%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP317-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 12:33:24 PM UTC 2026
% Result : Unsatisfiable 0.14s 5.43s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 75
% Syntax : Number of formulae : 296 ( 9 unt; 25 def)
% Number of atoms : 863 ( 364 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 990 ( 423 ~; 542 |; 0 &)
% ( 25 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 27 ( 25 usr; 26 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 42 ( 42 !; 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_c8,sk_c7) = sk_c9
| multiply(sk_c8,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c8,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c8,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c8,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c8,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c8,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c9,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c9,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c9,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c9,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c9
| multiply(sk_c2,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c2,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c2,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c9
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c4) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c4) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c4) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c4) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f51,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c4,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f55,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c4,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f56,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c4,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f57,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c4,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f58,negated_conjecture,
! [X3,X4,X5,X6,X1,X2] :
( inverse(X2) != sk_c9
| multiply(X2,sk_c9) != sk_c7
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c9
| inverse(sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c9
| multiply(X5,sk_c9) != X6
| inverse(X6) != sk_c9
| inverse(X5) != X6
| inverse(X4) != sk_c8
| multiply(X4,sk_c8) != sk_c9
| multiply(sk_c9,sk_c7) != sk_c8
| inverse(X3) != sk_c9
| multiply(X3,sk_c9) != sk_c8
| multiply(sk_c8,sk_c9) != sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f59,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f60,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f61,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f62,plain,
( multiply(sk_c8,sk_c7) = sk_c9
| multiply(sk_c8,sk_c9) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f63,plain,
( inverse(sk_c8) = sk_c7
| multiply(sk_c8,sk_c9) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f64,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c8,sk_c9) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f65,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c8,sk_c9) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f66,plain,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c8,sk_c9) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f67,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c8,sk_c9) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f68,plain,
( multiply(sk_c8,sk_c7) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f69,plain,
( inverse(sk_c8) = sk_c7
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f70,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f71,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f72,plain,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f73,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f74,plain,
( multiply(sk_c8,sk_c7) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f75,plain,
( inverse(sk_c8) = sk_c7
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f76,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f77,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f78,plain,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f79,plain,
( inverse(sk_c6) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f82,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c9,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f83,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c9,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f84,plain,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c9,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f85,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c9,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f86,plain,
( multiply(sk_c8,sk_c7) = sk_c9
| multiply(sk_c2,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f87,plain,
( inverse(sk_c8) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f88,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c2,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f89,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f90,plain,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f91,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c2,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f92,plain,
( multiply(sk_c8,sk_c7) = sk_c9
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f93,plain,
( inverse(sk_c8) = sk_c7
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f94,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f95,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f96,plain,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f97,plain,
( inverse(sk_c6) = sk_c9
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f100,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c4) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f101,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c4) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f102,plain,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c4) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f103,plain,
( inverse(sk_c6) = sk_c9
| inverse(sk_c4) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f106,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c3) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f107,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c3) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f108,plain,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c3) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f109,plain,
( inverse(sk_c6) = sk_c9
| inverse(sk_c3) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f112,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c4,sk_c9) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f113,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c4,sk_c9) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f114,plain,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c4,sk_c9) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f115,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c4,sk_c9) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f116,plain,
! [X2] :
( inverse(X2) != sk_c9
| multiply(X2,sk_c9) != sk_c7
| ! [X1] :
( inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c9
| inverse(sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c9
| ! [X5,X6] :
( multiply(X5,sk_c9) != X6
| inverse(X6) != sk_c9
| inverse(X5) != X6
| ! [X4] :
( inverse(X4) != sk_c8
| multiply(X4,sk_c8) != sk_c9
| multiply(sk_c9,sk_c7) != sk_c8
| ! [X3] :
( inverse(X3) != sk_c9
| multiply(X3,sk_c9) != sk_c8
| multiply(sk_c8,sk_c9) != sk_c7 ) ) ) ) ),
inference(miniscoping,[status(thm)],[f58]) ).
fof(f117,plain,
! [X0,X1,X2,X3,X4,X5] :
( inverse(X5) != sk_c9
| multiply(X5,sk_c9) != sk_c7
| inverse(X4) != sk_c8
| multiply(X4,sk_c8) != sk_c9
| inverse(sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c9
| multiply(X2,sk_c9) != X3
| inverse(X3) != sk_c9
| inverse(X2) != X3
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c9
| multiply(sk_c9,sk_c7) != sk_c8
| inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c8
| multiply(sk_c8,sk_c9) != sk_c7 ),
inference(cnf_transformation,[status(thm)],[f116]) ).
fof(f118,definition,
( sQ0_spl
<=> multiply(sk_c8,sk_c9) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f119,plain,
( ~ sQ0_spl
| multiply(sk_c8,sk_c9) = sk_c7 ),
inference(component_clause,[status(thm)],[f118]) ).
fof(f120,plain,
( sQ0_spl
| multiply(sk_c8,sk_c9) != sk_c7 ),
inference(component_clause,[status(thm)],[f118]) ).
fof(f121,definition,
( sQ1_spl
<=> multiply(sk_c8,sk_c7) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f123,plain,
( sQ1_spl
| multiply(sk_c8,sk_c7) != sk_c9 ),
inference(component_clause,[status(thm)],[f121]) ).
fof(f124,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f62,f118,f121]) ).
fof(f125,definition,
( sQ2_spl
<=> inverse(sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f126,plain,
( ~ sQ2_spl
| inverse(sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f125]) ).
fof(f127,plain,
( sQ2_spl
| inverse(sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f125]) ).
fof(f128,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f63,f118,f125]) ).
fof(f129,definition,
( sQ3_spl
<=> multiply(sk_c5,sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f130,plain,
( ~ sQ3_spl
| multiply(sk_c5,sk_c8) = sk_c9 ),
inference(component_clause,[status(thm)],[f129]) ).
fof(f132,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f64,f118,f129]) ).
fof(f133,definition,
( sQ4_spl
<=> inverse(sk_c5) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f134,plain,
( ~ sQ4_spl
| inverse(sk_c5) = sk_c8 ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f65,f118,f133]) ).
fof(f137,definition,
( sQ5_spl
<=> multiply(sk_c6,sk_c9) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f138,plain,
( ~ sQ5_spl
| multiply(sk_c6,sk_c9) = sk_c7 ),
inference(component_clause,[status(thm)],[f137]) ).
fof(f140,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f66,f118,f137]) ).
fof(f141,definition,
( sQ6_spl
<=> inverse(sk_c6) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f142,plain,
( ~ sQ6_spl
| inverse(sk_c6) = sk_c9 ),
inference(component_clause,[status(thm)],[f141]) ).
fof(f144,plain,
( sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f67,f118,f141]) ).
fof(f145,definition,
( sQ7_spl
<=> multiply(sk_c1,sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f146,plain,
( ~ sQ7_spl
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(component_clause,[status(thm)],[f145]) ).
fof(f148,plain,
( sQ1_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f68,f145,f121]) ).
fof(f149,plain,
( sQ2_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f69,f145,f125]) ).
fof(f150,plain,
( sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f70,f145,f129]) ).
fof(f151,plain,
( sQ4_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f71,f145,f133]) ).
fof(f152,plain,
( sQ5_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f72,f145,f137]) ).
fof(f153,plain,
( sQ6_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f73,f145,f141]) ).
fof(f154,definition,
( sQ8_spl
<=> inverse(sk_c1) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f155,plain,
( ~ sQ8_spl
| inverse(sk_c1) = sk_c9 ),
inference(component_clause,[status(thm)],[f154]) ).
fof(f157,plain,
( sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f74,f154,f121]) ).
fof(f158,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f75,f154,f125]) ).
fof(f159,plain,
( sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f76,f154,f129]) ).
fof(f160,plain,
( sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f77,f154,f133]) ).
fof(f161,plain,
( sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f78,f154,f137]) ).
fof(f162,plain,
( sQ6_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f79,f154,f141]) ).
fof(f163,definition,
( sQ9_spl
<=> multiply(sk_c9,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f164,plain,
( ~ sQ9_spl
| multiply(sk_c9,sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f163]) ).
fof(f165,plain,
( sQ9_spl
| multiply(sk_c9,sk_c7) != sk_c8 ),
inference(component_clause,[status(thm)],[f163]) ).
fof(f168,plain,
( sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f82,f163,f129]) ).
fof(f169,plain,
( sQ4_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f83,f163,f133]) ).
fof(f170,plain,
( sQ5_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f84,f163,f137]) ).
fof(f171,plain,
( sQ6_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f85,f163,f141]) ).
fof(f172,definition,
( sQ10_spl
<=> multiply(sk_c2,sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f173,plain,
( ~ sQ10_spl
| multiply(sk_c2,sk_c8) = sk_c9 ),
inference(component_clause,[status(thm)],[f172]) ).
fof(f175,plain,
( sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f86,f172,f121]) ).
fof(f176,plain,
( sQ2_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f87,f172,f125]) ).
fof(f177,plain,
( sQ3_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f88,f172,f129]) ).
fof(f178,plain,
( sQ4_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f89,f172,f133]) ).
fof(f179,plain,
( sQ5_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f90,f172,f137]) ).
fof(f180,plain,
( sQ6_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f91,f172,f141]) ).
fof(f181,definition,
( sQ11_spl
<=> inverse(sk_c2) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f182,plain,
( ~ sQ11_spl
| inverse(sk_c2) = sk_c8 ),
inference(component_clause,[status(thm)],[f181]) ).
fof(f184,plain,
( sQ1_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f92,f181,f121]) ).
fof(f185,plain,
( sQ2_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f93,f181,f125]) ).
fof(f186,plain,
( sQ3_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f94,f181,f129]) ).
fof(f187,plain,
( sQ4_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f95,f181,f133]) ).
fof(f188,plain,
( sQ5_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f96,f181,f137]) ).
fof(f189,plain,
( sQ6_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f97,f181,f141]) ).
fof(f190,definition,
( sQ12_spl
<=> inverse(sk_c4) = sk_c3 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f195,plain,
( sQ3_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f100,f190,f129]) ).
fof(f196,plain,
( sQ4_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f101,f190,f133]) ).
fof(f197,plain,
( sQ5_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f102,f190,f137]) ).
fof(f198,plain,
( sQ6_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f103,f190,f141]) ).
fof(f199,definition,
( sQ13_spl
<=> inverse(sk_c3) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f204,plain,
( sQ3_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f106,f199,f129]) ).
fof(f205,plain,
( sQ4_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f107,f199,f133]) ).
fof(f206,plain,
( sQ5_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f108,f199,f137]) ).
fof(f207,plain,
( sQ6_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f109,f199,f141]) ).
fof(f208,definition,
( sQ14_spl
<=> multiply(sk_c4,sk_c9) = sk_c3 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f209,plain,
( ~ sQ14_spl
| multiply(sk_c4,sk_c9) = sk_c3 ),
inference(component_clause,[status(thm)],[f208]) ).
fof(f213,plain,
( sQ3_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f112,f208,f129]) ).
fof(f214,plain,
( sQ4_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f113,f208,f133]) ).
fof(f215,plain,
( sQ5_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f114,f208,f137]) ).
fof(f216,plain,
( sQ6_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f115,f208,f141]) ).
fof(f217,definition,
! [X0] :
( sQ15_spl
<=> ( inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f218,plain,
! [X0] :
( ~ sQ15_spl
| inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c8 ),
inference(component_clause,[status(thm)],[f217]) ).
fof(f220,definition,
! [X1] :
( sQ16_spl
<=> ( inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f221,plain,
! [X0] :
( ~ sQ16_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c9 ),
inference(component_clause,[status(thm)],[f220]) ).
fof(f223,definition,
! [X2,X3] :
( sQ17_spl
<=> ( multiply(X2,sk_c9) != X3
| inverse(X3) != sk_c9
| inverse(X2) != X3 ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f224,plain,
! [X0,X1] :
( ~ sQ17_spl
| multiply(X0,sk_c9) != X1
| inverse(X1) != sk_c9
| inverse(X0) != X1 ),
inference(component_clause,[status(thm)],[f223]) ).
fof(f226,definition,
! [X5] :
( sQ18_spl
<=> ( inverse(X5) != sk_c9
| multiply(X5,sk_c9) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f227,plain,
! [X0] :
( ~ sQ18_spl
| inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c7 ),
inference(component_clause,[status(thm)],[f226]) ).
fof(f229,plain,
( sQ18_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sQ17_spl
| sQ16_spl
| ~ sQ9_spl
| sQ15_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f117,f118,f217,f163,f220,f223,f121,f125,f226]) ).
fof(f236,plain,
( ~ sQ11_spl
| multiply(sk_c8,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f182,f60]) ).
fof(f241,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f60,f61]) ).
fof(f242,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f59,f241]) ).
fof(f249,plain,
( ~ sQ5_spl
| ~ sQ18_spl
| inverse(sk_c6) != sk_c9 ),
inference(resolution,[status(thm)],[f227,f138]) ).
fof(f250,plain,
( ~ sQ7_spl
| ~ sQ18_spl
| inverse(sk_c1) != sk_c9
| sk_c8 != sk_c7 ),
inference(paramodulation,[status(thm)],[f146,f227]) ).
fof(f256,plain,
( ~ sQ5_spl
| ~ sQ18_spl
| ~ sQ6_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f142,f249]) ).
fof(f257,plain,
( ~ sQ5_spl
| ~ sQ18_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f256]) ).
fof(f258,plain,
( ~ sQ5_spl
| ~ sQ18_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f257]) ).
fof(f260,plain,
( ~ sQ14_spl
| ~ sQ17_spl
| inverse(sk_c3) != sk_c9
| inverse(sk_c4) != sk_c3 ),
inference(resolution,[status(thm)],[f224,f209]) ).
fof(f262,plain,
( ~ sQ17_spl
| inverse(sk_c9) != sk_c9
| inverse(identity) != sk_c9 ),
inference(resolution,[status(thm)],[f224,f59]) ).
fof(f278,plain,
( ~ sQ14_spl
| ~ sQ17_spl
| ~ sQ13_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f260,f190,f199,f223,f208]) ).
fof(f282,definition,
( sQ22_spl
<=> inverse(identity) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f284,plain,
( sQ22_spl
| inverse(identity) != sk_c9 ),
inference(component_clause,[status(thm)],[f282]) ).
fof(f286,definition,
( sQ23_spl
<=> inverse(sk_c9) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f288,plain,
( sQ23_spl
| inverse(sk_c9) != sk_c9 ),
inference(component_clause,[status(thm)],[f286]) ).
fof(f289,plain,
( ~ sQ17_spl
| ~ sQ23_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f262,f282,f286,f223]) ).
fof(f298,plain,
( ~ sQ10_spl
| ~ sQ16_spl
| inverse(sk_c2) != sk_c8 ),
inference(resolution,[status(thm)],[f221,f173]) ).
fof(f299,plain,
( ~ sQ3_spl
| ~ sQ16_spl
| inverse(sk_c5) != sk_c8 ),
inference(resolution,[status(thm)],[f221,f130]) ).
fof(f305,plain,
( ~ sQ10_spl
| ~ sQ16_spl
| ~ sQ11_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f182,f298]) ).
fof(f306,plain,
( ~ sQ10_spl
| ~ sQ16_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f305]) ).
fof(f307,plain,
( ~ sQ10_spl
| ~ sQ16_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f306]) ).
fof(f312,plain,
( ~ sQ7_spl
| ~ sQ15_spl
| inverse(sk_c1) != sk_c9 ),
inference(resolution,[status(thm)],[f218,f146]) ).
fof(f317,plain,
( ~ sQ15_spl
| inverse(identity) != sk_c9
| sk_c9 != sk_c8 ),
inference(paramodulation,[status(thm)],[f59,f218]) ).
fof(f319,plain,
( ~ sQ7_spl
| ~ sQ15_spl
| ~ sQ8_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f155,f312]) ).
fof(f320,plain,
( ~ sQ7_spl
| ~ sQ15_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f319]) ).
fof(f321,plain,
( ~ sQ7_spl
| ~ sQ15_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f320]) ).
fof(f363,plain,
( ~ sQ7_spl
| sk_c9 = multiply(inverse(sk_c1),sk_c8) ),
inference(paramodulation,[status(thm)],[f146,f242]) ).
fof(f371,plain,
( ~ sQ3_spl
| sk_c8 = multiply(inverse(sk_c5),sk_c9) ),
inference(paramodulation,[status(thm)],[f130,f242]) ).
fof(f378,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| sk_c9 = multiply(sk_c9,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f155,f363]) ).
fof(f383,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c8 = multiply(sk_c8,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f134,f371]) ).
fof(f452,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| sk_c8 = multiply(inverse(sk_c9),sk_c9) ),
inference(paramodulation,[status(thm)],[f378,f242]) ).
fof(f457,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| sk_c8 = identity ),
inference(forward_demodulation,[status(thm)],[f60,f452]) ).
fof(f479,plain,
( sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| multiply(identity,sk_c7) != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f457,f123]) ).
fof(f483,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| multiply(identity,sk_c9) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f457,f119]) ).
fof(f493,plain,
( sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c7 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f59,f479]) ).
fof(f495,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c9 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f59,f483]) ).
fof(f502,plain,
( ~ sQ11_spl
| ~ sQ7_spl
| ~ sQ8_spl
| multiply(identity,sk_c2) = identity ),
inference(forward_demodulation,[status(thm)],[f457,f236]) ).
fof(f503,plain,
( ~ sQ11_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c2 = identity ),
inference(forward_demodulation,[status(thm)],[f59,f502]) ).
fof(f504,plain,
( ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| multiply(sk_c2,identity) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f457,f173]) ).
fof(f505,plain,
( ~ sQ11_spl
| ~ sQ7_spl
| ~ sQ8_spl
| inverse(sk_c2) = identity ),
inference(forward_demodulation,[status(thm)],[f457,f182]) ).
fof(f515,plain,
( sQ2_spl
| ~ sQ7_spl
| ~ sQ8_spl
| inverse(identity) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f457,f127]) ).
fof(f526,plain,
( ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ11_spl
| multiply(identity,identity) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f503,f504]) ).
fof(f529,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ11_spl
| identity = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f540,f495]) ).
fof(f540,plain,
( ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ11_spl
| identity = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f59,f526]) ).
fof(f548,plain,
( ~ sQ11_spl
| ~ sQ7_spl
| ~ sQ8_spl
| inverse(identity) = identity ),
inference(forward_demodulation,[status(thm)],[f503,f505]) ).
fof(f557,plain,
( sQ2_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ11_spl
| identity != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f548,f515]) ).
fof(f558,plain,
( sQ2_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ10_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f529,f557]) ).
fof(f559,plain,
( sQ2_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f558]) ).
fof(f560,plain,
( sQ2_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f559]) ).
fof(f600,plain,
( sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| identity != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f529,f493]) ).
fof(f601,plain,
( sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f540,f600]) ).
fof(f602,plain,
( sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f601]) ).
fof(f603,plain,
( sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f602]) ).
fof(f617,definition,
( sQ24_spl
<=> sk_c8 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f619,plain,
( sQ24_spl
| sk_c8 != sk_c7 ),
inference(component_clause,[status(thm)],[f617]) ).
fof(f620,plain,
( ~ sQ7_spl
| ~ sQ18_spl
| ~ sQ8_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f250,f617,f154,f226,f145]) ).
fof(f628,definition,
( sQ27_spl
<=> identity = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f630,plain,
( sQ27_spl
| identity != sk_c7 ),
inference(component_clause,[status(thm)],[f628]) ).
fof(f642,plain,
( sQ22_spl
| ~ sQ11_spl
| ~ sQ7_spl
| ~ sQ8_spl
| identity != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f548,f284]) ).
fof(f643,plain,
( sQ22_spl
| ~ sQ11_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ10_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f540,f642]) ).
fof(f644,plain,
( sQ22_spl
| ~ sQ11_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f643]) ).
fof(f645,plain,
( sQ22_spl
| ~ sQ11_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f644]) ).
fof(f646,plain,
( sQ24_spl
| ~ sQ7_spl
| ~ sQ8_spl
| identity != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f457,f619]) ).
fof(f647,plain,
( sQ24_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f529,f646]) ).
fof(f648,plain,
( sQ24_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f647]) ).
fof(f649,plain,
( sQ24_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f648]) ).
fof(f651,definition,
( sQ30_spl
<=> identity = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f653,plain,
( sQ30_spl
| identity != sk_c8 ),
inference(component_clause,[status(thm)],[f651]) ).
fof(f655,definition,
( sQ31_spl
<=> sk_c9 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f657,plain,
( sQ31_spl
| sk_c9 != sk_c8 ),
inference(component_clause,[status(thm)],[f655]) ).
fof(f658,plain,
( ~ sQ15_spl
| ~ sQ22_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f317,f655,f282,f217]) ).
fof(f686,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c8 != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f383,f120]) ).
fof(f687,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c9 = multiply(inverse(sk_c8),sk_c8) ),
inference(paramodulation,[status(thm)],[f383,f242]) ).
fof(f689,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c9 = identity ),
inference(forward_demodulation,[status(thm)],[f60,f687]) ).
fof(f709,plain,
( ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(identity,sk_c7) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f689,f164]) ).
fof(f710,plain,
( sQ22_spl
| ~ sQ3_spl
| ~ sQ4_spl
| inverse(identity) != identity ),
inference(backward_demodulation,[status(thm)],[f689,f284]) ).
fof(f713,plain,
( ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| inverse(sk_c6) = identity ),
inference(backward_demodulation,[status(thm)],[f689,f142]) ).
fof(f714,plain,
( sQ23_spl
| ~ sQ3_spl
| ~ sQ4_spl
| inverse(sk_c9) != identity ),
inference(backward_demodulation,[status(thm)],[f689,f288]) ).
fof(f716,plain,
( sQ31_spl
| ~ sQ3_spl
| ~ sQ4_spl
| identity != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f689,f657]) ).
fof(f720,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c6,identity) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f689,f138]) ).
fof(f724,plain,
( ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c7 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f59,f709]) ).
fof(f725,plain,
( ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f724,f686]) ).
fof(f726,plain,
( ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f725]) ).
fof(f727,plain,
( sQ23_spl
| ~ sQ3_spl
| ~ sQ4_spl
| inverse(identity) != identity ),
inference(forward_demodulation,[status(thm)],[f689,f714]) ).
fof(f728,plain,
( sQ9_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(identity,sk_c7) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f689,f165]) ).
fof(f729,plain,
( sQ9_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c7 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f59,f728]) ).
fof(f763,plain,
( ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(identity,sk_c6) = identity ),
inference(paramodulation,[status(thm)],[f713,f60]) ).
fof(f765,plain,
( ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f59,f763]) ).
fof(f766,plain,
( ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| inverse(identity) = identity ),
inference(backward_demodulation,[status(thm)],[f765,f713]) ).
fof(f767,plain,
( ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f766,f710]) ).
fof(f768,plain,
( ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f767]) ).
fof(f797,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| multiply(identity,identity) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f765,f720]) ).
fof(f798,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| identity = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f59,f797]) ).
fof(f799,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| sQ27_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f798,f630]) ).
fof(f800,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| sQ27_spl ),
inference(contradiction_clause,[status(thm)],[f799]) ).
fof(f807,plain,
( sQ9_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| identity != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f798,f729]) ).
fof(f808,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| inverse(sk_c8) = identity ),
inference(backward_demodulation,[status(thm)],[f798,f126]) ).
fof(f820,plain,
( ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f766,f727]) ).
fof(f821,plain,
( ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sQ23_spl ),
inference(contradiction_clause,[status(thm)],[f820]) ).
fof(f829,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| multiply(identity,sk_c8) = identity ),
inference(paramodulation,[status(thm)],[f808,f60]) ).
fof(f831,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| sk_c8 = identity ),
inference(forward_demodulation,[status(thm)],[f59,f829]) ).
fof(f832,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f831,f653]) ).
fof(f833,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| sQ30_spl ),
inference(contradiction_clause,[status(thm)],[f832]) ).
fof(f842,plain,
( sQ9_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f807,f651,f141,f137,f133,f129,f163]) ).
fof(f843,plain,
( sQ31_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f716,f651,f133,f129,f655]) ).
fof(f892,plain,
( ~ sQ3_spl
| ~ sQ16_spl
| ~ sQ4_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f134,f299]) ).
fof(f893,plain,
( ~ sQ3_spl
| ~ sQ16_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f892]) ).
fof(f894,plain,
( ~ sQ3_spl
| ~ sQ16_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f893]) ).
fof(f895,plain,
$false,
inference(sat_refutation,[status(thm)],[f124,f128,f132,f136,f140,f144,f148,f149,f150,f151,f152,f153,f157,f158,f159,f160,f161,f162,f168,f169,f170,f171,f175,f176,f177,f178,f179,f180,f184,f185,f186,f187,f188,f189,f195,f196,f197,f198,f204,f205,f206,f207,f213,f214,f215,f216,f229,f258,f278,f289,f307,f321,f560,f603,f620,f645,f649,f658,f726,f768,f800,f821,f833,f842,f843,f894]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP317-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.38 % Computer : n018.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Sun Sep 20 20:11:19 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.39 % Drodi V4.1.1
% 0.14/5.43 % Refutation found
% 0.14/5.43 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/5.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/5.46 % Elapsed time: 0.063333 seconds
% 0.14/5.46 % CPU time: 0.269365 seconds
% 0.14/5.46 % Total memory used: 101.442 MB
% 0.14/5.46 % Net memory used: 101.243 MB
%------------------------------------------------------------------------------