%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP324-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 12:33:25 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.41s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 64
% Syntax : Number of formulae : 280 ( 12 unt; 27 def)
% Number of atoms : 915 ( 339 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 1178 ( 543 ~; 608 |; 0 &)
% ( 27 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 29 ( 27 usr; 28 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 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_c8,sk_c7) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c8) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c5) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( inverse(sk_c8) = sk_c6
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
( inverse(sk_c5) = sk_c7
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
! [X3,X4,X5,X1,X2] :
( inverse(X2) != sk_c7
| multiply(X2,sk_c7) != sk_c6
| inverse(sk_c8) != sk_c6
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| inverse(X5) != sk_c8
| multiply(X5,sk_c8) != X4
| multiply(sk_c8,X4) != sk_c7
| inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f42,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f43,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f44,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f45,plain,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f46,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f50,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f51,plain,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f52,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f53,plain,
( inverse(sk_c8) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f54,plain,
( multiply(sk_c5,sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f55,plain,
( inverse(sk_c5) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f56,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f57,plain,
( multiply(sk_c4,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f58,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f59,plain,
( inverse(sk_c8) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f60,plain,
( multiply(sk_c5,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f61,plain,
( inverse(sk_c5) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f62,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f63,plain,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f64,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f65,plain,
( inverse(sk_c8) = sk_c6
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f66,plain,
( multiply(sk_c5,sk_c7) = sk_c6
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f67,plain,
( inverse(sk_c5) = sk_c7
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f68,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f69,plain,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f70,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f71,plain,
( inverse(sk_c8) = sk_c6
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f72,plain,
( multiply(sk_c5,sk_c7) = sk_c6
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f73,plain,
( inverse(sk_c5) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f74,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f75,plain,
( multiply(sk_c4,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f76,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f77,plain,
( inverse(sk_c8) = sk_c6
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f78,plain,
( multiply(sk_c5,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f79,plain,
( inverse(sk_c5) = sk_c7
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f80,plain,
! [X2] :
( inverse(X2) != sk_c7
| multiply(X2,sk_c7) != sk_c6
| inverse(sk_c8) != sk_c6
| ! [X1] :
( inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| ! [X5] :
( inverse(X5) != sk_c8
| ! [X4] :
( multiply(X5,sk_c8) != X4
| multiply(sk_c8,X4) != sk_c7
| ! [X3] :
( inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ) ) ) ) ),
inference(miniscoping,[status(thm)],[f40]) ).
fof(f81,plain,
! [X0,X1,X2,X3,X4] :
( inverse(X4) != sk_c7
| multiply(X4,sk_c7) != sk_c6
| inverse(sk_c8) != sk_c6
| inverse(X3) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != X1
| multiply(sk_c8,X1) != sk_c7
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f82,definition,
( sQ0_spl
<=> multiply(sk_c7,sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f83,plain,
( ~ sQ0_spl
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(component_clause,[status(thm)],[f82]) ).
fof(f84,plain,
( sQ0_spl
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(component_clause,[status(thm)],[f82]) ).
fof(f85,definition,
( sQ1_spl
<=> multiply(sk_c8,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ1_spl
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f87,plain,
( sQ1_spl
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f88,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f44,f82,f85]) ).
fof(f89,definition,
( sQ2_spl
<=> multiply(sk_c4,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f90,plain,
( ~ sQ2_spl
| multiply(sk_c4,sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f89]) ).
fof(f92,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f45,f82,f89]) ).
fof(f93,definition,
( sQ3_spl
<=> inverse(sk_c4) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ3_spl
| inverse(sk_c4) = sk_c8 ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f96,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f46,f82,f93]) ).
fof(f97,definition,
( sQ4_spl
<=> inverse(sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f99,plain,
( sQ4_spl
| inverse(sk_c8) != sk_c6 ),
inference(component_clause,[status(thm)],[f97]) ).
fof(f101,definition,
( sQ5_spl
<=> multiply(sk_c5,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f102,plain,
( ~ sQ5_spl
| multiply(sk_c5,sk_c7) = sk_c6 ),
inference(component_clause,[status(thm)],[f101]) ).
fof(f105,definition,
( sQ6_spl
<=> inverse(sk_c5) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f106,plain,
( ~ sQ6_spl
| inverse(sk_c5) = sk_c7 ),
inference(component_clause,[status(thm)],[f105]) ).
fof(f109,definition,
( sQ7_spl
<=> multiply(sk_c1,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f110,plain,
( ~ sQ7_spl
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f109]) ).
fof(f112,plain,
( sQ1_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f50,f109,f85]) ).
fof(f113,plain,
( sQ2_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f51,f109,f89]) ).
fof(f114,plain,
( sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f52,f109,f93]) ).
fof(f115,plain,
( sQ4_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f53,f109,f97]) ).
fof(f116,plain,
( sQ5_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f54,f109,f101]) ).
fof(f117,plain,
( sQ6_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f55,f109,f105]) ).
fof(f118,definition,
( sQ8_spl
<=> inverse(sk_c1) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f119,plain,
( ~ sQ8_spl
| inverse(sk_c1) = sk_c7 ),
inference(component_clause,[status(thm)],[f118]) ).
fof(f121,plain,
( sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f56,f118,f85]) ).
fof(f122,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f57,f118,f89]) ).
fof(f123,plain,
( sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f58,f118,f93]) ).
fof(f124,plain,
( sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f59,f118,f97]) ).
fof(f125,plain,
( sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f60,f118,f101]) ).
fof(f126,plain,
( sQ6_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f61,f118,f105]) ).
fof(f127,definition,
( sQ9_spl
<=> multiply(sk_c8,sk_c3) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f128,plain,
( ~ sQ9_spl
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(component_clause,[status(thm)],[f127]) ).
fof(f130,plain,
( sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f62,f127,f85]) ).
fof(f131,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f63,f127,f89]) ).
fof(f132,plain,
( sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f64,f127,f93]) ).
fof(f133,plain,
( sQ4_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f65,f127,f97]) ).
fof(f134,plain,
( sQ5_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f66,f127,f101]) ).
fof(f135,plain,
( sQ6_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f67,f127,f105]) ).
fof(f136,definition,
( sQ10_spl
<=> multiply(sk_c2,sk_c8) = sk_c3 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f137,plain,
( ~ sQ10_spl
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f139,plain,
( sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f68,f136,f85]) ).
fof(f140,plain,
( sQ2_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f69,f136,f89]) ).
fof(f141,plain,
( sQ3_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f70,f136,f93]) ).
fof(f142,plain,
( sQ4_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f71,f136,f97]) ).
fof(f143,plain,
( sQ5_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f72,f136,f101]) ).
fof(f144,plain,
( sQ6_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f73,f136,f105]) ).
fof(f145,definition,
( sQ11_spl
<=> inverse(sk_c2) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f146,plain,
( ~ sQ11_spl
| inverse(sk_c2) = sk_c8 ),
inference(component_clause,[status(thm)],[f145]) ).
fof(f148,plain,
( sQ1_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f74,f145,f85]) ).
fof(f149,plain,
( sQ2_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f75,f145,f89]) ).
fof(f150,plain,
( sQ3_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f76,f145,f93]) ).
fof(f151,plain,
( sQ4_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f77,f145,f97]) ).
fof(f152,plain,
( sQ5_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f78,f145,f101]) ).
fof(f153,plain,
( sQ6_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f79,f145,f105]) ).
fof(f154,definition,
! [X0] :
( sQ12_spl
<=> ( inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f155,plain,
! [X0] :
( ~ sQ12_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c8 ),
inference(component_clause,[status(thm)],[f154]) ).
fof(f157,definition,
! [X1,X2] :
( sQ13_spl
<=> ( inverse(X2) != sk_c8
| multiply(X2,sk_c8) != X1
| multiply(sk_c8,X1) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f158,plain,
! [X0,X1] :
( ~ sQ13_spl
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != X0
| multiply(sk_c8,X0) != sk_c7 ),
inference(component_clause,[status(thm)],[f157]) ).
fof(f160,definition,
! [X3] :
( sQ14_spl
<=> ( inverse(X3) != sk_c8
| multiply(X3,sk_c8) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f161,plain,
! [X0] :
( ~ sQ14_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f160]) ).
fof(f163,definition,
! [X4] :
( sQ15_spl
<=> ( inverse(X4) != sk_c7
| multiply(X4,sk_c7) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f164,plain,
! [X0] :
( ~ sQ15_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6 ),
inference(component_clause,[status(thm)],[f163]) ).
fof(f166,plain,
( sQ15_spl
| ~ sQ4_spl
| sQ14_spl
| ~ sQ1_spl
| sQ13_spl
| sQ12_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f81,f82,f154,f157,f85,f160,f97,f163]) ).
fof(f174,plain,
( ~ sQ6_spl
| multiply(sk_c7,sk_c5) = identity ),
inference(paramodulation,[status(thm)],[f106,f42]) ).
fof(f175,plain,
( ~ sQ8_spl
| multiply(sk_c7,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f119,f42]) ).
fof(f176,plain,
( ~ sQ11_spl
| multiply(sk_c8,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f146,f42]) ).
fof(f177,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f42,f43]) ).
fof(f178,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f41,f177]) ).
fof(f183,plain,
( ~ sQ5_spl
| ~ sQ15_spl
| inverse(sk_c5) != sk_c7 ),
inference(resolution,[status(thm)],[f164,f102]) ).
fof(f185,plain,
( ~ sQ7_spl
| ~ sQ15_spl
| inverse(sk_c1) != sk_c7
| sk_c8 != sk_c6 ),
inference(paramodulation,[status(thm)],[f110,f164]) ).
fof(f187,plain,
( ~ sQ15_spl
| inverse(identity) != sk_c7
| sk_c7 != sk_c6 ),
inference(paramodulation,[status(thm)],[f41,f164]) ).
fof(f189,plain,
( ~ sQ5_spl
| ~ sQ15_spl
| ~ sQ6_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f106,f183]) ).
fof(f190,plain,
( ~ sQ5_spl
| ~ sQ15_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f189]) ).
fof(f191,plain,
( ~ sQ5_spl
| ~ sQ15_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f190]) ).
fof(f194,plain,
( ~ sQ2_spl
| ~ sQ14_spl
| inverse(sk_c4) != sk_c8 ),
inference(resolution,[status(thm)],[f161,f90]) ).
fof(f198,plain,
( ~ sQ14_spl
| inverse(identity) != sk_c8
| sk_c8 != sk_c7 ),
inference(paramodulation,[status(thm)],[f41,f161]) ).
fof(f201,plain,
( ~ sQ2_spl
| ~ sQ14_spl
| ~ sQ3_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f94,f194]) ).
fof(f202,plain,
( ~ sQ2_spl
| ~ sQ14_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f201]) ).
fof(f203,plain,
( ~ sQ2_spl
| ~ sQ14_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f202]) ).
fof(f205,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ13_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c3
| sk_c7 != sk_c7 ),
inference(paramodulation,[status(thm)],[f128,f158]) ).
fof(f206,definition,
( sQ16_spl
<=> sk_c7 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f208,plain,
( sQ16_spl
| sk_c7 != sk_c7 ),
inference(component_clause,[status(thm)],[f206]) ).
fof(f209,definition,
! [X0] :
( sQ17_spl
<=> ( inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c3 ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f210,plain,
! [X0] :
( ~ sQ17_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c3 ),
inference(component_clause,[status(thm)],[f209]) ).
fof(f212,plain,
( ~ sQ9_spl
| ~ sQ13_spl
| sQ17_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f205,f206,f209,f157,f127]) ).
fof(f213,plain,
( sQ16_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f208]) ).
fof(f214,plain,
sQ16_spl,
inference(contradiction_clause,[status(thm)],[f213]) ).
fof(f219,plain,
( ~ sQ7_spl
| ~ sQ12_spl
| inverse(sk_c1) != sk_c7 ),
inference(resolution,[status(thm)],[f155,f110]) ).
fof(f220,plain,
( ~ sQ5_spl
| ~ sQ12_spl
| inverse(sk_c5) != sk_c7
| sk_c6 != sk_c8 ),
inference(paramodulation,[status(thm)],[f102,f155]) ).
fof(f225,plain,
( ~ sQ7_spl
| ~ sQ12_spl
| ~ sQ8_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f119,f219]) ).
fof(f226,plain,
( ~ sQ7_spl
| ~ sQ12_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f225]) ).
fof(f227,plain,
( ~ sQ7_spl
| ~ sQ12_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f226]) ).
fof(f228,definition,
( sQ18_spl
<=> sk_c6 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f230,plain,
( sQ18_spl
| sk_c6 != sk_c8 ),
inference(component_clause,[status(thm)],[f228]) ).
fof(f231,plain,
( ~ sQ5_spl
| ~ sQ12_spl
| ~ sQ6_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f220,f228,f105,f154,f101]) ).
fof(f239,definition,
( sQ21_spl
<=> sk_c7 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f241,plain,
( sQ21_spl
| sk_c7 != sk_c8 ),
inference(component_clause,[status(thm)],[f239]) ).
fof(f242,definition,
( sQ22_spl
<=> inverse(identity) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f244,plain,
( sQ22_spl
| inverse(identity) != sk_c7 ),
inference(component_clause,[status(thm)],[f242]) ).
fof(f275,plain,
( ~ sQ2_spl
| sk_c8 = multiply(inverse(sk_c4),sk_c7) ),
inference(paramodulation,[status(thm)],[f90,f178]) ).
fof(f287,plain,
( ~ sQ10_spl
| sk_c8 = multiply(inverse(sk_c2),sk_c3) ),
inference(paramodulation,[status(thm)],[f137,f178]) ).
fof(f289,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| sk_c8 = multiply(sk_c8,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f94,f275]) ).
fof(f298,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| sk_c8 = multiply(sk_c8,sk_c3) ),
inference(forward_demodulation,[status(thm)],[f146,f287]) ).
fof(f299,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sk_c8 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f128,f298]) ).
fof(f330,plain,
( sQ21_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f299,f241]) ).
fof(f331,plain,
( sQ21_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f330]) ).
fof(f332,plain,
( sQ21_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f331]) ).
fof(f348,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c8 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f289,f86]) ).
fof(f349,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| sk_c7 = multiply(inverse(sk_c8),sk_c8) ),
inference(paramodulation,[status(thm)],[f289,f178]) ).
fof(f351,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| sk_c7 = identity ),
inference(forward_demodulation,[status(thm)],[f42,f349]) ).
fof(f353,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| multiply(sk_c7,sk_c8) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f348,f84]) ).
fof(f355,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| multiply(sk_c5,sk_c7) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f348,f102]) ).
fof(f358,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| multiply(identity,sk_c8) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f351,f353]) ).
fof(f362,plain,
( ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ3_spl
| multiply(identity,sk_c5) = identity ),
inference(backward_demodulation,[status(thm)],[f351,f174]) ).
fof(f363,plain,
( ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ3_spl
| inverse(sk_c5) = identity ),
inference(backward_demodulation,[status(thm)],[f351,f106]) ).
fof(f364,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f41,f358]) ).
fof(f365,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f364]) ).
fof(f366,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f365]) ).
fof(f367,plain,
( ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c5 = identity ),
inference(forward_demodulation,[status(thm)],[f41,f362]) ).
fof(f368,plain,
( sQ18_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f348,f230]) ).
fof(f369,plain,
( sQ18_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f368]) ).
fof(f370,plain,
( sQ18_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f369]) ).
fof(f375,plain,
! [X0,X1] :
( ~ sQ13_spl
| ~ sQ2_spl
| ~ sQ3_spl
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != X0
| multiply(sk_c8,X0) != identity ),
inference(forward_demodulation,[status(thm)],[f351,f158]) ).
fof(f376,plain,
( ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ3_spl
| inverse(identity) = identity ),
inference(forward_demodulation,[status(thm)],[f367,f363]) ).
fof(f380,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ6_spl
| multiply(identity,sk_c7) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f367,f355]) ).
fof(f381,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ6_spl
| sk_c7 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f41,f380]) ).
fof(f387,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ6_spl
| identity = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f351,f381]) ).
fof(f396,plain,
! [X0,X1] :
( ~ sQ13_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ6_spl
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != X0
| multiply(identity,X0) != identity ),
inference(forward_demodulation,[status(thm)],[f387,f375]) ).
fof(f397,plain,
! [X0,X1] :
( ~ sQ13_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ6_spl
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != X0
| X0 != identity ),
inference(forward_demodulation,[status(thm)],[f41,f396]) ).
fof(f398,plain,
! [X0,X1] :
( ~ sQ13_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ6_spl
| inverse(X1) != sk_c8
| multiply(X1,identity) != X0
| X0 != identity ),
inference(forward_demodulation,[status(thm)],[f387,f397]) ).
fof(f399,plain,
! [X0,X1] :
( ~ sQ13_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ6_spl
| inverse(X1) != identity
| multiply(X1,identity) != X0
| X0 != identity ),
inference(forward_demodulation,[status(thm)],[f387,f398]) ).
fof(f401,plain,
( ~ sQ13_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ6_spl
| inverse(inverse(identity)) != identity
| identity != identity ),
inference(resolution,[status(thm)],[f399,f42]) ).
fof(f411,definition,
( sQ23_spl
<=> identity = identity ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f413,plain,
( sQ23_spl
| identity != identity ),
inference(component_clause,[status(thm)],[f411]) ).
fof(f418,definition,
( sQ25_spl
<=> inverse(inverse(identity)) = identity ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f420,plain,
( sQ25_spl
| inverse(inverse(identity)) != identity ),
inference(component_clause,[status(thm)],[f418]) ).
fof(f421,plain,
( ~ sQ13_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ25_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f401,f411,f418,f105,f85,f101,f93,f89,f157]) ).
fof(f422,definition,
( sQ26_spl
<=> inverse(identity) = identity ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f424,plain,
( sQ26_spl
| inverse(identity) != identity ),
inference(component_clause,[status(thm)],[f422]) ).
fof(f428,definition,
! [X0] :
( sQ27_spl
<=> ( identity != X0
| X0 != identity ) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f429,plain,
! [X0] :
( ~ sQ27_spl
| identity != X0
| X0 != identity ),
inference(component_clause,[status(thm)],[f428]) ).
fof(f434,plain,
( sQ23_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f413]) ).
fof(f435,plain,
sQ23_spl,
inference(contradiction_clause,[status(thm)],[f434]) ).
fof(f436,plain,
( sQ25_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ3_spl
| inverse(identity) != identity ),
inference(forward_demodulation,[status(thm)],[f376,f420]) ).
fof(f437,plain,
( sQ25_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ3_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f376,f436]) ).
fof(f438,plain,
( sQ25_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f437]) ).
fof(f439,plain,
( sQ25_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f438]) ).
fof(f440,plain,
! [X0] :
( ~ sQ27_spl
| X0 != identity ),
inference(duplicate_literals_removal,[status(thm)],[f429]) ).
fof(f441,plain,
( ~ sQ27_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f42,f440]) ).
fof(f445,plain,
~ sQ27_spl,
inference(contradiction_clause,[status(thm)],[f441]) ).
fof(f449,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| multiply(sk_c1,sk_c7) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f299,f110]) ).
fof(f451,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| multiply(sk_c2,sk_c7) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f299,f137]) ).
fof(f454,plain,
( ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ9_spl
| inverse(sk_c2) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f299,f146]) ).
fof(f458,plain,
( sQ1_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| multiply(sk_c7,sk_c7) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f299,f87]) ).
fof(f459,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| multiply(sk_c7,sk_c7) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f299,f83]) ).
fof(f460,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f459,f458]) ).
fof(f461,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f460]) ).
fof(f467,definition,
( sQ28_spl
<=> sk_c6 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f469,plain,
( sQ28_spl
| sk_c6 != sk_c7 ),
inference(component_clause,[status(thm)],[f467]) ).
fof(f481,definition,
( sQ32_spl
<=> inverse(identity) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f483,plain,
( sQ32_spl
| inverse(identity) != sk_c8 ),
inference(component_clause,[status(thm)],[f481]) ).
fof(f484,plain,
( ~ sQ14_spl
| ~ sQ32_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f198,f239,f481,f160]) ).
fof(f491,plain,
( sQ32_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| inverse(identity) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f299,f483]) ).
fof(f501,plain,
( sQ4_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| inverse(sk_c7) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f299,f99]) ).
fof(f510,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sk_c7 = multiply(inverse(sk_c1),sk_c7) ),
inference(paramodulation,[status(thm)],[f449,f178]) ).
fof(f512,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| sk_c7 = multiply(sk_c7,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f119,f510]) ).
fof(f521,plain,
( ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ9_spl
| multiply(sk_c7,sk_c2) = identity ),
inference(forward_demodulation,[status(thm)],[f299,f176]) ).
fof(f553,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c7) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f299,f210]) ).
fof(f554,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f299,f553]) ).
fof(f555,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ17_spl
| inverse(sk_c2) != sk_c7 ),
inference(resolution,[status(thm)],[f554,f451]) ).
fof(f565,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ17_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f454,f555]) ).
fof(f566,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ17_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f565]) ).
fof(f567,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f566]) ).
fof(f596,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c7 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f512,f459]) ).
fof(f600,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| sk_c7 = multiply(inverse(sk_c7),sk_c7) ),
inference(paramodulation,[status(thm)],[f512,f178]) ).
fof(f602,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sQ28_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f596,f469]) ).
fof(f603,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sQ28_spl ),
inference(contradiction_clause,[status(thm)],[f602]) ).
fof(f606,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| sk_c7 = identity ),
inference(forward_demodulation,[status(thm)],[f42,f600]) ).
fof(f610,plain,
( sQ4_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| inverse(sk_c7) != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f596,f501]) ).
fof(f614,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| multiply(identity,sk_c1) = identity ),
inference(backward_demodulation,[status(thm)],[f606,f175]) ).
fof(f618,plain,
( ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| multiply(identity,sk_c2) = identity ),
inference(backward_demodulation,[status(thm)],[f606,f521]) ).
fof(f625,plain,
( sQ22_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| inverse(identity) != identity ),
inference(backward_demodulation,[status(thm)],[f606,f244]) ).
fof(f626,plain,
( ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| inverse(sk_c2) = identity ),
inference(backward_demodulation,[status(thm)],[f606,f454]) ).
fof(f629,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| inverse(sk_c1) = identity ),
inference(backward_demodulation,[status(thm)],[f606,f119]) ).
fof(f635,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sk_c1 = identity ),
inference(forward_demodulation,[status(thm)],[f41,f614]) ).
fof(f639,plain,
( ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c2 = identity ),
inference(forward_demodulation,[status(thm)],[f41,f618]) ).
fof(f653,plain,
( ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| inverse(identity) = identity ),
inference(forward_demodulation,[status(thm)],[f639,f626]) ).
fof(f654,plain,
( ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f653,f424]) ).
fof(f655,plain,
( ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sQ26_spl ),
inference(contradiction_clause,[status(thm)],[f654]) ).
fof(f656,plain,
( sQ22_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f625,f422,f118,f127,f145,f136,f109,f242]) ).
fof(f658,plain,
( sQ32_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f491,f242,f127,f145,f136,f481]) ).
fof(f660,plain,
( sQ4_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| inverse(identity) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f606,f610]) ).
fof(f661,plain,
( sQ4_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| inverse(identity) != identity ),
inference(forward_demodulation,[status(thm)],[f606,f660]) ).
fof(f672,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| inverse(identity) = identity ),
inference(forward_demodulation,[status(thm)],[f635,f629]) ).
fof(f681,plain,
( sQ4_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f672,f661]) ).
fof(f682,plain,
( sQ4_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f681]) ).
fof(f683,plain,
( sQ4_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f682]) ).
fof(f734,plain,
( ~ sQ7_spl
| ~ sQ15_spl
| ~ sQ8_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f185,f228,f118,f163,f109]) ).
fof(f739,plain,
( ~ sQ15_spl
| ~ sQ22_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f187,f467,f242,f163]) ).
fof(f743,plain,
$false,
inference(sat_refutation,[status(thm)],[f88,f92,f96,f112,f113,f114,f115,f116,f117,f121,f122,f123,f124,f125,f126,f130,f131,f132,f133,f134,f135,f139,f140,f141,f142,f143,f144,f148,f149,f150,f151,f152,f153,f166,f191,f203,f212,f214,f227,f231,f332,f366,f370,f421,f435,f439,f445,f461,f484,f567,f603,f655,f656,f658,f683,f734,f739]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP324-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n003.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 20:11:15 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.41 % Refutation found
% 0.09/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.45 % Elapsed time: 0.068673 seconds
% 0.09/0.45 % CPU time: 0.273762 seconds
% 0.09/0.45 % Total memory used: 106.889 MB
% 0.09/0.45 % Net memory used: 106.627 MB
%------------------------------------------------------------------------------