%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP235-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 12:33:10 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.39s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 61
% Syntax : Number of formulae : 275 ( 11 unt; 27 def)
% Number of atoms : 950 ( 328 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1258 ( 583 ~; 648 |; 0 &)
% ( 27 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 29 ( 27 usr; 28 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 51 ( 51 !; 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_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c2,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c2,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
! [X4,X5,X6,X1,X2,X3] :
( inverse(X3) != sk_c8
| multiply(X3,sk_c8) != X2
| multiply(sk_c8,X2) != sk_c7
| multiply(X1,sk_c7) != sk_c8
| inverse(X1) != sk_c8
| multiply(X6,sk_c8) != sk_c7
| inverse(X5) != X6
| multiply(X5,X6) != sk_c7
| multiply(X4,sk_c7) != sk_c8
| inverse(X4) != sk_c8
| inverse(sk_c8) != sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f36,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f37,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f38,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f39,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f40,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f41,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f42,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f43,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f44,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f45,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f46,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f47,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f48,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f49,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f50,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f51,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f52,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f53,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f54,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f55,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c2,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f56,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c2,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f57,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f58,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f59,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f60,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f61,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f62,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f63,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f64,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f65,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f66,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c3,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f67,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f68,plain,
! [X3] :
( inverse(X3) != sk_c8
| ! [X2] :
( multiply(X3,sk_c8) != X2
| multiply(sk_c8,X2) != sk_c7
| ! [X1] :
( multiply(X1,sk_c7) != sk_c8
| inverse(X1) != sk_c8
| ! [X6] :
( multiply(X6,sk_c8) != sk_c7
| ! [X5] :
( inverse(X5) != X6
| multiply(X5,X6) != sk_c7
| ! [X4] :
( multiply(X4,sk_c7) != sk_c8
| inverse(X4) != sk_c8
| inverse(sk_c8) != sk_c7 ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f34]) ).
fof(f69,plain,
! [X0,X1,X2,X3,X4,X5] :
( inverse(X5) != sk_c8
| multiply(X5,sk_c8) != X4
| multiply(sk_c8,X4) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| inverse(X3) != sk_c8
| multiply(X2,sk_c8) != sk_c7
| inverse(X1) != X2
| multiply(X1,X2) != sk_c7
| multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c8
| inverse(sk_c8) != sk_c7 ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f70,definition,
( sQ0_spl
<=> inverse(sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f71,plain,
( ~ sQ0_spl
| inverse(sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f72,plain,
( sQ0_spl
| inverse(sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f73,definition,
( sQ1_spl
<=> inverse(sk_c4) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f74,plain,
( ~ sQ1_spl
| inverse(sk_c4) = sk_c8 ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f76,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f38,f70,f73]) ).
fof(f77,definition,
( sQ2_spl
<=> multiply(sk_c4,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f78,plain,
( ~ sQ2_spl
| multiply(sk_c4,sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f77]) ).
fof(f80,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f39,f70,f77]) ).
fof(f81,definition,
( sQ3_spl
<=> multiply(sk_c8,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f82,plain,
( ~ sQ3_spl
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(component_clause,[status(thm)],[f81]) ).
fof(f84,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f40,f70,f81]) ).
fof(f85,definition,
( sQ4_spl
<=> multiply(sk_c5,sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ4_spl
| multiply(sk_c5,sk_c8) = sk_c6 ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f88,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f41,f70,f85]) ).
fof(f89,definition,
( sQ5_spl
<=> inverse(sk_c5) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f90,plain,
( ~ sQ5_spl
| inverse(sk_c5) = sk_c8 ),
inference(component_clause,[status(thm)],[f89]) ).
fof(f92,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f42,f70,f89]) ).
fof(f93,definition,
( sQ6_spl
<=> inverse(sk_c1) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ6_spl
| inverse(sk_c1) = sk_c8 ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f96,plain,
( sQ1_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f43,f93,f73]) ).
fof(f97,plain,
( sQ2_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f44,f93,f77]) ).
fof(f98,plain,
( sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f45,f93,f81]) ).
fof(f99,plain,
( sQ4_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f46,f93,f85]) ).
fof(f100,plain,
( sQ5_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f47,f93,f89]) ).
fof(f101,definition,
( sQ7_spl
<=> multiply(sk_c1,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f102,plain,
( ~ sQ7_spl
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f101]) ).
fof(f104,plain,
( sQ1_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f48,f101,f73]) ).
fof(f105,plain,
( sQ2_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f49,f101,f77]) ).
fof(f106,plain,
( sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f50,f101,f81]) ).
fof(f107,plain,
( sQ4_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f51,f101,f85]) ).
fof(f108,plain,
( sQ5_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f52,f101,f89]) ).
fof(f109,definition,
( sQ8_spl
<=> multiply(sk_c2,sk_c3) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f110,plain,
( ~ sQ8_spl
| multiply(sk_c2,sk_c3) = sk_c7 ),
inference(component_clause,[status(thm)],[f109]) ).
fof(f112,plain,
( sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f53,f109,f73]) ).
fof(f113,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f54,f109,f77]) ).
fof(f114,plain,
( sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f55,f109,f81]) ).
fof(f115,plain,
( sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f56,f109,f85]) ).
fof(f116,plain,
( sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f57,f109,f89]) ).
fof(f117,definition,
( sQ9_spl
<=> inverse(sk_c2) = sk_c3 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f118,plain,
( ~ sQ9_spl
| inverse(sk_c2) = sk_c3 ),
inference(component_clause,[status(thm)],[f117]) ).
fof(f120,plain,
( sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f58,f117,f73]) ).
fof(f121,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f59,f117,f77]) ).
fof(f122,plain,
( sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f60,f117,f81]) ).
fof(f123,plain,
( sQ4_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f61,f117,f85]) ).
fof(f124,plain,
( sQ5_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f62,f117,f89]) ).
fof(f125,definition,
( sQ10_spl
<=> multiply(sk_c3,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f126,plain,
( ~ sQ10_spl
| multiply(sk_c3,sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f125]) ).
fof(f128,plain,
( sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f63,f125,f73]) ).
fof(f129,plain,
( sQ2_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f64,f125,f77]) ).
fof(f130,plain,
( sQ3_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f65,f125,f81]) ).
fof(f131,plain,
( sQ4_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f66,f125,f85]) ).
fof(f132,plain,
( sQ5_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f67,f125,f89]) ).
fof(f133,definition,
! [X0] :
( sQ11_spl
<=> ( multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f134,plain,
! [X0] :
( ~ sQ11_spl
| multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c8 ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,definition,
! [X1,X2] :
( sQ12_spl
<=> ( multiply(X2,sk_c8) != sk_c7
| inverse(X1) != X2
| multiply(X1,X2) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f137,plain,
! [X0,X1] :
( ~ sQ12_spl
| multiply(X1,sk_c8) != sk_c7
| inverse(X0) != X1
| multiply(X0,X1) != sk_c7 ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f139,definition,
! [X4,X5] :
( sQ13_spl
<=> ( inverse(X5) != sk_c8
| multiply(X5,sk_c8) != X4
| multiply(sk_c8,X4) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f140,plain,
! [X0,X1] :
( ~ sQ13_spl
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != X0
| multiply(sk_c8,X0) != sk_c7 ),
inference(component_clause,[status(thm)],[f139]) ).
fof(f142,plain,
( sQ13_spl
| sQ12_spl
| sQ11_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f69,f70,f133,f136,f139]) ).
fof(f143,plain,
! [X0] :
( ~ sQ13_spl
| inverse(X0) != sk_c8
| multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ),
inference(destructive_equality_resolution,[status(thm)],[f140]) ).
fof(f146,plain,
! [X0] :
( ~ sQ8_spl
| multiply(sk_c7,X0) = multiply(sk_c2,multiply(sk_c3,X0)) ),
inference(paramodulation,[status(thm)],[f110,f37]) ).
fof(f147,plain,
! [X0] :
( ~ sQ10_spl
| multiply(sk_c7,X0) = multiply(sk_c3,multiply(sk_c8,X0)) ),
inference(paramodulation,[status(thm)],[f126,f37]) ).
fof(f148,plain,
! [X0] :
( ~ sQ2_spl
| multiply(sk_c8,X0) = multiply(sk_c4,multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f78,f37]) ).
fof(f156,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| multiply(sk_c7,sk_c8) = multiply(sk_c2,sk_c7) ),
inference(paramodulation,[status(thm)],[f126,f146]) ).
fof(f174,plain,
( ~ sQ10_spl
| ~ sQ13_spl
| inverse(sk_c3) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c7 ),
inference(paramodulation,[status(thm)],[f126,f143]) ).
fof(f175,plain,
( ~ sQ4_spl
| ~ sQ13_spl
| inverse(sk_c5) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7 ),
inference(paramodulation,[status(thm)],[f86,f143]) ).
fof(f179,definition,
( sQ15_spl
<=> inverse(sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f183,definition,
( sQ16_spl
<=> multiply(sk_c8,sk_c7) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f186,definition,
( sQ17_spl
<=> inverse(sk_c3) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f188,plain,
( sQ17_spl
| inverse(sk_c3) != sk_c8 ),
inference(component_clause,[status(thm)],[f186]) ).
fof(f189,plain,
( ~ sQ10_spl
| ~ sQ13_spl
| ~ sQ17_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f174,f183,f186,f139,f125]) ).
fof(f190,plain,
( ~ sQ4_spl
| ~ sQ13_spl
| ~ sQ5_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f175,f81,f89,f139,f85]) ).
fof(f191,plain,
! [X0] :
( ~ sQ12_spl
| multiply(inverse(X0),sk_c8) != sk_c7
| multiply(X0,inverse(X0)) != sk_c7 ),
inference(destructive_equality_resolution,[status(thm)],[f137]) ).
fof(f192,plain,
( ~ sQ6_spl
| ~ sQ12_spl
| multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c1,inverse(sk_c1)) != sk_c7 ),
inference(paramodulation,[status(thm)],[f94,f191]) ).
fof(f194,plain,
( ~ sQ1_spl
| ~ sQ12_spl
| multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c4,inverse(sk_c4)) != sk_c7 ),
inference(paramodulation,[status(thm)],[f74,f191]) ).
fof(f196,definition,
( sQ18_spl
<=> multiply(sk_c1,inverse(sk_c1)) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f198,plain,
( sQ18_spl
| multiply(sk_c1,inverse(sk_c1)) != sk_c7 ),
inference(component_clause,[status(thm)],[f196]) ).
fof(f199,definition,
( sQ19_spl
<=> multiply(sk_c8,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f201,plain,
( sQ19_spl
| multiply(sk_c8,sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f199]) ).
fof(f202,plain,
( ~ sQ6_spl
| ~ sQ12_spl
| ~ sQ19_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f192,f196,f199,f136,f93]) ).
fof(f207,definition,
( sQ21_spl
<=> multiply(sk_c4,inverse(sk_c4)) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f209,plain,
( sQ21_spl
| multiply(sk_c4,inverse(sk_c4)) != sk_c7 ),
inference(component_clause,[status(thm)],[f207]) ).
fof(f210,plain,
( ~ sQ1_spl
| ~ sQ12_spl
| ~ sQ19_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f194,f207,f199,f136,f73]) ).
fof(f216,plain,
( ~ sQ0_spl
| multiply(sk_c7,sk_c8) = identity ),
inference(paramodulation,[status(thm)],[f71,f36]) ).
fof(f217,plain,
( ~ sQ6_spl
| multiply(sk_c8,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f94,f36]) ).
fof(f220,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f36,f37]) ).
fof(f221,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ8_spl
| multiply(sk_c2,sk_c7) = identity ),
inference(forward_demodulation,[status(thm)],[f156,f216]) ).
fof(f222,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f35,f220]) ).
fof(f223,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| multiply(sk_c7,sk_c8) = identity ),
inference(backward_demodulation,[status(thm)],[f221,f156]) ).
fof(f244,plain,
( ~ sQ6_spl
| sk_c1 = multiply(inverse(sk_c8),identity) ),
inference(paramodulation,[status(thm)],[f217,f222]) ).
fof(f247,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f35,f222]) ).
fof(f250,plain,
( ~ sQ7_spl
| sk_c7 = multiply(inverse(sk_c1),sk_c8) ),
inference(paramodulation,[status(thm)],[f102,f222]) ).
fof(f253,plain,
( ~ sQ8_spl
| sk_c3 = multiply(inverse(sk_c2),sk_c7) ),
inference(paramodulation,[status(thm)],[f110,f222]) ).
fof(f257,plain,
( ~ sQ4_spl
| sk_c8 = multiply(inverse(sk_c5),sk_c6) ),
inference(paramodulation,[status(thm)],[f86,f222]) ).
fof(f260,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| sk_c1 = multiply(sk_c7,identity) ),
inference(forward_demodulation,[status(thm)],[f71,f244]) ).
fof(f262,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| sk_c7 = multiply(sk_c8,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f94,f250]) ).
fof(f265,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c3 = multiply(sk_c3,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f118,f253]) ).
fof(f266,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| sk_c8 = multiply(sk_c8,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f90,f257]) ).
fof(f283,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ10_spl
| multiply(sk_c7,sk_c8) = multiply(sk_c3,sk_c7) ),
inference(paramodulation,[status(thm)],[f262,f147]) ).
fof(f284,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| sk_c8 = multiply(inverse(sk_c8),sk_c7) ),
inference(paramodulation,[status(thm)],[f262,f222]) ).
fof(f286,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| identity = multiply(sk_c3,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f223,f283]) ).
fof(f287,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| sk_c8 = multiply(sk_c7,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f71,f284]) ).
fof(f288,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ13_spl
| inverse(sk_c7) != sk_c8
| multiply(sk_c8,identity) != sk_c7 ),
inference(paramodulation,[status(thm)],[f223,f143]) ).
fof(f289,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ13_spl
| inverse(sk_c8) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c7 ),
inference(paramodulation,[status(thm)],[f262,f143]) ).
fof(f290,plain,
( ~ sQ13_spl
| inverse(inverse(identity)) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7 ),
inference(paramodulation,[status(thm)],[f247,f143]) ).
fof(f291,plain,
( ~ sQ13_spl
| inverse(inverse(sk_c8)) != sk_c8
| multiply(sk_c8,identity) != sk_c7 ),
inference(paramodulation,[status(thm)],[f36,f143]) ).
fof(f292,plain,
( ~ sQ13_spl
| inverse(identity) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7 ),
inference(paramodulation,[status(thm)],[f35,f143]) ).
fof(f295,definition,
( sQ23_spl
<=> multiply(sk_c8,identity) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f298,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ15_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f288,f295,f179,f139,f70,f109,f125]) ).
fof(f299,definition,
( sQ24_spl
<=> inverse(sk_c8) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f302,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ13_spl
| ~ sQ24_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f289,f183,f299,f139,f93,f101]) ).
fof(f303,definition,
( sQ25_spl
<=> inverse(inverse(identity)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f306,plain,
( ~ sQ13_spl
| ~ sQ25_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f290,f199,f303,f139]) ).
fof(f307,definition,
( sQ26_spl
<=> inverse(inverse(sk_c8)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f310,plain,
( ~ sQ13_spl
| ~ sQ26_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f291,f295,f307,f139]) ).
fof(f311,definition,
( sQ27_spl
<=> inverse(identity) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f313,plain,
( sQ27_spl
| inverse(identity) != sk_c8 ),
inference(component_clause,[status(thm)],[f311]) ).
fof(f314,plain,
( ~ sQ13_spl
| ~ sQ27_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f292,f199,f311,f139]) ).
fof(f319,plain,
( ~ sQ2_spl
| ~ sQ11_spl
| sk_c8 != sk_c8
| inverse(sk_c4) != sk_c8 ),
inference(paramodulation,[status(thm)],[f78,f134]) ).
fof(f322,plain,
( ~ sQ11_spl
| sk_c7 != sk_c8
| inverse(identity) != sk_c8 ),
inference(paramodulation,[status(thm)],[f35,f134]) ).
fof(f324,definition,
( sQ28_spl
<=> sk_c8 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f326,plain,
( sQ28_spl
| sk_c8 != sk_c8 ),
inference(component_clause,[status(thm)],[f324]) ).
fof(f327,plain,
( ~ sQ2_spl
| ~ sQ11_spl
| ~ sQ28_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f319,f73,f324,f133,f77]) ).
fof(f328,definition,
( sQ29_spl
<=> sk_c7 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f330,plain,
( sQ29_spl
| sk_c7 != sk_c8 ),
inference(component_clause,[status(thm)],[f328]) ).
fof(f339,plain,
( ~ sQ11_spl
| ~ sQ29_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f322,f311,f328,f133]) ).
fof(f340,plain,
( sQ28_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f326]) ).
fof(f341,plain,
sQ28_spl,
inference(contradiction_clause,[status(thm)],[f340]) ).
fof(f362,plain,
( ~ sQ7_spl
| sk_c7 = multiply(inverse(sk_c1),sk_c8) ),
inference(paramodulation,[status(thm)],[f102,f222]) ).
fof(f364,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| sk_c7 = multiply(sk_c8,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f94,f362]) ).
fof(f365,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f364,f201]) ).
fof(f366,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| sQ19_spl ),
inference(contradiction_clause,[status(thm)],[f365]) ).
fof(f388,plain,
( sQ27_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ0_spl
| inverse(sk_c3) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f393,f313]) ).
fof(f392,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ0_spl
| multiply(sk_c3,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f393,f35]) ).
fof(f393,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ0_spl
| sk_c3 = identity ),
inference(forward_demodulation,[status(thm)],[f286,f265]) ).
fof(f394,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ13_spl
| inverse(sk_c3) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7 ),
inference(paramodulation,[status(thm)],[f392,f143]) ).
fof(f397,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ17_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f394,f199,f186,f139,f70,f125,f93,f101,f117,f109]) ).
fof(f398,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| sk_c1 = multiply(sk_c7,sk_c3) ),
inference(forward_demodulation,[status(thm)],[f393,f260]) ).
fof(f402,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ6_spl
| multiply(sk_c2,sk_c7) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f393,f221]) ).
fof(f403,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ6_spl
| sk_c7 = multiply(inverse(sk_c2),sk_c3) ),
inference(paramodulation,[status(thm)],[f402,f222]) ).
fof(f405,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ6_spl
| sk_c7 = multiply(sk_c3,sk_c3) ),
inference(forward_demodulation,[status(thm)],[f118,f403]) ).
fof(f406,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ6_spl
| sk_c7 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f392,f405]) ).
fof(f409,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| sk_c1 = multiply(sk_c3,sk_c3) ),
inference(backward_demodulation,[status(thm)],[f406,f398]) ).
fof(f410,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c8 = multiply(sk_c7,sk_c3) ),
inference(backward_demodulation,[status(thm)],[f406,f287]) ).
fof(f417,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ6_spl
| inverse(sk_c8) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f406,f71]) ).
fof(f419,plain,
( sQ29_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ6_spl
| sk_c3 != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f406,f330]) ).
fof(f421,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| sk_c1 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f392,f409]) ).
fof(f422,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c8 = multiply(sk_c3,sk_c3) ),
inference(forward_demodulation,[status(thm)],[f406,f410]) ).
fof(f423,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c8 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f392,f422]) ).
fof(f428,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| inverse(sk_c3) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f421,f94]) ).
fof(f429,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f428,f188]) ).
fof(f430,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f429]) ).
fof(f433,plain,
( sQ27_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f388,f186,f70,f125,f93,f101,f117,f109,f311]) ).
fof(f434,plain,
( sQ18_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| multiply(sk_c3,inverse(sk_c1)) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f421,f198]) ).
fof(f435,plain,
( sQ18_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| inverse(sk_c1) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f392,f434]) ).
fof(f436,plain,
( sQ18_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| inverse(sk_c3) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f421,f435]) ).
fof(f437,plain,
( sQ18_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| inverse(sk_c3) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f406,f436]) ).
fof(f440,plain,
( sQ21_spl
| ~ sQ1_spl
| multiply(sk_c4,sk_c8) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f74,f209]) ).
fof(f461,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ6_spl
| inverse(sk_c3) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f423,f417]) ).
fof(f469,plain,
( sQ18_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f461,f437]) ).
fof(f470,plain,
( sQ18_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f469]) ).
fof(f471,plain,
( sQ18_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f470]) ).
fof(f472,plain,
( sQ29_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ6_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f423,f419]) ).
fof(f473,plain,
( sQ29_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f472]) ).
fof(f474,plain,
( sQ29_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f473]) ).
fof(f479,plain,
( ~ sQ2_spl
| sk_c7 = multiply(inverse(sk_c4),sk_c8) ),
inference(paramodulation,[status(thm)],[f78,f222]) ).
fof(f481,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sk_c7 = multiply(sk_c8,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f74,f479]) ).
fof(f488,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c8 = multiply(sk_c7,sk_c6) ),
inference(backward_demodulation,[status(thm)],[f497,f266]) ).
fof(f489,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| multiply(sk_c4,sk_c7) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f497,f78]) ).
fof(f491,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| inverse(sk_c7) != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f497,f72]) ).
fof(f494,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| inverse(sk_c5) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f497,f90]) ).
fof(f496,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| inverse(sk_c4) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f497,f74]) ).
fof(f497,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sk_c8 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f266,f82]) ).
fof(f498,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c7 = multiply(sk_c7,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f497,f488]) ).
fof(f504,plain,
( sQ19_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| multiply(sk_c7,sk_c8) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f497,f201]) ).
fof(f505,plain,
( sQ19_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| multiply(sk_c7,sk_c7) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f497,f504]) ).
fof(f506,plain,
( sQ21_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| multiply(sk_c4,sk_c7) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f497,f440]) ).
fof(f517,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c7,sk_c5) = identity ),
inference(paramodulation,[status(thm)],[f494,f36]) ).
fof(f525,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sQ21_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f489,f506]) ).
fof(f526,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sQ21_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f525]) ).
fof(f574,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sk_c7 = multiply(sk_c7,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f497,f481]) ).
fof(f575,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sk_c7 = multiply(sk_c7,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f497,f574]) ).
fof(f576,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f575,f505]) ).
fof(f577,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sQ19_spl ),
inference(contradiction_clause,[status(thm)],[f576]) ).
fof(f584,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c6 = multiply(inverse(sk_c7),sk_c7) ),
inference(paramodulation,[status(thm)],[f498,f222]) ).
fof(f586,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f36,f584]) ).
fof(f589,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| multiply(sk_c6,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f586,f35]) ).
fof(f609,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f586,f517]) ).
fof(f624,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| multiply(sk_c7,X0) = multiply(sk_c4,multiply(sk_c7,X0)) ),
inference(forward_demodulation,[status(thm)],[f497,f148]) ).
fof(f626,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| multiply(sk_c7,sk_c5) = multiply(sk_c4,sk_c6) ),
inference(paramodulation,[status(thm)],[f609,f624]) ).
fof(f632,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| sk_c6 = multiply(sk_c4,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f609,f626]) ).
fof(f640,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| sk_c6 = multiply(inverse(sk_c4),sk_c6) ),
inference(paramodulation,[status(thm)],[f632,f222]) ).
fof(f642,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c6 = multiply(sk_c7,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f496,f640]) ).
fof(f643,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c6 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f498,f642]) ).
fof(f649,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ1_spl
| multiply(sk_c6,sk_c5) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f643,f609]) ).
fof(f654,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ1_spl
| inverse(sk_c7) != sk_c6 ),
inference(backward_demodulation,[status(thm)],[f643,f491]) ).
fof(f655,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ1_spl
| inverse(sk_c5) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f643,f494]) ).
fof(f664,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c5 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f589,f649]) ).
fof(f668,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ1_spl
| inverse(sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f643,f654]) ).
fof(f687,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ1_spl
| inverse(sk_c5) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f664,f668]) ).
fof(f688,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ1_spl
| inverse(sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f664,f687]) ).
fof(f689,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ1_spl
| inverse(sk_c5) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f664,f655]) ).
fof(f690,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f689,f688]) ).
fof(f691,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f690]) ).
fof(f692,plain,
$false,
inference(sat_refutation,[status(thm)],[f76,f80,f84,f88,f92,f96,f97,f98,f99,f100,f104,f105,f106,f107,f108,f112,f113,f114,f115,f116,f120,f121,f122,f123,f124,f128,f129,f130,f131,f132,f142,f189,f190,f202,f210,f298,f302,f306,f310,f314,f327,f339,f341,f366,f397,f430,f433,f471,f474,f526,f577,f691]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP235-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n017.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 20:02:26 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.12/0.39 % Refutation found
% 0.12/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.42 % Elapsed time: 0.056939 seconds
% 0.12/0.42 % CPU time: 0.201293 seconds
% 0.12/0.42 % Total memory used: 104.671 MB
% 0.12/0.42 % Net memory used: 104.431 MB
%------------------------------------------------------------------------------