%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP389-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 12:33:36 PM UTC 2026
% Result : Unsatisfiable 0.08s 0.39s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 71
% Syntax : Number of formulae : 307 ( 15 unt; 25 def)
% Number of atoms : 901 ( 378 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 1065 ( 471 ~; 569 |; 0 &)
% ( 25 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 27 ( 25 usr; 26 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 66 ( 66 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
( multiply(sk_c4,sk_c11) = sk_c10
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c4) = sk_c11
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c5,sk_c10) = sk_c9
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c5) = sk_c10
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c10
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c7) = sk_c8
| inverse(sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c4,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( inverse(sk_c4) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( multiply(sk_c5,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( inverse(sk_c5) = sk_c10
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c6) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c10
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( inverse(sk_c7) = sk_c8
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c10
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c4,sk_c11) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( inverse(sk_c4) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( inverse(sk_c6) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( multiply(sk_c4,sk_c11) = sk_c10
| multiply(sk_c2,sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( inverse(sk_c4) = sk_c11
| multiply(sk_c2,sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( multiply(sk_c5,sk_c10) = sk_c9
| multiply(sk_c2,sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( inverse(sk_c5) = sk_c10
| multiply(sk_c2,sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c10
| multiply(sk_c2,sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
( inverse(sk_c7) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c10
| multiply(sk_c2,sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
( multiply(sk_c4,sk_c11) = sk_c10
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,negated_conjecture,
( inverse(sk_c4) = sk_c11
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,negated_conjecture,
( multiply(sk_c5,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,negated_conjecture,
( inverse(sk_c5) = sk_c10
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c10
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,negated_conjecture,
( inverse(sk_c7) = sk_c8
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c10
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,negated_conjecture,
( multiply(sk_c4,sk_c11) = sk_c10
| multiply(sk_c3,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,negated_conjecture,
( inverse(sk_c4) = sk_c11
| multiply(sk_c3,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f51,negated_conjecture,
( multiply(sk_c5,sk_c10) = sk_c9
| multiply(sk_c3,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f52,negated_conjecture,
( inverse(sk_c5) = sk_c10
| multiply(sk_c3,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f53,negated_conjecture,
( inverse(sk_c6) = sk_c11
| multiply(sk_c3,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c11
| multiply(sk_c3,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f55,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c10
| multiply(sk_c3,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f56,negated_conjecture,
( inverse(sk_c7) = sk_c8
| multiply(sk_c3,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f57,negated_conjecture,
( multiply(sk_c8,sk_c9) = sk_c10
| multiply(sk_c3,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f58,negated_conjecture,
! [X4,X5,X6,X1,X2,X3,X7,X8] :
( multiply(X8,sk_c9) != sk_c10
| inverse(X7) != X8
| multiply(X7,X8) != sk_c10
| multiply(X3,sk_c10) != sk_c11
| inverse(X3) != sk_c11
| inverse(X2) != sk_c10
| multiply(X2,sk_c10) != sk_c9
| inverse(X1) != sk_c11
| multiply(X1,sk_c11) != sk_c10
| multiply(X6,sk_c9) != sk_c10
| inverse(X5) != X6
| multiply(X5,X6) != sk_c10
| multiply(X4,sk_c10) != sk_c11
| inverse(X4) != sk_c11
| inverse(sk_c10) != sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f59,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f60,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f61,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f62,plain,
( multiply(sk_c4,sk_c11) = sk_c10
| inverse(sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f63,plain,
( inverse(sk_c4) = sk_c11
| inverse(sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f64,plain,
( multiply(sk_c5,sk_c10) = sk_c9
| inverse(sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f65,plain,
( inverse(sk_c5) = sk_c10
| inverse(sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f68,plain,
( multiply(sk_c7,sk_c8) = sk_c10
| inverse(sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f69,plain,
( inverse(sk_c7) = sk_c8
| inverse(sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f71,plain,
( multiply(sk_c4,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f72,plain,
( inverse(sk_c4) = sk_c11
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f73,plain,
( multiply(sk_c5,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f74,plain,
( inverse(sk_c5) = sk_c10
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f75,plain,
( inverse(sk_c6) = sk_c11
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f76,plain,
( multiply(sk_c6,sk_c10) = sk_c11
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f77,plain,
( multiply(sk_c7,sk_c8) = sk_c10
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f78,plain,
( inverse(sk_c7) = sk_c8
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f79,plain,
( multiply(sk_c8,sk_c9) = sk_c10
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f80,plain,
( multiply(sk_c4,sk_c11) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f81,plain,
( inverse(sk_c4) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f84,plain,
( inverse(sk_c6) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f85,plain,
( multiply(sk_c6,sk_c10) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f89,plain,
( multiply(sk_c4,sk_c11) = sk_c10
| multiply(sk_c2,sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f90,plain,
( inverse(sk_c4) = sk_c11
| multiply(sk_c2,sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f91,plain,
( multiply(sk_c5,sk_c10) = sk_c9
| multiply(sk_c2,sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f92,plain,
( inverse(sk_c5) = sk_c10
| multiply(sk_c2,sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f95,plain,
( multiply(sk_c7,sk_c8) = sk_c10
| multiply(sk_c2,sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f96,plain,
( inverse(sk_c7) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f97,plain,
( multiply(sk_c8,sk_c9) = sk_c10
| multiply(sk_c2,sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f98,plain,
( multiply(sk_c4,sk_c11) = sk_c10
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f99,plain,
( inverse(sk_c4) = sk_c11
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f100,plain,
( multiply(sk_c5,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f101,plain,
( inverse(sk_c5) = sk_c10
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f104,plain,
( multiply(sk_c7,sk_c8) = sk_c10
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f105,plain,
( inverse(sk_c7) = sk_c8
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f106,plain,
( multiply(sk_c8,sk_c9) = sk_c10
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f107,plain,
( multiply(sk_c4,sk_c11) = sk_c10
| multiply(sk_c3,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f108,plain,
( inverse(sk_c4) = sk_c11
| multiply(sk_c3,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f109,plain,
( multiply(sk_c5,sk_c10) = sk_c9
| multiply(sk_c3,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f110,plain,
( inverse(sk_c5) = sk_c10
| multiply(sk_c3,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f111,plain,
( inverse(sk_c6) = sk_c11
| multiply(sk_c3,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f112,plain,
( multiply(sk_c6,sk_c10) = sk_c11
| multiply(sk_c3,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f113,plain,
( multiply(sk_c7,sk_c8) = sk_c10
| multiply(sk_c3,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f114,plain,
( inverse(sk_c7) = sk_c8
| multiply(sk_c3,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f115,plain,
( multiply(sk_c8,sk_c9) = sk_c10
| multiply(sk_c3,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f116,plain,
! [X8] :
( multiply(X8,sk_c9) != sk_c10
| ! [X7] :
( inverse(X7) != X8
| multiply(X7,X8) != sk_c10
| ! [X3] :
( multiply(X3,sk_c10) != sk_c11
| inverse(X3) != sk_c11
| ! [X2] :
( inverse(X2) != sk_c10
| multiply(X2,sk_c10) != sk_c9
| ! [X1] :
( inverse(X1) != sk_c11
| multiply(X1,sk_c11) != sk_c10
| ! [X6] :
( multiply(X6,sk_c9) != sk_c10
| ! [X5] :
( inverse(X5) != X6
| multiply(X5,X6) != sk_c10
| ! [X4] :
( multiply(X4,sk_c10) != sk_c11
| inverse(X4) != sk_c11
| inverse(sk_c10) != sk_c9 ) ) ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f58]) ).
fof(f117,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( multiply(X7,sk_c9) != sk_c10
| inverse(X6) != X7
| multiply(X6,X7) != sk_c10
| multiply(X5,sk_c10) != sk_c11
| inverse(X5) != sk_c11
| inverse(X4) != sk_c10
| multiply(X4,sk_c10) != sk_c9
| inverse(X3) != sk_c11
| multiply(X3,sk_c11) != sk_c10
| multiply(X2,sk_c9) != sk_c10
| inverse(X1) != X2
| multiply(X1,X2) != sk_c10
| multiply(X0,sk_c10) != sk_c11
| inverse(X0) != sk_c11
| inverse(sk_c10) != sk_c9 ),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f118,definition,
( sQ0_spl
<=> inverse(sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f119,plain,
( ~ sQ0_spl
| inverse(sk_c10) = sk_c9 ),
inference(component_clause,[status(thm)],[f118]) ).
fof(f120,plain,
( sQ0_spl
| inverse(sk_c10) != sk_c9 ),
inference(component_clause,[status(thm)],[f118]) ).
fof(f121,definition,
( sQ1_spl
<=> multiply(sk_c4,sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f122,plain,
( ~ sQ1_spl
| multiply(sk_c4,sk_c11) = sk_c10 ),
inference(component_clause,[status(thm)],[f121]) ).
fof(f124,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f62,f118,f121]) ).
fof(f125,definition,
( sQ2_spl
<=> inverse(sk_c4) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f126,plain,
( ~ sQ2_spl
| inverse(sk_c4) = sk_c11 ),
inference(component_clause,[status(thm)],[f125]) ).
fof(f128,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f63,f118,f125]) ).
fof(f129,definition,
( sQ3_spl
<=> multiply(sk_c5,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f130,plain,
( ~ sQ3_spl
| multiply(sk_c5,sk_c10) = sk_c9 ),
inference(component_clause,[status(thm)],[f129]) ).
fof(f132,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f64,f118,f129]) ).
fof(f133,definition,
( sQ4_spl
<=> inverse(sk_c5) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f134,plain,
( ~ sQ4_spl
| inverse(sk_c5) = sk_c10 ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f65,f118,f133]) ).
fof(f137,definition,
( sQ5_spl
<=> inverse(sk_c6) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f138,plain,
( ~ sQ5_spl
| inverse(sk_c6) = sk_c11 ),
inference(component_clause,[status(thm)],[f137]) ).
fof(f141,definition,
( sQ6_spl
<=> multiply(sk_c6,sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f142,plain,
( ~ sQ6_spl
| multiply(sk_c6,sk_c10) = sk_c11 ),
inference(component_clause,[status(thm)],[f141]) ).
fof(f145,definition,
( sQ7_spl
<=> multiply(sk_c7,sk_c8) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f146,plain,
( ~ sQ7_spl
| multiply(sk_c7,sk_c8) = sk_c10 ),
inference(component_clause,[status(thm)],[f145]) ).
fof(f148,plain,
( sQ7_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f68,f118,f145]) ).
fof(f149,definition,
( sQ8_spl
<=> inverse(sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f150,plain,
( ~ sQ8_spl
| inverse(sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f149]) ).
fof(f152,plain,
( sQ8_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f69,f118,f149]) ).
fof(f153,definition,
( sQ9_spl
<=> multiply(sk_c8,sk_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f154,plain,
( ~ sQ9_spl
| multiply(sk_c8,sk_c9) = sk_c10 ),
inference(component_clause,[status(thm)],[f153]) ).
fof(f157,definition,
( sQ10_spl
<=> inverse(sk_c1) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f158,plain,
( ~ sQ10_spl
| inverse(sk_c1) = sk_c11 ),
inference(component_clause,[status(thm)],[f157]) ).
fof(f160,plain,
( sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f71,f157,f121]) ).
fof(f161,plain,
( sQ2_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f72,f157,f125]) ).
fof(f162,plain,
( sQ3_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f73,f157,f129]) ).
fof(f163,plain,
( sQ4_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f74,f157,f133]) ).
fof(f164,plain,
( sQ5_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f75,f157,f137]) ).
fof(f165,plain,
( sQ6_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f76,f157,f141]) ).
fof(f166,plain,
( sQ7_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f77,f157,f145]) ).
fof(f167,plain,
( sQ8_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f78,f157,f149]) ).
fof(f168,plain,
( sQ9_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f79,f157,f153]) ).
fof(f169,definition,
( sQ11_spl
<=> multiply(sk_c1,sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f170,plain,
( ~ sQ11_spl
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(component_clause,[status(thm)],[f169]) ).
fof(f172,plain,
( sQ1_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f80,f169,f121]) ).
fof(f173,plain,
( sQ2_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f81,f169,f125]) ).
fof(f176,plain,
( sQ5_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f84,f169,f137]) ).
fof(f177,plain,
( sQ6_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f85,f169,f141]) ).
fof(f181,definition,
( sQ12_spl
<=> multiply(sk_c2,sk_c3) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f182,plain,
( ~ sQ12_spl
| multiply(sk_c2,sk_c3) = sk_c10 ),
inference(component_clause,[status(thm)],[f181]) ).
fof(f184,plain,
( sQ1_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f89,f181,f121]) ).
fof(f185,plain,
( sQ2_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f90,f181,f125]) ).
fof(f186,plain,
( sQ3_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f91,f181,f129]) ).
fof(f187,plain,
( sQ4_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f92,f181,f133]) ).
fof(f190,plain,
( sQ7_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f95,f181,f145]) ).
fof(f191,plain,
( sQ8_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f96,f181,f149]) ).
fof(f192,plain,
( sQ9_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f97,f181,f153]) ).
fof(f193,definition,
( sQ13_spl
<=> inverse(sk_c2) = sk_c3 ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f194,plain,
( ~ sQ13_spl
| inverse(sk_c2) = sk_c3 ),
inference(component_clause,[status(thm)],[f193]) ).
fof(f196,plain,
( sQ1_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f98,f193,f121]) ).
fof(f197,plain,
( sQ2_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f99,f193,f125]) ).
fof(f198,plain,
( sQ3_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f100,f193,f129]) ).
fof(f199,plain,
( sQ4_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f101,f193,f133]) ).
fof(f202,plain,
( sQ7_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f104,f193,f145]) ).
fof(f203,plain,
( sQ8_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f105,f193,f149]) ).
fof(f204,plain,
( sQ9_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f106,f193,f153]) ).
fof(f205,definition,
( sQ14_spl
<=> multiply(sk_c3,sk_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f206,plain,
( ~ sQ14_spl
| multiply(sk_c3,sk_c9) = sk_c10 ),
inference(component_clause,[status(thm)],[f205]) ).
fof(f208,plain,
( sQ1_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f107,f205,f121]) ).
fof(f209,plain,
( sQ2_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f108,f205,f125]) ).
fof(f210,plain,
( sQ3_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f109,f205,f129]) ).
fof(f211,plain,
( sQ4_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f110,f205,f133]) ).
fof(f212,plain,
( sQ5_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f111,f205,f137]) ).
fof(f213,plain,
( sQ6_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f112,f205,f141]) ).
fof(f214,plain,
( sQ7_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f113,f205,f145]) ).
fof(f215,plain,
( sQ8_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f114,f205,f149]) ).
fof(f216,plain,
( sQ9_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f115,f205,f153]) ).
fof(f217,definition,
! [X0] :
( sQ15_spl
<=> ( multiply(X0,sk_c10) != sk_c11
| inverse(X0) != sk_c11 ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f218,plain,
! [X0] :
( ~ sQ15_spl
| multiply(X0,sk_c10) != sk_c11
| inverse(X0) != sk_c11 ),
inference(component_clause,[status(thm)],[f217]) ).
fof(f220,definition,
! [X1,X2] :
( sQ16_spl
<=> ( multiply(X2,sk_c9) != sk_c10
| inverse(X1) != X2
| multiply(X1,X2) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f221,plain,
! [X0,X1] :
( ~ sQ16_spl
| multiply(X1,sk_c9) != sk_c10
| inverse(X0) != X1
| multiply(X0,X1) != sk_c10 ),
inference(component_clause,[status(thm)],[f220]) ).
fof(f223,definition,
! [X3] :
( sQ17_spl
<=> ( inverse(X3) != sk_c11
| multiply(X3,sk_c11) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f224,plain,
! [X0] :
( ~ sQ17_spl
| inverse(X0) != sk_c11
| multiply(X0,sk_c11) != sk_c10 ),
inference(component_clause,[status(thm)],[f223]) ).
fof(f226,definition,
! [X4] :
( sQ18_spl
<=> ( inverse(X4) != sk_c10
| multiply(X4,sk_c10) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f227,plain,
! [X0] :
( ~ sQ18_spl
| inverse(X0) != sk_c10
| multiply(X0,sk_c10) != sk_c9 ),
inference(component_clause,[status(thm)],[f226]) ).
fof(f229,plain,
( sQ18_spl
| sQ17_spl
| sQ16_spl
| sQ15_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f117,f118,f217,f220,f223,f226]) ).
fof(f230,plain,
( ~ sQ3_spl
| ~ sQ18_spl
| inverse(sk_c5) != sk_c10 ),
inference(resolution,[status(thm)],[f227,f130]) ).
fof(f234,plain,
( ~ sQ3_spl
| ~ sQ18_spl
| ~ sQ4_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f134,f230]) ).
fof(f235,plain,
( ~ sQ3_spl
| ~ sQ18_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f234]) ).
fof(f236,plain,
( ~ sQ3_spl
| ~ sQ18_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f235]) ).
fof(f237,plain,
! [X0] :
( ~ sQ16_spl
| multiply(inverse(X0),sk_c9) != sk_c10
| multiply(X0,inverse(X0)) != sk_c10 ),
inference(destructive_equality_resolution,[status(thm)],[f221]) ).
fof(f249,plain,
( ~ sQ1_spl
| ~ sQ17_spl
| inverse(sk_c4) != sk_c11 ),
inference(resolution,[status(thm)],[f224,f122]) ).
fof(f252,plain,
( ~ sQ1_spl
| ~ sQ17_spl
| ~ sQ2_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f126,f249]) ).
fof(f253,plain,
( ~ sQ1_spl
| ~ sQ17_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f252]) ).
fof(f254,plain,
( ~ sQ1_spl
| ~ sQ17_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f253]) ).
fof(f259,plain,
( ~ sQ10_spl
| multiply(sk_c11,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f158,f60]) ).
fof(f260,plain,
( ~ sQ13_spl
| multiply(sk_c3,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f194,f60]) ).
fof(f261,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f60,f61]) ).
fof(f262,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f59,f261]) ).
fof(f278,plain,
( ~ sQ10_spl
| sk_c1 = multiply(inverse(sk_c11),identity) ),
inference(paramodulation,[status(thm)],[f259,f262]) ).
fof(f283,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f59,f262]) ).
fof(f288,plain,
( ~ sQ7_spl
| sk_c8 = multiply(inverse(sk_c7),sk_c10) ),
inference(paramodulation,[status(thm)],[f146,f262]) ).
fof(f291,plain,
( ~ sQ11_spl
| sk_c10 = multiply(inverse(sk_c1),sk_c11) ),
inference(paramodulation,[status(thm)],[f170,f262]) ).
fof(f292,plain,
( ~ sQ12_spl
| sk_c3 = multiply(inverse(sk_c2),sk_c10) ),
inference(paramodulation,[status(thm)],[f182,f262]) ).
fof(f293,plain,
( ~ sQ13_spl
| sk_c2 = multiply(inverse(sk_c3),identity) ),
inference(paramodulation,[status(thm)],[f260,f262]) ).
fof(f294,plain,
( ~ sQ14_spl
| sk_c9 = multiply(inverse(sk_c3),sk_c10) ),
inference(paramodulation,[status(thm)],[f206,f262]) ).
fof(f297,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| sk_c8 = multiply(sk_c8,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f150,f288]) ).
fof(f298,plain,
( ~ sQ11_spl
| ~ sQ10_spl
| sk_c10 = multiply(sk_c11,sk_c11) ),
inference(forward_demodulation,[status(thm)],[f158,f291]) ).
fof(f299,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| sk_c3 = multiply(sk_c3,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f194,f292]) ).
fof(f305,plain,
! [X0] : X0 = multiply(inverse(inverse(identity)),X0),
inference(paramodulation,[status(thm)],[f283,f262]) ).
fof(f309,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| sk_c10 = multiply(inverse(sk_c8),sk_c8) ),
inference(paramodulation,[status(thm)],[f297,f262]) ).
fof(f311,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| sk_c10 = identity ),
inference(forward_demodulation,[status(thm)],[f60,f309]) ).
fof(f312,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ8_spl
| X0 = multiply(inverse(sk_c10),X0) ),
inference(backward_demodulation,[status(thm)],[f311,f283]) ).
fof(f318,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ8_spl
| multiply(inverse(X0),X0) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f311,f60]) ).
fof(f319,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ8_spl
| multiply(sk_c10,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f311,f59]) ).
fof(f320,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| X0 = multiply(sk_c9,X0) ),
inference(forward_demodulation,[status(thm)],[f119,f312]) ).
fof(f321,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| X0 = multiply(inverse(sk_c9),X0) ),
inference(paramodulation,[status(thm)],[f320,f262]) ).
fof(f323,plain,
( ~ sQ0_spl
| ~ sQ16_spl
| multiply(sk_c9,sk_c9) != sk_c10
| multiply(sk_c10,inverse(sk_c10)) != sk_c10 ),
inference(paramodulation,[status(thm)],[f119,f237]) ).
fof(f327,plain,
( ~ sQ13_spl
| ~ sQ16_spl
| multiply(sk_c3,sk_c9) != sk_c10
| multiply(sk_c2,inverse(sk_c2)) != sk_c10 ),
inference(paramodulation,[status(thm)],[f194,f237]) ).
fof(f328,definition,
( sQ19_spl
<=> multiply(sk_c10,inverse(sk_c10)) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f330,plain,
( sQ19_spl
| multiply(sk_c10,inverse(sk_c10)) != sk_c10 ),
inference(component_clause,[status(thm)],[f328]) ).
fof(f331,definition,
( sQ20_spl
<=> multiply(sk_c9,sk_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f333,plain,
( sQ20_spl
| multiply(sk_c9,sk_c9) != sk_c10 ),
inference(component_clause,[status(thm)],[f331]) ).
fof(f334,plain,
( ~ sQ0_spl
| ~ sQ16_spl
| ~ sQ20_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f323,f328,f331,f220,f118]) ).
fof(f350,definition,
( sQ25_spl
<=> multiply(sk_c2,inverse(sk_c2)) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f352,plain,
( sQ25_spl
| multiply(sk_c2,inverse(sk_c2)) != sk_c10 ),
inference(component_clause,[status(thm)],[f350]) ).
fof(f353,plain,
( ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ14_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f327,f350,f205,f220,f193]) ).
fof(f354,plain,
( sQ25_spl
| ~ sQ13_spl
| multiply(sk_c2,sk_c3) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f194,f352]) ).
fof(f355,plain,
( sQ25_spl
| ~ sQ13_spl
| ~ sQ12_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f182,f354]) ).
fof(f356,plain,
( sQ25_spl
| ~ sQ13_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f355]) ).
fof(f357,plain,
( sQ25_spl
| ~ sQ13_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f356]) ).
fof(f362,plain,
! [X0,X1] :
( ~ sQ7_spl
| ~ sQ8_spl
| multiply(sk_c10,X0) = multiply(inverse(X1),multiply(X1,X0)) ),
inference(paramodulation,[status(thm)],[f318,f61]) ).
fof(f363,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ8_spl
| multiply(sk_c10,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f262,f362]) ).
fof(f368,plain,
( ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| multiply(sk_c10,sk_c5) = sk_c10 ),
inference(paramodulation,[status(thm)],[f134,f318]) ).
fof(f370,plain,
( ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c5 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f319,f368]) ).
fof(f372,plain,
( ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| inverse(sk_c5) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f370,f134]) ).
fof(f373,plain,
( sQ0_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| inverse(sk_c5) != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f370,f120]) ).
fof(f376,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ4_spl
| sk_c5 = identity ),
inference(backward_demodulation,[status(thm)],[f370,f311]) ).
fof(f377,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ4_spl
| sk_c8 = multiply(sk_c8,sk_c5) ),
inference(backward_demodulation,[status(thm)],[f370,f297]) ).
fof(f380,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| multiply(sk_c5,sk_c5) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f370,f130]) ).
fof(f383,plain,
( ~ sQ9_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| multiply(sk_c8,sk_c9) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f370,f154]) ).
fof(f386,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ4_spl
| multiply(sk_c5,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f370,f363]) ).
fof(f391,plain,
( sQ0_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c5 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f372,f373]) ).
fof(f432,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c5 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f386,f380]) ).
fof(f433,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f432,f391]) ).
fof(f434,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f433]) ).
fof(f457,plain,
( ~ sQ9_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ3_spl
| multiply(sk_c8,sk_c5) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f432,f383]) ).
fof(f460,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c8 = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f474,f432]) ).
fof(f472,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ4_spl
| ~ sQ9_spl
| ~ sQ3_spl
| sk_c8 = identity ),
inference(backward_demodulation,[status(thm)],[f474,f376]) ).
fof(f473,plain,
( ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ3_spl
| sk_c8 = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f474,f370]) ).
fof(f474,plain,
( ~ sQ9_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ3_spl
| sk_c8 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f377,f457]) ).
fof(f505,definition,
( sQ28_spl
<=> sk_c10 = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f507,plain,
( sQ28_spl
| sk_c10 != sk_c10 ),
inference(component_clause,[status(thm)],[f505]) ).
fof(f509,plain,
( sQ28_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f507]) ).
fof(f510,plain,
sQ28_spl,
inference(contradiction_clause,[status(thm)],[f509]) ).
fof(f531,plain,
( ~ sQ11_spl
| ~ sQ10_spl
| sk_c11 = multiply(inverse(sk_c11),sk_c10) ),
inference(paramodulation,[status(thm)],[f298,f262]) ).
fof(f534,plain,
( sQ20_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c9 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f320,f333]) ).
fof(f535,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| sk_c10 = multiply(inverse(sk_c3),sk_c3) ),
inference(paramodulation,[status(thm)],[f299,f262]) ).
fof(f551,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c9 = sk_c10 ),
inference(paramodulation,[status(thm)],[f321,f318]) ).
fof(f560,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f551,f534]) ).
fof(f561,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sQ20_spl ),
inference(contradiction_clause,[status(thm)],[f560]) ).
fof(f575,plain,
! [X0] : multiply(identity,X0) = X0,
inference(paramodulation,[status(thm)],[f262,f283]) ).
fof(f587,plain,
( ~ sQ6_spl
| ~ sQ15_spl
| inverse(sk_c6) != sk_c11 ),
inference(resolution,[status(thm)],[f218,f142]) ).
fof(f588,plain,
( ~ sQ11_spl
| ~ sQ15_spl
| inverse(sk_c1) != sk_c11 ),
inference(resolution,[status(thm)],[f218,f170]) ).
fof(f596,plain,
( ~ sQ6_spl
| ~ sQ15_spl
| ~ sQ5_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f138,f587]) ).
fof(f597,plain,
( ~ sQ6_spl
| ~ sQ15_spl
| ~ sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f596]) ).
fof(f598,plain,
( ~ sQ6_spl
| ~ sQ15_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f597]) ).
fof(f633,plain,
inverse(identity) = identity,
inference(paramodulation,[status(thm)],[f60,f305]) ).
fof(f651,plain,
( ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ17_spl
| inverse(sk_c11) != sk_c11
| sk_c10 != sk_c10 ),
inference(paramodulation,[status(thm)],[f298,f224]) ).
fof(f662,definition,
( sQ31_spl
<=> inverse(sk_c11) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f664,plain,
( sQ31_spl
| inverse(sk_c11) != sk_c11 ),
inference(component_clause,[status(thm)],[f662]) ).
fof(f665,plain,
( ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ17_spl
| ~ sQ31_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f651,f505,f662,f223,f157,f169]) ).
fof(f674,plain,
( ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ10_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f158,f588]) ).
fof(f675,plain,
( ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f674]) ).
fof(f676,plain,
( ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f675]) ).
fof(f709,plain,
( sQ19_spl
| ~ sQ0_spl
| multiply(sk_c10,sk_c9) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f119,f330]) ).
fof(f726,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| sk_c10 = identity ),
inference(forward_demodulation,[status(thm)],[f60,f535]) ).
fof(f729,definition,
( sQ34_spl
<=> sk_c9 = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f731,plain,
( sQ34_spl
| sk_c9 != sk_c9 ),
inference(component_clause,[status(thm)],[f729]) ).
fof(f746,plain,
( sQ34_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f731]) ).
fof(f747,plain,
sQ34_spl,
inference(contradiction_clause,[status(thm)],[f746]) ).
fof(f749,plain,
( ~ sQ10_spl
| ~ sQ12_spl
| ~ sQ13_spl
| sk_c1 = multiply(inverse(sk_c11),sk_c10) ),
inference(backward_demodulation,[status(thm)],[f726,f278]) ).
fof(f752,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| inverse(identity) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f726,f633]) ).
fof(f753,plain,
( ~ sQ13_spl
| ~ sQ12_spl
| sk_c2 = multiply(inverse(sk_c3),sk_c10) ),
inference(backward_demodulation,[status(thm)],[f726,f293]) ).
fof(f755,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ13_spl
| multiply(inverse(X0),X0) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f726,f60]) ).
fof(f760,plain,
( ~ sQ10_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| sk_c1 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f531,f749]) ).
fof(f761,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| inverse(sk_c10) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f726,f752]) ).
fof(f762,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| sk_c9 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f119,f761]) ).
fof(f763,plain,
( ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ14_spl
| sk_c2 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f294,f753]) ).
fof(f772,plain,
( sQ31_spl
| ~ sQ10_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| inverse(sk_c11) != sk_c1 ),
inference(backward_demodulation,[status(thm)],[f760,f664]) ).
fof(f782,plain,
( ~ sQ10_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| inverse(sk_c1) = sk_c1 ),
inference(backward_demodulation,[status(thm)],[f760,f158]) ).
fof(f785,plain,
( sQ31_spl
| ~ sQ10_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| inverse(sk_c1) != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f760,f772]) ).
fof(f798,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ13_spl
| inverse(sk_c9) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f762,f119]) ).
fof(f802,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| inverse(X0) != sk_c10
| multiply(X0,sk_c9) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f762,f227]) ).
fof(f803,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f762,f802]) ).
fof(f805,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| multiply(inverse(X0),X0) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f762,f755]) ).
fof(f806,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| inverse(inverse(sk_c9)) != sk_c9 ),
inference(resolution,[status(thm)],[f805,f803]) ).
fof(f834,plain,
( ~ sQ10_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f782,f785]) ).
fof(f835,plain,
( ~ sQ10_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| sQ31_spl ),
inference(contradiction_clause,[status(thm)],[f834]) ).
fof(f839,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| inverse(sk_c2) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f763,f798]) ).
fof(f840,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sk_c3 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f194,f839]) ).
fof(f846,plain,
( ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ0_spl
| sk_c3 = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f848,f763]) ).
fof(f847,plain,
( ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ14_spl
| inverse(sk_c3) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f848,f194]) ).
fof(f848,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sk_c3 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f763,f840]) ).
fof(f933,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ14_spl
| inverse(inverse(sk_c3)) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f846,f806]) ).
fof(f934,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ14_spl
| inverse(sk_c3) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f847,f933]) ).
fof(f935,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ14_spl
| sk_c3 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f847,f934]) ).
fof(f936,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ14_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f846,f935]) ).
fof(f937,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ14_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f936]) ).
fof(f938,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f937]) ).
fof(f966,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ4_spl
| ~ sQ9_spl
| ~ sQ3_spl
| multiply(sk_c8,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f472,f575]) ).
fof(f1035,plain,
( sQ19_spl
| ~ sQ0_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ3_spl
| multiply(sk_c8,sk_c9) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f473,f709]) ).
fof(f1036,plain,
( sQ19_spl
| ~ sQ0_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ3_spl
| sk_c9 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f966,f1035]) ).
fof(f1037,plain,
( sQ19_spl
| ~ sQ0_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ3_spl
| sk_c8 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f460,f1036]) ).
fof(f1038,plain,
( sQ19_spl
| ~ sQ0_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ3_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f473,f1037]) ).
fof(f1039,plain,
( sQ19_spl
| ~ sQ0_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1038]) ).
fof(f1040,plain,
( sQ19_spl
| ~ sQ0_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f1039]) ).
fof(f1041,plain,
$false,
inference(sat_refutation,[status(thm)],[f124,f128,f132,f136,f148,f152,f160,f161,f162,f163,f164,f165,f166,f167,f168,f172,f173,f176,f177,f184,f185,f186,f187,f190,f191,f192,f196,f197,f198,f199,f202,f203,f204,f208,f209,f210,f211,f212,f213,f214,f215,f216,f229,f236,f254,f334,f353,f357,f434,f510,f561,f598,f665,f676,f747,f835,f938,f1040]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP389-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n005.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 20:10:49 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.08/0.39 % Refutation found
% 0.08/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.43 % Elapsed time: 0.060223 seconds
% 0.13/0.43 % CPU time: 0.203171 seconds
% 0.13/0.43 % Total memory used: 106.166 MB
% 0.13/0.43 % Net memory used: 105.995 MB
%------------------------------------------------------------------------------