%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP245-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 0.13s 0.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 66
% Syntax : Number of formulae : 293 ( 15 unt; 32 def)
% Number of atoms : 809 ( 341 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 941 ( 425 ~; 484 |; 0 &)
% ( 32 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 34 ( 32 usr; 33 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 70 ( 70 !; 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_c4) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( inverse(sk_c5) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( inverse(sk_c5) = sk_c9
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c9
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( inverse(sk_c5) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c5) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c10
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( inverse(sk_c5) = sk_c9
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c9
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c9
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c3,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c10
| multiply(sk_c3,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,negated_conjecture,
! [X4,X5,X6,X1,X2,X7,X3] :
( multiply(X3,sk_c8) != sk_c9
| inverse(X7) != X3
| multiply(X7,X3) != sk_c9
| multiply(X2,sk_c8) != sk_c9
| inverse(X2) != sk_c9
| multiply(X1,sk_c9) != sk_c10
| inverse(X1) != sk_c10
| multiply(X6,sk_c9) != sk_c10
| inverse(X6) != sk_c10
| inverse(X5) != sk_c9
| multiply(X5,sk_c9) != sk_c8
| inverse(X4) != sk_c10
| multiply(X4,sk_c10) != sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f48,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f49,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f50,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f52,plain,
( inverse(sk_c5) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f53,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f54,plain,
( multiply(sk_c6,sk_c7) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f55,plain,
( inverse(sk_c6) = sk_c7
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f56,plain,
( multiply(sk_c7,sk_c8) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f57,plain,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f59,plain,
( inverse(sk_c5) = sk_c9
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f60,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f61,plain,
( multiply(sk_c6,sk_c7) = sk_c9
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f62,plain,
( inverse(sk_c6) = sk_c7
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f63,plain,
( multiply(sk_c7,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f66,plain,
( inverse(sk_c5) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f67,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f68,plain,
( multiply(sk_c6,sk_c7) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f69,plain,
( inverse(sk_c6) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f70,plain,
( multiply(sk_c7,sk_c8) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f73,plain,
( inverse(sk_c5) = sk_c9
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f74,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f75,plain,
( multiply(sk_c6,sk_c7) = sk_c9
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f76,plain,
( inverse(sk_c6) = sk_c7
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f78,plain,
( inverse(sk_c4) = sk_c10
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f79,plain,
( multiply(sk_c4,sk_c9) = sk_c10
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f80,plain,
( inverse(sk_c5) = sk_c9
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f81,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f82,plain,
( multiply(sk_c6,sk_c7) = sk_c9
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f83,plain,
( inverse(sk_c6) = sk_c7
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f84,plain,
( multiply(sk_c7,sk_c8) = sk_c9
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f85,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c3,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f86,plain,
( multiply(sk_c4,sk_c9) = sk_c10
| multiply(sk_c3,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f92,plain,
! [X3] :
( multiply(X3,sk_c8) != sk_c9
| ! [X7] :
( inverse(X7) != X3
| multiply(X7,X3) != sk_c9
| ! [X2] :
( multiply(X2,sk_c8) != sk_c9
| inverse(X2) != sk_c9
| ! [X1] :
( multiply(X1,sk_c9) != sk_c10
| inverse(X1) != sk_c10
| ! [X6] :
( multiply(X6,sk_c9) != sk_c10
| inverse(X6) != sk_c10
| ! [X5] :
( inverse(X5) != sk_c9
| multiply(X5,sk_c9) != sk_c8
| ! [X4] :
( inverse(X4) != sk_c10
| multiply(X4,sk_c10) != sk_c9 ) ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f46]) ).
fof(f93,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( multiply(X6,sk_c8) != sk_c9
| inverse(X5) != X6
| multiply(X5,X6) != sk_c9
| multiply(X4,sk_c8) != sk_c9
| inverse(X4) != sk_c9
| multiply(X3,sk_c9) != sk_c10
| inverse(X3) != sk_c10
| multiply(X2,sk_c9) != sk_c10
| inverse(X2) != sk_c10
| inverse(X1) != sk_c9
| multiply(X1,sk_c9) != sk_c8
| inverse(X0) != sk_c10
| multiply(X0,sk_c10) != sk_c9 ),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f94,definition,
( sQ0_spl
<=> multiply(sk_c1,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f95,plain,
( ~ sQ0_spl
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(component_clause,[status(thm)],[f94]) ).
fof(f97,definition,
( sQ1_spl
<=> inverse(sk_c4) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f98,plain,
( ~ sQ1_spl
| inverse(sk_c4) = sk_c10 ),
inference(component_clause,[status(thm)],[f97]) ).
fof(f100,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f50,f94,f97]) ).
fof(f101,definition,
( sQ2_spl
<=> multiply(sk_c4,sk_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f102,plain,
( ~ sQ2_spl
| multiply(sk_c4,sk_c9) = sk_c10 ),
inference(component_clause,[status(thm)],[f101]) ).
fof(f105,definition,
( sQ3_spl
<=> inverse(sk_c5) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f106,plain,
( ~ sQ3_spl
| inverse(sk_c5) = sk_c9 ),
inference(component_clause,[status(thm)],[f105]) ).
fof(f108,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f52,f94,f105]) ).
fof(f109,definition,
( sQ4_spl
<=> multiply(sk_c5,sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f110,plain,
( ~ sQ4_spl
| multiply(sk_c5,sk_c8) = sk_c9 ),
inference(component_clause,[status(thm)],[f109]) ).
fof(f112,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f53,f94,f109]) ).
fof(f113,definition,
( sQ5_spl
<=> multiply(sk_c6,sk_c7) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f114,plain,
( ~ sQ5_spl
| multiply(sk_c6,sk_c7) = sk_c9 ),
inference(component_clause,[status(thm)],[f113]) ).
fof(f116,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f54,f94,f113]) ).
fof(f117,definition,
( sQ6_spl
<=> inverse(sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f118,plain,
( ~ sQ6_spl
| inverse(sk_c6) = sk_c7 ),
inference(component_clause,[status(thm)],[f117]) ).
fof(f120,plain,
( sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f55,f94,f117]) ).
fof(f121,definition,
( sQ7_spl
<=> multiply(sk_c7,sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f122,plain,
( ~ sQ7_spl
| multiply(sk_c7,sk_c8) = sk_c9 ),
inference(component_clause,[status(thm)],[f121]) ).
fof(f124,plain,
( sQ7_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f56,f94,f121]) ).
fof(f125,definition,
( sQ8_spl
<=> inverse(sk_c1) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f126,plain,
( ~ sQ8_spl
| inverse(sk_c1) = sk_c10 ),
inference(component_clause,[status(thm)],[f125]) ).
fof(f128,plain,
( sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f57,f125,f97]) ).
fof(f130,plain,
( sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f59,f125,f105]) ).
fof(f131,plain,
( sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f60,f125,f109]) ).
fof(f132,plain,
( sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f61,f125,f113]) ).
fof(f133,plain,
( sQ6_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f62,f125,f117]) ).
fof(f134,plain,
( sQ7_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f63,f125,f121]) ).
fof(f135,definition,
( sQ9_spl
<=> multiply(sk_c2,sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f136,plain,
( ~ sQ9_spl
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(component_clause,[status(thm)],[f135]) ).
fof(f140,plain,
( sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f66,f135,f105]) ).
fof(f141,plain,
( sQ4_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f67,f135,f109]) ).
fof(f142,plain,
( sQ5_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f68,f135,f113]) ).
fof(f143,plain,
( sQ6_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f69,f135,f117]) ).
fof(f144,plain,
( sQ7_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f70,f135,f121]) ).
fof(f145,definition,
( sQ10_spl
<=> inverse(sk_c2) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f146,plain,
( ~ sQ10_spl
| inverse(sk_c2) = sk_c9 ),
inference(component_clause,[status(thm)],[f145]) ).
fof(f147,plain,
( sQ10_spl
| inverse(sk_c2) != sk_c9 ),
inference(component_clause,[status(thm)],[f145]) ).
fof(f150,plain,
( sQ3_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f73,f145,f105]) ).
fof(f151,plain,
( sQ4_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f74,f145,f109]) ).
fof(f152,plain,
( sQ5_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f75,f145,f113]) ).
fof(f153,plain,
( sQ6_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f76,f145,f117]) ).
fof(f155,definition,
( sQ11_spl
<=> inverse(sk_c3) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f156,plain,
( ~ sQ11_spl
| inverse(sk_c3) = sk_c10 ),
inference(component_clause,[status(thm)],[f155]) ).
fof(f158,plain,
( sQ1_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f78,f155,f97]) ).
fof(f159,plain,
( sQ2_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f79,f155,f101]) ).
fof(f160,plain,
( sQ3_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f80,f155,f105]) ).
fof(f161,plain,
( sQ4_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f81,f155,f109]) ).
fof(f162,plain,
( sQ5_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f82,f155,f113]) ).
fof(f163,plain,
( sQ6_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f83,f155,f117]) ).
fof(f164,plain,
( sQ7_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f84,f155,f121]) ).
fof(f165,definition,
( sQ12_spl
<=> multiply(sk_c3,sk_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f166,plain,
( ~ sQ12_spl
| multiply(sk_c3,sk_c9) = sk_c10 ),
inference(component_clause,[status(thm)],[f165]) ).
fof(f168,plain,
( sQ1_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f85,f165,f97]) ).
fof(f169,plain,
( sQ2_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f86,f165,f101]) ).
fof(f175,definition,
! [X0] :
( sQ13_spl
<=> ( inverse(X0) != sk_c10
| multiply(X0,sk_c10) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f176,plain,
! [X0] :
( ~ sQ13_spl
| inverse(X0) != sk_c10
| multiply(X0,sk_c10) != sk_c9 ),
inference(component_clause,[status(thm)],[f175]) ).
fof(f178,definition,
! [X1] :
( sQ14_spl
<=> ( inverse(X1) != sk_c9
| multiply(X1,sk_c9) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f179,plain,
! [X0] :
( ~ sQ14_spl
| inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c8 ),
inference(component_clause,[status(thm)],[f178]) ).
fof(f181,definition,
! [X2] :
( sQ15_spl
<=> ( multiply(X2,sk_c9) != sk_c10
| inverse(X2) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f182,plain,
! [X0] :
( ~ sQ15_spl
| multiply(X0,sk_c9) != sk_c10
| inverse(X0) != sk_c10 ),
inference(component_clause,[status(thm)],[f181]) ).
fof(f184,definition,
! [X4] :
( sQ16_spl
<=> ( multiply(X4,sk_c8) != sk_c9
| inverse(X4) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f185,plain,
! [X0] :
( ~ sQ16_spl
| multiply(X0,sk_c8) != sk_c9
| inverse(X0) != sk_c9 ),
inference(component_clause,[status(thm)],[f184]) ).
fof(f187,definition,
! [X5,X6] :
( sQ17_spl
<=> ( multiply(X6,sk_c8) != sk_c9
| inverse(X5) != X6
| multiply(X5,X6) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f188,plain,
! [X0,X1] :
( ~ sQ17_spl
| multiply(X1,sk_c8) != sk_c9
| inverse(X0) != X1
| multiply(X0,X1) != sk_c9 ),
inference(component_clause,[status(thm)],[f187]) ).
fof(f190,plain,
( sQ17_spl
| sQ16_spl
| sQ15_spl
| sQ14_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f93,f175,f178,f181,f184,f187]) ).
fof(f191,plain,
! [X0] :
( ~ sQ17_spl
| multiply(inverse(X0),sk_c8) != sk_c9
| multiply(X0,inverse(X0)) != sk_c9 ),
inference(destructive_equality_resolution,[status(thm)],[f188]) ).
fof(f196,plain,
! [X0] :
( ~ sQ9_spl
| multiply(sk_c8,X0) = multiply(sk_c2,multiply(sk_c9,X0)) ),
inference(paramodulation,[status(thm)],[f136,f49]) ).
fof(f198,plain,
( ~ sQ3_spl
| multiply(sk_c9,sk_c5) = identity ),
inference(paramodulation,[status(thm)],[f106,f48]) ).
fof(f199,plain,
( ~ sQ6_spl
| multiply(sk_c7,sk_c6) = identity ),
inference(paramodulation,[status(thm)],[f118,f48]) ).
fof(f201,plain,
( ~ sQ10_spl
| multiply(sk_c9,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f146,f48]) ).
fof(f202,plain,
( ~ sQ11_spl
| multiply(sk_c10,sk_c3) = identity ),
inference(paramodulation,[status(thm)],[f156,f48]) ).
fof(f203,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f48,f49]) ).
fof(f204,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f47,f203]) ).
fof(f205,plain,
! [X0] :
( ~ sQ0_spl
| multiply(sk_c9,X0) = multiply(sk_c1,multiply(sk_c10,X0)) ),
inference(paramodulation,[status(thm)],[f95,f49]) ).
fof(f207,plain,
( ~ sQ1_spl
| multiply(sk_c10,sk_c4) = identity ),
inference(paramodulation,[status(thm)],[f98,f48]) ).
fof(f208,plain,
! [X0] :
( ~ sQ5_spl
| multiply(sk_c9,X0) = multiply(sk_c6,multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f114,f49]) ).
fof(f209,plain,
! [X0] :
( ~ sQ4_spl
| multiply(sk_c9,X0) = multiply(sk_c5,multiply(sk_c8,X0)) ),
inference(paramodulation,[status(thm)],[f110,f49]) ).
fof(f211,plain,
( ~ sQ17_spl
| multiply(inverse(identity),sk_c8) != sk_c9
| inverse(identity) != sk_c9 ),
inference(paramodulation,[status(thm)],[f47,f191]) ).
fof(f215,plain,
( ~ sQ6_spl
| ~ sQ17_spl
| multiply(inverse(sk_c6),sk_c8) != sk_c9
| multiply(sk_c6,sk_c7) != sk_c9 ),
inference(paramodulation,[status(thm)],[f118,f191]) ).
fof(f216,plain,
( ~ sQ8_spl
| ~ sQ17_spl
| multiply(inverse(sk_c1),sk_c8) != sk_c9
| multiply(sk_c1,sk_c10) != sk_c9 ),
inference(paramodulation,[status(thm)],[f126,f191]) ).
fof(f217,plain,
( ~ sQ10_spl
| ~ sQ17_spl
| multiply(inverse(sk_c2),sk_c8) != sk_c9
| multiply(sk_c2,sk_c9) != sk_c9 ),
inference(paramodulation,[status(thm)],[f146,f191]) ).
fof(f219,definition,
( sQ18_spl
<=> inverse(identity) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f221,plain,
( sQ18_spl
| inverse(identity) != sk_c9 ),
inference(component_clause,[status(thm)],[f219]) ).
fof(f222,definition,
( sQ19_spl
<=> multiply(inverse(identity),sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f225,plain,
( ~ sQ17_spl
| ~ sQ19_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f211,f219,f222,f187]) ).
fof(f240,definition,
( sQ24_spl
<=> multiply(inverse(sk_c6),sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f242,plain,
( sQ24_spl
| multiply(inverse(sk_c6),sk_c8) != sk_c9 ),
inference(component_clause,[status(thm)],[f240]) ).
fof(f243,plain,
( ~ sQ6_spl
| ~ sQ17_spl
| ~ sQ24_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f215,f113,f240,f187,f117]) ).
fof(f244,definition,
( sQ25_spl
<=> multiply(inverse(sk_c1),sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f247,plain,
( ~ sQ8_spl
| ~ sQ17_spl
| ~ sQ25_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f216,f94,f244,f187,f125]) ).
fof(f248,definition,
( sQ26_spl
<=> multiply(sk_c2,sk_c9) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f250,plain,
( sQ26_spl
| multiply(sk_c2,sk_c9) != sk_c9 ),
inference(component_clause,[status(thm)],[f248]) ).
fof(f251,definition,
( sQ27_spl
<=> multiply(inverse(sk_c2),sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f253,plain,
( sQ27_spl
| multiply(inverse(sk_c2),sk_c8) != sk_c9 ),
inference(component_clause,[status(thm)],[f251]) ).
fof(f254,plain,
( ~ sQ10_spl
| ~ sQ17_spl
| ~ sQ27_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f217,f248,f251,f187,f145]) ).
fof(f263,plain,
( sQ27_spl
| ~ sQ10_spl
| multiply(sk_c9,sk_c8) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f146,f253]) ).
fof(f268,plain,
( ~ sQ4_spl
| ~ sQ16_spl
| sk_c9 != sk_c9
| inverse(sk_c5) != sk_c9 ),
inference(paramodulation,[status(thm)],[f110,f185]) ).
fof(f270,plain,
( ~ sQ16_spl
| identity != sk_c9
| inverse(inverse(sk_c8)) != sk_c9 ),
inference(paramodulation,[status(thm)],[f48,f185]) ).
fof(f271,plain,
( ~ sQ16_spl
| sk_c8 != sk_c9
| inverse(identity) != sk_c9 ),
inference(paramodulation,[status(thm)],[f47,f185]) ).
fof(f273,definition,
( sQ30_spl
<=> sk_c9 = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f275,plain,
( sQ30_spl
| sk_c9 != sk_c9 ),
inference(component_clause,[status(thm)],[f273]) ).
fof(f276,plain,
( ~ sQ4_spl
| ~ sQ16_spl
| ~ sQ30_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f268,f105,f273,f184,f109]) ).
fof(f281,definition,
( sQ32_spl
<=> inverse(inverse(sk_c8)) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f283,plain,
( sQ32_spl
| inverse(inverse(sk_c8)) != sk_c9 ),
inference(component_clause,[status(thm)],[f281]) ).
fof(f284,definition,
( sQ33_spl
<=> identity = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f286,plain,
( sQ33_spl
| identity != sk_c9 ),
inference(component_clause,[status(thm)],[f284]) ).
fof(f287,plain,
( ~ sQ16_spl
| ~ sQ33_spl
| ~ sQ32_spl ),
inference(split_clause,[status(thm)],[f270,f281,f284,f184]) ).
fof(f288,definition,
( sQ34_spl
<=> sk_c8 = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f290,plain,
( sQ34_spl
| sk_c8 != sk_c9 ),
inference(component_clause,[status(thm)],[f288]) ).
fof(f291,plain,
( ~ sQ16_spl
| ~ sQ34_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f271,f219,f288,f184]) ).
fof(f292,plain,
( sQ30_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f275]) ).
fof(f293,plain,
sQ30_spl,
inference(contradiction_clause,[status(thm)],[f292]) ).
fof(f294,plain,
( ~ sQ2_spl
| ~ sQ15_spl
| inverse(sk_c4) != sk_c10 ),
inference(resolution,[status(thm)],[f182,f102]) ).
fof(f295,plain,
( ~ sQ12_spl
| ~ sQ15_spl
| inverse(sk_c3) != sk_c10 ),
inference(resolution,[status(thm)],[f182,f166]) ).
fof(f302,plain,
( ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ11_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f156,f295]) ).
fof(f303,plain,
( ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f302]) ).
fof(f304,plain,
( ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f303]) ).
fof(f306,plain,
( sQ24_spl
| ~ sQ6_spl
| multiply(sk_c7,sk_c8) != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f118,f242]) ).
fof(f308,plain,
( sQ24_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f122,f306]) ).
fof(f309,plain,
( sQ24_spl
| ~ sQ6_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f308]) ).
fof(f310,plain,
( sQ24_spl
| ~ sQ6_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f309]) ).
fof(f314,plain,
( ~ sQ14_spl
| inverse(inverse(sk_c9)) != sk_c9
| identity != sk_c8 ),
inference(paramodulation,[status(thm)],[f48,f179]) ).
fof(f315,plain,
( ~ sQ14_spl
| inverse(identity) != sk_c9
| sk_c9 != sk_c8 ),
inference(paramodulation,[status(thm)],[f47,f179]) ).
fof(f316,plain,
( ~ sQ9_spl
| ~ sQ14_spl
| inverse(sk_c2) != sk_c9
| sk_c8 != sk_c8 ),
inference(paramodulation,[status(thm)],[f136,f179]) ).
fof(f326,definition,
( sQ37_spl
<=> identity = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f329,definition,
( sQ38_spl
<=> inverse(inverse(sk_c9)) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f331,plain,
( sQ38_spl
| inverse(inverse(sk_c9)) != sk_c9 ),
inference(component_clause,[status(thm)],[f329]) ).
fof(f332,plain,
( ~ sQ14_spl
| ~ sQ38_spl
| ~ sQ37_spl ),
inference(split_clause,[status(thm)],[f314,f326,f329,f178]) ).
fof(f333,plain,
( ~ sQ14_spl
| ~ sQ18_spl
| ~ sQ34_spl ),
inference(split_clause,[status(thm)],[f315,f288,f219,f178]) ).
fof(f334,definition,
( sQ39_spl
<=> sk_c8 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f336,plain,
( sQ39_spl
| sk_c8 != sk_c8 ),
inference(component_clause,[status(thm)],[f334]) ).
fof(f337,plain,
( ~ sQ9_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f316,f334,f145,f178,f135]) ).
fof(f342,plain,
( sQ39_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f336]) ).
fof(f343,plain,
sQ39_spl,
inference(contradiction_clause,[status(thm)],[f342]) ).
fof(f352,plain,
( ~ sQ13_spl
| inverse(inverse(sk_c10)) != sk_c10
| identity != sk_c9 ),
inference(paramodulation,[status(thm)],[f48,f176]) ).
fof(f355,definition,
( sQ41_spl
<=> inverse(inverse(sk_c10)) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f357,plain,
( sQ41_spl
| inverse(inverse(sk_c10)) != sk_c10 ),
inference(component_clause,[status(thm)],[f355]) ).
fof(f358,plain,
( ~ sQ13_spl
| ~ sQ41_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f352,f284,f355,f175]) ).
fof(f375,plain,
( ~ sQ13_spl
| ~ sQ0_spl
| inverse(sk_c1) != sk_c10 ),
inference(resolution,[status(thm)],[f95,f176]) ).
fof(f376,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| inverse(sk_c1) != sk_c10
| sk_c9 != sk_c9 ),
inference(paramodulation,[status(thm)],[f95,f176]) ).
fof(f378,plain,
( ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f126,f375]) ).
fof(f379,plain,
( ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f378]) ).
fof(f380,plain,
( ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f379]) ).
fof(f381,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ8_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f376,f273,f125,f175,f94]) ).
fof(f402,plain,
( ~ sQ3_spl
| ~ sQ9_spl
| multiply(sk_c8,sk_c5) = multiply(sk_c2,identity) ),
inference(paramodulation,[status(thm)],[f198,f196]) ).
fof(f475,plain,
( ~ sQ3_spl
| sk_c5 = multiply(inverse(sk_c9),identity) ),
inference(paramodulation,[status(thm)],[f198,f204]) ).
fof(f476,plain,
( ~ sQ1_spl
| sk_c4 = multiply(inverse(sk_c10),identity) ),
inference(paramodulation,[status(thm)],[f207,f204]) ).
fof(f479,plain,
! [X0] :
( ~ sQ4_spl
| multiply(sk_c8,X0) = multiply(inverse(sk_c5),multiply(sk_c9,X0)) ),
inference(paramodulation,[status(thm)],[f209,f204]) ).
fof(f480,plain,
( ~ sQ4_spl
| sk_c8 = multiply(inverse(sk_c5),sk_c9) ),
inference(paramodulation,[status(thm)],[f110,f204]) ).
fof(f482,plain,
( ~ sQ6_spl
| sk_c6 = multiply(inverse(sk_c7),identity) ),
inference(paramodulation,[status(thm)],[f199,f204]) ).
fof(f486,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f204,f204]) ).
fof(f487,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f48,f204]) ).
fof(f495,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ3_spl
| multiply(sk_c8,X0) = multiply(sk_c9,multiply(sk_c9,X0)) ),
inference(forward_demodulation,[status(thm)],[f106,f479]) ).
fof(f496,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| sk_c8 = multiply(sk_c9,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f106,f480]) ).
fof(f503,plain,
( ~ sQ6_spl
| sk_c6 = inverse(sk_c7) ),
inference(backward_demodulation,[status(thm)],[f506,f482]) ).
fof(f504,plain,
( ~ sQ1_spl
| sk_c4 = inverse(sk_c10) ),
inference(backward_demodulation,[status(thm)],[f506,f476]) ).
fof(f505,plain,
( ~ sQ3_spl
| sk_c5 = inverse(sk_c9) ),
inference(backward_demodulation,[status(thm)],[f506,f475]) ).
fof(f506,plain,
! [X0] : X0 = multiply(X0,identity),
inference(forward_demodulation,[status(thm)],[f486,f487]) ).
fof(f509,plain,
( sQ26_spl
| ~ sQ9_spl
| sk_c8 != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f136,f250]) ).
fof(f511,plain,
( ~ sQ3_spl
| ~ sQ9_spl
| multiply(sk_c8,sk_c5) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f506,f402]) ).
fof(f519,plain,
( sQ41_spl
| ~ sQ1_spl
| inverse(sk_c4) != sk_c10 ),
inference(backward_demodulation,[status(thm)],[f504,f357]) ).
fof(f521,plain,
( sQ38_spl
| ~ sQ3_spl
| inverse(sk_c5) != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f505,f331]) ).
fof(f527,plain,
( sQ41_spl
| ~ sQ1_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f98,f519]) ).
fof(f528,plain,
( sQ41_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f527]) ).
fof(f529,plain,
( sQ41_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f528]) ).
fof(f530,plain,
( sQ38_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f521,f105,f329]) ).
fof(f538,plain,
inverse(identity) = identity,
inference(paramodulation,[status(thm)],[f48,f506]) ).
fof(f548,plain,
( sQ18_spl
| identity != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f538,f221]) ).
fof(f551,plain,
( ~ sQ9_spl
| sk_c9 = multiply(inverse(sk_c2),sk_c8) ),
inference(paramodulation,[status(thm)],[f136,f204]) ).
fof(f553,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| sk_c9 = multiply(sk_c9,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f146,f551]) ).
fof(f554,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| sQ27_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f553,f263]) ).
fof(f555,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| sQ27_spl ),
inference(contradiction_clause,[status(thm)],[f554]) ).
fof(f587,plain,
! [X0] :
( ~ sQ8_spl
| X0 = multiply(sk_c10,multiply(sk_c1,X0)) ),
inference(paramodulation,[status(thm)],[f126,f204]) ).
fof(f602,plain,
! [X0] :
( ~ sQ6_spl
| X0 = multiply(sk_c6,multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f503,f204]) ).
fof(f603,plain,
( ~ sQ6_spl
| multiply(sk_c6,sk_c7) = identity ),
inference(paramodulation,[status(thm)],[f503,f48]) ).
fof(f605,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sk_c8 = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f621,f496]) ).
fof(f606,plain,
( ~ sQ3_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sk_c5 = identity ),
inference(backward_demodulation,[status(thm)],[f621,f198]) ).
fof(f607,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ6_spl
| ~ sQ5_spl
| multiply(sk_c8,X0) = multiply(sk_c9,X0) ),
inference(backward_demodulation,[status(thm)],[f621,f495]) ).
fof(f621,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ5_spl
| X0 = multiply(sk_c9,X0) ),
inference(forward_demodulation,[status(thm)],[f208,f602]) ).
fof(f622,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| sk_c9 = identity ),
inference(forward_demodulation,[status(thm)],[f114,f603]) ).
fof(f623,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| sQ33_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f622,f286]) ).
fof(f624,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| sQ33_spl ),
inference(contradiction_clause,[status(thm)],[f623]) ).
fof(f625,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sQ34_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f605,f290]) ).
fof(f626,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sQ34_spl ),
inference(contradiction_clause,[status(thm)],[f625]) ).
fof(f634,plain,
( ~ sQ3_spl
| ~ sQ9_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sk_c5 = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f635,f511]) ).
fof(f635,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ6_spl
| ~ sQ5_spl
| multiply(sk_c8,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f621,f607]) ).
fof(f655,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c9 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f606,f622]) ).
fof(f675,plain,
( ~ sQ2_spl
| ~ sQ15_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f294,f97,f181,f101]) ).
fof(f685,plain,
( sQ10_spl
| ~ sQ3_spl
| ~ sQ9_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ5_spl
| inverse(sk_c9) != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f687,f147]) ).
fof(f687,plain,
( ~ sQ3_spl
| ~ sQ9_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sk_c9 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f655,f634]) ).
fof(f702,plain,
( sQ10_spl
| ~ sQ3_spl
| ~ sQ9_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sk_c5 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f505,f685]) ).
fof(f703,plain,
( sQ10_spl
| ~ sQ3_spl
| ~ sQ9_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f655,f702]) ).
fof(f704,plain,
( sQ10_spl
| ~ sQ3_spl
| ~ sQ9_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f703]) ).
fof(f705,plain,
( sQ10_spl
| ~ sQ3_spl
| ~ sQ9_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f704]) ).
fof(f710,plain,
! [X0] :
( ~ sQ10_spl
| X0 = multiply(sk_c9,multiply(sk_c2,X0)) ),
inference(paramodulation,[status(thm)],[f146,f204]) ).
fof(f712,plain,
( ~ sQ10_spl
| sk_c2 = multiply(inverse(sk_c9),identity) ),
inference(paramodulation,[status(thm)],[f201,f204]) ).
fof(f714,plain,
( ~ sQ10_spl
| sk_c2 = inverse(sk_c9) ),
inference(forward_demodulation,[status(thm)],[f506,f712]) ).
fof(f723,plain,
( ~ sQ11_spl
| sk_c3 = multiply(inverse(sk_c10),identity) ),
inference(paramodulation,[status(thm)],[f202,f204]) ).
fof(f725,plain,
( ~ sQ11_spl
| sk_c3 = inverse(sk_c10) ),
inference(forward_demodulation,[status(thm)],[f506,f723]) ).
fof(f738,plain,
! [X0] :
( ~ sQ11_spl
| X0 = multiply(sk_c3,multiply(sk_c10,X0)) ),
inference(paramodulation,[status(thm)],[f725,f204]) ).
fof(f749,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| sk_c8 = multiply(inverse(sk_c9),sk_c9) ),
inference(paramodulation,[status(thm)],[f553,f204]) ).
fof(f765,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| sk_c8 = identity ),
inference(forward_demodulation,[status(thm)],[f48,f749]) ).
fof(f778,plain,
( sQ33_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c8 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f765,f286]) ).
fof(f835,plain,
! [X0] :
( ~ sQ8_spl
| multiply(sk_c1,X0) = multiply(inverse(sk_c10),X0) ),
inference(paramodulation,[status(thm)],[f587,f204]) ).
fof(f841,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ8_spl
| X0 = multiply(sk_c1,multiply(sk_c10,X0)) ),
inference(backward_demodulation,[status(thm)],[f843,f738]) ).
fof(f843,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ11_spl
| multiply(sk_c1,X0) = multiply(sk_c3,X0) ),
inference(forward_demodulation,[status(thm)],[f725,f835]) ).
fof(f847,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ0_spl
| X0 = multiply(sk_c2,X0) ),
inference(backward_demodulation,[status(thm)],[f851,f710]) ).
fof(f851,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ0_spl
| X0 = multiply(sk_c9,X0) ),
inference(forward_demodulation,[status(thm)],[f205,f841]) ).
fof(f853,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c9 = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f847,f136]) ).
fof(f859,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sQ33_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f853,f778]) ).
fof(f860,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sQ33_spl ),
inference(contradiction_clause,[status(thm)],[f859]) ).
fof(f864,plain,
( sQ32_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ0_spl
| inverse(inverse(sk_c9)) != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f853,f283]) ).
fof(f873,plain,
( sQ32_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ0_spl
| inverse(sk_c2) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f714,f864]) ).
fof(f874,plain,
( sQ32_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f146,f873]) ).
fof(f875,plain,
( sQ32_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f874]) ).
fof(f876,plain,
( sQ32_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f875]) ).
fof(f884,plain,
( sQ26_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f853,f509]) ).
fof(f885,plain,
( sQ26_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f884]) ).
fof(f886,plain,
( sQ26_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f885]) ).
fof(f893,plain,
( sQ18_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f548,f284,f219]) ).
fof(f929,plain,
$false,
inference(sat_refutation,[status(thm)],[f100,f108,f112,f116,f120,f124,f128,f130,f131,f132,f133,f134,f140,f141,f142,f143,f144,f150,f151,f152,f153,f158,f159,f160,f161,f162,f163,f164,f168,f169,f190,f225,f243,f247,f254,f276,f287,f291,f293,f304,f310,f332,f333,f337,f343,f358,f380,f381,f529,f530,f555,f624,f626,f675,f705,f860,f876,f886,f893]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP245-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n014.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 20:07:20 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.13/0.40 % Refutation found
% 0.13/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.42 % Elapsed time: 0.059052 seconds
% 0.13/0.42 % CPU time: 0.221122 seconds
% 0.13/0.42 % Total memory used: 96.525 MB
% 0.13/0.42 % Net memory used: 96.324 MB
%------------------------------------------------------------------------------