%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP248-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 12:33:12 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.38s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 81
% Syntax : Number of formulae : 390 ( 13 unt; 35 def)
% Number of atoms : 1447 ( 444 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 1991 ( 934 ~;1022 |; 0 &)
% ( 35 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 37 ( 35 usr; 36 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 69 ( 69 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( inverse(sk_c5) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( inverse(sk_c5) = sk_c9
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c9
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( inverse(sk_c5) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c10
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c5) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c10
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( inverse(sk_c5) = sk_c9
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c9
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c9
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c3,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c10
| multiply(sk_c3,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,negated_conjecture,
( inverse(sk_c5) = sk_c9
| multiply(sk_c3,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c3,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c9
| multiply(sk_c3,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c9
| multiply(sk_c3,sk_c8) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,negated_conjecture,
! [X4,X5,X6,X1,X2,X7,X3] :
( multiply(X3,sk_c8) != sk_c9
| inverse(X7) != X3
| multiply(X7,X3) != sk_c9
| multiply(X2,sk_c8) != sk_c9
| inverse(X2) != sk_c9
| multiply(X1,sk_c9) != sk_c10
| inverse(X1) != sk_c10
| multiply(X6,sk_c8) != sk_c10
| inverse(X6) != sk_c10
| 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,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f51,plain,
( multiply(sk_c4,sk_c9) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f52,plain,
( inverse(sk_c5) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f53,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f54,plain,
( multiply(sk_c6,sk_c7) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f55,plain,
( inverse(sk_c6) = sk_c7
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f56,plain,
( multiply(sk_c7,sk_c8) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f57,plain,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f58,plain,
( multiply(sk_c4,sk_c9) = sk_c10
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f59,plain,
( inverse(sk_c5) = sk_c9
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f60,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f61,plain,
( multiply(sk_c6,sk_c7) = sk_c9
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f62,plain,
( inverse(sk_c6) = sk_c7
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f63,plain,
( multiply(sk_c7,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f64,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f65,plain,
( multiply(sk_c4,sk_c9) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f66,plain,
( inverse(sk_c5) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f67,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f68,plain,
( multiply(sk_c6,sk_c7) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f69,plain,
( inverse(sk_c6) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f70,plain,
( multiply(sk_c7,sk_c8) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f71,plain,
( inverse(sk_c4) = sk_c10
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f72,plain,
( multiply(sk_c4,sk_c9) = sk_c10
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f73,plain,
( inverse(sk_c5) = sk_c9
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f74,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f75,plain,
( multiply(sk_c6,sk_c7) = sk_c9
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f76,plain,
( inverse(sk_c6) = sk_c7
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f77,plain,
( multiply(sk_c7,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f78,plain,
( inverse(sk_c4) = sk_c10
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f79,plain,
( multiply(sk_c4,sk_c9) = sk_c10
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f80,plain,
( inverse(sk_c5) = sk_c9
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f81,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f82,plain,
( multiply(sk_c6,sk_c7) = sk_c9
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f83,plain,
( inverse(sk_c6) = sk_c7
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f84,plain,
( multiply(sk_c7,sk_c8) = sk_c9
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f85,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c3,sk_c8) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f86,plain,
( multiply(sk_c4,sk_c9) = sk_c10
| multiply(sk_c3,sk_c8) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f87,plain,
( inverse(sk_c5) = sk_c9
| multiply(sk_c3,sk_c8) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f88,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c3,sk_c8) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f89,plain,
( multiply(sk_c6,sk_c7) = sk_c9
| multiply(sk_c3,sk_c8) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f90,plain,
( inverse(sk_c6) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f91,plain,
( multiply(sk_c7,sk_c8) = sk_c9
| multiply(sk_c3,sk_c8) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f92,plain,
! [X3] :
( multiply(X3,sk_c8) != sk_c9
| ! [X7] :
( inverse(X7) != X3
| multiply(X7,X3) != sk_c9
| ! [X2] :
( multiply(X2,sk_c8) != sk_c9
| inverse(X2) != sk_c9
| ! [X1] :
( multiply(X1,sk_c9) != sk_c10
| inverse(X1) != sk_c10
| ! [X6] :
( multiply(X6,sk_c8) != sk_c10
| inverse(X6) != sk_c10
| ! [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] :
( multiply(X6,sk_c8) != sk_c9
| inverse(X5) != X6
| multiply(X5,X6) != sk_c9
| multiply(X4,sk_c8) != sk_c9
| inverse(X4) != sk_c9
| multiply(X3,sk_c9) != sk_c10
| inverse(X3) != sk_c10
| multiply(X2,sk_c8) != sk_c10
| inverse(X2) != sk_c10
| 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
<=> inverse(sk_c4) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f98,plain,
( ~ sQ1_spl
| inverse(sk_c4) = sk_c10 ),
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_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f102,plain,
( ~ sQ2_spl
| multiply(sk_c4,sk_c9) = 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
<=> inverse(sk_c5) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f106,plain,
( ~ sQ3_spl
| inverse(sk_c5) = 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
<=> 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
<=> multiply(sk_c6,sk_c7) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f114,plain,
( ~ sQ5_spl
| multiply(sk_c6,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
<=> inverse(sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f118,plain,
( ~ sQ6_spl
| inverse(sk_c6) = 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
<=> multiply(sk_c7,sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f122,plain,
( ~ sQ7_spl
| multiply(sk_c7,sk_c8) = sk_c9 ),
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(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_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_c10 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f156,plain,
( ~ sQ11_spl
| inverse(sk_c3) = sk_c10 ),
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_c10 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f166,plain,
( ~ sQ12_spl
| multiply(sk_c3,sk_c8) = sk_c10 ),
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_c10
| inverse(X2) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f182,plain,
! [X0] :
( ~ sQ15_spl
| multiply(X0,sk_c8) != sk_c10
| inverse(X0) != sk_c10 ),
inference(component_clause,[status(thm)],[f181]) ).
fof(f184,definition,
! [X3] :
( sQ16_spl
<=> ( multiply(X3,sk_c9) != sk_c10
| inverse(X3) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f185,plain,
! [X0] :
( ~ sQ16_spl
| multiply(X0,sk_c9) != sk_c10
| inverse(X0) != sk_c10 ),
inference(component_clause,[status(thm)],[f184]) ).
fof(f187,definition,
! [X4] :
( sQ17_spl
<=> ( multiply(X4,sk_c8) != sk_c9
| inverse(X4) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f188,plain,
! [X0] :
( ~ sQ17_spl
| multiply(X0,sk_c8) != sk_c9
| inverse(X0) != sk_c9 ),
inference(component_clause,[status(thm)],[f187]) ).
fof(f190,definition,
! [X5,X6] :
( sQ18_spl
<=> ( multiply(X6,sk_c8) != sk_c9
| inverse(X5) != X6
| multiply(X5,X6) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f191,plain,
! [X0,X1] :
( ~ sQ18_spl
| multiply(X1,sk_c8) != sk_c9
| inverse(X0) != X1
| multiply(X0,X1) != sk_c9 ),
inference(component_clause,[status(thm)],[f190]) ).
fof(f193,plain,
( sQ18_spl
| sQ17_spl
| sQ16_spl
| sQ15_spl
| sQ14_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f93,f175,f178,f181,f184,f187,f190]) ).
fof(f194,plain,
! [X0] :
( ~ sQ18_spl
| multiply(inverse(X0),sk_c8) != sk_c9
| multiply(X0,inverse(X0)) != sk_c9 ),
inference(destructive_equality_resolution,[status(thm)],[f191]) ).
fof(f196,plain,
! [X0] :
( ~ sQ2_spl
| multiply(sk_c10,X0) = multiply(sk_c4,multiply(sk_c9,X0)) ),
inference(paramodulation,[status(thm)],[f102,f49]) ).
fof(f198,plain,
! [X0] :
( ~ sQ5_spl
| multiply(sk_c9,X0) = multiply(sk_c6,multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f114,f49]) ).
fof(f200,plain,
! [X0] :
( ~ sQ0_spl
| multiply(sk_c9,X0) = multiply(sk_c1,multiply(sk_c10,X0)) ),
inference(paramodulation,[status(thm)],[f95,f49]) ).
fof(f213,plain,
( ~ sQ6_spl
| ~ sQ18_spl
| multiply(sk_c7,sk_c8) != sk_c9
| multiply(sk_c6,inverse(sk_c6)) != sk_c9 ),
inference(paramodulation,[status(thm)],[f118,f194]) ).
fof(f214,plain,
( ~ sQ8_spl
| ~ sQ18_spl
| multiply(sk_c10,sk_c8) != sk_c9
| multiply(sk_c1,inverse(sk_c1)) != sk_c9 ),
inference(paramodulation,[status(thm)],[f126,f194]) ).
fof(f215,plain,
( ~ sQ10_spl
| ~ sQ18_spl
| multiply(sk_c9,sk_c8) != sk_c9
| multiply(sk_c2,inverse(sk_c2)) != sk_c9 ),
inference(paramodulation,[status(thm)],[f146,f194]) ).
fof(f220,definition,
( sQ20_spl
<=> multiply(sk_c10,sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f227,definition,
( sQ22_spl
<=> multiply(sk_c9,sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f229,plain,
( sQ22_spl
| multiply(sk_c9,sk_c8) != sk_c9 ),
inference(component_clause,[status(thm)],[f227]) ).
fof(f231,definition,
( sQ23_spl
<=> multiply(sk_c6,inverse(sk_c6)) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f233,plain,
( sQ23_spl
| multiply(sk_c6,inverse(sk_c6)) != sk_c9 ),
inference(component_clause,[status(thm)],[f231]) ).
fof(f234,plain,
( ~ sQ6_spl
| ~ sQ18_spl
| ~ sQ7_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f213,f231,f121,f190,f117]) ).
fof(f235,definition,
( sQ24_spl
<=> multiply(sk_c1,inverse(sk_c1)) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f237,plain,
( sQ24_spl
| multiply(sk_c1,inverse(sk_c1)) != sk_c9 ),
inference(component_clause,[status(thm)],[f235]) ).
fof(f238,plain,
( ~ sQ8_spl
| ~ sQ18_spl
| ~ sQ20_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f214,f235,f220,f190,f125]) ).
fof(f239,definition,
( sQ25_spl
<=> multiply(sk_c2,inverse(sk_c2)) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f241,plain,
( sQ25_spl
| multiply(sk_c2,inverse(sk_c2)) != sk_c9 ),
inference(component_clause,[status(thm)],[f239]) ).
fof(f242,plain,
( ~ sQ10_spl
| ~ sQ18_spl
| ~ sQ22_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f215,f239,f227,f190,f145]) ).
fof(f248,plain,
( sQ25_spl
| ~ sQ10_spl
| multiply(sk_c2,sk_c9) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f146,f241]) ).
fof(f249,plain,
( sQ25_spl
| ~ sQ10_spl
| ~ sQ9_spl
| sk_c8 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f136,f248]) ).
fof(f250,plain,
( sQ24_spl
| ~ sQ8_spl
| multiply(sk_c1,sk_c10) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f126,f237]) ).
fof(f251,plain,
( sQ24_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f95,f250]) ).
fof(f252,plain,
( sQ24_spl
| ~ sQ8_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f251]) ).
fof(f253,plain,
( sQ24_spl
| ~ sQ8_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f252]) ).
fof(f256,plain,
( ~ sQ4_spl
| ~ sQ17_spl
| sk_c9 != sk_c9
| inverse(sk_c5) != sk_c9 ),
inference(paramodulation,[status(thm)],[f110,f188]) ).
fof(f258,definition,
( sQ27_spl
<=> sk_c9 = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f260,plain,
( sQ27_spl
| sk_c9 != sk_c9 ),
inference(component_clause,[status(thm)],[f258]) ).
fof(f261,plain,
( ~ sQ4_spl
| ~ sQ17_spl
| ~ sQ27_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f256,f105,f258,f187,f109]) ).
fof(f269,plain,
( sQ27_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f260]) ).
fof(f270,plain,
sQ27_spl,
inference(contradiction_clause,[status(thm)],[f269]) ).
fof(f274,plain,
( ~ sQ3_spl
| multiply(sk_c9,sk_c5) = identity ),
inference(paramodulation,[status(thm)],[f106,f48]) ).
fof(f279,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f48,f49]) ).
fof(f280,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f47,f279]) ).
fof(f287,plain,
( ~ sQ2_spl
| ~ sQ16_spl
| inverse(sk_c4) != sk_c10 ),
inference(resolution,[status(thm)],[f185,f102]) ).
fof(f293,plain,
( ~ sQ2_spl
| ~ sQ16_spl
| ~ sQ1_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f98,f287]) ).
fof(f294,plain,
( ~ sQ2_spl
| ~ sQ16_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f293]) ).
fof(f295,plain,
( ~ sQ2_spl
| ~ sQ16_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f294]) ).
fof(f296,plain,
( ~ sQ12_spl
| ~ sQ15_spl
| inverse(sk_c3) != sk_c10 ),
inference(resolution,[status(thm)],[f182,f166]) ).
fof(f303,plain,
( ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ11_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f156,f296]) ).
fof(f304,plain,
( ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f303]) ).
fof(f305,plain,
( ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f304]) ).
fof(f306,plain,
( ~ sQ9_spl
| ~ sQ14_spl
| inverse(sk_c2) != sk_c9 ),
inference(resolution,[status(thm)],[f179,f136]) ).
fof(f307,plain,
( ~ sQ14_spl
| inverse(inverse(sk_c9)) != sk_c9
| identity != sk_c8 ),
inference(paramodulation,[status(thm)],[f48,f179]) ).
fof(f312,plain,
( ~ sQ9_spl
| ~ sQ14_spl
| ~ sQ10_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f146,f306]) ).
fof(f313,plain,
( ~ sQ9_spl
| ~ sQ14_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f312]) ).
fof(f314,plain,
( ~ sQ9_spl
| ~ sQ14_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f313]) ).
fof(f320,definition,
( sQ30_spl
<=> identity = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f321,plain,
( ~ sQ30_spl
| identity = sk_c9 ),
inference(component_clause,[status(thm)],[f320]) ).
fof(f322,plain,
( sQ30_spl
| identity != sk_c9 ),
inference(component_clause,[status(thm)],[f320]) ).
fof(f331,definition,
( sQ33_spl
<=> identity = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f333,plain,
( sQ33_spl
| identity != sk_c8 ),
inference(component_clause,[status(thm)],[f331]) ).
fof(f334,definition,
( sQ34_spl
<=> inverse(inverse(sk_c9)) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f336,plain,
( sQ34_spl
| inverse(inverse(sk_c9)) != sk_c9 ),
inference(component_clause,[status(thm)],[f334]) ).
fof(f337,plain,
( ~ sQ14_spl
| ~ sQ34_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f307,f331,f334,f178]) ).
fof(f338,definition,
( sQ35_spl
<=> sk_c9 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f340,plain,
( sQ35_spl
| sk_c9 != sk_c8 ),
inference(component_clause,[status(thm)],[f338]) ).
fof(f352,definition,
( sQ39_spl
<=> sk_c8 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f354,plain,
( sQ39_spl
| sk_c8 != sk_c8 ),
inference(component_clause,[status(thm)],[f352]) ).
fof(f356,plain,
( sQ39_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f354]) ).
fof(f357,plain,
sQ39_spl,
inference(contradiction_clause,[status(thm)],[f356]) ).
fof(f360,plain,
( sQ23_spl
| ~ sQ6_spl
| multiply(sk_c6,sk_c7) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f118,f233]) ).
fof(f361,plain,
( sQ23_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f114,f360]) ).
fof(f362,plain,
( sQ23_spl
| ~ sQ6_spl
| ~ sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f361]) ).
fof(f363,plain,
( sQ23_spl
| ~ sQ6_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f362]) ).
fof(f366,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| inverse(sk_c1) != sk_c10
| sk_c9 != sk_c9 ),
inference(paramodulation,[status(thm)],[f95,f176]) ).
fof(f370,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ8_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f366,f258,f125,f175,f94]) ).
fof(f393,plain,
( ~ sQ2_spl
| sk_c9 = multiply(inverse(sk_c4),sk_c10) ),
inference(paramodulation,[status(thm)],[f102,f280]) ).
fof(f395,plain,
( ~ sQ4_spl
| sk_c8 = multiply(inverse(sk_c5),sk_c9) ),
inference(paramodulation,[status(thm)],[f110,f280]) ).
fof(f397,plain,
( ~ sQ5_spl
| sk_c7 = multiply(inverse(sk_c6),sk_c9) ),
inference(paramodulation,[status(thm)],[f114,f280]) ).
fof(f402,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sk_c9 = multiply(sk_c10,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f98,f393]) ).
fof(f404,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| sk_c8 = multiply(sk_c9,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f106,f395]) ).
fof(f406,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sk_c7 = multiply(sk_c7,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f118,f397]) ).
fof(f420,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ13_spl
| inverse(sk_c10) != sk_c10
| sk_c9 != sk_c9 ),
inference(paramodulation,[status(thm)],[f402,f176]) ).
fof(f423,definition,
( sQ41_spl
<=> inverse(sk_c10) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f425,plain,
( sQ41_spl
| inverse(sk_c10) != sk_c10 ),
inference(component_clause,[status(thm)],[f423]) ).
fof(f426,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ13_spl
| ~ sQ41_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f420,f258,f423,f175,f97,f101]) ).
fof(f430,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c9,sk_c9) = multiply(sk_c6,sk_c7) ),
inference(paramodulation,[status(thm)],[f406,f198]) ).
fof(f431,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sk_c9 = multiply(inverse(sk_c7),sk_c7) ),
inference(paramodulation,[status(thm)],[f406,f280]) ).
fof(f433,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sk_c8 = multiply(sk_c6,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f404,f430]) ).
fof(f434,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sk_c8 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f114,f433]) ).
fof(f437,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sk_c9 = identity ),
inference(forward_demodulation,[status(thm)],[f48,f431]) ).
fof(f438,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f437,f322]) ).
fof(f439,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sQ30_spl ),
inference(contradiction_clause,[status(thm)],[f438]) ).
fof(f440,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sk_c7 = multiply(sk_c7,sk_c8) ),
inference(backward_demodulation,[status(thm)],[f434,f406]) ).
fof(f442,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sk_c8 = multiply(sk_c10,sk_c10) ),
inference(backward_demodulation,[status(thm)],[f434,f402]) ).
fof(f444,plain,
( ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| multiply(sk_c8,sk_c5) = identity ),
inference(backward_demodulation,[status(thm)],[f434,f274]) ).
fof(f445,plain,
( ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| multiply(sk_c7,sk_c8) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f434,f122]) ).
fof(f446,plain,
( ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| inverse(sk_c5) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f434,f106]) ).
fof(f449,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| multiply(sk_c10,X0) = multiply(sk_c4,multiply(sk_c8,X0)) ),
inference(backward_demodulation,[status(thm)],[f434,f196]) ).
fof(f450,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| multiply(sk_c4,sk_c8) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f434,f102]) ).
fof(f454,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sk_c8 = identity ),
inference(forward_demodulation,[status(thm)],[f434,f437]) ).
fof(f455,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sQ33_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f454,f333]) ).
fof(f456,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sQ33_spl ),
inference(contradiction_clause,[status(thm)],[f455]) ).
fof(f459,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| inverse(X0) != sk_c10
| multiply(X0,sk_c10) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f434,f176]) ).
fof(f465,plain,
! [X0] :
( ~ sQ30_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| multiply(sk_c8,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f466,f47]) ).
fof(f466,plain,
( ~ sQ30_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| identity = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f434,f321]) ).
fof(f475,plain,
! [X0] :
( ~ sQ30_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ7_spl
| multiply(sk_c7,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f483,f465]) ).
fof(f476,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ7_spl
| multiply(sk_c4,sk_c7) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f483,f450]) ).
fof(f477,plain,
( ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ7_spl
| inverse(sk_c5) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f483,f446]) ).
fof(f480,plain,
( ~ sQ30_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ7_spl
| identity = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f483,f466]) ).
fof(f481,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ7_spl
| sk_c7 = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f483,f434]) ).
fof(f483,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ7_spl
| sk_c7 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f445,f440]) ).
fof(f500,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ7_spl
| sk_c7 = multiply(sk_c10,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f483,f442]) ).
fof(f504,plain,
( ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ7_spl
| multiply(sk_c7,sk_c5) = identity ),
inference(forward_demodulation,[status(thm)],[f483,f444]) ).
fof(f505,plain,
( ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ30_spl
| sk_c5 = identity ),
inference(forward_demodulation,[status(thm)],[f475,f504]) ).
fof(f507,plain,
( ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ30_spl
| inverse(sk_c7) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f508,f477]) ).
fof(f508,plain,
( ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ30_spl
| sk_c5 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f480,f505]) ).
fof(f560,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ7_spl
| inverse(X0) != sk_c10
| multiply(X0,sk_c10) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f483,f459]) ).
fof(f567,definition,
( sQ42_spl
<=> sk_c7 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f569,plain,
( sQ42_spl
| sk_c7 != sk_c7 ),
inference(component_clause,[status(thm)],[f567]) ).
fof(f650,plain,
( sQ42_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f569]) ).
fof(f651,plain,
sQ42_spl,
inference(contradiction_clause,[status(thm)],[f650]) ).
fof(f662,plain,
( sQ34_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ7_spl
| inverse(inverse(sk_c7)) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f481,f336]) ).
fof(f663,plain,
( sQ34_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ30_spl
| inverse(sk_c7) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f507,f662]) ).
fof(f664,plain,
( sQ34_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ30_spl
| sk_c7 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f507,f663]) ).
fof(f665,plain,
( sQ34_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ30_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f481,f664]) ).
fof(f666,plain,
( sQ34_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ30_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f665]) ).
fof(f667,plain,
( sQ34_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ30_spl ),
inference(contradiction_clause,[status(thm)],[f666]) ).
fof(f716,plain,
( ~ sQ1_spl
| multiply(sk_c10,sk_c4) = identity ),
inference(paramodulation,[status(thm)],[f98,f48]) ).
fof(f720,plain,
( ~ sQ0_spl
| sk_c10 = multiply(inverse(sk_c1),sk_c9) ),
inference(paramodulation,[status(thm)],[f95,f280]) ).
fof(f722,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| sk_c10 = multiply(sk_c10,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f126,f720]) ).
fof(f723,plain,
( ~ sQ10_spl
| multiply(sk_c9,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f146,f48]) ).
fof(f730,plain,
( ~ sQ9_spl
| sk_c9 = multiply(inverse(sk_c2),sk_c8) ),
inference(paramodulation,[status(thm)],[f136,f280]) ).
fof(f732,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| sk_c9 = multiply(sk_c9,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f146,f730]) ).
fof(f816,plain,
( ~ sQ1_spl
| ~ sQ30_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ7_spl
| multiply(sk_c10,sk_c4) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f480,f716]) ).
fof(f842,plain,
( ~ sQ13_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ1_spl
| inverse(sk_c10) != sk_c10 ),
inference(resolution,[status(thm)],[f500,f560]) ).
fof(f936,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ7_spl
| multiply(sk_c7,X0) = multiply(sk_c1,multiply(sk_c10,X0)) ),
inference(forward_demodulation,[status(thm)],[f481,f200]) ).
fof(f937,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ30_spl
| X0 = multiply(sk_c1,multiply(sk_c10,X0)) ),
inference(forward_demodulation,[status(thm)],[f475,f936]) ).
fof(f939,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ30_spl
| sk_c10 = multiply(sk_c1,sk_c7) ),
inference(paramodulation,[status(thm)],[f500,f937]) ).
fof(f940,plain,
( ~ sQ1_spl
| ~ sQ30_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c4 = multiply(sk_c1,sk_c7) ),
inference(paramodulation,[status(thm)],[f816,f937]) ).
fof(f966,plain,
( sQ41_spl
| ~ sQ1_spl
| ~ sQ30_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ2_spl
| inverse(sk_c10) != sk_c4 ),
inference(backward_demodulation,[status(thm)],[f969,f425]) ).
fof(f968,plain,
( ~ sQ1_spl
| ~ sQ30_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ2_spl
| inverse(sk_c4) = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f969,f98]) ).
fof(f969,plain,
( ~ sQ1_spl
| ~ sQ30_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ2_spl
| sk_c4 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f939,f940]) ).
fof(f973,plain,
( sQ41_spl
| ~ sQ1_spl
| ~ sQ30_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ2_spl
| inverse(sk_c4) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f969,f966]) ).
fof(f977,plain,
( ~ sQ1_spl
| ~ sQ30_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ2_spl
| sQ41_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f968,f973]) ).
fof(f978,plain,
( ~ sQ1_spl
| ~ sQ30_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ2_spl
| sQ41_spl ),
inference(contradiction_clause,[status(thm)],[f977]) ).
fof(f1053,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| sk_c8 = multiply(inverse(sk_c9),sk_c9) ),
inference(paramodulation,[status(thm)],[f732,f280]) ).
fof(f1055,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| sk_c8 = identity ),
inference(forward_demodulation,[status(thm)],[f48,f1053]) ).
fof(f1059,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c8,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f1055,f47]) ).
fof(f1060,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ10_spl
| multiply(inverse(X0),X0) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f1055,f48]) ).
fof(f1061,plain,
( sQ30_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c8 != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f1055,f322]) ).
fof(f1065,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| multiply(sk_c9,sk_c2) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f1055,f723]) ).
fof(f1076,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ17_spl
| sk_c9 != sk_c9
| inverse(sk_c9) != sk_c9 ),
inference(paramodulation,[status(thm)],[f732,f188]) ).
fof(f1078,definition,
( sQ55_spl
<=> inverse(sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f1080,plain,
( sQ55_spl
| inverse(sk_c8) != sk_c9 ),
inference(component_clause,[status(thm)],[f1078]) ).
fof(f1082,definition,
( sQ56_spl
<=> inverse(sk_c9) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f1084,plain,
( sQ56_spl
| inverse(sk_c9) != sk_c9 ),
inference(component_clause,[status(thm)],[f1082]) ).
fof(f1085,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ17_spl
| ~ sQ27_spl
| ~ sQ56_spl ),
inference(split_clause,[status(thm)],[f1076,f1082,f258,f187,f145,f135]) ).
fof(f1111,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| sk_c9 = multiply(inverse(sk_c10),sk_c10) ),
inference(paramodulation,[status(thm)],[f722,f280]) ).
fof(f1113,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c9 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f1060,f1111]) ).
fof(f1114,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1113,f249]) ).
fof(f1115,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sQ25_spl ),
inference(contradiction_clause,[status(thm)],[f1114]) ).
fof(f1119,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ16_spl
| sk_c10 != sk_c10
| inverse(sk_c10) != sk_c10 ),
inference(paramodulation,[status(thm)],[f722,f185]) ).
fof(f1124,definition,
( sQ59_spl
<=> sk_c10 = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f1126,plain,
( sQ59_spl
| sk_c10 != sk_c10 ),
inference(component_clause,[status(thm)],[f1124]) ).
fof(f1127,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ16_spl
| ~ sQ59_spl
| ~ sQ41_spl ),
inference(split_clause,[status(thm)],[f1119,f423,f1124,f184,f125,f94]) ).
fof(f1142,plain,
( sQ56_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| inverse(sk_c9) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f1113,f1084]) ).
fof(f1143,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ8_spl
| multiply(sk_c8,sk_c2) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f1113,f1065]) ).
fof(f1146,plain,
( ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c2) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f1113,f146]) ).
fof(f1148,plain,
( sQ56_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| inverse(sk_c8) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f1113,f1142]) ).
fof(f1149,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sk_c2 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f1059,f1143]) ).
fof(f1152,plain,
( sQ30_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f1113,f1061]) ).
fof(f1153,plain,
( sQ30_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1152]) ).
fof(f1154,plain,
( sQ30_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f1153]) ).
fof(f1157,plain,
( sQ59_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1126]) ).
fof(f1158,plain,
sQ59_spl,
inference(contradiction_clause,[status(thm)],[f1157]) ).
fof(f1160,plain,
( sQ55_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| inverse(sk_c8) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f1113,f1080]) ).
fof(f1178,plain,
( sQ35_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f1113,f340]) ).
fof(f1179,plain,
( sQ35_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1178]) ).
fof(f1180,plain,
( sQ35_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f1179]) ).
fof(f1187,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c9 = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f1149,f1113]) ).
fof(f1190,plain,
( ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ8_spl
| multiply(sk_c3,sk_c2) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f1149,f166]) ).
fof(f1192,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| multiply(sk_c2,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f1149,f1059]) ).
fof(f1198,plain,
( ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c2) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1149,f1146]) ).
fof(f1200,plain,
( sQ56_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| inverse(sk_c2) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f1149,f1148]) ).
fof(f1201,plain,
( sQ56_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c2 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f1198,f1200]) ).
fof(f1202,plain,
( sQ56_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1149,f1201]) ).
fof(f1203,plain,
( sQ56_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1202]) ).
fof(f1204,plain,
( sQ56_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f1203]) ).
fof(f1206,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(X0,sk_c2) != sk_c10
| inverse(X0) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1187,f185]) ).
fof(f1214,plain,
( sQ55_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| inverse(sk_c2) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f1149,f1160]) ).
fof(f1215,plain,
( sQ55_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c2 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f1198,f1214]) ).
fof(f1216,plain,
( sQ55_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1149,f1215]) ).
fof(f1217,plain,
( sQ55_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1216]) ).
fof(f1218,plain,
( sQ55_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f1217]) ).
fof(f1257,plain,
( ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ16_spl
| inverse(sk_c3) != sk_c10 ),
inference(resolution,[status(thm)],[f1206,f1190]) ).
fof(f1262,plain,
( ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ16_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f1257,f155,f184,f125,f94,f135,f145,f165]) ).
fof(f1277,plain,
( sQ22_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c2,sk_c8) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1187,f229]) ).
fof(f1278,plain,
( sQ22_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c8 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1192,f1277]) ).
fof(f1279,plain,
( sQ22_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c2 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1149,f1278]) ).
fof(f1280,plain,
( sQ22_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1187,f1279]) ).
fof(f1281,plain,
( sQ22_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1280]) ).
fof(f1282,plain,
( sQ22_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f1281]) ).
fof(f1464,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ7_spl
| multiply(sk_c10,X0) = multiply(sk_c4,multiply(sk_c7,X0)) ),
inference(forward_demodulation,[status(thm)],[f483,f449]) ).
fof(f1465,plain,
( ~ sQ1_spl
| ~ sQ30_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ2_spl
| multiply(sk_c4,sk_c4) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f1468,f816]) ).
fof(f1468,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ30_spl
| multiply(sk_c10,X0) = multiply(sk_c4,X0) ),
inference(forward_demodulation,[status(thm)],[f475,f1464]) ).
fof(f1482,plain,
( ~ sQ1_spl
| ~ sQ30_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ2_spl
| sk_c4 = multiply(inverse(sk_c4),sk_c7) ),
inference(paramodulation,[status(thm)],[f1465,f280]) ).
fof(f1484,plain,
( ~ sQ1_spl
| ~ sQ30_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ2_spl
| sk_c4 = multiply(sk_c10,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f98,f1482]) ).
fof(f1485,plain,
( ~ sQ1_spl
| ~ sQ30_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ2_spl
| sk_c4 = multiply(sk_c4,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f1468,f1484]) ).
fof(f1486,plain,
( ~ sQ1_spl
| ~ sQ30_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ2_spl
| sk_c4 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f476,f1485]) ).
fof(f1493,plain,
( ~ sQ1_spl
| ~ sQ30_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ2_spl
| inverse(sk_c4) = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f1486,f98]) ).
fof(f1497,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ30_spl
| multiply(sk_c4,sk_c7) = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f1486,f476]) ).
fof(f1498,plain,
( ~ sQ13_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ30_spl
| inverse(sk_c10) != sk_c4 ),
inference(backward_demodulation,[status(thm)],[f1486,f842]) ).
fof(f1503,plain,
( ~ sQ13_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ30_spl
| inverse(sk_c4) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f1486,f1498]) ).
fof(f1508,plain,
( ~ sQ13_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ30_spl
| sk_c4 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f1493,f1503]) ).
fof(f1509,plain,
( ~ sQ13_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ30_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1508]) ).
fof(f1510,plain,
( ~ sQ13_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ30_spl ),
inference(contradiction_clause,[status(thm)],[f1509]) ).
fof(f1521,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ1_spl
| ~ sQ30_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ2_spl
| multiply(X0,sk_c8) != sk_c10
| inverse(X0) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f1486,f182]) ).
fof(f1522,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ1_spl
| ~ sQ30_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ2_spl
| multiply(X0,sk_c7) != sk_c10
| inverse(X0) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f483,f1521]) ).
fof(f1523,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ1_spl
| ~ sQ30_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ2_spl
| multiply(X0,sk_c7) != sk_c4
| inverse(X0) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f1486,f1522]) ).
fof(f1526,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ30_spl
| ~ sQ15_spl
| inverse(sk_c4) != sk_c4 ),
inference(resolution,[status(thm)],[f1523,f1497]) ).
fof(f1533,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ30_spl
| ~ sQ15_spl
| sk_c4 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f1493,f1526]) ).
fof(f1534,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ30_spl
| ~ sQ15_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1533]) ).
fof(f1535,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ30_spl
| ~ sQ15_spl ),
inference(contradiction_clause,[status(thm)],[f1534]) ).
fof(f1536,plain,
$false,
inference(sat_refutation,[status(thm)],[f100,f104,f108,f112,f116,f120,f124,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,f193,f234,f238,f242,f253,f261,f270,f295,f305,f314,f337,f357,f363,f370,f426,f439,f456,f651,f667,f978,f1085,f1115,f1127,f1154,f1158,f1180,f1204,f1218,f1262,f1282,f1510,f1535]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP248-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n014.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 20:07:20 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.38 % Refutation found
% 0.09/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.42 % Elapsed time: 0.061135 seconds
% 0.12/0.42 % CPU time: 0.143807 seconds
% 0.12/0.42 % Total memory used: 28.235 MB
% 0.12/0.42 % Net memory used: 28.142 MB
%------------------------------------------------------------------------------