%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP255-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:33:13 PM UTC 2026
% Result : Unsatisfiable 0.04s 0.33s
% Output : CNFRefutation 0.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 62
% Syntax : Number of formulae : 348 ( 11 unt; 28 def)
% Number of atoms : 1376 ( 389 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1978 ( 950 ~;1000 |; 0 &)
% ( 28 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 30 ( 28 usr; 29 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 76 ( 76 !; 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_c7,sk_c8) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c5) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( inverse(sk_c5) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c5) = sk_c7
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c3,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/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
| multiply(X5,sk_c8) != sk_c6
| inverse(X5) != sk_c6
| inverse(X4) != sk_c7
| multiply(X4,sk_c7) != sk_c6
| inverse(X3) != sk_c8
| multiply(X3,sk_c8) != sk_c7 ),
file('/export/starexec/sandbox2/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_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f39,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f40,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f41,plain,
( inverse(sk_c5) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f42,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f43,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f44,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f45,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f46,plain,
( inverse(sk_c5) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f47,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f48,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f49,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f50,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f51,plain,
( inverse(sk_c5) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f52,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f53,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f54,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f55,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f56,plain,
( inverse(sk_c5) = sk_c7
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f57,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f58,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c3) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f59,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c3) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f60,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c3) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f61,plain,
( inverse(sk_c5) = sk_c7
| inverse(sk_c3) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f62,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c3) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f63,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c3,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f64,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f65,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f66,plain,
( inverse(sk_c5) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f67,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c6 ),
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] :
( multiply(X5,sk_c8) != sk_c6
| inverse(X5) != sk_c6
| ! [X4] :
( inverse(X4) != sk_c7
| multiply(X4,sk_c7) != sk_c6
| ! [X3] :
( inverse(X3) != sk_c8
| multiply(X3,sk_c8) != sk_c7 ) ) ) ) ),
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
| multiply(X2,sk_c8) != sk_c6
| inverse(X2) != sk_c6
| inverse(X1) != sk_c7
| multiply(X1,sk_c7) != sk_c6
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7 ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f70,definition,
( sQ0_spl
<=> multiply(sk_c1,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f71,plain,
( ~ sQ0_spl
| multiply(sk_c1,sk_c8) = sk_c7 ),
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(f88,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f41,f70,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(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(f95,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_c2,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f102,plain,
( ~ sQ7_spl
| multiply(sk_c2,sk_c7) = sk_c6 ),
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
<=> inverse(sk_c2) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f110,plain,
( ~ sQ8_spl
| inverse(sk_c2) = 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_c3) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f118,plain,
( ~ sQ9_spl
| inverse(sk_c3) = sk_c6 ),
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_c6 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f126,plain,
( ~ sQ10_spl
| multiply(sk_c3,sk_c8) = sk_c6 ),
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] :
( sQ12_spl
<=> ( inverse(X1) != sk_c7
| multiply(X1,sk_c7) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f137,plain,
! [X0] :
( ~ sQ12_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6 ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f139,definition,
! [X2] :
( sQ13_spl
<=> ( multiply(X2,sk_c8) != sk_c6
| inverse(X2) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f140,plain,
! [X0] :
( ~ sQ13_spl
| multiply(X0,sk_c8) != sk_c6
| inverse(X0) != sk_c6 ),
inference(component_clause,[status(thm)],[f139]) ).
fof(f142,definition,
! [X3] :
( sQ14_spl
<=> ( multiply(X3,sk_c7) != sk_c8
| inverse(X3) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f143,plain,
! [X0] :
( ~ sQ14_spl
| multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c8 ),
inference(component_clause,[status(thm)],[f142]) ).
fof(f145,definition,
! [X4] :
( sQ15_spl
<=> ( multiply(X4,sk_c6) != sk_c7
| inverse(X4) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f146,plain,
! [X0] :
( ~ sQ15_spl
| multiply(X0,sk_c6) != sk_c7
| inverse(X0) != sk_c7 ),
inference(component_clause,[status(thm)],[f145]) ).
fof(f148,plain,
( sQ15_spl
| sQ14_spl
| ~ sQ1_spl
| sQ13_spl
| sQ12_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f69,f133,f136,f139,f73,f142,f145]) ).
fof(f149,plain,
( ~ sQ5_spl
| ~ sQ15_spl
| inverse(sk_c5) != sk_c7 ),
inference(resolution,[status(thm)],[f146,f90]) ).
fof(f151,plain,
( ~ sQ5_spl
| ~ sQ15_spl
| ~ sQ4_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f86,f149]) ).
fof(f152,plain,
( ~ sQ5_spl
| ~ sQ15_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f151]) ).
fof(f153,plain,
( ~ sQ5_spl
| ~ sQ15_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f152]) ).
fof(f154,plain,
( ~ sQ3_spl
| ~ sQ14_spl
| inverse(sk_c4) != sk_c8 ),
inference(resolution,[status(thm)],[f143,f82]) ).
fof(f155,plain,
( ~ sQ7_spl
| ~ sQ14_spl
| sk_c6 != sk_c8
| inverse(sk_c2) != sk_c8 ),
inference(paramodulation,[status(thm)],[f102,f143]) ).
fof(f157,plain,
( ~ sQ3_spl
| ~ sQ14_spl
| ~ sQ2_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f78,f154]) ).
fof(f158,plain,
( ~ sQ3_spl
| ~ sQ14_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f157]) ).
fof(f159,plain,
( ~ sQ3_spl
| ~ sQ14_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f158]) ).
fof(f168,plain,
( ~ sQ10_spl
| ~ sQ13_spl
| inverse(sk_c3) != sk_c6 ),
inference(resolution,[status(thm)],[f140,f126]) ).
fof(f170,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| sk_c7 != sk_c6
| inverse(sk_c1) != sk_c6 ),
inference(paramodulation,[status(thm)],[f71,f140]) ).
fof(f172,plain,
( ~ sQ10_spl
| ~ sQ13_spl
| ~ sQ9_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f118,f168]) ).
fof(f173,plain,
( ~ sQ10_spl
| ~ sQ13_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f172]) ).
fof(f174,plain,
( ~ sQ10_spl
| ~ sQ13_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f173]) ).
fof(f176,plain,
( ~ sQ2_spl
| multiply(sk_c8,sk_c4) = identity ),
inference(paramodulation,[status(thm)],[f78,f36]) ).
fof(f177,plain,
( ~ sQ6_spl
| multiply(sk_c8,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f94,f36]) ).
fof(f180,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f36,f37]) ).
fof(f181,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f35,f180]) ).
fof(f196,plain,
( ~ sQ6_spl
| sk_c1 = multiply(inverse(sk_c8),identity) ),
inference(paramodulation,[status(thm)],[f177,f181]) ).
fof(f197,plain,
( ~ sQ2_spl
| sk_c4 = multiply(inverse(sk_c8),identity) ),
inference(paramodulation,[status(thm)],[f176,f181]) ).
fof(f199,plain,
( ~ sQ1_spl
| sk_c8 = multiply(inverse(sk_c7),sk_c6) ),
inference(paramodulation,[status(thm)],[f74,f181]) ).
fof(f204,plain,
( ~ sQ0_spl
| sk_c8 = multiply(inverse(sk_c1),sk_c7) ),
inference(paramodulation,[status(thm)],[f71,f181]) ).
fof(f207,plain,
( ~ sQ5_spl
| sk_c6 = multiply(inverse(sk_c5),sk_c7) ),
inference(paramodulation,[status(thm)],[f90,f181]) ).
fof(f209,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| sk_c8 = multiply(sk_c8,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f94,f204]) ).
fof(f219,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| sk_c7 = multiply(inverse(sk_c8),sk_c8) ),
inference(paramodulation,[status(thm)],[f209,f181]) ).
fof(f221,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| sk_c7 = identity ),
inference(forward_demodulation,[status(thm)],[f36,f219]) ).
fof(f225,plain,
( ~ sQ12_spl
| inverse(inverse(sk_c7)) != sk_c7
| identity != sk_c6 ),
inference(paramodulation,[status(thm)],[f36,f137]) ).
fof(f233,plain,
( ~ sQ6_spl
| ~ sQ11_spl
| multiply(sk_c1,sk_c8) != sk_c7 ),
inference(resolution,[status(thm)],[f134,f94]) ).
fof(f238,plain,
( ~ sQ6_spl
| ~ sQ11_spl
| ~ sQ0_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f71,f233]) ).
fof(f239,plain,
( ~ sQ6_spl
| ~ sQ11_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f238]) ).
fof(f240,plain,
( ~ sQ6_spl
| ~ sQ11_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f239]) ).
fof(f241,definition,
( sQ16_spl
<=> inverse(sk_c2) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f243,plain,
( sQ16_spl
| inverse(sk_c2) != sk_c8 ),
inference(component_clause,[status(thm)],[f241]) ).
fof(f244,definition,
( sQ17_spl
<=> sk_c6 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f245,plain,
( ~ sQ17_spl
| sk_c6 = sk_c8 ),
inference(component_clause,[status(thm)],[f244]) ).
fof(f246,plain,
( sQ17_spl
| sk_c6 != sk_c8 ),
inference(component_clause,[status(thm)],[f244]) ).
fof(f247,plain,
( ~ sQ7_spl
| ~ sQ14_spl
| ~ sQ17_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f155,f241,f244,f142,f101]) ).
fof(f248,plain,
( sQ16_spl
| ~ sQ8_spl
| sk_c7 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f110,f243]) ).
fof(f252,plain,
( ~ sQ6_spl
| ~ sQ14_spl
| multiply(sk_c1,sk_c7) != sk_c8
| sk_c8 != sk_c8 ),
inference(paramodulation,[status(thm)],[f94,f143]) ).
fof(f255,definition,
( sQ18_spl
<=> sk_c8 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f257,plain,
( sQ18_spl
| sk_c8 != sk_c8 ),
inference(component_clause,[status(thm)],[f255]) ).
fof(f259,definition,
( sQ19_spl
<=> multiply(sk_c1,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f262,plain,
( ~ sQ6_spl
| ~ sQ14_spl
| ~ sQ19_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f252,f255,f259,f142,f93]) ).
fof(f263,definition,
( sQ20_spl
<=> sk_c7 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f264,plain,
( ~ sQ20_spl
| sk_c7 = sk_c8 ),
inference(component_clause,[status(thm)],[f263]) ).
fof(f265,plain,
( sQ20_spl
| sk_c7 != sk_c8 ),
inference(component_clause,[status(thm)],[f263]) ).
fof(f274,plain,
( sQ18_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f257]) ).
fof(f275,plain,
sQ18_spl,
inference(contradiction_clause,[status(thm)],[f274]) ).
fof(f284,definition,
( sQ25_spl
<=> sk_c7 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f285,plain,
( ~ sQ25_spl
| sk_c7 = sk_c6 ),
inference(component_clause,[status(thm)],[f284]) ).
fof(f286,plain,
( sQ25_spl
| sk_c7 != sk_c6 ),
inference(component_clause,[status(thm)],[f284]) ).
fof(f291,definition,
( sQ27_spl
<=> identity = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f293,plain,
( sQ27_spl
| identity != sk_c6 ),
inference(component_clause,[status(thm)],[f291]) ).
fof(f294,definition,
( sQ28_spl
<=> inverse(inverse(sk_c7)) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f296,plain,
( sQ28_spl
| inverse(inverse(sk_c7)) != sk_c7 ),
inference(component_clause,[status(thm)],[f294]) ).
fof(f297,plain,
( ~ sQ12_spl
| ~ sQ28_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f225,f291,f294,f136]) ).
fof(f304,plain,
( ~ sQ3_spl
| sk_c7 = multiply(inverse(sk_c4),sk_c8) ),
inference(paramodulation,[status(thm)],[f82,f181]) ).
fof(f306,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| sk_c7 = multiply(sk_c8,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f78,f304]) ).
fof(f307,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| inverse(sk_c4) != sk_c7
| sk_c8 != sk_c6 ),
inference(paramodulation,[status(thm)],[f82,f137]) ).
fof(f312,definition,
( sQ30_spl
<=> inverse(sk_c4) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f314,plain,
( sQ30_spl
| inverse(sk_c4) != sk_c7 ),
inference(component_clause,[status(thm)],[f312]) ).
fof(f315,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| ~ sQ30_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f307,f244,f312,f136,f81]) ).
fof(f319,plain,
( sQ30_spl
| ~ sQ2_spl
| sk_c8 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f78,f314]) ).
fof(f339,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| sk_c6 = multiply(sk_c7,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f86,f207]) ).
fof(f342,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| sk_c7 = multiply(inverse(sk_c7),sk_c6) ),
inference(paramodulation,[status(thm)],[f339,f181]) ).
fof(f344,definition,
( sQ31_spl
<=> sk_c6 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f346,plain,
( sQ31_spl
| sk_c6 != sk_c6 ),
inference(component_clause,[status(thm)],[f344]) ).
fof(f351,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sk_c7 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f199,f342]) ).
fof(f352,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f351,f265]) ).
fof(f353,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sQ20_spl ),
inference(contradiction_clause,[status(thm)],[f352]) ).
fof(f354,plain,
( sQ31_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f346]) ).
fof(f355,plain,
sQ31_spl,
inference(contradiction_clause,[status(thm)],[f354]) ).
fof(f356,plain,
( sQ30_spl
| ~ sQ2_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f319,f263,f77,f312]) ).
fof(f366,plain,
( ~ sQ6_spl
| ~ sQ2_spl
| sk_c1 = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f197,f196]) ).
fof(f367,definition,
( sQ34_spl
<=> inverse(sk_c1) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f369,plain,
( sQ34_spl
| inverse(sk_c1) != sk_c6 ),
inference(component_clause,[status(thm)],[f367]) ).
fof(f370,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ25_spl
| ~ sQ34_spl ),
inference(split_clause,[status(thm)],[f170,f367,f284,f139,f70]) ).
fof(f375,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| inverse(sk_c1) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f351,f94]) ).
fof(f380,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sk_c7 = multiply(sk_c8,sk_c7) ),
inference(backward_demodulation,[status(thm)],[f351,f306]) ).
fof(f386,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sk_c7 = multiply(sk_c7,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f351,f380]) ).
fof(f387,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sk_c7 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f339,f386]) ).
fof(f393,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ6_spl
| multiply(inverse(X0),X0) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f221,f36]) ).
fof(f394,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ6_spl
| multiply(sk_c7,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f221,f35]) ).
fof(f395,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f387,f286]) ).
fof(f396,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sQ25_spl ),
inference(contradiction_clause,[status(thm)],[f395]) ).
fof(f397,plain,
( sQ34_spl
| ~ sQ6_spl
| ~ sQ2_spl
| inverse(sk_c4) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f366,f369]) ).
fof(f400,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c6 = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f387,f351]) ).
fof(f402,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ1_spl
| inverse(sk_c5) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f387,f86]) ).
fof(f405,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| multiply(X0,sk_c6) != sk_c6
| inverse(X0) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f400,f140]) ).
fof(f406,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c4) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f366,f375]) ).
fof(f407,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| inverse(sk_c4) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f387,f406]) ).
fof(f430,plain,
( sQ34_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f407,f397]) ).
fof(f431,plain,
( sQ34_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f430]) ).
fof(f432,plain,
( sQ34_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f431]) ).
fof(f433,plain,
( sQ27_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c7 != sk_c6 ),
inference(backward_demodulation,[status(thm)],[f221,f293]) ).
fof(f438,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ sQ6_spl
| multiply(sk_c7,X0) = multiply(inverse(X1),multiply(X1,X0)) ),
inference(paramodulation,[status(thm)],[f393,f37]) ).
fof(f439,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ6_spl
| multiply(sk_c7,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f181,f438]) ).
fof(f446,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| multiply(sk_c7,sk_c2) = sk_c7 ),
inference(paramodulation,[status(thm)],[f110,f393]) ).
fof(f448,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c2 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f394,f446]) ).
fof(f450,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| inverse(sk_c2) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f448,f110]) ).
fof(f451,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ8_spl
| multiply(sk_c2,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f448,f394]) ).
fof(f452,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ8_spl
| multiply(inverse(X0),X0) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f448,f393]) ).
fof(f455,plain,
( sQ25_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c2 != sk_c6 ),
inference(backward_demodulation,[status(thm)],[f448,f286]) ).
fof(f458,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| multiply(sk_c2,sk_c2) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f448,f102]) ).
fof(f463,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c2 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f464,f458]) ).
fof(f464,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ8_spl
| multiply(sk_c2,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f448,f439]) ).
fof(f467,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f463,f455]) ).
fof(f468,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sQ25_spl ),
inference(contradiction_clause,[status(thm)],[f467]) ).
fof(f481,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| multiply(X0,sk_c6) != sk_c7
| inverse(X0) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f448,f146]) ).
fof(f482,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| multiply(X0,sk_c6) != sk_c2
| inverse(X0) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f448,f481]) ).
fof(f495,plain,
( ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| inverse(sk_c3) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f463,f118]) ).
fof(f499,plain,
( sQ17_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c2 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f463,f246]) ).
fof(f504,plain,
( sQ27_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f433,f284,f93,f70,f291]) ).
fof(f509,plain,
( sQ28_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| inverse(inverse(sk_c2)) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f448,f296]) ).
fof(f510,plain,
( sQ28_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| inverse(sk_c2) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f450,f509]) ).
fof(f511,plain,
( sQ28_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c2 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f450,f510]) ).
fof(f512,plain,
( sQ28_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f448,f511]) ).
fof(f513,plain,
( sQ28_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f512]) ).
fof(f514,plain,
( sQ28_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f513]) ).
fof(f515,plain,
( ~ sQ20_spl
| ~ sQ25_spl
| sk_c6 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f285,f264]) ).
fof(f517,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ25_spl
| sk_c6 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f285,f351]) ).
fof(f520,plain,
( sQ6_spl
| ~ sQ20_spl
| ~ sQ25_spl
| inverse(sk_c1) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f515,f95]) ).
fof(f521,plain,
( ~ sQ0_spl
| ~ sQ20_spl
| ~ sQ25_spl
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f515,f71]) ).
fof(f522,plain,
( ~ sQ0_spl
| ~ sQ20_spl
| ~ sQ25_spl
| multiply(sk_c1,sk_c6) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f285,f521]) ).
fof(f525,plain,
( ~ sQ1_spl
| ~ sQ25_spl
| multiply(sk_c6,sk_c8) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f285,f74]) ).
fof(f533,plain,
( ~ sQ2_spl
| ~ sQ20_spl
| ~ sQ25_spl
| inverse(sk_c4) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f515,f78]) ).
fof(f539,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ20_spl
| ~ sQ25_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c6) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f515,f134]) ).
fof(f540,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ20_spl
| ~ sQ25_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f285,f539]) ).
fof(f541,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ20_spl
| ~ sQ25_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f515,f540]) ).
fof(f544,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ11_spl
| ~ sQ20_spl
| ~ sQ25_spl
| sk_c6 != sk_c6
| multiply(sk_c5,sk_c6) != sk_c6 ),
inference(paramodulation,[status(thm)],[f402,f541]) ).
fof(f546,definition,
( sQ36_spl
<=> multiply(sk_c5,sk_c6) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f548,plain,
( sQ36_spl
| multiply(sk_c5,sk_c6) != sk_c6 ),
inference(component_clause,[status(thm)],[f546]) ).
fof(f549,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ11_spl
| ~ sQ20_spl
| ~ sQ25_spl
| ~ sQ31_spl
| ~ sQ36_spl ),
inference(split_clause,[status(thm)],[f544,f546,f344,f284,f263,f133,f73,f89,f77,f81,f85]) ).
fof(f556,plain,
( sQ16_spl
| ~ sQ8_spl
| ~ sQ25_spl
| sk_c6 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f285,f248]) ).
fof(f564,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ25_spl
| sk_c2 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f285,f448]) ).
fof(f565,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ8_spl
| identity = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f36,f452]) ).
fof(f582,plain,
( sQ1_spl
| ~ sQ25_spl
| multiply(sk_c6,sk_c8) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f285,f75]) ).
fof(f606,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| X0 = multiply(sk_c2,multiply(sk_c3,X0)) ),
inference(paramodulation,[status(thm)],[f495,f181]) ).
fof(f607,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| X0 = multiply(sk_c3,X0) ),
inference(forward_demodulation,[status(thm)],[f451,f606]) ).
fof(f610,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ25_spl
| multiply(sk_c3,sk_c8) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f564,f126]) ).
fof(f611,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ25_spl
| sk_c8 = multiply(inverse(sk_c3),sk_c2) ),
inference(paramodulation,[status(thm)],[f610,f181]) ).
fof(f613,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ25_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sk_c8 = multiply(sk_c2,sk_c2) ),
inference(forward_demodulation,[status(thm)],[f495,f611]) ).
fof(f614,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ25_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sk_c8 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f451,f613]) ).
fof(f615,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ25_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f614,f499]) ).
fof(f616,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ25_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f615]) ).
fof(f630,plain,
( sQ16_spl
| ~ sQ8_spl
| ~ sQ25_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f556,f244,f284,f109,f241]) ).
fof(f633,plain,
( ~ sQ25_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c7 = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f564,f285]) ).
fof(f639,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ8_spl
| multiply(sk_c2,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f565,f35]) ).
fof(f643,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ8_spl
| multiply(inverse(X0),X0) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f565,f36]) ).
fof(f650,plain,
( ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| multiply(sk_c2,sk_c3) = sk_c2 ),
inference(paramodulation,[status(thm)],[f495,f643]) ).
fof(f652,plain,
( ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c3 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f639,f650]) ).
fof(f659,plain,
( ~ sQ25_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sk_c7 = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f652,f633]) ).
fof(f660,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ25_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sk_c8 = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f652,f614]) ).
fof(f661,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ25_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sk_c3 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f652,f564]) ).
fof(f665,plain,
( ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ25_spl
| ~ sQ9_spl
| ~ sQ7_spl
| inverse(sk_c1) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f660,f94]) ).
fof(f690,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ25_spl
| ~ sQ9_spl
| ~ sQ7_spl
| X0 = multiply(sk_c3,multiply(sk_c1,X0)) ),
inference(paramodulation,[status(thm)],[f665,f181]) ).
fof(f691,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ25_spl
| ~ sQ9_spl
| ~ sQ7_spl
| X0 = multiply(sk_c1,X0) ),
inference(forward_demodulation,[status(thm)],[f607,f690]) ).
fof(f698,plain,
( sQ1_spl
| ~ sQ25_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ7_spl
| multiply(sk_c3,sk_c8) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f661,f582]) ).
fof(f699,plain,
( sQ1_spl
| ~ sQ25_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sk_c8 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f607,f698]) ).
fof(f700,plain,
( sQ1_spl
| ~ sQ25_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| sk_c3 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f660,f699]) ).
fof(f701,plain,
( sQ1_spl
| ~ sQ25_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f661,f700]) ).
fof(f702,plain,
( sQ1_spl
| ~ sQ25_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f701]) ).
fof(f703,plain,
( sQ1_spl
| ~ sQ25_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f702]) ).
fof(f704,plain,
( ~ sQ20_spl
| ~ sQ25_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f515,f244,f284,f263]) ).
fof(f706,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ25_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f517,f244,f284,f73,f85,f89]) ).
fof(f755,plain,
( ~ sQ25_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sk_c6 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f285,f659]) ).
fof(f761,plain,
( ~ sQ1_spl
| ~ sQ25_spl
| sk_c8 = multiply(inverse(sk_c6),sk_c6) ),
inference(paramodulation,[status(thm)],[f525,f181]) ).
fof(f763,plain,
( ~ sQ1_spl
| ~ sQ25_spl
| sk_c8 = identity ),
inference(forward_demodulation,[status(thm)],[f36,f761]) ).
fof(f818,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ7_spl
| multiply(X0,sk_c6) != sk_c2
| inverse(X0) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f652,f482]) ).
fof(f819,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ25_spl
| multiply(X0,sk_c3) != sk_c2
| inverse(X0) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f755,f818]) ).
fof(f820,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ25_spl
| multiply(X0,sk_c3) != sk_c3
| inverse(X0) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f652,f819]) ).
fof(f821,plain,
( ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ25_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ15_spl
| multiply(sk_c1,sk_c3) != sk_c3 ),
inference(resolution,[status(thm)],[f820,f665]) ).
fof(f825,plain,
( ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ25_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ15_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f691,f821]) ).
fof(f826,plain,
( ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ25_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ15_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f825]) ).
fof(f827,plain,
( ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ25_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ15_spl ),
inference(contradiction_clause,[status(thm)],[f826]) ).
fof(f830,plain,
( ~ sQ1_spl
| ~ sQ25_spl
| ~ sQ17_spl
| sk_c6 = identity ),
inference(backward_demodulation,[status(thm)],[f245,f763]) ).
fof(f832,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ25_spl
| ~ sQ17_spl
| multiply(sk_c6,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f830,f35]) ).
fof(f836,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ1_spl
| X0 = multiply(sk_c6,multiply(sk_c5,X0)) ),
inference(paramodulation,[status(thm)],[f402,f181]) ).
fof(f837,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ25_spl
| ~ sQ17_spl
| X0 = multiply(sk_c5,X0) ),
inference(forward_demodulation,[status(thm)],[f832,f836]) ).
fof(f838,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ20_spl
| ~ sQ25_spl
| X0 = multiply(sk_c6,multiply(sk_c4,X0)) ),
inference(paramodulation,[status(thm)],[f533,f181]) ).
fof(f839,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ20_spl
| ~ sQ25_spl
| ~ sQ1_spl
| ~ sQ17_spl
| X0 = multiply(sk_c4,X0) ),
inference(forward_demodulation,[status(thm)],[f832,f838]) ).
fof(f842,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ20_spl
| ~ sQ25_spl
| multiply(sk_c6,X0) = multiply(sk_c1,multiply(sk_c6,X0)) ),
inference(paramodulation,[status(thm)],[f522,f37]) ).
fof(f843,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ20_spl
| ~ sQ25_spl
| ~ sQ1_spl
| ~ sQ17_spl
| X0 = multiply(sk_c1,multiply(sk_c6,X0)) ),
inference(forward_demodulation,[status(thm)],[f832,f842]) ).
fof(f844,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ20_spl
| ~ sQ25_spl
| ~ sQ1_spl
| ~ sQ17_spl
| X0 = multiply(sk_c1,X0) ),
inference(forward_demodulation,[status(thm)],[f832,f843]) ).
fof(f860,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ20_spl
| ~ sQ25_spl
| ~ sQ1_spl
| ~ sQ17_spl
| X0 = multiply(inverse(sk_c1),X0) ),
inference(paramodulation,[status(thm)],[f844,f181]) ).
fof(f867,plain,
( sQ36_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ25_spl
| ~ sQ17_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f837,f548]) ).
fof(f868,plain,
( sQ36_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ25_spl
| ~ sQ17_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f867]) ).
fof(f869,plain,
( sQ36_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ25_spl
| ~ sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f868]) ).
fof(f873,plain,
( ~ sQ2_spl
| ~ sQ17_spl
| multiply(sk_c6,sk_c4) = identity ),
inference(forward_demodulation,[status(thm)],[f245,f176]) ).
fof(f874,plain,
( ~ sQ2_spl
| ~ sQ17_spl
| ~ sQ1_spl
| ~ sQ25_spl
| sk_c4 = identity ),
inference(forward_demodulation,[status(thm)],[f832,f873]) ).
fof(f879,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ17_spl
| ~ sQ25_spl
| inverse(sk_c5) = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f885,f402]) ).
fof(f880,plain,
( sQ6_spl
| ~ sQ20_spl
| ~ sQ25_spl
| ~ sQ2_spl
| ~ sQ17_spl
| ~ sQ1_spl
| inverse(sk_c1) != sk_c4 ),
inference(backward_demodulation,[status(thm)],[f885,f520]) ).
fof(f882,plain,
( ~ sQ1_spl
| ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ2_spl
| sk_c4 = identity ),
inference(backward_demodulation,[status(thm)],[f885,f830]) ).
fof(f885,plain,
( ~ sQ2_spl
| ~ sQ17_spl
| ~ sQ1_spl
| ~ sQ25_spl
| sk_c4 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f830,f874]) ).
fof(f892,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ2_spl
| multiply(inverse(X0),X0) = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f882,f36]) ).
fof(f893,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ17_spl
| ~ sQ25_spl
| multiply(sk_c4,sk_c5) = sk_c4 ),
inference(paramodulation,[status(thm)],[f879,f892]) ).
fof(f897,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ17_spl
| ~ sQ25_spl
| ~ sQ20_spl
| sk_c5 = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f839,f893]) ).
fof(f899,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ20_spl
| multiply(inverse(X0),X0) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f897,f892]) ).
fof(f900,plain,
( sQ6_spl
| ~ sQ20_spl
| ~ sQ25_spl
| ~ sQ2_spl
| ~ sQ17_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| inverse(sk_c1) != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f897,f880]) ).
fof(f901,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ17_spl
| ~ sQ25_spl
| ~ sQ20_spl
| inverse(sk_c5) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f897,f879]) ).
fof(f909,plain,
( ~ sQ2_spl
| ~ sQ17_spl
| ~ sQ1_spl
| ~ sQ25_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ20_spl
| sk_c5 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f897,f885]) ).
fof(f957,plain,
( ~ sQ0_spl
| ~ sQ20_spl
| ~ sQ25_spl
| ~ sQ1_spl
| ~ sQ17_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| sk_c1 = sk_c5 ),
inference(paramodulation,[status(thm)],[f860,f899]) ).
fof(f964,plain,
( sQ6_spl
| ~ sQ20_spl
| ~ sQ25_spl
| ~ sQ2_spl
| ~ sQ17_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ0_spl
| inverse(sk_c5) != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f957,f900]) ).
fof(f967,plain,
( sQ6_spl
| ~ sQ20_spl
| ~ sQ25_spl
| ~ sQ2_spl
| ~ sQ17_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ0_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f901,f964]) ).
fof(f968,plain,
( sQ6_spl
| ~ sQ20_spl
| ~ sQ25_spl
| ~ sQ2_spl
| ~ sQ17_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f967]) ).
fof(f969,plain,
( sQ6_spl
| ~ sQ20_spl
| ~ sQ25_spl
| ~ sQ2_spl
| ~ sQ17_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f968]) ).
fof(f972,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ17_spl
| ~ sQ25_spl
| ~ sQ20_spl
| multiply(X0,sk_c6) != sk_c6
| inverse(X0) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f909,f405]) ).
fof(f973,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ17_spl
| ~ sQ25_spl
| ~ sQ20_spl
| multiply(X0,sk_c5) != sk_c6
| inverse(X0) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f909,f972]) ).
fof(f974,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ17_spl
| ~ sQ25_spl
| ~ sQ20_spl
| multiply(X0,sk_c5) != sk_c5
| inverse(X0) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f909,f973]) ).
fof(f975,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ17_spl
| ~ sQ25_spl
| ~ sQ20_spl
| ~ sQ13_spl
| multiply(sk_c5,sk_c5) != sk_c5 ),
inference(resolution,[status(thm)],[f974,f901]) ).
fof(f977,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ17_spl
| ~ sQ25_spl
| ~ sQ20_spl
| ~ sQ13_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f837,f975]) ).
fof(f978,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ17_spl
| ~ sQ25_spl
| ~ sQ20_spl
| ~ sQ13_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f977]) ).
fof(f979,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ17_spl
| ~ sQ25_spl
| ~ sQ20_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f978]) ).
fof(f980,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,f148,f153,f159,f174,f240,f247,f262,f275,f297,f315,f353,f355,f356,f370,f396,f432,f468,f504,f514,f549,f616,f630,f703,f704,f706,f827,f869,f969,f979]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP255-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.04/0.29 % Computer : n012.cluster.edu
% 0.04/0.29 % Model : x86_64 x86_64
% 0.04/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.29 % Memory : 8046.5625MB
% 0.04/0.29 % OS : Linux 6.8.0-71-generic
% 0.04/0.29 % CPULimit : 300
% 0.04/0.29 % WCLimit : 300
% 0.04/0.29 % DateTime : Sun Sep 20 20:07:22 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.31 % Drodi V4.1.1
% 0.04/0.33 % Refutation found
% 0.04/0.33 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.04/0.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.04/0.35 % Elapsed time: 0.052175 seconds
% 0.04/0.35 % CPU time: 0.170568 seconds
% 0.04/0.35 % Total memory used: 70.407 MB
% 0.04/0.35 % Net memory used: 70.172 MB
%------------------------------------------------------------------------------