%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP376-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 12:33:33 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.42s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 53
% Syntax : Number of formulae : 295 ( 13 unt; 20 def)
% Number of atoms : 1079 ( 338 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1487 ( 703 ~; 764 |; 0 &)
% ( 20 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 21 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 51 ( 51 !; 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_c6,sk_c7) = sk_c5
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c2,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c2,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c2) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c2) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c2) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
! [X3,X4,X1,X2] :
( multiply(X2,sk_c5) != sk_c6
| inverse(X2) != sk_c6
| multiply(X1,sk_c6) != sk_c7
| inverse(X1) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(X4) != sk_c5
| multiply(X4,sk_c5) != sk_c7
| multiply(sk_c5,sk_c6) != sk_c7
| inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c6
| inverse(sk_c7) != sk_c6 ),
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_c6,sk_c7) = sk_c5
| inverse(sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f39,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f40,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f41,plain,
( inverse(sk_c4) = sk_c6
| inverse(sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f42,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f43,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f44,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f45,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f46,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f47,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f48,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f49,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f50,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f51,plain,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f52,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f53,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f54,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f55,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f56,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f57,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f59,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c2,sk_c5) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f60,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c2,sk_c5) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f61,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f62,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f63,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c2) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f64,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c2) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f65,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f66,plain,
( inverse(sk_c4) = sk_c6
| inverse(sk_c2) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f67,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f68,plain,
! [X2] :
( multiply(X2,sk_c5) != sk_c6
| inverse(X2) != sk_c6
| ! [X1] :
( multiply(X1,sk_c6) != sk_c7
| inverse(X1) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| ! [X4] :
( inverse(X4) != sk_c5
| multiply(X4,sk_c5) != sk_c7
| multiply(sk_c5,sk_c6) != sk_c7
| ! [X3] :
( inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c6
| inverse(sk_c7) != sk_c6 ) ) ) ),
inference(miniscoping,[status(thm)],[f34]) ).
fof(f69,plain,
! [X0,X1,X2,X3] :
( multiply(X3,sk_c5) != sk_c6
| inverse(X3) != sk_c6
| multiply(X2,sk_c6) != sk_c7
| inverse(X2) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(X1) != sk_c5
| multiply(X1,sk_c5) != sk_c7
| multiply(sk_c5,sk_c6) != sk_c7
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6
| inverse(sk_c7) != sk_c6 ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f70,definition,
( sQ0_spl
<=> inverse(sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f71,plain,
( ~ sQ0_spl
| inverse(sk_c7) = sk_c6 ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f72,plain,
( sQ0_spl
| inverse(sk_c7) != sk_c6 ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f73,definition,
( sQ1_spl
<=> multiply(sk_c6,sk_c7) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f74,plain,
( ~ sQ1_spl
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f75,plain,
( sQ1_spl
| multiply(sk_c6,sk_c7) != sk_c5 ),
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_c3) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f78,plain,
( ~ sQ2_spl
| inverse(sk_c3) = 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
<=> multiply(sk_c3,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f82,plain,
( ~ sQ3_spl
| multiply(sk_c3,sk_c6) = sk_c7 ),
inference(component_clause,[status(thm)],[f81]) ).
fof(f84,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f40,f70,f81]) ).
fof(f85,definition,
( sQ4_spl
<=> inverse(sk_c4) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ4_spl
| inverse(sk_c4) = sk_c6 ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f88,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f41,f70,f85]) ).
fof(f89,definition,
( sQ5_spl
<=> multiply(sk_c4,sk_c5) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f90,plain,
( ~ sQ5_spl
| multiply(sk_c4,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_c1,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ6_spl
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f96,plain,
( sQ1_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f43,f93,f73]) ).
fof(f97,plain,
( sQ2_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f44,f93,f77]) ).
fof(f98,plain,
( sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f45,f93,f81]) ).
fof(f99,plain,
( sQ4_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f46,f93,f85]) ).
fof(f100,plain,
( sQ5_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f47,f93,f89]) ).
fof(f101,definition,
( sQ7_spl
<=> inverse(sk_c1) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f102,plain,
( ~ sQ7_spl
| inverse(sk_c1) = sk_c7 ),
inference(component_clause,[status(thm)],[f101]) ).
fof(f104,plain,
( sQ1_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f48,f101,f73]) ).
fof(f105,plain,
( sQ2_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f49,f101,f77]) ).
fof(f106,plain,
( sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f50,f101,f81]) ).
fof(f107,plain,
( sQ4_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f51,f101,f85]) ).
fof(f108,plain,
( sQ5_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f52,f101,f89]) ).
fof(f109,definition,
( sQ8_spl
<=> multiply(sk_c5,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f110,plain,
( ~ sQ8_spl
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(component_clause,[status(thm)],[f109]) ).
fof(f111,plain,
( sQ8_spl
| multiply(sk_c5,sk_c6) != sk_c7 ),
inference(component_clause,[status(thm)],[f109]) ).
fof(f112,plain,
( sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f53,f109,f73]) ).
fof(f113,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f54,f109,f77]) ).
fof(f114,plain,
( sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f55,f109,f81]) ).
fof(f115,plain,
( sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f56,f109,f85]) ).
fof(f116,plain,
( sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f57,f109,f89]) ).
fof(f117,definition,
( sQ9_spl
<=> multiply(sk_c2,sk_c5) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f118,plain,
( ~ sQ9_spl
| multiply(sk_c2,sk_c5) = sk_c7 ),
inference(component_clause,[status(thm)],[f117]) ).
fof(f121,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f59,f117,f77]) ).
fof(f122,plain,
( sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f60,f117,f81]) ).
fof(f123,plain,
( sQ4_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f61,f117,f85]) ).
fof(f124,plain,
( sQ5_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f62,f117,f89]) ).
fof(f125,definition,
( sQ10_spl
<=> inverse(sk_c2) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f126,plain,
( ~ sQ10_spl
| inverse(sk_c2) = sk_c5 ),
inference(component_clause,[status(thm)],[f125]) ).
fof(f128,plain,
( sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f63,f125,f73]) ).
fof(f129,plain,
( sQ2_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f64,f125,f77]) ).
fof(f130,plain,
( sQ3_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f65,f125,f81]) ).
fof(f131,plain,
( sQ4_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f66,f125,f85]) ).
fof(f132,plain,
( sQ5_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f67,f125,f89]) ).
fof(f133,definition,
! [X0] :
( sQ11_spl
<=> ( inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f134,plain,
! [X0] :
( ~ sQ11_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6 ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,definition,
! [X1] :
( sQ12_spl
<=> ( inverse(X1) != sk_c5
| multiply(X1,sk_c5) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f137,plain,
! [X0] :
( ~ sQ12_spl
| inverse(X0) != sk_c5
| multiply(X0,sk_c5) != sk_c7 ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f139,definition,
! [X2] :
( sQ13_spl
<=> ( multiply(X2,sk_c6) != sk_c7
| inverse(X2) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f140,plain,
! [X0] :
( ~ sQ13_spl
| multiply(X0,sk_c6) != sk_c7
| inverse(X0) != sk_c7 ),
inference(component_clause,[status(thm)],[f139]) ).
fof(f142,definition,
! [X3] :
( sQ14_spl
<=> ( multiply(X3,sk_c5) != sk_c6
| inverse(X3) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f143,plain,
! [X0] :
( ~ sQ14_spl
| multiply(X0,sk_c5) != sk_c6
| inverse(X0) != sk_c6 ),
inference(component_clause,[status(thm)],[f142]) ).
fof(f145,plain,
( sQ14_spl
| sQ13_spl
| ~ sQ1_spl
| sQ12_spl
| ~ sQ8_spl
| sQ11_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f69,f70,f133,f109,f136,f73,f139,f142]) ).
fof(f146,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| inverse(sk_c4) != sk_c6 ),
inference(resolution,[status(thm)],[f143,f90]) ).
fof(f147,plain,
( ~ sQ9_spl
| ~ sQ14_spl
| sk_c7 != sk_c6
| inverse(sk_c2) != sk_c6 ),
inference(paramodulation,[status(thm)],[f118,f143]) ).
fof(f149,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| ~ sQ4_spl
| sk_c6 != sk_c6 ),
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(f153,plain,
( ~ sQ3_spl
| ~ sQ13_spl
| inverse(sk_c3) != sk_c7 ),
inference(resolution,[status(thm)],[f140,f82]) ).
fof(f154,plain,
( ~ sQ8_spl
| ~ sQ13_spl
| sk_c7 != sk_c7
| inverse(sk_c5) != sk_c7 ),
inference(paramodulation,[status(thm)],[f110,f140]) ).
fof(f156,plain,
( ~ sQ3_spl
| ~ sQ13_spl
| ~ sQ2_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f78,f153]) ).
fof(f157,plain,
( ~ sQ3_spl
| ~ sQ13_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f156]) ).
fof(f158,plain,
( ~ sQ3_spl
| ~ sQ13_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f157]) ).
fof(f159,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| inverse(sk_c2) != sk_c5 ),
inference(resolution,[status(thm)],[f137,f118]) ).
fof(f161,plain,
( ~ sQ5_spl
| ~ sQ12_spl
| inverse(sk_c4) != sk_c5
| sk_c6 != sk_c7 ),
inference(paramodulation,[status(thm)],[f90,f137]) ).
fof(f162,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ10_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f126,f159]) ).
fof(f163,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f162]) ).
fof(f164,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f163]) ).
fof(f167,plain,
! [X0] :
( ~ sQ6_spl
| multiply(sk_c6,X0) = multiply(sk_c1,multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f94,f37]) ).
fof(f173,plain,
( ~ sQ6_spl
| ~ sQ11_spl
| inverse(sk_c1) != sk_c7 ),
inference(resolution,[status(thm)],[f134,f94]) ).
fof(f176,plain,
( ~ sQ6_spl
| ~ sQ11_spl
| ~ sQ7_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f102,f173]) ).
fof(f177,plain,
( ~ sQ6_spl
| ~ sQ11_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f176]) ).
fof(f178,plain,
( ~ sQ6_spl
| ~ sQ11_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f177]) ).
fof(f179,definition,
( sQ15_spl
<=> inverse(sk_c5) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f181,plain,
( sQ15_spl
| inverse(sk_c5) != sk_c7 ),
inference(component_clause,[status(thm)],[f179]) ).
fof(f182,definition,
( sQ16_spl
<=> sk_c7 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f184,plain,
( sQ16_spl
| sk_c7 != sk_c7 ),
inference(component_clause,[status(thm)],[f182]) ).
fof(f185,plain,
( ~ sQ8_spl
| ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f154,f179,f182,f139,f109]) ).
fof(f187,plain,
( sQ16_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f184]) ).
fof(f188,plain,
sQ16_spl,
inference(contradiction_clause,[status(thm)],[f187]) ).
fof(f190,plain,
( ~ sQ0_spl
| multiply(sk_c6,sk_c7) = identity ),
inference(paramodulation,[status(thm)],[f71,f36]) ).
fof(f191,plain,
( ~ sQ7_spl
| multiply(sk_c7,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f102,f36]) ).
fof(f192,plain,
( ~ sQ10_spl
| multiply(sk_c5,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f126,f36]) ).
fof(f193,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f36,f37]) ).
fof(f194,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f35,f193]) ).
fof(f243,plain,
( sQ1_spl
| ~ sQ0_spl
| identity != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f190,f75]) ).
fof(f250,plain,
( ~ sQ6_spl
| sk_c7 = multiply(inverse(sk_c1),sk_c6) ),
inference(paramodulation,[status(thm)],[f94,f194]) ).
fof(f251,plain,
( ~ sQ7_spl
| sk_c1 = multiply(inverse(sk_c7),identity) ),
inference(paramodulation,[status(thm)],[f191,f194]) ).
fof(f258,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| sk_c7 = multiply(sk_c7,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f102,f250]) ).
fof(f259,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| sk_c1 = multiply(sk_c6,identity) ),
inference(forward_demodulation,[status(thm)],[f71,f251]) ).
fof(f263,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| sk_c6 = multiply(inverse(sk_c7),sk_c7) ),
inference(paramodulation,[status(thm)],[f258,f194]) ).
fof(f265,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c6 = multiply(sk_c6,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f71,f263]) ).
fof(f266,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f190,f265]) ).
fof(f267,plain,
( sQ1_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c6 != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f266,f243]) ).
fof(f270,plain,
( ~ sQ10_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| multiply(sk_c5,sk_c2) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f266,f192]) ).
fof(f271,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c1 = multiply(sk_c6,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f266,f259]) ).
fof(f280,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| multiply(sk_c6,sk_c6) = multiply(sk_c1,sk_c7) ),
inference(paramodulation,[status(thm)],[f258,f167]) ).
fof(f283,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c1 = multiply(sk_c1,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f271,f280]) ).
fof(f284,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c1 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f94,f283]) ).
fof(f291,plain,
( sQ1_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c1 != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f284,f267]) ).
fof(f292,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c1 = identity ),
inference(backward_demodulation,[status(thm)],[f284,f266]) ).
fof(f294,plain,
( ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| multiply(sk_c5,sk_c1) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f284,f110]) ).
fof(f296,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| inverse(sk_c7) = sk_c1 ),
inference(backward_demodulation,[status(thm)],[f284,f71]) ).
fof(f300,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| multiply(sk_c1,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f292,f35]) ).
fof(f309,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| multiply(inverse(X0),X0) = sk_c1 ),
inference(forward_demodulation,[status(thm)],[f292,f36]) ).
fof(f310,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(sk_c1,sk_c7) = sk_c1 ),
inference(paramodulation,[status(thm)],[f296,f309]) ).
fof(f315,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c7 = sk_c1 ),
inference(forward_demodulation,[status(thm)],[f300,f310]) ).
fof(f318,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| inverse(sk_c1) = sk_c1 ),
inference(backward_demodulation,[status(thm)],[f315,f296]) ).
fof(f330,plain,
( ~ sQ10_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| multiply(sk_c5,sk_c2) = sk_c1 ),
inference(forward_demodulation,[status(thm)],[f284,f270]) ).
fof(f334,plain,
( ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| multiply(sk_c5,sk_c1) = sk_c1 ),
inference(forward_demodulation,[status(thm)],[f315,f294]) ).
fof(f336,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| multiply(sk_c1,X0) = multiply(sk_c5,multiply(sk_c1,X0)) ),
inference(paramodulation,[status(thm)],[f334,f37]) ).
fof(f337,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| X0 = multiply(sk_c5,multiply(sk_c1,X0)) ),
inference(forward_demodulation,[status(thm)],[f300,f336]) ).
fof(f338,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| X0 = multiply(sk_c5,X0) ),
inference(forward_demodulation,[status(thm)],[f300,f337]) ).
fof(f344,plain,
( ~ sQ10_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sk_c2 = sk_c1 ),
inference(backward_demodulation,[status(thm)],[f338,f330]) ).
fof(f348,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ8_spl
| inverse(sk_c1) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f344,f318]) ).
fof(f349,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c7 = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f344,f315]) ).
fof(f354,plain,
( sQ1_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c2 != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f344,f291]) ).
fof(f355,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c2 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f344,f284]) ).
fof(f356,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ8_spl
| inverse(sk_c2) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f344,f348]) ).
fof(f357,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c5 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f126,f356]) ).
fof(f359,plain,
( ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| inverse(sk_c2) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f357,f126]) ).
fof(f364,plain,
( sQ1_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f357,f354]) ).
fof(f365,plain,
( sQ1_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f364]) ).
fof(f366,plain,
( sQ1_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f365]) ).
fof(f367,plain,
( sQ15_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ8_spl
| inverse(sk_c2) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f357,f181]) ).
fof(f368,plain,
( sQ15_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ8_spl
| inverse(sk_c2) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f349,f367]) ).
fof(f391,plain,
( sQ15_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f359,f368]) ).
fof(f392,plain,
( sQ15_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f391]) ).
fof(f393,plain,
( sQ15_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f392]) ).
fof(f399,definition,
( sQ19_spl
<=> inverse(sk_c2) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f401,plain,
( sQ19_spl
| inverse(sk_c2) != sk_c6 ),
inference(component_clause,[status(thm)],[f399]) ).
fof(f402,definition,
( sQ20_spl
<=> sk_c7 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f404,plain,
( sQ20_spl
| sk_c7 != sk_c6 ),
inference(component_clause,[status(thm)],[f402]) ).
fof(f405,plain,
( ~ sQ9_spl
| ~ sQ14_spl
| ~ sQ20_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f147,f399,f402,f142,f117]) ).
fof(f411,plain,
( sQ19_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c2 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f359,f401]) ).
fof(f412,plain,
( sQ19_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f355,f411]) ).
fof(f413,plain,
( sQ19_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f412]) ).
fof(f414,plain,
( sQ19_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f413]) ).
fof(f415,plain,
( sQ20_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c2 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f349,f404]) ).
fof(f416,plain,
( sQ20_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f355,f415]) ).
fof(f417,plain,
( sQ20_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f416]) ).
fof(f418,plain,
( sQ20_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f417]) ).
fof(f421,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f35,f194]) ).
fof(f423,plain,
( ~ sQ3_spl
| sk_c6 = multiply(inverse(sk_c3),sk_c7) ),
inference(paramodulation,[status(thm)],[f82,f194]) ).
fof(f425,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| sk_c6 = multiply(sk_c7,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f78,f423]) ).
fof(f426,plain,
( ~ sQ1_spl
| sk_c7 = multiply(inverse(sk_c6),sk_c5) ),
inference(paramodulation,[status(thm)],[f74,f194]) ).
fof(f430,plain,
( ~ sQ2_spl
| multiply(sk_c7,sk_c3) = identity ),
inference(paramodulation,[status(thm)],[f78,f36]) ).
fof(f431,plain,
( ~ sQ4_spl
| multiply(sk_c6,sk_c4) = identity ),
inference(paramodulation,[status(thm)],[f86,f36]) ).
fof(f437,plain,
( ~ sQ5_spl
| sk_c5 = multiply(inverse(sk_c4),sk_c6) ),
inference(paramodulation,[status(thm)],[f90,f194]) ).
fof(f439,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 = multiply(sk_c6,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f86,f437]) ).
fof(f444,plain,
! [X0] : X0 = multiply(inverse(inverse(identity)),X0),
inference(paramodulation,[status(thm)],[f421,f194]) ).
fof(f446,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| sk_c7 = multiply(inverse(sk_c7),sk_c6) ),
inference(paramodulation,[status(thm)],[f425,f194]) ).
fof(f448,plain,
( ~ sQ2_spl
| sk_c3 = multiply(inverse(sk_c7),identity) ),
inference(paramodulation,[status(thm)],[f430,f194]) ).
fof(f460,plain,
( ~ sQ4_spl
| sk_c4 = multiply(inverse(sk_c6),identity) ),
inference(paramodulation,[status(thm)],[f431,f194]) ).
fof(f463,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| sk_c6 = multiply(inverse(sk_c6),sk_c5) ),
inference(paramodulation,[status(thm)],[f439,f194]) ).
fof(f498,plain,
inverse(identity) = identity,
inference(paramodulation,[status(thm)],[f36,f444]) ).
fof(f540,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sk_c3 = multiply(inverse(sk_c6),identity) ),
inference(backward_demodulation,[status(thm)],[f560,f448]) ).
fof(f541,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sk_c7 = multiply(inverse(sk_c6),sk_c6) ),
inference(backward_demodulation,[status(thm)],[f560,f446]) ).
fof(f550,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| multiply(sk_c6,sk_c3) = identity ),
inference(backward_demodulation,[status(thm)],[f560,f430]) ).
fof(f551,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sk_c6 = multiply(sk_c7,sk_c6) ),
inference(backward_demodulation,[status(thm)],[f560,f425]) ).
fof(f554,plain,
( sQ8_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| multiply(sk_c5,sk_c6) != sk_c6 ),
inference(backward_demodulation,[status(thm)],[f560,f111]) ).
fof(f558,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| inverse(sk_c6) != sk_c6 ),
inference(backward_demodulation,[status(thm)],[f560,f72]) ).
fof(f560,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sk_c6 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f426,f463]) ).
fof(f561,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sk_c3 = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f460,f540]) ).
fof(f562,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sk_c6 = multiply(inverse(sk_c6),sk_c6) ),
inference(forward_demodulation,[status(thm)],[f560,f541]) ).
fof(f563,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f36,f562]) ).
fof(f564,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sk_c6 = multiply(sk_c6,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f560,f551]) ).
fof(f565,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sk_c6 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f439,f564]) ).
fof(f569,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| inverse(identity) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f563,f498]) ).
fof(f573,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| multiply(sk_c6,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f563,f35]) ).
fof(f574,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| inverse(sk_c6) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f563,f569]) ).
fof(f575,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sk_c5 = identity ),
inference(backward_demodulation,[status(thm)],[f565,f563]) ).
fof(f576,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c5 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f565,f560]) ).
fof(f590,plain,
( sQ8_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| multiply(sk_c5,sk_c5) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f565,f554]) ).
fof(f591,plain,
( sQ8_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| multiply(sk_c5,sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f565,f590]) ).
fof(f598,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| inverse(sk_c5) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f565,f558]) ).
fof(f599,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| inverse(sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f565,f598]) ).
fof(f608,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| inverse(sk_c5) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f565,f574]) ).
fof(f609,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| inverse(sk_c5) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f565,f608]) ).
fof(f610,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f609,f599]) ).
fof(f611,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f610]) ).
fof(f622,plain,
( ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| multiply(sk_c5,sk_c7) = identity ),
inference(forward_demodulation,[status(thm)],[f565,f190]) ).
fof(f623,plain,
( ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| multiply(sk_c5,sk_c5) = identity ),
inference(forward_demodulation,[status(thm)],[f576,f622]) ).
fof(f624,plain,
( ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| multiply(sk_c5,sk_c5) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f575,f623]) ).
fof(f625,plain,
( ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f624,f591]) ).
fof(f626,plain,
( ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f625]) ).
fof(f647,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c5) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f576,f134]) ).
fof(f648,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f565,f647]) ).
fof(f649,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| inverse(X0) != sk_c5
| multiply(X0,sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f576,f648]) ).
fof(f653,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| multiply(sk_c5,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f565,f573]) ).
fof(f659,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| multiply(sk_c5,sk_c3) = identity ),
inference(forward_demodulation,[status(thm)],[f565,f550]) ).
fof(f660,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| sk_c3 = identity ),
inference(forward_demodulation,[status(thm)],[f653,f659]) ).
fof(f661,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| sk_c4 = identity ),
inference(forward_demodulation,[status(thm)],[f561,f660]) ).
fof(f662,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| inverse(sk_c5) = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f674,f609]) ).
fof(f663,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| multiply(sk_c4,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f674,f653]) ).
fof(f668,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c4 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f674,f576]) ).
fof(f672,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sk_c6 = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f674,f565]) ).
fof(f674,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| sk_c4 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f575,f661]) ).
fof(f675,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| inverse(sk_c4) = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f674,f662]) ).
fof(f708,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| inverse(X0) != sk_c5
| multiply(X0,sk_c4) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f674,f649]) ).
fof(f709,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| inverse(X0) != sk_c5
| multiply(X0,sk_c4) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f674,f708]) ).
fof(f710,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| inverse(X0) != sk_c4
| multiply(X0,sk_c4) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f674,f709]) ).
fof(f711,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ11_spl
| inverse(sk_c4) != sk_c4 ),
inference(resolution,[status(thm)],[f710,f663]) ).
fof(f714,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ11_spl
| sk_c4 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f675,f711]) ).
fof(f715,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f714]) ).
fof(f716,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f715]) ).
fof(f722,definition,
( sQ22_spl
<=> inverse(sk_c4) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f724,plain,
( sQ22_spl
| inverse(sk_c4) != sk_c5 ),
inference(component_clause,[status(thm)],[f722]) ).
fof(f725,plain,
( ~ sQ5_spl
| ~ sQ12_spl
| ~ sQ22_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f161,f402,f722,f136,f89]) ).
fof(f726,plain,
( sQ20_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c4 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f668,f404]) ).
fof(f727,plain,
( sQ20_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c4 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f672,f726]) ).
fof(f728,plain,
( sQ20_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f727]) ).
fof(f729,plain,
( sQ20_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f728]) ).
fof(f860,plain,
( sQ22_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sk_c4 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f675,f724]) ).
fof(f861,plain,
( sQ22_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| sk_c4 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f674,f860]) ).
fof(f862,plain,
( sQ22_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f861]) ).
fof(f863,plain,
( sQ22_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f862]) ).
fof(f864,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,f121,f122,f123,f124,f128,f129,f130,f131,f132,f145,f151,f158,f164,f178,f185,f188,f366,f393,f405,f414,f418,f611,f626,f716,f725,f729,f863]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP376-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n026.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 20 20:13:23 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.15/0.42 % Refutation found
% 0.15/0.42 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.44 % Elapsed time: 0.066245 seconds
% 0.15/0.44 % CPU time: 0.187747 seconds
% 0.15/0.44 % Total memory used: 103.759 MB
% 0.15/0.44 % Net memory used: 103.515 MB
%------------------------------------------------------------------------------