%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP374-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:33:33 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.39s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 52
% Syntax : Number of formulae : 259 ( 10 unt; 20 def)
% Number of atoms : 985 ( 316 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 1378 ( 652 ~; 706 |; 0 &)
% ( 20 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 21 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 61 ( 61 !; 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
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
! [X3,X4,X1,X2,X5] :
( inverse(X5) != sk_c8
| multiply(X5,sk_c8) != X2
| multiply(sk_c8,X2) != sk_c7
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| inverse(X4) != sk_c6
| multiply(X4,sk_c6) != sk_c7
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(X3) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c7 ),
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
| inverse(sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f45,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f46,plain,
( inverse(sk_c3) = sk_c8
| inverse(sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f47,plain,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f48,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f49,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f51,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f52,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f57,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f58,plain,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f62,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f63,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f64,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f65,plain,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f66,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f67,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f68,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f69,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f70,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f71,plain,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f72,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f73,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f74,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f75,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f76,plain,
( inverse(sk_c3) = sk_c8
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f77,plain,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f78,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f79,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f80,plain,
! [X5] :
( inverse(X5) != sk_c8
| ! [X2] :
( multiply(X5,sk_c8) != X2
| multiply(sk_c8,X2) != sk_c7
| ! [X1] :
( inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| ! [X4] :
( inverse(X4) != sk_c6
| multiply(X4,sk_c6) != sk_c7
| multiply(sk_c8,sk_c6) != sk_c7
| ! [X3] :
( inverse(X3) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c7 ) ) ) ) ),
inference(miniscoping,[status(thm)],[f40]) ).
fof(f81,plain,
! [X0,X1,X2,X3,X4] :
( inverse(X4) != sk_c8
| multiply(X4,sk_c8) != X3
| multiply(sk_c8,X3) != sk_c7
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| inverse(X1) != sk_c6
| multiply(X1,sk_c6) != sk_c7
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c7 ),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f82,definition,
( sQ0_spl
<=> inverse(sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f83,plain,
( ~ sQ0_spl
| inverse(sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f82]) ).
fof(f84,plain,
( sQ0_spl
| inverse(sk_c8) != sk_c7 ),
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_c3,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f90,plain,
( ~ sQ2_spl
| multiply(sk_c3,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_c3) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ3_spl
| inverse(sk_c3) = 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
<=> multiply(sk_c8,sk_c5) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f98,plain,
( ~ sQ4_spl
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(component_clause,[status(thm)],[f97]) ).
fof(f100,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f47,f82,f97]) ).
fof(f101,definition,
( sQ5_spl
<=> multiply(sk_c4,sk_c8) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f102,plain,
( ~ sQ5_spl
| multiply(sk_c4,sk_c8) = sk_c5 ),
inference(component_clause,[status(thm)],[f101]) ).
fof(f104,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f48,f82,f101]) ).
fof(f105,definition,
( sQ6_spl
<=> inverse(sk_c4) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f106,plain,
( ~ sQ6_spl
| inverse(sk_c4) = sk_c8 ),
inference(component_clause,[status(thm)],[f105]) ).
fof(f108,plain,
( sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f49,f82,f105]) ).
fof(f109,definition,
( sQ7_spl
<=> multiply(sk_c1,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f110,plain,
( ~ sQ7_spl
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f109]) ).
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(f118,definition,
( sQ8_spl
<=> inverse(sk_c1) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f119,plain,
( ~ sQ8_spl
| inverse(sk_c1) = sk_c8 ),
inference(component_clause,[status(thm)],[f118]) ).
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(f127,definition,
( sQ9_spl
<=> multiply(sk_c8,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f128,plain,
( ~ sQ9_spl
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(component_clause,[status(thm)],[f127]) ).
fof(f129,plain,
( sQ9_spl
| multiply(sk_c8,sk_c6) != 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_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f137,plain,
( ~ sQ10_spl
| multiply(sk_c2,sk_c6) = sk_c7 ),
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_c6 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f146,plain,
( ~ sQ11_spl
| inverse(sk_c2) = sk_c6 ),
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_c8
| multiply(X0,sk_c8) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f155,plain,
! [X0] :
( ~ sQ12_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f154]) ).
fof(f157,definition,
! [X1] :
( sQ13_spl
<=> ( inverse(X1) != sk_c6
| multiply(X1,sk_c6) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f158,plain,
! [X0] :
( ~ sQ13_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c7 ),
inference(component_clause,[status(thm)],[f157]) ).
fof(f160,definition,
! [X3,X4] :
( sQ14_spl
<=> ( inverse(X4) != sk_c8
| multiply(X4,sk_c8) != X3
| multiply(sk_c8,X3) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f161,plain,
! [X0,X1] :
( ~ sQ14_spl
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != X0
| multiply(sk_c8,X0) != sk_c7 ),
inference(component_clause,[status(thm)],[f160]) ).
fof(f163,plain,
( sQ14_spl
| ~ sQ1_spl
| sQ13_spl
| ~ sQ9_spl
| sQ12_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f81,f82,f154,f127,f157,f85,f160]) ).
fof(f164,plain,
! [X0] :
( ~ sQ14_spl
| inverse(X0) != sk_c8
| multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ),
inference(destructive_equality_resolution,[status(thm)],[f161]) ).
fof(f191,plain,
( ~ sQ7_spl
| ~ sQ14_spl
| inverse(sk_c1) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c7 ),
inference(paramodulation,[status(thm)],[f110,f164]) ).
fof(f192,plain,
( ~ sQ2_spl
| ~ sQ14_spl
| inverse(sk_c3) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c7 ),
inference(paramodulation,[status(thm)],[f90,f164]) ).
fof(f193,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| inverse(sk_c4) != sk_c8
| multiply(sk_c8,sk_c5) != sk_c7 ),
inference(paramodulation,[status(thm)],[f102,f164]) ).
fof(f194,definition,
( sQ15_spl
<=> multiply(sk_c8,sk_c7) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f196,plain,
( sQ15_spl
| multiply(sk_c8,sk_c7) != sk_c7 ),
inference(component_clause,[status(thm)],[f194]) ).
fof(f197,plain,
( ~ sQ7_spl
| ~ sQ14_spl
| ~ sQ8_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f191,f194,f118,f160,f109]) ).
fof(f198,plain,
( ~ sQ2_spl
| ~ sQ14_spl
| ~ sQ3_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f192,f194,f93,f160,f89]) ).
fof(f199,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| ~ sQ6_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f193,f97,f105,f160,f101]) ).
fof(f200,plain,
( ~ sQ9_spl
| ~ sQ13_spl
| inverse(sk_c8) != sk_c6 ),
inference(resolution,[status(thm)],[f158,f128]) ).
fof(f201,plain,
( ~ sQ10_spl
| ~ sQ13_spl
| inverse(sk_c2) != sk_c6 ),
inference(resolution,[status(thm)],[f158,f137]) ).
fof(f206,plain,
( ~ sQ9_spl
| ~ sQ13_spl
| ~ sQ0_spl
| sk_c7 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f83,f200]) ).
fof(f207,plain,
( ~ sQ10_spl
| ~ sQ13_spl
| ~ sQ11_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f146,f201]) ).
fof(f208,plain,
( ~ sQ10_spl
| ~ sQ13_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f207]) ).
fof(f209,plain,
( ~ sQ10_spl
| ~ sQ13_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f208]) ).
fof(f212,plain,
( ~ sQ6_spl
| multiply(sk_c8,sk_c4) = identity ),
inference(paramodulation,[status(thm)],[f106,f42]) ).
fof(f214,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f42,f43]) ).
fof(f215,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f41,f214]) ).
fof(f216,plain,
( sQ15_spl
| ~ sQ1_spl
| sk_c6 != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f86,f196]) ).
fof(f217,plain,
! [X0] :
( ~ sQ1_spl
| multiply(sk_c6,X0) = multiply(sk_c8,multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f86,f43]) ).
fof(f230,plain,
( ~ sQ2_spl
| sk_c8 = multiply(inverse(sk_c3),sk_c7) ),
inference(paramodulation,[status(thm)],[f90,f215]) ).
fof(f239,plain,
( ~ sQ5_spl
| sk_c8 = multiply(inverse(sk_c4),sk_c5) ),
inference(paramodulation,[status(thm)],[f102,f215]) ).
fof(f241,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| sk_c8 = multiply(sk_c8,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f94,f230]) ).
fof(f242,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c8 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f86,f241]) ).
fof(f243,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sk_c8 = multiply(sk_c8,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f106,f239]) ).
fof(f244,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sk_c8 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f98,f243]) ).
fof(f246,plain,
( ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(sk_c6,sk_c4) = identity ),
inference(backward_demodulation,[status(thm)],[f242,f212]) ).
fof(f249,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(sk_c3,sk_c6) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f242,f90]) ).
fof(f250,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| multiply(sk_c6,sk_c7) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f242,f86]) ).
fof(f253,plain,
( ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| inverse(sk_c4) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f242,f106]) ).
fof(f254,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c6 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f242,f244]) ).
fof(f258,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c6) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f242,f155]) ).
fof(f259,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f242,f258]) ).
fof(f261,plain,
( ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| inverse(identity) != sk_c6
| sk_c6 != sk_c7 ),
inference(paramodulation,[status(thm)],[f41,f259]) ).
fof(f270,definition,
( sQ18_spl
<=> sk_c6 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f272,plain,
( sQ18_spl
| sk_c6 != sk_c7 ),
inference(component_clause,[status(thm)],[f270]) ).
fof(f273,definition,
( sQ19_spl
<=> inverse(identity) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f275,plain,
( sQ19_spl
| inverse(identity) != sk_c6 ),
inference(component_clause,[status(thm)],[f273]) ).
fof(f276,plain,
( ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ19_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f261,f270,f273,f85,f93,f89,f154]) ).
fof(f277,plain,
( ~ sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| inverse(sk_c6) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f242,f83]) ).
fof(f286,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ12_spl
| inverse(sk_c3) != sk_c6
| sk_c7 != sk_c7 ),
inference(paramodulation,[status(thm)],[f249,f259]) ).
fof(f289,definition,
( sQ20_spl
<=> sk_c7 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f291,plain,
( sQ20_spl
| sk_c7 != sk_c7 ),
inference(component_clause,[status(thm)],[f289]) ).
fof(f292,definition,
( sQ21_spl
<=> inverse(sk_c3) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f295,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ12_spl
| ~ sQ21_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f286,f289,f292,f154,f85,f93,f89]) ).
fof(f296,plain,
( sQ20_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f291]) ).
fof(f297,plain,
sQ20_spl,
inference(contradiction_clause,[status(thm)],[f296]) ).
fof(f298,plain,
( sQ9_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(sk_c6,sk_c6) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f242,f129]) ).
fof(f302,plain,
( sQ18_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f254,f272]) ).
fof(f303,plain,
( sQ18_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f302]) ).
fof(f304,plain,
( sQ18_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f303]) ).
fof(f310,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| multiply(sk_c6,sk_c6) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f254,f250]) ).
fof(f311,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sk_c6 = multiply(inverse(sk_c6),sk_c6) ),
inference(paramodulation,[status(thm)],[f310,f215]) ).
fof(f313,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f42,f311]) ).
fof(f319,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| multiply(sk_c6,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f313,f41]) ).
fof(f320,plain,
( sQ19_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| inverse(sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f313,f275]) ).
fof(f321,plain,
( ~ sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| inverse(sk_c6) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f254,f277]) ).
fof(f322,plain,
( ~ sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f321,f320]) ).
fof(f323,plain,
( ~ sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sQ19_spl ),
inference(contradiction_clause,[status(thm)],[f322]) ).
fof(f324,plain,
( sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| inverse(sk_c6) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f242,f84]) ).
fof(f325,plain,
( sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| inverse(sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f254,f324]) ).
fof(f334,plain,
( ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c4 = identity ),
inference(forward_demodulation,[status(thm)],[f319,f246]) ).
fof(f336,plain,
( sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| inverse(sk_c6) != sk_c4 ),
inference(backward_demodulation,[status(thm)],[f344,f325]) ).
fof(f337,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| multiply(sk_c4,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f344,f319]) ).
fof(f339,plain,
( ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(sk_c4) = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f344,f253]) ).
fof(f341,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c4 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f344,f254]) ).
fof(f344,plain,
( ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c4 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f313,f334]) ).
fof(f345,plain,
( sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| inverse(sk_c4) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f344,f336]) ).
fof(f356,plain,
( ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f339,f345]) ).
fof(f357,plain,
( ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f356]) ).
fof(f360,plain,
( sQ9_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c4,sk_c6) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f344,f298]) ).
fof(f361,plain,
( sQ9_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c6 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f337,f360]) ).
fof(f362,plain,
( sQ9_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c4 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f344,f361]) ).
fof(f363,plain,
( sQ9_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c4 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f341,f362]) ).
fof(f364,plain,
( sQ9_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f363]) ).
fof(f365,plain,
( sQ9_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f364]) ).
fof(f384,plain,
( ~ sQ9_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f206,f270,f82,f157,f127]) ).
fof(f398,plain,
( ~ sQ10_spl
| sk_c6 = multiply(inverse(sk_c2),sk_c7) ),
inference(paramodulation,[status(thm)],[f137,f215]) ).
fof(f400,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| sk_c6 = multiply(sk_c6,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f146,f398]) ).
fof(f409,plain,
( ~ sQ0_spl
| multiply(sk_c7,sk_c8) = identity ),
inference(paramodulation,[status(thm)],[f83,f42]) ).
fof(f436,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| sk_c7 = multiply(inverse(sk_c6),sk_c6) ),
inference(paramodulation,[status(thm)],[f400,f215]) ).
fof(f440,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| sk_c7 = identity ),
inference(forward_demodulation,[status(thm)],[f42,f436]) ).
fof(f441,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ11_spl
| multiply(inverse(X0),X0) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f440,f42]) ).
fof(f444,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ11_spl
| multiply(sk_c7,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f440,f41]) ).
fof(f449,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| sk_c8 = identity ),
inference(forward_demodulation,[status(thm)],[f444,f409]) ).
fof(f450,plain,
( sQ1_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| multiply(sk_c7,sk_c7) != sk_c6 ),
inference(backward_demodulation,[status(thm)],[f455,f87]) ).
fof(f451,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| multiply(sk_c1,sk_c7) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f455,f110]) ).
fof(f452,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| multiply(sk_c7,sk_c6) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f455,f128]) ).
fof(f454,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| inverse(sk_c1) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f455,f119]) ).
fof(f455,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| sk_c8 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f440,f449]) ).
fof(f456,plain,
( sQ1_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| sk_c7 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f444,f450]) ).
fof(f457,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| sk_c6 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f444,f452]) ).
fof(f462,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f457,f456]) ).
fof(f463,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f462]) ).
fof(f466,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| multiply(sk_c6,X0) = multiply(sk_c7,multiply(sk_c7,X0)) ),
inference(forward_demodulation,[status(thm)],[f455,f217]) ).
fof(f467,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| multiply(sk_c6,X0) = multiply(sk_c7,X0) ),
inference(forward_demodulation,[status(thm)],[f444,f466]) ).
fof(f468,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| multiply(sk_c6,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f444,f467]) ).
fof(f472,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c7) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f455,f155]) ).
fof(f473,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f455,f472]) ).
fof(f474,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| multiply(inverse(X0),X0) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f457,f441]) ).
fof(f483,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| inverse(sk_c1) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f457,f454]) ).
fof(f504,plain,
( ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f259,f157,f85,f93,f89,f154]) ).
fof(f525,plain,
( sQ18_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f457,f272]) ).
fof(f526,plain,
( sQ18_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f525]) ).
fof(f527,plain,
( sQ18_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f526]) ).
fof(f539,plain,
( sQ15_spl
| ~ sQ1_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f216,f270,f85,f194]) ).
fof(f544,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c6) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f457,f473]) ).
fof(f545,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f457,f544]) ).
fof(f546,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f457,f545]) ).
fof(f553,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f457,f451]) ).
fof(f554,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| multiply(sk_c1,sk_c6) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f457,f553]) ).
fof(f556,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| multiply(sk_c6,X0) = multiply(sk_c1,multiply(sk_c6,X0)) ),
inference(paramodulation,[status(thm)],[f554,f43]) ).
fof(f558,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ1_spl
| X0 = multiply(sk_c1,multiply(sk_c6,X0)) ),
inference(forward_demodulation,[status(thm)],[f468,f556]) ).
fof(f559,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ1_spl
| X0 = multiply(sk_c1,X0) ),
inference(forward_demodulation,[status(thm)],[f468,f558]) ).
fof(f560,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| multiply(sk_c6,sk_c1) = sk_c6 ),
inference(paramodulation,[status(thm)],[f483,f474]) ).
fof(f562,plain,
( ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| multiply(sk_c6,sk_c2) = sk_c6 ),
inference(paramodulation,[status(thm)],[f146,f474]) ).
fof(f565,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ1_spl
| sk_c1 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f468,f560]) ).
fof(f566,plain,
( ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ1_spl
| sk_c2 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f468,f562]) ).
fof(f571,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ1_spl
| inverse(sk_c1) = sk_c1 ),
inference(backward_demodulation,[status(thm)],[f565,f483]) ).
fof(f579,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ1_spl
| sk_c2 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f580,f565]) ).
fof(f580,plain,
( ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ8_spl
| sk_c2 = sk_c1 ),
inference(forward_demodulation,[status(thm)],[f565,f566]) ).
fof(f585,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ8_spl
| X0 = multiply(sk_c2,X0) ),
inference(forward_demodulation,[status(thm)],[f580,f559]) ).
fof(f589,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ1_spl
| inverse(sk_c2) = sk_c1 ),
inference(forward_demodulation,[status(thm)],[f580,f571]) ).
fof(f590,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ1_spl
| inverse(sk_c2) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f580,f589]) ).
fof(f610,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ1_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c2) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f579,f546]) ).
fof(f611,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ1_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c2) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f579,f610]) ).
fof(f612,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ1_spl
| inverse(X0) != sk_c2
| multiply(X0,sk_c2) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f579,f611]) ).
fof(f614,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ12_spl
| inverse(sk_c2) != sk_c2 ),
inference(resolution,[status(thm)],[f612,f585]) ).
fof(f618,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ12_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f590,f614]) ).
fof(f619,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f618]) ).
fof(f620,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f619]) ).
fof(f621,plain,
$false,
inference(sat_refutation,[status(thm)],[f88,f92,f96,f100,f104,f108,f113,f114,f122,f123,f130,f131,f132,f133,f134,f135,f139,f140,f141,f142,f143,f144,f148,f149,f150,f151,f152,f153,f163,f197,f198,f199,f209,f276,f295,f297,f304,f323,f357,f365,f384,f463,f504,f527,f539,f620]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP374-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n011.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 20:10:40 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.11/0.37 % Drodi V4.1.1
% 0.11/0.39 % Refutation found
% 0.11/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.42 % Elapsed time: 0.053405 seconds
% 0.11/0.42 % CPU time: 0.132067 seconds
% 0.11/0.42 % Total memory used: 55.353 MB
% 0.11/0.42 % Net memory used: 55.277 MB
%------------------------------------------------------------------------------