%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP354-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 12:33:30 PM UTC 2026
% Result : Unsatisfiable 0.08s 0.34s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 61
% Syntax : Number of formulae : 291 ( 13 unt; 26 def)
% Number of atoms : 903 ( 346 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 1134 ( 522 ~; 586 |; 0 &)
% ( 26 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 28 ( 26 usr; 27 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 69 ( 69 !; 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_c3,sk_c9) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c3) = sk_c9
| multiply(sk_c8,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c8,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c9
| multiply(sk_c8,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( inverse(sk_c3) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c3) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( inverse(sk_c4) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c8
| inverse(sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( inverse(sk_c3) = sk_c9
| inverse(sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( inverse(sk_c3) = sk_c9
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c9
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c8
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
( inverse(sk_c3) = sk_c9
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,negated_conjecture,
( inverse(sk_c4) = sk_c9
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c8
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f50,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f51,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f52,negated_conjecture,
! [X3,X4,X1,X2,X5,X6] :
( multiply(X6,sk_c7) != sk_c8
| inverse(X5) != X6
| multiply(X5,X6) != sk_c8
| multiply(X2,sk_c8) != sk_c9
| inverse(X2) != sk_c9
| multiply(sk_c9,sk_c7) != sk_c8
| inverse(X1) != sk_c9
| multiply(X1,sk_c9) != sk_c8
| inverse(X4) != sk_c7
| multiply(X4,sk_c7) != sk_c8
| inverse(sk_c9) != sk_c7
| inverse(X3) != sk_c9
| multiply(X3,sk_c9) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f53,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f54,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f55,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f56,plain,
( multiply(sk_c3,sk_c9) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f57,plain,
( inverse(sk_c3) = sk_c9
| multiply(sk_c8,sk_c7) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f58,plain,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f59,plain,
( inverse(sk_c4) = sk_c9
| multiply(sk_c8,sk_c7) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f60,plain,
( multiply(sk_c4,sk_c8) = sk_c9
| multiply(sk_c8,sk_c7) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f64,plain,
( multiply(sk_c3,sk_c9) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f65,plain,
( inverse(sk_c3) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f66,plain,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f67,plain,
( inverse(sk_c4) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f68,plain,
( multiply(sk_c4,sk_c8) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f72,plain,
( multiply(sk_c3,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f73,plain,
( inverse(sk_c3) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f74,plain,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f75,plain,
( inverse(sk_c4) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f76,plain,
( multiply(sk_c4,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f80,plain,
( multiply(sk_c3,sk_c9) = sk_c8
| inverse(sk_c9) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f81,plain,
( inverse(sk_c3) = sk_c9
| inverse(sk_c9) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f82,plain,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c9) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f88,plain,
( multiply(sk_c3,sk_c9) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f89,plain,
( inverse(sk_c3) = sk_c9
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f90,plain,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f91,plain,
( inverse(sk_c4) = sk_c9
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f92,plain,
( multiply(sk_c4,sk_c8) = sk_c9
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f96,plain,
( multiply(sk_c3,sk_c9) = sk_c8
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f97,plain,
( inverse(sk_c3) = sk_c9
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f98,plain,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f99,plain,
( inverse(sk_c4) = sk_c9
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f100,plain,
( multiply(sk_c4,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f101,plain,
( multiply(sk_c5,sk_c6) = sk_c8
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f102,plain,
( inverse(sk_c5) = sk_c6
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f103,plain,
( multiply(sk_c6,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f104,plain,
! [X6] :
( multiply(X6,sk_c7) != sk_c8
| ! [X5] :
( inverse(X5) != X6
| multiply(X5,X6) != sk_c8
| ! [X2] :
( multiply(X2,sk_c8) != sk_c9
| inverse(X2) != sk_c9
| multiply(sk_c9,sk_c7) != sk_c8
| ! [X1] :
( inverse(X1) != sk_c9
| multiply(X1,sk_c9) != sk_c8
| ! [X4] :
( inverse(X4) != sk_c7
| multiply(X4,sk_c7) != sk_c8
| inverse(sk_c9) != sk_c7
| ! [X3] :
( inverse(X3) != sk_c9
| multiply(X3,sk_c9) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c9 ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f52]) ).
fof(f105,plain,
! [X0,X1,X2,X3,X4,X5] :
( multiply(X5,sk_c7) != sk_c8
| inverse(X4) != X5
| multiply(X4,X5) != sk_c8
| multiply(X3,sk_c8) != sk_c9
| inverse(X3) != sk_c9
| multiply(sk_c9,sk_c7) != sk_c8
| inverse(X2) != sk_c9
| multiply(X2,sk_c9) != sk_c8
| inverse(X1) != sk_c7
| multiply(X1,sk_c7) != sk_c8
| inverse(sk_c9) != sk_c7
| inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c9 ),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f106,definition,
( sQ0_spl
<=> multiply(sk_c8,sk_c7) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f107,plain,
( ~ sQ0_spl
| multiply(sk_c8,sk_c7) = sk_c9 ),
inference(component_clause,[status(thm)],[f106]) ).
fof(f108,plain,
( sQ0_spl
| multiply(sk_c8,sk_c7) != sk_c9 ),
inference(component_clause,[status(thm)],[f106]) ).
fof(f109,definition,
( sQ1_spl
<=> multiply(sk_c3,sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f110,plain,
( ~ sQ1_spl
| multiply(sk_c3,sk_c9) = sk_c8 ),
inference(component_clause,[status(thm)],[f109]) ).
fof(f112,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f56,f106,f109]) ).
fof(f113,definition,
( sQ2_spl
<=> inverse(sk_c3) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f114,plain,
( ~ sQ2_spl
| inverse(sk_c3) = sk_c9 ),
inference(component_clause,[status(thm)],[f113]) ).
fof(f116,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f57,f106,f113]) ).
fof(f117,definition,
( sQ3_spl
<=> multiply(sk_c9,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f118,plain,
( ~ sQ3_spl
| multiply(sk_c9,sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f117]) ).
fof(f119,plain,
( sQ3_spl
| multiply(sk_c9,sk_c7) != sk_c8 ),
inference(component_clause,[status(thm)],[f117]) ).
fof(f120,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f58,f106,f117]) ).
fof(f121,definition,
( sQ4_spl
<=> inverse(sk_c4) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f122,plain,
( ~ sQ4_spl
| inverse(sk_c4) = sk_c9 ),
inference(component_clause,[status(thm)],[f121]) ).
fof(f124,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f59,f106,f121]) ).
fof(f125,definition,
( sQ5_spl
<=> multiply(sk_c4,sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f126,plain,
( ~ sQ5_spl
| multiply(sk_c4,sk_c8) = sk_c9 ),
inference(component_clause,[status(thm)],[f125]) ).
fof(f128,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f60,f106,f125]) ).
fof(f129,definition,
( sQ6_spl
<=> multiply(sk_c5,sk_c6) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f130,plain,
( ~ sQ6_spl
| multiply(sk_c5,sk_c6) = sk_c8 ),
inference(component_clause,[status(thm)],[f129]) ).
fof(f133,definition,
( sQ7_spl
<=> inverse(sk_c5) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f134,plain,
( ~ sQ7_spl
| inverse(sk_c5) = sk_c6 ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f137,definition,
( sQ8_spl
<=> multiply(sk_c6,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f138,plain,
( ~ sQ8_spl
| multiply(sk_c6,sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f137]) ).
fof(f141,definition,
( sQ9_spl
<=> multiply(sk_c1,sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f142,plain,
( ~ sQ9_spl
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(component_clause,[status(thm)],[f141]) ).
fof(f144,plain,
( sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f64,f141,f109]) ).
fof(f145,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f65,f141,f113]) ).
fof(f146,plain,
( sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f66,f141,f117]) ).
fof(f147,plain,
( sQ4_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f67,f141,f121]) ).
fof(f148,plain,
( sQ5_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f68,f141,f125]) ).
fof(f152,definition,
( sQ10_spl
<=> inverse(sk_c1) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f153,plain,
( ~ sQ10_spl
| inverse(sk_c1) = sk_c9 ),
inference(component_clause,[status(thm)],[f152]) ).
fof(f155,plain,
( sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f72,f152,f109]) ).
fof(f156,plain,
( sQ2_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f73,f152,f113]) ).
fof(f157,plain,
( sQ3_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f74,f152,f117]) ).
fof(f158,plain,
( sQ4_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f75,f152,f121]) ).
fof(f159,plain,
( sQ5_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f76,f152,f125]) ).
fof(f163,definition,
( sQ11_spl
<=> inverse(sk_c9) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f164,plain,
( ~ sQ11_spl
| inverse(sk_c9) = sk_c7 ),
inference(component_clause,[status(thm)],[f163]) ).
fof(f165,plain,
( sQ11_spl
| inverse(sk_c9) != sk_c7 ),
inference(component_clause,[status(thm)],[f163]) ).
fof(f166,plain,
( sQ1_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f80,f163,f109]) ).
fof(f167,plain,
( sQ2_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f81,f163,f113]) ).
fof(f168,plain,
( sQ3_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f82,f163,f117]) ).
fof(f174,definition,
( sQ12_spl
<=> multiply(sk_c2,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f175,plain,
( ~ sQ12_spl
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f174]) ).
fof(f176,plain,
( sQ12_spl
| multiply(sk_c2,sk_c7) != sk_c8 ),
inference(component_clause,[status(thm)],[f174]) ).
fof(f177,plain,
( sQ1_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f88,f174,f109]) ).
fof(f178,plain,
( sQ2_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f89,f174,f113]) ).
fof(f179,plain,
( sQ3_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f90,f174,f117]) ).
fof(f180,plain,
( sQ4_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f91,f174,f121]) ).
fof(f181,plain,
( sQ5_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f92,f174,f125]) ).
fof(f185,definition,
( sQ13_spl
<=> inverse(sk_c2) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f186,plain,
( ~ sQ13_spl
| inverse(sk_c2) = sk_c7 ),
inference(component_clause,[status(thm)],[f185]) ).
fof(f188,plain,
( sQ1_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f96,f185,f109]) ).
fof(f189,plain,
( sQ2_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f97,f185,f113]) ).
fof(f190,plain,
( sQ3_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f98,f185,f117]) ).
fof(f191,plain,
( sQ4_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f99,f185,f121]) ).
fof(f192,plain,
( sQ5_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f100,f185,f125]) ).
fof(f193,plain,
( sQ6_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f101,f185,f129]) ).
fof(f194,plain,
( sQ7_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f102,f185,f133]) ).
fof(f195,plain,
( sQ8_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f103,f185,f137]) ).
fof(f196,definition,
! [X0] :
( sQ14_spl
<=> ( inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f197,plain,
! [X0] :
( ~ sQ14_spl
| inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c8 ),
inference(component_clause,[status(thm)],[f196]) ).
fof(f199,definition,
! [X1] :
( sQ15_spl
<=> ( inverse(X1) != sk_c7
| multiply(X1,sk_c7) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f200,plain,
! [X0] :
( ~ sQ15_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c8 ),
inference(component_clause,[status(thm)],[f199]) ).
fof(f202,definition,
! [X3] :
( sQ16_spl
<=> ( multiply(X3,sk_c8) != sk_c9
| inverse(X3) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f203,plain,
! [X0] :
( ~ sQ16_spl
| multiply(X0,sk_c8) != sk_c9
| inverse(X0) != sk_c9 ),
inference(component_clause,[status(thm)],[f202]) ).
fof(f205,definition,
! [X4,X5] :
( sQ17_spl
<=> ( multiply(X5,sk_c7) != sk_c8
| inverse(X4) != X5
| multiply(X4,X5) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f206,plain,
! [X0,X1] :
( ~ sQ17_spl
| multiply(X1,sk_c7) != sk_c8
| inverse(X0) != X1
| multiply(X0,X1) != sk_c8 ),
inference(component_clause,[status(thm)],[f205]) ).
fof(f208,plain,
( sQ17_spl
| sQ16_spl
| ~ sQ3_spl
| sQ15_spl
| ~ sQ11_spl
| sQ14_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f105,f106,f196,f163,f199,f117,f202,f205]) ).
fof(f209,plain,
! [X0] :
( ~ sQ17_spl
| multiply(inverse(X0),sk_c7) != sk_c8
| multiply(X0,inverse(X0)) != sk_c8 ),
inference(destructive_equality_resolution,[status(thm)],[f206]) ).
fof(f214,plain,
! [X0] :
( ~ sQ9_spl
| multiply(sk_c8,X0) = multiply(sk_c1,multiply(sk_c9,X0)) ),
inference(paramodulation,[status(thm)],[f142,f55]) ).
fof(f216,plain,
( ~ sQ2_spl
| multiply(sk_c9,sk_c3) = identity ),
inference(paramodulation,[status(thm)],[f114,f54]) ).
fof(f217,plain,
( ~ sQ4_spl
| multiply(sk_c9,sk_c4) = identity ),
inference(paramodulation,[status(thm)],[f122,f54]) ).
fof(f219,plain,
( ~ sQ10_spl
| multiply(sk_c9,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f153,f54]) ).
fof(f220,plain,
( ~ sQ13_spl
| multiply(sk_c7,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f186,f54]) ).
fof(f221,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f54,f55]) ).
fof(f222,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f53,f221]) ).
fof(f224,plain,
! [X0] :
( ~ sQ6_spl
| multiply(sk_c8,X0) = multiply(sk_c5,multiply(sk_c6,X0)) ),
inference(paramodulation,[status(thm)],[f130,f55]) ).
fof(f225,plain,
( ~ sQ11_spl
| multiply(sk_c7,sk_c9) = identity ),
inference(paramodulation,[status(thm)],[f164,f54]) ).
fof(f227,plain,
! [X0] :
( ~ sQ1_spl
| multiply(sk_c8,X0) = multiply(sk_c3,multiply(sk_c9,X0)) ),
inference(paramodulation,[status(thm)],[f110,f55]) ).
fof(f229,plain,
( ~ sQ17_spl
| multiply(inverse(identity),sk_c7) != sk_c8
| inverse(identity) != sk_c8 ),
inference(paramodulation,[status(thm)],[f53,f209]) ).
fof(f232,plain,
( ~ sQ2_spl
| ~ sQ17_spl
| multiply(inverse(sk_c3),sk_c7) != sk_c8
| multiply(sk_c3,sk_c9) != sk_c8 ),
inference(paramodulation,[status(thm)],[f114,f209]) ).
fof(f235,plain,
( ~ sQ10_spl
| ~ sQ17_spl
| multiply(inverse(sk_c1),sk_c7) != sk_c8
| multiply(sk_c1,sk_c9) != sk_c8 ),
inference(paramodulation,[status(thm)],[f153,f209]) ).
fof(f236,plain,
( ~ sQ13_spl
| ~ sQ17_spl
| multiply(inverse(sk_c2),sk_c7) != sk_c8
| multiply(sk_c2,sk_c7) != sk_c8 ),
inference(paramodulation,[status(thm)],[f186,f209]) ).
fof(f237,definition,
( sQ18_spl
<=> inverse(identity) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f240,definition,
( sQ19_spl
<=> multiply(inverse(identity),sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f243,plain,
( ~ sQ17_spl
| ~ sQ19_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f229,f237,f240,f205]) ).
fof(f248,definition,
( sQ21_spl
<=> multiply(inverse(sk_c3),sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f250,plain,
( sQ21_spl
| multiply(inverse(sk_c3),sk_c7) != sk_c8 ),
inference(component_clause,[status(thm)],[f248]) ).
fof(f251,plain,
( ~ sQ2_spl
| ~ sQ17_spl
| ~ sQ21_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f232,f109,f248,f205,f113]) ).
fof(f263,definition,
( sQ25_spl
<=> multiply(inverse(sk_c1),sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f265,plain,
( sQ25_spl
| multiply(inverse(sk_c1),sk_c7) != sk_c8 ),
inference(component_clause,[status(thm)],[f263]) ).
fof(f266,plain,
( ~ sQ10_spl
| ~ sQ17_spl
| ~ sQ25_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f235,f141,f263,f205,f152]) ).
fof(f267,definition,
( sQ26_spl
<=> multiply(inverse(sk_c2),sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f270,plain,
( ~ sQ13_spl
| ~ sQ17_spl
| ~ sQ26_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f236,f174,f267,f205,f185]) ).
fof(f272,plain,
( sQ25_spl
| ~ sQ10_spl
| multiply(sk_c9,sk_c7) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f153,f265]) ).
fof(f275,plain,
( ~ sQ5_spl
| ~ sQ16_spl
| sk_c9 != sk_c9
| inverse(sk_c4) != sk_c9 ),
inference(paramodulation,[status(thm)],[f126,f203]) ).
fof(f279,definition,
( sQ27_spl
<=> sk_c9 = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f281,plain,
( sQ27_spl
| sk_c9 != sk_c9 ),
inference(component_clause,[status(thm)],[f279]) ).
fof(f282,plain,
( ~ sQ5_spl
| ~ sQ16_spl
| ~ sQ27_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f275,f121,f279,f202,f125]) ).
fof(f297,plain,
( sQ27_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f281]) ).
fof(f298,plain,
sQ27_spl,
inference(contradiction_clause,[status(thm)],[f297]) ).
fof(f299,plain,
( ~ sQ8_spl
| ~ sQ15_spl
| inverse(sk_c6) != sk_c7 ),
inference(resolution,[status(thm)],[f200,f138]) ).
fof(f300,plain,
( ~ sQ12_spl
| ~ sQ15_spl
| inverse(sk_c2) != sk_c7 ),
inference(resolution,[status(thm)],[f200,f175]) ).
fof(f307,plain,
( ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ13_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f186,f300]) ).
fof(f308,plain,
( ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ13_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f307]) ).
fof(f309,plain,
( ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f308]) ).
fof(f310,plain,
( sQ21_spl
| ~ sQ2_spl
| multiply(sk_c9,sk_c7) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f114,f250]) ).
fof(f313,plain,
( sQ21_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f118,f310]) ).
fof(f314,plain,
( sQ21_spl
| ~ sQ2_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f313]) ).
fof(f315,plain,
( sQ21_spl
| ~ sQ2_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f314]) ).
fof(f325,plain,
( ~ sQ14_spl
| inverse(inverse(sk_c9)) != sk_c9
| identity != sk_c8 ),
inference(paramodulation,[status(thm)],[f54,f197]) ).
fof(f328,definition,
( sQ32_spl
<=> identity = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f330,plain,
( sQ32_spl
| identity != sk_c8 ),
inference(component_clause,[status(thm)],[f328]) ).
fof(f331,definition,
( sQ33_spl
<=> inverse(inverse(sk_c9)) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f333,plain,
( sQ33_spl
| inverse(inverse(sk_c9)) != sk_c9 ),
inference(component_clause,[status(thm)],[f331]) ).
fof(f334,plain,
( ~ sQ14_spl
| ~ sQ33_spl
| ~ sQ32_spl ),
inference(split_clause,[status(thm)],[f325,f328,f331,f196]) ).
fof(f337,plain,
( sQ25_spl
| ~ sQ10_spl
| ~ sQ3_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f118,f272]) ).
fof(f338,plain,
( sQ25_spl
| ~ sQ10_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f337]) ).
fof(f339,plain,
( sQ25_spl
| ~ sQ10_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f338]) ).
fof(f340,plain,
( sQ33_spl
| ~ sQ11_spl
| inverse(sk_c7) != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f164,f333]) ).
fof(f346,plain,
( ~ sQ14_spl
| ~ sQ1_spl
| inverse(sk_c3) != sk_c9 ),
inference(resolution,[status(thm)],[f110,f197]) ).
fof(f349,plain,
( ~ sQ14_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f114,f346]) ).
fof(f350,plain,
( ~ sQ14_spl
| ~ sQ1_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f349]) ).
fof(f351,plain,
( ~ sQ14_spl
| ~ sQ1_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f350]) ).
fof(f356,plain,
! [X0] :
( ~ sQ13_spl
| multiply(identity,X0) = multiply(sk_c7,multiply(sk_c2,X0)) ),
inference(paramodulation,[status(thm)],[f220,f55]) ).
fof(f357,plain,
! [X0] :
( ~ sQ13_spl
| X0 = multiply(sk_c7,multiply(sk_c2,X0)) ),
inference(forward_demodulation,[status(thm)],[f53,f356]) ).
fof(f358,plain,
! [X0] :
( ~ sQ2_spl
| multiply(identity,X0) = multiply(sk_c9,multiply(sk_c3,X0)) ),
inference(paramodulation,[status(thm)],[f216,f55]) ).
fof(f359,plain,
! [X0] :
( ~ sQ2_spl
| X0 = multiply(sk_c9,multiply(sk_c3,X0)) ),
inference(forward_demodulation,[status(thm)],[f53,f358]) ).
fof(f362,plain,
! [X0] :
( ~ sQ4_spl
| multiply(identity,X0) = multiply(sk_c9,multiply(sk_c4,X0)) ),
inference(paramodulation,[status(thm)],[f217,f55]) ).
fof(f363,plain,
! [X0] :
( ~ sQ4_spl
| X0 = multiply(sk_c9,multiply(sk_c4,X0)) ),
inference(forward_demodulation,[status(thm)],[f53,f362]) ).
fof(f378,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| multiply(sk_c8,sk_c4) = multiply(sk_c3,identity) ),
inference(paramodulation,[status(thm)],[f217,f227]) ).
fof(f379,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| multiply(sk_c8,sk_c3) = multiply(sk_c3,identity) ),
inference(paramodulation,[status(thm)],[f216,f227]) ).
fof(f380,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| multiply(sk_c8,sk_c7) = multiply(sk_c3,sk_c8) ),
inference(paramodulation,[status(thm)],[f118,f227]) ).
fof(f383,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| multiply(sk_c8,sk_c3) = multiply(sk_c8,sk_c4) ),
inference(forward_demodulation,[status(thm)],[f378,f379]) ).
fof(f389,plain,
( ~ sQ8_spl
| ~ sQ6_spl
| multiply(sk_c8,sk_c7) = multiply(sk_c5,sk_c8) ),
inference(paramodulation,[status(thm)],[f138,f224]) ).
fof(f427,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c9 = multiply(sk_c9,sk_c8) ),
inference(paramodulation,[status(thm)],[f110,f359]) ).
fof(f449,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| sk_c8 = multiply(sk_c9,sk_c9) ),
inference(paramodulation,[status(thm)],[f126,f363]) ).
fof(f466,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| multiply(sk_c8,sk_c9) = multiply(sk_c3,sk_c8) ),
inference(paramodulation,[status(thm)],[f449,f227]) ).
fof(f469,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| multiply(sk_c8,sk_c9) != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f470,f108]) ).
fof(f470,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| multiply(sk_c8,sk_c9) = multiply(sk_c8,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f380,f466]) ).
fof(f475,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| sk_c4 = multiply(inverse(sk_c8),multiply(sk_c8,sk_c3)) ),
inference(paramodulation,[status(thm)],[f383,f222]) ).
fof(f476,plain,
! [X0] :
( ~ sQ13_spl
| multiply(sk_c2,X0) = multiply(inverse(sk_c7),X0) ),
inference(paramodulation,[status(thm)],[f357,f222]) ).
fof(f478,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| sk_c9 = multiply(inverse(sk_c9),sk_c8) ),
inference(paramodulation,[status(thm)],[f449,f222]) ).
fof(f479,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 = multiply(inverse(sk_c9),sk_c9) ),
inference(paramodulation,[status(thm)],[f427,f222]) ).
fof(f481,plain,
! [X0] :
( ~ sQ4_spl
| multiply(sk_c4,X0) = multiply(inverse(sk_c9),X0) ),
inference(paramodulation,[status(thm)],[f363,f222]) ).
fof(f484,plain,
( ~ sQ4_spl
| sk_c4 = multiply(inverse(sk_c9),identity) ),
inference(paramodulation,[status(thm)],[f217,f222]) ).
fof(f486,plain,
( ~ sQ3_spl
| sk_c7 = multiply(inverse(sk_c9),sk_c8) ),
inference(paramodulation,[status(thm)],[f118,f222]) ).
fof(f488,plain,
( ~ sQ1_spl
| sk_c9 = multiply(inverse(sk_c3),sk_c8) ),
inference(paramodulation,[status(thm)],[f110,f222]) ).
fof(f491,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f222,f222]) ).
fof(f492,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f54,f222]) ).
fof(f500,plain,
( ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| multiply(sk_c3,sk_c8) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f503,f126]) ).
fof(f503,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| sk_c4 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f222,f475]) ).
fof(f509,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c8,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f512,f53]) ).
fof(f512,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 = identity ),
inference(forward_demodulation,[status(thm)],[f54,f479]) ).
fof(f518,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ1_spl
| multiply(sk_c3,X0) = multiply(inverse(sk_c9),X0) ),
inference(forward_demodulation,[status(thm)],[f503,f481]) ).
fof(f522,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c3 = multiply(inverse(sk_c9),identity) ),
inference(forward_demodulation,[status(thm)],[f503,f484]) ).
fof(f523,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c3 = multiply(sk_c3,identity) ),
inference(forward_demodulation,[status(thm)],[f518,f522]) ).
fof(f524,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c3 = multiply(sk_c3,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f512,f523]) ).
fof(f530,plain,
( sQ12_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c2,sk_c9) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f535,f176]) ).
fof(f533,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c2,X0) = multiply(inverse(sk_c9),X0) ),
inference(backward_demodulation,[status(thm)],[f535,f476]) ).
fof(f535,plain,
( ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c7 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f478,f486]) ).
fof(f540,plain,
! [X0] : X0 = multiply(X0,identity),
inference(forward_demodulation,[status(thm)],[f491,f492]) ).
fof(f544,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| X0 = multiply(X0,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f512,f540]) ).
fof(f556,plain,
( ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| sk_c3 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f524,f500]) ).
fof(f561,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c9 != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f509,f469]) ).
fof(f575,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ1_spl
| multiply(sk_c2,X0) = multiply(sk_c3,X0) ),
inference(forward_demodulation,[status(thm)],[f518,f533]) ).
fof(f576,plain,
( sQ12_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ13_spl
| ~ sQ2_spl
| ~ sQ1_spl
| multiply(sk_c9,sk_c9) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f578,f530]) ).
fof(f578,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ1_spl
| multiply(sk_c2,X0) = multiply(sk_c9,X0) ),
inference(forward_demodulation,[status(thm)],[f556,f575]) ).
fof(f585,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f561,f279,f113,f117,f109,f121,f125,f106]) ).
fof(f587,plain,
( sQ12_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ13_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f449,f576]) ).
fof(f588,plain,
( sQ12_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ13_spl
| ~ sQ2_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f587]) ).
fof(f589,plain,
( sQ12_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ13_spl
| ~ sQ2_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f588]) ).
fof(f592,plain,
( ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ0_spl
| sk_c9 = multiply(sk_c5,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f107,f389]) ).
fof(f606,plain,
! [X0] :
( ~ sQ11_spl
| X0 = multiply(sk_c7,multiply(sk_c9,X0)) ),
inference(paramodulation,[status(thm)],[f164,f222]) ).
fof(f608,plain,
( ~ sQ10_spl
| sk_c1 = multiply(inverse(sk_c9),identity) ),
inference(paramodulation,[status(thm)],[f219,f222]) ).
fof(f610,plain,
( ~ sQ10_spl
| sk_c1 = inverse(sk_c9) ),
inference(forward_demodulation,[status(thm)],[f540,f608]) ).
fof(f611,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| multiply(sk_c9,sk_c7) = identity ),
inference(backward_demodulation,[status(thm)],[f616,f219]) ).
fof(f612,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| inverse(sk_c7) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f616,f153]) ).
fof(f613,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| multiply(sk_c7,sk_c9) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f616,f142]) ).
fof(f615,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| multiply(sk_c8,X0) = multiply(sk_c7,multiply(sk_c9,X0)) ),
inference(backward_demodulation,[status(thm)],[f616,f214]) ).
fof(f616,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| sk_c1 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f164,f610]) ).
fof(f618,plain,
( sQ3_spl
| ~ sQ10_spl
| ~ sQ11_spl
| identity != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f611,f119]) ).
fof(f620,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| sQ33_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f612,f340]) ).
fof(f621,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| sQ33_spl ),
inference(contradiction_clause,[status(thm)],[f620]) ).
fof(f622,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| identity = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f225,f613]) ).
fof(f623,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| sQ32_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f622,f330]) ).
fof(f624,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| sQ32_spl ),
inference(contradiction_clause,[status(thm)],[f623]) ).
fof(f625,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| sk_c7 = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f637,f107]) ).
fof(f637,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| multiply(sk_c8,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f606,f615]) ).
fof(f638,plain,
( sQ3_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ32_spl ),
inference(split_clause,[status(thm)],[f618,f328,f163,f152,f117]) ).
fof(f645,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| multiply(sk_c9,sk_c7) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f622,f611]) ).
fof(f646,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| X0 = multiply(X0,sk_c8) ),
inference(backward_demodulation,[status(thm)],[f622,f540]) ).
fof(f654,plain,
( ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| inverse(sk_c9) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f625,f164]) ).
fof(f676,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f645,f117,f141,f163,f152]) ).
fof(f692,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| X0 != sk_c9
| inverse(X0) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f646,f203]) ).
fof(f693,plain,
( ~ sQ16_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| inverse(sk_c9) != sk_c9 ),
inference(destructive_equality_resolution,[status(thm)],[f692]) ).
fof(f694,plain,
( ~ sQ16_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f693,f654]) ).
fof(f695,plain,
( ~ sQ16_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f694]) ).
fof(f843,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c9 = inverse(sk_c3) ),
inference(forward_demodulation,[status(thm)],[f544,f488]) ).
fof(f844,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c9 = inverse(sk_c9) ),
inference(forward_demodulation,[status(thm)],[f556,f843]) ).
fof(f847,plain,
( ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c9 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f544,f592]) ).
fof(f865,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c7 = inverse(sk_c9) ),
inference(forward_demodulation,[status(thm)],[f544,f486]) ).
fof(f867,plain,
( sQ11_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f865,f165]) ).
fof(f868,plain,
( sQ11_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f867]) ).
fof(f869,plain,
( sQ11_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f868]) ).
fof(f877,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sk_c9 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f865,f844]) ).
fof(f936,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c9) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f847,f134]) ).
fof(f937,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c7 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f865,f936]) ).
fof(f939,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c9 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f877,f937]) ).
fof(f973,plain,
( ~ sQ8_spl
| ~ sQ15_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(sk_c9) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f939,f299]) ).
fof(f974,plain,
( ~ sQ8_spl
| ~ sQ15_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f865,f973]) ).
fof(f975,plain,
( ~ sQ8_spl
| ~ sQ15_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c9 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f877,f974]) ).
fof(f976,plain,
( ~ sQ8_spl
| ~ sQ15_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f877,f975]) ).
fof(f977,plain,
( ~ sQ8_spl
| ~ sQ15_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f976]) ).
fof(f978,plain,
( ~ sQ8_spl
| ~ sQ15_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f977]) ).
fof(f979,plain,
$false,
inference(sat_refutation,[status(thm)],[f112,f116,f120,f124,f128,f144,f145,f146,f147,f148,f155,f156,f157,f158,f159,f166,f167,f168,f177,f178,f179,f180,f181,f188,f189,f190,f191,f192,f193,f194,f195,f208,f243,f251,f266,f270,f282,f298,f309,f315,f334,f339,f351,f585,f589,f621,f624,f638,f676,f695,f869,f978]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP354-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Sun Sep 20 20:10:23 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.31 % Drodi V4.1.1
% 0.08/0.34 % Refutation found
% 0.08/0.34 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/0.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.36 % Elapsed time: 0.056981 seconds
% 0.08/0.36 % CPU time: 0.135565 seconds
% 0.08/0.36 % Total memory used: 106.022 MB
% 0.08/0.36 % Net memory used: 105.851 MB
%------------------------------------------------------------------------------