%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP256-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 12:33:14 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 74
% Syntax : Number of formulae : 318 ( 16 unt; 32 def)
% Number of atoms : 914 ( 378 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 1089 ( 493 ~; 564 |; 0 &)
% ( 32 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 34 ( 32 usr; 33 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 84 ( 84 !; 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_c4,sk_c10) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c3,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,negated_conjecture,
! [X4,X5,X6,X1,X2,X3,X7] :
( inverse(X7) != sk_c9
| multiply(X7,sk_c9) != X3
| multiply(sk_c9,X3) != sk_c8
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c9
| inverse(X1) != sk_c10
| multiply(X1,sk_c10) != sk_c9
| multiply(X6,sk_c9) != sk_c8
| inverse(X6) != sk_c8
| inverse(X5) != sk_c9
| multiply(X5,sk_c9) != sk_c8
| inverse(X4) != sk_c10
| multiply(X4,sk_c10) != sk_c9 ),
file('/export/starexec/sandbox/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,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f51,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f52,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f53,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f54,plain,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f55,plain,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f56,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f57,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f58,plain,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f59,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f60,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f61,plain,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f62,plain,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f63,plain,
( inverse(sk_c6) = sk_c9
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f64,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f65,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f66,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f67,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f68,plain,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f69,plain,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f70,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f71,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f72,plain,
( inverse(sk_c4) = sk_c10
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f73,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f74,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f75,plain,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f76,plain,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f77,plain,
( inverse(sk_c6) = sk_c9
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f80,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f81,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f82,plain,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f83,plain,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f84,plain,
( inverse(sk_c6) = sk_c9
| inverse(sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f87,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c3,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f88,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c3,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f89,plain,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c3,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f90,plain,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c3,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f91,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c3,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f92,plain,
! [X7] :
( inverse(X7) != sk_c9
| ! [X3] :
( multiply(X7,sk_c9) != X3
| multiply(sk_c9,X3) != sk_c8
| ! [X2] :
( inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c9
| ! [X1] :
( inverse(X1) != sk_c10
| multiply(X1,sk_c10) != sk_c9
| ! [X6] :
( multiply(X6,sk_c9) != sk_c8
| inverse(X6) != sk_c8
| ! [X5] :
( inverse(X5) != sk_c9
| multiply(X5,sk_c9) != sk_c8
| ! [X4] :
( inverse(X4) != sk_c10
| multiply(X4,sk_c10) != sk_c9 ) ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f46]) ).
fof(f93,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( inverse(X6) != sk_c9
| multiply(X6,sk_c9) != X5
| multiply(sk_c9,X5) != sk_c8
| inverse(X4) != sk_c8
| multiply(X4,sk_c8) != sk_c9
| inverse(X3) != sk_c10
| multiply(X3,sk_c10) != sk_c9
| multiply(X2,sk_c9) != sk_c8
| inverse(X2) != sk_c8
| inverse(X1) != sk_c9
| multiply(X1,sk_c9) != sk_c8
| inverse(X0) != sk_c10
| multiply(X0,sk_c10) != sk_c9 ),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f94,definition,
( sQ0_spl
<=> multiply(sk_c1,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f95,plain,
( ~ sQ0_spl
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(component_clause,[status(thm)],[f94]) ).
fof(f97,definition,
( sQ1_spl
<=> multiply(sk_c4,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f98,plain,
( ~ sQ1_spl
| multiply(sk_c4,sk_c10) = 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
<=> inverse(sk_c4) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f102,plain,
( ~ sQ2_spl
| inverse(sk_c4) = sk_c10 ),
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_c9,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f114,plain,
( ~ sQ5_spl
| multiply(sk_c9,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
<=> multiply(sk_c6,sk_c9) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f118,plain,
( ~ sQ6_spl
| multiply(sk_c6,sk_c9) = sk_c7 ),
inference(component_clause,[status(thm)],[f117]) ).
fof(f120,plain,
( sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f55,f94,f117]) ).
fof(f121,definition,
( sQ7_spl
<=> inverse(sk_c6) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f122,plain,
( ~ sQ7_spl
| inverse(sk_c6) = sk_c9 ),
inference(component_clause,[status(thm)],[f121]) ).
fof(f124,plain,
( sQ7_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f56,f94,f121]) ).
fof(f125,definition,
( sQ8_spl
<=> inverse(sk_c1) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f126,plain,
( ~ sQ8_spl
| inverse(sk_c1) = sk_c10 ),
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(f134,plain,
( sQ7_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f63,f125,f121]) ).
fof(f135,definition,
( sQ9_spl
<=> multiply(sk_c2,sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f136,plain,
( ~ sQ9_spl
| multiply(sk_c2,sk_c9) = sk_c8 ),
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(f144,plain,
( sQ7_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f70,f135,f121]) ).
fof(f145,definition,
( sQ10_spl
<=> inverse(sk_c2) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f146,plain,
( ~ sQ10_spl
| inverse(sk_c2) = sk_c9 ),
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(f154,plain,
( sQ7_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f77,f145,f121]) ).
fof(f155,definition,
( sQ11_spl
<=> inverse(sk_c3) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f156,plain,
( ~ sQ11_spl
| inverse(sk_c3) = sk_c8 ),
inference(component_clause,[status(thm)],[f155]) ).
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(f164,plain,
( sQ7_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f84,f155,f121]) ).
fof(f165,definition,
( sQ12_spl
<=> multiply(sk_c3,sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f166,plain,
( ~ sQ12_spl
| multiply(sk_c3,sk_c9) = sk_c8 ),
inference(component_clause,[status(thm)],[f165]) ).
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(f174,plain,
( sQ7_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f91,f165,f121]) ).
fof(f175,definition,
! [X0] :
( sQ13_spl
<=> ( inverse(X0) != sk_c10
| multiply(X0,sk_c10) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f176,plain,
! [X0] :
( ~ sQ13_spl
| inverse(X0) != sk_c10
| multiply(X0,sk_c10) != sk_c9 ),
inference(component_clause,[status(thm)],[f175]) ).
fof(f178,definition,
! [X1] :
( sQ14_spl
<=> ( inverse(X1) != sk_c9
| multiply(X1,sk_c9) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f179,plain,
! [X0] :
( ~ sQ14_spl
| inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c8 ),
inference(component_clause,[status(thm)],[f178]) ).
fof(f181,definition,
! [X2] :
( sQ15_spl
<=> ( multiply(X2,sk_c9) != sk_c8
| inverse(X2) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f182,plain,
! [X0] :
( ~ sQ15_spl
| multiply(X0,sk_c9) != sk_c8
| inverse(X0) != sk_c8 ),
inference(component_clause,[status(thm)],[f181]) ).
fof(f184,definition,
! [X4] :
( sQ16_spl
<=> ( inverse(X4) != sk_c8
| multiply(X4,sk_c8) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f185,plain,
! [X0] :
( ~ sQ16_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c9 ),
inference(component_clause,[status(thm)],[f184]) ).
fof(f187,definition,
! [X5,X6] :
( sQ17_spl
<=> ( inverse(X6) != sk_c9
| multiply(X6,sk_c9) != X5
| multiply(sk_c9,X5) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f188,plain,
! [X0,X1] :
( ~ sQ17_spl
| inverse(X1) != sk_c9
| multiply(X1,sk_c9) != X0
| multiply(sk_c9,X0) != sk_c8 ),
inference(component_clause,[status(thm)],[f187]) ).
fof(f190,plain,
( sQ17_spl
| sQ16_spl
| sQ15_spl
| sQ14_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f93,f175,f178,f181,f184,f187]) ).
fof(f191,plain,
! [X0] :
( ~ sQ17_spl
| inverse(X0) != sk_c9
| multiply(sk_c9,multiply(X0,sk_c9)) != sk_c8 ),
inference(destructive_equality_resolution,[status(thm)],[f188]) ).
fof(f196,plain,
! [X0] :
( ~ sQ9_spl
| multiply(sk_c8,X0) = multiply(sk_c2,multiply(sk_c9,X0)) ),
inference(paramodulation,[status(thm)],[f136,f49]) ).
fof(f198,plain,
( ~ sQ4_spl
| multiply(sk_c8,sk_c5) = identity ),
inference(paramodulation,[status(thm)],[f110,f48]) ).
fof(f199,plain,
( ~ sQ7_spl
| multiply(sk_c9,sk_c6) = identity ),
inference(paramodulation,[status(thm)],[f122,f48]) ).
fof(f200,plain,
( ~ sQ8_spl
| multiply(sk_c10,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f126,f48]) ).
fof(f201,plain,
( ~ sQ10_spl
| multiply(sk_c9,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f146,f48]) ).
fof(f203,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f48,f49]) ).
fof(f204,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f47,f203]) ).
fof(f205,plain,
! [X0] :
( ~ sQ0_spl
| multiply(sk_c9,X0) = multiply(sk_c1,multiply(sk_c10,X0)) ),
inference(paramodulation,[status(thm)],[f95,f49]) ).
fof(f206,plain,
! [X0] :
( ~ sQ6_spl
| multiply(sk_c7,X0) = multiply(sk_c6,multiply(sk_c9,X0)) ),
inference(paramodulation,[status(thm)],[f118,f49]) ).
fof(f208,plain,
! [X0] :
( ~ sQ5_spl
| multiply(sk_c8,X0) = multiply(sk_c9,multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f114,f49]) ).
fof(f209,plain,
! [X0] :
( ~ sQ3_spl
| multiply(sk_c9,X0) = multiply(sk_c5,multiply(sk_c8,X0)) ),
inference(paramodulation,[status(thm)],[f106,f49]) ).
fof(f211,plain,
( ~ sQ6_spl
| ~ sQ17_spl
| inverse(sk_c6) != sk_c9
| multiply(sk_c9,sk_c7) != sk_c8 ),
inference(paramodulation,[status(thm)],[f118,f191]) ).
fof(f212,plain,
( ~ sQ17_spl
| inverse(inverse(sk_c9)) != sk_c9
| multiply(sk_c9,identity) != sk_c8 ),
inference(paramodulation,[status(thm)],[f48,f191]) ).
fof(f217,plain,
( ~ sQ6_spl
| ~ sQ17_spl
| ~ sQ7_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f211,f113,f121,f187,f117]) ).
fof(f218,definition,
( sQ18_spl
<=> multiply(sk_c9,identity) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f221,definition,
( sQ19_spl
<=> inverse(inverse(sk_c9)) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f224,plain,
( ~ sQ17_spl
| ~ sQ19_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f212,f218,f221,f187]) ).
fof(f228,definition,
( sQ21_spl
<=> inverse(identity) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f236,definition,
( sQ23_spl
<=> inverse(sk_c3) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f241,plain,
( ~ sQ3_spl
| ~ sQ16_spl
| inverse(sk_c5) != sk_c8 ),
inference(resolution,[status(thm)],[f185,f106]) ).
fof(f244,plain,
( ~ sQ16_spl
| inverse(identity) != sk_c8
| sk_c8 != sk_c9 ),
inference(paramodulation,[status(thm)],[f47,f185]) ).
fof(f246,plain,
( ~ sQ3_spl
| ~ sQ16_spl
| ~ sQ4_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f110,f241]) ).
fof(f247,plain,
( ~ sQ3_spl
| ~ sQ16_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f246]) ).
fof(f248,plain,
( ~ sQ3_spl
| ~ sQ16_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f247]) ).
fof(f250,plain,
( ~ sQ12_spl
| ~ sQ15_spl
| inverse(sk_c3) != sk_c8 ),
inference(resolution,[status(thm)],[f182,f166]) ).
fof(f257,plain,
( ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ11_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f156,f250]) ).
fof(f258,plain,
( ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f257]) ).
fof(f259,plain,
( ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f258]) ).
fof(f261,plain,
( ~ sQ14_spl
| inverse(inverse(sk_c9)) != sk_c9
| identity != sk_c8 ),
inference(paramodulation,[status(thm)],[f48,f179]) ).
fof(f262,plain,
( ~ sQ14_spl
| inverse(identity) != sk_c9
| sk_c9 != sk_c8 ),
inference(paramodulation,[status(thm)],[f47,f179]) ).
fof(f263,plain,
! [X0,X1] :
( ~ sQ14_spl
| inverse(multiply(X0,X1)) != sk_c9
| multiply(X0,multiply(X1,sk_c9)) != sk_c8 ),
inference(paramodulation,[status(thm)],[f49,f179]) ).
fof(f264,plain,
( ~ sQ12_spl
| ~ sQ14_spl
| inverse(sk_c3) != sk_c9
| sk_c8 != sk_c8 ),
inference(paramodulation,[status(thm)],[f166,f179]) ).
fof(f265,definition,
( sQ24_spl
<=> identity = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f267,plain,
( sQ24_spl
| identity != sk_c8 ),
inference(component_clause,[status(thm)],[f265]) ).
fof(f268,plain,
( ~ sQ14_spl
| ~ sQ19_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f261,f265,f221,f178]) ).
fof(f269,definition,
( sQ25_spl
<=> sk_c9 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f271,plain,
( sQ25_spl
| sk_c9 != sk_c8 ),
inference(component_clause,[status(thm)],[f269]) ).
fof(f272,plain,
( ~ sQ14_spl
| ~ sQ21_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f262,f269,f228,f178]) ).
fof(f273,definition,
( sQ26_spl
<=> sk_c8 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f275,plain,
( sQ26_spl
| sk_c8 != sk_c8 ),
inference(component_clause,[status(thm)],[f273]) ).
fof(f276,plain,
( ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ23_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f264,f273,f236,f178,f165]) ).
fof(f277,plain,
( sQ26_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f275]) ).
fof(f278,plain,
sQ26_spl,
inference(contradiction_clause,[status(thm)],[f277]) ).
fof(f288,plain,
( ~ sQ1_spl
| ~ sQ13_spl
| inverse(sk_c4) != sk_c10 ),
inference(resolution,[status(thm)],[f176,f98]) ).
fof(f289,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| inverse(sk_c1) != sk_c10 ),
inference(resolution,[status(thm)],[f176,f95]) ).
fof(f295,plain,
( ~ sQ1_spl
| ~ sQ13_spl
| ~ sQ2_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f102,f288]) ).
fof(f296,plain,
( ~ sQ1_spl
| ~ sQ13_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f295]) ).
fof(f297,plain,
( ~ sQ1_spl
| ~ sQ13_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f296]) ).
fof(f299,plain,
( ~ sQ9_spl
| ~ sQ14_spl
| inverse(sk_c2) != sk_c9 ),
inference(resolution,[status(thm)],[f179,f136]) ).
fof(f301,plain,
( ~ sQ6_spl
| ~ sQ14_spl
| inverse(sk_c6) != sk_c9
| sk_c7 != sk_c8 ),
inference(paramodulation,[status(thm)],[f118,f179]) ).
fof(f305,plain,
( ~ sQ9_spl
| ~ sQ14_spl
| ~ sQ10_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f146,f299]) ).
fof(f306,plain,
( ~ sQ9_spl
| ~ sQ14_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f305]) ).
fof(f307,plain,
( ~ sQ9_spl
| ~ sQ14_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f306]) ).
fof(f309,definition,
( sQ27_spl
<=> sk_c7 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f311,plain,
( sQ27_spl
| sk_c7 != sk_c8 ),
inference(component_clause,[status(thm)],[f309]) ).
fof(f312,plain,
( ~ sQ6_spl
| ~ sQ14_spl
| ~ sQ7_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f301,f309,f121,f178,f117]) ).
fof(f316,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ8_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f126,f289]) ).
fof(f317,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f316]) ).
fof(f318,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f317]) ).
fof(f324,plain,
! [X0] :
( ~ sQ4_spl
| multiply(identity,X0) = multiply(sk_c8,multiply(sk_c5,X0)) ),
inference(paramodulation,[status(thm)],[f198,f49]) ).
fof(f325,plain,
! [X0] :
( ~ sQ4_spl
| X0 = multiply(sk_c8,multiply(sk_c5,X0)) ),
inference(forward_demodulation,[status(thm)],[f47,f324]) ).
fof(f328,plain,
! [X0] :
( ~ sQ7_spl
| multiply(identity,X0) = multiply(sk_c9,multiply(sk_c6,X0)) ),
inference(paramodulation,[status(thm)],[f199,f49]) ).
fof(f329,plain,
! [X0] :
( ~ sQ7_spl
| X0 = multiply(sk_c9,multiply(sk_c6,X0)) ),
inference(forward_demodulation,[status(thm)],[f47,f328]) ).
fof(f365,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| inverse(multiply(sk_c9,sk_c7)) != sk_c9
| multiply(sk_c8,sk_c9) != sk_c8 ),
inference(paramodulation,[status(thm)],[f208,f263]) ).
fof(f375,definition,
( sQ28_spl
<=> multiply(sk_c8,sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f377,plain,
( sQ28_spl
| multiply(sk_c8,sk_c9) != sk_c8 ),
inference(component_clause,[status(thm)],[f375]) ).
fof(f378,definition,
( sQ29_spl
<=> inverse(multiply(sk_c9,sk_c7)) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f381,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| ~ sQ29_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f365,f375,f378,f178,f113]) ).
fof(f411,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c8 = multiply(sk_c8,sk_c9) ),
inference(paramodulation,[status(thm)],[f106,f325]) ).
fof(f412,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ3_spl
| multiply(sk_c9,multiply(sk_c5,X0)) = multiply(sk_c5,X0) ),
inference(paramodulation,[status(thm)],[f325,f209]) ).
fof(f413,plain,
( ~ sQ4_spl
| ~ sQ14_spl
| inverse(multiply(sk_c8,sk_c5)) != sk_c9
| sk_c9 != sk_c8 ),
inference(paramodulation,[status(thm)],[f325,f263]) ).
fof(f415,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sQ28_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f411,f377]) ).
fof(f416,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sQ28_spl ),
inference(contradiction_clause,[status(thm)],[f415]) ).
fof(f417,definition,
( sQ35_spl
<=> inverse(multiply(sk_c8,sk_c5)) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f420,plain,
( ~ sQ4_spl
| ~ sQ14_spl
| ~ sQ35_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f413,f269,f417,f178,f109]) ).
fof(f423,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ7_spl
| multiply(sk_c9,X0) = multiply(sk_c9,multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f206,f329]) ).
fof(f424,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| sk_c9 = multiply(sk_c9,sk_c7) ),
inference(paramodulation,[status(thm)],[f118,f329]) ).
fof(f428,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| X0 = multiply(sk_c9,multiply(sk_c5,X0)) ),
inference(backward_demodulation,[status(thm)],[f435,f325]) ).
fof(f429,plain,
( ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| multiply(sk_c9,sk_c5) = identity ),
inference(backward_demodulation,[status(thm)],[f435,f198]) ).
fof(f430,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(sk_c9,X0) = multiply(sk_c9,multiply(sk_c7,X0)) ),
inference(backward_demodulation,[status(thm)],[f435,f208]) ).
fof(f435,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| multiply(sk_c9,X0) = multiply(sk_c8,X0) ),
inference(forward_demodulation,[status(thm)],[f208,f423]) ).
fof(f436,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| sk_c9 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f114,f424]) ).
fof(f437,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f436,f271]) ).
fof(f438,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| sQ25_spl ),
inference(contradiction_clause,[status(thm)],[f437]) ).
fof(f443,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ3_spl
| X0 = multiply(sk_c5,X0) ),
inference(forward_demodulation,[status(thm)],[f412,f428]) ).
fof(f452,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| multiply(X0,sk_c9) != sk_c8
| inverse(X0) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f436,f182]) ).
fof(f453,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| multiply(X0,sk_c9) != sk_c9
| inverse(X0) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f436,f452]) ).
fof(f458,definition,
( sQ37_spl
<=> inverse(identity) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f460,plain,
( sQ37_spl
| inverse(identity) != sk_c8 ),
inference(component_clause,[status(thm)],[f458]) ).
fof(f469,plain,
( sQ24_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| identity != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f436,f267]) ).
fof(f484,definition,
( sQ40_spl
<=> sk_c9 = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f486,plain,
( sQ40_spl
| sk_c9 != sk_c9 ),
inference(component_clause,[status(thm)],[f484]) ).
fof(f490,plain,
! [X0] :
( ~ sQ6_spl
| multiply(sk_c9,X0) = multiply(inverse(sk_c6),multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f206,f204]) ).
fof(f491,plain,
( ~ sQ6_spl
| sk_c9 = multiply(inverse(sk_c6),sk_c7) ),
inference(paramodulation,[status(thm)],[f118,f204]) ).
fof(f497,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f204,f204]) ).
fof(f498,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f48,f204]) ).
fof(f510,plain,
! [X0] : X0 = multiply(X0,identity),
inference(forward_demodulation,[status(thm)],[f497,f498]) ).
fof(f513,plain,
( ~ sQ15_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| inverse(sk_c5) != sk_c9 ),
inference(resolution,[status(thm)],[f443,f453]) ).
fof(f521,plain,
( sQ40_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f486]) ).
fof(f522,plain,
sQ40_spl,
inference(contradiction_clause,[status(thm)],[f521]) ).
fof(f523,plain,
( ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c5 = identity ),
inference(paramodulation,[status(thm)],[f443,f510]) ).
fof(f524,plain,
inverse(identity) = identity,
inference(paramodulation,[status(thm)],[f48,f510]) ).
fof(f531,plain,
inverse(identity) = identity,
inference(paramodulation,[status(thm)],[f510,f48]) ).
fof(f536,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ3_spl
| X0 = multiply(X0,sk_c5) ),
inference(backward_demodulation,[status(thm)],[f523,f510]) ).
fof(f538,plain,
( sQ24_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sk_c5 != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f523,f469]) ).
fof(f545,plain,
( ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ3_spl
| inverse(sk_c5) = identity ),
inference(forward_demodulation,[status(thm)],[f523,f524]) ).
fof(f547,plain,
( ~ sQ15_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sk_c5 != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f548,f513]) ).
fof(f548,plain,
( ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ3_spl
| inverse(sk_c5) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f523,f545]) ).
fof(f563,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(sk_c7,X0) = multiply(inverse(sk_c9),multiply(sk_c9,X0)) ),
inference(paramodulation,[status(thm)],[f430,f204]) ).
fof(f572,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(sk_c7,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f204,f563]) ).
fof(f591,definition,
( sQ43_spl
<=> multiply(sk_c9,sk_c9) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f593,plain,
( sQ43_spl
| multiply(sk_c9,sk_c9) != sk_c9 ),
inference(component_clause,[status(thm)],[f591]) ).
fof(f610,plain,
( sQ37_spl
| identity != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f531,f460]) ).
fof(f619,plain,
! [X0] :
( ~ sQ10_spl
| X0 = multiply(sk_c9,multiply(sk_c2,X0)) ),
inference(paramodulation,[status(thm)],[f146,f204]) ).
fof(f620,plain,
( ~ sQ9_spl
| sk_c9 = multiply(inverse(sk_c2),sk_c8) ),
inference(paramodulation,[status(thm)],[f136,f204]) ).
fof(f623,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| sk_c9 = multiply(sk_c9,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f146,f620]) ).
fof(f624,plain,
( ~ sQ12_spl
| sk_c9 = multiply(inverse(sk_c3),sk_c8) ),
inference(paramodulation,[status(thm)],[f166,f204]) ).
fof(f626,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| sk_c9 = multiply(sk_c8,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f156,f624]) ).
fof(f633,plain,
( ~ sQ8_spl
| sk_c1 = multiply(inverse(sk_c10),identity) ),
inference(paramodulation,[status(thm)],[f200,f204]) ).
fof(f636,plain,
( ~ sQ8_spl
| sk_c1 = inverse(sk_c10) ),
inference(forward_demodulation,[status(thm)],[f510,f633]) ).
fof(f642,plain,
! [X0] :
( ~ sQ8_spl
| X0 = multiply(sk_c1,multiply(sk_c10,X0)) ),
inference(paramodulation,[status(thm)],[f636,f204]) ).
fof(f644,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ8_spl
| ~ sQ0_spl
| inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f660,f191]) ).
fof(f648,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c9 = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f660,f623]) ).
fof(f650,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| X0 = multiply(sk_c2,X0) ),
inference(backward_demodulation,[status(thm)],[f660,f619]) ).
fof(f652,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c2 = identity ),
inference(backward_demodulation,[status(thm)],[f660,f201]) ).
fof(f654,plain,
( sQ43_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c9 != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f660,f593]) ).
fof(f657,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| multiply(sk_c8,X0) = multiply(sk_c2,X0) ),
inference(backward_demodulation,[status(thm)],[f660,f196]) ).
fof(f660,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ0_spl
| X0 = multiply(sk_c9,X0) ),
inference(forward_demodulation,[status(thm)],[f205,f642]) ).
fof(f661,plain,
( ~ sQ17_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f644,f178,f94,f125,f187]) ).
fof(f668,plain,
( sQ37_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c2 != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f652,f610]) ).
fof(f670,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| inverse(identity) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f652,f531]) ).
fof(f674,plain,
( sQ43_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ40_spl ),
inference(split_clause,[status(thm)],[f654,f484,f94,f125,f591]) ).
fof(f677,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| sk_c9 = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f680,f626]) ).
fof(f680,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| multiply(sk_c8,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f650,f657]) ).
fof(f704,plain,
( ~ sQ16_spl
| ~ sQ37_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f244,f269,f458,f184]) ).
fof(f710,plain,
( sQ37_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ9_spl
| sk_c2 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f648,f668]) ).
fof(f711,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| inverse(sk_c2) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f652,f670]) ).
fof(f712,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c9 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f146,f711]) ).
fof(f713,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sQ37_spl
| ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f712,f710]) ).
fof(f714,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sQ37_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f713]) ).
fof(f720,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| sQ25_spl ),
inference(split_clause,[status(thm)],[f677,f269,f145,f94,f125,f135,f155,f165]) ).
fof(f757,plain,
( ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c9 = identity ),
inference(forward_demodulation,[status(thm)],[f536,f429]) ).
fof(f758,plain,
( ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c9 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f523,f757]) ).
fof(f759,plain,
( ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f758,f547]) ).
fof(f760,plain,
( ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ15_spl ),
inference(contradiction_clause,[status(thm)],[f759]) ).
fof(f761,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ7_spl
| sk_c9 = multiply(sk_c9,sk_c7) ),
inference(backward_demodulation,[status(thm)],[f762,f491]) ).
fof(f762,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ7_spl
| multiply(sk_c9,X0) = multiply(inverse(sk_c6),X0) ),
inference(forward_demodulation,[status(thm)],[f572,f490]) ).
fof(f772,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ3_spl
| X0 = multiply(sk_c9,X0) ),
inference(forward_demodulation,[status(thm)],[f443,f428]) ).
fof(f817,plain,
( ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c5 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f548,f110]) ).
fof(f818,plain,
( ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c5 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f436,f817]) ).
fof(f819,plain,
( ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f818,f538]) ).
fof(f820,plain,
( ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sQ24_spl ),
inference(contradiction_clause,[status(thm)],[f819]) ).
fof(f835,plain,
( sQ27_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| sk_c7 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f436,f311]) ).
fof(f856,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sk_c9 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f772,f761]) ).
fof(f857,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sQ27_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f856,f835]) ).
fof(f858,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sQ27_spl ),
inference(contradiction_clause,[status(thm)],[f857]) ).
fof(f859,plain,
$false,
inference(sat_refutation,[status(thm)],[f100,f104,f108,f112,f116,f120,f124,f128,f129,f130,f131,f132,f133,f134,f138,f139,f140,f141,f142,f143,f144,f148,f149,f150,f151,f152,f153,f154,f160,f161,f162,f163,f164,f170,f171,f172,f173,f174,f190,f217,f224,f248,f259,f268,f272,f276,f278,f297,f307,f312,f318,f381,f416,f420,f438,f522,f661,f674,f704,f714,f720,f760,f820,f858]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP256-1 : 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 : n002.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
% 0.09/0.35 % DateTime : Sun Sep 20 20:10:48 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 0.13/0.40 % Refutation found
% 0.13/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.43 % Elapsed time: 0.059510 seconds
% 0.13/0.43 % CPU time: 0.221206 seconds
% 0.13/0.43 % Total memory used: 99.182 MB
% 0.13/0.43 % Net memory used: 99.058 MB
%------------------------------------------------------------------------------