%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP210-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 12:33:06 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.42s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 79
% Syntax : Number of formulae : 319 ( 13 unt; 35 def)
% Number of atoms : 894 ( 383 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 1025 ( 450 ~; 540 |; 0 &)
% ( 35 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 37 ( 35 usr; 36 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 74 ( 74 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c10
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c9
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c9
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c10
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c9
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c7) = sk_c10
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c10
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c9
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c9
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( inverse(sk_c7) = sk_c10
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c3,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c10
| multiply(sk_c3,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c9
| multiply(sk_c3,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c3,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
( multiply(sk_c6,sk_c10) = sk_c9
| multiply(sk_c3,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c3,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c3,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,negated_conjecture,
( inverse(sk_c7) = sk_c10
| multiply(sk_c3,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
! [X4,X5,X6,X1,X3,X2,X7,X8] :
( inverse(X8) != sk_c10
| multiply(X8,sk_c10) != X7
| multiply(sk_c10,X7) != sk_c9
| multiply(X2,sk_c10) != sk_c9
| inverse(X3) != X2
| multiply(X3,X2) != sk_c9
| multiply(X1,sk_c9) != sk_c10
| inverse(X1) != sk_c10
| multiply(X6,sk_c9) != sk_c10
| inverse(X6) != sk_c10
| multiply(X5,sk_c9) != sk_c10
| inverse(X4) != X5
| multiply(X4,X5) != 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_c4) = sk_c10
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f49,plain,
( multiply(sk_c4,sk_c9) = sk_c10
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f50,plain,
( multiply(sk_c5,sk_c6) = sk_c9
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f51,plain,
( inverse(sk_c5) = sk_c6
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f52,plain,
( multiply(sk_c6,sk_c10) = sk_c9
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f53,plain,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f54,plain,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f55,plain,
( inverse(sk_c7) = sk_c10
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f56,plain,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f57,plain,
( multiply(sk_c4,sk_c9) = sk_c10
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f58,plain,
( multiply(sk_c5,sk_c6) = sk_c9
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f59,plain,
( inverse(sk_c5) = sk_c6
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f60,plain,
( multiply(sk_c6,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f61,plain,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f62,plain,
( multiply(sk_c7,sk_c10) = sk_c8
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f63,plain,
( inverse(sk_c7) = sk_c10
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f64,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f65,plain,
( multiply(sk_c4,sk_c9) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f66,plain,
( multiply(sk_c5,sk_c6) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f67,plain,
( inverse(sk_c5) = sk_c6
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f68,plain,
( multiply(sk_c6,sk_c10) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f69,plain,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f70,plain,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f71,plain,
( inverse(sk_c7) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f72,plain,
( inverse(sk_c4) = sk_c10
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f73,plain,
( multiply(sk_c4,sk_c9) = sk_c10
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f74,plain,
( multiply(sk_c5,sk_c6) = sk_c9
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f75,plain,
( inverse(sk_c5) = sk_c6
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f76,plain,
( multiply(sk_c6,sk_c10) = sk_c9
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f77,plain,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f78,plain,
( multiply(sk_c7,sk_c10) = sk_c8
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f79,plain,
( inverse(sk_c7) = sk_c10
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f80,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c3,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f81,plain,
( multiply(sk_c4,sk_c9) = sk_c10
| multiply(sk_c3,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f82,plain,
( multiply(sk_c5,sk_c6) = sk_c9
| multiply(sk_c3,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f83,plain,
( inverse(sk_c5) = sk_c6
| multiply(sk_c3,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f84,plain,
( multiply(sk_c6,sk_c10) = sk_c9
| multiply(sk_c3,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f85,plain,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c3,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f86,plain,
( multiply(sk_c7,sk_c10) = sk_c8
| multiply(sk_c3,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f87,plain,
( inverse(sk_c7) = sk_c10
| multiply(sk_c3,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f88,plain,
! [X8] :
( inverse(X8) != sk_c10
| ! [X7] :
( multiply(X8,sk_c10) != X7
| multiply(sk_c10,X7) != sk_c9
| ! [X2] :
( multiply(X2,sk_c10) != sk_c9
| ! [X3] :
( inverse(X3) != X2
| multiply(X3,X2) != sk_c9
| ! [X1] :
( multiply(X1,sk_c9) != sk_c10
| inverse(X1) != sk_c10
| ! [X6] :
( multiply(X6,sk_c9) != sk_c10
| inverse(X6) != sk_c10
| ! [X5] :
( multiply(X5,sk_c9) != sk_c10
| ! [X4] :
( inverse(X4) != X5
| multiply(X4,X5) != 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_c10) != sk_c9
| inverse(X4) != X5
| multiply(X4,X5) != sk_c9
| multiply(X3,sk_c9) != sk_c10
| inverse(X3) != sk_c10
| multiply(X2,sk_c9) != sk_c10
| inverse(X2) != sk_c10
| multiply(X1,sk_c9) != sk_c10
| inverse(X0) != X1
| multiply(X0,X1) != sk_c10 ),
inference(cnf_transformation,[status(thm)],[f88]) ).
fof(f90,definition,
( sQ0_spl
<=> multiply(sk_c1,sk_c2) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f91,plain,
( ~ sQ0_spl
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(component_clause,[status(thm)],[f90]) ).
fof(f93,definition,
( sQ1_spl
<=> inverse(sk_c4) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ1_spl
| inverse(sk_c4) = 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_c4,sk_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f98,plain,
( ~ sQ2_spl
| multiply(sk_c4,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_c5,sk_c6) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f102,plain,
( ~ sQ3_spl
| multiply(sk_c5,sk_c6) = 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
<=> inverse(sk_c5) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f106,plain,
( ~ sQ4_spl
| inverse(sk_c5) = sk_c6 ),
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
<=> multiply(sk_c6,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f112,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f52,f90,f109]) ).
fof(f113,definition,
( sQ6_spl
<=> multiply(sk_c10,sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f114,plain,
( ~ sQ6_spl
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(component_clause,[status(thm)],[f113]) ).
fof(f116,plain,
( sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f53,f90,f113]) ).
fof(f117,definition,
( sQ7_spl
<=> multiply(sk_c7,sk_c10) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f118,plain,
( ~ sQ7_spl
| multiply(sk_c7,sk_c10) = sk_c8 ),
inference(component_clause,[status(thm)],[f117]) ).
fof(f120,plain,
( sQ7_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f54,f90,f117]) ).
fof(f121,definition,
( sQ8_spl
<=> inverse(sk_c7) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f122,plain,
( ~ sQ8_spl
| inverse(sk_c7) = sk_c10 ),
inference(component_clause,[status(thm)],[f121]) ).
fof(f124,plain,
( sQ8_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f55,f90,f121]) ).
fof(f125,definition,
( sQ9_spl
<=> inverse(sk_c1) = sk_c2 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f126,plain,
( ~ sQ9_spl
| inverse(sk_c1) = sk_c2 ),
inference(component_clause,[status(thm)],[f125]) ).
fof(f128,plain,
( sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f56,f125,f93]) ).
fof(f129,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f57,f125,f97]) ).
fof(f130,plain,
( sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f58,f125,f101]) ).
fof(f131,plain,
( sQ4_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f59,f125,f105]) ).
fof(f132,plain,
( sQ5_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f60,f125,f109]) ).
fof(f133,plain,
( sQ6_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f61,f125,f113]) ).
fof(f134,plain,
( sQ7_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f62,f125,f117]) ).
fof(f135,plain,
( sQ8_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f63,f125,f121]) ).
fof(f136,definition,
( sQ10_spl
<=> multiply(sk_c2,sk_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f137,plain,
( ~ sQ10_spl
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f139,plain,
( sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f64,f136,f93]) ).
fof(f140,plain,
( sQ2_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f65,f136,f97]) ).
fof(f141,plain,
( sQ3_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f66,f136,f101]) ).
fof(f142,plain,
( sQ4_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f67,f136,f105]) ).
fof(f143,plain,
( sQ5_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f68,f136,f109]) ).
fof(f144,plain,
( sQ6_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f69,f136,f113]) ).
fof(f145,plain,
( sQ7_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f70,f136,f117]) ).
fof(f146,plain,
( sQ8_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f71,f136,f121]) ).
fof(f147,definition,
( sQ11_spl
<=> inverse(sk_c3) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f148,plain,
( ~ sQ11_spl
| inverse(sk_c3) = sk_c10 ),
inference(component_clause,[status(thm)],[f147]) ).
fof(f150,plain,
( sQ1_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f72,f147,f93]) ).
fof(f151,plain,
( sQ2_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f73,f147,f97]) ).
fof(f152,plain,
( sQ3_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f74,f147,f101]) ).
fof(f153,plain,
( sQ4_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f75,f147,f105]) ).
fof(f154,plain,
( sQ5_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f76,f147,f109]) ).
fof(f155,plain,
( sQ6_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f77,f147,f113]) ).
fof(f156,plain,
( sQ7_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f78,f147,f117]) ).
fof(f157,plain,
( sQ8_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f79,f147,f121]) ).
fof(f158,definition,
( sQ12_spl
<=> multiply(sk_c3,sk_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f159,plain,
( ~ sQ12_spl
| multiply(sk_c3,sk_c9) = sk_c10 ),
inference(component_clause,[status(thm)],[f158]) ).
fof(f161,plain,
( sQ1_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f80,f158,f93]) ).
fof(f162,plain,
( sQ2_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f81,f158,f97]) ).
fof(f163,plain,
( sQ3_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f82,f158,f101]) ).
fof(f164,plain,
( sQ4_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f83,f158,f105]) ).
fof(f165,plain,
( sQ5_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f84,f158,f109]) ).
fof(f166,plain,
( sQ6_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f85,f158,f113]) ).
fof(f167,plain,
( sQ7_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f86,f158,f117]) ).
fof(f168,plain,
( sQ8_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f87,f158,f121]) ).
fof(f169,definition,
! [X0,X1] :
( sQ13_spl
<=> ( multiply(X1,sk_c9) != sk_c10
| inverse(X0) != X1
| multiply(X0,X1) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f170,plain,
! [X0,X1] :
( ~ sQ13_spl
| multiply(X1,sk_c9) != sk_c10
| inverse(X0) != X1
| multiply(X0,X1) != sk_c10 ),
inference(component_clause,[status(thm)],[f169]) ).
fof(f172,definition,
! [X2] :
( sQ14_spl
<=> ( multiply(X2,sk_c9) != sk_c10
| inverse(X2) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f173,plain,
! [X0] :
( ~ sQ14_spl
| multiply(X0,sk_c9) != sk_c10
| inverse(X0) != sk_c10 ),
inference(component_clause,[status(thm)],[f172]) ).
fof(f175,definition,
! [X4,X5] :
( sQ15_spl
<=> ( multiply(X5,sk_c10) != sk_c9
| inverse(X4) != X5
| multiply(X4,X5) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f176,plain,
! [X0,X1] :
( ~ sQ15_spl
| multiply(X1,sk_c10) != sk_c9
| inverse(X0) != X1
| multiply(X0,X1) != sk_c9 ),
inference(component_clause,[status(thm)],[f175]) ).
fof(f178,definition,
! [X6,X7] :
( sQ16_spl
<=> ( inverse(X7) != sk_c10
| multiply(X7,sk_c10) != X6
| multiply(sk_c10,X6) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f179,plain,
! [X0,X1] :
( ~ sQ16_spl
| inverse(X1) != sk_c10
| multiply(X1,sk_c10) != X0
| multiply(sk_c10,X0) != sk_c9 ),
inference(component_clause,[status(thm)],[f178]) ).
fof(f181,plain,
( sQ16_spl
| sQ15_spl
| sQ14_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f89,f169,f172,f175,f178]) ).
fof(f182,plain,
! [X0] :
( ~ sQ16_spl
| inverse(X0) != sk_c10
| multiply(sk_c10,multiply(X0,sk_c10)) != sk_c9 ),
inference(destructive_equality_resolution,[status(thm)],[f179]) ).
fof(f184,plain,
! [X0] :
( ~ sQ10_spl
| multiply(sk_c10,X0) = multiply(sk_c2,multiply(sk_c9,X0)) ),
inference(paramodulation,[status(thm)],[f137,f47]) ).
fof(f185,plain,
! [X0] :
( ~ sQ12_spl
| multiply(sk_c10,X0) = multiply(sk_c3,multiply(sk_c9,X0)) ),
inference(paramodulation,[status(thm)],[f159,f47]) ).
fof(f188,plain,
! [X0] :
( ~ sQ0_spl
| multiply(sk_c10,X0) = multiply(sk_c1,multiply(sk_c2,X0)) ),
inference(paramodulation,[status(thm)],[f91,f47]) ).
fof(f193,plain,
( ~ sQ9_spl
| multiply(sk_c2,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f126,f46]) ).
fof(f194,plain,
( ~ sQ11_spl
| multiply(sk_c10,sk_c3) = identity ),
inference(paramodulation,[status(thm)],[f148,f46]) ).
fof(f195,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f46,f47]) ).
fof(f196,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f45,f195]) ).
fof(f203,plain,
( ~ sQ7_spl
| ~ sQ16_spl
| inverse(sk_c7) != sk_c10
| multiply(sk_c10,sk_c8) != sk_c9 ),
inference(paramodulation,[status(thm)],[f118,f182]) ).
fof(f205,plain,
( ~ sQ16_spl
| inverse(identity) != sk_c10
| multiply(sk_c10,sk_c10) != sk_c9 ),
inference(paramodulation,[status(thm)],[f45,f182]) ).
fof(f214,plain,
( ~ sQ7_spl
| ~ sQ16_spl
| ~ sQ8_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f203,f113,f121,f178,f117]) ).
fof(f218,definition,
( sQ20_spl
<=> inverse(inverse(sk_c10)) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f220,plain,
( sQ20_spl
| inverse(inverse(sk_c10)) != sk_c10 ),
inference(component_clause,[status(thm)],[f218]) ).
fof(f222,definition,
( sQ21_spl
<=> multiply(sk_c10,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f224,plain,
( sQ21_spl
| multiply(sk_c10,sk_c10) != sk_c9 ),
inference(component_clause,[status(thm)],[f222]) ).
fof(f225,definition,
( sQ22_spl
<=> inverse(identity) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f227,plain,
( sQ22_spl
| inverse(identity) != sk_c10 ),
inference(component_clause,[status(thm)],[f225]) ).
fof(f228,plain,
( ~ sQ16_spl
| ~ sQ22_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f205,f222,f225,f178]) ).
fof(f229,plain,
! [X0] :
( ~ sQ15_spl
| multiply(inverse(X0),sk_c10) != sk_c9
| multiply(X0,inverse(X0)) != sk_c9 ),
inference(destructive_equality_resolution,[status(thm)],[f176]) ).
fof(f230,plain,
! [X0] :
( ~ sQ13_spl
| multiply(inverse(X0),sk_c9) != sk_c10
| multiply(X0,inverse(X0)) != sk_c10 ),
inference(destructive_equality_resolution,[status(thm)],[f170]) ).
fof(f231,plain,
( ~ sQ15_spl
| identity != sk_c9
| multiply(sk_c10,inverse(sk_c10)) != sk_c9 ),
inference(paramodulation,[status(thm)],[f46,f229]) ).
fof(f232,plain,
( ~ sQ1_spl
| ~ sQ15_spl
| multiply(sk_c10,sk_c10) != sk_c9
| multiply(sk_c4,inverse(sk_c4)) != sk_c9 ),
inference(paramodulation,[status(thm)],[f94,f229]) ).
fof(f233,plain,
( ~ sQ4_spl
| ~ sQ15_spl
| multiply(sk_c6,sk_c10) != sk_c9
| multiply(sk_c5,inverse(sk_c5)) != sk_c9 ),
inference(paramodulation,[status(thm)],[f106,f229]) ).
fof(f235,plain,
( ~ sQ9_spl
| ~ sQ15_spl
| multiply(sk_c2,sk_c10) != sk_c9
| multiply(sk_c1,inverse(sk_c1)) != sk_c9 ),
inference(paramodulation,[status(thm)],[f126,f229]) ).
fof(f236,plain,
( ~ sQ11_spl
| ~ sQ15_spl
| multiply(sk_c10,sk_c10) != sk_c9
| multiply(sk_c3,inverse(sk_c3)) != sk_c9 ),
inference(paramodulation,[status(thm)],[f148,f229]) ).
fof(f237,definition,
( sQ23_spl
<=> multiply(sk_c10,inverse(sk_c10)) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f240,definition,
( sQ24_spl
<=> identity = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f242,plain,
( sQ24_spl
| identity != sk_c9 ),
inference(component_clause,[status(thm)],[f240]) ).
fof(f243,plain,
( ~ sQ15_spl
| ~ sQ24_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f231,f237,f240,f175]) ).
fof(f244,definition,
( sQ25_spl
<=> multiply(sk_c4,inverse(sk_c4)) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f247,plain,
( ~ sQ1_spl
| ~ sQ15_spl
| ~ sQ21_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f232,f244,f222,f175,f93]) ).
fof(f248,definition,
( sQ26_spl
<=> multiply(sk_c5,inverse(sk_c5)) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f250,plain,
( sQ26_spl
| multiply(sk_c5,inverse(sk_c5)) != sk_c9 ),
inference(component_clause,[status(thm)],[f248]) ).
fof(f251,plain,
( ~ sQ4_spl
| ~ sQ15_spl
| ~ sQ5_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f233,f248,f109,f175,f105]) ).
fof(f256,definition,
( sQ28_spl
<=> multiply(sk_c1,inverse(sk_c1)) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f257,plain,
( ~ sQ28_spl
| multiply(sk_c1,inverse(sk_c1)) = sk_c9 ),
inference(component_clause,[status(thm)],[f256]) ).
fof(f258,plain,
( sQ28_spl
| multiply(sk_c1,inverse(sk_c1)) != sk_c9 ),
inference(component_clause,[status(thm)],[f256]) ).
fof(f259,definition,
( sQ29_spl
<=> multiply(sk_c2,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f261,plain,
( sQ29_spl
| multiply(sk_c2,sk_c10) != sk_c9 ),
inference(component_clause,[status(thm)],[f259]) ).
fof(f262,plain,
( ~ sQ9_spl
| ~ sQ15_spl
| ~ sQ29_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f235,f256,f259,f175,f125]) ).
fof(f263,definition,
( sQ30_spl
<=> multiply(sk_c3,inverse(sk_c3)) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f266,plain,
( ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ21_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f236,f263,f222,f175,f147]) ).
fof(f268,plain,
( sQ28_spl
| ~ sQ9_spl
| multiply(sk_c1,sk_c2) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f126,f258]) ).
fof(f269,plain,
( sQ28_spl
| ~ sQ9_spl
| ~ sQ0_spl
| sk_c10 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f91,f268]) ).
fof(f270,plain,
( sQ26_spl
| ~ sQ4_spl
| multiply(sk_c5,sk_c6) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f106,f250]) ).
fof(f271,plain,
( sQ26_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f102,f270]) ).
fof(f272,plain,
( sQ26_spl
| ~ sQ4_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f271]) ).
fof(f273,plain,
( sQ26_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f272]) ).
fof(f275,plain,
( ~ sQ1_spl
| ~ sQ14_spl
| multiply(sk_c4,sk_c9) != sk_c10 ),
inference(resolution,[status(thm)],[f173,f94]) ).
fof(f276,plain,
( ~ sQ11_spl
| ~ sQ14_spl
| multiply(sk_c3,sk_c9) != sk_c10 ),
inference(resolution,[status(thm)],[f173,f148]) ).
fof(f280,plain,
( ~ sQ1_spl
| ~ sQ14_spl
| ~ sQ2_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f98,f275]) ).
fof(f281,plain,
( ~ sQ1_spl
| ~ sQ14_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f280]) ).
fof(f282,plain,
( ~ sQ1_spl
| ~ sQ14_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f281]) ).
fof(f283,plain,
( ~ sQ13_spl
| identity != sk_c10
| multiply(sk_c9,inverse(sk_c9)) != sk_c10 ),
inference(paramodulation,[status(thm)],[f46,f230]) ).
fof(f284,plain,
( ~ sQ9_spl
| ~ sQ13_spl
| multiply(sk_c2,sk_c9) != sk_c10
| multiply(sk_c1,inverse(sk_c1)) != sk_c10 ),
inference(paramodulation,[status(thm)],[f126,f230]) ).
fof(f285,plain,
( ~ sQ11_spl
| ~ sQ13_spl
| multiply(sk_c10,sk_c9) != sk_c10
| multiply(sk_c3,inverse(sk_c3)) != sk_c10 ),
inference(paramodulation,[status(thm)],[f148,f230]) ).
fof(f286,definition,
( sQ31_spl
<=> multiply(sk_c9,inverse(sk_c9)) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f289,definition,
( sQ32_spl
<=> identity = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f291,plain,
( sQ32_spl
| identity != sk_c10 ),
inference(component_clause,[status(thm)],[f289]) ).
fof(f292,plain,
( ~ sQ13_spl
| ~ sQ32_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f283,f286,f289,f169]) ).
fof(f293,definition,
( sQ33_spl
<=> multiply(sk_c1,inverse(sk_c1)) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f295,plain,
( sQ33_spl
| multiply(sk_c1,inverse(sk_c1)) != sk_c10 ),
inference(component_clause,[status(thm)],[f293]) ).
fof(f296,plain,
( ~ sQ9_spl
| ~ sQ13_spl
| ~ sQ10_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f284,f293,f136,f169,f125]) ).
fof(f297,definition,
( sQ34_spl
<=> multiply(sk_c3,inverse(sk_c3)) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f299,plain,
( sQ34_spl
| multiply(sk_c3,inverse(sk_c3)) != sk_c10 ),
inference(component_clause,[status(thm)],[f297]) ).
fof(f300,definition,
( sQ35_spl
<=> multiply(sk_c10,sk_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f302,plain,
( sQ35_spl
| multiply(sk_c10,sk_c9) != sk_c10 ),
inference(component_clause,[status(thm)],[f300]) ).
fof(f303,plain,
( ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ35_spl
| ~ sQ34_spl ),
inference(split_clause,[status(thm)],[f285,f297,f300,f169,f147]) ).
fof(f304,plain,
( sQ34_spl
| ~ sQ11_spl
| multiply(sk_c3,sk_c10) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f148,f299]) ).
fof(f305,plain,
( sQ33_spl
| ~ sQ9_spl
| multiply(sk_c1,sk_c2) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f126,f295]) ).
fof(f306,plain,
( sQ33_spl
| ~ sQ9_spl
| ~ sQ0_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f91,f305]) ).
fof(f307,plain,
( sQ33_spl
| ~ sQ9_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f306]) ).
fof(f308,plain,
( sQ33_spl
| ~ sQ9_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f307]) ).
fof(f312,plain,
! [X0] :
( ~ sQ11_spl
| multiply(identity,X0) = multiply(sk_c10,multiply(sk_c3,X0)) ),
inference(paramodulation,[status(thm)],[f194,f47]) ).
fof(f313,plain,
! [X0] :
( ~ sQ11_spl
| X0 = multiply(sk_c10,multiply(sk_c3,X0)) ),
inference(forward_demodulation,[status(thm)],[f45,f312]) ).
fof(f326,plain,
( ~ sQ11_spl
| sk_c3 = multiply(inverse(sk_c10),identity) ),
inference(paramodulation,[status(thm)],[f194,f196]) ).
fof(f327,plain,
( ~ sQ2_spl
| sk_c9 = multiply(inverse(sk_c4),sk_c10) ),
inference(paramodulation,[status(thm)],[f98,f196]) ).
fof(f329,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f196,f196]) ).
fof(f330,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f46,f196]) ).
fof(f332,plain,
( ~ sQ0_spl
| sk_c2 = multiply(inverse(sk_c1),sk_c10) ),
inference(paramodulation,[status(thm)],[f91,f196]) ).
fof(f334,plain,
! [X0] :
( ~ sQ10_spl
| multiply(sk_c9,X0) = multiply(inverse(sk_c2),multiply(sk_c10,X0)) ),
inference(paramodulation,[status(thm)],[f184,f196]) ).
fof(f335,plain,
( ~ sQ9_spl
| sk_c1 = multiply(inverse(sk_c2),identity) ),
inference(paramodulation,[status(thm)],[f193,f196]) ).
fof(f337,plain,
( ~ sQ12_spl
| sk_c9 = multiply(inverse(sk_c3),sk_c10) ),
inference(paramodulation,[status(thm)],[f159,f196]) ).
fof(f340,plain,
( ~ sQ11_spl
| sk_c3 = inverse(sk_c10) ),
inference(backward_demodulation,[status(thm)],[f341,f326]) ).
fof(f341,plain,
! [X0] : X0 = multiply(X0,identity),
inference(forward_demodulation,[status(thm)],[f329,f330]) ).
fof(f342,plain,
( sQ29_spl
| ~ sQ0_spl
| ~ sQ9_spl
| sk_c2 != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f343,f261]) ).
fof(f343,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| sk_c2 = multiply(sk_c2,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f126,f332]) ).
fof(f344,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ9_spl
| multiply(sk_c9,X0) = multiply(sk_c1,multiply(sk_c10,X0)) ),
inference(backward_demodulation,[status(thm)],[f345,f334]) ).
fof(f345,plain,
( ~ sQ9_spl
| sk_c1 = inverse(sk_c2) ),
inference(forward_demodulation,[status(thm)],[f341,f335]) ).
fof(f347,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| sk_c9 = multiply(sk_c10,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f148,f337]) ).
fof(f348,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f347,f224]) ).
fof(f349,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| sQ21_spl ),
inference(contradiction_clause,[status(thm)],[f348]) ).
fof(f351,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sk_c9 = multiply(sk_c10,sk_c10) ),
inference(backward_demodulation,[status(thm)],[f94,f327]) ).
fof(f357,plain,
inverse(identity) = identity,
inference(paramodulation,[status(thm)],[f46,f341]) ).
fof(f366,plain,
( sQ22_spl
| identity != sk_c10 ),
inference(backward_demodulation,[status(thm)],[f357,f227]) ).
fof(f375,plain,
( ~ sQ7_spl
| sk_c10 = multiply(inverse(sk_c7),sk_c8) ),
inference(paramodulation,[status(thm)],[f118,f196]) ).
fof(f377,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| sk_c10 = multiply(sk_c10,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f122,f375]) ).
fof(f378,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| sk_c10 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f114,f377]) ).
fof(f382,plain,
( sQ35_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| multiply(sk_c10,sk_c10) != sk_c10 ),
inference(backward_demodulation,[status(thm)],[f378,f302]) ).
fof(f387,plain,
( ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| multiply(sk_c4,sk_c10) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f378,f98]) ).
fof(f392,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| sk_c10 = multiply(sk_c10,sk_c10) ),
inference(backward_demodulation,[status(thm)],[f378,f351]) ).
fof(f393,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| multiply(inverse(X0),sk_c10) != sk_c10
| multiply(X0,inverse(X0)) != sk_c10 ),
inference(backward_demodulation,[status(thm)],[f378,f230]) ).
fof(f411,plain,
( sQ35_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c9 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f351,f382]) ).
fof(f412,plain,
( sQ35_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f378,f411]) ).
fof(f413,plain,
( sQ35_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f412]) ).
fof(f414,plain,
( sQ35_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f413]) ).
fof(f456,plain,
( ~ sQ1_spl
| ~ sQ13_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| multiply(sk_c10,sk_c10) != sk_c10
| multiply(sk_c4,inverse(sk_c4)) != sk_c10 ),
inference(paramodulation,[status(thm)],[f94,f393]) ).
fof(f457,definition,
( sQ36_spl
<=> multiply(sk_c10,inverse(sk_c10)) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f459,plain,
( sQ36_spl
| multiply(sk_c10,inverse(sk_c10)) != sk_c10 ),
inference(component_clause,[status(thm)],[f457]) ).
fof(f464,definition,
( sQ38_spl
<=> multiply(sk_c10,sk_c10) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f466,plain,
( sQ38_spl
| multiply(sk_c10,sk_c10) != sk_c10 ),
inference(component_clause,[status(thm)],[f464]) ).
fof(f468,definition,
( sQ39_spl
<=> multiply(sk_c4,inverse(sk_c4)) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f470,plain,
( sQ39_spl
| multiply(sk_c4,inverse(sk_c4)) != sk_c10 ),
inference(component_clause,[status(thm)],[f468]) ).
fof(f471,plain,
( ~ sQ1_spl
| ~ sQ13_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ38_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f456,f468,f464,f113,f121,f117,f169,f93]) ).
fof(f472,plain,
( sQ38_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f392,f466]) ).
fof(f473,plain,
( sQ38_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f472]) ).
fof(f474,plain,
( sQ38_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f473]) ).
fof(f475,plain,
( sQ39_spl
| ~ sQ1_spl
| multiply(sk_c4,sk_c10) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f94,f470]) ).
fof(f476,plain,
( sQ39_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f387,f475]) ).
fof(f477,plain,
( sQ39_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f476]) ).
fof(f478,plain,
( sQ39_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f477]) ).
fof(f482,plain,
( sQ20_spl
| ~ sQ11_spl
| inverse(sk_c3) != sk_c10 ),
inference(backward_demodulation,[status(thm)],[f340,f220]) ).
fof(f484,plain,
( sQ36_spl
| ~ sQ11_spl
| multiply(sk_c10,sk_c3) != sk_c10 ),
inference(backward_demodulation,[status(thm)],[f340,f459]) ).
fof(f485,plain,
( ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f159,f276]) ).
fof(f486,plain,
( ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f485]) ).
fof(f487,plain,
( ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f486]) ).
fof(f494,plain,
( sQ20_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f482,f147,f218]) ).
fof(f496,plain,
( sQ36_spl
| ~ sQ11_spl
| identity != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f194,f484]) ).
fof(f510,plain,
( ~ sQ11_spl
| multiply(sk_c3,sk_c10) = identity ),
inference(paramodulation,[status(thm)],[f340,f46]) ).
fof(f511,plain,
( sQ34_spl
| ~ sQ11_spl
| identity != sk_c10 ),
inference(backward_demodulation,[status(thm)],[f510,f304]) ).
fof(f515,plain,
! [X0] :
( ~ sQ9_spl
| X0 = multiply(sk_c1,multiply(sk_c2,X0)) ),
inference(paramodulation,[status(thm)],[f345,f196]) ).
fof(f516,plain,
( ~ sQ9_spl
| multiply(sk_c1,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f345,f46]) ).
fof(f517,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| sk_c9 = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f526,f347]) ).
fof(f518,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| X0 = multiply(sk_c3,X0) ),
inference(backward_demodulation,[status(thm)],[f526,f313]) ).
fof(f522,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| multiply(sk_c9,X0) = multiply(sk_c1,X0) ),
inference(backward_demodulation,[status(thm)],[f526,f344]) ).
fof(f523,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ9_spl
| ~ sQ0_spl
| X0 = multiply(sk_c3,multiply(sk_c9,X0)) ),
inference(backward_demodulation,[status(thm)],[f526,f185]) ).
fof(f526,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ0_spl
| X0 = multiply(sk_c10,X0) ),
inference(forward_demodulation,[status(thm)],[f188,f515]) ).
fof(f527,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| sk_c10 = identity ),
inference(forward_demodulation,[status(thm)],[f91,f516]) ).
fof(f528,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| sQ32_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f527,f291]) ).
fof(f529,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| sQ32_spl ),
inference(contradiction_clause,[status(thm)],[f528]) ).
fof(f530,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| sQ28_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f517,f269]) ).
fof(f531,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| sQ28_spl ),
inference(contradiction_clause,[status(thm)],[f530]) ).
fof(f539,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| X0 = multiply(sk_c9,X0) ),
inference(forward_demodulation,[status(thm)],[f518,f523]) ).
fof(f544,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ10_spl
| X0 = multiply(sk_c1,X0) ),
inference(forward_demodulation,[status(thm)],[f522,f539]) ).
fof(f557,plain,
( sQ34_spl
| ~ sQ11_spl
| ~ sQ32_spl ),
inference(split_clause,[status(thm)],[f511,f289,f147,f297]) ).
fof(f558,plain,
( sQ36_spl
| ~ sQ11_spl
| ~ sQ32_spl ),
inference(split_clause,[status(thm)],[f496,f289,f147,f457]) ).
fof(f559,plain,
( sQ22_spl
| ~ sQ32_spl ),
inference(split_clause,[status(thm)],[f366,f289,f225]) ).
fof(f560,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| sk_c9 = identity ),
inference(forward_demodulation,[status(thm)],[f527,f517]) ).
fof(f561,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f560,f242]) ).
fof(f562,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ0_spl
| sQ24_spl ),
inference(contradiction_clause,[status(thm)],[f561]) ).
fof(f563,plain,
( ~ sQ28_spl
| ~ sQ12_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ10_spl
| inverse(sk_c1) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f544,f257]) ).
fof(f568,plain,
( ~ sQ28_spl
| ~ sQ12_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ10_spl
| sk_c2 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f126,f563]) ).
fof(f572,plain,
( sQ29_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ28_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f568,f342]) ).
fof(f573,plain,
( sQ29_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ28_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f572]) ).
fof(f574,plain,
( sQ29_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ28_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f573]) ).
fof(f575,plain,
$false,
inference(sat_refutation,[status(thm)],[f96,f100,f104,f108,f112,f116,f120,f124,f128,f129,f130,f131,f132,f133,f134,f135,f139,f140,f141,f142,f143,f144,f145,f146,f150,f151,f152,f153,f154,f155,f156,f157,f161,f162,f163,f164,f165,f166,f167,f168,f181,f214,f228,f243,f247,f251,f262,f266,f273,f282,f292,f296,f303,f308,f349,f414,f471,f474,f478,f487,f494,f529,f531,f557,f558,f559,f562,f574]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP210-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n015.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 20:09:21 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.14/0.42 % Refutation found
% 0.14/0.42 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.45 % Elapsed time: 0.074910 seconds
% 0.14/0.45 % CPU time: 0.322985 seconds
% 0.14/0.45 % Total memory used: 77.561 MB
% 0.14/0.45 % Net memory used: 77.419 MB
%------------------------------------------------------------------------------