%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP330-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 12:33:26 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.42s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 93
% Syntax : Number of formulae : 540 ( 16 unt; 43 def)
% Number of atoms : 2466 ( 608 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 3709 (1783 ~;1883 |; 0 &)
% ( 43 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 45 ( 43 usr; 44 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 117 ( 117 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c10,sk_c11) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c10,sk_c11) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c10,sk_c11) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c10,sk_c11) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c10,sk_c11) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c10,sk_c11) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c10,sk_c11) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c6) = sk_c8
| multiply(sk_c10,sk_c11) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c7) = sk_c6
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( inverse(sk_c6) = sk_c8
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c3) = sk_c11
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( inverse(sk_c7) = sk_c6
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( inverse(sk_c6) = sk_c8
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,negated_conjecture,
( inverse(sk_c6) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
( inverse(sk_c3) = sk_c11
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f51,negated_conjecture,
( inverse(sk_c7) = sk_c6
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f52,negated_conjecture,
( inverse(sk_c6) = sk_c8
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f53,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox2/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
| inverse(X4) != sk_c9
| multiply(X4,sk_c9) != sk_c10
| inverse(X3) != sk_c10
| multiply(X3,sk_c10) != sk_c11
| multiply(sk_c10,sk_c11) != sk_c9 ),
file('/export/starexec/sandbox2/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_c10,sk_c11) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f59,plain,
( inverse(sk_c3) = sk_c11
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f60,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f61,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f62,plain,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f63,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f64,plain,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f66,plain,
( inverse(sk_c6) = sk_c8
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f68,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f69,plain,
( inverse(sk_c3) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f70,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f71,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f72,plain,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f73,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f74,plain,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f75,plain,
( inverse(sk_c7) = sk_c6
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f76,plain,
( inverse(sk_c6) = sk_c8
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f77,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f78,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f79,plain,
( inverse(sk_c3) = sk_c11
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f80,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f81,plain,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f82,plain,
( multiply(sk_c5,sk_c8) = sk_c11
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f83,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f84,plain,
( multiply(sk_c8,sk_c10) = sk_c11
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f85,plain,
( inverse(sk_c7) = sk_c6
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f86,plain,
( inverse(sk_c6) = sk_c8
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f87,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f88,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f89,plain,
( inverse(sk_c3) = sk_c11
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f90,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f91,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f92,plain,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f93,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f94,plain,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f96,plain,
( inverse(sk_c6) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f98,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f99,plain,
( inverse(sk_c3) = sk_c11
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f100,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f101,plain,
( inverse(sk_c4) = sk_c10
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f102,plain,
( multiply(sk_c5,sk_c8) = sk_c11
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f103,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f104,plain,
( multiply(sk_c8,sk_c10) = sk_c11
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f105,plain,
( inverse(sk_c7) = sk_c6
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f106,plain,
( inverse(sk_c6) = sk_c8
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f107,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f53]) ).
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
| ! [X4] :
( inverse(X4) != sk_c9
| multiply(X4,sk_c9) != sk_c10
| ! [X3] :
( inverse(X3) != sk_c10
| multiply(X3,sk_c10) != sk_c11
| multiply(sk_c10,sk_c11) != sk_c9 ) ) ) ) ) ),
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
| inverse(X1) != sk_c9
| multiply(X1,sk_c9) != sk_c10
| inverse(X0) != sk_c10
| multiply(X0,sk_c10) != sk_c11
| multiply(sk_c10,sk_c11) != sk_c9 ),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f110,definition,
( sQ0_spl
<=> multiply(sk_c10,sk_c11) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f111,plain,
( ~ sQ0_spl
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(component_clause,[status(thm)],[f110]) ).
fof(f112,plain,
( sQ0_spl
| multiply(sk_c10,sk_c11) != sk_c9 ),
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(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(f149,definition,
( sQ10_spl
<=> multiply(sk_c7,sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f150,plain,
( ~ sQ10_spl
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(component_clause,[status(thm)],[f149]) ).
fof(f153,definition,
( sQ11_spl
<=> multiply(sk_c1,sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f154,plain,
( ~ sQ11_spl
| multiply(sk_c1,sk_c10) = 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(f165,plain,
( sQ10_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f77,f153,f149]) ).
fof(f166,definition,
( sQ12_spl
<=> inverse(sk_c1) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f167,plain,
( ~ sQ12_spl
| inverse(sk_c1) = sk_c10 ),
inference(component_clause,[status(thm)],[f166]) ).
fof(f168,plain,
( sQ12_spl
| inverse(sk_c1) != sk_c10 ),
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(f178,plain,
( sQ10_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f87,f166,f149]) ).
fof(f179,definition,
( sQ13_spl
<=> multiply(sk_c2,sk_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f180,plain,
( ~ sQ13_spl
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(component_clause,[status(thm)],[f179]) ).
fof(f181,plain,
( sQ13_spl
| multiply(sk_c2,sk_c9) != 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(f190,plain,
( sQ9_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f96,f179,f145]) ).
fof(f192,definition,
( sQ14_spl
<=> inverse(sk_c2) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f193,plain,
( ~ sQ14_spl
| inverse(sk_c2) = sk_c9 ),
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(f204,plain,
( sQ10_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f107,f192,f149]) ).
fof(f205,definition,
! [X0] :
( sQ15_spl
<=> ( inverse(X0) != sk_c10
| multiply(X0,sk_c10) != sk_c11 ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f206,plain,
! [X0] :
( ~ sQ15_spl
| inverse(X0) != sk_c10
| multiply(X0,sk_c10) != sk_c11 ),
inference(component_clause,[status(thm)],[f205]) ).
fof(f208,definition,
! [X1] :
( sQ16_spl
<=> ( inverse(X1) != sk_c9
| multiply(X1,sk_c9) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f209,plain,
! [X0] :
( ~ sQ16_spl
| inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c10 ),
inference(component_clause,[status(thm)],[f208]) ).
fof(f211,definition,
! [X2] :
( sQ17_spl
<=> ( inverse(X2) != sk_c11
| multiply(X2,sk_c11) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f212,plain,
! [X0] :
( ~ sQ17_spl
| inverse(X0) != sk_c11
| multiply(X0,sk_c11) != sk_c10 ),
inference(component_clause,[status(thm)],[f211]) ).
fof(f214,definition,
! [X3] :
( sQ18_spl
<=> ( inverse(X3) != sk_c10
| multiply(X3,sk_c10) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f215,plain,
! [X0] :
( ~ sQ18_spl
| inverse(X0) != sk_c10
| multiply(X0,sk_c10) != sk_c9 ),
inference(component_clause,[status(thm)],[f214]) ).
fof(f217,definition,
! [X4,X5,X6,X7] :
( sQ19_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,[sQ19_spl])],[split_symbol_definition]) ).
fof(f218,plain,
! [X0,X1,X2,X3] :
( ~ sQ19_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)],[f217]) ).
fof(f220,plain,
( sQ19_spl
| sQ18_spl
| sQ17_spl
| sQ16_spl
| sQ15_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f109,f110,f205,f208,f211,f214,f217]) ).
fof(f221,plain,
! [X0,X1] :
( ~ sQ19_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)],[f218]) ).
fof(f228,plain,
( ~ sQ6_spl
| multiply(sk_c8,sk_c5) = identity ),
inference(paramodulation,[status(thm)],[f134,f56]) ).
fof(f229,plain,
( ~ sQ8_spl
| multiply(sk_c6,sk_c7) = identity ),
inference(paramodulation,[status(thm)],[f142,f56]) ).
fof(f230,plain,
( ~ sQ9_spl
| multiply(sk_c8,sk_c6) = identity ),
inference(paramodulation,[status(thm)],[f146,f56]) ).
fof(f231,plain,
( ~ sQ12_spl
| multiply(sk_c10,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f167,f56]) ).
fof(f232,plain,
( ~ sQ14_spl
| multiply(sk_c9,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f193,f56]) ).
fof(f233,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f56,f57]) ).
fof(f234,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f55,f233]) ).
fof(f235,plain,
! [X0] :
( ~ sQ10_spl
| multiply(sk_c6,X0) = multiply(sk_c7,multiply(sk_c8,X0)) ),
inference(paramodulation,[status(thm)],[f150,f57]) ).
fof(f236,plain,
! [X0] :
( ~ sQ7_spl
| multiply(sk_c11,X0) = multiply(sk_c8,multiply(sk_c10,X0)) ),
inference(paramodulation,[status(thm)],[f138,f57]) ).
fof(f237,plain,
( ~ sQ4_spl
| multiply(sk_c10,sk_c4) = identity ),
inference(paramodulation,[status(thm)],[f126,f56]) ).
fof(f238,plain,
( ~ sQ2_spl
| multiply(sk_c11,sk_c3) = identity ),
inference(paramodulation,[status(thm)],[f118,f56]) ).
fof(f239,plain,
! [X0] :
( ~ sQ5_spl
| multiply(sk_c11,X0) = multiply(sk_c5,multiply(sk_c8,X0)) ),
inference(paramodulation,[status(thm)],[f130,f57]) ).
fof(f240,plain,
! [X0] :
( ~ sQ3_spl
| multiply(sk_c9,X0) = multiply(sk_c4,multiply(sk_c10,X0)) ),
inference(paramodulation,[status(thm)],[f122,f57]) ).
fof(f241,plain,
! [X0] :
( ~ sQ1_spl
| multiply(sk_c10,X0) = multiply(sk_c3,multiply(sk_c11,X0)) ),
inference(paramodulation,[status(thm)],[f114,f57]) ).
fof(f242,plain,
( ~ sQ19_spl
| inverse(inverse(identity)) != inverse(identity)
| multiply(inverse(identity),sk_c10) != sk_c11
| multiply(identity,inverse(identity)) != sk_c11 ),
inference(resolution,[status(thm)],[f221,f55]) ).
fof(f243,plain,
! [X0] :
( ~ sQ19_spl
| multiply(X0,inverse(identity)) != inverse(X0)
| inverse(inverse(X0)) != inverse(identity)
| multiply(inverse(identity),sk_c10) != sk_c11
| inverse(identity) != sk_c11 ),
inference(paramodulation,[status(thm)],[f55,f221]) ).
fof(f250,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ19_spl
| multiply(X0,inverse(sk_c1)) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c1)
| multiply(inverse(sk_c1),sk_c10) != sk_c11
| multiply(sk_c1,sk_c10) != sk_c11 ),
inference(paramodulation,[status(thm)],[f167,f221]) ).
fof(f252,definition,
( sQ20_spl
<=> multiply(identity,inverse(identity)) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f254,plain,
( sQ20_spl
| multiply(identity,inverse(identity)) != sk_c11 ),
inference(component_clause,[status(thm)],[f252]) ).
fof(f255,definition,
( sQ21_spl
<=> multiply(inverse(identity),sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f256,plain,
( ~ sQ21_spl
| multiply(inverse(identity),sk_c10) = sk_c11 ),
inference(component_clause,[status(thm)],[f255]) ).
fof(f257,plain,
( sQ21_spl
| multiply(inverse(identity),sk_c10) != sk_c11 ),
inference(component_clause,[status(thm)],[f255]) ).
fof(f258,definition,
( sQ22_spl
<=> inverse(inverse(identity)) = inverse(identity) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f260,plain,
( sQ22_spl
| inverse(inverse(identity)) != inverse(identity) ),
inference(component_clause,[status(thm)],[f258]) ).
fof(f261,plain,
( ~ sQ19_spl
| ~ sQ22_spl
| ~ sQ21_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f242,f252,f255,f258,f217]) ).
fof(f262,definition,
( sQ23_spl
<=> inverse(identity) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f264,plain,
( sQ23_spl
| inverse(identity) != sk_c11 ),
inference(component_clause,[status(thm)],[f262]) ).
fof(f265,definition,
! [X0] :
( sQ24_spl
<=> ( multiply(X0,inverse(identity)) != inverse(X0)
| inverse(inverse(X0)) != inverse(identity) ) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f268,plain,
( ~ sQ19_spl
| sQ24_spl
| ~ sQ21_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f243,f262,f255,f265,f217]) ).
fof(f289,definition,
( sQ31_spl
<=> multiply(inverse(sk_c5),sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f291,plain,
( sQ31_spl
| multiply(inverse(sk_c5),sk_c10) != sk_c11 ),
inference(component_clause,[status(thm)],[f289]) ).
fof(f296,definition,
( sQ33_spl
<=> multiply(sk_c7,sk_c6) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f297,plain,
( ~ sQ33_spl
| multiply(sk_c7,sk_c6) = sk_c11 ),
inference(component_clause,[status(thm)],[f296]) ).
fof(f298,plain,
( sQ33_spl
| multiply(sk_c7,sk_c6) != sk_c11 ),
inference(component_clause,[status(thm)],[f296]) ).
fof(f316,definition,
( sQ39_spl
<=> multiply(inverse(sk_c1),sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f318,plain,
( sQ39_spl
| multiply(inverse(sk_c1),sk_c10) != sk_c11 ),
inference(component_clause,[status(thm)],[f316]) ).
fof(f319,definition,
! [X0] :
( sQ40_spl
<=> ( multiply(X0,inverse(sk_c1)) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c1) ) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f322,plain,
( ~ sQ12_spl
| ~ sQ19_spl
| sQ40_spl
| ~ sQ39_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f250,f153,f316,f319,f217,f166]) ).
fof(f342,plain,
( sQ20_spl
| inverse(identity) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f55,f254]) ).
fof(f345,plain,
( ~ sQ3_spl
| ~ sQ18_spl
| inverse(sk_c4) != sk_c10
| sk_c9 != sk_c9 ),
inference(paramodulation,[status(thm)],[f122,f215]) ).
fof(f347,plain,
( ~ sQ18_spl
| inverse(inverse(sk_c10)) != sk_c10
| identity != sk_c9 ),
inference(paramodulation,[status(thm)],[f56,f215]) ).
fof(f348,plain,
( ~ sQ18_spl
| inverse(identity) != sk_c10
| sk_c10 != sk_c9 ),
inference(paramodulation,[status(thm)],[f55,f215]) ).
fof(f349,plain,
( ~ sQ11_spl
| ~ sQ18_spl
| inverse(sk_c1) != sk_c10
| sk_c11 != sk_c9 ),
inference(paramodulation,[status(thm)],[f154,f215]) ).
fof(f351,definition,
( sQ44_spl
<=> sk_c9 = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f353,plain,
( sQ44_spl
| sk_c9 != sk_c9 ),
inference(component_clause,[status(thm)],[f351]) ).
fof(f354,plain,
( ~ sQ3_spl
| ~ sQ18_spl
| ~ sQ4_spl
| ~ sQ44_spl ),
inference(split_clause,[status(thm)],[f345,f351,f125,f214,f121]) ).
fof(f355,definition,
( sQ45_spl
<=> sk_c11 = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f356,plain,
( ~ sQ45_spl
| sk_c11 = sk_c9 ),
inference(component_clause,[status(thm)],[f355]) ).
fof(f357,plain,
( sQ45_spl
| sk_c11 != sk_c9 ),
inference(component_clause,[status(thm)],[f355]) ).
fof(f358,definition,
( sQ46_spl
<=> inverse(sk_c8) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f359,plain,
( ~ sQ46_spl
| inverse(sk_c8) = sk_c10 ),
inference(component_clause,[status(thm)],[f358]) ).
fof(f360,plain,
( sQ46_spl
| inverse(sk_c8) != sk_c10 ),
inference(component_clause,[status(thm)],[f358]) ).
fof(f362,definition,
( sQ47_spl
<=> identity = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f363,plain,
( ~ sQ47_spl
| identity = sk_c9 ),
inference(component_clause,[status(thm)],[f362]) ).
fof(f364,plain,
( sQ47_spl
| identity != sk_c9 ),
inference(component_clause,[status(thm)],[f362]) ).
fof(f365,definition,
( sQ48_spl
<=> inverse(inverse(sk_c10)) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f368,plain,
( ~ sQ18_spl
| ~ sQ48_spl
| ~ sQ47_spl ),
inference(split_clause,[status(thm)],[f347,f362,f365,f214]) ).
fof(f369,definition,
( sQ49_spl
<=> sk_c10 = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f371,plain,
( sQ49_spl
| sk_c10 != sk_c9 ),
inference(component_clause,[status(thm)],[f369]) ).
fof(f372,definition,
( sQ50_spl
<=> inverse(identity) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f374,plain,
( sQ50_spl
| inverse(identity) != sk_c10 ),
inference(component_clause,[status(thm)],[f372]) ).
fof(f375,plain,
( ~ sQ18_spl
| ~ sQ50_spl
| ~ sQ49_spl ),
inference(split_clause,[status(thm)],[f348,f369,f372,f214]) ).
fof(f376,plain,
( ~ sQ11_spl
| ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ45_spl ),
inference(split_clause,[status(thm)],[f349,f355,f166,f214,f153]) ).
fof(f377,plain,
( sQ44_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f353]) ).
fof(f378,plain,
sQ44_spl,
inference(contradiction_clause,[status(thm)],[f377]) ).
fof(f382,plain,
( ~ sQ0_spl
| ~ sQ17_spl
| inverse(sk_c10) != sk_c11
| sk_c9 != sk_c10 ),
inference(paramodulation,[status(thm)],[f111,f212]) ).
fof(f383,plain,
( ~ sQ1_spl
| ~ sQ17_spl
| inverse(sk_c3) != sk_c11
| sk_c10 != sk_c10 ),
inference(paramodulation,[status(thm)],[f114,f212]) ).
fof(f385,plain,
( ~ sQ17_spl
| inverse(identity) != sk_c11
| sk_c11 != sk_c10 ),
inference(paramodulation,[status(thm)],[f55,f212]) ).
fof(f387,definition,
( sQ51_spl
<=> inverse(sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f388,plain,
( ~ sQ51_spl
| inverse(sk_c10) = sk_c11 ),
inference(component_clause,[status(thm)],[f387]) ).
fof(f389,plain,
( sQ51_spl
| inverse(sk_c10) != sk_c11 ),
inference(component_clause,[status(thm)],[f387]) ).
fof(f390,plain,
( ~ sQ0_spl
| ~ sQ17_spl
| ~ sQ51_spl
| ~ sQ49_spl ),
inference(split_clause,[status(thm)],[f382,f369,f387,f211,f110]) ).
fof(f391,definition,
( sQ52_spl
<=> sk_c10 = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f393,plain,
( sQ52_spl
| sk_c10 != sk_c10 ),
inference(component_clause,[status(thm)],[f391]) ).
fof(f394,plain,
( ~ sQ1_spl
| ~ sQ17_spl
| ~ sQ2_spl
| ~ sQ52_spl ),
inference(split_clause,[status(thm)],[f383,f391,f117,f211,f113]) ).
fof(f395,definition,
( sQ53_spl
<=> identity = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f396,plain,
( ~ sQ53_spl
| identity = sk_c10 ),
inference(component_clause,[status(thm)],[f395]) ).
fof(f397,plain,
( sQ53_spl
| identity != sk_c10 ),
inference(component_clause,[status(thm)],[f395]) ).
fof(f402,definition,
( sQ55_spl
<=> sk_c11 = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f404,plain,
( sQ55_spl
| sk_c11 != sk_c10 ),
inference(component_clause,[status(thm)],[f402]) ).
fof(f405,plain,
( ~ sQ17_spl
| ~ sQ23_spl
| ~ sQ55_spl ),
inference(split_clause,[status(thm)],[f385,f402,f262,f211]) ).
fof(f406,plain,
( sQ52_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f393]) ).
fof(f407,plain,
sQ52_spl,
inference(contradiction_clause,[status(thm)],[f406]) ).
fof(f409,plain,
( ~ sQ13_spl
| ~ sQ16_spl
| inverse(sk_c2) != sk_c9 ),
inference(resolution,[status(thm)],[f209,f180]) ).
fof(f411,plain,
( ~ sQ16_spl
| inverse(identity) != sk_c9
| sk_c9 != sk_c10 ),
inference(paramodulation,[status(thm)],[f55,f209]) ).
fof(f414,plain,
( ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ14_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f193,f409]) ).
fof(f415,plain,
( ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ14_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f414]) ).
fof(f416,plain,
( ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f415]) ).
fof(f418,plain,
( sQ31_spl
| ~ sQ6_spl
| multiply(sk_c8,sk_c10) != sk_c11 ),
inference(backward_demodulation,[status(thm)],[f134,f291]) ).
fof(f428,plain,
( sQ31_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f138,f418]) ).
fof(f429,plain,
( sQ31_spl
| ~ sQ6_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f428]) ).
fof(f430,plain,
( sQ31_spl
| ~ sQ6_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f429]) ).
fof(f441,plain,
( ~ sQ15_spl
| inverse(inverse(sk_c10)) != sk_c10
| identity != sk_c11 ),
inference(paramodulation,[status(thm)],[f56,f206]) ).
fof(f442,plain,
( ~ sQ15_spl
| inverse(identity) != sk_c10
| sk_c10 != sk_c11 ),
inference(paramodulation,[status(thm)],[f55,f206]) ).
fof(f444,definition,
( sQ56_spl
<=> identity = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f447,plain,
( ~ sQ15_spl
| ~ sQ48_spl
| ~ sQ56_spl ),
inference(split_clause,[status(thm)],[f441,f444,f365,f205]) ).
fof(f448,plain,
( ~ sQ15_spl
| ~ sQ50_spl
| ~ sQ55_spl ),
inference(split_clause,[status(thm)],[f442,f402,f372,f205]) ).
fof(f450,plain,
( sQ39_spl
| ~ sQ12_spl
| multiply(sk_c10,sk_c10) != sk_c11 ),
inference(backward_demodulation,[status(thm)],[f167,f318]) ).
fof(f463,plain,
! [X0] :
( ~ sQ14_spl
| multiply(identity,X0) = multiply(sk_c9,multiply(sk_c2,X0)) ),
inference(paramodulation,[status(thm)],[f232,f57]) ).
fof(f464,plain,
! [X0] :
( ~ sQ14_spl
| X0 = multiply(sk_c9,multiply(sk_c2,X0)) ),
inference(forward_demodulation,[status(thm)],[f55,f463]) ).
fof(f466,plain,
( ~ sQ7_spl
| ~ sQ15_spl
| inverse(sk_c8) != sk_c10
| sk_c11 != sk_c11 ),
inference(paramodulation,[status(thm)],[f138,f206]) ).
fof(f468,definition,
( sQ57_spl
<=> sk_c11 = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f470,plain,
( sQ57_spl
| sk_c11 != sk_c11 ),
inference(component_clause,[status(thm)],[f468]) ).
fof(f471,plain,
( ~ sQ7_spl
| ~ sQ15_spl
| ~ sQ46_spl
| ~ sQ57_spl ),
inference(split_clause,[status(thm)],[f466,f468,f358,f205,f137]) ).
fof(f472,plain,
( sQ57_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f470]) ).
fof(f473,plain,
sQ57_spl,
inference(contradiction_clause,[status(thm)],[f472]) ).
fof(f484,plain,
( ~ sQ7_spl
| ~ sQ5_spl
| multiply(sk_c11,sk_c10) = multiply(sk_c5,sk_c11) ),
inference(paramodulation,[status(thm)],[f138,f239]) ).
fof(f497,plain,
! [X0] :
( ~ sQ8_spl
| multiply(identity,X0) = multiply(sk_c6,multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f229,f57]) ).
fof(f498,plain,
! [X0] :
( ~ sQ8_spl
| X0 = multiply(sk_c6,multiply(sk_c7,X0)) ),
inference(forward_demodulation,[status(thm)],[f55,f497]) ).
fof(f509,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| multiply(sk_c10,sk_c3) = multiply(sk_c3,identity) ),
inference(paramodulation,[status(thm)],[f238,f241]) ).
fof(f512,plain,
( ~ sQ4_spl
| ~ sQ7_spl
| multiply(sk_c11,sk_c4) = multiply(sk_c8,identity) ),
inference(paramodulation,[status(thm)],[f237,f236]) ).
fof(f526,plain,
( ~ sQ4_spl
| sk_c4 = multiply(inverse(sk_c10),identity) ),
inference(paramodulation,[status(thm)],[f237,f234]) ).
fof(f527,plain,
( ~ sQ2_spl
| sk_c3 = multiply(inverse(sk_c11),identity) ),
inference(paramodulation,[status(thm)],[f238,f234]) ).
fof(f528,plain,
( ~ sQ8_spl
| sk_c7 = multiply(inverse(sk_c6),identity) ),
inference(paramodulation,[status(thm)],[f229,f234]) ).
fof(f529,plain,
( ~ sQ9_spl
| sk_c6 = multiply(inverse(sk_c8),identity) ),
inference(paramodulation,[status(thm)],[f230,f234]) ).
fof(f531,plain,
( ~ sQ6_spl
| sk_c5 = multiply(inverse(sk_c8),identity) ),
inference(paramodulation,[status(thm)],[f228,f234]) ).
fof(f532,plain,
( ~ sQ7_spl
| sk_c10 = multiply(inverse(sk_c8),sk_c11) ),
inference(paramodulation,[status(thm)],[f138,f234]) ).
fof(f533,plain,
! [X0] :
( ~ sQ14_spl
| multiply(sk_c2,X0) = multiply(inverse(sk_c9),X0) ),
inference(paramodulation,[status(thm)],[f464,f234]) ).
fof(f536,plain,
( ~ sQ5_spl
| sk_c8 = multiply(inverse(sk_c5),sk_c11) ),
inference(paramodulation,[status(thm)],[f130,f234]) ).
fof(f537,plain,
! [X0] :
( ~ sQ3_spl
| multiply(sk_c10,X0) = multiply(inverse(sk_c4),multiply(sk_c9,X0)) ),
inference(paramodulation,[status(thm)],[f240,f234]) ).
fof(f538,plain,
( ~ sQ3_spl
| sk_c10 = multiply(inverse(sk_c4),sk_c9) ),
inference(paramodulation,[status(thm)],[f122,f234]) ).
fof(f540,plain,
( ~ sQ1_spl
| sk_c11 = multiply(inverse(sk_c3),sk_c10) ),
inference(paramodulation,[status(thm)],[f114,f234]) ).
fof(f544,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f234,f234]) ).
fof(f545,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f56,f234]) ).
fof(f546,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f55,f234]) ).
fof(f549,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 = multiply(sk_c8,identity) ),
inference(forward_demodulation,[status(thm)],[f146,f528]) ).
fof(f551,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ4_spl
| ~ sQ7_spl
| sk_c7 = multiply(sk_c11,sk_c4) ),
inference(forward_demodulation,[status(thm)],[f512,f549]) ).
fof(f560,plain,
( ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ9_spl
| multiply(sk_c11,sk_c10) = multiply(sk_c6,sk_c11) ),
inference(backward_demodulation,[status(thm)],[f561,f484]) ).
fof(f561,plain,
( ~ sQ6_spl
| ~ sQ9_spl
| sk_c5 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f529,f531]) ).
fof(f564,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sk_c8 = multiply(sk_c8,sk_c11) ),
inference(forward_demodulation,[status(thm)],[f134,f536]) ).
fof(f565,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c10,X0) = multiply(sk_c10,multiply(sk_c9,X0)) ),
inference(forward_demodulation,[status(thm)],[f126,f537]) ).
fof(f566,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c10 = multiply(sk_c10,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f126,f538]) ).
fof(f568,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c11 = multiply(sk_c11,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f118,f540]) ).
fof(f574,plain,
( ~ sQ9_spl
| sk_c6 = inverse(sk_c8) ),
inference(backward_demodulation,[status(thm)],[f579,f529]) ).
fof(f575,plain,
( ~ sQ2_spl
| sk_c3 = inverse(sk_c11) ),
inference(backward_demodulation,[status(thm)],[f579,f527]) ).
fof(f576,plain,
( ~ sQ4_spl
| sk_c4 = inverse(sk_c10) ),
inference(backward_demodulation,[status(thm)],[f579,f526]) ).
fof(f578,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| multiply(sk_c10,sk_c3) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f579,f509]) ).
fof(f579,plain,
! [X0] : X0 = multiply(X0,identity),
inference(forward_demodulation,[status(thm)],[f544,f545]) ).
fof(f583,plain,
( ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c11 = multiply(sk_c6,sk_c11) ),
inference(forward_demodulation,[status(thm)],[f568,f560]) ).
fof(f584,plain,
( ~ sQ7_spl
| ~ sQ9_spl
| sk_c10 = multiply(sk_c6,sk_c11) ),
inference(backward_demodulation,[status(thm)],[f574,f532]) ).
fof(f587,plain,
( ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| multiply(sk_c10,sk_c3) = identity ),
inference(backward_demodulation,[status(thm)],[f606,f238]) ).
fof(f589,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ2_spl
| multiply(sk_c10,X0) = multiply(sk_c3,multiply(sk_c10,X0)) ),
inference(backward_demodulation,[status(thm)],[f606,f241]) ).
fof(f590,plain,
( sQ0_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c10,sk_c10) != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f606,f112]) ).
fof(f593,plain,
( ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ2_spl
| multiply(sk_c3,sk_c10) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f606,f114]) ).
fof(f594,plain,
( ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| sk_c3 = inverse(sk_c10) ),
inference(backward_demodulation,[status(thm)],[f606,f575]) ).
fof(f599,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c11 = multiply(sk_c10,sk_c10) ),
inference(backward_demodulation,[status(thm)],[f606,f568]) ).
fof(f601,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 = multiply(sk_c8,sk_c10) ),
inference(backward_demodulation,[status(thm)],[f606,f564]) ).
fof(f603,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c7 = multiply(sk_c10,sk_c4) ),
inference(backward_demodulation,[status(thm)],[f606,f551]) ).
fof(f606,plain,
( ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c10 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f583,f584]) ).
fof(f613,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| multiply(sk_c3,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f616,f55]) ).
fof(f614,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| X0 = multiply(inverse(sk_c3),X0) ),
inference(backward_demodulation,[status(thm)],[f616,f546]) ).
fof(f615,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| X0 = multiply(X0,sk_c3) ),
inference(backward_demodulation,[status(thm)],[f616,f579]) ).
fof(f616,plain,
( ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| sk_c3 = identity ),
inference(forward_demodulation,[status(thm)],[f578,f587]) ).
fof(f620,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ4_spl
| multiply(sk_c9,X0) = multiply(sk_c3,multiply(sk_c10,X0)) ),
inference(backward_demodulation,[status(thm)],[f626,f240]) ).
fof(f622,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ4_spl
| multiply(sk_c3,sk_c10) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f626,f122]) ).
fof(f626,plain,
( ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ4_spl
| sk_c3 = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f576,f594]) ).
fof(f632,plain,
( sQ0_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c10 != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f633,f590]) ).
fof(f633,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c10 = multiply(sk_c10,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f606,f599]) ).
fof(f635,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f138,f601]) ).
fof(f637,plain,
( ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c6) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f643,f146]) ).
fof(f638,plain,
( ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c7,sk_c10) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f643,f150]) ).
fof(f643,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f606,f635]) ).
fof(f646,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c7 = identity ),
inference(forward_demodulation,[status(thm)],[f237,f603]) ).
fof(f647,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c3) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f649,f142]) ).
fof(f649,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c7 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f616,f646]) ).
fof(f660,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| X0 = multiply(sk_c11,X0) ),
inference(forward_demodulation,[status(thm)],[f118,f614]) ).
fof(f667,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| X0 = multiply(sk_c10,X0) ),
inference(forward_demodulation,[status(thm)],[f606,f660]) ).
fof(f668,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ4_spl
| multiply(sk_c9,X0) = multiply(sk_c10,X0) ),
inference(forward_demodulation,[status(thm)],[f589,f620]) ).
fof(f669,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ4_spl
| X0 = multiply(sk_c2,X0) ),
inference(backward_demodulation,[status(thm)],[f670,f464]) ).
fof(f670,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ4_spl
| multiply(sk_c9,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f667,f668]) ).
fof(f672,plain,
( sQ13_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ4_spl
| multiply(sk_c2,sk_c10) != sk_c10 ),
inference(backward_demodulation,[status(thm)],[f676,f181]) ).
fof(f676,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ4_spl
| sk_c10 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f593,f622]) ).
fof(f680,plain,
( sQ0_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f676,f632]) ).
fof(f681,plain,
( sQ0_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f680]) ).
fof(f682,plain,
( sQ0_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f681]) ).
fof(f687,plain,
( ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ4_spl
| multiply(sk_c3,sk_c10) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f649,f638]) ).
fof(f688,plain,
( ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ4_spl
| inverse(sk_c10) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f691,f637]) ).
fof(f690,plain,
( ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ4_spl
| sk_c5 = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f691,f561]) ).
fof(f691,plain,
( ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ4_spl
| sk_c10 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f613,f687]) ).
fof(f697,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ10_spl
| inverse(sk_c3) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f691,f647]) ).
fof(f702,plain,
( sQ13_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ14_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f669,f672]) ).
fof(f703,plain,
( sQ13_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ14_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f702]) ).
fof(f704,plain,
( sQ13_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f703]) ).
fof(f711,plain,
( sQ21_spl
| sk_c10 != sk_c11 ),
inference(backward_demodulation,[status(thm)],[f546,f257]) ).
fof(f712,plain,
( sQ46_spl
| ~ sQ6_spl
| sk_c5 != sk_c10 ),
inference(backward_demodulation,[status(thm)],[f713,f360]) ).
fof(f713,plain,
( ~ sQ6_spl
| sk_c5 = inverse(sk_c8) ),
inference(forward_demodulation,[status(thm)],[f579,f531]) ).
fof(f720,plain,
( ~ sQ0_spl
| sk_c11 = multiply(inverse(sk_c10),sk_c9) ),
inference(paramodulation,[status(thm)],[f111,f234]) ).
fof(f723,plain,
( ~ sQ13_spl
| sk_c9 = multiply(inverse(sk_c2),sk_c10) ),
inference(paramodulation,[status(thm)],[f180,f234]) ).
fof(f726,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| sk_c9 = multiply(sk_c9,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f193,f723]) ).
fof(f727,plain,
( ~ sQ15_spl
| ~ sQ11_spl
| inverse(sk_c1) != sk_c10 ),
inference(resolution,[status(thm)],[f154,f206]) ).
fof(f729,plain,
( ~ sQ11_spl
| sk_c10 = multiply(inverse(sk_c1),sk_c11) ),
inference(paramodulation,[status(thm)],[f154,f234]) ).
fof(f731,plain,
( ~ sQ15_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f167,f727]) ).
fof(f732,plain,
( ~ sQ15_spl
| ~ sQ11_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f731]) ).
fof(f733,plain,
( ~ sQ15_spl
| ~ sQ11_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f732]) ).
fof(f735,plain,
( ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sQ55_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f606,f404]) ).
fof(f736,plain,
( ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sQ55_spl ),
inference(contradiction_clause,[status(thm)],[f735]) ).
fof(f738,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| X0 = multiply(X0,sk_c3) ),
inference(backward_demodulation,[status(thm)],[f616,f579]) ).
fof(f739,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| X0 = multiply(inverse(sk_c3),X0) ),
inference(backward_demodulation,[status(thm)],[f616,f546]) ).
fof(f741,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| multiply(inverse(X0),X0) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f616,f56]) ).
fof(f744,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ4_spl
| multiply(sk_c10,X0) = multiply(inverse(sk_c3),multiply(sk_c9,X0)) ),
inference(backward_demodulation,[status(thm)],[f626,f537]) ).
fof(f758,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 = multiply(sk_c10,sk_c11) ),
inference(backward_demodulation,[status(thm)],[f643,f564]) ).
fof(f780,plain,
( ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ4_spl
| sQ46_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f690,f712]) ).
fof(f781,plain,
( ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ4_spl
| sQ46_spl ),
inference(contradiction_clause,[status(thm)],[f780]) ).
fof(f799,plain,
( ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| multiply(sk_c11,sk_c3) = multiply(sk_c8,identity) ),
inference(forward_demodulation,[status(thm)],[f626,f512]) ).
fof(f800,plain,
( ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| sk_c11 = multiply(sk_c8,identity) ),
inference(forward_demodulation,[status(thm)],[f615,f799]) ).
fof(f801,plain,
( ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| sk_c11 = multiply(sk_c10,identity) ),
inference(forward_demodulation,[status(thm)],[f643,f800]) ).
fof(f802,plain,
( ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| sk_c11 = identity ),
inference(forward_demodulation,[status(thm)],[f667,f801]) ).
fof(f804,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ4_spl
| X0 = multiply(X0,sk_c11) ),
inference(backward_demodulation,[status(thm)],[f809,f615]) ).
fof(f806,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c7 = sk_c11 ),
inference(backward_demodulation,[status(thm)],[f809,f649]) ).
fof(f808,plain,
( ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ4_spl
| sk_c11 = identity ),
inference(backward_demodulation,[status(thm)],[f809,f616]) ).
fof(f809,plain,
( ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| sk_c11 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f616,f802]) ).
fof(f811,plain,
( ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c10 = multiply(inverse(sk_c10),sk_c11) ),
inference(forward_demodulation,[status(thm)],[f643,f532]) ).
fof(f812,plain,
( ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ4_spl
| sk_c10 = multiply(sk_c10,sk_c11) ),
inference(forward_demodulation,[status(thm)],[f688,f811]) ).
fof(f817,plain,
( ~ sQ11_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ4_spl
| sk_c10 = multiply(inverse(sk_c1),sk_c10) ),
inference(backward_demodulation,[status(thm)],[f819,f729]) ).
fof(f819,plain,
( ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ4_spl
| sk_c10 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f667,f812]) ).
fof(f928,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| sk_c10 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f667,f566]) ).
fof(f929,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| X0 = multiply(sk_c10,multiply(sk_c9,X0)) ),
inference(forward_demodulation,[status(thm)],[f667,f565]) ).
fof(f930,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| X0 = multiply(sk_c9,X0) ),
inference(forward_demodulation,[status(thm)],[f667,f929]) ).
fof(f937,plain,
( sQ50_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| inverse(sk_c3) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f616,f374]) ).
fof(f938,plain,
( sQ50_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ4_spl
| ~ sQ10_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f697,f937]) ).
fof(f939,plain,
( sQ50_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ4_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f938]) ).
fof(f940,plain,
( sQ50_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ4_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f939]) ).
fof(f941,plain,
( sQ23_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ4_spl
| inverse(identity) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f819,f264]) ).
fof(f960,plain,
( sQ51_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ4_spl
| sk_c10 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f688,f389]) ).
fof(f961,plain,
( sQ51_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ4_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f819,f960]) ).
fof(f962,plain,
( sQ51_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f961]) ).
fof(f963,plain,
( sQ51_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f962]) ).
fof(f977,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| sk_c10 = multiply(sk_c10,sk_c11) ),
inference(backward_demodulation,[status(thm)],[f167,f729]) ).
fof(f982,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| multiply(sk_c2,X0) = multiply(inverse(sk_c10),X0) ),
inference(backward_demodulation,[status(thm)],[f993,f533]) ).
fof(f983,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sk_c11 = multiply(inverse(sk_c10),sk_c10) ),
inference(backward_demodulation,[status(thm)],[f993,f720]) ).
fof(f984,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| sk_c9 = multiply(sk_c10,sk_c10) ),
inference(backward_demodulation,[status(thm)],[f993,f726]) ).
fof(f985,plain,
( sQ45_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| sk_c11 != sk_c10 ),
inference(backward_demodulation,[status(thm)],[f993,f357]) ).
fof(f986,plain,
( ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| multiply(sk_c2,sk_c10) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f993,f180]) ).
fof(f991,plain,
( sQ47_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| identity != sk_c10 ),
inference(backward_demodulation,[status(thm)],[f993,f364]) ).
fof(f993,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| sk_c10 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f111,f977]) ).
fof(f996,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ14_spl
| sk_c11 = multiply(sk_c2,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f982,f983]) ).
fof(f997,plain,
( sQ39_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ0_spl
| sk_c10 != sk_c11 ),
inference(backward_demodulation,[status(thm)],[f998,f450]) ).
fof(f998,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| sk_c10 = multiply(sk_c10,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f993,f984]) ).
fof(f999,plain,
( ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ14_spl
| sk_c11 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f996,f986]) ).
fof(f1000,plain,
( ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ14_spl
| sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f999,f711]) ).
fof(f1001,plain,
( ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ14_spl
| sQ21_spl ),
inference(contradiction_clause,[status(thm)],[f1000]) ).
fof(f1003,plain,
( ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ14_spl
| sQ39_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f999,f997]) ).
fof(f1004,plain,
( ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ14_spl
| sQ39_spl ),
inference(contradiction_clause,[status(thm)],[f1003]) ).
fof(f1005,plain,
( ~ sQ21_spl
| sk_c10 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f546,f256]) ).
fof(f1006,plain,
( ~ sQ21_spl
| sQ45_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1005,f985]) ).
fof(f1007,plain,
( ~ sQ21_spl
| sQ45_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f1006]) ).
fof(f1008,plain,
( sQ49_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f993,f371]) ).
fof(f1009,plain,
( sQ49_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1008]) ).
fof(f1010,plain,
( sQ49_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f1009]) ).
fof(f1022,plain,
( ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ14_spl
| multiply(sk_c1,sk_c10) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f999,f154]) ).
fof(f1029,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ14_spl
| inverse(X0) != sk_c11
| multiply(X0,sk_c10) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f999,f212]) ).
fof(f1030,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ14_spl
| inverse(X0) != sk_c10
| multiply(X0,sk_c10) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f999,f1029]) ).
fof(f1063,plain,
( ~ sQ17_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ14_spl
| inverse(sk_c1) != sk_c10 ),
inference(resolution,[status(thm)],[f1022,f1030]) ).
fof(f1067,plain,
( ~ sQ17_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f1063,f166,f192,f110,f153,f179,f211]) ).
fof(f1074,plain,
( ~ sQ12_spl
| sk_c1 = multiply(inverse(sk_c10),identity) ),
inference(paramodulation,[status(thm)],[f231,f234]) ).
fof(f1087,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| sk_c10 = multiply(inverse(sk_c10),sk_c10) ),
inference(paramodulation,[status(thm)],[f998,f234]) ).
fof(f1089,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| sk_c10 = identity ),
inference(forward_demodulation,[status(thm)],[f56,f1087]) ).
fof(f1090,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| sQ53_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1089,f397]) ).
fof(f1091,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| sQ53_spl ),
inference(contradiction_clause,[status(thm)],[f1090]) ).
fof(f1101,plain,
( sQ47_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ53_spl ),
inference(split_clause,[status(thm)],[f991,f395,f110,f166,f153,f362]) ).
fof(f1182,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| multiply(inverse(X0),X0) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f1184,f56]) ).
fof(f1184,plain,
( ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| identity = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f56,f741]) ).
fof(f1185,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ4_spl
| multiply(sk_c10,X0) = multiply(sk_c9,X0) ),
inference(forward_demodulation,[status(thm)],[f739,f744]) ).
fof(f1186,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ4_spl
| multiply(sk_c10,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f930,f1185]) ).
fof(f1202,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| sk_c8 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f111,f758]) ).
fof(f1204,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c8 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f928,f1202]) ).
fof(f1231,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ4_spl
| X0 = multiply(X0,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f606,f804]) ).
fof(f1233,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c7 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f606,f806]) ).
fof(f1235,plain,
( ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ4_spl
| sk_c10 = identity ),
inference(forward_demodulation,[status(thm)],[f606,f808]) ).
fof(f1236,plain,
( ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ4_spl
| identity = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f1239,f1184]) ).
fof(f1239,plain,
( ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ4_spl
| sk_c10 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f1184,f1235]) ).
fof(f1246,plain,
( ~ sQ11_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ4_spl
| sk_c10 = inverse(sk_c1) ),
inference(forward_demodulation,[status(thm)],[f1231,f817]) ).
fof(f1247,plain,
( ~ sQ11_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ4_spl
| sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1246,f168]) ).
fof(f1248,plain,
( ~ sQ11_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ4_spl
| sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f1247]) ).
fof(f1571,plain,
( ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ4_spl
| sQ53_spl ),
inference(split_clause,[status(thm)],[f1236,f395,f125,f113,f133,f129,f145,f137,f117]) ).
fof(f1605,plain,
( sQ33_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c10,sk_c6) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1233,f298]) ).
fof(f1606,plain,
( sQ33_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c6 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1186,f1605]) ).
fof(f1607,plain,
( sQ33_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ10_spl
| sk_c10 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f691,f1606]) ).
fof(f1608,plain,
( sQ33_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ10_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f606,f1607]) ).
fof(f1609,plain,
( sQ33_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1608]) ).
fof(f1610,plain,
( sQ33_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f1609]) ).
fof(f1665,plain,
( sQ21_spl
| ~ sQ55_spl ),
inference(split_clause,[status(thm)],[f711,f402,f255]) ).
fof(f1675,plain,
( ~ sQ47_spl
| ~ sQ53_spl
| identity = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f1676,f363]) ).
fof(f1676,plain,
( ~ sQ53_spl
| ~ sQ47_spl
| sk_c9 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f363,f396]) ).
fof(f1677,plain,
( ~ sQ45_spl
| ~ sQ53_spl
| ~ sQ47_spl
| sk_c11 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1676,f356]) ).
fof(f1682,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ45_spl
| ~ sQ53_spl
| ~ sQ47_spl
| sk_c10 = multiply(inverse(sk_c10),sk_c10) ),
inference(forward_demodulation,[status(thm)],[f1677,f983]) ).
fof(f1685,plain,
( ~ sQ12_spl
| ~ sQ47_spl
| sk_c1 = multiply(inverse(sk_c10),sk_c9) ),
inference(forward_demodulation,[status(thm)],[f363,f1074]) ).
fof(f1686,plain,
( ~ sQ12_spl
| ~ sQ47_spl
| ~ sQ53_spl
| sk_c1 = multiply(inverse(sk_c10),sk_c10) ),
inference(forward_demodulation,[status(thm)],[f1676,f1685]) ).
fof(f1687,plain,
( ~ sQ12_spl
| ~ sQ47_spl
| ~ sQ53_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ45_spl
| sk_c1 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1682,f1686]) ).
fof(f1689,plain,
( ~ sQ12_spl
| ~ sQ47_spl
| ~ sQ53_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ45_spl
| inverse(sk_c10) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1687,f167]) ).
fof(f1739,plain,
! [X0] :
( ~ sQ47_spl
| X0 = multiply(X0,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f363,f579]) ).
fof(f1743,plain,
! [X0] :
( ~ sQ47_spl
| ~ sQ53_spl
| X0 = multiply(X0,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f1676,f1739]) ).
fof(f1762,plain,
( sQ20_spl
| ~ sQ45_spl
| ~ sQ53_spl
| ~ sQ47_spl
| inverse(identity) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1677,f342]) ).
fof(f1763,plain,
( sQ20_spl
| ~ sQ45_spl
| ~ sQ53_spl
| ~ sQ47_spl
| inverse(sk_c10) != sk_c10 ),
inference(backward_demodulation,[status(thm)],[f1675,f1762]) ).
fof(f2041,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ4_spl
| X0 = multiply(X0,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f1239,f738]) ).
fof(f2076,plain,
( sQ23_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ4_spl
| ~ sQ50_spl ),
inference(split_clause,[status(thm)],[f941,f372,f125,f141,f149,f117,f113,f145,f133,f129,f137,f262]) ).
fof(f2247,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| X0 = multiply(sk_c10,multiply(sk_c7,X0)) ),
inference(forward_demodulation,[status(thm)],[f691,f498]) ).
fof(f2260,plain,
( ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| multiply(sk_c10,sk_c7) = identity ),
inference(forward_demodulation,[status(thm)],[f691,f229]) ).
fof(f2273,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ4_spl
| multiply(sk_c10,X0) = multiply(sk_c7,multiply(sk_c8,X0)) ),
inference(forward_demodulation,[status(thm)],[f691,f235]) ).
fof(f2296,plain,
( ~ sQ46_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| inverse(sk_c10) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1204,f359]) ).
fof(f2326,plain,
( ~ sQ33_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c10,sk_c6) = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1233,f297]) ).
fof(f2329,plain,
( sQ20_spl
| ~ sQ45_spl
| ~ sQ53_spl
| ~ sQ47_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ11_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1689,f1763]) ).
fof(f2330,plain,
( sQ20_spl
| ~ sQ45_spl
| ~ sQ53_spl
| ~ sQ47_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f2329]) ).
fof(f2331,plain,
( sQ20_spl
| ~ sQ45_spl
| ~ sQ53_spl
| ~ sQ47_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f2330]) ).
fof(f2358,plain,
( sQ22_spl
| ~ sQ47_spl
| ~ sQ53_spl
| inverse(inverse(sk_c10)) != inverse(identity) ),
inference(forward_demodulation,[status(thm)],[f1675,f260]) ).
fof(f2359,plain,
( sQ22_spl
| ~ sQ47_spl
| ~ sQ53_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ45_spl
| inverse(sk_c10) != inverse(identity) ),
inference(forward_demodulation,[status(thm)],[f1689,f2358]) ).
fof(f2360,plain,
( sQ22_spl
| ~ sQ47_spl
| ~ sQ53_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ45_spl
| sk_c10 != inverse(identity) ),
inference(forward_demodulation,[status(thm)],[f1689,f2359]) ).
fof(f2361,plain,
( sQ22_spl
| ~ sQ47_spl
| ~ sQ53_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ45_spl
| sk_c10 != inverse(sk_c10) ),
inference(forward_demodulation,[status(thm)],[f1675,f2360]) ).
fof(f2362,plain,
( sQ22_spl
| ~ sQ47_spl
| ~ sQ53_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ45_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1689,f2361]) ).
fof(f2363,plain,
( sQ22_spl
| ~ sQ47_spl
| ~ sQ53_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ45_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f2362]) ).
fof(f2364,plain,
( sQ22_spl
| ~ sQ47_spl
| ~ sQ53_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ45_spl ),
inference(contradiction_clause,[status(thm)],[f2363]) ).
fof(f2369,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ53_spl
| ~ sQ47_spl
| inverse(X0) != sk_c9
| multiply(X0,sk_c10) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1676,f209]) ).
fof(f2370,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ53_spl
| ~ sQ47_spl
| inverse(X0) != sk_c9
| X0 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1743,f2369]) ).
fof(f2371,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ53_spl
| ~ sQ47_spl
| inverse(X0) != sk_c10
| X0 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1676,f2370]) ).
fof(f2372,plain,
( ~ sQ16_spl
| ~ sQ53_spl
| ~ sQ47_spl
| inverse(sk_c10) != sk_c10 ),
inference(destructive_equality_resolution,[status(thm)],[f2371]) ).
fof(f2373,plain,
( ~ sQ16_spl
| ~ sQ53_spl
| ~ sQ47_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ45_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2372,f1689]) ).
fof(f2374,plain,
( ~ sQ16_spl
| ~ sQ53_spl
| ~ sQ47_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ45_spl ),
inference(contradiction_clause,[status(thm)],[f2373]) ).
fof(f2379,definition,
( sQ60_spl
<=> inverse(identity) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f2382,plain,
( ~ sQ16_spl
| ~ sQ60_spl
| ~ sQ49_spl ),
inference(split_clause,[status(thm)],[f411,f369,f2379,f208]) ).
fof(f2383,plain,
( ~ sQ33_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ10_spl
| multiply(sk_c10,sk_c10) = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f691,f2326]) ).
fof(f2387,plain,
( ~ sQ46_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ51_spl
| sk_c11 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f388,f2296]) ).
fof(f2396,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ4_spl
| multiply(sk_c10,X0) = multiply(sk_c10,multiply(sk_c8,X0)) ),
inference(forward_demodulation,[status(thm)],[f1233,f2273]) ).
fof(f2397,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ3_spl
| multiply(sk_c10,X0) = multiply(sk_c10,multiply(sk_c10,X0)) ),
inference(forward_demodulation,[status(thm)],[f1204,f2396]) ).
fof(f2406,plain,
( ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| multiply(sk_c10,sk_c10) = identity ),
inference(forward_demodulation,[status(thm)],[f1233,f2260]) ).
fof(f2407,plain,
( ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ33_spl
| sk_c11 = identity ),
inference(forward_demodulation,[status(thm)],[f2383,f2406]) ).
fof(f2408,plain,
( ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ33_spl
| ~ sQ46_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ51_spl
| sk_c10 = identity ),
inference(forward_demodulation,[status(thm)],[f2387,f2407]) ).
fof(f2414,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| X0 = multiply(sk_c10,multiply(sk_c10,X0)) ),
inference(forward_demodulation,[status(thm)],[f1233,f2247]) ).
fof(f2418,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ0_spl
| ~ sQ3_spl
| X0 = multiply(sk_c10,X0) ),
inference(forward_demodulation,[status(thm)],[f2397,f2414]) ).
fof(f2691,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sk_c11 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f2418,f111]) ).
fof(f2694,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ46_spl
| ~ sQ51_spl
| sk_c10 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f2387,f2691]) ).
fof(f2773,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ46_spl
| ~ sQ51_spl
| inverse(X0) != sk_c9
| multiply(X0,sk_c10) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f2694,f209]) ).
fof(f2774,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ46_spl
| ~ sQ51_spl
| inverse(X0) != sk_c10
| multiply(X0,sk_c10) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f2694,f2773]) ).
fof(f2825,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ46_spl
| ~ sQ51_spl
| inverse(X0) != sk_c10
| X0 != sk_c10 ),
inference(backward_demodulation,[status(thm)],[f2041,f2774]) ).
fof(f2837,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ4_spl
| multiply(inverse(X0),X0) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1239,f1182]) ).
fof(f2852,plain,
( ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ46_spl
| ~ sQ51_spl
| inverse(sk_c10) != sk_c10 ),
inference(destructive_equality_resolution,[status(thm)],[f2825]) ).
fof(f2867,plain,
( ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ4_spl
| inverse(sk_c10) = sk_c10 ),
inference(paramodulation,[status(thm)],[f2837,f2041]) ).
fof(f2870,plain,
( ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ4_spl
| inverse(sk_c10) = sk_c10 ),
inference(paramodulation,[status(thm)],[f2041,f2837]) ).
fof(f2874,plain,
( ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ3_spl
| ~ sQ46_spl
| ~ sQ51_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2867,f2852]) ).
fof(f2875,plain,
( ~ sQ2_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ16_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ3_spl
| ~ sQ46_spl
| ~ sQ51_spl ),
inference(contradiction_clause,[status(thm)],[f2874]) ).
fof(f2918,plain,
( sQ20_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f342,f262,f252]) ).
fof(f2923,plain,
( sQ22_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ33_spl
| ~ sQ46_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ51_spl
| inverse(inverse(sk_c10)) != inverse(identity) ),
inference(forward_demodulation,[status(thm)],[f2408,f260]) ).
fof(f2924,plain,
( sQ22_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ33_spl
| ~ sQ46_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ51_spl
| inverse(sk_c10) != inverse(identity) ),
inference(forward_demodulation,[status(thm)],[f2870,f2923]) ).
fof(f2925,plain,
( sQ22_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ33_spl
| ~ sQ46_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ51_spl
| sk_c10 != inverse(identity) ),
inference(forward_demodulation,[status(thm)],[f2870,f2924]) ).
fof(f2926,plain,
( sQ22_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ33_spl
| ~ sQ46_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ51_spl
| sk_c10 != inverse(sk_c10) ),
inference(forward_demodulation,[status(thm)],[f2408,f2925]) ).
fof(f2927,plain,
( sQ22_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ33_spl
| ~ sQ46_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ51_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f2870,f2926]) ).
fof(f2928,plain,
( sQ22_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ33_spl
| ~ sQ46_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ51_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f2927]) ).
fof(f2929,plain,
( sQ22_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ33_spl
| ~ sQ46_spl
| ~ sQ0_spl
| ~ sQ3_spl
| ~ sQ51_spl ),
inference(contradiction_clause,[status(thm)],[f2928]) ).
fof(f2930,plain,
$false,
inference(sat_refutation,[status(thm)],[f116,f120,f124,f128,f132,f136,f140,f148,f156,f157,f158,f159,f160,f161,f162,f163,f164,f165,f169,f170,f171,f172,f173,f174,f175,f176,f177,f178,f182,f183,f184,f185,f186,f187,f188,f190,f195,f196,f197,f198,f199,f200,f201,f202,f203,f204,f220,f261,f268,f322,f354,f368,f375,f376,f378,f390,f394,f405,f407,f416,f430,f447,f448,f471,f473,f682,f704,f733,f736,f781,f940,f963,f1001,f1004,f1007,f1010,f1067,f1091,f1101,f1248,f1571,f1610,f1665,f2076,f2331,f2364,f2374,f2382,f2875,f2918,f2929]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP330-1 : 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 : n011.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 20:09:41 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.12/0.42 % Refutation found
% 0.12/0.42 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.44 % Elapsed time: 0.078615 seconds
% 0.12/0.44 % CPU time: 0.399291 seconds
% 0.12/0.44 % Total memory used: 64.639 MB
% 0.12/0.44 % Net memory used: 64.091 MB
%------------------------------------------------------------------------------