%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP252-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:33:13 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.39s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 81
% Syntax : Number of formulae : 361 ( 12 unt; 37 def)
% Number of atoms : 1216 ( 412 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 1584 ( 729 ~; 818 |; 0 &)
% ( 37 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 39 ( 37 usr; 38 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 72 ( 72 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( inverse(sk_c6) = sk_c8
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c9
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c6) = sk_c8
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( inverse(sk_c6) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( inverse(sk_c6) = sk_c8
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c9
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
( inverse(sk_c6) = sk_c8
| inverse(sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c3,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c3,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c3,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c9
| multiply(sk_c3,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
( inverse(sk_c6) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,negated_conjecture,
! [X4,X5,X6,X1,X2,X3,X7] :
( inverse(X7) != sk_c8
| multiply(X7,sk_c8) != X3
| multiply(sk_c8,X3) != sk_c9
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c9
| inverse(X1) != sk_c10
| multiply(X1,sk_c10) != sk_c9
| multiply(X6,sk_c8) != sk_c9
| inverse(X6) != sk_c9
| inverse(X5) != sk_c9
| multiply(X5,sk_c9) != sk_c8
| inverse(X4) != sk_c10
| multiply(X4,sk_c10) != sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f48,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f49,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f50,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f51,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f52,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f53,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f54,plain,
( multiply(sk_c8,sk_c7) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f55,plain,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f56,plain,
( inverse(sk_c6) = sk_c8
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f57,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f58,plain,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f59,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f60,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f61,plain,
( multiply(sk_c8,sk_c7) = sk_c9
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f62,plain,
( multiply(sk_c6,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f63,plain,
( inverse(sk_c6) = sk_c8
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f66,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f67,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f68,plain,
( multiply(sk_c8,sk_c7) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f69,plain,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f70,plain,
( inverse(sk_c6) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f71,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f72,plain,
( inverse(sk_c4) = sk_c10
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f73,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f74,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f75,plain,
( multiply(sk_c8,sk_c7) = sk_c9
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f76,plain,
( multiply(sk_c6,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f77,plain,
( inverse(sk_c6) = sk_c8
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f78,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c3) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f79,plain,
( inverse(sk_c4) = sk_c10
| inverse(sk_c3) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f80,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c3) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f81,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c3) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f82,plain,
( multiply(sk_c8,sk_c7) = sk_c9
| inverse(sk_c3) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f83,plain,
( multiply(sk_c6,sk_c8) = sk_c7
| inverse(sk_c3) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f84,plain,
( inverse(sk_c6) = sk_c8
| inverse(sk_c3) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f85,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c3,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f86,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c3,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f87,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c3,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f88,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f89,plain,
( multiply(sk_c8,sk_c7) = sk_c9
| multiply(sk_c3,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f90,plain,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f91,plain,
( inverse(sk_c6) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f92,plain,
! [X7] :
( inverse(X7) != sk_c8
| ! [X3] :
( multiply(X7,sk_c8) != X3
| multiply(sk_c8,X3) != sk_c9
| ! [X2] :
( inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c9
| ! [X1] :
( inverse(X1) != sk_c10
| multiply(X1,sk_c10) != sk_c9
| ! [X6] :
( multiply(X6,sk_c8) != sk_c9
| inverse(X6) != sk_c9
| ! [X5] :
( inverse(X5) != sk_c9
| multiply(X5,sk_c9) != sk_c8
| ! [X4] :
( inverse(X4) != sk_c10
| multiply(X4,sk_c10) != sk_c9 ) ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f46]) ).
fof(f93,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( inverse(X6) != sk_c8
| multiply(X6,sk_c8) != X5
| multiply(sk_c8,X5) != sk_c9
| inverse(X4) != sk_c8
| multiply(X4,sk_c8) != sk_c9
| inverse(X3) != sk_c10
| multiply(X3,sk_c10) != sk_c9
| multiply(X2,sk_c8) != sk_c9
| inverse(X2) != sk_c9
| inverse(X1) != sk_c9
| multiply(X1,sk_c9) != sk_c8
| inverse(X0) != sk_c10
| multiply(X0,sk_c10) != sk_c9 ),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f94,definition,
( sQ0_spl
<=> multiply(sk_c1,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f95,plain,
( ~ sQ0_spl
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(component_clause,[status(thm)],[f94]) ).
fof(f97,definition,
( sQ1_spl
<=> multiply(sk_c4,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f98,plain,
( ~ sQ1_spl
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(component_clause,[status(thm)],[f97]) ).
fof(f100,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f50,f94,f97]) ).
fof(f101,definition,
( sQ2_spl
<=> inverse(sk_c4) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f102,plain,
( ~ sQ2_spl
| inverse(sk_c4) = sk_c10 ),
inference(component_clause,[status(thm)],[f101]) ).
fof(f104,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f51,f94,f101]) ).
fof(f105,definition,
( sQ3_spl
<=> multiply(sk_c5,sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f106,plain,
( ~ sQ3_spl
| multiply(sk_c5,sk_c8) = sk_c9 ),
inference(component_clause,[status(thm)],[f105]) ).
fof(f108,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f52,f94,f105]) ).
fof(f109,definition,
( sQ4_spl
<=> inverse(sk_c5) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f110,plain,
( ~ sQ4_spl
| inverse(sk_c5) = sk_c8 ),
inference(component_clause,[status(thm)],[f109]) ).
fof(f112,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f53,f94,f109]) ).
fof(f113,definition,
( sQ5_spl
<=> multiply(sk_c8,sk_c7) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f114,plain,
( ~ sQ5_spl
| multiply(sk_c8,sk_c7) = sk_c9 ),
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_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f118,plain,
( ~ sQ6_spl
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f117]) ).
fof(f120,plain,
( sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f55,f94,f117]) ).
fof(f121,definition,
( sQ7_spl
<=> inverse(sk_c6) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f122,plain,
( ~ sQ7_spl
| inverse(sk_c6) = sk_c8 ),
inference(component_clause,[status(thm)],[f121]) ).
fof(f124,plain,
( sQ7_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f56,f94,f121]) ).
fof(f125,definition,
( sQ8_spl
<=> inverse(sk_c1) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f126,plain,
( ~ sQ8_spl
| inverse(sk_c1) = sk_c10 ),
inference(component_clause,[status(thm)],[f125]) ).
fof(f128,plain,
( sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f57,f125,f97]) ).
fof(f129,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f58,f125,f101]) ).
fof(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_c2,sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f136,plain,
( ~ sQ9_spl
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(component_clause,[status(thm)],[f135]) ).
fof(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_c2) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f146,plain,
( ~ sQ10_spl
| inverse(sk_c2) = sk_c9 ),
inference(component_clause,[status(thm)],[f145]) ).
fof(f148,plain,
( sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f71,f145,f97]) ).
fof(f149,plain,
( sQ2_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f72,f145,f101]) ).
fof(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
<=> inverse(sk_c3) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f156,plain,
( ~ sQ11_spl
| inverse(sk_c3) = sk_c9 ),
inference(component_clause,[status(thm)],[f155]) ).
fof(f158,plain,
( sQ1_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f78,f155,f97]) ).
fof(f159,plain,
( sQ2_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f79,f155,f101]) ).
fof(f160,plain,
( sQ3_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f80,f155,f105]) ).
fof(f161,plain,
( sQ4_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f81,f155,f109]) ).
fof(f162,plain,
( sQ5_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f82,f155,f113]) ).
fof(f163,plain,
( sQ6_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f83,f155,f117]) ).
fof(f164,plain,
( sQ7_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f84,f155,f121]) ).
fof(f165,definition,
( sQ12_spl
<=> multiply(sk_c3,sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f166,plain,
( ~ sQ12_spl
| multiply(sk_c3,sk_c8) = sk_c9 ),
inference(component_clause,[status(thm)],[f165]) ).
fof(f168,plain,
( sQ1_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f85,f165,f97]) ).
fof(f169,plain,
( sQ2_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f86,f165,f101]) ).
fof(f170,plain,
( sQ3_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f87,f165,f105]) ).
fof(f171,plain,
( sQ4_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f88,f165,f109]) ).
fof(f172,plain,
( sQ5_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f89,f165,f113]) ).
fof(f173,plain,
( sQ6_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f90,f165,f117]) ).
fof(f174,plain,
( sQ7_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f91,f165,f121]) ).
fof(f175,definition,
! [X0] :
( sQ13_spl
<=> ( inverse(X0) != sk_c10
| multiply(X0,sk_c10) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f176,plain,
! [X0] :
( ~ sQ13_spl
| inverse(X0) != sk_c10
| multiply(X0,sk_c10) != sk_c9 ),
inference(component_clause,[status(thm)],[f175]) ).
fof(f178,definition,
! [X1] :
( sQ14_spl
<=> ( inverse(X1) != sk_c9
| multiply(X1,sk_c9) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f179,plain,
! [X0] :
( ~ sQ14_spl
| inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c8 ),
inference(component_clause,[status(thm)],[f178]) ).
fof(f181,definition,
! [X2] :
( sQ15_spl
<=> ( multiply(X2,sk_c8) != sk_c9
| inverse(X2) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f182,plain,
! [X0] :
( ~ sQ15_spl
| multiply(X0,sk_c8) != sk_c9
| inverse(X0) != sk_c9 ),
inference(component_clause,[status(thm)],[f181]) ).
fof(f184,definition,
! [X4] :
( sQ16_spl
<=> ( inverse(X4) != sk_c8
| multiply(X4,sk_c8) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f185,plain,
! [X0] :
( ~ sQ16_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c9 ),
inference(component_clause,[status(thm)],[f184]) ).
fof(f187,definition,
! [X5,X6] :
( sQ17_spl
<=> ( inverse(X6) != sk_c8
| multiply(X6,sk_c8) != X5
| multiply(sk_c8,X5) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f188,plain,
! [X0,X1] :
( ~ sQ17_spl
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != X0
| multiply(sk_c8,X0) != sk_c9 ),
inference(component_clause,[status(thm)],[f187]) ).
fof(f190,plain,
( sQ17_spl
| sQ16_spl
| sQ15_spl
| sQ14_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f93,f175,f178,f181,f184,f187]) ).
fof(f191,plain,
! [X0] :
( ~ sQ17_spl
| inverse(X0) != sk_c8
| multiply(sk_c8,multiply(X0,sk_c8)) != sk_c9 ),
inference(destructive_equality_resolution,[status(thm)],[f188]) ).
fof(f194,plain,
! [X0] :
( ~ sQ3_spl
| multiply(sk_c9,X0) = multiply(sk_c5,multiply(sk_c8,X0)) ),
inference(paramodulation,[status(thm)],[f106,f49]) ).
fof(f196,plain,
! [X0] :
( ~ sQ6_spl
| multiply(sk_c7,X0) = multiply(sk_c6,multiply(sk_c8,X0)) ),
inference(paramodulation,[status(thm)],[f118,f49]) ).
fof(f210,plain,
( ~ sQ3_spl
| ~ sQ17_spl
| inverse(sk_c5) != sk_c8
| multiply(sk_c8,sk_c9) != sk_c9 ),
inference(paramodulation,[status(thm)],[f106,f191]) ).
fof(f211,plain,
( ~ sQ6_spl
| ~ sQ17_spl
| inverse(sk_c6) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c9 ),
inference(paramodulation,[status(thm)],[f118,f191]) ).
fof(f213,definition,
( sQ18_spl
<=> multiply(sk_c8,sk_c9) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f216,plain,
( ~ sQ3_spl
| ~ sQ17_spl
| ~ sQ4_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f210,f213,f109,f187,f105]) ).
fof(f217,plain,
( ~ sQ6_spl
| ~ sQ17_spl
| ~ sQ7_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f211,f113,f121,f187,f117]) ).
fof(f218,definition,
( sQ19_spl
<=> inverse(sk_c3) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f220,plain,
( sQ19_spl
| inverse(sk_c3) != sk_c8 ),
inference(component_clause,[status(thm)],[f218]) ).
fof(f222,plain,
( sQ19_spl
| ~ sQ11_spl
| sk_c9 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f156,f220]) ).
fof(f225,plain,
( ~ sQ6_spl
| ~ sQ16_spl
| inverse(sk_c6) != sk_c8
| sk_c7 != sk_c9 ),
inference(paramodulation,[status(thm)],[f118,f185]) ).
fof(f226,plain,
( ~ sQ12_spl
| ~ sQ16_spl
| inverse(sk_c3) != sk_c8
| sk_c9 != sk_c9 ),
inference(paramodulation,[status(thm)],[f166,f185]) ).
fof(f228,definition,
( sQ20_spl
<=> sk_c7 = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f230,plain,
( sQ20_spl
| sk_c7 != sk_c9 ),
inference(component_clause,[status(thm)],[f228]) ).
fof(f231,plain,
( ~ sQ6_spl
| ~ sQ16_spl
| ~ sQ7_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f225,f228,f121,f184,f117]) ).
fof(f232,definition,
( sQ21_spl
<=> sk_c9 = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f234,plain,
( sQ21_spl
| sk_c9 != sk_c9 ),
inference(component_clause,[status(thm)],[f232]) ).
fof(f235,plain,
( ~ sQ12_spl
| ~ sQ16_spl
| ~ sQ19_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f226,f232,f218,f184,f165]) ).
fof(f236,plain,
( sQ21_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f234]) ).
fof(f237,plain,
sQ21_spl,
inference(contradiction_clause,[status(thm)],[f236]) ).
fof(f239,plain,
( ~ sQ4_spl
| multiply(sk_c8,sk_c5) = identity ),
inference(paramodulation,[status(thm)],[f110,f48]) ).
fof(f243,plain,
( ~ sQ11_spl
| multiply(sk_c9,sk_c3) = identity ),
inference(paramodulation,[status(thm)],[f156,f48]) ).
fof(f244,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f48,f49]) ).
fof(f245,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f47,f244]) ).
fof(f269,plain,
( ~ sQ3_spl
| sk_c8 = multiply(inverse(sk_c5),sk_c9) ),
inference(paramodulation,[status(thm)],[f106,f245]) ).
fof(f279,plain,
( ~ sQ0_spl
| sk_c10 = multiply(inverse(sk_c1),sk_c9) ),
inference(paramodulation,[status(thm)],[f95,f245]) ).
fof(f280,plain,
( ~ sQ9_spl
| sk_c9 = multiply(inverse(sk_c2),sk_c8) ),
inference(paramodulation,[status(thm)],[f136,f245]) ).
fof(f283,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c8 = multiply(sk_c8,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f110,f269]) ).
fof(f286,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| sk_c10 = multiply(sk_c10,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f126,f279]) ).
fof(f287,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| sk_c9 = multiply(sk_c9,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f146,f280]) ).
fof(f290,plain,
( ~ sQ3_spl
| ~ sQ15_spl
| inverse(sk_c5) != sk_c9 ),
inference(resolution,[status(thm)],[f182,f106]) ).
fof(f291,plain,
( ~ sQ12_spl
| ~ sQ15_spl
| inverse(sk_c3) != sk_c9 ),
inference(resolution,[status(thm)],[f182,f166]) ).
fof(f293,plain,
( ~ sQ15_spl
| identity != sk_c9
| inverse(inverse(sk_c8)) != sk_c9 ),
inference(paramodulation,[status(thm)],[f48,f182]) ).
fof(f294,plain,
( ~ sQ15_spl
| sk_c8 != sk_c9
| inverse(identity) != sk_c9 ),
inference(paramodulation,[status(thm)],[f47,f182]) ).
fof(f298,plain,
( ~ sQ3_spl
| ~ sQ15_spl
| ~ sQ4_spl
| sk_c8 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f110,f290]) ).
fof(f299,plain,
( ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ11_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f156,f291]) ).
fof(f300,plain,
( ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f299]) ).
fof(f301,plain,
( ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f300]) ).
fof(f302,plain,
( ~ sQ9_spl
| ~ sQ14_spl
| inverse(sk_c2) != sk_c9 ),
inference(resolution,[status(thm)],[f179,f136]) ).
fof(f307,plain,
( ~ sQ9_spl
| ~ sQ14_spl
| ~ sQ10_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f146,f302]) ).
fof(f308,plain,
( ~ sQ9_spl
| ~ sQ14_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f307]) ).
fof(f309,plain,
( ~ sQ9_spl
| ~ sQ14_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f308]) ).
fof(f313,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c9 = multiply(inverse(sk_c8),sk_c8) ),
inference(paramodulation,[status(thm)],[f283,f245]) ).
fof(f315,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c9 = identity ),
inference(forward_demodulation,[status(thm)],[f48,f313]) ).
fof(f316,plain,
( ~ sQ11_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c9,sk_c3) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f315,f243]) ).
fof(f319,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| multiply(sk_c8,sk_c5) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f315,f239]) ).
fof(f320,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| multiply(inverse(X0),X0) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f315,f48]) ).
fof(f321,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c9,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f315,f47]) ).
fof(f325,plain,
( ~ sQ1_spl
| ~ sQ13_spl
| inverse(sk_c4) != sk_c10 ),
inference(resolution,[status(thm)],[f176,f98]) ).
fof(f326,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| inverse(sk_c1) != sk_c10 ),
inference(resolution,[status(thm)],[f176,f95]) ).
fof(f331,plain,
( ~ sQ1_spl
| ~ sQ13_spl
| ~ sQ2_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f102,f325]) ).
fof(f332,plain,
( ~ sQ1_spl
| ~ sQ13_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f331]) ).
fof(f333,plain,
( ~ sQ1_spl
| ~ sQ13_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f332]) ).
fof(f334,definition,
( sQ22_spl
<=> identity = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f336,plain,
( sQ22_spl
| identity != sk_c8 ),
inference(component_clause,[status(thm)],[f334]) ).
fof(f341,definition,
( sQ24_spl
<=> sk_c9 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f343,plain,
( sQ24_spl
| sk_c9 != sk_c8 ),
inference(component_clause,[status(thm)],[f341]) ).
fof(f344,definition,
( sQ25_spl
<=> inverse(identity) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f346,plain,
( sQ25_spl
| inverse(identity) != sk_c9 ),
inference(component_clause,[status(thm)],[f344]) ).
fof(f348,definition,
( sQ26_spl
<=> sk_c8 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f350,plain,
( sQ26_spl
| sk_c8 != sk_c8 ),
inference(component_clause,[status(thm)],[f348]) ).
fof(f352,plain,
( sQ26_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f350]) ).
fof(f353,plain,
sQ26_spl,
inference(contradiction_clause,[status(thm)],[f352]) ).
fof(f354,plain,
( sQ25_spl
| ~ sQ3_spl
| ~ sQ4_spl
| inverse(sk_c9) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f315,f346]) ).
fof(f370,plain,
( sQ25_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ11_spl
| inverse(sk_c9) != sk_c3 ),
inference(backward_demodulation,[status(thm)],[f384,f354]) ).
fof(f383,plain,
( ~ sQ11_spl
| ~ sQ3_spl
| ~ sQ4_spl
| inverse(sk_c3) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f384,f156]) ).
fof(f384,plain,
( ~ sQ11_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c3 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f321,f316]) ).
fof(f385,plain,
( sQ25_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ11_spl
| inverse(sk_c3) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f384,f370]) ).
fof(f399,definition,
( sQ27_spl
<=> sk_c3 = sk_c3 ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f401,plain,
( sQ27_spl
| sk_c3 != sk_c3 ),
inference(component_clause,[status(thm)],[f399]) ).
fof(f410,plain,
( sQ27_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f401]) ).
fof(f411,plain,
sQ27_spl,
inference(contradiction_clause,[status(thm)],[f410]) ).
fof(f418,plain,
( ~ sQ11_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f383,f385]) ).
fof(f419,plain,
( ~ sQ11_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sQ25_spl ),
inference(contradiction_clause,[status(thm)],[f418]) ).
fof(f436,plain,
( ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c8,sk_c6) = sk_c9 ),
inference(paramodulation,[status(thm)],[f122,f320]) ).
fof(f451,definition,
( sQ30_spl
<=> inverse(sk_c9) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f453,plain,
( sQ30_spl
| inverse(sk_c9) != sk_c9 ),
inference(component_clause,[status(thm)],[f451]) ).
fof(f474,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ8_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f126,f326]) ).
fof(f475,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f474]) ).
fof(f476,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f475]) ).
fof(f525,definition,
( sQ33_spl
<=> inverse(sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f526,plain,
( ~ sQ33_spl
| inverse(sk_c8) = sk_c9 ),
inference(component_clause,[status(thm)],[f525]) ).
fof(f527,plain,
( sQ33_spl
| inverse(sk_c8) != sk_c9 ),
inference(component_clause,[status(thm)],[f525]) ).
fof(f557,definition,
( sQ34_spl
<=> sk_c7 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f559,plain,
( sQ34_spl
| sk_c7 != sk_c8 ),
inference(component_clause,[status(thm)],[f557]) ).
fof(f564,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| X0 = multiply(sk_c5,multiply(sk_c8,X0)) ),
inference(forward_demodulation,[status(thm)],[f321,f194]) ).
fof(f566,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| sk_c5 = multiply(sk_c5,sk_c9) ),
inference(paramodulation,[status(thm)],[f319,f564]) ).
fof(f568,plain,
( ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c6 = multiply(sk_c5,sk_c9) ),
inference(paramodulation,[status(thm)],[f436,f564]) ).
fof(f569,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c7 = multiply(sk_c5,sk_c9) ),
inference(paramodulation,[status(thm)],[f114,f564]) ).
fof(f587,definition,
( sQ38_spl
<=> sk_c5 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f589,plain,
( sQ38_spl
| sk_c5 != sk_c8 ),
inference(component_clause,[status(thm)],[f587]) ).
fof(f596,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| X0 = multiply(sk_c6,multiply(sk_c8,X0)) ),
inference(backward_demodulation,[status(thm)],[f600,f564]) ).
fof(f599,plain,
( ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ4_spl
| multiply(sk_c6,sk_c8) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f600,f106]) ).
fof(f600,plain,
( ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c6 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f566,f568]) ).
fof(f602,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ6_spl
| X0 = multiply(sk_c7,X0) ),
inference(forward_demodulation,[status(thm)],[f196,f596]) ).
fof(f603,plain,
( ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ6_spl
| sk_c7 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f118,f599]) ).
fof(f611,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ6_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c9) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f603,f179]) ).
fof(f621,plain,
( sQ24_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ6_spl
| sk_c7 != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f603,f343]) ).
fof(f623,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ6_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f603,f611]) ).
fof(f652,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| sk_c7 = multiply(sk_c6,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f600,f569]) ).
fof(f653,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ6_spl
| sk_c7 = multiply(sk_c6,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f603,f652]) ).
fof(f654,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ14_spl
| inverse(sk_c6) != sk_c7
| sk_c7 != sk_c8 ),
inference(paramodulation,[status(thm)],[f653,f623]) ).
fof(f656,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ6_spl
| multiply(sk_c7,X0) = multiply(sk_c6,multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f653,f49]) ).
fof(f657,definition,
( sQ43_spl
<=> inverse(sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f659,plain,
( sQ43_spl
| inverse(sk_c6) != sk_c7 ),
inference(component_clause,[status(thm)],[f657]) ).
fof(f660,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ14_spl
| ~ sQ43_spl
| ~ sQ34_spl ),
inference(split_clause,[status(thm)],[f654,f557,f657,f178,f117,f121,f109,f105,f113]) ).
fof(f662,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ6_spl
| X0 = multiply(sk_c6,multiply(sk_c7,X0)) ),
inference(forward_demodulation,[status(thm)],[f602,f656]) ).
fof(f663,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ6_spl
| X0 = multiply(sk_c6,X0) ),
inference(forward_demodulation,[status(thm)],[f602,f662]) ).
fof(f665,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| sk_c8 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f663,f118]) ).
fof(f669,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| sQ34_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f665,f559]) ).
fof(f670,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| sQ34_spl ),
inference(contradiction_clause,[status(thm)],[f669]) ).
fof(f672,plain,
( sQ20_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ6_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f603,f230]) ).
fof(f673,plain,
( sQ20_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f672]) ).
fof(f674,plain,
( sQ20_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f673]) ).
fof(f675,plain,
( sQ24_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ34_spl ),
inference(split_clause,[status(thm)],[f621,f557,f117,f109,f121,f105,f341]) ).
fof(f678,plain,
( sQ43_spl
| ~ sQ7_spl
| sk_c8 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f122,f659]) ).
fof(f695,plain,
( sQ43_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f665,f678]) ).
fof(f696,plain,
( sQ43_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f695]) ).
fof(f697,plain,
( sQ43_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f696]) ).
fof(f704,definition,
( sQ44_spl
<=> inverse(inverse(sk_c8)) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f707,definition,
( sQ45_spl
<=> identity = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f709,plain,
( sQ45_spl
| identity != sk_c9 ),
inference(component_clause,[status(thm)],[f707]) ).
fof(f710,plain,
( ~ sQ15_spl
| ~ sQ45_spl
| ~ sQ44_spl ),
inference(split_clause,[status(thm)],[f293,f704,f707,f181]) ).
fof(f711,plain,
( ~ sQ15_spl
| ~ sQ24_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f294,f344,f341,f181]) ).
fof(f719,plain,
( ~ sQ3_spl
| ~ sQ15_spl
| ~ sQ4_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f298,f341,f109,f181,f105]) ).
fof(f750,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| sk_c9 = multiply(inverse(sk_c10),sk_c10) ),
inference(paramodulation,[status(thm)],[f286,f245]) ).
fof(f752,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| sk_c9 = identity ),
inference(forward_demodulation,[status(thm)],[f48,f750]) ).
fof(f753,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| sQ45_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f752,f709]) ).
fof(f754,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| sQ45_spl ),
inference(contradiction_clause,[status(thm)],[f753]) ).
fof(f757,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| multiply(sk_c9,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f752,f47]) ).
fof(f758,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| multiply(inverse(X0),X0) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f752,f48]) ).
fof(f759,plain,
( sQ22_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sk_c9 != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f752,f336]) ).
fof(f771,definition,
( sQ47_spl
<=> inverse(sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f773,plain,
( sQ47_spl
| inverse(sk_c9) != sk_c8 ),
inference(component_clause,[status(thm)],[f771]) ).
fof(f775,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sk_c9 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f757,f287]) ).
fof(f776,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sQ19_spl
| ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f775,f222]) ).
fof(f777,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sQ19_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f776]) ).
fof(f779,plain,
( sQ47_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| inverse(sk_c8) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f775,f773]) ).
fof(f780,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c8,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f775,f757]) ).
fof(f781,plain,
( ~ sQ12_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| multiply(sk_c3,sk_c8) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f775,f166]) ).
fof(f787,plain,
( ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| inverse(sk_c3) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f775,f156]) ).
fof(f791,plain,
( sQ33_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| inverse(sk_c8) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f775,f527]) ).
fof(f793,plain,
( sQ30_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| inverse(sk_c9) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f775,f453]) ).
fof(f802,plain,
( sQ30_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| inverse(sk_c8) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f775,f793]) ).
fof(f803,plain,
( sQ22_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f775,f759]) ).
fof(f804,plain,
( sQ22_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f803]) ).
fof(f805,plain,
( sQ22_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f804]) ).
fof(f806,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(inverse(X0),X0) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f775,f758]) ).
fof(f809,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c8,X0) = multiply(inverse(X1),multiply(X1,X0)) ),
inference(paramodulation,[status(thm)],[f806,f49]) ).
fof(f810,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c8,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f245,f809]) ).
fof(f813,plain,
( ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| multiply(sk_c8,sk_c3) = sk_c8 ),
inference(paramodulation,[status(thm)],[f787,f806]) ).
fof(f815,plain,
( ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sk_c3 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f780,f813]) ).
fof(f817,plain,
( ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| inverse(sk_c3) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f815,f787]) ).
fof(f819,plain,
( sQ47_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ11_spl
| inverse(sk_c8) != sk_c3 ),
inference(backward_demodulation,[status(thm)],[f815,f779]) ).
fof(f822,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ11_spl
| sk_c9 = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f815,f775]) ).
fof(f827,plain,
( sQ38_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sk_c5 != sk_c3 ),
inference(backward_demodulation,[status(thm)],[f815,f589]) ).
fof(f830,plain,
( sQ47_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ11_spl
| inverse(sk_c3) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f815,f819]) ).
fof(f832,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| inverse(X0) != sk_c8
| multiply(sk_c3,multiply(X0,sk_c8)) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f815,f191]) ).
fof(f833,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| inverse(X0) != sk_c8
| multiply(sk_c3,multiply(X0,sk_c3)) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f815,f832]) ).
fof(f834,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| inverse(X0) != sk_c8
| multiply(sk_c3,multiply(X0,sk_c3)) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f822,f833]) ).
fof(f835,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| inverse(X0) != sk_c3
| multiply(sk_c3,multiply(X0,sk_c3)) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f815,f834]) ).
fof(f837,plain,
( ~ sQ12_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ11_spl
| multiply(sk_c3,sk_c3) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f815,f781]) ).
fof(f838,plain,
( ~ sQ12_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ11_spl
| multiply(sk_c3,sk_c3) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f815,f837]) ).
fof(f839,plain,
( ~ sQ12_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ17_spl
| inverse(sk_c3) != sk_c3
| multiply(sk_c3,sk_c3) != sk_c3 ),
inference(paramodulation,[status(thm)],[f838,f835]) ).
fof(f842,definition,
( sQ48_spl
<=> multiply(sk_c3,sk_c3) = sk_c3 ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f844,plain,
( sQ48_spl
| multiply(sk_c3,sk_c3) != sk_c3 ),
inference(component_clause,[status(thm)],[f842]) ).
fof(f845,definition,
( sQ49_spl
<=> inverse(sk_c3) = sk_c3 ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f847,plain,
( sQ49_spl
| inverse(sk_c3) != sk_c3 ),
inference(component_clause,[status(thm)],[f845]) ).
fof(f848,plain,
( ~ sQ12_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ17_spl
| ~ sQ49_spl
| ~ sQ48_spl ),
inference(split_clause,[status(thm)],[f839,f842,f845,f187,f155,f125,f94,f145,f135,f165]) ).
fof(f849,plain,
( sQ48_spl
| ~ sQ12_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ11_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f838,f844]) ).
fof(f850,plain,
( sQ48_spl
| ~ sQ12_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f849]) ).
fof(f851,plain,
( sQ48_spl
| ~ sQ12_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f850]) ).
fof(f854,plain,
( sQ33_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ11_spl
| inverse(sk_c3) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f815,f791]) ).
fof(f855,plain,
( sQ33_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ11_spl
| inverse(sk_c3) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f815,f854]) ).
fof(f857,plain,
( sQ30_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ11_spl
| inverse(sk_c3) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f815,f802]) ).
fof(f858,plain,
( sQ30_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ11_spl
| inverse(sk_c3) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f815,f857]) ).
fof(f863,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| multiply(sk_c3,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f815,f810]) ).
fof(f866,plain,
( ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sQ33_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f817,f855]) ).
fof(f867,plain,
( ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sQ33_spl ),
inference(contradiction_clause,[status(thm)],[f866]) ).
fof(f868,plain,
( ~ sQ33_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| inverse(sk_c3) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f815,f526]) ).
fof(f869,plain,
( ~ sQ33_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| inverse(sk_c3) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f822,f868]) ).
fof(f883,plain,
( ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sQ47_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f817,f830]) ).
fof(f884,plain,
( ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sQ47_spl ),
inference(contradiction_clause,[status(thm)],[f883]) ).
fof(f887,plain,
( ~ sQ33_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f869,f858]) ).
fof(f888,plain,
( ~ sQ33_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sQ30_spl ),
inference(contradiction_clause,[status(thm)],[f887]) ).
fof(f937,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| multiply(sk_c3,sk_c5) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f815,f319]) ).
fof(f938,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sk_c5 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f863,f937]) ).
fof(f939,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sk_c5 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f822,f938]) ).
fof(f940,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sQ38_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f939,f827]) ).
fof(f941,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sQ38_spl ),
inference(contradiction_clause,[status(thm)],[f940]) ).
fof(f976,plain,
( sQ49_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f817,f847]) ).
fof(f977,plain,
( sQ49_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f976]) ).
fof(f978,plain,
( sQ49_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f977]) ).
fof(f979,plain,
$false,
inference(sat_refutation,[status(thm)],[f100,f104,f108,f112,f116,f120,f124,f128,f129,f130,f131,f132,f133,f134,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,f216,f217,f231,f235,f237,f301,f309,f333,f353,f411,f419,f476,f660,f670,f674,f675,f697,f710,f711,f719,f754,f777,f805,f848,f851,f867,f884,f888,f941,f978]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP252-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n020.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 20 20:08:32 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 0.15/0.39 % Refutation found
% 0.15/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.42 % Elapsed time: 0.043195 seconds
% 0.15/0.42 % CPU time: 0.154852 seconds
% 0.15/0.42 % Total memory used: 31.763 MB
% 0.15/0.42 % Net memory used: 31.684 MB
%------------------------------------------------------------------------------