%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP260-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 12:33:14 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.41s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 86
% Syntax : Number of formulae : 423 ( 10 unt; 37 def)
% Number of atoms : 1872 ( 534 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 2757 (1308 ~;1412 |; 0 &)
% ( 37 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 39 ( 37 usr; 38 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 101 ( 101 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c7) = sk_c6
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c6) = sk_c8
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c3) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c7) = sk_c6
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( inverse(sk_c6) = sk_c8
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( inverse(sk_c7) = sk_c6
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( inverse(sk_c6) = sk_c8
| multiply(sk_c2,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( inverse(sk_c3) = sk_c11
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,negated_conjecture,
( inverse(sk_c7) = sk_c6
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,negated_conjecture,
( inverse(sk_c6) = sk_c8
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c9,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c9,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c9,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c9,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c9,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c9,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f50,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c9,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f51,negated_conjecture,
( inverse(sk_c7) = sk_c6
| multiply(sk_c9,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f52,negated_conjecture,
( inverse(sk_c6) = sk_c8
| multiply(sk_c9,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
! [X3,X4,X1,X2,X5,X6,X7,X8] :
( multiply(X7,X6) != X8
| inverse(X8) != X6
| inverse(X7) != X8
| multiply(X6,sk_c10) != sk_c11
| inverse(X5) != X6
| multiply(X5,X6) != sk_c11
| inverse(X2) != sk_c10
| multiply(X2,sk_c10) != sk_c9
| inverse(X1) != sk_c11
| multiply(X1,sk_c11) != sk_c10
| multiply(sk_c9,sk_c11) != sk_c10
| inverse(X4) != sk_c10
| multiply(X4,sk_c10) != sk_c9
| inverse(X3) != sk_c11
| multiply(X3,sk_c11) != sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f55,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f56,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f57,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f58,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f59,plain,
( inverse(sk_c3) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f60,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f61,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f62,plain,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f63,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f64,plain,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f65,plain,
( inverse(sk_c7) = sk_c6
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f66,plain,
( inverse(sk_c6) = sk_c8
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f68,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f69,plain,
( inverse(sk_c3) = sk_c11
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f70,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f71,plain,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f72,plain,
( multiply(sk_c5,sk_c8) = sk_c11
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f73,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f74,plain,
( multiply(sk_c8,sk_c10) = sk_c11
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f75,plain,
( inverse(sk_c7) = sk_c6
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f76,plain,
( inverse(sk_c6) = sk_c8
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f78,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f79,plain,
( inverse(sk_c3) = sk_c11
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f80,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f81,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f82,plain,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f83,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f84,plain,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f85,plain,
( inverse(sk_c7) = sk_c6
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f86,plain,
( inverse(sk_c6) = sk_c8
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f88,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f89,plain,
( inverse(sk_c3) = sk_c11
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f90,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f91,plain,
( inverse(sk_c4) = sk_c10
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f92,plain,
( multiply(sk_c5,sk_c8) = sk_c11
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f93,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f94,plain,
( multiply(sk_c8,sk_c10) = sk_c11
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f95,plain,
( inverse(sk_c7) = sk_c6
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f96,plain,
( inverse(sk_c6) = sk_c8
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f98,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c9,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f99,plain,
( inverse(sk_c3) = sk_c11
| multiply(sk_c9,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f100,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c9,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f101,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c9,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f102,plain,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c9,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f103,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c9,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f104,plain,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c9,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f105,plain,
( inverse(sk_c7) = sk_c6
| multiply(sk_c9,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f106,plain,
( inverse(sk_c6) = sk_c8
| multiply(sk_c9,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f108,plain,
! [X6,X7,X8] :
( multiply(X7,X6) != X8
| inverse(X8) != X6
| inverse(X7) != X8
| multiply(X6,sk_c10) != sk_c11
| ! [X5] :
( inverse(X5) != X6
| multiply(X5,X6) != sk_c11
| ! [X2] :
( inverse(X2) != sk_c10
| multiply(X2,sk_c10) != sk_c9
| ! [X1] :
( inverse(X1) != sk_c11
| multiply(X1,sk_c11) != sk_c10
| multiply(sk_c9,sk_c11) != sk_c10
| ! [X4] :
( inverse(X4) != sk_c10
| multiply(X4,sk_c10) != sk_c9
| ! [X3] :
( inverse(X3) != sk_c11
| multiply(X3,sk_c11) != sk_c10 ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f54]) ).
fof(f109,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( multiply(X6,X5) != X7
| inverse(X7) != X5
| inverse(X6) != X7
| multiply(X5,sk_c10) != sk_c11
| inverse(X4) != X5
| multiply(X4,X5) != sk_c11
| inverse(X3) != sk_c10
| multiply(X3,sk_c10) != sk_c9
| inverse(X2) != sk_c11
| multiply(X2,sk_c11) != sk_c10
| multiply(sk_c9,sk_c11) != sk_c10
| inverse(X1) != sk_c10
| multiply(X1,sk_c10) != sk_c9
| inverse(X0) != sk_c11
| multiply(X0,sk_c11) != sk_c10 ),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f110,definition,
( sQ0_spl
<=> multiply(sk_c1,sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f111,plain,
( ~ sQ0_spl
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(component_clause,[status(thm)],[f110]) ).
fof(f113,definition,
( sQ1_spl
<=> multiply(sk_c3,sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f114,plain,
( ~ sQ1_spl
| multiply(sk_c3,sk_c11) = sk_c10 ),
inference(component_clause,[status(thm)],[f113]) ).
fof(f116,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f58,f110,f113]) ).
fof(f117,definition,
( sQ2_spl
<=> inverse(sk_c3) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f118,plain,
( ~ sQ2_spl
| inverse(sk_c3) = sk_c11 ),
inference(component_clause,[status(thm)],[f117]) ).
fof(f120,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f59,f110,f117]) ).
fof(f121,definition,
( sQ3_spl
<=> multiply(sk_c4,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f122,plain,
( ~ sQ3_spl
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(component_clause,[status(thm)],[f121]) ).
fof(f124,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f60,f110,f121]) ).
fof(f125,definition,
( sQ4_spl
<=> inverse(sk_c4) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f126,plain,
( ~ sQ4_spl
| inverse(sk_c4) = sk_c10 ),
inference(component_clause,[status(thm)],[f125]) ).
fof(f128,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f61,f110,f125]) ).
fof(f129,definition,
( sQ5_spl
<=> multiply(sk_c5,sk_c8) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f130,plain,
( ~ sQ5_spl
| multiply(sk_c5,sk_c8) = sk_c11 ),
inference(component_clause,[status(thm)],[f129]) ).
fof(f132,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f62,f110,f129]) ).
fof(f133,definition,
( sQ6_spl
<=> inverse(sk_c5) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f134,plain,
( ~ sQ6_spl
| inverse(sk_c5) = sk_c8 ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,plain,
( sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f63,f110,f133]) ).
fof(f137,definition,
( sQ7_spl
<=> multiply(sk_c8,sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f138,plain,
( ~ sQ7_spl
| multiply(sk_c8,sk_c10) = sk_c11 ),
inference(component_clause,[status(thm)],[f137]) ).
fof(f140,plain,
( sQ7_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f64,f110,f137]) ).
fof(f141,definition,
( sQ8_spl
<=> inverse(sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f142,plain,
( ~ sQ8_spl
| inverse(sk_c7) = sk_c6 ),
inference(component_clause,[status(thm)],[f141]) ).
fof(f144,plain,
( sQ8_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f65,f110,f141]) ).
fof(f145,definition,
( sQ9_spl
<=> inverse(sk_c6) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f146,plain,
( ~ sQ9_spl
| inverse(sk_c6) = sk_c8 ),
inference(component_clause,[status(thm)],[f145]) ).
fof(f148,plain,
( sQ9_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f66,f110,f145]) ).
fof(f153,definition,
( sQ11_spl
<=> inverse(sk_c1) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f154,plain,
( ~ sQ11_spl
| inverse(sk_c1) = sk_c11 ),
inference(component_clause,[status(thm)],[f153]) ).
fof(f156,plain,
( sQ1_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f68,f153,f113]) ).
fof(f157,plain,
( sQ2_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f69,f153,f117]) ).
fof(f158,plain,
( sQ3_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f70,f153,f121]) ).
fof(f159,plain,
( sQ4_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f71,f153,f125]) ).
fof(f160,plain,
( sQ5_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f72,f153,f129]) ).
fof(f161,plain,
( sQ6_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f73,f153,f133]) ).
fof(f162,plain,
( sQ7_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f74,f153,f137]) ).
fof(f163,plain,
( sQ8_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f75,f153,f141]) ).
fof(f164,plain,
( sQ9_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f76,f153,f145]) ).
fof(f166,definition,
( sQ12_spl
<=> multiply(sk_c2,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f167,plain,
( ~ sQ12_spl
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(component_clause,[status(thm)],[f166]) ).
fof(f169,plain,
( sQ1_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f78,f166,f113]) ).
fof(f170,plain,
( sQ2_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f79,f166,f117]) ).
fof(f171,plain,
( sQ3_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f80,f166,f121]) ).
fof(f172,plain,
( sQ4_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f81,f166,f125]) ).
fof(f173,plain,
( sQ5_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f82,f166,f129]) ).
fof(f174,plain,
( sQ6_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f83,f166,f133]) ).
fof(f175,plain,
( sQ7_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f84,f166,f137]) ).
fof(f176,plain,
( sQ8_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f85,f166,f141]) ).
fof(f177,plain,
( sQ9_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f86,f166,f145]) ).
fof(f179,definition,
( sQ13_spl
<=> inverse(sk_c2) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f180,plain,
( ~ sQ13_spl
| inverse(sk_c2) = sk_c10 ),
inference(component_clause,[status(thm)],[f179]) ).
fof(f182,plain,
( sQ1_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f88,f179,f113]) ).
fof(f183,plain,
( sQ2_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f89,f179,f117]) ).
fof(f184,plain,
( sQ3_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f90,f179,f121]) ).
fof(f185,plain,
( sQ4_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f91,f179,f125]) ).
fof(f186,plain,
( sQ5_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f92,f179,f129]) ).
fof(f187,plain,
( sQ6_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f93,f179,f133]) ).
fof(f188,plain,
( sQ7_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f94,f179,f137]) ).
fof(f189,plain,
( sQ8_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f95,f179,f141]) ).
fof(f190,plain,
( sQ9_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f96,f179,f145]) ).
fof(f192,definition,
( sQ14_spl
<=> multiply(sk_c9,sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f193,plain,
( ~ sQ14_spl
| multiply(sk_c9,sk_c11) = sk_c10 ),
inference(component_clause,[status(thm)],[f192]) ).
fof(f194,plain,
( sQ14_spl
| multiply(sk_c9,sk_c11) != sk_c10 ),
inference(component_clause,[status(thm)],[f192]) ).
fof(f195,plain,
( sQ1_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f98,f192,f113]) ).
fof(f196,plain,
( sQ2_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f99,f192,f117]) ).
fof(f197,plain,
( sQ3_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f100,f192,f121]) ).
fof(f198,plain,
( sQ4_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f101,f192,f125]) ).
fof(f199,plain,
( sQ5_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f102,f192,f129]) ).
fof(f200,plain,
( sQ6_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f103,f192,f133]) ).
fof(f201,plain,
( sQ7_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f104,f192,f137]) ).
fof(f202,plain,
( sQ8_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f105,f192,f141]) ).
fof(f203,plain,
( sQ9_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f106,f192,f145]) ).
fof(f205,definition,
! [X0] :
( sQ15_spl
<=> ( inverse(X0) != sk_c11
| multiply(X0,sk_c11) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f206,plain,
! [X0] :
( ~ sQ15_spl
| inverse(X0) != sk_c11
| multiply(X0,sk_c11) != sk_c10 ),
inference(component_clause,[status(thm)],[f205]) ).
fof(f208,definition,
! [X1] :
( sQ16_spl
<=> ( inverse(X1) != sk_c10
| multiply(X1,sk_c10) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f209,plain,
! [X0] :
( ~ sQ16_spl
| inverse(X0) != sk_c10
| multiply(X0,sk_c10) != sk_c9 ),
inference(component_clause,[status(thm)],[f208]) ).
fof(f211,definition,
! [X4,X5,X6,X7] :
( sQ17_spl
<=> ( multiply(X6,X5) != X7
| inverse(X7) != X5
| inverse(X6) != X7
| multiply(X5,sk_c10) != sk_c11
| inverse(X4) != X5
| multiply(X4,X5) != sk_c11 ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f212,plain,
! [X0,X1,X2,X3] :
( ~ sQ17_spl
| multiply(X2,X1) != X3
| inverse(X3) != X1
| inverse(X2) != X3
| multiply(X1,sk_c10) != sk_c11
| inverse(X0) != X1
| multiply(X0,X1) != sk_c11 ),
inference(component_clause,[status(thm)],[f211]) ).
fof(f214,plain,
( sQ17_spl
| ~ sQ14_spl
| sQ16_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f109,f205,f208,f192,f211]) ).
fof(f215,plain,
! [X0,X1] :
( ~ sQ17_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c10) != sk_c11
| multiply(X0,inverse(X0)) != sk_c11 ),
inference(destructive_equality_resolution,[status(thm)],[f212]) ).
fof(f229,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ17_spl
| multiply(X0,sk_c10) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c4)
| multiply(inverse(sk_c4),sk_c10) != sk_c11
| multiply(sk_c4,inverse(sk_c4)) != sk_c11 ),
inference(paramodulation,[status(thm)],[f126,f215]) ).
fof(f230,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ17_spl
| multiply(X0,sk_c8) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c5)
| multiply(inverse(sk_c5),sk_c10) != sk_c11
| multiply(sk_c5,inverse(sk_c5)) != sk_c11 ),
inference(paramodulation,[status(thm)],[f134,f215]) ).
fof(f232,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ17_spl
| multiply(X0,sk_c8) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c6)
| multiply(inverse(sk_c6),sk_c10) != sk_c11
| multiply(sk_c6,inverse(sk_c6)) != sk_c11 ),
inference(paramodulation,[status(thm)],[f146,f215]) ).
fof(f245,definition,
( sQ21_spl
<=> multiply(sk_c4,inverse(sk_c4)) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f247,plain,
( sQ21_spl
| multiply(sk_c4,inverse(sk_c4)) != sk_c11 ),
inference(component_clause,[status(thm)],[f245]) ).
fof(f248,definition,
( sQ22_spl
<=> multiply(inverse(sk_c4),sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f250,plain,
( sQ22_spl
| multiply(inverse(sk_c4),sk_c10) != sk_c11 ),
inference(component_clause,[status(thm)],[f248]) ).
fof(f251,definition,
! [X0] :
( sQ23_spl
<=> ( multiply(X0,sk_c10) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c4) ) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f254,plain,
( ~ sQ4_spl
| ~ sQ17_spl
| sQ23_spl
| ~ sQ22_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f229,f245,f248,f251,f211,f125]) ).
fof(f255,definition,
( sQ24_spl
<=> multiply(sk_c5,inverse(sk_c5)) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f257,plain,
( sQ24_spl
| multiply(sk_c5,inverse(sk_c5)) != sk_c11 ),
inference(component_clause,[status(thm)],[f255]) ).
fof(f258,definition,
( sQ25_spl
<=> multiply(inverse(sk_c5),sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f260,plain,
( sQ25_spl
| multiply(inverse(sk_c5),sk_c10) != sk_c11 ),
inference(component_clause,[status(thm)],[f258]) ).
fof(f261,definition,
! [X0] :
( sQ26_spl
<=> ( multiply(X0,sk_c8) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c5) ) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f264,plain,
( ~ sQ6_spl
| ~ sQ17_spl
| sQ26_spl
| ~ sQ25_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f230,f255,f258,f261,f211,f133]) ).
fof(f275,definition,
( sQ30_spl
<=> multiply(sk_c6,inverse(sk_c6)) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f277,plain,
( sQ30_spl
| multiply(sk_c6,inverse(sk_c6)) != sk_c11 ),
inference(component_clause,[status(thm)],[f275]) ).
fof(f278,definition,
( sQ31_spl
<=> multiply(inverse(sk_c6),sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f280,plain,
( sQ31_spl
| multiply(inverse(sk_c6),sk_c10) != sk_c11 ),
inference(component_clause,[status(thm)],[f278]) ).
fof(f281,definition,
! [X0] :
( sQ32_spl
<=> ( multiply(X0,sk_c8) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c6) ) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f284,plain,
( ~ sQ9_spl
| ~ sQ17_spl
| sQ32_spl
| ~ sQ31_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f232,f275,f278,f281,f211,f145]) ).
fof(f288,definition,
( sQ34_spl
<=> multiply(inverse(sk_c1),sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f289,plain,
( ~ sQ34_spl
| multiply(inverse(sk_c1),sk_c10) = sk_c11 ),
inference(component_clause,[status(thm)],[f288]) ).
fof(f290,plain,
( sQ34_spl
| multiply(inverse(sk_c1),sk_c10) != sk_c11 ),
inference(component_clause,[status(thm)],[f288]) ).
fof(f310,plain,
( sQ34_spl
| ~ sQ11_spl
| multiply(sk_c11,sk_c10) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f154,f290]) ).
fof(f313,plain,
( ~ sQ3_spl
| ~ sQ16_spl
| inverse(sk_c4) != sk_c10 ),
inference(resolution,[status(thm)],[f209,f122]) ).
fof(f314,plain,
( ~ sQ12_spl
| ~ sQ16_spl
| inverse(sk_c2) != sk_c10 ),
inference(resolution,[status(thm)],[f209,f167]) ).
fof(f319,plain,
( ~ sQ12_spl
| ~ sQ16_spl
| ~ sQ13_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f180,f314]) ).
fof(f320,plain,
( ~ sQ12_spl
| ~ sQ16_spl
| ~ sQ13_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f319]) ).
fof(f321,plain,
( ~ sQ12_spl
| ~ sQ16_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f320]) ).
fof(f324,plain,
( ~ sQ8_spl
| multiply(sk_c6,sk_c7) = identity ),
inference(paramodulation,[status(thm)],[f142,f56]) ).
fof(f329,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f56,f57]) ).
fof(f330,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f55,f329]) ).
fof(f342,plain,
( ~ sQ1_spl
| ~ sQ15_spl
| inverse(sk_c3) != sk_c11 ),
inference(resolution,[status(thm)],[f206,f114]) ).
fof(f343,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| inverse(sk_c1) != sk_c11 ),
inference(resolution,[status(thm)],[f206,f111]) ).
fof(f350,plain,
( ~ sQ1_spl
| ~ sQ15_spl
| ~ sQ2_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f118,f342]) ).
fof(f351,plain,
( ~ sQ1_spl
| ~ sQ15_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f350]) ).
fof(f352,plain,
( ~ sQ1_spl
| ~ sQ15_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f351]) ).
fof(f386,plain,
( sQ31_spl
| ~ sQ9_spl
| multiply(sk_c8,sk_c10) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f146,f280]) ).
fof(f387,plain,
( sQ31_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f138,f386]) ).
fof(f388,plain,
( sQ31_spl
| ~ sQ9_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f387]) ).
fof(f389,plain,
( sQ31_spl
| ~ sQ9_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f388]) ).
fof(f391,plain,
( sQ30_spl
| ~ sQ9_spl
| multiply(sk_c6,sk_c8) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f146,f277]) ).
fof(f398,plain,
( sQ25_spl
| ~ sQ6_spl
| multiply(sk_c8,sk_c10) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f134,f260]) ).
fof(f399,plain,
( sQ25_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f138,f398]) ).
fof(f400,plain,
( sQ25_spl
| ~ sQ6_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f399]) ).
fof(f401,plain,
( sQ25_spl
| ~ sQ6_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f400]) ).
fof(f403,plain,
( sQ24_spl
| ~ sQ6_spl
| multiply(sk_c5,sk_c8) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f134,f257]) ).
fof(f404,plain,
( sQ24_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f130,f403]) ).
fof(f405,plain,
( sQ24_spl
| ~ sQ6_spl
| ~ sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f404]) ).
fof(f406,plain,
( sQ24_spl
| ~ sQ6_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f405]) ).
fof(f408,definition,
( sQ42_spl
<=> sk_c9 = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f410,plain,
( sQ42_spl
| sk_c9 != sk_c9 ),
inference(component_clause,[status(thm)],[f408]) ).
fof(f412,definition,
( sQ43_spl
<=> sk_c11 = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f414,plain,
( sQ43_spl
| sk_c11 != sk_c9 ),
inference(component_clause,[status(thm)],[f412]) ).
fof(f419,plain,
( ~ sQ3_spl
| ~ sQ16_spl
| ~ sQ4_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f126,f313]) ).
fof(f420,plain,
( ~ sQ3_spl
| ~ sQ16_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f419]) ).
fof(f421,plain,
( ~ sQ3_spl
| ~ sQ16_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f420]) ).
fof(f423,plain,
( sQ42_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f410]) ).
fof(f424,plain,
sQ42_spl,
inference(contradiction_clause,[status(thm)],[f423]) ).
fof(f428,plain,
( sQ22_spl
| ~ sQ4_spl
| multiply(sk_c10,sk_c10) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f126,f250]) ).
fof(f429,plain,
( sQ21_spl
| ~ sQ4_spl
| multiply(sk_c4,sk_c10) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f126,f247]) ).
fof(f430,plain,
( sQ21_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sk_c9 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f122,f429]) ).
fof(f465,plain,
( ~ sQ8_spl
| sk_c7 = multiply(inverse(sk_c6),identity) ),
inference(paramodulation,[status(thm)],[f324,f330]) ).
fof(f473,plain,
( ~ sQ1_spl
| sk_c11 = multiply(inverse(sk_c3),sk_c10) ),
inference(paramodulation,[status(thm)],[f114,f330]) ).
fof(f475,plain,
( ~ sQ3_spl
| sk_c10 = multiply(inverse(sk_c4),sk_c9) ),
inference(paramodulation,[status(thm)],[f122,f330]) ).
fof(f482,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 = multiply(sk_c8,identity) ),
inference(forward_demodulation,[status(thm)],[f146,f465]) ).
fof(f484,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c11 = multiply(sk_c11,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f118,f473]) ).
fof(f486,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c10 = multiply(sk_c10,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f126,f475]) ).
fof(f514,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c10 = multiply(inverse(sk_c11),sk_c11) ),
inference(paramodulation,[status(thm)],[f484,f330]) ).
fof(f518,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c10 = identity ),
inference(forward_demodulation,[status(thm)],[f56,f514]) ).
fof(f520,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c7 = multiply(sk_c8,sk_c10) ),
inference(backward_demodulation,[status(thm)],[f518,f482]) ).
fof(f528,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(inverse(X0),X0) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f518,f56]) ).
fof(f529,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c10,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f518,f55]) ).
fof(f530,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| sk_c7 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f138,f520]) ).
fof(f535,plain,
! [X0,X1] :
( ~ sQ17_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c10) != sk_c7
| multiply(X0,inverse(X0)) != sk_c11 ),
inference(backward_demodulation,[status(thm)],[f530,f215]) ).
fof(f537,plain,
( sQ30_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| multiply(sk_c6,sk_c8) != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f530,f391]) ).
fof(f539,plain,
( sQ43_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| sk_c7 != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f530,f414]) ).
fof(f543,plain,
( ~ sQ14_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| multiply(sk_c9,sk_c7) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f530,f193]) ).
fof(f545,plain,
( ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| multiply(sk_c5,sk_c8) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f530,f130]) ).
fof(f546,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c8,sk_c10) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f530,f138]) ).
fof(f548,plain,
! [X0,X1] :
( ~ sQ17_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c10) != sk_c7
| multiply(X0,inverse(X0)) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f530,f535]) ).
fof(f554,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c9,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f562,f529]) ).
fof(f556,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c9 = identity ),
inference(backward_demodulation,[status(thm)],[f562,f518]) ).
fof(f559,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c4) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f562,f126]) ).
fof(f562,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c10 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f529,f486]) ).
fof(f563,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(inverse(X0),X0) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f562,f528]) ).
fof(f571,plain,
! [X0,X1] :
( ~ sQ17_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c9) != sk_c7
| multiply(X0,inverse(X0)) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f562,f548]) ).
fof(f637,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ17_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| multiply(X0,sk_c9) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c4)
| multiply(inverse(sk_c4),sk_c9) != sk_c7
| multiply(sk_c4,inverse(sk_c4)) != sk_c7 ),
inference(paramodulation,[status(thm)],[f559,f571]) ).
fof(f638,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c9,sk_c4) = sk_c9 ),
inference(paramodulation,[status(thm)],[f559,f563]) ).
fof(f639,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| X0 = multiply(sk_c9,multiply(sk_c4,X0)) ),
inference(paramodulation,[status(thm)],[f559,f330]) ).
fof(f640,definition,
( sQ60_spl
<=> multiply(sk_c4,inverse(sk_c4)) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f642,plain,
( sQ60_spl
| multiply(sk_c4,inverse(sk_c4)) != sk_c7 ),
inference(component_clause,[status(thm)],[f640]) ).
fof(f643,definition,
( sQ61_spl
<=> multiply(inverse(sk_c4),sk_c9) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f645,plain,
( sQ61_spl
| multiply(inverse(sk_c4),sk_c9) != sk_c7 ),
inference(component_clause,[status(thm)],[f643]) ).
fof(f646,definition,
! [X0] :
( sQ62_spl
<=> ( multiply(X0,sk_c9) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c4) ) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f647,plain,
! [X0] :
( ~ sQ62_spl
| multiply(X0,sk_c9) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c4) ),
inference(component_clause,[status(thm)],[f646]) ).
fof(f649,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ17_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sQ62_spl
| ~ sQ61_spl
| ~ sQ60_spl ),
inference(split_clause,[status(thm)],[f637,f640,f643,f646,f137,f145,f141,f211,f117,f113,f121,f125]) ).
fof(f650,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c4 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f554,f638]) ).
fof(f651,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| X0 = multiply(sk_c4,X0) ),
inference(forward_demodulation,[status(thm)],[f554,f639]) ).
fof(f653,plain,
( sQ61_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c9,sk_c9) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f559,f645]) ).
fof(f654,plain,
( sQ61_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c9 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f554,f653]) ).
fof(f655,plain,
( sQ60_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c4,sk_c9) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f559,f642]) ).
fof(f656,plain,
( ~ sQ14_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c7 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f554,f543]) ).
fof(f657,plain,
( ~ sQ14_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c7 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f562,f656]) ).
fof(f660,plain,
( sQ21_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f430,f412,f121,f125,f245]) ).
fof(f664,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c9) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f650,f559]) ).
fof(f675,plain,
( sQ61_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ14_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f657,f654]) ).
fof(f676,plain,
( sQ61_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ14_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f675]) ).
fof(f677,plain,
( sQ61_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ14_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f676]) ).
fof(f691,plain,
( ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| sk_c8 = multiply(inverse(sk_c5),sk_c7) ),
inference(paramodulation,[status(thm)],[f545,f330]) ).
fof(f693,plain,
( ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ6_spl
| sk_c8 = multiply(sk_c8,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f134,f691]) ).
fof(f714,plain,
( ~ sQ12_spl
| sk_c10 = multiply(inverse(sk_c2),sk_c9) ),
inference(paramodulation,[status(thm)],[f167,f330]) ).
fof(f716,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| sk_c10 = multiply(sk_c10,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f180,f714]) ).
fof(f735,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| X0 = multiply(sk_c9,X0) ),
inference(forward_demodulation,[status(thm)],[f650,f651]) ).
fof(f765,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(inverse(X0),X0) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f556,f56]) ).
fof(f797,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c8,sk_c9) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f562,f546]) ).
fof(f811,plain,
( ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ6_spl
| sk_c7 = multiply(inverse(sk_c8),sk_c8) ),
inference(paramodulation,[status(thm)],[f693,f330]) ).
fof(f813,plain,
( ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c7 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f765,f811]) ).
fof(f814,plain,
( ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sQ43_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f813,f539]) ).
fof(f815,plain,
( ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sQ43_spl ),
inference(contradiction_clause,[status(thm)],[f814]) ).
fof(f828,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c8,sk_c7) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f813,f797]) ).
fof(f833,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ6_spl
| multiply(inverse(X0),X0) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f813,f765]) ).
fof(f837,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ6_spl
| X0 = multiply(sk_c7,X0) ),
inference(backward_demodulation,[status(thm)],[f813,f735]) ).
fof(f838,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ6_spl
| inverse(sk_c9) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f813,f664]) ).
fof(f839,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ6_spl
| sk_c10 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f813,f562]) ).
fof(f841,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ6_spl
| sk_c4 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f813,f650]) ).
fof(f842,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c8 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f693,f828]) ).
fof(f843,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ6_spl
| inverse(sk_c7) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f813,f838]) ).
fof(f844,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ6_spl
| sk_c6 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f142,f843]) ).
fof(f851,plain,
( ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| inverse(sk_c6) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f842,f146]) ).
fof(f854,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c8 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f844,f842]) ).
fof(f856,plain,
( ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c6 = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f844,f813]) ).
fof(f860,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c6 = sk_c11 ),
inference(backward_demodulation,[status(thm)],[f844,f530]) ).
fof(f861,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ6_spl
| sk_c10 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f844,f839]) ).
fof(f863,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ6_spl
| sk_c4 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f844,f841]) ).
fof(f865,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ6_spl
| X0 = multiply(sk_c6,X0) ),
inference(forward_demodulation,[status(thm)],[f844,f837]) ).
fof(f871,plain,
( ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| inverse(sk_c6) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f844,f851]) ).
fof(f923,plain,
( sQ14_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c6,sk_c11) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f856,f194]) ).
fof(f924,plain,
( sQ14_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c11 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f865,f923]) ).
fof(f925,plain,
( sQ14_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c6 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f860,f924]) ).
fof(f926,plain,
( sQ14_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f861,f925]) ).
fof(f927,plain,
( sQ14_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f926]) ).
fof(f928,plain,
( sQ14_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f927]) ).
fof(f970,plain,
( ~ sQ13_spl
| multiply(sk_c10,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f180,f56]) ).
fof(f971,plain,
( ~ sQ11_spl
| multiply(sk_c11,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f154,f56]) ).
fof(f982,plain,
( ~ sQ0_spl
| sk_c11 = multiply(inverse(sk_c1),sk_c10) ),
inference(paramodulation,[status(thm)],[f111,f330]) ).
fof(f984,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| sk_c11 = multiply(sk_c11,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f154,f982]) ).
fof(f985,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| sQ34_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f984,f310]) ).
fof(f986,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| sQ34_spl ),
inference(contradiction_clause,[status(thm)],[f985]) ).
fof(f987,plain,
( ~ sQ34_spl
| ~ sQ11_spl
| multiply(sk_c11,sk_c10) = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f154,f289]) ).
fof(f1004,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| sk_c9 = multiply(inverse(sk_c10),sk_c10) ),
inference(paramodulation,[status(thm)],[f716,f330]) ).
fof(f1006,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| sk_c9 = identity ),
inference(forward_demodulation,[status(thm)],[f56,f1004]) ).
fof(f1009,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ13_spl
| multiply(inverse(X0),X0) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f1006,f56]) ).
fof(f1011,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ13_spl
| multiply(sk_c9,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f1006,f55]) ).
fof(f1012,plain,
( ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| sk_c11 = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f1011,f193]) ).
fof(f1021,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ11_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f154,f343]) ).
fof(f1022,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1021]) ).
fof(f1023,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f1022]) ).
fof(f1051,plain,
( ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| inverse(sk_c1) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f1012,f154]) ).
fof(f1058,plain,
! [X0,X1] :
( ~ sQ17_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c10) != sk_c11
| multiply(X0,inverse(X0)) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1012,f215]) ).
fof(f1059,plain,
! [X0,X1] :
( ~ sQ17_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c10) != sk_c10
| multiply(X0,inverse(X0)) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1012,f1058]) ).
fof(f1120,plain,
( ~ sQ13_spl
| ~ sQ12_spl
| multiply(sk_c10,sk_c2) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1006,f970]) ).
fof(f1124,plain,
( ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| multiply(sk_c10,sk_c1) = identity ),
inference(forward_demodulation,[status(thm)],[f1012,f971]) ).
fof(f1125,plain,
( ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| multiply(sk_c10,sk_c1) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1006,f1124]) ).
fof(f1135,plain,
( ~ sQ34_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| multiply(sk_c10,sk_c10) = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1012,f987]) ).
fof(f1136,plain,
( ~ sQ34_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| multiply(sk_c10,sk_c10) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1012,f1135]) ).
fof(f1137,plain,
( ~ sQ34_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| sk_c10 = multiply(inverse(sk_c10),sk_c10) ),
inference(paramodulation,[status(thm)],[f1136,f330]) ).
fof(f1139,plain,
( ~ sQ34_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| sk_c10 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1009,f1137]) ).
fof(f1146,plain,
( ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ34_spl
| multiply(sk_c9,sk_c1) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f1139,f1125]) ).
fof(f1147,plain,
( ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ34_spl
| ~ sQ11_spl
| ~ sQ14_spl
| multiply(sk_c9,sk_c2) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f1139,f1120]) ).
fof(f1148,plain,
( ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ34_spl
| inverse(sk_c1) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f1139,f1051]) ).
fof(f1149,plain,
! [X0,X1] :
( ~ sQ17_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ34_spl
| ~ sQ11_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c10) != sk_c9
| multiply(X0,inverse(X0)) != sk_c10 ),
inference(backward_demodulation,[status(thm)],[f1139,f1059]) ).
fof(f1161,plain,
( ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ34_spl
| sk_c1 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1011,f1146]) ).
fof(f1162,plain,
( ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ34_spl
| ~ sQ11_spl
| ~ sQ14_spl
| sk_c2 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1011,f1147]) ).
fof(f1163,plain,
! [X0,X1] :
( ~ sQ17_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ34_spl
| ~ sQ11_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c10) != sk_c9
| multiply(X0,inverse(X0)) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1139,f1149]) ).
fof(f1164,plain,
! [X0,X1] :
( ~ sQ17_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ34_spl
| ~ sQ11_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c9) != sk_c9
| multiply(X0,inverse(X0)) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1139,f1163]) ).
fof(f1170,plain,
( ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ34_spl
| sk_c1 = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f1162,f1161]) ).
fof(f1174,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ34_spl
| ~ sQ11_spl
| ~ sQ14_spl
| multiply(sk_c2,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f1162,f1011]) ).
fof(f1188,plain,
( ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ34_spl
| inverse(sk_c2) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1170,f1148]) ).
fof(f1189,plain,
( ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ34_spl
| inverse(sk_c2) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1162,f1188]) ).
fof(f1210,plain,
! [X0,X1] :
( ~ sQ17_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ34_spl
| ~ sQ11_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c9) != sk_c9
| multiply(X0,inverse(X0)) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1162,f1164]) ).
fof(f1211,plain,
! [X0,X1] :
( ~ sQ17_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ34_spl
| ~ sQ11_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c2) != sk_c9
| multiply(X0,inverse(X0)) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1162,f1210]) ).
fof(f1212,plain,
! [X0,X1] :
( ~ sQ17_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ34_spl
| ~ sQ11_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c2) != sk_c2
| multiply(X0,inverse(X0)) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1162,f1211]) ).
fof(f1215,definition,
( sQ75_spl
<=> multiply(sk_c2,inverse(sk_c2)) = sk_c2 ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f1217,plain,
( sQ75_spl
| multiply(sk_c2,inverse(sk_c2)) != sk_c2 ),
inference(component_clause,[status(thm)],[f1215]) ).
fof(f1218,definition,
( sQ76_spl
<=> multiply(inverse(sk_c2),sk_c2) = sk_c2 ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f1220,plain,
( sQ76_spl
| multiply(inverse(sk_c2),sk_c2) != sk_c2 ),
inference(component_clause,[status(thm)],[f1218]) ).
fof(f1226,plain,
( sQ76_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ34_spl
| multiply(sk_c2,sk_c2) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1189,f1220]) ).
fof(f1227,plain,
( sQ75_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ34_spl
| multiply(sk_c2,sk_c2) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1189,f1217]) ).
fof(f1231,plain,
( ~ sQ17_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ34_spl
| ~ sQ11_spl
| inverse(inverse(sk_c2)) != inverse(sk_c2)
| multiply(inverse(sk_c2),sk_c2) != sk_c2
| multiply(sk_c2,inverse(sk_c2)) != sk_c2 ),
inference(resolution,[status(thm)],[f1174,f1212]) ).
fof(f1235,definition,
( sQ78_spl
<=> inverse(inverse(sk_c2)) = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f1237,plain,
( sQ78_spl
| inverse(inverse(sk_c2)) != inverse(sk_c2) ),
inference(component_clause,[status(thm)],[f1235]) ).
fof(f1238,plain,
( ~ sQ17_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ34_spl
| ~ sQ11_spl
| ~ sQ78_spl
| ~ sQ76_spl
| ~ sQ75_spl ),
inference(split_clause,[status(thm)],[f1231,f1215,f1218,f1235,f153,f288,f179,f166,f192,f211]) ).
fof(f1244,plain,
( sQ78_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ34_spl
| inverse(sk_c2) != inverse(sk_c2) ),
inference(forward_demodulation,[status(thm)],[f1189,f1237]) ).
fof(f1245,plain,
( sQ78_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ34_spl
| sk_c2 != inverse(sk_c2) ),
inference(forward_demodulation,[status(thm)],[f1189,f1244]) ).
fof(f1246,plain,
( sQ78_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ34_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1189,f1245]) ).
fof(f1247,plain,
( sQ78_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ34_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1246]) ).
fof(f1248,plain,
( sQ78_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ34_spl ),
inference(contradiction_clause,[status(thm)],[f1247]) ).
fof(f1341,plain,
( sQ76_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ34_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1174,f1226]) ).
fof(f1342,plain,
( sQ76_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ34_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1341]) ).
fof(f1343,plain,
( sQ76_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ34_spl ),
inference(contradiction_clause,[status(thm)],[f1342]) ).
fof(f1358,plain,
( sQ75_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ34_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1174,f1227]) ).
fof(f1359,plain,
( sQ75_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ34_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1358]) ).
fof(f1360,plain,
( sQ75_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ34_spl ),
inference(contradiction_clause,[status(thm)],[f1359]) ).
fof(f1453,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ6_spl
| multiply(inverse(X0),X0) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f844,f833]) ).
fof(f1522,plain,
( sQ60_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ6_spl
| multiply(sk_c6,sk_c9) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f863,f655]) ).
fof(f1523,plain,
( sQ60_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ6_spl
| sk_c9 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f865,f1522]) ).
fof(f1524,plain,
( sQ60_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ6_spl
| sk_c6 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f856,f1523]) ).
fof(f1525,plain,
( sQ60_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ6_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f844,f1524]) ).
fof(f1526,plain,
( sQ60_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1525]) ).
fof(f1527,plain,
( sQ60_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f1526]) ).
fof(f1532,plain,
( sQ22_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ6_spl
| multiply(sk_c6,sk_c10) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f861,f428]) ).
fof(f1533,plain,
( sQ22_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ6_spl
| sk_c10 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f865,f1532]) ).
fof(f1534,plain,
( sQ22_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ6_spl
| sk_c6 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f861,f1533]) ).
fof(f1535,plain,
( sQ22_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ6_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f860,f1534]) ).
fof(f1536,plain,
( sQ22_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1535]) ).
fof(f1537,plain,
( sQ22_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f1536]) ).
fof(f1607,plain,
( sQ30_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c8 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f865,f537]) ).
fof(f1608,plain,
( sQ30_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c6 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f854,f1607]) ).
fof(f1609,plain,
( sQ30_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f844,f1608]) ).
fof(f1610,plain,
( sQ30_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1609]) ).
fof(f1611,plain,
( sQ30_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f1610]) ).
fof(f1781,plain,
! [X0] :
( ~ sQ62_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ6_spl
| multiply(X0,sk_c9) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c6) ),
inference(forward_demodulation,[status(thm)],[f863,f647]) ).
fof(f1782,plain,
! [X0] :
( ~ sQ62_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ6_spl
| multiply(X0,sk_c9) != inverse(X0)
| inverse(inverse(X0)) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f871,f1781]) ).
fof(f1783,plain,
! [X0] :
( ~ sQ62_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ6_spl
| multiply(X0,sk_c6) != inverse(X0)
| inverse(inverse(X0)) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f856,f1782]) ).
fof(f1785,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ62_spl
| sk_c6 != inverse(inverse(sk_c6))
| inverse(inverse(inverse(sk_c6))) != sk_c6 ),
inference(paramodulation,[status(thm)],[f1453,f1783]) ).
fof(f1787,definition,
( sQ86_spl
<=> inverse(inverse(sk_c6)) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f1789,plain,
( sQ86_spl
| inverse(inverse(sk_c6)) != sk_c6 ),
inference(component_clause,[status(thm)],[f1787]) ).
fof(f1794,definition,
( sQ88_spl
<=> inverse(inverse(inverse(sk_c6))) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition]) ).
fof(f1796,plain,
( sQ88_spl
| inverse(inverse(inverse(sk_c6))) != sk_c6 ),
inference(component_clause,[status(thm)],[f1794]) ).
fof(f1797,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ62_spl
| ~ sQ86_spl
| ~ sQ88_spl ),
inference(split_clause,[status(thm)],[f1785,f1794,f1787,f646,f133,f137,f145,f141,f129,f125,f121,f117,f113]) ).
fof(f1798,plain,
( sQ86_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| inverse(sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f871,f1789]) ).
fof(f1799,plain,
( sQ86_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f871,f1798]) ).
fof(f1800,plain,
( sQ86_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1799]) ).
fof(f1801,plain,
( sQ86_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f1800]) ).
fof(f1802,plain,
( sQ88_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| inverse(inverse(sk_c6)) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f871,f1796]) ).
fof(f1803,plain,
( sQ88_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| inverse(sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f871,f1802]) ).
fof(f1804,plain,
( sQ88_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f871,f1803]) ).
fof(f1805,plain,
( sQ88_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1804]) ).
fof(f1806,plain,
( sQ88_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f1805]) ).
fof(f1807,plain,
$false,
inference(sat_refutation,[status(thm)],[f116,f120,f124,f128,f132,f136,f140,f144,f148,f156,f157,f158,f159,f160,f161,f162,f163,f164,f169,f170,f171,f172,f173,f174,f175,f176,f177,f182,f183,f184,f185,f186,f187,f188,f189,f190,f195,f196,f197,f198,f199,f200,f201,f202,f203,f214,f254,f264,f284,f321,f352,f389,f401,f406,f421,f424,f649,f660,f677,f815,f928,f986,f1023,f1238,f1248,f1343,f1360,f1527,f1537,f1611,f1797,f1801,f1806]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP260-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n003.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 20:09:30 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.12/0.41 % Refutation found
% 0.12/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.44 % Elapsed time: 0.073932 seconds
% 0.12/0.44 % CPU time: 0.332760 seconds
% 0.12/0.44 % Total memory used: 109.686 MB
% 0.12/0.44 % Net memory used: 109.431 MB
%------------------------------------------------------------------------------