%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP369-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 12:33:32 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.42s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 70
% Syntax : Number of formulae : 336 ( 10 unt; 26 def)
% Number of atoms : 1118 ( 397 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 1449 ( 667 ~; 756 |; 0 &)
% ( 26 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 28 ( 26 usr; 27 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 72 ( 72 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c7,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c7,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c7,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c7,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c7,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c9,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c9,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c9,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c9,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c9,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c9,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c9,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c1,sk_c9) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c1,sk_c9) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c1,sk_c9) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c3,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c3,sk_c7) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,negated_conjecture,
! [X4,X5,X6,X1,X2,X3] :
( inverse(X3) != sk_c9
| multiply(X3,sk_c9) != sk_c7
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c9
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c7
| inverse(X6) != sk_c7
| multiply(X6,sk_c7) != sk_c9
| inverse(X5) != sk_c9
| multiply(X5,sk_c9) != X4
| multiply(sk_c9,X4) != sk_c8
| multiply(sk_c7,sk_c9) != sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f48,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f49,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f50,plain,
( inverse(sk_c8) = sk_c7
| multiply(sk_c7,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f51,plain,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c7,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f52,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c7,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f53,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c7,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f54,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c7,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f57,plain,
( inverse(sk_c8) = sk_c7
| multiply(sk_c9,sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f58,plain,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c9,sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f59,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c9,sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f60,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c9,sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f61,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c9,sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f62,plain,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c9,sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f63,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c9,sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f64,plain,
( inverse(sk_c8) = sk_c7
| multiply(sk_c1,sk_c9) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f65,plain,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c1,sk_c9) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f66,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f67,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f68,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f69,plain,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c1,sk_c9) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f70,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f71,plain,
( inverse(sk_c8) = sk_c7
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f72,plain,
( multiply(sk_c4,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f73,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f74,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f75,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f76,plain,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f77,plain,
( inverse(sk_c6) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f78,plain,
( inverse(sk_c8) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f79,plain,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f80,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f81,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c3,sk_c7) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f82,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c3,sk_c7) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f83,plain,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c3,sk_c7) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f84,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c3,sk_c7) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f85,plain,
( inverse(sk_c8) = sk_c7
| inverse(sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f86,plain,
( multiply(sk_c4,sk_c8) = sk_c7
| inverse(sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f87,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f88,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f89,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f90,plain,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f91,plain,
( inverse(sk_c6) = sk_c9
| inverse(sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f92,plain,
! [X3] :
( inverse(X3) != sk_c9
| multiply(X3,sk_c9) != sk_c7
| ! [X2] :
( inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c9
| ! [X1] :
( inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c7
| ! [X6] :
( inverse(X6) != sk_c7
| multiply(X6,sk_c7) != sk_c9
| ! [X5] :
( inverse(X5) != sk_c9
| ! [X4] :
( multiply(X5,sk_c9) != X4
| multiply(sk_c9,X4) != sk_c8
| multiply(sk_c7,sk_c9) != sk_c8 ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f46]) ).
fof(f93,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(X3) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c7
| inverse(X2) != sk_c7
| multiply(X2,sk_c7) != sk_c9
| inverse(X1) != sk_c9
| multiply(X1,sk_c9) != X0
| multiply(sk_c9,X0) != sk_c8
| multiply(sk_c7,sk_c9) != sk_c8 ),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f94,definition,
( sQ0_spl
<=> multiply(sk_c7,sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f95,plain,
( ~ sQ0_spl
| multiply(sk_c7,sk_c9) = sk_c8 ),
inference(component_clause,[status(thm)],[f94]) ).
fof(f96,plain,
( sQ0_spl
| multiply(sk_c7,sk_c9) != sk_c8 ),
inference(component_clause,[status(thm)],[f94]) ).
fof(f97,definition,
( sQ1_spl
<=> inverse(sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f98,plain,
( ~ sQ1_spl
| inverse(sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f97]) ).
fof(f99,plain,
( sQ1_spl
| inverse(sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f97]) ).
fof(f100,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f50,f94,f97]) ).
fof(f101,definition,
( sQ2_spl
<=> multiply(sk_c4,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f102,plain,
( ~ sQ2_spl
| multiply(sk_c4,sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f101]) ).
fof(f104,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f51,f94,f101]) ).
fof(f105,definition,
( sQ3_spl
<=> inverse(sk_c4) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f106,plain,
( ~ sQ3_spl
| inverse(sk_c4) = sk_c8 ),
inference(component_clause,[status(thm)],[f105]) ).
fof(f108,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f52,f94,f105]) ).
fof(f109,definition,
( sQ4_spl
<=> multiply(sk_c5,sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f110,plain,
( ~ sQ4_spl
| multiply(sk_c5,sk_c8) = sk_c9 ),
inference(component_clause,[status(thm)],[f109]) ).
fof(f112,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f53,f94,f109]) ).
fof(f113,definition,
( sQ5_spl
<=> inverse(sk_c5) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f114,plain,
( ~ sQ5_spl
| inverse(sk_c5) = sk_c8 ),
inference(component_clause,[status(thm)],[f113]) ).
fof(f116,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f54,f94,f113]) ).
fof(f117,definition,
( sQ6_spl
<=> multiply(sk_c6,sk_c9) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f118,plain,
( ~ sQ6_spl
| multiply(sk_c6,sk_c9) = sk_c7 ),
inference(component_clause,[status(thm)],[f117]) ).
fof(f121,definition,
( sQ7_spl
<=> inverse(sk_c6) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f122,plain,
( ~ sQ7_spl
| inverse(sk_c6) = sk_c9 ),
inference(component_clause,[status(thm)],[f121]) ).
fof(f125,definition,
( sQ8_spl
<=> multiply(sk_c9,sk_c2) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f126,plain,
( ~ sQ8_spl
| multiply(sk_c9,sk_c2) = sk_c8 ),
inference(component_clause,[status(thm)],[f125]) ).
fof(f128,plain,
( sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f57,f125,f97]) ).
fof(f129,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f58,f125,f101]) ).
fof(f130,plain,
( sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f59,f125,f105]) ).
fof(f131,plain,
( sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f60,f125,f109]) ).
fof(f132,plain,
( sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f61,f125,f113]) ).
fof(f133,plain,
( sQ6_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f62,f125,f117]) ).
fof(f134,plain,
( sQ7_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f63,f125,f121]) ).
fof(f135,definition,
( sQ9_spl
<=> multiply(sk_c1,sk_c9) = sk_c2 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f136,plain,
( ~ sQ9_spl
| multiply(sk_c1,sk_c9) = sk_c2 ),
inference(component_clause,[status(thm)],[f135]) ).
fof(f138,plain,
( sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f64,f135,f97]) ).
fof(f139,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f65,f135,f101]) ).
fof(f140,plain,
( sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f66,f135,f105]) ).
fof(f141,plain,
( sQ4_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f67,f135,f109]) ).
fof(f142,plain,
( sQ5_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f68,f135,f113]) ).
fof(f143,plain,
( sQ6_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f69,f135,f117]) ).
fof(f144,plain,
( sQ7_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f70,f135,f121]) ).
fof(f145,definition,
( sQ10_spl
<=> inverse(sk_c1) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f146,plain,
( ~ sQ10_spl
| inverse(sk_c1) = sk_c9 ),
inference(component_clause,[status(thm)],[f145]) ).
fof(f148,plain,
( sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f71,f145,f97]) ).
fof(f149,plain,
( sQ2_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f72,f145,f101]) ).
fof(f150,plain,
( sQ3_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f73,f145,f105]) ).
fof(f151,plain,
( sQ4_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f74,f145,f109]) ).
fof(f152,plain,
( sQ5_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f75,f145,f113]) ).
fof(f153,plain,
( sQ6_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f76,f145,f117]) ).
fof(f154,plain,
( sQ7_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f77,f145,f121]) ).
fof(f155,definition,
( sQ11_spl
<=> multiply(sk_c3,sk_c7) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f156,plain,
( ~ sQ11_spl
| multiply(sk_c3,sk_c7) = sk_c9 ),
inference(component_clause,[status(thm)],[f155]) ).
fof(f157,plain,
( sQ11_spl
| multiply(sk_c3,sk_c7) != sk_c9 ),
inference(component_clause,[status(thm)],[f155]) ).
fof(f158,plain,
( sQ1_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f78,f155,f97]) ).
fof(f159,plain,
( sQ2_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f79,f155,f101]) ).
fof(f160,plain,
( sQ3_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f80,f155,f105]) ).
fof(f161,plain,
( sQ4_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f81,f155,f109]) ).
fof(f162,plain,
( sQ5_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f82,f155,f113]) ).
fof(f163,plain,
( sQ6_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f83,f155,f117]) ).
fof(f164,plain,
( sQ7_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f84,f155,f121]) ).
fof(f165,definition,
( sQ12_spl
<=> inverse(sk_c3) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f166,plain,
( ~ sQ12_spl
| inverse(sk_c3) = sk_c7 ),
inference(component_clause,[status(thm)],[f165]) ).
fof(f168,plain,
( sQ1_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f85,f165,f97]) ).
fof(f169,plain,
( sQ2_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f86,f165,f101]) ).
fof(f170,plain,
( sQ3_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f87,f165,f105]) ).
fof(f171,plain,
( sQ4_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f88,f165,f109]) ).
fof(f172,plain,
( sQ5_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f89,f165,f113]) ).
fof(f173,plain,
( sQ6_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f90,f165,f117]) ).
fof(f174,plain,
( sQ7_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f91,f165,f121]) ).
fof(f175,definition,
! [X0,X1] :
( sQ13_spl
<=> ( inverse(X1) != sk_c9
| multiply(X1,sk_c9) != X0
| multiply(sk_c9,X0) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f176,plain,
! [X0,X1] :
( ~ sQ13_spl
| inverse(X1) != sk_c9
| multiply(X1,sk_c9) != X0
| multiply(sk_c9,X0) != sk_c8 ),
inference(component_clause,[status(thm)],[f175]) ).
fof(f178,definition,
! [X2] :
( sQ14_spl
<=> ( inverse(X2) != sk_c7
| multiply(X2,sk_c7) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f179,plain,
! [X0] :
( ~ sQ14_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c9 ),
inference(component_clause,[status(thm)],[f178]) ).
fof(f181,definition,
! [X3] :
( sQ15_spl
<=> ( inverse(X3) != sk_c8
| multiply(X3,sk_c8) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f182,plain,
! [X0] :
( ~ sQ15_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f181]) ).
fof(f184,definition,
! [X4] :
( sQ16_spl
<=> ( inverse(X4) != sk_c8
| multiply(X4,sk_c8) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f185,plain,
! [X0] :
( ~ sQ16_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c9 ),
inference(component_clause,[status(thm)],[f184]) ).
fof(f187,definition,
! [X5] :
( sQ17_spl
<=> ( inverse(X5) != sk_c9
| multiply(X5,sk_c9) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f188,plain,
! [X0] :
( ~ sQ17_spl
| inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c7 ),
inference(component_clause,[status(thm)],[f187]) ).
fof(f190,plain,
( sQ17_spl
| sQ16_spl
| sQ15_spl
| ~ sQ1_spl
| sQ14_spl
| sQ13_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f93,f94,f175,f178,f97,f181,f184,f187]) ).
fof(f197,plain,
( ~ sQ3_spl
| multiply(sk_c8,sk_c4) = identity ),
inference(paramodulation,[status(thm)],[f106,f48]) ).
fof(f198,plain,
( ~ sQ5_spl
| multiply(sk_c8,sk_c5) = identity ),
inference(paramodulation,[status(thm)],[f114,f48]) ).
fof(f199,plain,
( ~ sQ7_spl
| multiply(sk_c9,sk_c6) = identity ),
inference(paramodulation,[status(thm)],[f122,f48]) ).
fof(f200,plain,
( ~ sQ10_spl
| multiply(sk_c9,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f146,f48]) ).
fof(f201,plain,
( ~ sQ12_spl
| multiply(sk_c7,sk_c3) = identity ),
inference(paramodulation,[status(thm)],[f166,f48]) ).
fof(f202,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f48,f49]) ).
fof(f203,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f47,f202]) ).
fof(f205,plain,
! [X0] :
( ~ sQ6_spl
| multiply(sk_c7,X0) = multiply(sk_c6,multiply(sk_c9,X0)) ),
inference(paramodulation,[status(thm)],[f118,f49]) ).
fof(f206,plain,
! [X0] :
( ~ sQ4_spl
| multiply(sk_c9,X0) = multiply(sk_c5,multiply(sk_c8,X0)) ),
inference(paramodulation,[status(thm)],[f110,f49]) ).
fof(f207,plain,
! [X0] :
( ~ sQ2_spl
| multiply(sk_c7,X0) = multiply(sk_c4,multiply(sk_c8,X0)) ),
inference(paramodulation,[status(thm)],[f102,f49]) ).
fof(f209,plain,
! [X0] :
( ~ sQ3_spl
| multiply(identity,X0) = multiply(sk_c8,multiply(sk_c4,X0)) ),
inference(paramodulation,[status(thm)],[f197,f49]) ).
fof(f210,plain,
! [X0] :
( ~ sQ3_spl
| X0 = multiply(sk_c8,multiply(sk_c4,X0)) ),
inference(forward_demodulation,[status(thm)],[f47,f209]) ).
fof(f211,plain,
( ~ sQ6_spl
| ~ sQ17_spl
| inverse(sk_c6) != sk_c9 ),
inference(resolution,[status(thm)],[f188,f118]) ).
fof(f215,plain,
( ~ sQ17_spl
| inverse(identity) != sk_c9
| sk_c9 != sk_c7 ),
inference(paramodulation,[status(thm)],[f47,f188]) ).
fof(f216,plain,
( ~ sQ9_spl
| ~ sQ17_spl
| inverse(sk_c1) != sk_c9
| sk_c2 != sk_c7 ),
inference(paramodulation,[status(thm)],[f136,f188]) ).
fof(f218,plain,
( ~ sQ6_spl
| ~ sQ17_spl
| ~ sQ7_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f122,f211]) ).
fof(f219,plain,
( ~ sQ6_spl
| ~ sQ17_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f218]) ).
fof(f220,plain,
( ~ sQ6_spl
| ~ sQ17_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f219]) ).
fof(f221,plain,
! [X0] :
( ~ sQ13_spl
| inverse(X0) != sk_c9
| multiply(sk_c9,multiply(X0,sk_c9)) != sk_c8 ),
inference(destructive_equality_resolution,[status(thm)],[f176]) ).
fof(f222,plain,
( ~ sQ4_spl
| ~ sQ16_spl
| inverse(sk_c5) != sk_c8 ),
inference(resolution,[status(thm)],[f185,f110]) ).
fof(f226,plain,
( ~ sQ16_spl
| inverse(identity) != sk_c8
| sk_c8 != sk_c9 ),
inference(paramodulation,[status(thm)],[f47,f185]) ).
fof(f228,plain,
( ~ sQ4_spl
| ~ sQ16_spl
| ~ sQ5_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f114,f222]) ).
fof(f229,plain,
( ~ sQ4_spl
| ~ sQ16_spl
| ~ sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f228]) ).
fof(f230,plain,
( ~ sQ4_spl
| ~ sQ16_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f229]) ).
fof(f231,plain,
( ~ sQ2_spl
| ~ sQ15_spl
| inverse(sk_c4) != sk_c8 ),
inference(resolution,[status(thm)],[f182,f102]) ).
fof(f235,plain,
( ~ sQ15_spl
| inverse(identity) != sk_c8
| sk_c8 != sk_c7 ),
inference(paramodulation,[status(thm)],[f47,f182]) ).
fof(f237,plain,
( ~ sQ2_spl
| ~ sQ15_spl
| ~ sQ3_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f106,f231]) ).
fof(f238,plain,
( ~ sQ2_spl
| ~ sQ15_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f237]) ).
fof(f239,plain,
( ~ sQ2_spl
| ~ sQ15_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f238]) ).
fof(f240,plain,
( ~ sQ11_spl
| ~ sQ14_spl
| inverse(sk_c3) != sk_c7 ),
inference(resolution,[status(thm)],[f179,f156]) ).
fof(f245,plain,
( ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f166,f240]) ).
fof(f246,plain,
( ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f245]) ).
fof(f247,plain,
( ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f246]) ).
fof(f248,plain,
( ~ sQ1_spl
| multiply(sk_c7,sk_c8) = identity ),
inference(paramodulation,[status(thm)],[f98,f48]) ).
fof(f254,plain,
! [X0] :
( ~ sQ12_spl
| multiply(identity,X0) = multiply(sk_c7,multiply(sk_c3,X0)) ),
inference(paramodulation,[status(thm)],[f201,f49]) ).
fof(f255,plain,
! [X0] :
( ~ sQ12_spl
| X0 = multiply(sk_c7,multiply(sk_c3,X0)) ),
inference(forward_demodulation,[status(thm)],[f47,f254]) ).
fof(f258,plain,
( ~ sQ6_spl
| ~ sQ13_spl
| inverse(sk_c6) != sk_c9
| multiply(sk_c9,sk_c7) != sk_c8 ),
inference(paramodulation,[status(thm)],[f118,f221]) ).
fof(f261,plain,
( ~ sQ9_spl
| ~ sQ13_spl
| inverse(sk_c1) != sk_c9
| multiply(sk_c9,sk_c2) != sk_c8 ),
inference(paramodulation,[status(thm)],[f136,f221]) ).
fof(f263,definition,
( sQ18_spl
<=> multiply(sk_c9,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f265,plain,
( sQ18_spl
| multiply(sk_c9,sk_c7) != sk_c8 ),
inference(component_clause,[status(thm)],[f263]) ).
fof(f266,plain,
( ~ sQ6_spl
| ~ sQ13_spl
| ~ sQ7_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f258,f263,f121,f175,f117]) ).
fof(f277,definition,
( sQ22_spl
<=> inverse(identity) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f279,plain,
( sQ22_spl
| inverse(identity) != sk_c9 ),
inference(component_clause,[status(thm)],[f277]) ).
fof(f281,plain,
( ~ sQ9_spl
| ~ sQ13_spl
| ~ sQ10_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f261,f125,f145,f175,f135]) ).
fof(f295,plain,
! [X0] :
( ~ sQ5_spl
| multiply(identity,X0) = multiply(sk_c8,multiply(sk_c5,X0)) ),
inference(paramodulation,[status(thm)],[f198,f49]) ).
fof(f298,plain,
! [X0] :
( ~ sQ5_spl
| X0 = multiply(sk_c8,multiply(sk_c5,X0)) ),
inference(forward_demodulation,[status(thm)],[f47,f295]) ).
fof(f299,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| multiply(sk_c7,sk_c6) = multiply(sk_c6,identity) ),
inference(paramodulation,[status(thm)],[f199,f205]) ).
fof(f300,plain,
! [X0] :
( ~ sQ7_spl
| multiply(identity,X0) = multiply(sk_c9,multiply(sk_c6,X0)) ),
inference(paramodulation,[status(thm)],[f199,f49]) ).
fof(f301,plain,
! [X0] :
( ~ sQ7_spl
| X0 = multiply(sk_c9,multiply(sk_c6,X0)) ),
inference(forward_demodulation,[status(thm)],[f47,f300]) ).
fof(f302,plain,
! [X0] :
( ~ sQ1_spl
| multiply(identity,X0) = multiply(sk_c7,multiply(sk_c8,X0)) ),
inference(paramodulation,[status(thm)],[f248,f49]) ).
fof(f303,plain,
! [X0] :
( ~ sQ1_spl
| X0 = multiply(sk_c7,multiply(sk_c8,X0)) ),
inference(forward_demodulation,[status(thm)],[f47,f302]) ).
fof(f305,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| sk_c8 = multiply(sk_c8,sk_c7) ),
inference(paramodulation,[status(thm)],[f102,f210]) ).
fof(f322,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| sk_c8 = multiply(sk_c8,sk_c9) ),
inference(paramodulation,[status(thm)],[f110,f298]) ).
fof(f327,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| multiply(sk_c7,sk_c9) = multiply(sk_c4,sk_c8) ),
inference(paramodulation,[status(thm)],[f322,f207]) ).
fof(f328,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| multiply(sk_c9,sk_c9) = multiply(sk_c5,sk_c8) ),
inference(paramodulation,[status(thm)],[f322,f206]) ).
fof(f330,plain,
( sQ0_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| sk_c7 != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f331,f96]) ).
fof(f331,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| multiply(sk_c7,sk_c9) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f102,f327]) ).
fof(f332,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| multiply(sk_c9,sk_c9) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f110,f328]) ).
fof(f339,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ6_spl
| multiply(sk_c7,multiply(sk_c6,X0)) = multiply(sk_c6,X0) ),
inference(paramodulation,[status(thm)],[f301,f205]) ).
fof(f342,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| sk_c9 = multiply(sk_c7,sk_c8) ),
inference(paramodulation,[status(thm)],[f322,f303]) ).
fof(f343,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c7 = multiply(sk_c7,sk_c8) ),
inference(paramodulation,[status(thm)],[f305,f303]) ).
fof(f347,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| sk_c4 = multiply(sk_c7,identity) ),
inference(paramodulation,[status(thm)],[f197,f303]) ).
fof(f355,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| multiply(sk_c9,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f359,f47]) ).
fof(f359,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| sk_c9 = identity ),
inference(forward_demodulation,[status(thm)],[f248,f342]) ).
fof(f360,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c7 = identity ),
inference(forward_demodulation,[status(thm)],[f248,f343]) ).
fof(f363,plain,
( sQ0_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c9 != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f383,f330]) ).
fof(f364,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| X0 = multiply(sk_c9,multiply(sk_c3,X0)) ),
inference(backward_demodulation,[status(thm)],[f383,f255]) ).
fof(f370,plain,
( sQ11_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| multiply(sk_c3,sk_c9) != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f383,f157]) ).
fof(f372,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| multiply(sk_c4,sk_c8) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f383,f102]) ).
fof(f383,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sk_c7 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f359,f360]) ).
fof(f398,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sk_c4 = multiply(sk_c9,identity) ),
inference(forward_demodulation,[status(thm)],[f383,f347]) ).
fof(f399,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sk_c4 = multiply(sk_c9,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f359,f398]) ).
fof(f402,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sk_c4 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f332,f399]) ).
fof(f411,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| X0 = multiply(sk_c6,X0) ),
inference(backward_demodulation,[status(thm)],[f355,f301]) ).
fof(f430,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| X0 = multiply(sk_c3,X0) ),
inference(forward_demodulation,[status(thm)],[f355,f364]) ).
fof(f438,plain,
( sQ11_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ12_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f430,f370]) ).
fof(f439,plain,
( sQ11_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f438]) ).
fof(f440,plain,
( sQ11_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f439]) ).
fof(f441,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| multiply(sk_c9,sk_c8) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f402,f372]) ).
fof(f444,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sk_c8 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f355,f441]) ).
fof(f476,plain,
( sQ18_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| sk_c7 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f355,f265]) ).
fof(f477,plain,
( sQ18_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c9 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f383,f476]) ).
fof(f478,plain,
( sQ18_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f444,f477]) ).
fof(f479,plain,
( sQ18_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f478]) ).
fof(f480,plain,
( sQ18_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f479]) ).
fof(f482,definition,
( sQ23_spl
<=> sk_c7 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f484,plain,
( sQ23_spl
| sk_c7 != sk_c7 ),
inference(component_clause,[status(thm)],[f482]) ).
fof(f486,definition,
( sQ24_spl
<=> sk_c9 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f497,definition,
( sQ27_spl
<=> sk_c8 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f498,plain,
( ~ sQ27_spl
| sk_c8 = sk_c7 ),
inference(component_clause,[status(thm)],[f497]) ).
fof(f499,plain,
( sQ27_spl
| sk_c8 != sk_c7 ),
inference(component_clause,[status(thm)],[f497]) ).
fof(f500,definition,
( sQ28_spl
<=> inverse(identity) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f502,plain,
( sQ28_spl
| inverse(identity) != sk_c8 ),
inference(component_clause,[status(thm)],[f500]) ).
fof(f503,plain,
( ~ sQ15_spl
| ~ sQ28_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f235,f497,f500,f181]) ).
fof(f505,plain,
( sQ23_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f484]) ).
fof(f506,plain,
sQ23_spl,
inference(contradiction_clause,[status(thm)],[f505]) ).
fof(f511,definition,
( sQ30_spl
<=> sk_c8 = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f513,plain,
( sQ30_spl
| sk_c8 != sk_c9 ),
inference(component_clause,[status(thm)],[f511]) ).
fof(f514,plain,
( ~ sQ16_spl
| ~ sQ28_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f226,f511,f500,f184]) ).
fof(f526,plain,
( ~ sQ9_spl
| sk_c9 = multiply(inverse(sk_c1),sk_c2) ),
inference(paramodulation,[status(thm)],[f136,f203]) ).
fof(f527,plain,
( ~ sQ8_spl
| sk_c2 = multiply(inverse(sk_c9),sk_c8) ),
inference(paramodulation,[status(thm)],[f126,f203]) ).
fof(f528,plain,
( ~ sQ0_spl
| sk_c9 = multiply(inverse(sk_c7),sk_c8) ),
inference(paramodulation,[status(thm)],[f95,f203]) ).
fof(f529,plain,
( ~ sQ11_spl
| sk_c7 = multiply(inverse(sk_c3),sk_c9) ),
inference(paramodulation,[status(thm)],[f156,f203]) ).
fof(f532,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| sk_c9 = multiply(sk_c9,sk_c2) ),
inference(forward_demodulation,[status(thm)],[f146,f526]) ).
fof(f533,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c9 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f126,f532]) ).
fof(f534,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f533,f513]) ).
fof(f535,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sQ30_spl ),
inference(contradiction_clause,[status(thm)],[f534]) ).
fof(f536,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| sk_c7 = multiply(sk_c7,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f166,f529]) ).
fof(f537,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| sk_c7 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f95,f536]) ).
fof(f538,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| sQ27_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f537,f499]) ).
fof(f539,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| sQ27_spl ),
inference(contradiction_clause,[status(thm)],[f538]) ).
fof(f543,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| sk_c9 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f411,f118]) ).
fof(f544,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| multiply(sk_c7,X0) = multiply(sk_c9,X0) ),
inference(backward_demodulation,[status(thm)],[f411,f205]) ).
fof(f545,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| multiply(sk_c7,sk_c6) = identity ),
inference(forward_demodulation,[status(thm)],[f411,f299]) ).
fof(f546,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| multiply(sk_c7,X0) = multiply(sk_c6,X0) ),
inference(forward_demodulation,[status(thm)],[f411,f339]) ).
fof(f547,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| sk_c6 = identity ),
inference(backward_demodulation,[status(thm)],[f554,f545]) ).
fof(f554,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| multiply(sk_c7,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f411,f546]) ).
fof(f582,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f444,f363]) ).
fof(f583,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f582]) ).
fof(f584,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sk_c9 = multiply(inverse(sk_c8),sk_c8) ),
inference(backward_demodulation,[status(thm)],[f537,f528]) ).
fof(f589,plain,
( sQ28_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| inverse(identity) != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f533,f502]) ).
fof(f599,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ0_spl
| multiply(sk_c8,sk_c3) = identity ),
inference(forward_demodulation,[status(thm)],[f537,f201]) ).
fof(f600,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| multiply(sk_c9,sk_c3) = identity ),
inference(forward_demodulation,[status(thm)],[f533,f599]) ).
fof(f609,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ0_spl
| inverse(sk_c3) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f537,f166]) ).
fof(f610,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| inverse(sk_c3) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f533,f609]) ).
fof(f613,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c2 = multiply(inverse(sk_c9),sk_c9) ),
inference(forward_demodulation,[status(thm)],[f533,f527]) ).
fof(f615,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| multiply(sk_c9,sk_c3) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f621,f600]) ).
fof(f616,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c9,sk_c1) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f621,f200]) ).
fof(f618,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c2,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f621,f47]) ).
fof(f620,plain,
( sQ22_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| inverse(sk_c2) != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f621,f279]) ).
fof(f621,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c2 = identity ),
inference(forward_demodulation,[status(thm)],[f48,f613]) ).
fof(f622,plain,
( ~ sQ27_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c9 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f533,f498]) ).
fof(f626,plain,
( sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| inverse(sk_c9) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f533,f99]) ).
fof(f627,plain,
( sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| inverse(sk_c9) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f537,f626]) ).
fof(f628,plain,
( sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| inverse(sk_c9) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f533,f627]) ).
fof(f629,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sk_c9 = identity ),
inference(forward_demodulation,[status(thm)],[f48,f584]) ).
fof(f635,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c9 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f621,f629]) ).
fof(f647,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| multiply(sk_c9,sk_c3) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f635,f615]) ).
fof(f648,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| multiply(sk_c9,sk_c1) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f635,f616]) ).
fof(f652,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sk_c1 = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f660,f648]) ).
fof(f653,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c3 = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f660,f647]) ).
fof(f660,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| multiply(sk_c9,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f635,f618]) ).
fof(f662,plain,
( sQ22_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| inverse(sk_c9) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f635,f620]) ).
fof(f673,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| inverse(sk_c9) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f652,f146]) ).
fof(f675,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| inverse(sk_c9) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f653,f610]) ).
fof(f681,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f673,f628]) ).
fof(f682,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f681]) ).
fof(f756,plain,
( ~ sQ17_spl
| ~ sQ22_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f215,f486,f277,f187]) ).
fof(f757,definition,
( sQ32_spl
<=> sk_c2 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f760,plain,
( ~ sQ9_spl
| ~ sQ17_spl
| ~ sQ10_spl
| ~ sQ32_spl ),
inference(split_clause,[status(thm)],[f216,f757,f145,f187,f135]) ).
fof(f766,plain,
( sQ22_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f675,f662]) ).
fof(f767,plain,
( sQ22_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f766]) ).
fof(f768,plain,
( sQ22_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f767]) ).
fof(f787,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(sk_c7,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f360,f47]) ).
fof(f801,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| X0 = multiply(sk_c9,X0) ),
inference(forward_demodulation,[status(thm)],[f787,f544]) ).
fof(f802,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c6 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f360,f547]) ).
fof(f804,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c6 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f543,f802]) ).
fof(f820,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| inverse(sk_c9) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f804,f122]) ).
fof(f907,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c9) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f543,f179]) ).
fof(f908,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f543,f907]) ).
fof(f968,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ14_spl
| inverse(sk_c9) != sk_c9 ),
inference(resolution,[status(thm)],[f908,f801]) ).
fof(f972,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ14_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f820,f968]) ).
fof(f973,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ14_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f972]) ).
fof(f974,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f973]) ).
fof(f975,plain,
( sQ28_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f589,f277,f125,f145,f135,f500]) ).
fof(f1001,plain,
( ~ sQ27_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f622,f486,f125,f145,f135,f497]) ).
fof(f1038,plain,
$false,
inference(sat_refutation,[status(thm)],[f100,f104,f108,f112,f116,f128,f129,f130,f131,f132,f133,f134,f138,f139,f140,f141,f142,f143,f144,f148,f149,f150,f151,f152,f153,f154,f158,f159,f160,f161,f162,f163,f164,f168,f169,f170,f171,f172,f173,f174,f190,f220,f230,f239,f247,f266,f281,f440,f480,f503,f506,f514,f535,f539,f583,f682,f756,f760,f768,f974,f975,f1001]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP369-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n019.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 20:10:21 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 0.11/0.42 % Refutation found
% 0.11/0.42 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.45 % Elapsed time: 0.069904 seconds
% 0.11/0.45 % CPU time: 0.237081 seconds
% 0.11/0.45 % Total memory used: 105.911 MB
% 0.11/0.45 % Net memory used: 105.692 MB
%------------------------------------------------------------------------------