%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP218-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 12:33:07 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.40s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 66
% Syntax : Number of formulae : 275 ( 10 unt; 22 def)
% Number of atoms : 1036 ( 358 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 1406 ( 645 ~; 739 |; 0 &)
% ( 22 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 24 ( 22 usr; 23 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 69 ( 69 !; 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_c6) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( inverse(sk_c7) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c6) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( inverse(sk_c6) = sk_c10
| multiply(sk_c2,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c10
| multiply(sk_c2,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c2,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c2,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c6) = sk_c10
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c10
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( inverse(sk_c7) = sk_c10
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( inverse(sk_c6) = sk_c10
| multiply(sk_c3,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c10
| multiply(sk_c3,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c3,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c3,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c3,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( inverse(sk_c6) = sk_c10
| multiply(sk_c10,sk_c5) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c10
| multiply(sk_c10,sk_c5) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c10,sk_c5) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c10,sk_c5) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c10,sk_c5) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( inverse(sk_c6) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c4,sk_c10) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c4,sk_c10) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
( inverse(sk_c6) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,negated_conjecture,
( inverse(sk_c7) = sk_c10
| inverse(sk_c4) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
! [X4,X5,X6,X7,X8,X1,X2,X3] :
( inverse(X3) != sk_c10
| multiply(X3,sk_c10) != X2
| multiply(sk_c10,X2) != sk_c9
| multiply(X1,sk_c9) != sk_c10
| inverse(X1) != sk_c10
| inverse(X8) != sk_c10
| multiply(X8,sk_c10) != X7
| multiply(sk_c10,X7) != sk_c9
| multiply(X6,sk_c10) != sk_c9
| inverse(X5) != X6
| multiply(X5,X6) != sk_c9
| multiply(X4,sk_c9) != sk_c10
| inverse(X4) != sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f46,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f47,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f48,plain,
( inverse(sk_c6) = sk_c10
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f49,plain,
( multiply(sk_c6,sk_c9) = sk_c10
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f50,plain,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f51,plain,
( multiply(sk_c7,sk_c10) = sk_c8
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f52,plain,
( inverse(sk_c7) = sk_c10
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f53,plain,
( inverse(sk_c6) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f54,plain,
( multiply(sk_c6,sk_c9) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f55,plain,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f56,plain,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f57,plain,
( inverse(sk_c7) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f58,plain,
( inverse(sk_c6) = sk_c10
| multiply(sk_c2,sk_c3) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f59,plain,
( multiply(sk_c6,sk_c9) = sk_c10
| multiply(sk_c2,sk_c3) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f60,plain,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c2,sk_c3) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f61,plain,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f62,plain,
( inverse(sk_c7) = sk_c10
| multiply(sk_c2,sk_c3) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f63,plain,
( inverse(sk_c6) = sk_c10
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f64,plain,
( multiply(sk_c6,sk_c9) = sk_c10
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f65,plain,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f66,plain,
( multiply(sk_c7,sk_c10) = sk_c8
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f67,plain,
( inverse(sk_c7) = sk_c10
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f68,plain,
( inverse(sk_c6) = sk_c10
| multiply(sk_c3,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f69,plain,
( multiply(sk_c6,sk_c9) = sk_c10
| multiply(sk_c3,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f70,plain,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c3,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f71,plain,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c3,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f72,plain,
( inverse(sk_c7) = sk_c10
| multiply(sk_c3,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f73,plain,
( inverse(sk_c6) = sk_c10
| multiply(sk_c10,sk_c5) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f74,plain,
( multiply(sk_c6,sk_c9) = sk_c10
| multiply(sk_c10,sk_c5) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f75,plain,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c10,sk_c5) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f76,plain,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c10,sk_c5) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f77,plain,
( inverse(sk_c7) = sk_c10
| multiply(sk_c10,sk_c5) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f78,plain,
( inverse(sk_c6) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f79,plain,
( multiply(sk_c6,sk_c9) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f80,plain,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c4,sk_c10) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f81,plain,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c4,sk_c10) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f82,plain,
( inverse(sk_c7) = sk_c10
| multiply(sk_c4,sk_c10) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f83,plain,
( inverse(sk_c6) = sk_c10
| inverse(sk_c4) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f84,plain,
( multiply(sk_c6,sk_c9) = sk_c10
| inverse(sk_c4) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f85,plain,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c4) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f86,plain,
( multiply(sk_c7,sk_c10) = sk_c8
| inverse(sk_c4) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f87,plain,
( inverse(sk_c7) = sk_c10
| inverse(sk_c4) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f88,plain,
! [X3] :
( inverse(X3) != sk_c10
| ! [X2] :
( multiply(X3,sk_c10) != X2
| multiply(sk_c10,X2) != sk_c9
| ! [X1] :
( multiply(X1,sk_c9) != sk_c10
| inverse(X1) != sk_c10
| ! [X8] :
( inverse(X8) != sk_c10
| ! [X7] :
( multiply(X8,sk_c10) != X7
| multiply(sk_c10,X7) != sk_c9
| ! [X6] :
( multiply(X6,sk_c10) != sk_c9
| ! [X5] :
( inverse(X5) != X6
| multiply(X5,X6) != sk_c9
| ! [X4] :
( multiply(X4,sk_c9) != sk_c10
| inverse(X4) != sk_c10 ) ) ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f44]) ).
fof(f89,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( inverse(X7) != sk_c10
| multiply(X7,sk_c10) != X6
| multiply(sk_c10,X6) != sk_c9
| multiply(X5,sk_c9) != sk_c10
| inverse(X5) != sk_c10
| inverse(X4) != sk_c10
| multiply(X4,sk_c10) != X3
| multiply(sk_c10,X3) != sk_c9
| multiply(X2,sk_c10) != sk_c9
| inverse(X1) != X2
| multiply(X1,X2) != sk_c9
| multiply(X0,sk_c9) != sk_c10
| inverse(X0) != sk_c10 ),
inference(cnf_transformation,[status(thm)],[f88]) ).
fof(f90,definition,
( sQ0_spl
<=> inverse(sk_c1) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f91,plain,
( ~ sQ0_spl
| inverse(sk_c1) = sk_c10 ),
inference(component_clause,[status(thm)],[f90]) ).
fof(f93,definition,
( sQ1_spl
<=> inverse(sk_c6) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ1_spl
| inverse(sk_c6) = sk_c10 ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f96,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f48,f90,f93]) ).
fof(f97,definition,
( sQ2_spl
<=> multiply(sk_c6,sk_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f98,plain,
( ~ sQ2_spl
| multiply(sk_c6,sk_c9) = sk_c10 ),
inference(component_clause,[status(thm)],[f97]) ).
fof(f100,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f49,f90,f97]) ).
fof(f101,definition,
( sQ3_spl
<=> multiply(sk_c10,sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f102,plain,
( ~ sQ3_spl
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(component_clause,[status(thm)],[f101]) ).
fof(f104,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f50,f90,f101]) ).
fof(f105,definition,
( sQ4_spl
<=> multiply(sk_c7,sk_c10) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f106,plain,
( ~ sQ4_spl
| multiply(sk_c7,sk_c10) = sk_c8 ),
inference(component_clause,[status(thm)],[f105]) ).
fof(f108,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f51,f90,f105]) ).
fof(f109,definition,
( sQ5_spl
<=> inverse(sk_c7) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f110,plain,
( ~ sQ5_spl
| inverse(sk_c7) = sk_c10 ),
inference(component_clause,[status(thm)],[f109]) ).
fof(f112,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f52,f90,f109]) ).
fof(f113,definition,
( sQ6_spl
<=> multiply(sk_c1,sk_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f114,plain,
( ~ sQ6_spl
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(component_clause,[status(thm)],[f113]) ).
fof(f116,plain,
( sQ1_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f53,f113,f93]) ).
fof(f117,plain,
( sQ2_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f54,f113,f97]) ).
fof(f118,plain,
( sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f55,f113,f101]) ).
fof(f119,plain,
( sQ4_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f56,f113,f105]) ).
fof(f120,plain,
( sQ5_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f57,f113,f109]) ).
fof(f121,definition,
( sQ7_spl
<=> multiply(sk_c2,sk_c3) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f122,plain,
( ~ sQ7_spl
| multiply(sk_c2,sk_c3) = sk_c9 ),
inference(component_clause,[status(thm)],[f121]) ).
fof(f124,plain,
( sQ1_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f58,f121,f93]) ).
fof(f125,plain,
( sQ2_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f59,f121,f97]) ).
fof(f126,plain,
( sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f60,f121,f101]) ).
fof(f127,plain,
( sQ4_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f61,f121,f105]) ).
fof(f128,plain,
( sQ5_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f62,f121,f109]) ).
fof(f129,definition,
( sQ8_spl
<=> inverse(sk_c2) = sk_c3 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f130,plain,
( ~ sQ8_spl
| inverse(sk_c2) = sk_c3 ),
inference(component_clause,[status(thm)],[f129]) ).
fof(f132,plain,
( sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f63,f129,f93]) ).
fof(f133,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f64,f129,f97]) ).
fof(f134,plain,
( sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f65,f129,f101]) ).
fof(f135,plain,
( sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f66,f129,f105]) ).
fof(f136,plain,
( sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f67,f129,f109]) ).
fof(f137,definition,
( sQ9_spl
<=> multiply(sk_c3,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f138,plain,
( ~ sQ9_spl
| multiply(sk_c3,sk_c10) = sk_c9 ),
inference(component_clause,[status(thm)],[f137]) ).
fof(f140,plain,
( sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f68,f137,f93]) ).
fof(f141,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f69,f137,f97]) ).
fof(f142,plain,
( sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f70,f137,f101]) ).
fof(f143,plain,
( sQ4_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f71,f137,f105]) ).
fof(f144,plain,
( sQ5_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f72,f137,f109]) ).
fof(f145,definition,
( sQ10_spl
<=> multiply(sk_c10,sk_c5) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f146,plain,
( ~ sQ10_spl
| multiply(sk_c10,sk_c5) = sk_c9 ),
inference(component_clause,[status(thm)],[f145]) ).
fof(f148,plain,
( sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f73,f145,f93]) ).
fof(f149,plain,
( sQ2_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f74,f145,f97]) ).
fof(f150,plain,
( sQ3_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f75,f145,f101]) ).
fof(f151,plain,
( sQ4_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f76,f145,f105]) ).
fof(f152,plain,
( sQ5_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f77,f145,f109]) ).
fof(f153,definition,
( sQ11_spl
<=> multiply(sk_c4,sk_c10) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f154,plain,
( ~ sQ11_spl
| multiply(sk_c4,sk_c10) = sk_c5 ),
inference(component_clause,[status(thm)],[f153]) ).
fof(f156,plain,
( sQ1_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f78,f153,f93]) ).
fof(f157,plain,
( sQ2_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f79,f153,f97]) ).
fof(f158,plain,
( sQ3_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f80,f153,f101]) ).
fof(f159,plain,
( sQ4_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f81,f153,f105]) ).
fof(f160,plain,
( sQ5_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f82,f153,f109]) ).
fof(f161,definition,
( sQ12_spl
<=> inverse(sk_c4) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f162,plain,
( ~ sQ12_spl
| inverse(sk_c4) = sk_c10 ),
inference(component_clause,[status(thm)],[f161]) ).
fof(f164,plain,
( sQ1_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f83,f161,f93]) ).
fof(f165,plain,
( sQ2_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f84,f161,f97]) ).
fof(f166,plain,
( sQ3_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f85,f161,f101]) ).
fof(f167,plain,
( sQ4_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f86,f161,f105]) ).
fof(f168,plain,
( sQ5_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f87,f161,f109]) ).
fof(f169,definition,
! [X0] :
( sQ13_spl
<=> ( multiply(X0,sk_c9) != sk_c10
| inverse(X0) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f170,plain,
! [X0] :
( ~ sQ13_spl
| multiply(X0,sk_c9) != sk_c10
| inverse(X0) != sk_c10 ),
inference(component_clause,[status(thm)],[f169]) ).
fof(f172,definition,
! [X1,X2] :
( sQ14_spl
<=> ( multiply(X2,sk_c10) != sk_c9
| inverse(X1) != X2
| multiply(X1,X2) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f173,plain,
! [X0,X1] :
( ~ sQ14_spl
| multiply(X1,sk_c10) != sk_c9
| inverse(X0) != X1
| multiply(X0,X1) != sk_c9 ),
inference(component_clause,[status(thm)],[f172]) ).
fof(f175,definition,
! [X3,X4] :
( sQ15_spl
<=> ( inverse(X4) != sk_c10
| multiply(X4,sk_c10) != X3
| multiply(sk_c10,X3) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f176,plain,
! [X0,X1] :
( ~ sQ15_spl
| inverse(X1) != sk_c10
| multiply(X1,sk_c10) != X0
| multiply(sk_c10,X0) != sk_c9 ),
inference(component_clause,[status(thm)],[f175]) ).
fof(f178,plain,
( sQ15_spl
| sQ14_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f89,f169,f172,f175]) ).
fof(f179,plain,
! [X0] :
( ~ sQ15_spl
| inverse(X0) != sk_c10
| multiply(sk_c10,multiply(X0,sk_c10)) != sk_c9 ),
inference(destructive_equality_resolution,[status(thm)],[f176]) ).
fof(f193,plain,
( ~ sQ11_spl
| ~ sQ15_spl
| inverse(sk_c4) != sk_c10
| multiply(sk_c10,sk_c5) != sk_c9 ),
inference(paramodulation,[status(thm)],[f154,f179]) ).
fof(f194,plain,
( ~ sQ4_spl
| ~ sQ15_spl
| inverse(sk_c7) != sk_c10
| multiply(sk_c10,sk_c8) != sk_c9 ),
inference(paramodulation,[status(thm)],[f106,f179]) ).
fof(f202,plain,
( ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ12_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f193,f145,f161,f175,f153]) ).
fof(f203,plain,
( ~ sQ4_spl
| ~ sQ15_spl
| ~ sQ5_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f194,f101,f109,f175,f105]) ).
fof(f209,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f46,f47]) ).
fof(f210,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f45,f209]) ).
fof(f227,plain,
( ~ sQ6_spl
| sk_c9 = multiply(inverse(sk_c1),sk_c10) ),
inference(paramodulation,[status(thm)],[f114,f210]) ).
fof(f228,plain,
( ~ sQ7_spl
| sk_c3 = multiply(inverse(sk_c2),sk_c9) ),
inference(paramodulation,[status(thm)],[f122,f210]) ).
fof(f231,plain,
( ~ sQ11_spl
| sk_c10 = multiply(inverse(sk_c4),sk_c5) ),
inference(paramodulation,[status(thm)],[f154,f210]) ).
fof(f236,plain,
( ~ sQ4_spl
| sk_c10 = multiply(inverse(sk_c7),sk_c8) ),
inference(paramodulation,[status(thm)],[f106,f210]) ).
fof(f238,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| sk_c9 = multiply(sk_c10,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f91,f227]) ).
fof(f239,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| sk_c3 = multiply(sk_c3,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f130,f228]) ).
fof(f240,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| sk_c10 = multiply(sk_c10,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f162,f231]) ).
fof(f241,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| sk_c10 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f146,f240]) ).
fof(f242,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| sk_c10 = multiply(sk_c10,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f110,f236]) ).
fof(f248,plain,
( ~ sQ6_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| multiply(sk_c1,sk_c9) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f241,f114]) ).
fof(f249,plain,
( ~ sQ9_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| multiply(sk_c3,sk_c9) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f241,f138]) ).
fof(f250,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| multiply(sk_c9,sk_c5) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f241,f146]) ).
fof(f252,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| inverse(sk_c1) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f241,f91]) ).
fof(f254,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl
| inverse(sk_c4) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f241,f162]) ).
fof(f262,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| multiply(X0,sk_c9) != sk_c10
| inverse(X0) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f241,f170]) ).
fof(f263,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| multiply(X0,sk_c9) != sk_c9
| inverse(X0) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f241,f262]) ).
fof(f278,definition,
( sQ21_spl
<=> sk_c9 = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f280,plain,
( sQ21_spl
| sk_c9 != sk_c9 ),
inference(component_clause,[status(thm)],[f278]) ).
fof(f282,plain,
( ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ6_spl
| inverse(sk_c1) != sk_c9 ),
inference(resolution,[status(thm)],[f248,f263]) ).
fof(f286,plain,
( ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ6_spl
| ~ sQ0_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f252,f282]) ).
fof(f287,plain,
( ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ6_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f286]) ).
fof(f288,plain,
( ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ6_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f287]) ).
fof(f290,plain,
! [X0,X1] :
( ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| multiply(X1,sk_c9) != sk_c9
| inverse(X0) != X1
| multiply(X0,X1) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f241,f173]) ).
fof(f291,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| multiply(inverse(X0),sk_c9) != sk_c9
| multiply(X0,inverse(X0)) != sk_c9 ),
inference(destructive_equality_resolution,[status(thm)],[f290]) ).
fof(f292,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| sk_c9 = multiply(sk_c9,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f241,f238]) ).
fof(f293,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| sk_c9 = multiply(sk_c9,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f241,f292]) ).
fof(f294,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| sk_c9 = multiply(inverse(sk_c9),sk_c9) ),
inference(paramodulation,[status(thm)],[f293,f210]) ).
fof(f296,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| sk_c9 = identity ),
inference(forward_demodulation,[status(thm)],[f46,f294]) ).
fof(f299,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| multiply(sk_c9,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f296,f45]) ).
fof(f305,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| multiply(sk_c9,X0) = multiply(sk_c3,multiply(sk_c9,X0)) ),
inference(paramodulation,[status(thm)],[f249,f47]) ).
fof(f306,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ6_spl
| ~ sQ0_spl
| X0 = multiply(sk_c3,multiply(sk_c9,X0)) ),
inference(forward_demodulation,[status(thm)],[f299,f305]) ).
fof(f307,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ6_spl
| ~ sQ0_spl
| X0 = multiply(sk_c3,X0) ),
inference(forward_demodulation,[status(thm)],[f299,f306]) ).
fof(f319,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c3 = identity ),
inference(backward_demodulation,[status(thm)],[f326,f296]) ).
fof(f322,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| inverse(sk_c4) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f326,f254]) ).
fof(f326,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ6_spl
| ~ sQ0_spl
| sk_c3 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f307,f239]) ).
fof(f330,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| X0 = multiply(sk_c3,multiply(sk_c4,X0)) ),
inference(paramodulation,[status(thm)],[f322,f210]) ).
fof(f331,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| X0 = multiply(sk_c4,X0) ),
inference(forward_demodulation,[status(thm)],[f307,f330]) ).
fof(f332,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| multiply(sk_c3,sk_c5) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f326,f250]) ).
fof(f333,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| sk_c5 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f307,f332]) ).
fof(f334,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| inverse(sk_c4) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f342,f322]) ).
fof(f337,plain,
( ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c5 = identity ),
inference(backward_demodulation,[status(thm)],[f342,f319]) ).
fof(f339,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ6_spl
| ~ sQ0_spl
| sk_c5 = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f342,f326]) ).
fof(f341,plain,
( ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| inverse(sk_c2) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f342,f130]) ).
fof(f342,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| sk_c5 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f326,f333]) ).
fof(f364,plain,
( sQ21_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f280]) ).
fof(f365,plain,
sQ21_spl,
inference(contradiction_clause,[status(thm)],[f364]) ).
fof(f366,plain,
! [X0] :
( ~ sQ14_spl
| multiply(inverse(X0),sk_c10) != sk_c9
| multiply(X0,inverse(X0)) != sk_c9 ),
inference(destructive_equality_resolution,[status(thm)],[f173]) ).
fof(f368,plain,
( ~ sQ2_spl
| sk_c9 = multiply(inverse(sk_c6),sk_c10) ),
inference(paramodulation,[status(thm)],[f98,f210]) ).
fof(f370,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sk_c9 = multiply(sk_c10,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f94,f368]) ).
fof(f382,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| inverse(sk_c6) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f383,f94]) ).
fof(f383,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c10 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f102,f242]) ).
fof(f396,definition,
( sQ23_spl
<=> multiply(sk_c9,sk_c9) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f398,plain,
( sQ23_spl
| multiply(sk_c9,sk_c9) != sk_c9 ),
inference(component_clause,[status(thm)],[f396]) ).
fof(f449,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| multiply(X0,sk_c9) != sk_c10
| inverse(X0) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f383,f170]) ).
fof(f450,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| multiply(X0,sk_c9) != sk_c9
| inverse(X0) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f383,f449]) ).
fof(f453,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ13_spl
| multiply(sk_c6,sk_c9) != sk_c9
| sk_c9 != sk_c9 ),
inference(paramodulation,[status(thm)],[f382,f450]) ).
fof(f455,definition,
( sQ27_spl
<=> multiply(sk_c6,sk_c9) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f457,plain,
( sQ27_spl
| multiply(sk_c6,sk_c9) != sk_c9 ),
inference(component_clause,[status(thm)],[f455]) ).
fof(f458,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ13_spl
| ~ sQ27_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f453,f278,f455,f169,f101,f109,f105,f93]) ).
fof(f490,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c9 = multiply(sk_c9,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f383,f370]) ).
fof(f491,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c9 = multiply(sk_c9,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f383,f490]) ).
fof(f494,plain,
( sQ23_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f491,f398]) ).
fof(f495,plain,
( sQ23_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f494]) ).
fof(f496,plain,
( sQ23_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f495]) ).
fof(f521,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c5,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f337,f45]) ).
fof(f531,plain,
( ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| inverse(sk_c2) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f342,f130]) ).
fof(f538,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(inverse(X0),X0) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f337,f46]) ).
fof(f539,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| multiply(sk_c5,sk_c4) = sk_c5 ),
inference(paramodulation,[status(thm)],[f334,f538]) ).
fof(f540,plain,
( ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| multiply(sk_c5,sk_c2) = sk_c5 ),
inference(paramodulation,[status(thm)],[f531,f538]) ).
fof(f545,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| sk_c4 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f521,f539]) ).
fof(f546,plain,
( ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| sk_c2 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f521,f540]) ).
fof(f568,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ6_spl
| ~ sQ0_spl
| sk_c4 = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f545,f339]) ).
fof(f574,plain,
( ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| sk_c2 = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f545,f546]) ).
fof(f580,plain,
( ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| inverse(sk_c4) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f574,f341]) ).
fof(f581,plain,
( ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| inverse(sk_c4) = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f545,f580]) ).
fof(f604,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| multiply(inverse(X0),sk_c9) != sk_c9
| multiply(X0,inverse(X0)) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f568,f291]) ).
fof(f605,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| multiply(inverse(X0),sk_c4) != sk_c9
| multiply(X0,inverse(X0)) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f568,f604]) ).
fof(f606,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| multiply(inverse(X0),sk_c4) != sk_c4
| multiply(X0,inverse(X0)) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f568,f605]) ).
fof(f607,plain,
( ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ14_spl
| multiply(sk_c4,sk_c4) != sk_c4
| multiply(sk_c4,inverse(sk_c4)) != sk_c4 ),
inference(paramodulation,[status(thm)],[f581,f606]) ).
fof(f608,definition,
( sQ29_spl
<=> multiply(sk_c4,inverse(sk_c4)) = sk_c4 ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f610,plain,
( sQ29_spl
| multiply(sk_c4,inverse(sk_c4)) != sk_c4 ),
inference(component_clause,[status(thm)],[f608]) ).
fof(f611,definition,
( sQ30_spl
<=> multiply(sk_c4,sk_c4) = sk_c4 ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f613,plain,
( sQ30_spl
| multiply(sk_c4,sk_c4) != sk_c4 ),
inference(component_clause,[status(thm)],[f611]) ).
fof(f614,plain,
( ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ30_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f607,f608,f611,f172,f90,f113,f137,f121,f161,f153,f145,f129]) ).
fof(f615,plain,
( sQ29_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| inverse(sk_c4) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f331,f610]) ).
fof(f616,plain,
( sQ29_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| sk_c4 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f581,f615]) ).
fof(f617,plain,
( sQ29_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f616]) ).
fof(f618,plain,
( sQ29_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f617]) ).
fof(f619,plain,
( sQ30_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| sk_c4 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f331,f613]) ).
fof(f620,plain,
( sQ30_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f619]) ).
fof(f621,plain,
( sQ30_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f620]) ).
fof(f629,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| inverse(sk_c6) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f383,f94]) ).
fof(f647,plain,
( ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| multiply(sk_c6,sk_c9) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f383,f98]) ).
fof(f686,plain,
( sQ27_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f647,f457]) ).
fof(f687,plain,
( sQ27_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f686]) ).
fof(f688,plain,
( sQ27_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f687]) ).
fof(f689,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| multiply(inverse(X0),sk_c9) != sk_c9
| multiply(X0,inverse(X0)) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f383,f366]) ).
fof(f713,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ14_spl
| multiply(sk_c9,sk_c9) != sk_c9
| multiply(sk_c6,inverse(sk_c6)) != sk_c9 ),
inference(paramodulation,[status(thm)],[f629,f689]) ).
fof(f728,definition,
( sQ35_spl
<=> multiply(sk_c6,inverse(sk_c6)) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f730,plain,
( sQ35_spl
| multiply(sk_c6,inverse(sk_c6)) != sk_c9 ),
inference(component_clause,[status(thm)],[f728]) ).
fof(f731,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ14_spl
| ~ sQ23_spl
| ~ sQ35_spl ),
inference(split_clause,[status(thm)],[f713,f728,f396,f172,f101,f109,f105,f93]) ).
fof(f733,plain,
( sQ35_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| multiply(sk_c6,sk_c9) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f629,f730]) ).
fof(f734,plain,
( sQ35_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f647,f733]) ).
fof(f735,plain,
( sQ35_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f734]) ).
fof(f736,plain,
( sQ35_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f735]) ).
fof(f737,plain,
$false,
inference(sat_refutation,[status(thm)],[f96,f100,f104,f108,f112,f116,f117,f118,f119,f120,f124,f125,f126,f127,f128,f132,f133,f134,f135,f136,f140,f141,f142,f143,f144,f148,f149,f150,f151,f152,f156,f157,f158,f159,f160,f164,f165,f166,f167,f168,f178,f202,f203,f288,f365,f458,f496,f614,f618,f621,f688,f731,f736]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP218-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n001.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 20:12:13 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 0.12/0.40 % Refutation found
% 0.12/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.44 % Elapsed time: 0.076912 seconds
% 0.12/0.44 % CPU time: 0.256674 seconds
% 0.12/0.44 % Total memory used: 105.003 MB
% 0.12/0.44 % Net memory used: 104.863 MB
%------------------------------------------------------------------------------