%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP219-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 12:33:08 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 63
% Syntax : Number of formulae : 257 ( 14 unt; 27 def)
% Number of atoms : 718 ( 314 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 832 ( 371 ~; 434 |; 0 &)
% ( 27 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 4 ( 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 : 65 ( 65 !; 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,
( inverse(sk_c6) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c7) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c2,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c9
| multiply(sk_c2,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c9
| multiply(sk_c2,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c7) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c7) = sk_c8
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c9
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c9
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( inverse(sk_c7) = sk_c8
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c9,sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c9
| multiply(sk_c9,sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c9
| multiply(sk_c9,sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c7) = sk_c8
| multiply(sk_c9,sk_c5) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c4,sk_c9) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c9
| multiply(sk_c4,sk_c9) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c9
| multiply(sk_c4,sk_c9) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( inverse(sk_c7) = sk_c8
| multiply(sk_c4,sk_c9) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c9
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c9
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( inverse(sk_c7) = sk_c8
| inverse(sk_c4) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
! [X3,X4,X5,X6,X7,X1,X2] :
( inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c9
| multiply(X1,sk_c8) != sk_c9
| inverse(X1) != sk_c9
| inverse(X7) != sk_c9
| multiply(X7,sk_c9) != X6
| multiply(sk_c9,X6) != sk_c8
| multiply(X5,sk_c9) != sk_c8
| inverse(X4) != X5
| multiply(X4,X5) != sk_c8
| multiply(X3,sk_c8) != sk_c9
| inverse(X3) != sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f38,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f39,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f40,plain,
( inverse(sk_c6) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f41,plain,
( multiply(sk_c6,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f42,plain,
( multiply(sk_c7,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f43,plain,
( inverse(sk_c7) = sk_c8
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f44,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f45,plain,
( multiply(sk_c6,sk_c8) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f46,plain,
( multiply(sk_c7,sk_c8) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f47,plain,
( inverse(sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f48,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c2,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f49,plain,
( multiply(sk_c6,sk_c8) = sk_c9
| multiply(sk_c2,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f50,plain,
( multiply(sk_c7,sk_c8) = sk_c9
| multiply(sk_c2,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f51,plain,
( inverse(sk_c7) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f52,plain,
( inverse(sk_c6) = sk_c9
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f53,plain,
( multiply(sk_c6,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f54,plain,
( multiply(sk_c7,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f55,plain,
( inverse(sk_c7) = sk_c8
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f56,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c3,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f57,plain,
( multiply(sk_c6,sk_c8) = sk_c9
| multiply(sk_c3,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f58,plain,
( multiply(sk_c7,sk_c8) = sk_c9
| multiply(sk_c3,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f59,plain,
( inverse(sk_c7) = sk_c8
| multiply(sk_c3,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f60,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c9,sk_c5) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f61,plain,
( multiply(sk_c6,sk_c8) = sk_c9
| multiply(sk_c9,sk_c5) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f62,plain,
( multiply(sk_c7,sk_c8) = sk_c9
| multiply(sk_c9,sk_c5) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f63,plain,
( inverse(sk_c7) = sk_c8
| multiply(sk_c9,sk_c5) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f64,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c4,sk_c9) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f65,plain,
( multiply(sk_c6,sk_c8) = sk_c9
| multiply(sk_c4,sk_c9) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f66,plain,
( multiply(sk_c7,sk_c8) = sk_c9
| multiply(sk_c4,sk_c9) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f67,plain,
( inverse(sk_c7) = sk_c8
| multiply(sk_c4,sk_c9) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f68,plain,
( inverse(sk_c6) = sk_c9
| inverse(sk_c4) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f69,plain,
( multiply(sk_c6,sk_c8) = sk_c9
| inverse(sk_c4) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f70,plain,
( multiply(sk_c7,sk_c8) = sk_c9
| inverse(sk_c4) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f71,plain,
( inverse(sk_c7) = sk_c8
| inverse(sk_c4) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f72,plain,
! [X2] :
( inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c9
| ! [X1] :
( multiply(X1,sk_c8) != sk_c9
| inverse(X1) != sk_c9
| ! [X7] :
( inverse(X7) != sk_c9
| ! [X6] :
( multiply(X7,sk_c9) != X6
| multiply(sk_c9,X6) != sk_c8
| ! [X5] :
( multiply(X5,sk_c9) != sk_c8
| ! [X4] :
( inverse(X4) != X5
| multiply(X4,X5) != sk_c8
| ! [X3] :
( multiply(X3,sk_c8) != sk_c9
| inverse(X3) != sk_c9 ) ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f36]) ).
fof(f73,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( inverse(X6) != sk_c8
| multiply(X6,sk_c8) != sk_c9
| multiply(X5,sk_c8) != sk_c9
| inverse(X5) != sk_c9
| inverse(X4) != sk_c9
| multiply(X4,sk_c9) != X3
| multiply(sk_c9,X3) != sk_c8
| multiply(X2,sk_c9) != sk_c8
| inverse(X1) != X2
| multiply(X1,X2) != sk_c8
| multiply(X0,sk_c8) != sk_c9
| inverse(X0) != sk_c9 ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f74,definition,
( sQ0_spl
<=> inverse(sk_c1) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f75,plain,
( ~ sQ0_spl
| inverse(sk_c1) = sk_c9 ),
inference(component_clause,[status(thm)],[f74]) ).
fof(f77,definition,
( sQ1_spl
<=> inverse(sk_c6) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f78,plain,
( ~ sQ1_spl
| inverse(sk_c6) = sk_c9 ),
inference(component_clause,[status(thm)],[f77]) ).
fof(f80,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f40,f74,f77]) ).
fof(f81,definition,
( sQ2_spl
<=> multiply(sk_c6,sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f82,plain,
( ~ sQ2_spl
| multiply(sk_c6,sk_c8) = sk_c9 ),
inference(component_clause,[status(thm)],[f81]) ).
fof(f84,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f41,f74,f81]) ).
fof(f85,definition,
( sQ3_spl
<=> multiply(sk_c7,sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ3_spl
| multiply(sk_c7,sk_c8) = sk_c9 ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f88,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f42,f74,f85]) ).
fof(f89,definition,
( sQ4_spl
<=> inverse(sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f90,plain,
( ~ sQ4_spl
| inverse(sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f89]) ).
fof(f92,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f43,f74,f89]) ).
fof(f93,definition,
( sQ5_spl
<=> multiply(sk_c1,sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ5_spl
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f96,plain,
( sQ1_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f44,f93,f77]) ).
fof(f97,plain,
( sQ2_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f45,f93,f81]) ).
fof(f98,plain,
( sQ3_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f46,f93,f85]) ).
fof(f99,plain,
( sQ4_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f47,f93,f89]) ).
fof(f100,definition,
( sQ6_spl
<=> multiply(sk_c2,sk_c3) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f103,plain,
( sQ1_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f48,f100,f77]) ).
fof(f104,plain,
( sQ2_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f49,f100,f81]) ).
fof(f105,plain,
( sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f50,f100,f85]) ).
fof(f106,plain,
( sQ4_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f51,f100,f89]) ).
fof(f107,definition,
( sQ7_spl
<=> inverse(sk_c2) = sk_c3 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f108,plain,
( ~ sQ7_spl
| inverse(sk_c2) = sk_c3 ),
inference(component_clause,[status(thm)],[f107]) ).
fof(f110,plain,
( sQ1_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f52,f107,f77]) ).
fof(f111,plain,
( sQ2_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f53,f107,f81]) ).
fof(f112,plain,
( sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f54,f107,f85]) ).
fof(f113,plain,
( sQ4_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f55,f107,f89]) ).
fof(f114,definition,
( sQ8_spl
<=> multiply(sk_c3,sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f115,plain,
( ~ sQ8_spl
| multiply(sk_c3,sk_c9) = sk_c8 ),
inference(component_clause,[status(thm)],[f114]) ).
fof(f117,plain,
( sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f56,f114,f77]) ).
fof(f118,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f57,f114,f81]) ).
fof(f119,plain,
( sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f58,f114,f85]) ).
fof(f120,plain,
( sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f59,f114,f89]) ).
fof(f121,definition,
( sQ9_spl
<=> multiply(sk_c9,sk_c5) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f122,plain,
( ~ sQ9_spl
| multiply(sk_c9,sk_c5) = sk_c8 ),
inference(component_clause,[status(thm)],[f121]) ).
fof(f124,plain,
( sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f60,f121,f77]) ).
fof(f125,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f61,f121,f81]) ).
fof(f126,plain,
( sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f62,f121,f85]) ).
fof(f127,plain,
( sQ4_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f63,f121,f89]) ).
fof(f128,definition,
( sQ10_spl
<=> multiply(sk_c4,sk_c9) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f129,plain,
( ~ sQ10_spl
| multiply(sk_c4,sk_c9) = sk_c5 ),
inference(component_clause,[status(thm)],[f128]) ).
fof(f131,plain,
( sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f64,f128,f77]) ).
fof(f132,plain,
( sQ2_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f65,f128,f81]) ).
fof(f133,plain,
( sQ3_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f66,f128,f85]) ).
fof(f134,plain,
( sQ4_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f67,f128,f89]) ).
fof(f135,definition,
( sQ11_spl
<=> inverse(sk_c4) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f136,plain,
( ~ sQ11_spl
| inverse(sk_c4) = sk_c9 ),
inference(component_clause,[status(thm)],[f135]) ).
fof(f138,plain,
( sQ1_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f68,f135,f77]) ).
fof(f139,plain,
( sQ2_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f69,f135,f81]) ).
fof(f140,plain,
( sQ3_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f70,f135,f85]) ).
fof(f141,plain,
( sQ4_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f71,f135,f89]) ).
fof(f142,definition,
! [X0] :
( sQ12_spl
<=> ( multiply(X0,sk_c8) != sk_c9
| inverse(X0) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f143,plain,
! [X0] :
( ~ sQ12_spl
| multiply(X0,sk_c8) != sk_c9
| inverse(X0) != sk_c9 ),
inference(component_clause,[status(thm)],[f142]) ).
fof(f145,definition,
! [X1,X2] :
( sQ13_spl
<=> ( multiply(X2,sk_c9) != sk_c8
| inverse(X1) != X2
| multiply(X1,X2) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f146,plain,
! [X0,X1] :
( ~ sQ13_spl
| multiply(X1,sk_c9) != sk_c8
| inverse(X0) != X1
| multiply(X0,X1) != sk_c8 ),
inference(component_clause,[status(thm)],[f145]) ).
fof(f148,definition,
! [X3,X4] :
( sQ14_spl
<=> ( inverse(X4) != sk_c9
| multiply(X4,sk_c9) != X3
| multiply(sk_c9,X3) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f149,plain,
! [X0,X1] :
( ~ sQ14_spl
| inverse(X1) != sk_c9
| multiply(X1,sk_c9) != X0
| multiply(sk_c9,X0) != sk_c8 ),
inference(component_clause,[status(thm)],[f148]) ).
fof(f151,definition,
! [X6] :
( sQ15_spl
<=> ( inverse(X6) != sk_c8
| multiply(X6,sk_c8) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f152,plain,
! [X0] :
( ~ sQ15_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c9 ),
inference(component_clause,[status(thm)],[f151]) ).
fof(f154,plain,
( sQ15_spl
| sQ14_spl
| sQ13_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f73,f142,f145,f148,f151]) ).
fof(f156,plain,
! [X0] :
( ~ sQ3_spl
| multiply(sk_c9,X0) = multiply(sk_c7,multiply(sk_c8,X0)) ),
inference(paramodulation,[status(thm)],[f86,f39]) ).
fof(f159,plain,
! [X0] :
( ~ sQ2_spl
| multiply(sk_c9,X0) = multiply(sk_c6,multiply(sk_c8,X0)) ),
inference(paramodulation,[status(thm)],[f82,f39]) ).
fof(f163,plain,
( ~ sQ11_spl
| multiply(sk_c9,sk_c4) = identity ),
inference(paramodulation,[status(thm)],[f136,f38]) ).
fof(f164,plain,
( ~ sQ1_spl
| multiply(sk_c9,sk_c6) = identity ),
inference(paramodulation,[status(thm)],[f78,f38]) ).
fof(f165,plain,
( ~ sQ4_spl
| multiply(sk_c8,sk_c7) = identity ),
inference(paramodulation,[status(thm)],[f90,f38]) ).
fof(f166,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f38,f39]) ).
fof(f167,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f37,f166]) ).
fof(f175,plain,
( ~ sQ5_spl
| ~ sQ15_spl
| inverse(sk_c1) != sk_c8 ),
inference(resolution,[status(thm)],[f152,f94]) ).
fof(f177,plain,
( ~ sQ3_spl
| ~ sQ15_spl
| inverse(sk_c7) != sk_c8 ),
inference(resolution,[status(thm)],[f152,f86]) ).
fof(f180,plain,
( ~ sQ15_spl
| inverse(identity) != sk_c8
| sk_c8 != sk_c9 ),
inference(paramodulation,[status(thm)],[f37,f152]) ).
fof(f184,plain,
( ~ sQ5_spl
| ~ sQ15_spl
| ~ sQ0_spl
| sk_c9 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f75,f175]) ).
fof(f186,plain,
( ~ sQ3_spl
| ~ sQ15_spl
| ~ sQ4_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f90,f177]) ).
fof(f187,plain,
( ~ sQ3_spl
| ~ sQ15_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f186]) ).
fof(f188,plain,
( ~ sQ3_spl
| ~ sQ15_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f187]) ).
fof(f189,plain,
! [X0] :
( ~ sQ14_spl
| inverse(X0) != sk_c9
| multiply(sk_c9,multiply(X0,sk_c9)) != sk_c8 ),
inference(destructive_equality_resolution,[status(thm)],[f149]) ).
fof(f191,plain,
( ~ sQ10_spl
| ~ sQ14_spl
| inverse(sk_c4) != sk_c9
| multiply(sk_c9,sk_c5) != sk_c8 ),
inference(paramodulation,[status(thm)],[f129,f189]) ).
fof(f192,plain,
( ~ sQ14_spl
| inverse(inverse(sk_c9)) != sk_c9
| multiply(sk_c9,identity) != sk_c8 ),
inference(paramodulation,[status(thm)],[f38,f189]) ).
fof(f193,plain,
( ~ sQ14_spl
| inverse(identity) != sk_c9
| multiply(sk_c9,sk_c9) != sk_c8 ),
inference(paramodulation,[status(thm)],[f37,f189]) ).
fof(f202,plain,
( ~ sQ10_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f191,f121,f135,f148,f128]) ).
fof(f203,definition,
( sQ18_spl
<=> multiply(sk_c9,identity) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f204,plain,
( ~ sQ18_spl
| multiply(sk_c9,identity) = sk_c8 ),
inference(component_clause,[status(thm)],[f203]) ).
fof(f205,plain,
( sQ18_spl
| multiply(sk_c9,identity) != sk_c8 ),
inference(component_clause,[status(thm)],[f203]) ).
fof(f206,definition,
( sQ19_spl
<=> inverse(inverse(sk_c9)) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f208,plain,
( sQ19_spl
| inverse(inverse(sk_c9)) != sk_c9 ),
inference(component_clause,[status(thm)],[f206]) ).
fof(f209,plain,
( ~ sQ14_spl
| ~ sQ19_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f192,f203,f206,f148]) ).
fof(f210,definition,
( sQ20_spl
<=> multiply(sk_c9,sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f212,plain,
( sQ20_spl
| multiply(sk_c9,sk_c9) != sk_c8 ),
inference(component_clause,[status(thm)],[f210]) ).
fof(f213,definition,
( sQ21_spl
<=> inverse(identity) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f216,plain,
( ~ sQ14_spl
| ~ sQ21_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f193,f210,f213,f148]) ).
fof(f217,plain,
! [X0] :
( ~ sQ13_spl
| multiply(inverse(X0),sk_c9) != sk_c8
| multiply(X0,inverse(X0)) != sk_c8 ),
inference(destructive_equality_resolution,[status(thm)],[f146]) ).
fof(f218,plain,
( ~ sQ13_spl
| multiply(inverse(identity),sk_c9) != sk_c8
| inverse(identity) != sk_c8 ),
inference(paramodulation,[status(thm)],[f37,f217]) ).
fof(f221,plain,
( ~ sQ7_spl
| ~ sQ13_spl
| multiply(inverse(sk_c2),sk_c9) != sk_c8
| multiply(sk_c2,sk_c3) != sk_c8 ),
inference(paramodulation,[status(thm)],[f108,f217]) ).
fof(f224,plain,
( ~ sQ4_spl
| ~ sQ13_spl
| multiply(inverse(sk_c7),sk_c9) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c8 ),
inference(paramodulation,[status(thm)],[f90,f217]) ).
fof(f225,definition,
( sQ22_spl
<=> inverse(identity) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f228,definition,
( sQ23_spl
<=> multiply(inverse(identity),sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f230,plain,
( sQ23_spl
| multiply(inverse(identity),sk_c9) != sk_c8 ),
inference(component_clause,[status(thm)],[f228]) ).
fof(f231,plain,
( ~ sQ13_spl
| ~ sQ23_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f218,f225,f228,f145]) ).
fof(f239,definition,
( sQ26_spl
<=> multiply(inverse(sk_c2),sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f241,plain,
( sQ26_spl
| multiply(inverse(sk_c2),sk_c9) != sk_c8 ),
inference(component_clause,[status(thm)],[f239]) ).
fof(f242,plain,
( ~ sQ7_spl
| ~ sQ13_spl
| ~ sQ26_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f221,f100,f239,f145,f107]) ).
fof(f257,definition,
( sQ31_spl
<=> multiply(sk_c7,sk_c8) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f259,plain,
( sQ31_spl
| multiply(sk_c7,sk_c8) != sk_c8 ),
inference(component_clause,[status(thm)],[f257]) ).
fof(f260,definition,
( sQ32_spl
<=> multiply(inverse(sk_c7),sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f262,plain,
( sQ32_spl
| multiply(inverse(sk_c7),sk_c9) != sk_c8 ),
inference(component_clause,[status(thm)],[f260]) ).
fof(f263,plain,
( ~ sQ4_spl
| ~ sQ13_spl
| ~ sQ32_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f224,f257,f260,f145,f89]) ).
fof(f266,plain,
! [X0] :
( ~ sQ11_spl
| multiply(identity,X0) = multiply(sk_c9,multiply(sk_c4,X0)) ),
inference(paramodulation,[status(thm)],[f163,f39]) ).
fof(f267,plain,
! [X0] :
( ~ sQ11_spl
| X0 = multiply(sk_c9,multiply(sk_c4,X0)) ),
inference(forward_demodulation,[status(thm)],[f37,f266]) ).
fof(f278,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| sk_c9 = multiply(sk_c9,sk_c5) ),
inference(paramodulation,[status(thm)],[f129,f267]) ).
fof(f284,plain,
( ~ sQ5_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| multiply(sk_c1,sk_c9) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f297,f94]) ).
fof(f292,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| multiply(X0,sk_c9) != sk_c9
| inverse(X0) != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f297,f143]) ).
fof(f297,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sk_c9 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f122,f278]) ).
fof(f318,plain,
( ~ sQ5_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ12_spl
| inverse(sk_c1) != sk_c9 ),
inference(resolution,[status(thm)],[f292,f284]) ).
fof(f325,plain,
( ~ sQ5_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ0_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f75,f318]) ).
fof(f326,plain,
( ~ sQ5_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f325]) ).
fof(f327,plain,
( ~ sQ5_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f326]) ).
fof(f339,definition,
( sQ33_spl
<=> sk_c9 = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f341,plain,
( sQ33_spl
| sk_c9 != sk_c9 ),
inference(component_clause,[status(thm)],[f339]) ).
fof(f353,definition,
( sQ37_spl
<=> sk_c8 = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f354,plain,
( ~ sQ37_spl
| sk_c8 = sk_c9 ),
inference(component_clause,[status(thm)],[f353]) ).
fof(f355,plain,
( sQ37_spl
| sk_c8 != sk_c9 ),
inference(component_clause,[status(thm)],[f353]) ).
fof(f356,plain,
( ~ sQ15_spl
| ~ sQ22_spl
| ~ sQ37_spl ),
inference(split_clause,[status(thm)],[f180,f353,f225,f151]) ).
fof(f359,plain,
( ~ sQ5_spl
| ~ sQ15_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f297,f184]) ).
fof(f360,plain,
( ~ sQ5_spl
| ~ sQ15_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f359]) ).
fof(f361,plain,
( ~ sQ5_spl
| ~ sQ15_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f360]) ).
fof(f367,plain,
( sQ33_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f341]) ).
fof(f368,plain,
sQ33_spl,
inference(contradiction_clause,[status(thm)],[f367]) ).
fof(f369,plain,
( sQ31_spl
| ~ sQ3_spl
| sk_c9 != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f86,f259]) ).
fof(f371,plain,
( sQ32_spl
| ~ sQ4_spl
| multiply(sk_c8,sk_c9) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f90,f262]) ).
fof(f372,plain,
( sQ26_spl
| ~ sQ7_spl
| multiply(sk_c3,sk_c9) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f108,f241]) ).
fof(f373,plain,
( sQ26_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f115,f372]) ).
fof(f374,plain,
( sQ26_spl
| ~ sQ7_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f373]) ).
fof(f375,plain,
( sQ26_spl
| ~ sQ7_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f374]) ).
fof(f433,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| multiply(sk_c9,sk_c7) = multiply(sk_c6,identity) ),
inference(paramodulation,[status(thm)],[f165,f159]) ).
fof(f434,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| multiply(sk_c9,sk_c7) = multiply(sk_c7,identity) ),
inference(paramodulation,[status(thm)],[f165,f156]) ).
fof(f443,plain,
( ~ sQ1_spl
| sk_c6 = multiply(inverse(sk_c9),identity) ),
inference(paramodulation,[status(thm)],[f164,f167]) ).
fof(f446,plain,
( ~ sQ2_spl
| sk_c8 = multiply(inverse(sk_c6),sk_c9) ),
inference(paramodulation,[status(thm)],[f82,f167]) ).
fof(f448,plain,
( ~ sQ3_spl
| sk_c8 = multiply(inverse(sk_c7),sk_c9) ),
inference(paramodulation,[status(thm)],[f86,f167]) ).
fof(f449,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f167,f167]) ).
fof(f450,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f38,f167]) ).
fof(f451,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f37,f167]) ).
fof(f456,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sk_c8 = multiply(sk_c9,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f78,f446]) ).
fof(f457,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f456,f212]) ).
fof(f458,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sQ20_spl ),
inference(contradiction_clause,[status(thm)],[f457]) ).
fof(f460,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c8 = multiply(sk_c8,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f90,f448]) ).
fof(f461,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sQ32_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f460,f371]) ).
fof(f462,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sQ32_spl ),
inference(contradiction_clause,[status(thm)],[f461]) ).
fof(f463,plain,
( sQ18_spl
| sk_c9 != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f468,f205]) ).
fof(f464,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| multiply(sk_c9,sk_c7) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f468,f433]) ).
fof(f465,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| multiply(sk_c9,sk_c7) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f468,f434]) ).
fof(f466,plain,
( ~ sQ1_spl
| sk_c6 = inverse(sk_c9) ),
inference(backward_demodulation,[status(thm)],[f468,f443]) ).
fof(f468,plain,
! [X0] : X0 = multiply(X0,identity),
inference(forward_demodulation,[status(thm)],[f449,f450]) ).
fof(f469,plain,
( sQ23_spl
| sk_c9 != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f451,f230]) ).
fof(f480,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| inverse(sk_c6) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f484,f90]) ).
fof(f482,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| multiply(sk_c9,sk_c6) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f484,f464]) ).
fof(f484,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c6 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f464,f465]) ).
fof(f486,plain,
( sQ19_spl
| ~ sQ1_spl
| inverse(sk_c6) != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f466,f208]) ).
fof(f492,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c9 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f78,f480]) ).
fof(f493,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sQ37_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f492,f355]) ).
fof(f494,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sQ37_spl ),
inference(contradiction_clause,[status(thm)],[f493]) ).
fof(f503,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| X0 = multiply(inverse(sk_c6),X0) ),
inference(backward_demodulation,[status(thm)],[f505,f451]) ).
fof(f504,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| X0 = multiply(X0,sk_c6) ),
inference(backward_demodulation,[status(thm)],[f505,f468]) ).
fof(f505,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| identity = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f164,f482]) ).
fof(f506,plain,
( sQ19_spl
| ~ sQ1_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f78,f486]) ).
fof(f507,plain,
( sQ19_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f506]) ).
fof(f508,plain,
( sQ19_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f507]) ).
fof(f512,plain,
( sQ23_spl
| ~ sQ37_spl ),
inference(split_clause,[status(thm)],[f469,f353,f228]) ).
fof(f513,plain,
( sQ18_spl
| ~ sQ37_spl ),
inference(split_clause,[status(thm)],[f463,f353,f203]) ).
fof(f514,plain,
( sQ31_spl
| ~ sQ3_spl
| ~ sQ37_spl ),
inference(split_clause,[status(thm)],[f369,f353,f85,f257]) ).
fof(f543,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| X0 = multiply(sk_c9,X0) ),
inference(forward_demodulation,[status(thm)],[f78,f503]) ).
fof(f545,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ37_spl
| multiply(X0,sk_c9) != sk_c9
| inverse(X0) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f354,f143]) ).
fof(f567,plain,
( ~ sQ18_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| identity = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f543,f204]) ).
fof(f568,plain,
( ~ sQ18_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c6 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f505,f567]) ).
fof(f569,plain,
( ~ sQ18_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ37_spl
| sk_c6 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f354,f568]) ).
fof(f581,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ18_spl
| ~ sQ37_spl
| X0 = multiply(X0,sk_c9) ),
inference(backward_demodulation,[status(thm)],[f569,f504]) ).
fof(f586,plain,
( ~ sQ1_spl
| ~ sQ18_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ37_spl
| sk_c9 = inverse(sk_c9) ),
inference(backward_demodulation,[status(thm)],[f569,f466]) ).
fof(f598,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ37_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ18_spl
| X0 != sk_c9
| inverse(X0) != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f581,f545]) ).
fof(f604,plain,
( ~ sQ12_spl
| ~ sQ37_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ18_spl
| inverse(sk_c9) != sk_c9 ),
inference(destructive_equality_resolution,[status(thm)],[f598]) ).
fof(f605,plain,
( ~ sQ12_spl
| ~ sQ37_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f604,f586]) ).
fof(f606,plain,
( ~ sQ12_spl
| ~ sQ37_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f605]) ).
fof(f607,plain,
$false,
inference(sat_refutation,[status(thm)],[f80,f84,f88,f92,f96,f97,f98,f99,f103,f104,f105,f106,f110,f111,f112,f113,f117,f118,f119,f120,f124,f125,f126,f127,f131,f132,f133,f134,f138,f139,f140,f141,f154,f188,f202,f209,f216,f231,f242,f263,f327,f356,f361,f368,f375,f458,f462,f494,f508,f512,f513,f514,f606]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP219-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n018.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 20:08:43 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.39 % Refutation found
% 0.09/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.41 % Elapsed time: 0.052758 seconds
% 0.09/0.41 % CPU time: 0.167548 seconds
% 0.09/0.41 % Total memory used: 90.945 MB
% 0.09/0.41 % Net memory used: 90.830 MB
%------------------------------------------------------------------------------