%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP281-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 12:33:18 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.39s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 50
% Syntax : Number of formulae : 257 ( 12 unt; 18 def)
% Number of atoms : 931 ( 311 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1280 ( 606 ~; 656 |; 0 &)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 19 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 62 ( 62 !; 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_c7,sk_c8) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c5) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( inverse(sk_c5) = sk_c7
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
! [X3,X4,X5,X1,X2] :
( multiply(X2,sk_c6) != sk_c7
| inverse(X2) != sk_c7
| multiply(X1,sk_c7) != sk_c8
| inverse(X1) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6
| inverse(X5) != sk_c8
| multiply(X5,sk_c8) != X4
| multiply(sk_c8,X4) != sk_c7
| inverse(X3) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
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,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f39,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f40,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f43,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f44,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f45,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f46,plain,
( inverse(sk_c5) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f47,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f48,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f49,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f50,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f51,plain,
( inverse(sk_c5) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f52,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f53,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f54,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f55,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f56,plain,
( inverse(sk_c5) = sk_c7
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f57,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f58,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f59,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f60,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f61,plain,
( inverse(sk_c5) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f62,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f63,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f64,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f65,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f66,plain,
( inverse(sk_c5) = sk_c7
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f67,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f68,plain,
! [X2] :
( multiply(X2,sk_c6) != sk_c7
| inverse(X2) != sk_c7
| ! [X1] :
( multiply(X1,sk_c7) != sk_c8
| inverse(X1) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6
| ! [X5] :
( inverse(X5) != sk_c8
| ! [X4] :
( multiply(X5,sk_c8) != X4
| multiply(sk_c8,X4) != sk_c7
| ! [X3] :
( inverse(X3) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ) ) ) ) ),
inference(miniscoping,[status(thm)],[f34]) ).
fof(f69,plain,
! [X0,X1,X2,X3,X4] :
( multiply(X4,sk_c6) != sk_c7
| inverse(X4) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| inverse(X3) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != X1
| multiply(sk_c8,X1) != sk_c7
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f70,definition,
( sQ0_spl
<=> multiply(sk_c8,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f71,plain,
( ~ sQ0_spl
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f73,definition,
( sQ1_spl
<=> multiply(sk_c7,sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f74,plain,
( ~ sQ1_spl
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f75,plain,
( sQ1_spl
| multiply(sk_c7,sk_c8) != sk_c6 ),
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
<=> inverse(sk_c4) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f78,plain,
( ~ sQ2_spl
| inverse(sk_c4) = 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_c4,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f82,plain,
( ~ sQ3_spl
| multiply(sk_c4,sk_c7) = sk_c8 ),
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
<=> inverse(sk_c5) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ4_spl
| inverse(sk_c5) = sk_c7 ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f89,definition,
( sQ5_spl
<=> multiply(sk_c5,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f90,plain,
( ~ sQ5_spl
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(component_clause,[status(thm)],[f89]) ).
fof(f93,definition,
( sQ6_spl
<=> multiply(sk_c1,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ6_spl
| multiply(sk_c1,sk_c8) = sk_c7 ),
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
<=> inverse(sk_c1) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f102,plain,
( ~ sQ7_spl
| inverse(sk_c1) = 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_c8,sk_c3) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f110,plain,
( ~ sQ8_spl
| multiply(sk_c8,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
<=> multiply(sk_c2,sk_c8) = sk_c3 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f118,plain,
( ~ sQ9_spl
| multiply(sk_c2,sk_c8) = 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
<=> inverse(sk_c2) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f126,plain,
( ~ sQ10_spl
| inverse(sk_c2) = sk_c8 ),
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
<=> ( inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f134,plain,
! [X0] :
( ~ sQ11_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,definition,
! [X1,X2] :
( sQ12_spl
<=> ( inverse(X2) != sk_c8
| multiply(X2,sk_c8) != X1
| multiply(sk_c8,X1) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f137,plain,
! [X0,X1] :
( ~ sQ12_spl
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != X0
| multiply(sk_c8,X0) != sk_c7 ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f139,definition,
! [X3] :
( sQ13_spl
<=> ( multiply(X3,sk_c7) != sk_c8
| inverse(X3) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f140,plain,
! [X0] :
( ~ sQ13_spl
| multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c8 ),
inference(component_clause,[status(thm)],[f139]) ).
fof(f142,definition,
! [X4] :
( sQ14_spl
<=> ( multiply(X4,sk_c6) != sk_c7
| inverse(X4) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f143,plain,
! [X0] :
( ~ sQ14_spl
| multiply(X0,sk_c6) != sk_c7
| inverse(X0) != sk_c7 ),
inference(component_clause,[status(thm)],[f142]) ).
fof(f145,plain,
( sQ14_spl
| sQ13_spl
| ~ sQ1_spl
| sQ12_spl
| sQ11_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f69,f70,f133,f136,f73,f139,f142]) ).
fof(f146,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| inverse(sk_c5) != sk_c7 ),
inference(resolution,[status(thm)],[f143,f90]) ).
fof(f148,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| ~ sQ4_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f86,f146]) ).
fof(f149,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f148]) ).
fof(f150,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f149]) ).
fof(f151,plain,
( ~ sQ3_spl
| ~ sQ13_spl
| inverse(sk_c4) != sk_c8 ),
inference(resolution,[status(thm)],[f140,f82]) ).
fof(f152,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| sk_c6 != sk_c8
| inverse(sk_c8) != sk_c8 ),
inference(paramodulation,[status(thm)],[f71,f140]) ).
fof(f154,plain,
( ~ sQ3_spl
| ~ sQ13_spl
| ~ sQ2_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f78,f151]) ).
fof(f155,plain,
( ~ sQ3_spl
| ~ sQ13_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f154]) ).
fof(f156,plain,
( ~ sQ3_spl
| ~ sQ13_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f155]) ).
fof(f157,plain,
! [X0] :
( ~ sQ12_spl
| inverse(X0) != sk_c8
| multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ),
inference(destructive_equality_resolution,[status(thm)],[f137]) ).
fof(f158,plain,
( ~ sQ6_spl
| ~ sQ11_spl
| inverse(sk_c1) != sk_c8 ),
inference(resolution,[status(thm)],[f134,f94]) ).
fof(f161,plain,
( ~ sQ6_spl
| ~ sQ11_spl
| ~ sQ7_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f102,f158]) ).
fof(f162,plain,
( ~ sQ6_spl
| ~ sQ11_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f161]) ).
fof(f163,plain,
( ~ sQ6_spl
| ~ sQ11_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f162]) ).
fof(f169,plain,
! [X0] :
( ~ sQ3_spl
| multiply(sk_c8,X0) = multiply(sk_c4,multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f82,f37]) ).
fof(f170,plain,
! [X0] :
( ~ sQ5_spl
| multiply(sk_c7,X0) = multiply(sk_c5,multiply(sk_c6,X0)) ),
inference(paramodulation,[status(thm)],[f90,f37]) ).
fof(f175,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| inverse(sk_c2) != sk_c8
| multiply(sk_c8,sk_c3) != sk_c7 ),
inference(paramodulation,[status(thm)],[f118,f157]) ).
fof(f180,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f175,f109,f125,f136,f117]) ).
fof(f182,definition,
( sQ16_spl
<=> inverse(sk_c8) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f184,plain,
( sQ16_spl
| inverse(sk_c8) != sk_c8 ),
inference(component_clause,[status(thm)],[f182]) ).
fof(f185,definition,
( sQ17_spl
<=> sk_c6 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f186,plain,
( ~ sQ17_spl
| sk_c6 = sk_c8 ),
inference(component_clause,[status(thm)],[f185]) ).
fof(f187,plain,
( sQ17_spl
| sk_c6 != sk_c8 ),
inference(component_clause,[status(thm)],[f185]) ).
fof(f188,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ17_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f152,f182,f185,f139,f70]) ).
fof(f195,plain,
( ~ sQ10_spl
| multiply(sk_c8,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f126,f36]) ).
fof(f196,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f36,f37]) ).
fof(f197,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f35,f196]) ).
fof(f198,plain,
! [X0] :
( ~ sQ1_spl
| multiply(sk_c6,X0) = multiply(sk_c7,multiply(sk_c8,X0)) ),
inference(paramodulation,[status(thm)],[f74,f37]) ).
fof(f208,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f35,f197]) ).
fof(f210,plain,
( ~ sQ6_spl
| sk_c8 = multiply(inverse(sk_c1),sk_c7) ),
inference(paramodulation,[status(thm)],[f94,f197]) ).
fof(f215,plain,
( ~ sQ9_spl
| sk_c8 = multiply(inverse(sk_c2),sk_c3) ),
inference(paramodulation,[status(thm)],[f118,f197]) ).
fof(f219,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| sk_c8 = multiply(sk_c8,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f102,f210]) ).
fof(f220,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c8 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f71,f219]) ).
fof(f221,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f220,f187]) ).
fof(f222,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f221]) ).
fof(f223,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| sk_c8 = multiply(sk_c8,sk_c3) ),
inference(forward_demodulation,[status(thm)],[f126,f215]) ).
fof(f224,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c8 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f110,f223]) ).
fof(f226,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| multiply(sk_c7,sk_c2) = identity ),
inference(backward_demodulation,[status(thm)],[f224,f195]) ).
fof(f229,plain,
( sQ16_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| inverse(sk_c8) != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f224,f184]) ).
fof(f231,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| multiply(sk_c7,sk_c7) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f224,f71]) ).
fof(f233,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c7,sk_c3) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f224,f110]) ).
fof(f237,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| inverse(sk_c2) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f224,f126]) ).
fof(f238,plain,
( sQ16_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| inverse(sk_c7) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f224,f229]) ).
fof(f243,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ17_spl
| sk_c8 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f246,f224]) ).
fof(f246,plain,
( ~ sQ17_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c6 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f224,f186]) ).
fof(f247,plain,
( sQ16_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ17_spl
| inverse(sk_c6) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f246,f238]) ).
fof(f248,plain,
( sQ16_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ17_spl
| inverse(sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f246,f247]) ).
fof(f266,definition,
( sQ22_spl
<=> sk_c6 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f268,plain,
( sQ22_spl
| sk_c6 != sk_c6 ),
inference(component_clause,[status(thm)],[f266]) ).
fof(f270,plain,
( sQ1_spl
| ~ sQ17_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| multiply(sk_c6,sk_c8) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f246,f75]) ).
fof(f271,plain,
( sQ1_spl
| ~ sQ17_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| multiply(sk_c6,sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f243,f270]) ).
fof(f272,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ17_spl
| multiply(sk_c6,sk_c7) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f246,f231]) ).
fof(f273,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ17_spl
| multiply(sk_c6,sk_c6) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f246,f272]) ).
fof(f274,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ17_spl
| sk_c6 = multiply(inverse(sk_c6),sk_c6) ),
inference(paramodulation,[status(thm)],[f273,f197]) ).
fof(f276,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ17_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f36,f274]) ).
fof(f281,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ17_spl
| multiply(inverse(X0),X0) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f276,f36]) ).
fof(f282,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ17_spl
| multiply(sk_c6,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f276,f35]) ).
fof(f285,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ17_spl
| inverse(sk_c2) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f246,f237]) ).
fof(f290,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ17_spl
| multiply(sk_c6,sk_c3) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f246,f233]) ).
fof(f291,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ17_spl
| ~ sQ0_spl
| sk_c3 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f282,f290]) ).
fof(f292,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ17_spl
| multiply(sk_c3,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f300,f282]) ).
fof(f294,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ17_spl
| ~ sQ0_spl
| inverse(sk_c2) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f300,f285]) ).
fof(f296,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ17_spl
| sk_c3 = identity ),
inference(backward_demodulation,[status(thm)],[f300,f276]) ).
fof(f299,plain,
( ~ sQ17_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c3 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f300,f246]) ).
fof(f300,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ17_spl
| ~ sQ0_spl
| sk_c3 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f246,f291]) ).
fof(f304,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ17_spl
| ~ sQ0_spl
| X0 = multiply(sk_c3,multiply(sk_c2,X0)) ),
inference(paramodulation,[status(thm)],[f294,f197]) ).
fof(f305,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ17_spl
| ~ sQ0_spl
| X0 = multiply(sk_c2,X0) ),
inference(forward_demodulation,[status(thm)],[f292,f304]) ).
fof(f329,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ17_spl
| ~ sQ0_spl
| multiply(sk_c3,sk_c2) = identity ),
inference(forward_demodulation,[status(thm)],[f299,f226]) ).
fof(f330,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ17_spl
| ~ sQ0_spl
| sk_c2 = identity ),
inference(forward_demodulation,[status(thm)],[f292,f329]) ).
fof(f333,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ17_spl
| ~ sQ0_spl
| inverse(sk_c2) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f340,f294]) ).
fof(f336,plain,
( ~ sQ17_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c2 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f340,f299]) ).
fof(f339,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ17_spl
| ~ sQ0_spl
| sk_c2 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f340,f300]) ).
fof(f340,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ17_spl
| ~ sQ0_spl
| sk_c2 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f296,f330]) ).
fof(f351,plain,
( sQ1_spl
| ~ sQ17_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| multiply(sk_c2,sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f339,f271]) ).
fof(f352,plain,
( sQ1_spl
| ~ sQ17_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f305,f351]) ).
fof(f353,plain,
( sQ1_spl
| ~ sQ17_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c2 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f339,f352]) ).
fof(f354,plain,
( sQ1_spl
| ~ sQ17_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f339,f353]) ).
fof(f355,plain,
( sQ1_spl
| ~ sQ17_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f354]) ).
fof(f356,plain,
( sQ1_spl
| ~ sQ17_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f355]) ).
fof(f357,plain,
( sQ16_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ17_spl
| ~ sQ0_spl
| inverse(sk_c2) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f339,f248]) ).
fof(f358,plain,
( sQ16_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ17_spl
| ~ sQ0_spl
| sk_c2 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f333,f357]) ).
fof(f359,plain,
( sQ16_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ17_spl
| ~ sQ0_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f339,f358]) ).
fof(f360,plain,
( sQ16_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ17_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f359]) ).
fof(f361,plain,
( sQ16_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ17_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f360]) ).
fof(f376,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ17_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| multiply(X0,sk_c6) != sk_c7
| inverse(X0) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f336,f143]) ).
fof(f377,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ17_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| multiply(X0,sk_c2) != sk_c7
| inverse(X0) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f339,f376]) ).
fof(f378,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ17_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| multiply(X0,sk_c2) != sk_c2
| inverse(X0) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f336,f377]) ).
fof(f384,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ17_spl
| multiply(inverse(X0),X0) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f339,f281]) ).
fof(f392,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ17_spl
| ~ sQ14_spl
| inverse(inverse(sk_c2)) != sk_c2 ),
inference(resolution,[status(thm)],[f378,f384]) ).
fof(f399,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ17_spl
| ~ sQ14_spl
| inverse(sk_c2) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f333,f392]) ).
fof(f400,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ17_spl
| ~ sQ14_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f333,f399]) ).
fof(f401,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ17_spl
| ~ sQ14_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f400]) ).
fof(f402,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ17_spl
| ~ sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f401]) ).
fof(f403,plain,
( sQ22_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f268]) ).
fof(f404,plain,
sQ22_spl,
inference(contradiction_clause,[status(thm)],[f403]) ).
fof(f406,plain,
! [X0] :
( ~ sQ2_spl
| X0 = multiply(sk_c8,multiply(sk_c4,X0)) ),
inference(paramodulation,[status(thm)],[f78,f197]) ).
fof(f407,plain,
( ~ sQ5_spl
| sk_c6 = multiply(inverse(sk_c5),sk_c7) ),
inference(paramodulation,[status(thm)],[f90,f197]) ).
fof(f409,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| sk_c6 = multiply(sk_c7,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f86,f407]) ).
fof(f410,plain,
! [X0] : multiply(identity,X0) = X0,
inference(paramodulation,[status(thm)],[f197,f208]) ).
fof(f420,plain,
( ~ sQ3_spl
| sk_c7 = multiply(inverse(sk_c4),sk_c8) ),
inference(paramodulation,[status(thm)],[f82,f197]) ).
fof(f422,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| sk_c7 = multiply(sk_c8,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f78,f420]) ).
fof(f486,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| multiply(sk_c8,sk_c8) = multiply(sk_c4,sk_c6) ),
inference(paramodulation,[status(thm)],[f74,f169]) ).
fof(f490,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c7 = multiply(sk_c4,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f422,f486]) ).
fof(f496,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| multiply(sk_c6,sk_c8) = multiply(sk_c7,sk_c7) ),
inference(paramodulation,[status(thm)],[f422,f198]) ).
fof(f500,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c6,sk_c8) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f409,f496]) ).
fof(f503,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c6 = multiply(sk_c8,sk_c7) ),
inference(paramodulation,[status(thm)],[f490,f406]) ).
fof(f506,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f503,f70,f77,f81,f73]) ).
fof(f510,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c7,sk_c8) = multiply(sk_c5,sk_c6) ),
inference(paramodulation,[status(thm)],[f500,f170]) ).
fof(f511,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c8 = multiply(inverse(sk_c6),sk_c6) ),
inference(paramodulation,[status(thm)],[f500,f197]) ).
fof(f513,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c6 = multiply(sk_c5,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f74,f510]) ).
fof(f514,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c6 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f90,f513]) ).
fof(f515,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c8 = identity ),
inference(forward_demodulation,[status(thm)],[f36,f511]) ).
fof(f522,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c6 = multiply(sk_c8,sk_c8) ),
inference(backward_demodulation,[status(thm)],[f514,f422]) ).
fof(f528,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| multiply(sk_c5,sk_c6) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f514,f90]) ).
fof(f529,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| inverse(sk_c5) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f514,f86]) ).
fof(f536,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c8,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f515,f410]) ).
fof(f550,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| X0 = multiply(sk_c4,X0) ),
inference(backward_demodulation,[status(thm)],[f536,f406]) ).
fof(f563,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c6 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f536,f522]) ).
fof(f564,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f563,f187]) ).
fof(f565,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f564]) ).
fof(f590,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f536,f157]) ).
fof(f591,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f514,f590]) ).
fof(f593,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ12_spl
| inverse(sk_c4) != sk_c8
| sk_c8 != sk_c6 ),
inference(paramodulation,[status(thm)],[f550,f591]) ).
fof(f597,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f593,f185,f77,f136,f85,f89,f73,f81]) ).
fof(f603,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f514,f134]) ).
fof(f648,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f563,f603]) ).
fof(f649,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f563,f648]) ).
fof(f651,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ11_spl
| inverse(sk_c5) != sk_c6 ),
inference(resolution,[status(thm)],[f649,f528]) ).
fof(f660,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ11_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f529,f651]) ).
fof(f661,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f660]) ).
fof(f662,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f661]) ).
fof(f663,plain,
$false,
inference(sat_refutation,[status(thm)],[f76,f80,f84,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,f145,f150,f156,f163,f180,f188,f222,f356,f361,f402,f404,f506,f565,f597,f662]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP281-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n010.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sun Sep 20 20:08:54 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.11/0.36 % Drodi V4.1.1
% 0.11/0.39 % Refutation found
% 0.11/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.43 % Elapsed time: 0.075538 seconds
% 0.11/0.43 % CPU time: 0.265434 seconds
% 0.11/0.43 % Total memory used: 104.463 MB
% 0.11/0.43 % Net memory used: 104.209 MB
%------------------------------------------------------------------------------