%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP367-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:33:32 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 56
% Syntax : Number of formulae : 287 ( 14 unt; 22 def)
% Number of atoms : 1073 ( 333 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1483 ( 697 ~; 764 |; 0 &)
% ( 22 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 24 ( 22 usr; 23 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 55 ( 55 !; 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_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c8,sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c8,sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c8,sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c8,sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c8,sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( inverse(sk_c5) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c3,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c3,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( inverse(sk_c5) = sk_c7
| inverse(sk_c3) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c3) = 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
| inverse(X5) != sk_c6
| multiply(X5,sk_c6) != sk_c8
| inverse(X4) != sk_c8
| multiply(X4,sk_c8) != X3
| multiply(sk_c8,X3) != sk_c7
| multiply(sk_c6,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_c6,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f39,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f40,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f41,plain,
( inverse(sk_c5) = sk_c7
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f42,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f43,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c8,sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f44,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c8,sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f45,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c8,sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f46,plain,
( inverse(sk_c5) = sk_c7
| multiply(sk_c8,sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f47,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c8,sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f48,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f49,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f50,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f51,plain,
( inverse(sk_c5) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f52,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f53,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f54,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f55,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f56,plain,
( inverse(sk_c5) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f57,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f58,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c3,sk_c6) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f59,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c3,sk_c6) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f60,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c3,sk_c6) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f61,plain,
( inverse(sk_c5) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f62,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c3,sk_c6) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f63,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c3) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f64,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c3) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f65,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c3) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f66,plain,
( inverse(sk_c5) = sk_c7
| inverse(sk_c3) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f67,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c3) = 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] :
( inverse(X5) != sk_c6
| multiply(X5,sk_c6) != sk_c8
| ! [X4] :
( inverse(X4) != sk_c8
| ! [X3] :
( multiply(X4,sk_c8) != X3
| multiply(sk_c8,X3) != sk_c7
| multiply(sk_c6,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
| inverse(X2) != sk_c6
| multiply(X2,sk_c6) != sk_c8
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != X0
| multiply(sk_c8,X0) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7 ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f70,definition,
( sQ0_spl
<=> multiply(sk_c6,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f71,plain,
( ~ sQ0_spl
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f72,plain,
( sQ0_spl
| multiply(sk_c6,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
<=> multiply(sk_c8,sk_c2) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ6_spl
| multiply(sk_c8,sk_c2) = sk_c7 ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f96,plain,
( sQ1_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f43,f93,f73]) ).
fof(f97,plain,
( sQ2_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f44,f93,f77]) ).
fof(f98,plain,
( sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f45,f93,f81]) ).
fof(f99,plain,
( sQ4_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f46,f93,f85]) ).
fof(f100,plain,
( sQ5_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f47,f93,f89]) ).
fof(f101,definition,
( sQ7_spl
<=> multiply(sk_c1,sk_c8) = sk_c2 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f102,plain,
( ~ sQ7_spl
| multiply(sk_c1,sk_c8) = sk_c2 ),
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_c1) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f110,plain,
( ~ sQ8_spl
| inverse(sk_c1) = sk_c8 ),
inference(component_clause,[status(thm)],[f109]) ).
fof(f112,plain,
( sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f53,f109,f73]) ).
fof(f113,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f54,f109,f77]) ).
fof(f114,plain,
( sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f55,f109,f81]) ).
fof(f115,plain,
( sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f56,f109,f85]) ).
fof(f116,plain,
( sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f57,f109,f89]) ).
fof(f117,definition,
( sQ9_spl
<=> multiply(sk_c3,sk_c6) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f118,plain,
( ~ sQ9_spl
| multiply(sk_c3,sk_c6) = sk_c8 ),
inference(component_clause,[status(thm)],[f117]) ).
fof(f120,plain,
( sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f58,f117,f73]) ).
fof(f121,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f59,f117,f77]) ).
fof(f122,plain,
( sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f60,f117,f81]) ).
fof(f123,plain,
( sQ4_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f61,f117,f85]) ).
fof(f124,plain,
( sQ5_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f62,f117,f89]) ).
fof(f125,definition,
( sQ10_spl
<=> inverse(sk_c3) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f126,plain,
( ~ sQ10_spl
| inverse(sk_c3) = 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,X1] :
( sQ11_spl
<=> ( inverse(X1) != sk_c8
| multiply(X1,sk_c8) != X0
| multiply(sk_c8,X0) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f134,plain,
! [X0,X1] :
( ~ sQ11_spl
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != X0
| multiply(sk_c8,X0) != sk_c7 ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,definition,
! [X2] :
( sQ12_spl
<=> ( inverse(X2) != sk_c6
| multiply(X2,sk_c6) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f137,plain,
! [X0] :
( ~ sQ12_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c8 ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f139,definition,
! [X3] :
( sQ13_spl
<=> ( multiply(X3,sk_c7) != sk_c8
| inverse(X3) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f140,plain,
! [X0] :
( ~ sQ13_spl
| multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c8 ),
inference(component_clause,[status(thm)],[f139]) ).
fof(f142,definition,
! [X4] :
( sQ14_spl
<=> ( multiply(X4,sk_c6) != sk_c7
| inverse(X4) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f143,plain,
! [X0] :
( ~ sQ14_spl
| multiply(X0,sk_c6) != sk_c7
| inverse(X0) != sk_c7 ),
inference(component_clause,[status(thm)],[f142]) ).
fof(f145,plain,
( sQ14_spl
| sQ13_spl
| ~ sQ1_spl
| sQ12_spl
| sQ11_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f69,f70,f133,f136,f73,f139,f142]) ).
fof(f146,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| inverse(sk_c5) != sk_c7 ),
inference(resolution,[status(thm)],[f143,f90]) ).
fof(f147,plain,
( ~ sQ9_spl
| ~ sQ14_spl
| sk_c8 != sk_c7
| inverse(sk_c3) != sk_c7 ),
inference(paramodulation,[status(thm)],[f118,f143]) ).
fof(f149,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| ~ sQ4_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f86,f146]) ).
fof(f150,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f149]) ).
fof(f151,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f150]) ).
fof(f152,plain,
( ~ sQ3_spl
| ~ sQ13_spl
| inverse(sk_c4) != sk_c8 ),
inference(resolution,[status(thm)],[f140,f82]) ).
fof(f154,plain,
( ~ sQ3_spl
| ~ sQ13_spl
| ~ sQ2_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f78,f152]) ).
fof(f155,plain,
( ~ sQ3_spl
| ~ sQ13_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f154]) ).
fof(f156,plain,
( ~ sQ3_spl
| ~ sQ13_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f155]) ).
fof(f157,plain,
! [X0] :
( ~ sQ11_spl
| inverse(X0) != sk_c8
| multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ),
inference(destructive_equality_resolution,[status(thm)],[f134]) ).
fof(f158,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| inverse(sk_c3) != sk_c6 ),
inference(resolution,[status(thm)],[f137,f118]) ).
fof(f160,plain,
( ~ sQ5_spl
| ~ sQ12_spl
| inverse(sk_c5) != sk_c6
| sk_c7 != sk_c8 ),
inference(paramodulation,[status(thm)],[f90,f137]) ).
fof(f161,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ10_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f126,f158]) ).
fof(f162,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f161]) ).
fof(f163,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f162]) ).
fof(f170,plain,
! [X0] :
( ~ sQ5_spl
| multiply(sk_c7,X0) = multiply(sk_c5,multiply(sk_c6,X0)) ),
inference(paramodulation,[status(thm)],[f90,f37]) ).
fof(f175,plain,
( ~ sQ7_spl
| ~ sQ11_spl
| inverse(sk_c1) != sk_c8
| multiply(sk_c8,sk_c2) != sk_c7 ),
inference(paramodulation,[status(thm)],[f102,f157]) ).
fof(f183,plain,
( ~ sQ7_spl
| ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f175,f93,f109,f133,f101]) ).
fof(f189,plain,
( ~ sQ8_spl
| multiply(sk_c8,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f110,f36]) ).
fof(f190,plain,
( ~ sQ10_spl
| multiply(sk_c6,sk_c3) = identity ),
inference(paramodulation,[status(thm)],[f126,f36]) ).
fof(f191,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f36,f37]) ).
fof(f192,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f35,f191]) ).
fof(f193,plain,
! [X0] :
( ~ sQ1_spl
| multiply(sk_c6,X0) = multiply(sk_c7,multiply(sk_c8,X0)) ),
inference(paramodulation,[status(thm)],[f74,f37]) ).
fof(f203,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f35,f192]) ).
fof(f209,plain,
( ~ sQ7_spl
| sk_c8 = multiply(inverse(sk_c1),sk_c2) ),
inference(paramodulation,[status(thm)],[f102,f192]) ).
fof(f210,plain,
( ~ sQ9_spl
| sk_c6 = multiply(inverse(sk_c3),sk_c8) ),
inference(paramodulation,[status(thm)],[f118,f192]) ).
fof(f214,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| sk_c8 = multiply(sk_c8,sk_c2) ),
inference(forward_demodulation,[status(thm)],[f110,f209]) ).
fof(f215,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| sk_c8 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f94,f214]) ).
fof(f216,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| sk_c6 = multiply(sk_c6,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f126,f210]) ).
fof(f217,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| sk_c6 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f71,f216]) ).
fof(f219,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| multiply(sk_c7,sk_c1) = identity ),
inference(backward_demodulation,[status(thm)],[f215,f189]) ).
fof(f224,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| multiply(sk_c6,sk_c7) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f215,f71]) ).
fof(f225,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| multiply(sk_c7,sk_c2) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f215,f94]) ).
fof(f227,plain,
( ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| multiply(sk_c3,sk_c6) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f215,f118]) ).
fof(f229,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| inverse(sk_c1) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f215,f110]) ).
fof(f230,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| multiply(sk_c7,sk_c3) = identity ),
inference(backward_demodulation,[status(thm)],[f217,f190]) ).
fof(f232,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| inverse(sk_c3) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f217,f126]) ).
fof(f242,plain,
! [X0] : X0 = multiply(inverse(inverse(identity)),X0),
inference(paramodulation,[status(thm)],[f203,f192]) ).
fof(f244,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f215,f140]) ).
fof(f245,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| multiply(X0,sk_c7) != sk_c7
| inverse(X0) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f215,f244]) ).
fof(f248,plain,
( ~ sQ13_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| sk_c7 != sk_c7
| inverse(inverse(identity)) != sk_c7 ),
inference(paramodulation,[status(thm)],[f203,f245]) ).
fof(f250,plain,
( ~ sQ13_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| sk_c7 != sk_c7
| inverse(identity) != sk_c7 ),
inference(paramodulation,[status(thm)],[f35,f245]) ).
fof(f252,definition,
( sQ18_spl
<=> inverse(inverse(identity)) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f254,plain,
( sQ18_spl
| inverse(inverse(identity)) != sk_c7 ),
inference(component_clause,[status(thm)],[f252]) ).
fof(f255,definition,
( sQ19_spl
<=> sk_c7 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f257,plain,
( sQ19_spl
| sk_c7 != sk_c7 ),
inference(component_clause,[status(thm)],[f255]) ).
fof(f258,plain,
( ~ sQ13_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ19_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f248,f252,f255,f93,f109,f101,f139]) ).
fof(f262,definition,
( sQ21_spl
<=> identity = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f264,plain,
( sQ21_spl
| identity != sk_c7 ),
inference(component_clause,[status(thm)],[f262]) ).
fof(f266,definition,
( sQ22_spl
<=> inverse(identity) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f267,plain,
( ~ sQ22_spl
| inverse(identity) = sk_c7 ),
inference(component_clause,[status(thm)],[f266]) ).
fof(f268,plain,
( sQ22_spl
| inverse(identity) != sk_c7 ),
inference(component_clause,[status(thm)],[f266]) ).
fof(f269,plain,
( ~ sQ13_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ19_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f250,f266,f255,f93,f109,f101,f139]) ).
fof(f270,plain,
( sQ19_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f257]) ).
fof(f271,plain,
sQ19_spl,
inference(contradiction_clause,[status(thm)],[f270]) ).
fof(f272,plain,
( sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| multiply(sk_c7,sk_c7) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f215,f75]) ).
fof(f273,plain,
( sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| multiply(sk_c7,sk_c7) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f217,f272]) ).
fof(f274,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c7,sk_c7) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f217,f224]) ).
fof(f275,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c7 = multiply(inverse(sk_c7),sk_c7) ),
inference(paramodulation,[status(thm)],[f274,f192]) ).
fof(f277,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c7 = identity ),
inference(forward_demodulation,[status(thm)],[f36,f275]) ).
fof(f278,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c2 = multiply(inverse(sk_c7),sk_c7) ),
inference(paramodulation,[status(thm)],[f225,f192]) ).
fof(f280,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c2 = identity ),
inference(forward_demodulation,[status(thm)],[f36,f278]) ).
fof(f283,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c7,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f277,f35]) ).
fof(f284,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c2 = identity ),
inference(backward_demodulation,[status(thm)],[f292,f277]) ).
fof(f287,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| inverse(sk_c3) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f292,f232]) ).
fof(f288,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| inverse(sk_c1) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f292,f229]) ).
fof(f289,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c6 = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f292,f217]) ).
fof(f290,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c8 = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f292,f215]) ).
fof(f292,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c2 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f277,f280]) ).
fof(f299,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c2,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f292,f283]) ).
fof(f302,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| X0 = multiply(sk_c2,multiply(sk_c3,X0)) ),
inference(paramodulation,[status(thm)],[f287,f192]) ).
fof(f303,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| X0 = multiply(sk_c3,X0) ),
inference(forward_demodulation,[status(thm)],[f299,f302]) ).
fof(f304,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| X0 = multiply(sk_c2,multiply(sk_c1,X0)) ),
inference(paramodulation,[status(thm)],[f288,f192]) ).
fof(f305,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| X0 = multiply(sk_c1,X0) ),
inference(forward_demodulation,[status(thm)],[f299,f304]) ).
fof(f313,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c2,sk_c1) = identity ),
inference(forward_demodulation,[status(thm)],[f292,f219]) ).
fof(f314,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c1 = identity ),
inference(forward_demodulation,[status(thm)],[f299,f313]) ).
fof(f317,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| inverse(sk_c3) = sk_c1 ),
inference(backward_demodulation,[status(thm)],[f323,f287]) ).
fof(f319,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c8 = sk_c1 ),
inference(backward_demodulation,[status(thm)],[f323,f290]) ).
fof(f320,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c6 = sk_c1 ),
inference(backward_demodulation,[status(thm)],[f323,f289]) ).
fof(f321,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c1 = identity ),
inference(backward_demodulation,[status(thm)],[f323,f284]) ).
fof(f323,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c1 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f284,f314]) ).
fof(f324,plain,
( ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ0_spl
| sk_c6 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f303,f227]) ).
fof(f325,plain,
( ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ0_spl
| sk_c1 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f320,f324]) ).
fof(f339,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| multiply(sk_c1,sk_c3) = identity ),
inference(forward_demodulation,[status(thm)],[f325,f230]) ).
fof(f340,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| sk_c3 = identity ),
inference(forward_demodulation,[status(thm)],[f305,f339]) ).
fof(f341,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| inverse(sk_c3) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f350,f317]) ).
fof(f344,plain,
( ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ0_spl
| sk_c3 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f350,f325]) ).
fof(f345,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c3 = identity ),
inference(backward_demodulation,[status(thm)],[f350,f321]) ).
fof(f347,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c8 = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f350,f319]) ).
fof(f350,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| sk_c3 = sk_c1 ),
inference(forward_demodulation,[status(thm)],[f321,f340]) ).
fof(f357,plain,
( sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| multiply(sk_c3,sk_c7) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f344,f273]) ).
fof(f358,plain,
( sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f303,f357]) ).
fof(f359,plain,
( sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| sk_c3 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f344,f358]) ).
fof(f360,plain,
( sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f344,f359]) ).
fof(f361,plain,
( sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f360]) ).
fof(f362,plain,
( sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f361]) ).
fof(f363,plain,
( sQ18_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| inverse(inverse(sk_c3)) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f345,f254]) ).
fof(f364,plain,
( sQ18_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| inverse(sk_c3) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f341,f363]) ).
fof(f365,plain,
( sQ18_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c3 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f341,f364]) ).
fof(f366,plain,
( sQ18_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f344,f365]) ).
fof(f367,plain,
( sQ18_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f366]) ).
fof(f368,plain,
( sQ18_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f367]) ).
fof(f387,definition,
( sQ23_spl
<=> inverse(sk_c3) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f389,plain,
( sQ23_spl
| inverse(sk_c3) != sk_c7 ),
inference(component_clause,[status(thm)],[f387]) ).
fof(f390,definition,
( sQ24_spl
<=> sk_c8 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f392,plain,
( sQ24_spl
| sk_c8 != sk_c7 ),
inference(component_clause,[status(thm)],[f390]) ).
fof(f393,plain,
( ~ sQ9_spl
| ~ sQ14_spl
| ~ sQ24_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f147,f387,f390,f142,f117]) ).
fof(f396,plain,
( sQ23_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c3 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f341,f389]) ).
fof(f397,plain,
( sQ23_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f344,f396]) ).
fof(f398,plain,
( sQ23_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f397]) ).
fof(f399,plain,
( sQ23_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f398]) ).
fof(f400,plain,
( sQ24_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c3 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f347,f392]) ).
fof(f401,plain,
( sQ24_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f344,f400]) ).
fof(f402,plain,
( sQ24_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f401]) ).
fof(f403,plain,
( sQ24_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f402]) ).
fof(f405,plain,
! [X0] :
( ~ sQ2_spl
| X0 = multiply(sk_c8,multiply(sk_c4,X0)) ),
inference(paramodulation,[status(thm)],[f78,f192]) ).
fof(f408,plain,
! [X0] : multiply(identity,X0) = X0,
inference(paramodulation,[status(thm)],[f192,f203]) ).
fof(f414,plain,
( ~ sQ3_spl
| sk_c7 = multiply(inverse(sk_c4),sk_c8) ),
inference(paramodulation,[status(thm)],[f82,f192]) ).
fof(f416,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| sk_c7 = multiply(sk_c8,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f78,f414]) ).
fof(f417,plain,
( ~ sQ5_spl
| sk_c6 = multiply(inverse(sk_c5),sk_c7) ),
inference(paramodulation,[status(thm)],[f90,f192]) ).
fof(f419,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| sk_c6 = multiply(sk_c7,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f86,f417]) ).
fof(f458,plain,
inverse(identity) = identity,
inference(paramodulation,[status(thm)],[f36,f242]) ).
fof(f466,plain,
( sQ22_spl
| identity != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f458,f268]) ).
fof(f488,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| multiply(sk_c6,sk_c8) = multiply(sk_c7,sk_c7) ),
inference(paramodulation,[status(thm)],[f416,f193]) ).
fof(f492,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c6,sk_c8) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f419,f488]) ).
fof(f495,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c6 != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f492,f72]) ).
fof(f496,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c7,sk_c8) = multiply(sk_c5,sk_c6) ),
inference(paramodulation,[status(thm)],[f492,f170]) ).
fof(f497,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c8 = multiply(inverse(sk_c6),sk_c6) ),
inference(paramodulation,[status(thm)],[f492,f192]) ).
fof(f499,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c6 = multiply(sk_c5,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f74,f496]) ).
fof(f500,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c6 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f90,f499]) ).
fof(f501,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c8 = identity ),
inference(forward_demodulation,[status(thm)],[f36,f497]) ).
fof(f502,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f500,f495]) ).
fof(f503,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f502]) ).
fof(f505,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(identity) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f501,f458]) ).
fof(f510,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c8,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f501,f408]) ).
fof(f511,plain,
( sQ21_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c8 != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f501,f264]) ).
fof(f512,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(sk_c8) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f501,f505]) ).
fof(f523,plain,
( ~ sQ2_spl
| ~ sQ11_spl
| inverse(sk_c4) != sk_c8
| sk_c8 != sk_c7 ),
inference(paramodulation,[status(thm)],[f405,f157]) ).
fof(f526,plain,
( ~ sQ11_spl
| ~ sQ2_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f523,f390,f77,f133]) ).
fof(f534,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c7 = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f510,f416]) ).
fof(f540,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f534,f511]) ).
fof(f541,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sQ21_spl ),
inference(contradiction_clause,[status(thm)],[f540]) ).
fof(f544,plain,
( sQ22_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f466,f262,f266]) ).
fof(f551,plain,
( ~ sQ22_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(sk_c8) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f501,f267]) ).
fof(f552,plain,
( ~ sQ22_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c8 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f512,f551]) ).
fof(f555,definition,
( sQ26_spl
<=> inverse(sk_c5) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f557,plain,
( sQ26_spl
| inverse(sk_c5) != sk_c6 ),
inference(component_clause,[status(thm)],[f555]) ).
fof(f558,plain,
( ~ sQ5_spl
| ~ sQ12_spl
| ~ sQ26_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f160,f390,f555,f136,f89]) ).
fof(f581,plain,
( ~ sQ22_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f552,f392]) ).
fof(f582,plain,
( ~ sQ22_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sQ24_spl ),
inference(contradiction_clause,[status(thm)],[f581]) ).
fof(f593,plain,
( sQ26_spl
| ~ sQ4_spl
| sk_c7 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f86,f557]) ).
fof(f594,plain,
( sQ26_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f500,f593]) ).
fof(f595,plain,
( sQ26_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f594]) ).
fof(f596,plain,
( sQ26_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f595]) ).
fof(f597,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,f145,f151,f156,f163,f183,f258,f269,f271,f362,f368,f393,f399,f403,f503,f526,f541,f544,f558,f582,f596]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP367-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n017.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 20:05:26 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.14/0.39 % Refutation found
% 0.14/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.42 % Elapsed time: 0.042582 seconds
% 0.14/0.42 % CPU time: 0.120577 seconds
% 0.14/0.42 % Total memory used: 30.213 MB
% 0.14/0.42 % Net memory used: 30.162 MB
%------------------------------------------------------------------------------