0,sk_c9) != sk_c11
| inverse(X0) != sk_c11 ),
inference(component_clause,[status(thm)],[f223]) ).
fof(f226,definition,
! [X5] :
( sQ18_spl
<=> ( multiply(X5,sk_c10) != sk_c11
| inverse(X5) != sk_c11 ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f227,plain,
! [X0] :
( ~ sQ18_spl
| multiply(X0,sk_c10) != sk_c11
| inverse(X0) != sk_c11 ),
inference(component_clause,[status(thm)],[f226]) ).
fof(f229,definition,
! [X6,X7] :
( sQ19_spl
<=> ( multiply(X7,sk_c9) != sk_c10
| inverse(X6) != X7
| multiply(X6,X7) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f230,plain,
! [X0,X1] :
( ~ sQ19_spl
| multiply(X1,sk_c9) != sk_c10
| inverse(X0) != X1
| multiply(X0,X1) != sk_c10 ),
inference(component_clause,[status(thm)],[f229]) ).
fof(f232,plain,
( sQ19_spl
| sQ18_spl
| sQ17_spl
| sQ16_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f117,f217,f220,f223,f226,f229]) ).
fof(f233,plain,
! [X0] :
( ~ sQ19_spl
| multiply(inverse(X0),sk_c9) != sk_c10
| multiply(X0,inverse(X0)) != sk_c10 ),
inference(destructive_equality_resolution,[status(thm)],[f230]) ).
fof(f236,plain,
! [X0] :
( ~ sQ3_spl
| multiply(sk_c9,X0) = multiply(sk_c5,multiply(sk_c10,X0)) ),
inference(paramodulation,[status(thm)],[f130,f61]) ).
fof(f241,plain,
! [X0] :
( ~ sQ11_spl
| multiply(sk_c9,X0) = multiply(sk_c2,multiply(sk_c10,X0)) ),
inference(paramodulation,[status(thm)],[f170,f61]) ).
fof(f242,plain,
! [X0] :
( ~ sQ14_spl
| multiply(sk_c11,X0) = multiply(sk_c3,multiply(sk_c9,X0)) ),
inference(paramodulation,[status(thm)],[f206,f61]) ).
fof(f245,plain,
( ~ sQ2_spl
| ~ sQ19_spl
| multiply(sk_c11,sk_c9) != sk_c10
| multiply(sk_c4,inverse(sk_c4)) != sk_c10 ),
inference(paramodulation,[status(thm)],[f126,f233]) ).
fof(f246,plain,
( ~ sQ4_spl
| ~ sQ19_spl
| multiply(sk_c10,sk_c9) != sk_c10
| multiply(sk_c5,inverse(sk_c5)) != sk_c10 ),
inference(paramodulation,[status(thm)],[f134,f233]) ).
fof(f250,plain,
( ~ sQ12_spl
| ~ sQ19_spl
| multiply(sk_c10,sk_c9) != sk_c10
| multiply(sk_c2,inverse(sk_c2)) != sk_c10 ),
inference(paramodulation,[status(thm)],[f182,f233]) ).
fof(f252,definition,
( sQ20_spl
<=> multiply(sk_c4,inverse(sk_c4)) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f254,plain,
( sQ20_spl
| multiply(sk_c4,inverse(sk_c4)) != sk_c10 ),
inference(component_clause,[status(thm)],[f252]) ).
fof(f255,definition,
( sQ21_spl
<=> multiply(sk_c11,sk_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f258,plain,
( ~ sQ2_spl
| ~ sQ19_spl
| ~ sQ21_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f245,f252,f255,f229,f125]) ).
fof(f259,definition,
( sQ22_spl
<=> multiply(sk_c5,inverse(sk_c5)) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f261,plain,
( sQ22_spl
| multiply(sk_c5,inverse(sk_c5)) != sk_c10 ),
inference(component_clause,[status(thm)],[f259]) ).
fof(f262,definition,
( sQ23_spl
<=> multiply(sk_c10,sk_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f264,plain,
( sQ23_spl
| multiply(sk_c10,sk_c9) != sk_c10 ),
inference(component_clause,[status(thm)],[f262]) ).
fof(f265,plain,
( ~ sQ4_spl
| ~ sQ19_spl
| ~ sQ23_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f246,f259,f262,f229,f133]) ).
fof(f278,definition,
( sQ27_spl
<=> multiply(sk_c2,inverse(sk_c2)) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f280,plain,
( sQ27_spl
| multiply(sk_c2,inverse(sk_c2)) != sk_c10 ),
inference(component_clause,[status(thm)],[f278]) ).
fof(f281,plain,
( ~ sQ12_spl
| ~ sQ19_spl
| ~ sQ23_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f250,f278,f262,f229,f181]) ).
fof(f287,plain,
( sQ27_spl
| ~ sQ12_spl
| multiply(sk_c2,sk_c10) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f182,f280]) ).
fof(f288,plain,
( sQ27_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sk_c9 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f170,f287]) ).
fof(f296,plain,
( ~ sQ6_spl
| ~ sQ18_spl
| sk_c11 != sk_c11
| inverse(sk_c6) != sk_c11 ),
inference(paramodulation,[status(thm)],[f142,f227]) ).
fof(f305,definition,
( sQ31_spl
<=> sk_c11 = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f307,plain,
( sQ31_spl
| sk_c11 != sk_c11 ),
inference(component_clause,[status(thm)],[f305]) ).
fof(f308,plain,
( ~ sQ6_spl
| ~ sQ18_spl
| ~ sQ31_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f296,f137,f305,f226,f141]) ).
fof(f314,plain,
( sQ31_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f307]) ).
fof(f315,plain,
sQ31_spl,
inference(contradiction_clause,[status(thm)],[f314]) ).
fof(f320,plain,
( ~ sQ4_spl
| multiply(sk_c10,sk_c5) = identity ),
inference(paramodulation,[status(thm)],[f134,f60]) ).
fof(f323,plain,
( ~ sQ12_spl
| multiply(sk_c10,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f182,f60]) ).
fof(f325,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f60,f61]) ).
fof(f326,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f59,f325]) ).
fof(f328,plain,
( ~ sQ14_spl
| ~ sQ17_spl
| inverse(sk_c3) != sk_c11 ),
inference(resolution,[status(thm)],[f224,f206]) ).
fof(f334,plain,
( ~ sQ14_spl
| ~ sQ17_spl
| ~ sQ13_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f194,f328]) ).
fof(f335,plain,
( ~ sQ14_spl
| ~ sQ17_spl
| ~ sQ13_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f334]) ).
fof(f336,plain,
( ~ sQ14_spl
| ~ sQ17_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f335]) ).
fof(f337,plain,
( ~ sQ3_spl
| ~ sQ16_spl
| inverse(sk_c5) != sk_c10 ),
inference(resolution,[status(thm)],[f221,f130]) ).
fof(f338,plain,
( ~ sQ11_spl
| ~ sQ16_spl
| inverse(sk_c2) != sk_c10 ),
inference(resolution,[status(thm)],[f221,f170]) ).
fof(f345,plain,
( ~ sQ3_spl
| ~ sQ16_spl
| ~ sQ4_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f134,f337]) ).
fof(f346,plain,
( ~ sQ3_spl
| ~ sQ16_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f345]) ).
fof(f347,plain,
( ~ sQ3_spl
| ~ sQ16_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f346]) ).
fof(f348,plain,
( ~ sQ1_spl
| ~ sQ15_spl
| inverse(sk_c4) != sk_c11 ),
inference(resolution,[status(thm)],[f218,f122]) ).
fof(f353,plain,
( ~ sQ1_spl
| ~ sQ15_spl
| ~ sQ2_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f126,f348]) ).
fof(f354,plain,
( ~ sQ1_spl
| ~ sQ15_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f353]) ).
fof(f355,plain,
( ~ sQ1_spl
| ~ sQ15_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f354]) ).
fof(f392,plain,
( sQ22_spl
| ~ sQ4_spl
| multiply(sk_c5,sk_c10) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f134,f261]) ).
fof(f393,plain,
( sQ22_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sk_c9 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f130,f392]) ).
fof(f409,plain,
( sQ20_spl
| ~ sQ2_spl
| multiply(sk_c4,sk_c11) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f126,f254]) ).
fof(f410,plain,
( sQ20_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f122,f409]) ).
fof(f411,plain,
( sQ20_spl
| ~ sQ2_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f410]) ).
fof(f412,plain,
( sQ20_spl
| ~ sQ2_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f411]) ).
fof(f431,plain,
( ~ sQ1_spl
| sk_c11 = multiply(inverse(sk_c4),sk_c10) ),
inference(paramodulation,[status(thm)],[f122,f326]) ).
fof(f432,plain,
( ~ sQ3_spl
| sk_c10 = multiply(inverse(sk_c5),sk_c9) ),
inference(paramodulation,[status(thm)],[f130,f326]) ).
fof(f435,plain,
( ~ sQ11_spl
| sk_c10 = multiply(inverse(sk_c2),sk_c9) ),
inference(paramodulation,[status(thm)],[f170,f326]) ).
fof(f439,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c11 = multiply(sk_c11,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f126,f431]) ).
fof(f440,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c10 = multiply(sk_c10,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f134,f432]) ).
fof(f441,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f440,f264]) ).
fof(f442,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sQ23_spl ),
inference(contradiction_clause,[status(thm)],[f441]) ).
fof(f445,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| sk_c10 = multiply(sk_c10,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f182,f435]) ).
fof(f459,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c10 = multiply(inverse(sk_c11),sk_c11) ),
inference(paramodulation,[status(thm)],[f439,f326]) ).
fof(f462,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c10 = identity ),
inference(forward_demodulation,[status(thm)],[f60,f459]) ).
fof(f471,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(inverse(X0),X0) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f462,f60]) ).
fof(f472,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c10,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f462,f59]) ).
fof(f486,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c10 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f472,f445]) ).
fof(f487,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sQ27_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f486,f288]) ).
fof(f488,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sQ27_spl ),
inference(contradiction_clause,[status(thm)],[f487]) ).
fof(f491,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c10,sk_c5) = sk_c10 ),
inference(paramodulation,[status(thm)],[f134,f471]) ).
fof(f496,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c5 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f472,f491]) ).
fof(f499,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c9,sk_c10) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f500,f130]) ).
fof(f500,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c9,X0) = multiply(sk_c5,X0) ),
inference(forward_demodulation,[status(thm)],[f472,f236]) ).
fof(f513,plain,
( sQ22_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c9 != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f496,f393]) ).
fof(f517,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| multiply(sk_c5,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f496,f472]) ).
fof(f519,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| sk_c5 = identity ),
inference(backward_demodulation,[status(thm)],[f496,f462]) ).
fof(f527,plain,
( ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c6,sk_c5) = sk_c11 ),
inference(backward_demodulation,[status(thm)],[f496,f142]) ).
fof(f530,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ3_spl
| multiply(sk_c9,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f500,f517]) ).
fof(f539,definition,
( sQ42_spl
<=> identity = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f541,plain,
( sQ42_spl
| identity != sk_c10 ),
inference(component_clause,[status(thm)],[f539]) ).
fof(f551,plain,
( ~ sQ0_spl
| sk_c11 = multiply(inverse(sk_c1),sk_c10) ),
inference(paramodulation,[status(thm)],[f119,f326]) ).
fof(f553,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| sk_c11 = multiply(sk_c11,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f158,f551]) ).
fof(f592,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| sk_c9 = multiply(inverse(sk_c10),sk_c10) ),
inference(paramodulation,[status(thm)],[f445,f326]) ).
fof(f594,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| sk_c9 = identity ),
inference(forward_demodulation,[status(thm)],[f60,f592]) ).
fof(f599,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ12_spl
| multiply(sk_c9,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f594,f59]) ).
fof(f606,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| multiply(sk_c10,sk_c2) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f594,f323]) ).
fof(f610,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| inverse(sk_c1) != sk_c11 ),
inference(resolution,[status(thm)],[f218,f119]) ).
fof(f614,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f610,f157,f217,f118]) ).
fof(f616,definition,
( sQ45_spl
<=> sk_c10 = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f618,plain,
( sQ45_spl
| sk_c10 != sk_c10 ),
inference(component_clause,[status(thm)],[f616]) ).
fof(f620,plain,
( sQ45_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f618]) ).
fof(f621,plain,
sQ45_spl,
inference(contradiction_clause,[status(thm)],[f620]) ).
fof(f630,plain,
( ~ sQ4_spl
| ~ sQ11_spl
| ~ sQ12_spl
| multiply(sk_c10,sk_c5) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f594,f320]) ).
fof(f696,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ12_spl
| X0 = multiply(sk_c2,multiply(sk_c10,X0)) ),
inference(forward_demodulation,[status(thm)],[f599,f241]) ).
fof(f698,plain,
( ~ sQ4_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sk_c5 = multiply(sk_c2,sk_c9) ),
inference(paramodulation,[status(thm)],[f630,f696]) ).
fof(f699,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| sk_c2 = multiply(sk_c2,sk_c9) ),
inference(paramodulation,[status(thm)],[f606,f696]) ).
fof(f714,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sk_c11 = multiply(sk_c3,sk_c10) ),
inference(backward_demodulation,[status(thm)],[f716,f553]) ).
fof(f716,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| multiply(sk_c11,X0) = multiply(sk_c3,X0) ),
inference(forward_demodulation,[status(thm)],[f599,f242]) ).
fof(f735,plain,
( sQ3_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ4_spl
| multiply(sk_c2,sk_c10) != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f737,f131]) ).
fof(f737,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ4_spl
| sk_c2 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f698,f699]) ).
fof(f739,plain,
( sQ3_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ4_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f170,f735]) ).
fof(f740,plain,
( sQ3_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f739]) ).
fof(f741,plain,
( sQ3_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f740]) ).
fof(f836,plain,
( ~ sQ18_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| inverse(sk_c3) != sk_c11 ),
inference(resolution,[status(thm)],[f714,f227]) ).
fof(f838,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sk_c10 = multiply(inverse(sk_c3),sk_c11) ),
inference(paramodulation,[status(thm)],[f714,f326]) ).
fof(f840,plain,
( ~ sQ18_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f836,f193,f181,f169,f205,f157,f118,f226]) ).
fof(f842,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| sk_c10 = multiply(sk_c11,sk_c11) ),
inference(forward_demodulation,[status(thm)],[f194,f838]) ).
fof(f847,plain,
( ~ sQ11_spl
| ~ sQ16_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f338,f181,f220,f169]) ).
fof(f858,definition,
( sQ61_spl
<=> inverse(identity) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f860,plain,
( sQ61_spl
| inverse(identity) != sk_c10 ),
inference(component_clause,[status(thm)],[f858]) ).
fof(f862,definition,
( sQ62_spl
<=> sk_c9 = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f864,plain,
( sQ62_spl
| sk_c9 != sk_c9 ),
inference(component_clause,[status(thm)],[f862]) ).
fof(f866,plain,
( sQ62_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f864]) ).
fof(f867,plain,
sQ62_spl,
inference(contradiction_clause,[status(thm)],[f866]) ).
fof(f872,plain,
( sQ23_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f445,f264]) ).
fof(f873,plain,
( sQ23_spl
| ~ sQ11_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f872]) ).
fof(f874,plain,
( sQ23_spl
| ~ sQ11_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f873]) ).
fof(f875,plain,
( sQ27_spl
| ~ sQ12_spl
| multiply(sk_c2,sk_c10) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f182,f280]) ).
fof(f876,plain,
( sQ27_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sk_c9 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f170,f875]) ).
fof(f904,plain,
( sQ42_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| identity != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f496,f541]) ).
fof(f925,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c5) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f496,f134]) ).
fof(f927,plain,
( sQ42_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f519,f904]) ).
fof(f928,plain,
( sQ42_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f927]) ).
fof(f929,plain,
( sQ42_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f928]) ).
fof(f931,plain,
( sQ61_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| inverse(sk_c5) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f519,f860]) ).
fof(f932,plain,
( sQ61_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| sk_c5 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f925,f931]) ).
fof(f933,plain,
( sQ61_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f496,f932]) ).
fof(f934,plain,
( sQ61_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f933]) ).
fof(f935,plain,
( sQ61_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f934]) ).
fof(f949,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| sk_c10 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f530,f499]) ).
fof(f950,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| sk_c5 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f496,f949]) ).
fof(f951,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f950,f513]) ).
fof(f952,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f951]) ).
fof(f1039,plain,
( ~ sQ14_spl
| sk_c9 = multiply(inverse(sk_c3),sk_c11) ),
inference(paramodulation,[status(thm)],[f206,f326]) ).
fof(f1041,plain,
( ~ sQ14_spl
| ~ sQ13_spl
| sk_c9 = multiply(sk_c11,sk_c11) ),
inference(forward_demodulation,[status(thm)],[f194,f1039]) ).
fof(f1042,plain,
( ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sk_c9 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f842,f1041]) ).
fof(f1043,plain,
( ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sQ27_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1042,f876]) ).
fof(f1044,plain,
( ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sQ27_spl ),
inference(contradiction_clause,[status(thm)],[f1043]) ).
fof(f1146,plain,
( ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| multiply(sk_c6,sk_c9) = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f950,f527]) ).
fof(f1147,plain,
( ~ sQ17_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| inverse(sk_c6) != sk_c11 ),
inference(resolution,[status(thm)],[f1146,f224]) ).
fof(f1151,plain,
( ~ sQ17_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1147,f137,f129,f125,f121,f133,f141,f223]) ).
fof(f1155,plain,
$false,
inference(sat_refutation,[status(thm)],[f124,f128,f136,f140,f144,f160,f161,f163,f164,f165,f172,f173,f174,f175,f176,f177,f184,f185,f186,f187,f188,f189,f196,f197,f198,f199,f200,f201,f208,f209,f210,f211,f212,f213,f232,f258,f265,f281,f308,f315,f336,f347,f355,f412,f442,f488,f614,f621,f741,f840,f847,f867,f874,f929,f935,f952,f1044,f1151]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP246-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n006.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 20:07:12 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.41 % Refutation found
% 0.09/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.43 % Elapsed time: 0.070070 seconds
% 0.09/0.43 % CPU time: 0.288565 seconds
% 0.09/0.43 % Total memory used: 107.995 MB
% 0.09/0.43 % Net memory used: 107.877 MB
%------------------------------------------------------------------------------