%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP298-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : 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 12:33:21 PM UTC 2026
% Result : Unsatisfiable 0.13s 5.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 55
% Syntax : Number of formulae : 279 ( 13 unt; 23 def)
% Number of atoms : 854 ( 324 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 1062 ( 487 ~; 552 |; 0 &)
% ( 23 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 25 ( 23 usr; 24 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 79 ( 79 !; 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_c2,sk_c8) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c2) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( inverse(sk_c4) = sk_c5
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c2,sk_c8) = sk_c7
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( inverse(sk_c2) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c7
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c6,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
! [X2,X1,X3,X4,X5] :
( multiply(X5,sk_c6) != sk_c7
| inverse(X4) != X5
| multiply(X4,X5) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| inverse(X3) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f38,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f39,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f40,plain,
( multiply(sk_c2,sk_c8) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f41,plain,
( inverse(sk_c2) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f42,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f43,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f44,plain,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f48,plain,
( multiply(sk_c2,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f49,plain,
( inverse(sk_c2) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f50,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f51,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f52,plain,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f53,plain,
( multiply(sk_c4,sk_c5) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f54,plain,
( inverse(sk_c4) = sk_c5
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f55,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f56,plain,
( multiply(sk_c2,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f57,plain,
( inverse(sk_c2) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f58,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f59,plain,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f60,plain,
( multiply(sk_c3,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f61,plain,
( multiply(sk_c4,sk_c5) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f62,plain,
( inverse(sk_c4) = sk_c5
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f63,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f64,plain,
( multiply(sk_c2,sk_c8) = sk_c7
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f65,plain,
( inverse(sk_c2) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f67,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f68,plain,
( multiply(sk_c3,sk_c7) = sk_c8
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f69,plain,
( multiply(sk_c4,sk_c5) = sk_c7
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f70,plain,
( inverse(sk_c4) = sk_c5
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f71,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f72,plain,
! [X5] :
( multiply(X5,sk_c6) != sk_c7
| ! [X4] :
( inverse(X4) != X5
| multiply(X4,X5) != sk_c7
| ! [X3] :
( multiply(X3,sk_c7) != sk_c8
| inverse(X3) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| ! [X1] :
( inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| ! [X2] :
( inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ) ) ) ) ),
inference(miniscoping,[status(thm)],[f36]) ).
fof(f73,plain,
! [X0,X1,X2,X3,X4] :
( multiply(X4,sk_c6) != sk_c7
| inverse(X3) != X4
| multiply(X3,X4) != sk_c7
| multiply(X2,sk_c7) != sk_c8
| inverse(X2) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f74,definition,
( sQ0_spl
<=> multiply(sk_c8,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f75,plain,
( ~ sQ0_spl
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(component_clause,[status(thm)],[f74]) ).
fof(f77,definition,
( sQ1_spl
<=> multiply(sk_c2,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f78,plain,
( ~ sQ1_spl
| multiply(sk_c2,sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f77]) ).
fof(f80,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f40,f74,f77]) ).
fof(f81,definition,
( sQ2_spl
<=> inverse(sk_c2) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f82,plain,
( ~ sQ2_spl
| inverse(sk_c2) = sk_c8 ),
inference(component_clause,[status(thm)],[f81]) ).
fof(f84,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f41,f74,f81]) ).
fof(f85,definition,
( sQ3_spl
<=> multiply(sk_c8,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ3_spl
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f87,plain,
( sQ3_spl
| multiply(sk_c8,sk_c6) != sk_c7 ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f88,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f42,f74,f85]) ).
fof(f89,definition,
( sQ4_spl
<=> inverse(sk_c3) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f90,plain,
( ~ sQ4_spl
| inverse(sk_c3) = sk_c8 ),
inference(component_clause,[status(thm)],[f89]) ).
fof(f92,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f43,f74,f89]) ).
fof(f93,definition,
( sQ5_spl
<=> multiply(sk_c3,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ5_spl
| multiply(sk_c3,sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f96,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f44,f74,f93]) ).
fof(f97,definition,
( sQ6_spl
<=> multiply(sk_c4,sk_c5) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f98,plain,
( ~ sQ6_spl
| multiply(sk_c4,sk_c5) = sk_c7 ),
inference(component_clause,[status(thm)],[f97]) ).
fof(f101,definition,
( sQ7_spl
<=> inverse(sk_c4) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f102,plain,
( ~ sQ7_spl
| inverse(sk_c4) = sk_c5 ),
inference(component_clause,[status(thm)],[f101]) ).
fof(f105,definition,
( sQ8_spl
<=> multiply(sk_c5,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f106,plain,
( ~ sQ8_spl
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(component_clause,[status(thm)],[f105]) ).
fof(f109,definition,
( sQ9_spl
<=> multiply(sk_c1,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f110,plain,
( ~ sQ9_spl
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f109]) ).
fof(f112,plain,
( sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f48,f109,f77]) ).
fof(f113,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f49,f109,f81]) ).
fof(f114,plain,
( sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f50,f109,f85]) ).
fof(f115,plain,
( sQ4_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f51,f109,f89]) ).
fof(f116,plain,
( sQ5_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f52,f109,f93]) ).
fof(f117,plain,
( sQ6_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f53,f109,f97]) ).
fof(f118,plain,
( sQ7_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f54,f109,f101]) ).
fof(f119,plain,
( sQ8_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f55,f109,f105]) ).
fof(f120,definition,
( sQ10_spl
<=> inverse(sk_c1) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f121,plain,
( ~ sQ10_spl
| inverse(sk_c1) = sk_c8 ),
inference(component_clause,[status(thm)],[f120]) ).
fof(f123,plain,
( sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f56,f120,f77]) ).
fof(f124,plain,
( sQ2_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f57,f120,f81]) ).
fof(f125,plain,
( sQ3_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f58,f120,f85]) ).
fof(f126,plain,
( sQ4_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f59,f120,f89]) ).
fof(f127,plain,
( sQ5_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f60,f120,f93]) ).
fof(f128,plain,
( sQ6_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f61,f120,f97]) ).
fof(f129,plain,
( sQ7_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f62,f120,f101]) ).
fof(f130,plain,
( sQ8_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f63,f120,f105]) ).
fof(f131,definition,
( sQ11_spl
<=> multiply(sk_c6,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f132,plain,
( ~ sQ11_spl
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f131]) ).
fof(f133,plain,
( sQ11_spl
| multiply(sk_c6,sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f131]) ).
fof(f134,plain,
( sQ1_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f64,f131,f77]) ).
fof(f135,plain,
( sQ2_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f65,f131,f81]) ).
fof(f137,plain,
( sQ4_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f67,f131,f89]) ).
fof(f138,plain,
( sQ5_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f68,f131,f93]) ).
fof(f139,plain,
( sQ6_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f69,f131,f97]) ).
fof(f140,plain,
( sQ7_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f70,f131,f101]) ).
fof(f141,plain,
( sQ8_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f71,f131,f105]) ).
fof(f142,definition,
! [X0] :
( sQ12_spl
<=> ( inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f143,plain,
! [X0] :
( ~ sQ12_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f142]) ).
fof(f145,definition,
! [X2] :
( sQ13_spl
<=> ( multiply(X2,sk_c7) != sk_c8
| inverse(X2) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f146,plain,
! [X0] :
( ~ sQ13_spl
| multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c8 ),
inference(component_clause,[status(thm)],[f145]) ).
fof(f148,definition,
! [X3,X4] :
( sQ14_spl
<=> ( multiply(X4,sk_c6) != sk_c7
| inverse(X3) != X4
| multiply(X3,X4) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f149,plain,
! [X0,X1] :
( ~ sQ14_spl
| multiply(X1,sk_c6) != sk_c7
| inverse(X0) != X1
| multiply(X0,X1) != sk_c7 ),
inference(component_clause,[status(thm)],[f148]) ).
fof(f151,plain,
( sQ14_spl
| sQ13_spl
| ~ sQ3_spl
| ~ sQ11_spl
| sQ12_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f73,f74,f142,f131,f85,f145,f148]) ).
fof(f152,plain,
! [X0] :
( ~ sQ14_spl
| multiply(inverse(X0),sk_c6) != sk_c7
| multiply(X0,inverse(X0)) != sk_c7 ),
inference(destructive_equality_resolution,[status(thm)],[f149]) ).
fof(f154,plain,
! [X0] :
( ~ sQ9_spl
| multiply(sk_c7,X0) = multiply(sk_c1,multiply(sk_c8,X0)) ),
inference(paramodulation,[status(thm)],[f110,f39]) ).
fof(f159,plain,
( ~ sQ2_spl
| multiply(sk_c8,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f82,f38]) ).
fof(f160,plain,
( ~ sQ4_spl
| multiply(sk_c8,sk_c3) = identity ),
inference(paramodulation,[status(thm)],[f90,f38]) ).
fof(f161,plain,
( ~ sQ7_spl
| multiply(sk_c5,sk_c4) = identity ),
inference(paramodulation,[status(thm)],[f102,f38]) ).
fof(f162,plain,
( ~ sQ10_spl
| multiply(sk_c8,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f121,f38]) ).
fof(f163,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f38,f39]) ).
fof(f164,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f37,f163]) ).
fof(f166,plain,
! [X0] :
( ~ sQ5_spl
| multiply(sk_c8,X0) = multiply(sk_c3,multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f94,f39]) ).
fof(f167,plain,
! [X0] :
( ~ sQ1_spl
| multiply(sk_c7,X0) = multiply(sk_c2,multiply(sk_c8,X0)) ),
inference(paramodulation,[status(thm)],[f78,f39]) ).
fof(f168,plain,
! [X0] :
( ~ sQ11_spl
| multiply(sk_c7,X0) = multiply(sk_c6,multiply(sk_c8,X0)) ),
inference(paramodulation,[status(thm)],[f132,f39]) ).
fof(f169,plain,
! [X0] :
( ~ sQ0_spl
| multiply(sk_c6,X0) = multiply(sk_c8,multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f75,f39]) ).
fof(f170,plain,
! [X0] :
( ~ sQ2_spl
| multiply(identity,X0) = multiply(sk_c8,multiply(sk_c2,X0)) ),
inference(paramodulation,[status(thm)],[f159,f39]) ).
fof(f171,plain,
! [X0] :
( ~ sQ2_spl
| X0 = multiply(sk_c8,multiply(sk_c2,X0)) ),
inference(forward_demodulation,[status(thm)],[f37,f170]) ).
fof(f172,plain,
! [X0] :
( ~ sQ4_spl
| multiply(identity,X0) = multiply(sk_c8,multiply(sk_c3,X0)) ),
inference(paramodulation,[status(thm)],[f160,f39]) ).
fof(f173,plain,
! [X0] :
( ~ sQ4_spl
| X0 = multiply(sk_c8,multiply(sk_c3,X0)) ),
inference(forward_demodulation,[status(thm)],[f37,f172]) ).
fof(f176,plain,
( ~ sQ2_spl
| ~ sQ14_spl
| multiply(inverse(sk_c2),sk_c6) != sk_c7
| multiply(sk_c2,sk_c8) != sk_c7 ),
inference(paramodulation,[status(thm)],[f82,f152]) ).
fof(f178,plain,
( ~ sQ7_spl
| ~ sQ14_spl
| multiply(inverse(sk_c4),sk_c6) != sk_c7
| multiply(sk_c4,sk_c5) != sk_c7 ),
inference(paramodulation,[status(thm)],[f102,f152]) ).
fof(f179,plain,
( ~ sQ10_spl
| ~ sQ14_spl
| multiply(inverse(sk_c1),sk_c6) != sk_c7
| multiply(sk_c1,sk_c8) != sk_c7 ),
inference(paramodulation,[status(thm)],[f121,f152]) ).
fof(f187,definition,
( sQ17_spl
<=> multiply(inverse(sk_c2),sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f189,plain,
( sQ17_spl
| multiply(inverse(sk_c2),sk_c6) != sk_c7 ),
inference(component_clause,[status(thm)],[f187]) ).
fof(f190,plain,
( ~ sQ2_spl
| ~ sQ14_spl
| ~ sQ17_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f176,f77,f187,f148,f81]) ).
fof(f198,definition,
( sQ20_spl
<=> multiply(inverse(sk_c4),sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f200,plain,
( sQ20_spl
| multiply(inverse(sk_c4),sk_c6) != sk_c7 ),
inference(component_clause,[status(thm)],[f198]) ).
fof(f201,plain,
( ~ sQ7_spl
| ~ sQ14_spl
| ~ sQ20_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f178,f97,f198,f148,f101]) ).
fof(f202,definition,
( sQ21_spl
<=> multiply(inverse(sk_c1),sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f204,plain,
( sQ21_spl
| multiply(inverse(sk_c1),sk_c6) != sk_c7 ),
inference(component_clause,[status(thm)],[f202]) ).
fof(f205,plain,
( ~ sQ10_spl
| ~ sQ14_spl
| ~ sQ21_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f179,f109,f202,f148,f120]) ).
fof(f206,plain,
( sQ21_spl
| ~ sQ10_spl
| multiply(sk_c8,sk_c6) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f121,f204]) ).
fof(f208,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| sk_c6 != sk_c8
| inverse(sk_c8) != sk_c8 ),
inference(paramodulation,[status(thm)],[f75,f146]) ).
fof(f209,plain,
( ~ sQ5_spl
| ~ sQ13_spl
| sk_c8 != sk_c8
| inverse(sk_c3) != sk_c8 ),
inference(paramodulation,[status(thm)],[f94,f146]) ).
fof(f213,definition,
( sQ22_spl
<=> inverse(sk_c8) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f215,plain,
( sQ22_spl
| inverse(sk_c8) != sk_c8 ),
inference(component_clause,[status(thm)],[f213]) ).
fof(f216,definition,
( sQ23_spl
<=> sk_c6 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f218,plain,
( sQ23_spl
| sk_c6 != sk_c8 ),
inference(component_clause,[status(thm)],[f216]) ).
fof(f219,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ23_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f208,f213,f216,f145,f74]) ).
fof(f220,definition,
( sQ24_spl
<=> sk_c8 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f222,plain,
( sQ24_spl
| sk_c8 != sk_c8 ),
inference(component_clause,[status(thm)],[f220]) ).
fof(f223,plain,
( ~ sQ5_spl
| ~ sQ13_spl
| ~ sQ24_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f209,f89,f220,f145,f93]) ).
fof(f238,plain,
( sQ24_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f222]) ).
fof(f239,plain,
sQ24_spl,
inference(contradiction_clause,[status(thm)],[f238]) ).
fof(f240,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| inverse(sk_c6) != sk_c8 ),
inference(resolution,[status(thm)],[f143,f132]) ).
fof(f241,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| inverse(sk_c1) != sk_c8 ),
inference(resolution,[status(thm)],[f143,f110]) ).
fof(f243,plain,
( ~ sQ12_spl
| inverse(inverse(sk_c8)) != sk_c8
| identity != sk_c7 ),
inference(paramodulation,[status(thm)],[f38,f143]) ).
fof(f247,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ10_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f121,f241]) ).
fof(f248,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f247]) ).
fof(f249,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f248]) ).
fof(f253,plain,
! [X0] :
( ~ sQ10_spl
| multiply(identity,X0) = multiply(sk_c8,multiply(sk_c1,X0)) ),
inference(paramodulation,[status(thm)],[f162,f39]) ).
fof(f254,plain,
! [X0] :
( ~ sQ10_spl
| X0 = multiply(sk_c8,multiply(sk_c1,X0)) ),
inference(forward_demodulation,[status(thm)],[f37,f253]) ).
fof(f258,plain,
! [X0] :
( ~ sQ3_spl
| multiply(sk_c7,X0) = multiply(sk_c8,multiply(sk_c6,X0)) ),
inference(paramodulation,[status(thm)],[f86,f39]) ).
fof(f267,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| multiply(sk_c7,sk_c1) = multiply(sk_c6,identity) ),
inference(paramodulation,[status(thm)],[f162,f168]) ).
fof(f291,plain,
! [X0] :
( ~ sQ7_spl
| multiply(identity,X0) = multiply(sk_c5,multiply(sk_c4,X0)) ),
inference(paramodulation,[status(thm)],[f161,f39]) ).
fof(f292,plain,
! [X0] :
( ~ sQ7_spl
| X0 = multiply(sk_c5,multiply(sk_c4,X0)) ),
inference(forward_demodulation,[status(thm)],[f37,f291]) ).
fof(f300,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 = multiply(sk_c8,sk_c7) ),
inference(paramodulation,[status(thm)],[f78,f171]) ).
fof(f301,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ1_spl
| multiply(sk_c7,multiply(sk_c2,X0)) = multiply(sk_c2,X0) ),
inference(paramodulation,[status(thm)],[f171,f167]) ).
fof(f302,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ11_spl
| multiply(sk_c7,multiply(sk_c2,X0)) = multiply(sk_c6,X0) ),
inference(paramodulation,[status(thm)],[f171,f168]) ).
fof(f307,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ11_spl
| ~ sQ1_spl
| X0 = multiply(sk_c8,multiply(sk_c6,X0)) ),
inference(backward_demodulation,[status(thm)],[f311,f171]) ).
fof(f311,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ11_spl
| ~ sQ1_spl
| multiply(sk_c2,X0) = multiply(sk_c6,X0) ),
inference(forward_demodulation,[status(thm)],[f301,f302]) ).
fof(f314,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ3_spl
| multiply(sk_c8,X0) = multiply(sk_c3,X0) ),
inference(backward_demodulation,[status(thm)],[f328,f166]) ).
fof(f328,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ3_spl
| X0 = multiply(sk_c7,X0) ),
inference(forward_demodulation,[status(thm)],[f258,f307]) ).
fof(f336,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ3_spl
| X0 = multiply(sk_c8,multiply(sk_c8,X0)) ),
inference(backward_demodulation,[status(thm)],[f314,f173]) ).
fof(f364,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ11_spl
| ~ sQ1_spl
| sk_c6 = multiply(sk_c8,sk_c7) ),
inference(paramodulation,[status(thm)],[f86,f336]) ).
fof(f365,plain,
( ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ3_spl
| sk_c2 = multiply(sk_c8,identity) ),
inference(paramodulation,[status(thm)],[f159,f336]) ).
fof(f380,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| multiply(sk_c7,sk_c1) = multiply(sk_c1,identity) ),
inference(paramodulation,[status(thm)],[f162,f154]) ).
fof(f430,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c8,X0) = multiply(sk_c8,multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f154,f254]) ).
fof(f431,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| sk_c8 = multiply(sk_c8,sk_c7) ),
inference(paramodulation,[status(thm)],[f110,f254]) ).
fof(f432,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ11_spl
| multiply(sk_c7,multiply(sk_c1,X0)) = multiply(sk_c6,X0) ),
inference(paramodulation,[status(thm)],[f254,f168]) ).
fof(f433,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ9_spl
| multiply(sk_c7,multiply(sk_c1,X0)) = multiply(sk_c1,X0) ),
inference(paramodulation,[status(thm)],[f254,f154]) ).
fof(f436,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| multiply(sk_c7,X0) = multiply(sk_c8,multiply(sk_c8,X0)) ),
inference(backward_demodulation,[status(thm)],[f443,f168]) ).
fof(f437,plain,
( ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| multiply(sk_c8,sk_c8) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f443,f132]) ).
fof(f441,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| multiply(sk_c7,sk_c1) = multiply(sk_c8,identity) ),
inference(backward_demodulation,[status(thm)],[f443,f267]) ).
fof(f443,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| multiply(sk_c8,X0) = multiply(sk_c6,X0) ),
inference(forward_demodulation,[status(thm)],[f169,f430]) ).
fof(f449,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| sk_c8 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f75,f431]) ).
fof(f450,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| multiply(sk_c7,multiply(sk_c1,X0)) = multiply(sk_c8,X0) ),
inference(forward_demodulation,[status(thm)],[f443,f432]) ).
fof(f453,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ11_spl
| ~ sQ0_spl
| X0 = multiply(sk_c8,multiply(sk_c8,X0)) ),
inference(backward_demodulation,[status(thm)],[f456,f254]) ).
fof(f456,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ11_spl
| ~ sQ0_spl
| multiply(sk_c8,X0) = multiply(sk_c1,X0) ),
inference(forward_demodulation,[status(thm)],[f450,f433]) ).
fof(f473,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| sk_c1 = multiply(sk_c8,identity) ),
inference(backward_demodulation,[status(thm)],[f475,f441]) ).
fof(f475,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ11_spl
| ~ sQ0_spl
| X0 = multiply(sk_c7,X0) ),
inference(forward_demodulation,[status(thm)],[f436,f453]) ).
fof(f491,plain,
( ~ sQ10_spl
| sk_c1 = multiply(inverse(sk_c8),identity) ),
inference(paramodulation,[status(thm)],[f162,f164]) ).
fof(f492,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f164,f164]) ).
fof(f493,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f38,f164]) ).
fof(f499,plain,
( ~ sQ10_spl
| sk_c1 = inverse(sk_c8) ),
inference(backward_demodulation,[status(thm)],[f503,f491]) ).
fof(f500,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| sk_c1 = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f503,f473]) ).
fof(f503,plain,
! [X0] : X0 = multiply(X0,identity),
inference(forward_demodulation,[status(thm)],[f492,f493]) ).
fof(f509,plain,
( sQ22_spl
| ~ sQ10_spl
| sk_c1 != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f499,f215]) ).
fof(f511,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| multiply(sk_c8,sk_c8) = identity ),
inference(backward_demodulation,[status(thm)],[f500,f162]) ).
fof(f516,plain,
( sQ22_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f500,f509]) ).
fof(f517,plain,
( sQ22_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f516]) ).
fof(f518,plain,
( sQ22_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f517]) ).
fof(f519,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| multiply(sk_c7,sk_c1) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f503,f267]) ).
fof(f520,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ11_spl
| sk_c6 = multiply(sk_c1,identity) ),
inference(forward_demodulation,[status(thm)],[f519,f380]) ).
fof(f527,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ11_spl
| multiply(sk_c8,sk_c6) = identity ),
inference(backward_demodulation,[status(thm)],[f528,f162]) ).
fof(f528,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ11_spl
| sk_c6 = sk_c1 ),
inference(forward_demodulation,[status(thm)],[f503,f520]) ).
fof(f552,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ11_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f364,f74,f77,f131,f81,f93,f89,f85]) ).
fof(f553,plain,
( ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ3_spl
| sk_c2 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f503,f365]) ).
fof(f572,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| sk_c7 = identity ),
inference(forward_demodulation,[status(thm)],[f437,f511]) ).
fof(f578,plain,
( sQ3_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ11_spl
| identity != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f527,f87]) ).
fof(f579,plain,
( sQ3_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ11_spl
| ~ sQ0_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f572,f578]) ).
fof(f580,plain,
( sQ3_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ11_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f579]) ).
fof(f581,plain,
( sQ3_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ11_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f580]) ).
fof(f588,plain,
( sQ23_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f449,f218]) ).
fof(f589,plain,
( sQ23_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f588]) ).
fof(f590,plain,
( sQ23_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f589]) ).
fof(f638,plain,
( ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f300,f75]) ).
fof(f654,plain,
( ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ3_spl
| inverse(sk_c8) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f553,f82]) ).
fof(f692,definition,
( sQ40_spl
<=> identity = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f695,definition,
( sQ41_spl
<=> inverse(inverse(sk_c8)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f697,plain,
( sQ41_spl
| inverse(inverse(sk_c8)) != sk_c8 ),
inference(component_clause,[status(thm)],[f695]) ).
fof(f698,plain,
( ~ sQ12_spl
| ~ sQ41_spl
| ~ sQ40_spl ),
inference(split_clause,[status(thm)],[f243,f692,f695,f142]) ).
fof(f700,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c8) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f638,f240]) ).
fof(f701,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f654,f700]) ).
fof(f702,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f701]) ).
fof(f703,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f702]) ).
fof(f730,plain,
( sQ21_spl
| ~ sQ10_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f206,f85,f120,f202]) ).
fof(f736,plain,
( ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c8,sk_c8) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f638,f132]) ).
fof(f783,plain,
( sQ17_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(inverse(sk_c2),sk_c8) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f638,f189]) ).
fof(f784,plain,
( sQ17_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c8,sk_c8) != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f82,f783]) ).
fof(f826,plain,
( sQ17_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ11_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f736,f784]) ).
fof(f827,plain,
( sQ17_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f826]) ).
fof(f828,plain,
( sQ17_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f827]) ).
fof(f831,plain,
( sQ20_spl
| ~ sQ7_spl
| multiply(sk_c5,sk_c6) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f102,f200]) ).
fof(f832,plain,
( sQ20_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f106,f831]) ).
fof(f833,plain,
( sQ20_spl
| ~ sQ7_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f832]) ).
fof(f834,plain,
( sQ20_spl
| ~ sQ7_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f833]) ).
fof(f854,plain,
( ~ sQ5_spl
| sk_c7 = multiply(inverse(sk_c3),sk_c8) ),
inference(paramodulation,[status(thm)],[f94,f164]) ).
fof(f856,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| sk_c7 = multiply(sk_c8,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f90,f854]) ).
fof(f857,plain,
( ~ sQ8_spl
| sk_c6 = multiply(inverse(sk_c5),sk_c7) ),
inference(paramodulation,[status(thm)],[f106,f164]) ).
fof(f859,plain,
( ~ sQ2_spl
| sk_c2 = multiply(inverse(sk_c8),identity) ),
inference(paramodulation,[status(thm)],[f159,f164]) ).
fof(f861,plain,
( sQ41_spl
| ~ sQ2_spl
| inverse(sk_c2) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f862,f697]) ).
fof(f862,plain,
( ~ sQ2_spl
| sk_c2 = inverse(sk_c8) ),
inference(forward_demodulation,[status(thm)],[f503,f859]) ).
fof(f864,plain,
( sQ41_spl
| ~ sQ2_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f82,f861]) ).
fof(f865,plain,
( sQ41_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f864]) ).
fof(f866,plain,
( sQ41_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f865]) ).
fof(f868,plain,
( sQ11_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c8,sk_c8) != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f638,f133]) ).
fof(f877,plain,
( sQ11_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f856,f868]) ).
fof(f878,plain,
( sQ11_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f877]) ).
fof(f879,plain,
( sQ11_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f878]) ).
fof(f881,plain,
( ~ sQ2_spl
| multiply(sk_c2,sk_c8) = identity ),
inference(paramodulation,[status(thm)],[f862,f38]) ).
fof(f882,plain,
! [X0] :
( ~ sQ2_spl
| X0 = multiply(sk_c2,multiply(sk_c8,X0)) ),
inference(paramodulation,[status(thm)],[f862,f164]) ).
fof(f888,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ1_spl
| X0 = multiply(X0,sk_c7) ),
inference(backward_demodulation,[status(thm)],[f890,f503]) ).
fof(f890,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sk_c7 = identity ),
inference(forward_demodulation,[status(thm)],[f78,f881]) ).
fof(f905,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ1_spl
| X0 = multiply(sk_c7,X0) ),
inference(forward_demodulation,[status(thm)],[f167,f882]) ).
fof(f913,plain,
( ~ sQ8_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c6 = inverse(sk_c5) ),
inference(backward_demodulation,[status(thm)],[f888,f857]) ).
fof(f941,plain,
! [X0] :
( ~ sQ3_spl
| multiply(sk_c7,X0) = multiply(sk_c8,multiply(sk_c6,X0)) ),
inference(paramodulation,[status(thm)],[f86,f39]) ).
fof(f943,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| X0 = multiply(sk_c8,multiply(sk_c6,X0)) ),
inference(forward_demodulation,[status(thm)],[f905,f941]) ).
fof(f951,plain,
! [X0] :
( ~ sQ7_spl
| multiply(sk_c4,X0) = multiply(inverse(sk_c5),X0) ),
inference(paramodulation,[status(thm)],[f292,f164]) ).
fof(f953,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ2_spl
| ~ sQ1_spl
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f955,f98]) ).
fof(f955,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ2_spl
| ~ sQ1_spl
| multiply(sk_c4,X0) = multiply(sk_c6,X0) ),
inference(forward_demodulation,[status(thm)],[f913,f951]) ).
fof(f957,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| sk_c5 = multiply(sk_c8,sk_c7) ),
inference(paramodulation,[status(thm)],[f953,f943]) ).
fof(f961,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f966,f953]) ).
fof(f966,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| sk_c5 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f888,f957]) ).
fof(f973,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f961,f131,f85,f77,f81,f105,f101,f97]) ).
fof(f975,plain,
$false,
inference(sat_refutation,[status(thm)],[f80,f84,f88,f92,f96,f112,f113,f114,f115,f116,f117,f118,f119,f123,f124,f125,f126,f127,f128,f129,f130,f134,f135,f137,f138,f139,f140,f141,f151,f190,f201,f205,f219,f223,f239,f249,f518,f552,f581,f590,f698,f703,f730,f828,f834,f866,f879,f973]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP298-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.36 % Computer : n026.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Sun Sep 20 20:11:12 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.38 % Drodi V4.1.1
% 0.13/5.41 % Refutation found
% 0.13/5.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/5.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/5.45 % Elapsed time: 0.063621 seconds
% 0.13/5.45 % CPU time: 0.252893 seconds
% 0.13/5.45 % Total memory used: 105.671 MB
% 0.13/5.45 % Net memory used: 105.422 MB
%------------------------------------------------------------------------------