%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP368-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 0.11s 0.41s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 48
% Syntax : Number of formulae : 267 ( 9 unt; 16 def)
% Number of atoms : 1067 ( 318 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1524 ( 724 ~; 784 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 17 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 57 ( 57 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c5,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c6) = sk_c5
| multiply(sk_c5,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c5,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c7,sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( inverse(sk_c6) = sk_c5
| multiply(sk_c7,sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c7,sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c7,sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c7
| multiply(sk_c7,sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c6) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( inverse(sk_c6) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( inverse(sk_c4) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c3,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c6) = sk_c5
| multiply(sk_c3,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c3,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c3,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c7
| multiply(sk_c3,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c3) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( inverse(sk_c6) = sk_c5
| inverse(sk_c3) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( multiply(sk_c7,sk_c5) = sk_c6
| inverse(sk_c3) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( inverse(sk_c4) = sk_c7
| inverse(sk_c3) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c7
| inverse(sk_c3) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
! [X2,X3,X4,X1] :
( multiply(X1,sk_c6) != sk_c7
| inverse(X1) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c6
| inverse(sk_c6) != sk_c5
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(X4) != sk_c5
| multiply(X4,sk_c5) != sk_c7
| inverse(X3) != sk_c7
| multiply(X3,sk_c7) != X2
| multiply(sk_c7,X2) != sk_c6
| multiply(sk_c5,sk_c7) != sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f36,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f37,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f38,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c5,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f39,plain,
( inverse(sk_c6) = sk_c5
| multiply(sk_c5,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f40,plain,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c5,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f43,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c7,sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f44,plain,
( inverse(sk_c6) = sk_c5
| multiply(sk_c7,sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f45,plain,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c7,sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f46,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c7,sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f47,plain,
( multiply(sk_c4,sk_c6) = sk_c7
| multiply(sk_c7,sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f48,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f49,plain,
( inverse(sk_c6) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f50,plain,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f51,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f52,plain,
( multiply(sk_c4,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f53,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f54,plain,
( inverse(sk_c6) = sk_c5
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f55,plain,
( multiply(sk_c7,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f56,plain,
( inverse(sk_c4) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f57,plain,
( multiply(sk_c4,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f58,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c3,sk_c5) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f59,plain,
( inverse(sk_c6) = sk_c5
| multiply(sk_c3,sk_c5) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f60,plain,
( multiply(sk_c7,sk_c5) = sk_c6
| multiply(sk_c3,sk_c5) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f61,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c3,sk_c5) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f62,plain,
( multiply(sk_c4,sk_c6) = sk_c7
| multiply(sk_c3,sk_c5) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f63,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c3) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f64,plain,
( inverse(sk_c6) = sk_c5
| inverse(sk_c3) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f65,plain,
( multiply(sk_c7,sk_c5) = sk_c6
| inverse(sk_c3) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f66,plain,
( inverse(sk_c4) = sk_c7
| inverse(sk_c3) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f67,plain,
( multiply(sk_c4,sk_c6) = sk_c7
| inverse(sk_c3) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f68,plain,
! [X1] :
( multiply(X1,sk_c6) != sk_c7
| inverse(X1) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c6
| inverse(sk_c6) != sk_c5
| multiply(sk_c6,sk_c7) != sk_c5
| ! [X4] :
( inverse(X4) != sk_c5
| multiply(X4,sk_c5) != sk_c7
| ! [X3] :
( inverse(X3) != sk_c7
| ! [X2] :
( multiply(X3,sk_c7) != X2
| multiply(sk_c7,X2) != sk_c6
| multiply(sk_c5,sk_c7) != sk_c6 ) ) ) ),
inference(miniscoping,[status(thm)],[f34]) ).
fof(f69,plain,
! [X0,X1,X2,X3] :
( multiply(X3,sk_c6) != sk_c7
| inverse(X3) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c6
| inverse(sk_c6) != sk_c5
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(X2) != sk_c5
| multiply(X2,sk_c5) != sk_c7
| inverse(X1) != sk_c7
| multiply(X1,sk_c7) != X0
| multiply(sk_c7,X0) != sk_c6
| multiply(sk_c5,sk_c7) != sk_c6 ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f70,definition,
( sQ0_spl
<=> multiply(sk_c5,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f71,plain,
( ~ sQ0_spl
| multiply(sk_c5,sk_c7) = sk_c6 ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f72,plain,
( sQ0_spl
| multiply(sk_c5,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_c6) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f78,plain,
( ~ sQ2_spl
| inverse(sk_c6) = sk_c5 ),
inference(component_clause,[status(thm)],[f77]) ).
fof(f79,plain,
( sQ2_spl
| inverse(sk_c6) != sk_c5 ),
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_c7,sk_c5) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f82,plain,
( ~ sQ3_spl
| multiply(sk_c7,sk_c5) = sk_c6 ),
inference(component_clause,[status(thm)],[f81]) ).
fof(f83,plain,
( sQ3_spl
| multiply(sk_c7,sk_c5) != sk_c6 ),
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_c7 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ4_spl
| inverse(sk_c4) = sk_c7 ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f89,definition,
( sQ5_spl
<=> multiply(sk_c4,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f90,plain,
( ~ sQ5_spl
| multiply(sk_c4,sk_c6) = sk_c7 ),
inference(component_clause,[status(thm)],[f89]) ).
fof(f93,definition,
( sQ6_spl
<=> multiply(sk_c7,sk_c2) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ6_spl
| multiply(sk_c7,sk_c2) = 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
<=> multiply(sk_c1,sk_c7) = sk_c2 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f102,plain,
( ~ sQ7_spl
| multiply(sk_c1,sk_c7) = 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_c7 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f110,plain,
( ~ sQ8_spl
| inverse(sk_c1) = 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_c3,sk_c5) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f118,plain,
( ~ sQ9_spl
| multiply(sk_c3,sk_c5) = sk_c7 ),
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_c5 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f126,plain,
( ~ sQ10_spl
| inverse(sk_c3) = 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,X1] :
( sQ11_spl
<=> ( inverse(X1) != sk_c7
| multiply(X1,sk_c7) != X0
| multiply(sk_c7,X0) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f134,plain,
! [X0,X1] :
( ~ sQ11_spl
| inverse(X1) != sk_c7
| multiply(X1,sk_c7) != X0
| multiply(sk_c7,X0) != sk_c6 ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,definition,
! [X2] :
( sQ12_spl
<=> ( inverse(X2) != sk_c5
| multiply(X2,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,
! [X3] :
( sQ13_spl
<=> ( multiply(X3,sk_c6) != sk_c7
| inverse(X3) != 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,plain,
( sQ13_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sQ12_spl
| sQ11_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f69,f70,f133,f136,f73,f77,f81,f139]) ).
fof(f143,plain,
( ~ sQ5_spl
| ~ sQ13_spl
| inverse(sk_c4) != sk_c7 ),
inference(resolution,[status(thm)],[f140,f90]) ).
fof(f145,plain,
( ~ sQ5_spl
| ~ sQ13_spl
| ~ sQ4_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f86,f143]) ).
fof(f146,plain,
( ~ sQ5_spl
| ~ sQ13_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f145]) ).
fof(f147,plain,
( ~ sQ5_spl
| ~ sQ13_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f146]) ).
fof(f149,plain,
! [X0] :
( ~ sQ0_spl
| multiply(sk_c6,X0) = multiply(sk_c5,multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f71,f37]) ).
fof(f156,plain,
( ~ sQ10_spl
| ~ sQ12_spl
| multiply(sk_c3,sk_c5) != sk_c7 ),
inference(resolution,[status(thm)],[f137,f126]) ).
fof(f159,plain,
( ~ sQ10_spl
| ~ sQ12_spl
| ~ sQ9_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f118,f156]) ).
fof(f160,plain,
( ~ sQ10_spl
| ~ sQ12_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f159]) ).
fof(f161,plain,
( ~ sQ10_spl
| ~ sQ12_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f160]) ).
fof(f162,plain,
! [X0] :
( ~ sQ11_spl
| inverse(X0) != sk_c7
| multiply(sk_c7,multiply(X0,sk_c7)) != sk_c6 ),
inference(destructive_equality_resolution,[status(thm)],[f134]) ).
fof(f165,plain,
( ~ sQ10_spl
| multiply(sk_c5,sk_c3) = identity ),
inference(paramodulation,[status(thm)],[f126,f36]) ).
fof(f166,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f36,f37]) ).
fof(f167,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f35,f166]) ).
fof(f182,plain,
( ~ sQ7_spl
| sk_c7 = multiply(inverse(sk_c1),sk_c2) ),
inference(paramodulation,[status(thm)],[f102,f167]) ).
fof(f183,plain,
( ~ sQ9_spl
| sk_c5 = multiply(inverse(sk_c3),sk_c7) ),
inference(paramodulation,[status(thm)],[f118,f167]) ).
fof(f186,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| sk_c7 = multiply(sk_c7,sk_c2) ),
inference(forward_demodulation,[status(thm)],[f110,f182]) ).
fof(f187,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| sk_c7 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f94,f186]) ).
fof(f188,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| sk_c5 = multiply(sk_c5,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f126,f183]) ).
fof(f189,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| sk_c5 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f71,f188]) ).
fof(f192,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| multiply(sk_c5,sk_c6) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f187,f71]) ).
fof(f194,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| multiply(sk_c6,sk_c2) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f187,f94]) ).
fof(f195,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| multiply(sk_c1,sk_c6) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f187,f102]) ).
fof(f198,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| inverse(sk_c1) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f187,f110]) ).
fof(f199,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| multiply(sk_c6,sk_c3) = identity ),
inference(backward_demodulation,[status(thm)],[f189,f165]) ).
fof(f200,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| inverse(sk_c3) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f189,f126]) ).
fof(f228,definition,
( sQ16_spl
<=> multiply(sk_c6,identity) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f230,plain,
( sQ16_spl
| multiply(sk_c6,identity) != sk_c6 ),
inference(component_clause,[status(thm)],[f228]) ).
fof(f244,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c6,sk_c6) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f189,f192]) ).
fof(f246,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c6 = multiply(inverse(sk_c6),sk_c6) ),
inference(paramodulation,[status(thm)],[f244,f167]) ).
fof(f252,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f36,f246]) ).
fof(f253,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c2 = multiply(inverse(sk_c6),sk_c6) ),
inference(paramodulation,[status(thm)],[f194,f167]) ).
fof(f255,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c2 = identity ),
inference(forward_demodulation,[status(thm)],[f36,f253]) ).
fof(f258,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(inverse(X0),X0) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f252,f36]) ).
fof(f259,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c6,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f252,f35]) ).
fof(f260,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c2 = identity ),
inference(backward_demodulation,[status(thm)],[f269,f252]) ).
fof(f264,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| inverse(sk_c3) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f269,f200]) ).
fof(f265,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| inverse(sk_c1) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f269,f198]) ).
fof(f267,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c5 = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f269,f189]) ).
fof(f268,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c7 = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f269,f187]) ).
fof(f269,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c2 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f252,f255]) ).
fof(f285,plain,
( sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| inverse(sk_c2) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f269,f79]) ).
fof(f286,plain,
( sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| inverse(sk_c2) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f267,f285]) ).
fof(f289,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c2,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f269,f259]) ).
fof(f292,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)],[f264,f167]) ).
fof(f293,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| X0 = multiply(sk_c3,X0) ),
inference(forward_demodulation,[status(thm)],[f289,f292]) ).
fof(f320,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| multiply(sk_c2,sk_c3) = identity ),
inference(forward_demodulation,[status(thm)],[f269,f199]) ).
fof(f321,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c3 = identity ),
inference(forward_demodulation,[status(thm)],[f289,f320]) ).
fof(f323,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| inverse(sk_c1) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f331,f265]) ).
fof(f324,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| inverse(sk_c3) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f331,f264]) ).
fof(f327,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c7 = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f331,f268]) ).
fof(f328,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c5 = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f331,f267]) ).
fof(f330,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c3 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f331,f269]) ).
fof(f331,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c3 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f260,f321]) ).
fof(f335,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(inverse(X0),X0) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f330,f258]) ).
fof(f336,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c3,sk_c1) = sk_c3 ),
inference(paramodulation,[status(thm)],[f323,f335]) ).
fof(f339,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c1 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f293,f336]) ).
fof(f351,plain,
( sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| inverse(sk_c3) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f331,f286]) ).
fof(f352,plain,
( sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c3 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f324,f351]) ).
fof(f353,plain,
( sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f331,f352]) ).
fof(f354,plain,
( sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f353]) ).
fof(f355,plain,
( sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f354]) ).
fof(f375,plain,
( sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c3,sk_c7) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f330,f75]) ).
fof(f376,plain,
( sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c7 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f293,f375]) ).
fof(f377,plain,
( sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c3 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f327,f376]) ).
fof(f378,plain,
( sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f328,f377]) ).
fof(f379,plain,
( sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f378]) ).
fof(f380,plain,
( sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f379]) ).
fof(f388,plain,
( sQ3_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c3,sk_c5) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f327,f83]) ).
fof(f389,plain,
( sQ3_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c5 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f293,f388]) ).
fof(f390,plain,
( sQ3_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c3 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f328,f389]) ).
fof(f391,plain,
( sQ3_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f330,f390]) ).
fof(f392,plain,
( sQ3_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f391]) ).
fof(f393,plain,
( sQ3_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f392]) ).
fof(f410,plain,
( sQ16_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| multiply(sk_c6,sk_c2) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f255,f230]) ).
fof(f413,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| sk_c6 = multiply(inverse(sk_c1),sk_c2) ),
inference(paramodulation,[status(thm)],[f195,f167]) ).
fof(f415,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| sk_c6 = multiply(sk_c6,sk_c2) ),
inference(forward_demodulation,[status(thm)],[f198,f413]) ).
fof(f416,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f415,f410]) ).
fof(f417,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| sQ16_spl ),
inference(contradiction_clause,[status(thm)],[f416]) ).
fof(f426,plain,
( ~ sQ4_spl
| multiply(sk_c7,sk_c4) = identity ),
inference(paramodulation,[status(thm)],[f86,f36]) ).
fof(f427,plain,
( ~ sQ2_spl
| multiply(sk_c5,sk_c6) = identity ),
inference(paramodulation,[status(thm)],[f78,f36]) ).
fof(f432,plain,
( ~ sQ1_spl
| sk_c7 = multiply(inverse(sk_c6),sk_c5) ),
inference(paramodulation,[status(thm)],[f74,f167]) ).
fof(f433,plain,
! [X0] :
( ~ sQ1_spl
| multiply(sk_c5,X0) = multiply(sk_c6,multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f74,f37]) ).
fof(f434,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c7 = multiply(sk_c5,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f78,f432]) ).
fof(f443,plain,
( ~ sQ5_spl
| sk_c6 = multiply(inverse(sk_c4),sk_c7) ),
inference(paramodulation,[status(thm)],[f90,f167]) ).
fof(f445,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| sk_c6 = multiply(sk_c7,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f86,f443]) ).
fof(f446,plain,
( ~ sQ7_spl
| ~ sQ11_spl
| inverse(sk_c1) != sk_c7
| multiply(sk_c7,sk_c2) != sk_c6 ),
inference(paramodulation,[status(thm)],[f102,f162]) ).
fof(f448,plain,
( ~ sQ1_spl
| ~ sQ11_spl
| inverse(sk_c6) != sk_c7
| multiply(sk_c7,sk_c5) != sk_c6 ),
inference(paramodulation,[status(thm)],[f74,f162]) ).
fof(f453,plain,
( ~ sQ7_spl
| ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f446,f93,f109,f133,f101]) ).
fof(f461,definition,
( sQ22_spl
<=> inverse(sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f463,plain,
( sQ22_spl
| inverse(sk_c6) != sk_c7 ),
inference(component_clause,[status(thm)],[f461]) ).
fof(f464,plain,
( ~ sQ1_spl
| ~ sQ11_spl
| ~ sQ22_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f448,f81,f461,f133,f73]) ).
fof(f483,plain,
( sQ22_spl
| ~ sQ2_spl
| sk_c5 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f78,f463]) ).
fof(f522,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| multiply(sk_c6,sk_c7) = multiply(sk_c5,sk_c6) ),
inference(paramodulation,[status(thm)],[f445,f149]) ).
fof(f526,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ1_spl
| sk_c5 = multiply(sk_c5,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f74,f522]) ).
fof(f527,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c5 = identity ),
inference(forward_demodulation,[status(thm)],[f427,f526]) ).
fof(f533,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c7,sk_c4) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f527,f426]) ).
fof(f535,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(inverse(X0),X0) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f527,f36]) ).
fof(f537,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c5,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f527,f35]) ).
fof(f542,plain,
! [X0,X1] :
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c5,X0) = multiply(inverse(X1),multiply(X1,X0)) ),
inference(paramodulation,[status(thm)],[f535,f37]) ).
fof(f544,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c5,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f167,f542]) ).
fof(f545,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sk_c7 = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f537,f434]) ).
fof(f547,plain,
( ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c7 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f537,f71]) ).
fof(f551,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f545,f483]) ).
fof(f552,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f551]) ).
fof(f564,plain,
( ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c4) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f547,f86]) ).
fof(f570,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sk_c6 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f547,f545]) ).
fof(f572,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c6,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f570,f544]) ).
fof(f575,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| X0 = multiply(sk_c6,multiply(sk_c4,X0)) ),
inference(paramodulation,[status(thm)],[f564,f167]) ).
fof(f576,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| X0 = multiply(sk_c4,X0) ),
inference(forward_demodulation,[status(thm)],[f572,f575]) ).
fof(f584,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c6,sk_c4) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f547,f533]) ).
fof(f585,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c4 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f572,f584]) ).
fof(f591,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sk_c4 = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f593,f570]) ).
fof(f592,plain,
( ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c7 = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f593,f547]) ).
fof(f593,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c4 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f570,f585]) ).
fof(f597,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| inverse(X0) != sk_c4
| multiply(X0,sk_c5) != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f591,f137]) ).
fof(f598,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| inverse(X0) != sk_c4
| multiply(X0,sk_c4) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f591,f597]) ).
fof(f669,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c7 = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f671,f187]) ).
fof(f671,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c6 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f187,f327]) ).
fof(f679,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| inverse(sk_c3) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f339,f198]) ).
fof(f680,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| inverse(sk_c3) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f671,f679]) ).
fof(f782,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(X0,sk_c6) != sk_c7
| inverse(X0) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f669,f140]) ).
fof(f783,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(X0,sk_c3) != sk_c7
| inverse(X0) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f671,f782]) ).
fof(f784,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(X0,sk_c3) != sk_c3
| inverse(X0) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f669,f783]) ).
fof(f785,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ13_spl
| multiply(sk_c3,sk_c3) != sk_c3 ),
inference(resolution,[status(thm)],[f784,f680]) ).
fof(f787,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ13_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f293,f785]) ).
fof(f788,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ13_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f787]) ).
fof(f789,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f788]) ).
fof(f803,plain,
( ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ1_spl
| inverse(sk_c4) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f593,f78]) ).
fof(f804,plain,
( ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ1_spl
| inverse(sk_c4) = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f591,f803]) ).
fof(f820,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| inverse(X0) != sk_c4
| multiply(X0,sk_c4) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f592,f598]) ).
fof(f821,plain,
( ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ12_spl
| multiply(sk_c4,sk_c4) != sk_c4 ),
inference(resolution,[status(thm)],[f820,f804]) ).
fof(f823,plain,
( ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ12_spl
| sk_c4 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f576,f821]) ).
fof(f824,plain,
( ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f823]) ).
fof(f825,plain,
( ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f824]) ).
fof(f853,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| multiply(sk_c5,sk_c5) = multiply(sk_c6,sk_c6) ),
inference(paramodulation,[status(thm)],[f82,f433]) ).
fof(f856,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c7 = multiply(sk_c6,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f434,f853]) ).
fof(f878,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c6 = multiply(inverse(sk_c6),sk_c7) ),
inference(paramodulation,[status(thm)],[f856,f167]) ).
fof(f880,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c6 = multiply(sk_c5,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f78,f878]) ).
fof(f881,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f880,f72]) ).
fof(f882,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f881]) ).
fof(f883,plain,
$false,
inference(sat_refutation,[status(thm)],[f76,f80,f84,f96,f97,f98,f99,f100,f104,f105,f106,f107,f108,f112,f113,f114,f115,f116,f120,f121,f122,f123,f124,f128,f129,f130,f131,f132,f142,f147,f161,f355,f380,f393,f417,f453,f464,f552,f789,f825,f882]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP368-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n020.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 20 20:11:03 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.39 % Drodi V4.1.1
% 0.11/0.41 % Refutation found
% 0.11/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.43 % Elapsed time: 0.049784 seconds
% 0.11/0.43 % CPU time: 0.166484 seconds
% 0.11/0.43 % Total memory used: 37.830 MB
% 0.11/0.43 % Net memory used: 37.716 MB
%------------------------------------------------------------------------------