%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP227-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 12:33:09 PM UTC 2026
% Result : Unsatisfiable 0.25s 0.50s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 68
% Syntax : Number of formulae : 357 ( 11 unt; 34 def)
% Number of atoms : 1343 ( 400 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1894 ( 908 ~; 952 |; 0 &)
% ( 34 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 36 ( 34 usr; 35 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 66 ( 66 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| 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_c5,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
! [X4,X5,X6,X1,X3,X2] :
( multiply(X2,sk_c8) != sk_c7
| inverse(X3) != X2
| multiply(X3,X2) != sk_c7
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c7
| inverse(X6) != sk_c8
| multiply(X6,sk_c8) != X5
| multiply(sk_c8,X5) != sk_c7
| multiply(X4,sk_c7) != sk_c8
| inverse(X4) != sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f36,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f37,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f38,plain,
( inverse(sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f39,plain,
( multiply(sk_c4,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f40,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f41,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f42,plain,
( inverse(sk_c5) = sk_c6
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f43,plain,
( multiply(sk_c6,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f44,plain,
( inverse(sk_c8) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f45,plain,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f46,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f47,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f48,plain,
( inverse(sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f49,plain,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f50,plain,
( inverse(sk_c8) = sk_c7
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f51,plain,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f52,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f53,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f54,plain,
( inverse(sk_c5) = sk_c6
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f55,plain,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f56,plain,
( inverse(sk_c8) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f57,plain,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f58,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f59,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f60,plain,
( inverse(sk_c5) = sk_c6
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f61,plain,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f62,plain,
( inverse(sk_c8) = sk_c7
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f63,plain,
( multiply(sk_c4,sk_c8) = sk_c7
| 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_c5,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f66,plain,
( inverse(sk_c5) = sk_c6
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f67,plain,
( multiply(sk_c6,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f68,plain,
! [X2] :
( multiply(X2,sk_c8) != sk_c7
| ! [X3] :
( inverse(X3) != X2
| multiply(X3,X2) != sk_c7
| ! [X1] :
( inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c7
| ! [X6] :
( inverse(X6) != sk_c8
| ! [X5] :
( multiply(X6,sk_c8) != X5
| multiply(sk_c8,X5) != sk_c7
| ! [X4] :
( multiply(X4,sk_c7) != sk_c8
| inverse(X4) != sk_c8 ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f34]) ).
fof(f69,plain,
! [X0,X1,X2,X3,X4,X5] :
( multiply(X5,sk_c8) != sk_c7
| inverse(X4) != X5
| multiply(X4,X5) != sk_c7
| inverse(X3) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c7
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != X1
| multiply(sk_c8,X1) != sk_c7
| multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c8 ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f70,definition,
( sQ0_spl
<=> inverse(sk_c1) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f71,plain,
( ~ sQ0_spl
| inverse(sk_c1) = sk_c8 ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f73,definition,
( sQ1_spl
<=> inverse(sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f74,plain,
( ~ sQ1_spl
| inverse(sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f75,plain,
( sQ1_spl
| inverse(sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f76,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f38,f70,f73]) ).
fof(f77,definition,
( sQ2_spl
<=> multiply(sk_c4,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f78,plain,
( ~ sQ2_spl
| multiply(sk_c4,sk_c8) = sk_c7 ),
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
<=> inverse(sk_c4) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f82,plain,
( ~ sQ3_spl
| inverse(sk_c4) = 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
<=> multiply(sk_c5,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ4_spl
| multiply(sk_c5,sk_c6) = 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
<=> inverse(sk_c5) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f90,plain,
( ~ sQ5_spl
| inverse(sk_c5) = sk_c6 ),
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
<=> multiply(sk_c6,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ6_spl
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f96,plain,
( sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f43,f70,f93]) ).
fof(f97,definition,
( sQ7_spl
<=> multiply(sk_c1,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f98,plain,
( ~ sQ7_spl
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f97]) ).
fof(f100,plain,
( sQ1_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f44,f97,f73]) ).
fof(f101,plain,
( sQ2_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f45,f97,f77]) ).
fof(f102,plain,
( sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f46,f97,f81]) ).
fof(f103,plain,
( sQ4_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f47,f97,f85]) ).
fof(f104,plain,
( sQ5_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f48,f97,f89]) ).
fof(f105,plain,
( sQ6_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f49,f97,f93]) ).
fof(f106,definition,
( sQ8_spl
<=> multiply(sk_c8,sk_c3) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f107,plain,
( ~ sQ8_spl
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(component_clause,[status(thm)],[f106]) ).
fof(f109,plain,
( sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f50,f106,f73]) ).
fof(f110,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f51,f106,f77]) ).
fof(f111,plain,
( sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f52,f106,f81]) ).
fof(f112,plain,
( sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f53,f106,f85]) ).
fof(f113,plain,
( sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f54,f106,f89]) ).
fof(f114,plain,
( sQ6_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f55,f106,f93]) ).
fof(f115,definition,
( sQ9_spl
<=> multiply(sk_c2,sk_c8) = sk_c3 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f116,plain,
( ~ sQ9_spl
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(component_clause,[status(thm)],[f115]) ).
fof(f118,plain,
( sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f56,f115,f73]) ).
fof(f119,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f57,f115,f77]) ).
fof(f120,plain,
( sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f58,f115,f81]) ).
fof(f121,plain,
( sQ4_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f59,f115,f85]) ).
fof(f122,plain,
( sQ5_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f60,f115,f89]) ).
fof(f123,plain,
( sQ6_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f61,f115,f93]) ).
fof(f124,definition,
( sQ10_spl
<=> inverse(sk_c2) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f125,plain,
( ~ sQ10_spl
| inverse(sk_c2) = sk_c8 ),
inference(component_clause,[status(thm)],[f124]) ).
fof(f127,plain,
( sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f62,f124,f73]) ).
fof(f128,plain,
( sQ2_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f63,f124,f77]) ).
fof(f129,plain,
( sQ3_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f64,f124,f81]) ).
fof(f130,plain,
( sQ4_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f65,f124,f85]) ).
fof(f131,plain,
( sQ5_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f66,f124,f89]) ).
fof(f132,plain,
( sQ6_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f67,f124,f93]) ).
fof(f133,definition,
! [X0] :
( sQ11_spl
<=> ( multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f134,plain,
! [X0] :
( ~ sQ11_spl
| multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c8 ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,definition,
! [X1,X2] :
( sQ12_spl
<=> ( 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
<=> ( inverse(X3) != sk_c8
| multiply(X3,sk_c8) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f140,plain,
! [X0] :
( ~ sQ13_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f139]) ).
fof(f142,definition,
! [X4,X5] :
( sQ14_spl
<=> ( multiply(X5,sk_c8) != sk_c7
| inverse(X4) != X5
| multiply(X4,X5) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f143,plain,
! [X0,X1] :
( ~ sQ14_spl
| multiply(X1,sk_c8) != sk_c7
| inverse(X0) != X1
| multiply(X0,X1) != sk_c7 ),
inference(component_clause,[status(thm)],[f142]) ).
fof(f145,plain,
( sQ14_spl
| sQ13_spl
| ~ sQ1_spl
| sQ12_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f69,f133,f136,f73,f139,f142]) ).
fof(f146,plain,
! [X0] :
( ~ sQ14_spl
| multiply(inverse(X0),sk_c8) != sk_c7
| multiply(X0,inverse(X0)) != sk_c7 ),
inference(destructive_equality_resolution,[status(thm)],[f143]) ).
fof(f149,plain,
! [X0] :
( ~ sQ4_spl
| multiply(sk_c7,X0) = multiply(sk_c5,multiply(sk_c6,X0)) ),
inference(paramodulation,[status(thm)],[f86,f37]) ).
fof(f153,plain,
! [X0] :
( ~ sQ9_spl
| multiply(sk_c3,X0) = multiply(sk_c2,multiply(sk_c8,X0)) ),
inference(paramodulation,[status(thm)],[f116,f37]) ).
fof(f162,plain,
( ~ sQ3_spl
| ~ sQ14_spl
| multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c4,inverse(sk_c4)) != sk_c7 ),
inference(paramodulation,[status(thm)],[f82,f146]) ).
fof(f163,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| multiply(sk_c6,sk_c8) != sk_c7
| multiply(sk_c5,inverse(sk_c5)) != sk_c7 ),
inference(paramodulation,[status(thm)],[f90,f146]) ).
fof(f164,plain,
( ~ sQ0_spl
| ~ sQ14_spl
| multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c1,inverse(sk_c1)) != sk_c7 ),
inference(paramodulation,[status(thm)],[f71,f146]) ).
fof(f165,plain,
( ~ sQ10_spl
| ~ sQ14_spl
| multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c2,inverse(sk_c2)) != sk_c7 ),
inference(paramodulation,[status(thm)],[f125,f146]) ).
fof(f166,definition,
( sQ15_spl
<=> multiply(sk_c4,inverse(sk_c4)) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f168,plain,
( sQ15_spl
| multiply(sk_c4,inverse(sk_c4)) != sk_c7 ),
inference(component_clause,[status(thm)],[f166]) ).
fof(f169,definition,
( sQ16_spl
<=> multiply(sk_c8,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f171,plain,
( sQ16_spl
| multiply(sk_c8,sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f169]) ).
fof(f172,plain,
( ~ sQ3_spl
| ~ sQ14_spl
| ~ sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f162,f166,f169,f142,f81]) ).
fof(f173,definition,
( sQ17_spl
<=> multiply(sk_c5,inverse(sk_c5)) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f175,plain,
( sQ17_spl
| multiply(sk_c5,inverse(sk_c5)) != sk_c7 ),
inference(component_clause,[status(thm)],[f173]) ).
fof(f176,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| ~ sQ6_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f163,f173,f93,f142,f89]) ).
fof(f177,definition,
( sQ18_spl
<=> multiply(sk_c1,inverse(sk_c1)) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f179,plain,
( sQ18_spl
| multiply(sk_c1,inverse(sk_c1)) != sk_c7 ),
inference(component_clause,[status(thm)],[f177]) ).
fof(f180,plain,
( ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ16_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f164,f177,f169,f142,f70]) ).
fof(f181,definition,
( sQ19_spl
<=> multiply(sk_c2,inverse(sk_c2)) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f183,plain,
( sQ19_spl
| multiply(sk_c2,inverse(sk_c2)) != sk_c7 ),
inference(component_clause,[status(thm)],[f181]) ).
fof(f184,plain,
( ~ sQ10_spl
| ~ sQ14_spl
| ~ sQ16_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f165,f181,f169,f142,f124]) ).
fof(f185,plain,
( sQ19_spl
| ~ sQ10_spl
| multiply(sk_c2,sk_c8) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f125,f183]) ).
fof(f190,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| sk_c8 != sk_c8
| multiply(sk_c1,sk_c8) != sk_c7 ),
inference(paramodulation,[status(thm)],[f71,f140]) ).
fof(f191,plain,
( ~ sQ10_spl
| ~ sQ13_spl
| sk_c8 != sk_c8
| multiply(sk_c2,sk_c8) != sk_c7 ),
inference(paramodulation,[status(thm)],[f125,f140]) ).
fof(f193,definition,
( sQ20_spl
<=> multiply(sk_c1,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f195,plain,
( sQ20_spl
| multiply(sk_c1,sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f193]) ).
fof(f196,definition,
( sQ21_spl
<=> sk_c8 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f198,plain,
( sQ21_spl
| sk_c8 != sk_c8 ),
inference(component_clause,[status(thm)],[f196]) ).
fof(f199,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ21_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f190,f193,f196,f139,f70]) ).
fof(f200,definition,
( sQ22_spl
<=> multiply(sk_c2,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f202,plain,
( sQ22_spl
| multiply(sk_c2,sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f200]) ).
fof(f203,plain,
( ~ sQ10_spl
| ~ sQ13_spl
| ~ sQ21_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f191,f200,f196,f139,f124]) ).
fof(f204,plain,
( sQ21_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f198]) ).
fof(f205,plain,
sQ21_spl,
inference(contradiction_clause,[status(thm)],[f204]) ).
fof(f206,plain,
( sQ22_spl
| ~ sQ9_spl
| sk_c3 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f116,f202]) ).
fof(f207,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(f209,plain,
( ~ sQ0_spl
| multiply(sk_c8,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f71,f36]) ).
fof(f211,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f36,f37]) ).
fof(f212,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f35,f211]) ).
fof(f223,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f35,f212]) ).
fof(f229,plain,
( ~ sQ7_spl
| sk_c7 = multiply(inverse(sk_c1),sk_c8) ),
inference(paramodulation,[status(thm)],[f98,f212]) ).
fof(f231,plain,
( ~ sQ0_spl
| sk_c1 = multiply(inverse(sk_c8),identity) ),
inference(paramodulation,[status(thm)],[f209,f212]) ).
fof(f233,plain,
( ~ sQ9_spl
| sk_c8 = multiply(inverse(sk_c2),sk_c3) ),
inference(paramodulation,[status(thm)],[f116,f212]) ).
fof(f235,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| sk_c7 = multiply(sk_c8,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f71,f229]) ).
fof(f236,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f235,f171]) ).
fof(f237,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| sQ16_spl ),
inference(contradiction_clause,[status(thm)],[f236]) ).
fof(f238,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| sk_c8 = multiply(sk_c8,sk_c3) ),
inference(forward_demodulation,[status(thm)],[f125,f233]) ).
fof(f239,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c8 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f107,f238]) ).
fof(f241,plain,
( ~ sQ12_spl
| inverse(inverse(sk_c8)) != sk_c8
| multiply(sk_c8,identity) != sk_c7 ),
inference(paramodulation,[status(thm)],[f36,f207]) ).
fof(f242,plain,
( ~ sQ12_spl
| inverse(identity) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7 ),
inference(paramodulation,[status(thm)],[f35,f207]) ).
fof(f244,plain,
( ~ sQ2_spl
| ~ sQ12_spl
| inverse(sk_c4) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c7 ),
inference(paramodulation,[status(thm)],[f78,f207]) ).
fof(f245,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| inverse(sk_c2) != sk_c8
| multiply(sk_c8,sk_c3) != sk_c7 ),
inference(paramodulation,[status(thm)],[f116,f207]) ).
fof(f246,definition,
( sQ23_spl
<=> multiply(sk_c8,identity) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f249,definition,
( sQ24_spl
<=> inverse(inverse(sk_c8)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f252,plain,
( ~ sQ12_spl
| ~ sQ24_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f241,f246,f249,f136]) ).
fof(f253,definition,
( sQ25_spl
<=> inverse(identity) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f254,plain,
( ~ sQ25_spl
| inverse(identity) = sk_c8 ),
inference(component_clause,[status(thm)],[f253]) ).
fof(f255,plain,
( sQ25_spl
| inverse(identity) != sk_c8 ),
inference(component_clause,[status(thm)],[f253]) ).
fof(f256,plain,
( ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f242,f169,f253,f136]) ).
fof(f257,definition,
( sQ26_spl
<=> multiply(sk_c8,sk_c7) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f260,plain,
( ~ sQ2_spl
| ~ sQ12_spl
| ~ sQ3_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f244,f257,f81,f136,f77]) ).
fof(f261,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f245,f106,f124,f136,f115]) ).
fof(f263,plain,
( ~ sQ1_spl
| multiply(sk_c7,sk_c8) = identity ),
inference(paramodulation,[status(thm)],[f74,f36]) ).
fof(f264,plain,
( sQ15_spl
| ~ sQ3_spl
| multiply(sk_c4,sk_c8) != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f82,f168]) ).
fof(f266,plain,
( ~ sQ3_spl
| multiply(sk_c8,sk_c4) = identity ),
inference(paramodulation,[status(thm)],[f82,f36]) ).
fof(f267,plain,
( sQ15_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f78,f264]) ).
fof(f268,plain,
( sQ15_spl
| ~ sQ3_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f267]) ).
fof(f269,plain,
( sQ15_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f268]) ).
fof(f270,plain,
( ~ sQ0_spl
| ~ sQ1_spl
| sk_c1 = multiply(sk_c7,identity) ),
inference(forward_demodulation,[status(thm)],[f74,f231]) ).
fof(f278,plain,
( ~ sQ11_spl
| identity != sk_c8
| inverse(inverse(sk_c7)) != sk_c8 ),
inference(paramodulation,[status(thm)],[f36,f134]) ).
fof(f279,plain,
( ~ sQ11_spl
| sk_c7 != sk_c8
| inverse(identity) != sk_c8 ),
inference(paramodulation,[status(thm)],[f35,f134]) ).
fof(f281,definition,
( sQ27_spl
<=> inverse(inverse(sk_c7)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f284,definition,
( sQ28_spl
<=> identity = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f287,plain,
( ~ sQ11_spl
| ~ sQ28_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f278,f281,f284,f133]) ).
fof(f288,definition,
( sQ29_spl
<=> sk_c7 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f290,plain,
( sQ29_spl
| sk_c7 != sk_c8 ),
inference(component_clause,[status(thm)],[f288]) ).
fof(f291,plain,
( ~ sQ11_spl
| ~ sQ29_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f279,f253,f288,f133]) ).
fof(f296,plain,
( ~ sQ11_spl
| sk_c7 != sk_c8
| inverse(inverse(identity)) != sk_c8 ),
inference(paramodulation,[status(thm)],[f223,f134]) ).
fof(f299,definition,
( sQ30_spl
<=> inverse(inverse(identity)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f301,plain,
( sQ30_spl
| inverse(inverse(identity)) != sk_c8 ),
inference(component_clause,[status(thm)],[f299]) ).
fof(f302,plain,
( ~ sQ11_spl
| ~ sQ29_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f296,f299,f288,f133]) ).
fof(f307,plain,
( ~ sQ3_spl
| sk_c4 = multiply(inverse(sk_c8),identity) ),
inference(paramodulation,[status(thm)],[f266,f212]) ).
fof(f309,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| sk_c4 = multiply(sk_c7,identity) ),
inference(forward_demodulation,[status(thm)],[f74,f307]) ).
fof(f311,plain,
( ~ sQ6_spl
| ~ sQ4_spl
| multiply(sk_c7,sk_c8) = multiply(sk_c5,sk_c7) ),
inference(paramodulation,[status(thm)],[f94,f149]) ).
fof(f314,plain,
( ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| identity = multiply(sk_c5,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f263,f311]) ).
fof(f326,plain,
( ~ sQ0_spl
| sk_c1 = multiply(inverse(sk_c8),identity) ),
inference(paramodulation,[status(thm)],[f209,f212]) ).
fof(f328,plain,
( ~ sQ0_spl
| ~ sQ1_spl
| sk_c1 = multiply(sk_c7,identity) ),
inference(forward_demodulation,[status(thm)],[f74,f326]) ).
fof(f340,plain,
( sQ20_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ0_spl
| multiply(sk_c4,sk_c8) != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f342,f195]) ).
fof(f342,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ0_spl
| sk_c4 = sk_c1 ),
inference(forward_demodulation,[status(thm)],[f270,f309]) ).
fof(f343,plain,
( sQ20_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ0_spl
| ~ sQ2_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f78,f340]) ).
fof(f344,plain,
( sQ20_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ0_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f343]) ).
fof(f345,plain,
( sQ20_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ0_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f344]) ).
fof(f347,plain,
( sQ18_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ0_spl
| multiply(sk_c4,inverse(sk_c1)) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f342,f179]) ).
fof(f348,plain,
( sQ18_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ0_spl
| multiply(sk_c4,inverse(sk_c4)) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f342,f347]) ).
fof(f349,plain,
( sQ18_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ0_spl
| multiply(sk_c4,sk_c8) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f82,f348]) ).
fof(f350,plain,
( sQ18_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ0_spl
| ~ sQ2_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f78,f349]) ).
fof(f351,plain,
( sQ18_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ0_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f350]) ).
fof(f352,plain,
( sQ18_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ0_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f351]) ).
fof(f353,plain,
( sQ17_spl
| ~ sQ5_spl
| multiply(sk_c5,sk_c6) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f90,f175]) ).
fof(f354,plain,
( sQ17_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f86,f353]) ).
fof(f355,plain,
( sQ17_spl
| ~ sQ5_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f354]) ).
fof(f356,plain,
( sQ17_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f355]) ).
fof(f362,plain,
( ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sk_c7 = multiply(inverse(sk_c5),identity) ),
inference(paramodulation,[status(thm)],[f314,f212]) ).
fof(f364,plain,
( ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ5_spl
| sk_c7 = multiply(sk_c6,identity) ),
inference(forward_demodulation,[status(thm)],[f90,f362]) ).
fof(f366,plain,
( ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ3_spl
| sk_c4 = multiply(sk_c7,identity) ),
inference(forward_demodulation,[status(thm)],[f342,f328]) ).
fof(f373,plain,
( ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ5_spl
| multiply(sk_c7,identity) = multiply(sk_c5,sk_c7) ),
inference(paramodulation,[status(thm)],[f364,f149]) ).
fof(f376,plain,
( ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ3_spl
| sk_c4 = multiply(sk_c5,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f366,f373]) ).
fof(f377,plain,
( ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ3_spl
| sk_c4 = identity ),
inference(forward_demodulation,[status(thm)],[f314,f376]) ).
fof(f380,plain,
( ~ sQ1_spl
| ~ sQ12_spl
| inverse(sk_c7) != sk_c8
| multiply(sk_c8,identity) != sk_c7 ),
inference(paramodulation,[status(thm)],[f263,f207]) ).
fof(f382,plain,
( ~ sQ12_spl
| inverse(inverse(identity)) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7 ),
inference(paramodulation,[status(thm)],[f223,f207]) ).
fof(f388,definition,
( sQ31_spl
<=> inverse(sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f391,plain,
( ~ sQ1_spl
| ~ sQ12_spl
| ~ sQ31_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f380,f246,f388,f136,f73]) ).
fof(f396,plain,
( ~ sQ12_spl
| ~ sQ30_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f382,f169,f299,f136]) ).
fof(f409,plain,
( sQ25_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ3_spl
| inverse(sk_c4) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f377,f255]) ).
fof(f412,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ3_spl
| multiply(sk_c4,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f377,f35]) ).
fof(f416,plain,
( sQ25_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ3_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f82,f409]) ).
fof(f417,plain,
( sQ25_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f416]) ).
fof(f418,plain,
( sQ25_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f417]) ).
fof(f426,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ3_spl
| sk_c8 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f412,f78]) ).
fof(f429,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ3_spl
| sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f426,f290]) ).
fof(f430,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ3_spl
| sQ29_spl ),
inference(contradiction_clause,[status(thm)],[f429]) ).
fof(f438,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| multiply(sk_c2,sk_c7) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f239,f116]) ).
fof(f441,plain,
( ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| multiply(sk_c1,sk_c7) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f239,f98]) ).
fof(f445,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| inverse(sk_c2) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f239,f125]) ).
fof(f447,plain,
( sQ25_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| inverse(identity) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f239,f255]) ).
fof(f450,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| inverse(sk_c1) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f239,f71]) ).
fof(f453,plain,
( sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| inverse(sk_c7) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f239,f75]) ).
fof(f456,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c7 = multiply(sk_c7,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f239,f235]) ).
fof(f457,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c7 = multiply(sk_c7,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f239,f456]) ).
fof(f460,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c7,sk_c3) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f239,f107]) ).
fof(f470,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f239,f134]) ).
fof(f471,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| multiply(X0,sk_c7) != sk_c7
| inverse(X0) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f239,f470]) ).
fof(f472,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ11_spl
| multiply(sk_c1,sk_c7) != sk_c7 ),
inference(resolution,[status(thm)],[f471,f450]) ).
fof(f476,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ7_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f441,f472]) ).
fof(f477,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f476]) ).
fof(f478,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f477]) ).
fof(f490,plain,
( sQ19_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| multiply(sk_c2,sk_c7) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f239,f185]) ).
fof(f491,plain,
( sQ19_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| sk_c3 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f438,f490]) ).
fof(f493,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| multiply(sk_c3,X0) = multiply(sk_c2,multiply(sk_c7,X0)) ),
inference(forward_demodulation,[status(thm)],[f239,f153]) ).
fof(f495,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c3,sk_c3) = multiply(sk_c2,sk_c7) ),
inference(paramodulation,[status(thm)],[f460,f493]) ).
fof(f496,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| multiply(sk_c3,sk_c7) = multiply(sk_c2,sk_c7) ),
inference(paramodulation,[status(thm)],[f457,f493]) ).
fof(f499,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c3,sk_c3) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f438,f495]) ).
fof(f500,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| multiply(sk_c3,sk_c7) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f438,f496]) ).
fof(f533,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c3 = multiply(inverse(sk_c3),sk_c3) ),
inference(paramodulation,[status(thm)],[f499,f212]) ).
fof(f535,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c3 = identity ),
inference(forward_demodulation,[status(thm)],[f36,f533]) ).
fof(f541,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(inverse(X0),X0) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f535,f36]) ).
fof(f542,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c3,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f535,f35]) ).
fof(f543,plain,
( sQ25_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| inverse(sk_c3) != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f535,f447]) ).
fof(f554,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c7 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f542,f500]) ).
fof(f555,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f554,f206]) ).
fof(f556,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f555]) ).
fof(f559,plain,
( sQ25_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| inverse(sk_c3) != sk_c3 ),
inference(backward_demodulation,[status(thm)],[f554,f543]) ).
fof(f565,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| inverse(sk_c1) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f554,f450]) ).
fof(f566,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| inverse(sk_c2) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f554,f445]) ).
fof(f571,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c8 = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f554,f239]) ).
fof(f588,plain,
( sQ19_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f554,f491]) ).
fof(f589,plain,
( sQ19_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f588]) ).
fof(f590,plain,
( sQ19_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f589]) ).
fof(f595,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| multiply(sk_c3,sk_c1) = sk_c3 ),
inference(paramodulation,[status(thm)],[f565,f541]) ).
fof(f597,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| sk_c1 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f542,f595]) ).
fof(f599,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| inverse(sk_c3) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f597,f565]) ).
fof(f600,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f599,f559]) ).
fof(f601,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| sQ25_spl ),
inference(contradiction_clause,[status(thm)],[f600]) ).
fof(f602,plain,
( ~ sQ25_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| inverse(sk_c3) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f535,f254]) ).
fof(f603,plain,
( ~ sQ25_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ0_spl
| inverse(sk_c3) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f571,f602]) ).
fof(f605,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| multiply(sk_c3,sk_c2) = sk_c3 ),
inference(paramodulation,[status(thm)],[f566,f541]) ).
fof(f607,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c2 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f542,f605]) ).
fof(f614,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c7 = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f607,f554]) ).
fof(f632,plain,
( sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| inverse(sk_c2) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f614,f453]) ).
fof(f633,plain,
( sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| inverse(sk_c2) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f614,f632]) ).
fof(f640,plain,
( ~ sQ25_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ0_spl
| inverse(sk_c2) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f607,f603]) ).
fof(f641,plain,
( ~ sQ25_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ0_spl
| inverse(sk_c2) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f607,f640]) ).
fof(f644,plain,
( sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ25_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f641,f633]) ).
fof(f645,plain,
( sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ25_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f644]) ).
fof(f646,plain,
( sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ25_spl ),
inference(contradiction_clause,[status(thm)],[f645]) ).
fof(f654,plain,
( ~ sQ11_spl
| ~ sQ3_spl
| multiply(sk_c4,sk_c7) != sk_c8 ),
inference(resolution,[status(thm)],[f82,f134]) ).
fof(f655,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| multiply(sk_c4,sk_c7) != sk_c8
| sk_c8 != sk_c8 ),
inference(paramodulation,[status(thm)],[f82,f134]) ).
fof(f658,definition,
( sQ33_spl
<=> multiply(sk_c4,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f661,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| ~ sQ33_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f655,f196,f658,f133,f81]) ).
fof(f662,plain,
( ~ sQ1_spl
| ~ sQ11_spl
| multiply(sk_c8,sk_c7) != sk_c8
| sk_c7 != sk_c8 ),
inference(paramodulation,[status(thm)],[f74,f134]) ).
fof(f665,definition,
( sQ34_spl
<=> multiply(sk_c8,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f667,plain,
( sQ34_spl
| multiply(sk_c8,sk_c7) != sk_c8 ),
inference(component_clause,[status(thm)],[f665]) ).
fof(f668,plain,
( ~ sQ1_spl
| ~ sQ11_spl
| ~ sQ34_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f662,f288,f665,f133,f73]) ).
fof(f669,plain,
( ~ sQ2_spl
| sk_c8 = multiply(inverse(sk_c4),sk_c7) ),
inference(paramodulation,[status(thm)],[f78,f212]) ).
fof(f671,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| sk_c8 = multiply(sk_c8,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f82,f669]) ).
fof(f704,plain,
( ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ5_spl
| multiply(sk_c7,identity) = multiply(sk_c5,sk_c7) ),
inference(paramodulation,[status(thm)],[f364,f149]) ).
fof(f707,plain,
( ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c4 = multiply(sk_c5,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f309,f704]) ).
fof(f720,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| sQ34_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f671,f667]) ).
fof(f721,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| sQ34_spl ),
inference(contradiction_clause,[status(thm)],[f720]) ).
fof(f749,plain,
( sQ30_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ3_spl
| inverse(inverse(sk_c4)) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f754,f301]) ).
fof(f750,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ3_spl
| X0 = multiply(inverse(sk_c4),X0) ),
inference(backward_demodulation,[status(thm)],[f754,f223]) ).
fof(f752,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ3_spl
| multiply(inverse(X0),X0) = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f754,f36]) ).
fof(f753,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ3_spl
| multiply(sk_c4,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f754,f35]) ).
fof(f754,plain,
( ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c4 = identity ),
inference(forward_demodulation,[status(thm)],[f314,f707]) ).
fof(f755,plain,
( sQ30_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ3_spl
| inverse(sk_c8) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f82,f749]) ).
fof(f756,plain,
( sQ30_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c7 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f74,f755]) ).
fof(f757,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ3_spl
| X0 = multiply(sk_c8,X0) ),
inference(forward_demodulation,[status(thm)],[f82,f750]) ).
fof(f771,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ3_spl
| X0 = multiply(inverse(sk_c8),X0) ),
inference(paramodulation,[status(thm)],[f757,f212]) ).
fof(f773,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ3_spl
| X0 = multiply(sk_c7,X0) ),
inference(forward_demodulation,[status(thm)],[f74,f771]) ).
fof(f774,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c8 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f753,f78]) ).
fof(f777,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f774,f756]) ).
fof(f778,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sQ30_spl ),
inference(contradiction_clause,[status(thm)],[f777]) ).
fof(f789,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| inverse(sk_c7) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f774,f74]) ).
fof(f816,plain,
( ~ sQ11_spl
| ~ sQ3_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ5_spl
| sk_c7 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f753,f654]) ).
fof(f817,plain,
( ~ sQ11_spl
| ~ sQ3_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ2_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f774,f816]) ).
fof(f818,plain,
( ~ sQ11_spl
| ~ sQ3_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f817]) ).
fof(f819,plain,
( ~ sQ11_spl
| ~ sQ3_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f818]) ).
fof(f834,plain,
( sQ16_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ3_spl
| multiply(sk_c7,sk_c8) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f774,f171]) ).
fof(f835,plain,
( sQ16_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c8 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f773,f834]) ).
fof(f836,plain,
( sQ16_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f774,f835]) ).
fof(f837,plain,
( sQ16_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f836]) ).
fof(f838,plain,
( sQ16_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f837]) ).
fof(f841,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ3_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c7) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f774,f140]) ).
fof(f842,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ3_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f774,f841]) ).
fof(f846,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| multiply(sk_c7,sk_c7) = sk_c4 ),
inference(paramodulation,[status(thm)],[f789,f752]) ).
fof(f848,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c7 = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f773,f846]) ).
fof(f850,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| inverse(sk_c7) = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f848,f789]) ).
fof(f858,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| inverse(sk_c4) = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f848,f850]) ).
fof(f863,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ3_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c4) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f848,f842]) ).
fof(f864,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ3_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c4) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f848,f863]) ).
fof(f865,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ3_spl
| inverse(X0) != sk_c4
| multiply(X0,sk_c4) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f848,f864]) ).
fof(f866,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ13_spl
| multiply(sk_c4,sk_c4) != sk_c4 ),
inference(resolution,[status(thm)],[f865,f858]) ).
fof(f869,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ13_spl
| sk_c4 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f753,f866]) ).
fof(f870,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ13_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f869]) ).
fof(f871,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f870]) ).
fof(f872,plain,
$false,
inference(sat_refutation,[status(thm)],[f76,f80,f84,f88,f92,f96,f100,f101,f102,f103,f104,f105,f109,f110,f111,f112,f113,f114,f118,f119,f120,f121,f122,f123,f127,f128,f129,f130,f131,f132,f145,f172,f176,f180,f184,f199,f203,f205,f237,f252,f256,f260,f261,f269,f287,f291,f302,f345,f352,f356,f391,f396,f418,f430,f478,f556,f590,f601,f646,f661,f668,f721,f778,f819,f838,f871]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP227-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n002.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sun Sep 20 20:09:31 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.45 % Drodi V4.1.1
% 0.25/0.50 % Refutation found
% 0.25/0.50 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.25/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.25/0.54 % Elapsed time: 0.099565 seconds
% 0.25/0.54 % CPU time: 0.364303 seconds
% 0.25/0.54 % Total memory used: 106.212 MB
% 0.25/0.54 % Net memory used: 105.928 MB
%------------------------------------------------------------------------------