%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP251-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:33:13 PM UTC 2026
% Result : Unsatisfiable 0.08s 0.38s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 70
% Syntax : Number of formulae : 281 ( 11 unt; 32 def)
% Number of atoms : 823 ( 338 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 996 ( 454 ~; 510 |; 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 : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 56 ( 56 !; 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,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c3,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c3,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c3,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c3,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/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_c8) != sk_c9
| inverse(X6) != sk_c9
| inverse(X5) != sk_c9
| multiply(X5,sk_c9) != sk_c8
| inverse(X4) != sk_c10
| multiply(X4,sk_c10) != sk_c9 ),
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,
( 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(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(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(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(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(f78,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c3) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f79,plain,
( inverse(sk_c4) = sk_c10
| inverse(sk_c3) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f80,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c3) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f81,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c3) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f82,plain,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c3) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f83,plain,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c3) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f84,plain,
( inverse(sk_c6) = sk_c9
| inverse(sk_c3) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f85,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c3,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f86,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c3,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f87,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c3,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f88,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f89,plain,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f90,plain,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f91,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c3,sk_c8) = sk_c9 ),
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_c8) != sk_c9
| inverse(X6) != sk_c9
| ! [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_c8) != sk_c9
| inverse(X2) != sk_c9
| 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(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(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(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(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(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_c9 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f156,plain,
( ~ sQ11_spl
| inverse(sk_c3) = sk_c9 ),
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(f164,plain,
( sQ7_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f84,f155,f121]) ).
fof(f165,definition,
( sQ12_spl
<=> multiply(sk_c3,sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f166,plain,
( ~ sQ12_spl
| multiply(sk_c3,sk_c8) = 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(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_c8) != sk_c9
| inverse(X2) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f182,plain,
! [X0] :
( ~ sQ15_spl
| multiply(X0,sk_c8) != sk_c9
| inverse(X0) != sk_c9 ),
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(f197,plain,
! [X0] :
( ~ sQ0_spl
| multiply(sk_c9,X0) = multiply(sk_c1,multiply(sk_c10,X0)) ),
inference(paramodulation,[status(thm)],[f95,f49]) ).
fof(f203,plain,
( ~ sQ6_spl
| ~ sQ17_spl
| inverse(sk_c6) != sk_c9
| multiply(sk_c9,sk_c7) != sk_c8 ),
inference(paramodulation,[status(thm)],[f118,f191]) ).
fof(f204,plain,
( ~ sQ9_spl
| ~ sQ17_spl
| inverse(sk_c2) != sk_c9
| multiply(sk_c9,sk_c8) != sk_c8 ),
inference(paramodulation,[status(thm)],[f136,f191]) ).
fof(f205,plain,
( ~ sQ6_spl
| ~ sQ17_spl
| ~ sQ7_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f203,f113,f121,f187,f117]) ).
fof(f206,definition,
( sQ18_spl
<=> multiply(sk_c9,sk_c8) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f208,plain,
( sQ18_spl
| multiply(sk_c9,sk_c8) != sk_c8 ),
inference(component_clause,[status(thm)],[f206]) ).
fof(f209,plain,
( ~ sQ9_spl
| ~ sQ17_spl
| ~ sQ10_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f204,f206,f145,f187,f135]) ).
fof(f217,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f48,f49]) ).
fof(f218,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f47,f217]) ).
fof(f245,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f47,f218]) ).
fof(f247,plain,
( ~ sQ1_spl
| sk_c10 = multiply(inverse(sk_c4),sk_c9) ),
inference(paramodulation,[status(thm)],[f98,f218]) ).
fof(f249,plain,
( ~ sQ6_spl
| sk_c9 = multiply(inverse(sk_c6),sk_c7) ),
inference(paramodulation,[status(thm)],[f118,f218]) ).
fof(f250,plain,
( ~ sQ0_spl
| sk_c10 = multiply(inverse(sk_c1),sk_c9) ),
inference(paramodulation,[status(thm)],[f95,f218]) ).
fof(f251,plain,
( ~ sQ9_spl
| sk_c9 = multiply(inverse(sk_c2),sk_c8) ),
inference(paramodulation,[status(thm)],[f136,f218]) ).
fof(f252,plain,
( ~ sQ12_spl
| sk_c8 = multiply(inverse(sk_c3),sk_c9) ),
inference(paramodulation,[status(thm)],[f166,f218]) ).
fof(f254,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c10 = multiply(sk_c10,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f102,f247]) ).
fof(f256,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| sk_c9 = multiply(sk_c9,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f122,f249]) ).
fof(f257,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| sk_c10 = multiply(sk_c10,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f126,f250]) ).
fof(f258,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| sk_c9 = multiply(sk_c9,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f146,f251]) ).
fof(f259,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| sk_c8 = multiply(sk_c9,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f156,f252]) ).
fof(f267,plain,
( ~ sQ4_spl
| ~ sQ16_spl
| multiply(sk_c5,sk_c8) != sk_c9 ),
inference(resolution,[status(thm)],[f185,f110]) ).
fof(f273,plain,
( ~ sQ11_spl
| ~ sQ16_spl
| sk_c9 != sk_c8
| multiply(sk_c3,sk_c8) != sk_c9 ),
inference(paramodulation,[status(thm)],[f156,f185]) ).
fof(f274,plain,
( ~ sQ4_spl
| ~ sQ16_spl
| ~ sQ3_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f106,f267]) ).
fof(f275,plain,
( ~ sQ4_spl
| ~ sQ16_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f274]) ).
fof(f276,plain,
( ~ sQ4_spl
| ~ sQ16_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f275]) ).
fof(f277,plain,
( ~ sQ12_spl
| ~ sQ15_spl
| inverse(sk_c3) != sk_c9 ),
inference(resolution,[status(thm)],[f182,f166]) ).
fof(f278,plain,
( ~ sQ15_spl
| sk_c8 != sk_c9
| inverse(inverse(identity)) != sk_c9 ),
inference(paramodulation,[status(thm)],[f245,f182]) ).
fof(f283,plain,
( ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ11_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f156,f277]) ).
fof(f284,plain,
( ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f283]) ).
fof(f285,plain,
( ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f284]) ).
fof(f286,plain,
( ~ sQ14_spl
| inverse(inverse(identity)) != sk_c9
| sk_c9 != sk_c8 ),
inference(paramodulation,[status(thm)],[f245,f179]) ).
fof(f287,plain,
( ~ sQ14_spl
| inverse(inverse(sk_c9)) != sk_c9
| identity != sk_c8 ),
inference(paramodulation,[status(thm)],[f48,f179]) ).
fof(f288,plain,
( ~ sQ14_spl
| inverse(identity) != sk_c9
| sk_c9 != sk_c8 ),
inference(paramodulation,[status(thm)],[f47,f179]) ).
fof(f290,plain,
( ~ sQ6_spl
| ~ sQ14_spl
| inverse(sk_c6) != sk_c9
| sk_c7 != sk_c8 ),
inference(paramodulation,[status(thm)],[f118,f179]) ).
fof(f291,definition,
( sQ19_spl
<=> sk_c9 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f293,plain,
( sQ19_spl
| sk_c9 != sk_c8 ),
inference(component_clause,[status(thm)],[f291]) ).
fof(f294,definition,
( sQ20_spl
<=> inverse(inverse(identity)) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f296,plain,
( sQ20_spl
| inverse(inverse(identity)) != sk_c9 ),
inference(component_clause,[status(thm)],[f294]) ).
fof(f297,plain,
( ~ sQ14_spl
| ~ sQ20_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f286,f291,f294,f178]) ).
fof(f298,definition,
( sQ21_spl
<=> identity = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f301,definition,
( sQ22_spl
<=> inverse(inverse(sk_c9)) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f304,plain,
( ~ sQ14_spl
| ~ sQ22_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f287,f298,f301,f178]) ).
fof(f305,definition,
( sQ23_spl
<=> inverse(identity) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f308,plain,
( ~ sQ14_spl
| ~ sQ23_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f288,f291,f305,f178]) ).
fof(f309,definition,
( sQ24_spl
<=> sk_c7 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f311,plain,
( sQ24_spl
| sk_c7 != sk_c8 ),
inference(component_clause,[status(thm)],[f309]) ).
fof(f312,plain,
( ~ sQ6_spl
| ~ sQ14_spl
| ~ sQ7_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f290,f309,f121,f178,f117]) ).
fof(f313,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c9 = multiply(inverse(sk_c10),sk_c10) ),
inference(paramodulation,[status(thm)],[f254,f218]) ).
fof(f315,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c9 = identity ),
inference(forward_demodulation,[status(thm)],[f48,f313]) ).
fof(f320,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(inverse(X0),X0) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f315,f48]) ).
fof(f321,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c9,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f315,f47]) ).
fof(f329,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(sk_c7,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f337,f321]) ).
fof(f330,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c7 = identity ),
inference(backward_demodulation,[status(thm)],[f337,f315]) ).
fof(f333,plain,
( ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ2_spl
| multiply(sk_c4,sk_c10) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f337,f98]) ).
fof(f336,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c6) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f337,f122]) ).
fof(f337,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c9 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f321,f256]) ).
fof(f348,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c7,sk_c7) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f337,f114]) ).
fof(f351,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c7 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f329,f348]) ).
fof(f353,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(X0) != sk_c10
| multiply(X0,sk_c10) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f337,f176]) ).
fof(f354,plain,
( ~ sQ2_spl
| ~ sQ13_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| multiply(sk_c4,sk_c10) != sk_c7 ),
inference(resolution,[status(thm)],[f353,f102]) ).
fof(f367,definition,
( sQ28_spl
<=> sk_c10 = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f369,plain,
( sQ28_spl
| sk_c10 != sk_c10 ),
inference(component_clause,[status(thm)],[f367]) ).
fof(f372,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(inverse(X0),X0) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f337,f320]) ).
fof(f373,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c7,sk_c6) = sk_c7 ),
inference(paramodulation,[status(thm)],[f336,f372]) ).
fof(f377,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c6 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f329,f373]) ).
fof(f382,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c6 = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f377,f351]) ).
fof(f383,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c6) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f377,f336]) ).
fof(f386,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c6 = identity ),
inference(backward_demodulation,[status(thm)],[f377,f330]) ).
fof(f387,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c9 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f377,f337]) ).
fof(f402,plain,
( ~ sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ2_spl
| multiply(sk_c4,sk_c10) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f377,f333]) ).
fof(f435,plain,
( ~ sQ2_spl
| ~ sQ13_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| sk_c6 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f402,f354]) ).
fof(f436,plain,
( ~ sQ2_spl
| ~ sQ13_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f377,f435]) ).
fof(f437,plain,
( ~ sQ2_spl
| ~ sQ13_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f436]) ).
fof(f438,plain,
( ~ sQ2_spl
| ~ sQ13_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f437]) ).
fof(f439,plain,
( sQ19_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c6 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f387,f293]) ).
fof(f440,plain,
( sQ19_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f382,f439]) ).
fof(f441,plain,
( sQ19_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f440]) ).
fof(f442,plain,
( sQ19_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f441]) ).
fof(f447,plain,
( ~ sQ15_spl
| ~ sQ19_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f278,f294,f291,f181]) ).
fof(f451,definition,
( sQ30_spl
<=> identity = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f452,plain,
( ~ sQ30_spl
| identity = sk_c9 ),
inference(component_clause,[status(thm)],[f451]) ).
fof(f453,plain,
( sQ30_spl
| identity != sk_c9 ),
inference(component_clause,[status(thm)],[f451]) ).
fof(f464,plain,
( sQ20_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| inverse(inverse(sk_c6)) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f386,f296]) ).
fof(f465,plain,
( sQ20_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| inverse(sk_c6) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f383,f464]) ).
fof(f466,plain,
( sQ20_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c6 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f383,f465]) ).
fof(f467,plain,
( sQ20_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f387,f466]) ).
fof(f468,plain,
( sQ20_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f467]) ).
fof(f469,plain,
( sQ20_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f468]) ).
fof(f470,plain,
( sQ28_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f369]) ).
fof(f471,plain,
sQ28_spl,
inference(contradiction_clause,[status(thm)],[f470]) ).
fof(f488,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ17_spl
| inverse(sk_c10) != sk_c9
| multiply(sk_c9,sk_c10) != sk_c8 ),
inference(paramodulation,[status(thm)],[f257,f191]) ).
fof(f489,plain,
( ~ sQ17_spl
| inverse(identity) != sk_c9
| multiply(sk_c9,sk_c9) != sk_c8 ),
inference(paramodulation,[status(thm)],[f47,f191]) ).
fof(f492,definition,
( sQ32_spl
<=> multiply(sk_c9,sk_c10) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f495,definition,
( sQ33_spl
<=> inverse(sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f498,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ17_spl
| ~ sQ33_spl
| ~ sQ32_spl ),
inference(split_clause,[status(thm)],[f488,f492,f495,f187,f125,f94]) ).
fof(f499,definition,
( sQ34_spl
<=> multiply(sk_c9,sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f501,plain,
( sQ34_spl
| multiply(sk_c9,sk_c9) != sk_c8 ),
inference(component_clause,[status(thm)],[f499]) ).
fof(f502,plain,
( ~ sQ17_spl
| ~ sQ23_spl
| ~ sQ34_spl ),
inference(split_clause,[status(thm)],[f489,f499,f305,f187]) ).
fof(f503,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f315,f453]) ).
fof(f504,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sQ30_spl ),
inference(contradiction_clause,[status(thm)],[f503]) ).
fof(f508,plain,
! [X0] :
( ~ sQ30_spl
| multiply(sk_c9,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f452,f47]) ).
fof(f511,plain,
( ~ sQ5_spl
| ~ sQ30_spl
| sk_c7 = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f508,f114]) ).
fof(f515,plain,
( ~ sQ5_spl
| ~ sQ30_spl
| sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f511,f311]) ).
fof(f516,plain,
( ~ sQ5_spl
| ~ sQ30_spl
| sQ24_spl ),
inference(contradiction_clause,[status(thm)],[f515]) ).
fof(f530,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| inverse(sk_c1) != sk_c10 ),
inference(resolution,[status(thm)],[f176,f95]) ).
fof(f533,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ8_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f126,f530]) ).
fof(f534,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f533]) ).
fof(f535,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f534]) ).
fof(f550,plain,
( sQ34_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f259,f501]) ).
fof(f551,plain,
( sQ34_spl
| ~ sQ12_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f550]) ).
fof(f552,plain,
( sQ34_spl
| ~ sQ12_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f551]) ).
fof(f555,plain,
( sQ18_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c9 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f258,f208]) ).
fof(f559,plain,
( ~ sQ9_spl
| ~ sQ14_spl
| inverse(sk_c2) != sk_c9 ),
inference(resolution,[status(thm)],[f179,f136]) ).
fof(f568,plain,
( ~ sQ9_spl
| ~ sQ14_spl
| ~ sQ10_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f146,f559]) ).
fof(f569,plain,
( ~ sQ9_spl
| ~ sQ14_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f568]) ).
fof(f570,plain,
( ~ sQ9_spl
| ~ sQ14_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f569]) ).
fof(f572,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ17_spl
| inverse(sk_c9) != sk_c9
| multiply(sk_c9,sk_c8) != sk_c8 ),
inference(paramodulation,[status(thm)],[f259,f191]) ).
fof(f575,plain,
( ~ sQ17_spl
| inverse(inverse(identity)) != sk_c9
| multiply(sk_c9,sk_c9) != sk_c8 ),
inference(paramodulation,[status(thm)],[f245,f191]) ).
fof(f576,plain,
( ~ sQ17_spl
| inverse(inverse(sk_c9)) != sk_c9
| multiply(sk_c9,identity) != sk_c8 ),
inference(paramodulation,[status(thm)],[f48,f191]) ).
fof(f579,definition,
( sQ35_spl
<=> inverse(sk_c9) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f582,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ17_spl
| ~ sQ35_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f572,f206,f579,f187,f155,f165]) ).
fof(f585,plain,
( ~ sQ17_spl
| ~ sQ20_spl
| ~ sQ34_spl ),
inference(split_clause,[status(thm)],[f575,f499,f294,f187]) ).
fof(f586,definition,
( sQ36_spl
<=> multiply(sk_c9,identity) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f589,plain,
( ~ sQ17_spl
| ~ sQ22_spl
| ~ sQ36_spl ),
inference(split_clause,[status(thm)],[f576,f586,f301,f187]) ).
fof(f605,plain,
( ~ sQ11_spl
| ~ sQ16_spl
| ~ sQ19_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f273,f165,f291,f184,f155]) ).
fof(f678,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| multiply(sk_c9,sk_c9) = multiply(sk_c1,sk_c10) ),
inference(paramodulation,[status(thm)],[f257,f197]) ).
fof(f682,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sk_c8 = multiply(sk_c1,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f259,f678]) ).
fof(f683,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sk_c8 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f95,f682]) ).
fof(f684,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sQ18_spl
| ~ sQ9_spl
| ~ sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f683,f555]) ).
fof(f685,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sQ18_spl
| ~ sQ9_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f684]) ).
fof(f689,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f683,f291,f155,f165,f125,f94]) ).
fof(f691,plain,
$false,
inference(sat_refutation,[status(thm)],[f100,f104,f116,f120,f124,f128,f129,f132,f133,f134,f138,f139,f142,f143,f144,f148,f149,f152,f153,f154,f158,f159,f160,f161,f162,f163,f164,f168,f169,f170,f171,f172,f173,f174,f190,f205,f209,f276,f285,f297,f304,f308,f312,f438,f442,f447,f469,f471,f498,f502,f504,f516,f535,f552,f570,f582,f585,f589,f605,f685,f689]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP251-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n026.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 20:10:21 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.08/0.38 % Refutation found
% 0.08/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.41 % Elapsed time: 0.053432 seconds
% 0.13/0.41 % CPU time: 0.125978 seconds
% 0.13/0.41 % Total memory used: 24.269 MB
% 0.13/0.41 % Net memory used: 24.238 MB
%------------------------------------------------------------------------------