%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP239-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : 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 12:33:11 PM UTC 2026
% Result : Unsatisfiable 0.02s 15.24s
% Output : CNFRefutation 0.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 72
% Syntax : Number of formulae : 289 ( 10 unt; 32 def)
% Number of atoms : 853 ( 347 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 1014 ( 450 ~; 532 |; 0 &)
% ( 32 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 34 ( 32 usr; 33 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 52 ( 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
( inverse(sk_c4) = sk_c9
| inverse(sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c9
| inverse(sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| inverse(sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c4) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
( inverse(sk_c4) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,negated_conjecture,
! [X4,X5,X6,X1,X2,X7,X3] :
( multiply(X3,sk_c9) != sk_c8
| inverse(X7) != X3
| multiply(X7,X3) != sk_c8
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c9
| multiply(X1,sk_c8) != sk_c9
| inverse(X1) != sk_c9
| inverse(X6) != sk_c9
| multiply(X6,sk_c9) != X5
| multiply(sk_c9,X5) != sk_c8
| multiply(X4,sk_c8) != sk_c9
| inverse(X4) != sk_c9
| inverse(sk_c9) != sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f48,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f49,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f50,plain,
( inverse(sk_c4) = sk_c9
| inverse(sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f51,plain,
( multiply(sk_c4,sk_c8) = sk_c9
| inverse(sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f52,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f53,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f54,plain,
( multiply(sk_c6,sk_c7) = sk_c8
| inverse(sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f55,plain,
( inverse(sk_c6) = sk_c7
| inverse(sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f57,plain,
( inverse(sk_c4) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f58,plain,
( multiply(sk_c4,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f59,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f60,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f61,plain,
( multiply(sk_c6,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f62,plain,
( inverse(sk_c6) = sk_c7
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f64,plain,
( inverse(sk_c4) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f65,plain,
( multiply(sk_c4,sk_c8) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f66,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f67,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f68,plain,
( multiply(sk_c6,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f69,plain,
( inverse(sk_c6) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f71,plain,
( inverse(sk_c4) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f72,plain,
( multiply(sk_c4,sk_c8) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f73,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f74,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f75,plain,
( multiply(sk_c6,sk_c7) = sk_c8
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f76,plain,
( inverse(sk_c6) = sk_c7
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f78,plain,
( inverse(sk_c4) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f79,plain,
( multiply(sk_c4,sk_c8) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f80,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f81,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f82,plain,
( multiply(sk_c6,sk_c7) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f83,plain,
( inverse(sk_c6) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f85,plain,
( inverse(sk_c4) = sk_c9
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f86,plain,
( multiply(sk_c4,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f87,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f88,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f89,plain,
( multiply(sk_c6,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f90,plain,
( inverse(sk_c6) = sk_c7
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f92,plain,
! [X3] :
( multiply(X3,sk_c9) != sk_c8
| ! [X7] :
( inverse(X7) != X3
| multiply(X7,X3) != sk_c8
| ! [X2] :
( inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c9
| ! [X1] :
( multiply(X1,sk_c8) != sk_c9
| inverse(X1) != sk_c9
| ! [X6] :
( inverse(X6) != sk_c9
| ! [X5] :
( multiply(X6,sk_c9) != X5
| multiply(sk_c9,X5) != sk_c8
| ! [X4] :
( multiply(X4,sk_c8) != sk_c9
| inverse(X4) != sk_c9
| inverse(sk_c9) != sk_c8 ) ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f46]) ).
fof(f93,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( multiply(X6,sk_c9) != sk_c8
| inverse(X5) != X6
| multiply(X5,X6) != sk_c8
| inverse(X4) != sk_c8
| multiply(X4,sk_c8) != sk_c9
| multiply(X3,sk_c8) != sk_c9
| inverse(X3) != sk_c9
| inverse(X2) != sk_c9
| multiply(X2,sk_c9) != X1
| multiply(sk_c9,X1) != sk_c8
| multiply(X0,sk_c8) != sk_c9
| inverse(X0) != sk_c9
| inverse(sk_c9) != sk_c8 ),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f94,definition,
( sQ0_spl
<=> inverse(sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f95,plain,
( ~ sQ0_spl
| inverse(sk_c9) = sk_c8 ),
inference(component_clause,[status(thm)],[f94]) ).
fof(f96,plain,
( sQ0_spl
| inverse(sk_c9) != sk_c8 ),
inference(component_clause,[status(thm)],[f94]) ).
fof(f97,definition,
( sQ1_spl
<=> inverse(sk_c4) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f98,plain,
( ~ sQ1_spl
| inverse(sk_c4) = sk_c9 ),
inference(component_clause,[status(thm)],[f97]) ).
fof(f100,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f50,f94,f97]) ).
fof(f101,definition,
( sQ2_spl
<=> multiply(sk_c4,sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f102,plain,
( ~ sQ2_spl
| multiply(sk_c4,sk_c8) = sk_c9 ),
inference(component_clause,[status(thm)],[f101]) ).
fof(f104,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f51,f94,f101]) ).
fof(f105,definition,
( sQ3_spl
<=> multiply(sk_c5,sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f106,plain,
( ~ sQ3_spl
| multiply(sk_c5,sk_c8) = sk_c9 ),
inference(component_clause,[status(thm)],[f105]) ).
fof(f108,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f52,f94,f105]) ).
fof(f109,definition,
( sQ4_spl
<=> inverse(sk_c5) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f110,plain,
( ~ sQ4_spl
| inverse(sk_c5) = sk_c8 ),
inference(component_clause,[status(thm)],[f109]) ).
fof(f112,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f53,f94,f109]) ).
fof(f113,definition,
( sQ5_spl
<=> multiply(sk_c6,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f114,plain,
( ~ sQ5_spl
| multiply(sk_c6,sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f113]) ).
fof(f116,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f54,f94,f113]) ).
fof(f117,definition,
( sQ6_spl
<=> inverse(sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f118,plain,
( ~ sQ6_spl
| inverse(sk_c6) = sk_c7 ),
inference(component_clause,[status(thm)],[f117]) ).
fof(f120,plain,
( sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f55,f94,f117]) ).
fof(f125,definition,
( sQ8_spl
<=> inverse(sk_c1) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f126,plain,
( ~ sQ8_spl
| inverse(sk_c1) = sk_c9 ),
inference(component_clause,[status(thm)],[f125]) ).
fof(f128,plain,
( sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f57,f125,f97]) ).
fof(f129,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f58,f125,f101]) ).
fof(f130,plain,
( sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f59,f125,f105]) ).
fof(f131,plain,
( sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f60,f125,f109]) ).
fof(f132,plain,
( sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f61,f125,f113]) ).
fof(f133,plain,
( sQ6_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f62,f125,f117]) ).
fof(f135,definition,
( sQ9_spl
<=> multiply(sk_c1,sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f136,plain,
( ~ sQ9_spl
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(component_clause,[status(thm)],[f135]) ).
fof(f138,plain,
( sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f64,f135,f97]) ).
fof(f139,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f65,f135,f101]) ).
fof(f140,plain,
( sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f66,f135,f105]) ).
fof(f141,plain,
( sQ4_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f67,f135,f109]) ).
fof(f142,plain,
( sQ5_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f68,f135,f113]) ).
fof(f143,plain,
( sQ6_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f69,f135,f117]) ).
fof(f145,definition,
( sQ10_spl
<=> multiply(sk_c9,sk_c3) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f146,plain,
( ~ sQ10_spl
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(component_clause,[status(thm)],[f145]) ).
fof(f147,plain,
( sQ10_spl
| multiply(sk_c9,sk_c3) != sk_c8 ),
inference(component_clause,[status(thm)],[f145]) ).
fof(f148,plain,
( sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f71,f145,f97]) ).
fof(f149,plain,
( sQ2_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f72,f145,f101]) ).
fof(f150,plain,
( sQ3_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f73,f145,f105]) ).
fof(f151,plain,
( sQ4_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f74,f145,f109]) ).
fof(f152,plain,
( sQ5_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f75,f145,f113]) ).
fof(f153,plain,
( sQ6_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f76,f145,f117]) ).
fof(f155,definition,
( sQ11_spl
<=> multiply(sk_c2,sk_c9) = sk_c3 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f156,plain,
( ~ sQ11_spl
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(component_clause,[status(thm)],[f155]) ).
fof(f158,plain,
( sQ1_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f78,f155,f97]) ).
fof(f159,plain,
( sQ2_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f79,f155,f101]) ).
fof(f160,plain,
( sQ3_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f80,f155,f105]) ).
fof(f161,plain,
( sQ4_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f81,f155,f109]) ).
fof(f162,plain,
( sQ5_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f82,f155,f113]) ).
fof(f163,plain,
( sQ6_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f83,f155,f117]) ).
fof(f165,definition,
( sQ12_spl
<=> inverse(sk_c2) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f166,plain,
( ~ sQ12_spl
| inverse(sk_c2) = sk_c9 ),
inference(component_clause,[status(thm)],[f165]) ).
fof(f168,plain,
( sQ1_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f85,f165,f97]) ).
fof(f169,plain,
( sQ2_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f86,f165,f101]) ).
fof(f170,plain,
( sQ3_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f87,f165,f105]) ).
fof(f171,plain,
( sQ4_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f88,f165,f109]) ).
fof(f172,plain,
( sQ5_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f89,f165,f113]) ).
fof(f173,plain,
( sQ6_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f90,f165,f117]) ).
fof(f175,definition,
! [X0] :
( sQ13_spl
<=> ( multiply(X0,sk_c8) != sk_c9
| inverse(X0) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f176,plain,
! [X0] :
( ~ sQ13_spl
| multiply(X0,sk_c8) != sk_c9
| inverse(X0) != sk_c9 ),
inference(component_clause,[status(thm)],[f175]) ).
fof(f178,definition,
! [X1,X2] :
( sQ14_spl
<=> ( inverse(X2) != sk_c9
| multiply(X2,sk_c9) != X1
| multiply(sk_c9,X1) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f179,plain,
! [X0,X1] :
( ~ sQ14_spl
| inverse(X1) != sk_c9
| multiply(X1,sk_c9) != X0
| multiply(sk_c9,X0) != sk_c8 ),
inference(component_clause,[status(thm)],[f178]) ).
fof(f181,definition,
! [X4] :
( sQ15_spl
<=> ( inverse(X4) != sk_c8
| multiply(X4,sk_c8) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f182,plain,
! [X0] :
( ~ sQ15_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c9 ),
inference(component_clause,[status(thm)],[f181]) ).
fof(f184,definition,
! [X5,X6] :
( sQ16_spl
<=> ( multiply(X6,sk_c9) != sk_c8
| inverse(X5) != X6
| multiply(X5,X6) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f185,plain,
! [X0,X1] :
( ~ sQ16_spl
| multiply(X1,sk_c9) != sk_c8
| inverse(X0) != X1
| multiply(X0,X1) != sk_c8 ),
inference(component_clause,[status(thm)],[f184]) ).
fof(f187,plain,
( sQ16_spl
| sQ15_spl
| sQ14_spl
| sQ13_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f93,f94,f175,f178,f181,f184]) ).
fof(f188,plain,
! [X0] :
( ~ sQ16_spl
| multiply(inverse(X0),sk_c9) != sk_c8
| multiply(X0,inverse(X0)) != sk_c8 ),
inference(destructive_equality_resolution,[status(thm)],[f185]) ).
fof(f206,plain,
( ~ sQ1_spl
| ~ sQ16_spl
| multiply(sk_c9,sk_c9) != sk_c8
| multiply(sk_c4,inverse(sk_c4)) != sk_c8 ),
inference(paramodulation,[status(thm)],[f98,f188]) ).
fof(f207,plain,
( ~ sQ4_spl
| ~ sQ16_spl
| multiply(sk_c8,sk_c9) != sk_c8
| multiply(sk_c5,inverse(sk_c5)) != sk_c8 ),
inference(paramodulation,[status(thm)],[f110,f188]) ).
fof(f209,plain,
( ~ sQ8_spl
| ~ sQ16_spl
| multiply(sk_c9,sk_c9) != sk_c8
| multiply(sk_c1,inverse(sk_c1)) != sk_c8 ),
inference(paramodulation,[status(thm)],[f126,f188]) ).
fof(f210,plain,
( ~ sQ12_spl
| ~ sQ16_spl
| multiply(sk_c9,sk_c9) != sk_c8
| multiply(sk_c2,inverse(sk_c2)) != sk_c8 ),
inference(paramodulation,[status(thm)],[f166,f188]) ).
fof(f214,definition,
( sQ18_spl
<=> multiply(sk_c8,sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f216,plain,
( sQ18_spl
| multiply(sk_c8,sk_c9) != sk_c8 ),
inference(component_clause,[status(thm)],[f214]) ).
fof(f218,definition,
( sQ19_spl
<=> multiply(sk_c4,inverse(sk_c4)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f221,definition,
( sQ20_spl
<=> multiply(sk_c9,sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f223,plain,
( sQ20_spl
| multiply(sk_c9,sk_c9) != sk_c8 ),
inference(component_clause,[status(thm)],[f221]) ).
fof(f224,plain,
( ~ sQ1_spl
| ~ sQ16_spl
| ~ sQ20_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f206,f218,f221,f184,f97]) ).
fof(f225,definition,
( sQ21_spl
<=> multiply(sk_c5,inverse(sk_c5)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f227,plain,
( sQ21_spl
| multiply(sk_c5,inverse(sk_c5)) != sk_c8 ),
inference(component_clause,[status(thm)],[f225]) ).
fof(f228,plain,
( ~ sQ4_spl
| ~ sQ16_spl
| ~ sQ18_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f207,f225,f214,f184,f109]) ).
fof(f233,definition,
( sQ23_spl
<=> multiply(sk_c1,inverse(sk_c1)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f235,plain,
( sQ23_spl
| multiply(sk_c1,inverse(sk_c1)) != sk_c8 ),
inference(component_clause,[status(thm)],[f233]) ).
fof(f236,plain,
( ~ sQ8_spl
| ~ sQ16_spl
| ~ sQ20_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f209,f233,f221,f184,f125]) ).
fof(f237,definition,
( sQ24_spl
<=> multiply(sk_c2,inverse(sk_c2)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f240,plain,
( ~ sQ12_spl
| ~ sQ16_spl
| ~ sQ20_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f210,f237,f221,f184,f165]) ).
fof(f243,plain,
( sQ23_spl
| ~ sQ8_spl
| multiply(sk_c1,sk_c9) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f126,f235]) ).
fof(f249,plain,
( ~ sQ2_spl
| ~ sQ15_spl
| inverse(sk_c4) != sk_c8
| sk_c9 != sk_c9 ),
inference(paramodulation,[status(thm)],[f102,f182]) ).
fof(f250,plain,
( ~ sQ3_spl
| ~ sQ15_spl
| inverse(sk_c5) != sk_c8
| sk_c9 != sk_c9 ),
inference(paramodulation,[status(thm)],[f106,f182]) ).
fof(f251,plain,
( ~ sQ9_spl
| ~ sQ15_spl
| inverse(sk_c1) != sk_c8
| sk_c9 != sk_c9 ),
inference(paramodulation,[status(thm)],[f136,f182]) ).
fof(f253,definition,
( sQ25_spl
<=> sk_c9 = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f255,plain,
( sQ25_spl
| sk_c9 != sk_c9 ),
inference(component_clause,[status(thm)],[f253]) ).
fof(f256,definition,
( sQ26_spl
<=> inverse(sk_c4) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f258,plain,
( sQ26_spl
| inverse(sk_c4) != sk_c8 ),
inference(component_clause,[status(thm)],[f256]) ).
fof(f259,plain,
( ~ sQ2_spl
| ~ sQ15_spl
| ~ sQ26_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f249,f253,f256,f181,f101]) ).
fof(f260,plain,
( ~ sQ3_spl
| ~ sQ15_spl
| ~ sQ4_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f250,f253,f109,f181,f105]) ).
fof(f261,definition,
( sQ27_spl
<=> inverse(sk_c1) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f263,plain,
( sQ27_spl
| inverse(sk_c1) != sk_c8 ),
inference(component_clause,[status(thm)],[f261]) ).
fof(f264,plain,
( ~ sQ9_spl
| ~ sQ15_spl
| ~ sQ27_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f251,f253,f261,f181,f135]) ).
fof(f265,plain,
( sQ25_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f255]) ).
fof(f266,plain,
sQ25_spl,
inference(contradiction_clause,[status(thm)],[f265]) ).
fof(f268,plain,
! [X0] :
( ~ sQ14_spl
| inverse(X0) != sk_c9
| multiply(sk_c9,multiply(X0,sk_c9)) != sk_c8 ),
inference(destructive_equality_resolution,[status(thm)],[f179]) ).
fof(f270,plain,
( ~ sQ0_spl
| multiply(sk_c8,sk_c9) = identity ),
inference(paramodulation,[status(thm)],[f95,f48]) ).
fof(f273,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f48,f49]) ).
fof(f274,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f47,f273]) ).
fof(f275,plain,
( sQ18_spl
| ~ sQ0_spl
| identity != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f270,f216]) ).
fof(f282,plain,
( ~ sQ0_spl
| ~ sQ14_spl
| inverse(sk_c8) != sk_c9
| multiply(sk_c9,identity) != sk_c8 ),
inference(paramodulation,[status(thm)],[f270,f268]) ).
fof(f283,plain,
( ~ sQ14_spl
| inverse(inverse(sk_c9)) != sk_c9
| multiply(sk_c9,identity) != sk_c8 ),
inference(paramodulation,[status(thm)],[f48,f268]) ).
fof(f284,plain,
( ~ sQ14_spl
| inverse(identity) != sk_c9
| multiply(sk_c9,sk_c9) != sk_c8 ),
inference(paramodulation,[status(thm)],[f47,f268]) ).
fof(f286,plain,
( ~ sQ11_spl
| ~ sQ14_spl
| inverse(sk_c2) != sk_c9
| multiply(sk_c9,sk_c3) != sk_c8 ),
inference(paramodulation,[status(thm)],[f156,f268]) ).
fof(f287,definition,
( sQ28_spl
<=> multiply(sk_c9,identity) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f290,definition,
( sQ29_spl
<=> inverse(sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f292,plain,
( sQ29_spl
| inverse(sk_c8) != sk_c9 ),
inference(component_clause,[status(thm)],[f290]) ).
fof(f293,plain,
( ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ29_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f282,f287,f290,f178,f94]) ).
fof(f294,definition,
( sQ30_spl
<=> inverse(inverse(sk_c9)) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f297,plain,
( ~ sQ14_spl
| ~ sQ30_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f283,f287,f294,f178]) ).
fof(f298,definition,
( sQ31_spl
<=> inverse(identity) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f300,plain,
( sQ31_spl
| inverse(identity) != sk_c9 ),
inference(component_clause,[status(thm)],[f298]) ).
fof(f301,plain,
( ~ sQ14_spl
| ~ sQ31_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f284,f221,f298,f178]) ).
fof(f302,plain,
( ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f286,f145,f165,f178,f155]) ).
fof(f303,plain,
( ~ sQ13_spl
| identity != sk_c9
| inverse(inverse(sk_c8)) != sk_c9 ),
inference(paramodulation,[status(thm)],[f48,f176]) ).
fof(f304,plain,
( ~ sQ13_spl
| sk_c8 != sk_c9
| inverse(identity) != sk_c9 ),
inference(paramodulation,[status(thm)],[f47,f176]) ).
fof(f306,definition,
( sQ32_spl
<=> inverse(inverse(sk_c8)) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f309,definition,
( sQ33_spl
<=> identity = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f311,plain,
( sQ33_spl
| identity != sk_c9 ),
inference(component_clause,[status(thm)],[f309]) ).
fof(f312,plain,
( ~ sQ13_spl
| ~ sQ33_spl
| ~ sQ32_spl ),
inference(split_clause,[status(thm)],[f303,f306,f309,f175]) ).
fof(f313,definition,
( sQ34_spl
<=> sk_c8 = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f315,plain,
( sQ34_spl
| sk_c8 != sk_c9 ),
inference(component_clause,[status(thm)],[f313]) ).
fof(f316,plain,
( ~ sQ13_spl
| ~ sQ34_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f304,f298,f313,f175]) ).
fof(f317,plain,
( sQ26_spl
| ~ sQ1_spl
| sk_c9 != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f98,f258]) ).
fof(f325,plain,
( sQ21_spl
| ~ sQ4_spl
| multiply(sk_c5,sk_c8) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f110,f227]) ).
fof(f327,plain,
( sQ27_spl
| ~ sQ8_spl
| sk_c9 != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f126,f263]) ).
fof(f344,plain,
( sQ21_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sk_c9 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f106,f325]) ).
fof(f356,plain,
( ~ sQ9_spl
| sk_c8 = multiply(inverse(sk_c1),sk_c9) ),
inference(paramodulation,[status(thm)],[f136,f274]) ).
fof(f359,plain,
( ~ sQ3_spl
| sk_c8 = multiply(inverse(sk_c5),sk_c9) ),
inference(paramodulation,[status(thm)],[f106,f274]) ).
fof(f360,plain,
( ~ sQ2_spl
| sk_c8 = multiply(inverse(sk_c4),sk_c9) ),
inference(paramodulation,[status(thm)],[f102,f274]) ).
fof(f365,plain,
( ~ sQ5_spl
| sk_c7 = multiply(inverse(sk_c6),sk_c8) ),
inference(paramodulation,[status(thm)],[f114,f274]) ).
fof(f369,plain,
( ~ sQ11_spl
| sk_c9 = multiply(inverse(sk_c2),sk_c3) ),
inference(paramodulation,[status(thm)],[f156,f274]) ).
fof(f371,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| sk_c8 = multiply(sk_c9,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f126,f356]) ).
fof(f372,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f371,f223]) ).
fof(f373,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| sQ20_spl ),
inference(contradiction_clause,[status(thm)],[f372]) ).
fof(f374,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c8 = multiply(sk_c8,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f110,f359]) ).
fof(f375,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sk_c8 = identity ),
inference(forward_demodulation,[status(thm)],[f270,f374]) ).
fof(f376,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f375,f275]) ).
fof(f377,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f376]) ).
fof(f378,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sk_c8 = multiply(sk_c9,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f98,f360]) ).
fof(f379,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sk_c7 = multiply(sk_c7,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f118,f365]) ).
fof(f380,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| sk_c9 = multiply(sk_c9,sk_c3) ),
inference(forward_demodulation,[status(thm)],[f166,f369]) ).
fof(f392,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sk_c8 = multiply(inverse(sk_c7),sk_c7) ),
inference(paramodulation,[status(thm)],[f379,f274]) ).
fof(f395,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sk_c8 = identity ),
inference(forward_demodulation,[status(thm)],[f48,f392]) ).
fof(f400,plain,
( sQ31_spl
| ~ sQ5_spl
| ~ sQ6_spl
| inverse(sk_c8) != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f395,f300]) ).
fof(f401,plain,
( sQ33_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c8 != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f395,f311]) ).
fof(f403,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ6_spl
| multiply(inverse(X0),X0) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f395,f48]) ).
fof(f404,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c8,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f395,f47]) ).
fof(f408,plain,
( sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sk_c9 != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f380,f147]) ).
fof(f411,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c8,sk_c5) = sk_c8 ),
inference(paramodulation,[status(thm)],[f110,f403]) ).
fof(f417,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c5 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f404,f411]) ).
fof(f420,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| multiply(sk_c5,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f417,f404]) ).
fof(f424,plain,
( sQ0_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| inverse(sk_c9) != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f417,f96]) ).
fof(f432,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| inverse(sk_c5) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f417,f110]) ).
fof(f434,plain,
( sQ34_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c5 != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f417,f315]) ).
fof(f454,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c5 = multiply(sk_c8,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f417,f374]) ).
fof(f455,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c5 = multiply(sk_c5,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f417,f454]) ).
fof(f456,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c5 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f420,f455]) ).
fof(f457,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sQ34_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f456,f434]) ).
fof(f458,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sQ34_spl ),
inference(contradiction_clause,[status(thm)],[f457]) ).
fof(f459,plain,
( sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ34_spl ),
inference(split_clause,[status(thm)],[f408,f313,f165,f155,f145]) ).
fof(f460,plain,
( sQ33_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ34_spl ),
inference(split_clause,[status(thm)],[f401,f313,f117,f113,f309]) ).
fof(f461,plain,
( sQ21_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ34_spl ),
inference(split_clause,[status(thm)],[f344,f313,f105,f109,f225]) ).
fof(f462,plain,
( sQ26_spl
| ~ sQ1_spl
| ~ sQ34_spl ),
inference(split_clause,[status(thm)],[f317,f313,f97,f256]) ).
fof(f464,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sk_c9 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f380,f146]) ).
fof(f470,plain,
( sQ27_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f464,f327]) ).
fof(f471,plain,
( sQ27_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f470]) ).
fof(f472,plain,
( sQ27_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f471]) ).
fof(f477,plain,
( sQ34_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f464,f315]) ).
fof(f478,plain,
( sQ34_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f477]) ).
fof(f479,plain,
( sQ34_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f478]) ).
fof(f484,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| inverse(sk_c8) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f464,f95]) ).
fof(f495,plain,
( sQ31_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| inverse(identity) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f464,f300]) ).
fof(f500,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| multiply(sk_c1,sk_c8) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f464,f136]) ).
fof(f510,plain,
( sQ23_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| multiply(sk_c1,sk_c8) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f464,f243]) ).
fof(f511,plain,
( sQ23_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ9_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f500,f510]) ).
fof(f512,plain,
( sQ23_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f511]) ).
fof(f513,plain,
( sQ23_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f512]) ).
fof(f520,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sk_c8 = multiply(sk_c8,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f464,f371]) ).
fof(f521,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sk_c8 = multiply(sk_c8,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f464,f520]) ).
fof(f534,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| multiply(sk_c8,sk_c8) = identity ),
inference(forward_demodulation,[status(thm)],[f464,f270]) ).
fof(f537,plain,
( sQ31_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ8_spl
| inverse(sk_c8) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f538,f495]) ).
fof(f538,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ9_spl
| ~ sQ8_spl
| sk_c8 = identity ),
inference(forward_demodulation,[status(thm)],[f521,f534]) ).
fof(f539,plain,
( sQ31_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ8_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f484,f537]) ).
fof(f540,plain,
( sQ31_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f539]) ).
fof(f541,plain,
( sQ31_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f540]) ).
fof(f542,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f378,f221,f97,f101]) ).
fof(f558,plain,
( sQ0_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| inverse(sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f456,f424]) ).
fof(f559,plain,
( sQ0_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f432,f558]) ).
fof(f560,plain,
( sQ0_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f559]) ).
fof(f561,plain,
( sQ0_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f560]) ).
fof(f571,plain,
( sQ29_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| inverse(sk_c5) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f417,f292]) ).
fof(f572,plain,
( sQ29_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c5 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f432,f571]) ).
fof(f573,plain,
( sQ29_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f456,f572]) ).
fof(f574,plain,
( sQ29_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f573]) ).
fof(f575,plain,
( sQ29_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f574]) ).
fof(f667,plain,
( sQ31_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f400,f290,f117,f113,f298]) ).
fof(f668,plain,
$false,
inference(sat_refutation,[status(thm)],[f100,f104,f108,f112,f116,f120,f128,f129,f130,f131,f132,f133,f138,f139,f140,f141,f142,f143,f148,f149,f150,f151,f152,f153,f158,f159,f160,f161,f162,f163,f168,f169,f170,f171,f172,f173,f187,f224,f228,f236,f240,f259,f260,f264,f266,f293,f297,f301,f302,f312,f316,f373,f377,f458,f459,f460,f461,f462,f472,f479,f513,f541,f542,f561,f575,f667]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP239-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.02/15.23 % CPULimit : 300
% 0.02/15.23 % WCLimit : 300
% 0.02/15.23 % DateTime : Sun Sep 20 20:07:07 UTC 2026
% 0.02/15.23 % CPUTime :
% 0.02/15.23 % Drodi V4.1.1
% 0.02/15.24 % Refutation found
% 0.02/15.24 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.02/15.24 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.02/15.26 % Elapsed time: 0.031252 seconds
% 0.02/15.26 % CPU time: 0.075304 seconds
% 0.02/15.26 % Total memory used: 27.762 MB
% 0.02/15.26 % Net memory used: 27.688 MB
%------------------------------------------------------------------------------