%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP325-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:33:25 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.46s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 87
% Syntax : Number of formulae : 412 ( 14 unt; 37 def)
% Number of atoms : 1476 ( 480 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 1982 ( 918 ~;1027 |; 0 &)
% ( 37 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 39 ( 37 usr; 38 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 73 ( 73 !; 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_c9,sk_c10) = sk_c8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c9) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c5) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c7) = sk_c6
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c6) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c6
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( inverse(sk_c9) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( inverse(sk_c5) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( inverse(sk_c7) = sk_c6
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c6) = sk_c10
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c6
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c10,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c10,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c9) = sk_c8
| multiply(sk_c10,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c10,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c5) = sk_c9
| multiply(sk_c10,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c10,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( inverse(sk_c7) = sk_c6
| multiply(sk_c10,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( inverse(sk_c6) = sk_c10
| multiply(sk_c10,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c6
| multiply(sk_c10,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( inverse(sk_c9) = sk_c8
| multiply(sk_c2,sk_c10) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
( inverse(sk_c5) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
( inverse(sk_c7) = sk_c6
| multiply(sk_c2,sk_c10) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
( inverse(sk_c6) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c6
| multiply(sk_c2,sk_c10) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,negated_conjecture,
( inverse(sk_c9) = sk_c8
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
( inverse(sk_c5) = sk_c9
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,negated_conjecture,
( inverse(sk_c7) = sk_c6
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,negated_conjecture,
( inverse(sk_c6) = sk_c10
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,negated_conjecture,
( multiply(sk_c7,sk_c10) = sk_c6
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,negated_conjecture,
! [X4,X5,X6,X1,X2,X3,X7] :
( multiply(X3,sk_c10) != X7
| inverse(X7) != sk_c10
| inverse(X3) != X7
| multiply(X2,sk_c8) != sk_c9
| inverse(X2) != sk_c9
| multiply(sk_c10,sk_c8) != sk_c9
| inverse(sk_c9) != sk_c8
| inverse(X1) != sk_c10
| multiply(X1,sk_c10) != sk_c9
| inverse(X6) != sk_c10
| multiply(X6,sk_c10) != X5
| multiply(sk_c10,X5) != sk_c9
| inverse(X4) != sk_c9
| multiply(X4,sk_c9) != sk_c10
| multiply(sk_c9,sk_c10) != sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f51,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f52,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f53,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f54,plain,
multiply(sk_c9,sk_c10) = sk_c8,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f55,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f56,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f57,plain,
( inverse(sk_c9) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f58,plain,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f59,plain,
( inverse(sk_c5) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f60,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f61,plain,
( inverse(sk_c7) = sk_c6
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f62,plain,
( inverse(sk_c6) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f63,plain,
( multiply(sk_c7,sk_c10) = sk_c6
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f64,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f65,plain,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f66,plain,
( inverse(sk_c9) = sk_c8
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f67,plain,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f68,plain,
( inverse(sk_c5) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f69,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f70,plain,
( inverse(sk_c7) = sk_c6
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f71,plain,
( inverse(sk_c6) = sk_c10
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f72,plain,
( multiply(sk_c7,sk_c10) = sk_c6
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f73,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c10,sk_c3) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f74,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c10,sk_c3) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f75,plain,
( inverse(sk_c9) = sk_c8
| multiply(sk_c10,sk_c3) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f76,plain,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c10,sk_c3) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f77,plain,
( inverse(sk_c5) = sk_c9
| multiply(sk_c10,sk_c3) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f78,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c10,sk_c3) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f79,plain,
( inverse(sk_c7) = sk_c6
| multiply(sk_c10,sk_c3) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f80,plain,
( inverse(sk_c6) = sk_c10
| multiply(sk_c10,sk_c3) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f81,plain,
( multiply(sk_c7,sk_c10) = sk_c6
| multiply(sk_c10,sk_c3) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f82,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f83,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f84,plain,
( inverse(sk_c9) = sk_c8
| multiply(sk_c2,sk_c10) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f85,plain,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f86,plain,
( inverse(sk_c5) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f87,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c2,sk_c10) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f88,plain,
( inverse(sk_c7) = sk_c6
| multiply(sk_c2,sk_c10) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f89,plain,
( inverse(sk_c6) = sk_c10
| multiply(sk_c2,sk_c10) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f90,plain,
( multiply(sk_c7,sk_c10) = sk_c6
| multiply(sk_c2,sk_c10) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f91,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f92,plain,
( inverse(sk_c4) = sk_c10
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f93,plain,
( inverse(sk_c9) = sk_c8
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f94,plain,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f95,plain,
( inverse(sk_c5) = sk_c9
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f96,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f97,plain,
( inverse(sk_c7) = sk_c6
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f98,plain,
( inverse(sk_c6) = sk_c10
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f99,plain,
( multiply(sk_c7,sk_c10) = sk_c6
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f100,plain,
! [X3,X7] :
( multiply(X3,sk_c10) != X7
| inverse(X7) != sk_c10
| inverse(X3) != X7
| ! [X2] :
( multiply(X2,sk_c8) != sk_c9
| inverse(X2) != sk_c9
| multiply(sk_c10,sk_c8) != sk_c9
| inverse(sk_c9) != sk_c8
| ! [X1] :
( inverse(X1) != sk_c10
| multiply(X1,sk_c10) != sk_c9
| ! [X6] :
( inverse(X6) != sk_c10
| ! [X5] :
( multiply(X6,sk_c10) != X5
| multiply(sk_c10,X5) != sk_c9
| ! [X4] :
( inverse(X4) != sk_c9
| multiply(X4,sk_c9) != sk_c10
| multiply(sk_c9,sk_c10) != sk_c8 ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f50]) ).
fof(f101,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( multiply(X5,sk_c10) != X6
| inverse(X6) != sk_c10
| inverse(X5) != X6
| multiply(X4,sk_c8) != sk_c9
| inverse(X4) != sk_c9
| multiply(sk_c10,sk_c8) != sk_c9
| inverse(sk_c9) != sk_c8
| inverse(X3) != sk_c10
| multiply(X3,sk_c10) != sk_c9
| inverse(X2) != sk_c10
| multiply(X2,sk_c10) != X1
| multiply(sk_c10,X1) != sk_c9
| inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c10
| multiply(sk_c9,sk_c10) != sk_c8 ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f102,definition,
( sQ0_spl
<=> multiply(sk_c1,sk_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f103,plain,
( ~ sQ0_spl
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(component_clause,[status(thm)],[f102]) ).
fof(f105,definition,
( sQ1_spl
<=> multiply(sk_c4,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f106,plain,
( ~ sQ1_spl
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(component_clause,[status(thm)],[f105]) ).
fof(f108,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f55,f102,f105]) ).
fof(f109,definition,
( sQ2_spl
<=> inverse(sk_c4) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f110,plain,
( ~ sQ2_spl
| inverse(sk_c4) = sk_c10 ),
inference(component_clause,[status(thm)],[f109]) ).
fof(f112,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f56,f102,f109]) ).
fof(f113,definition,
( sQ3_spl
<=> inverse(sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f114,plain,
( ~ sQ3_spl
| inverse(sk_c9) = sk_c8 ),
inference(component_clause,[status(thm)],[f113]) ).
fof(f115,plain,
( sQ3_spl
| inverse(sk_c9) != sk_c8 ),
inference(component_clause,[status(thm)],[f113]) ).
fof(f116,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f57,f102,f113]) ).
fof(f117,definition,
( sQ4_spl
<=> multiply(sk_c10,sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f118,plain,
( ~ sQ4_spl
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(component_clause,[status(thm)],[f117]) ).
fof(f119,plain,
( sQ4_spl
| multiply(sk_c10,sk_c8) != sk_c9 ),
inference(component_clause,[status(thm)],[f117]) ).
fof(f120,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f58,f102,f117]) ).
fof(f121,definition,
( sQ5_spl
<=> inverse(sk_c5) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f122,plain,
( ~ sQ5_spl
| inverse(sk_c5) = sk_c9 ),
inference(component_clause,[status(thm)],[f121]) ).
fof(f124,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f59,f102,f121]) ).
fof(f125,definition,
( sQ6_spl
<=> multiply(sk_c5,sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f126,plain,
( ~ sQ6_spl
| multiply(sk_c5,sk_c8) = sk_c9 ),
inference(component_clause,[status(thm)],[f125]) ).
fof(f128,plain,
( sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f60,f102,f125]) ).
fof(f129,definition,
( sQ7_spl
<=> inverse(sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f130,plain,
( ~ sQ7_spl
| inverse(sk_c7) = sk_c6 ),
inference(component_clause,[status(thm)],[f129]) ).
fof(f132,plain,
( sQ7_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f61,f102,f129]) ).
fof(f133,definition,
( sQ8_spl
<=> inverse(sk_c6) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f134,plain,
( ~ sQ8_spl
| inverse(sk_c6) = sk_c10 ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,plain,
( sQ8_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f62,f102,f133]) ).
fof(f137,definition,
( sQ9_spl
<=> multiply(sk_c7,sk_c10) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f138,plain,
( ~ sQ9_spl
| multiply(sk_c7,sk_c10) = sk_c6 ),
inference(component_clause,[status(thm)],[f137]) ).
fof(f140,plain,
( sQ9_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f63,f102,f137]) ).
fof(f141,definition,
( sQ10_spl
<=> inverse(sk_c1) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f142,plain,
( ~ sQ10_spl
| inverse(sk_c1) = sk_c9 ),
inference(component_clause,[status(thm)],[f141]) ).
fof(f144,plain,
( sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f64,f141,f105]) ).
fof(f145,plain,
( sQ2_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f65,f141,f109]) ).
fof(f146,plain,
( sQ3_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f66,f141,f113]) ).
fof(f147,plain,
( sQ4_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f67,f141,f117]) ).
fof(f148,plain,
( sQ5_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f68,f141,f121]) ).
fof(f149,plain,
( sQ6_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f69,f141,f125]) ).
fof(f150,plain,
( sQ7_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f70,f141,f129]) ).
fof(f151,plain,
( sQ8_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f71,f141,f133]) ).
fof(f152,plain,
( sQ9_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f72,f141,f137]) ).
fof(f153,definition,
( sQ11_spl
<=> multiply(sk_c10,sk_c3) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f154,plain,
( ~ sQ11_spl
| multiply(sk_c10,sk_c3) = sk_c9 ),
inference(component_clause,[status(thm)],[f153]) ).
fof(f156,plain,
( sQ1_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f73,f153,f105]) ).
fof(f157,plain,
( sQ2_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f74,f153,f109]) ).
fof(f158,plain,
( sQ3_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f75,f153,f113]) ).
fof(f159,plain,
( sQ4_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f76,f153,f117]) ).
fof(f160,plain,
( sQ5_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f77,f153,f121]) ).
fof(f161,plain,
( sQ6_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f78,f153,f125]) ).
fof(f162,plain,
( sQ7_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f79,f153,f129]) ).
fof(f163,plain,
( sQ8_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f80,f153,f133]) ).
fof(f164,plain,
( sQ9_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f81,f153,f137]) ).
fof(f165,definition,
( sQ12_spl
<=> multiply(sk_c2,sk_c10) = sk_c3 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f166,plain,
( ~ sQ12_spl
| multiply(sk_c2,sk_c10) = sk_c3 ),
inference(component_clause,[status(thm)],[f165]) ).
fof(f168,plain,
( sQ1_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f82,f165,f105]) ).
fof(f169,plain,
( sQ2_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f83,f165,f109]) ).
fof(f170,plain,
( sQ3_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f84,f165,f113]) ).
fof(f171,plain,
( sQ4_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f85,f165,f117]) ).
fof(f172,plain,
( sQ5_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f86,f165,f121]) ).
fof(f173,plain,
( sQ6_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f87,f165,f125]) ).
fof(f174,plain,
( sQ7_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f88,f165,f129]) ).
fof(f175,plain,
( sQ8_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f89,f165,f133]) ).
fof(f176,plain,
( sQ9_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f90,f165,f137]) ).
fof(f177,definition,
( sQ13_spl
<=> inverse(sk_c2) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f178,plain,
( ~ sQ13_spl
| inverse(sk_c2) = sk_c10 ),
inference(component_clause,[status(thm)],[f177]) ).
fof(f180,plain,
( sQ1_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f91,f177,f105]) ).
fof(f181,plain,
( sQ2_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f92,f177,f109]) ).
fof(f182,plain,
( sQ3_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f93,f177,f113]) ).
fof(f183,plain,
( sQ4_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f94,f177,f117]) ).
fof(f184,plain,
( sQ5_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f95,f177,f121]) ).
fof(f185,plain,
( sQ6_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f96,f177,f125]) ).
fof(f186,plain,
( sQ7_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f97,f177,f129]) ).
fof(f187,plain,
( sQ8_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f98,f177,f133]) ).
fof(f188,plain,
( sQ9_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f99,f177,f137]) ).
fof(f189,definition,
( sQ14_spl
<=> multiply(sk_c9,sk_c10) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f191,plain,
( sQ14_spl
| multiply(sk_c9,sk_c10) != sk_c8 ),
inference(component_clause,[status(thm)],[f189]) ).
fof(f192,definition,
! [X0] :
( sQ15_spl
<=> ( inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f193,plain,
! [X0] :
( ~ sQ15_spl
| inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c10 ),
inference(component_clause,[status(thm)],[f192]) ).
fof(f195,definition,
! [X1,X2] :
( sQ16_spl
<=> ( inverse(X2) != sk_c10
| multiply(X2,sk_c10) != X1
| multiply(sk_c10,X1) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f196,plain,
! [X0,X1] :
( ~ sQ16_spl
| inverse(X1) != sk_c10
| multiply(X1,sk_c10) != X0
| multiply(sk_c10,X0) != sk_c9 ),
inference(component_clause,[status(thm)],[f195]) ).
fof(f198,definition,
! [X3] :
( sQ17_spl
<=> ( inverse(X3) != sk_c10
| multiply(X3,sk_c10) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f199,plain,
! [X0] :
( ~ sQ17_spl
| inverse(X0) != sk_c10
| multiply(X0,sk_c10) != sk_c9 ),
inference(component_clause,[status(thm)],[f198]) ).
fof(f201,definition,
! [X4] :
( sQ18_spl
<=> ( multiply(X4,sk_c8) != sk_c9
| inverse(X4) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f202,plain,
! [X0] :
( ~ sQ18_spl
| multiply(X0,sk_c8) != sk_c9
| inverse(X0) != sk_c9 ),
inference(component_clause,[status(thm)],[f201]) ).
fof(f204,definition,
! [X5,X6] :
( sQ19_spl
<=> ( multiply(X5,sk_c10) != X6
| inverse(X6) != sk_c10
| inverse(X5) != X6 ) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f205,plain,
! [X0,X1] :
( ~ sQ19_spl
| multiply(X0,sk_c10) != X1
| inverse(X1) != sk_c10
| inverse(X0) != X1 ),
inference(component_clause,[status(thm)],[f204]) ).
fof(f207,plain,
( sQ19_spl
| sQ18_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sQ17_spl
| sQ16_spl
| sQ15_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f101,f189,f192,f195,f198,f113,f117,f201,f204]) ).
fof(f208,plain,
! [X0] :
( ~ sQ19_spl
| multiply(X0,sk_c10) != inverse(X0)
| inverse(inverse(X0)) != sk_c10 ),
inference(destructive_equality_resolution,[status(thm)],[f205]) ).
fof(f210,plain,
! [X0] :
( ~ sQ1_spl
| multiply(sk_c9,X0) = multiply(sk_c4,multiply(sk_c10,X0)) ),
inference(paramodulation,[status(thm)],[f106,f53]) ).
fof(f221,plain,
( ~ sQ7_spl
| ~ sQ19_spl
| multiply(sk_c7,sk_c10) != inverse(sk_c7)
| inverse(sk_c6) != sk_c10 ),
inference(paramodulation,[status(thm)],[f130,f208]) ).
fof(f223,plain,
( ~ sQ10_spl
| ~ sQ19_spl
| multiply(sk_c1,sk_c10) != inverse(sk_c1)
| inverse(sk_c9) != sk_c10 ),
inference(paramodulation,[status(thm)],[f142,f208]) ).
fof(f232,definition,
( sQ22_spl
<=> inverse(sk_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f234,plain,
( sQ22_spl
| inverse(sk_c9) != sk_c10 ),
inference(component_clause,[status(thm)],[f232]) ).
fof(f239,definition,
( sQ24_spl
<=> multiply(sk_c7,sk_c10) = inverse(sk_c7) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f241,plain,
( sQ24_spl
| multiply(sk_c7,sk_c10) != inverse(sk_c7) ),
inference(component_clause,[status(thm)],[f239]) ).
fof(f242,plain,
( ~ sQ7_spl
| ~ sQ19_spl
| ~ sQ24_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f221,f133,f239,f204,f129]) ).
fof(f247,definition,
( sQ26_spl
<=> multiply(sk_c1,sk_c10) = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f249,plain,
( sQ26_spl
| multiply(sk_c1,sk_c10) != inverse(sk_c1) ),
inference(component_clause,[status(thm)],[f247]) ).
fof(f250,plain,
( ~ sQ10_spl
| ~ sQ19_spl
| ~ sQ26_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f223,f232,f247,f204,f141]) ).
fof(f257,plain,
( sQ26_spl
| ~ sQ10_spl
| multiply(sk_c1,sk_c10) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f142,f249]) ).
fof(f258,plain,
( sQ24_spl
| ~ sQ9_spl
| sk_c6 != inverse(sk_c7) ),
inference(forward_demodulation,[status(thm)],[f138,f241]) ).
fof(f263,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f52,f53]) ).
fof(f264,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f51,f263]) ).
fof(f271,plain,
( ~ sQ18_spl
| sk_c8 != sk_c9
| inverse(identity) != sk_c9 ),
inference(paramodulation,[status(thm)],[f51,f202]) ).
fof(f273,plain,
( ~ sQ6_spl
| ~ sQ18_spl
| sk_c9 != sk_c9
| inverse(sk_c5) != sk_c9 ),
inference(paramodulation,[status(thm)],[f126,f202]) ).
fof(f281,definition,
( sQ30_spl
<=> inverse(identity) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f283,plain,
( sQ30_spl
| inverse(identity) != sk_c9 ),
inference(component_clause,[status(thm)],[f281]) ).
fof(f284,definition,
( sQ31_spl
<=> sk_c8 = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f286,plain,
( sQ31_spl
| sk_c8 != sk_c9 ),
inference(component_clause,[status(thm)],[f284]) ).
fof(f287,plain,
( ~ sQ18_spl
| ~ sQ31_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f271,f281,f284,f201]) ).
fof(f288,definition,
( sQ32_spl
<=> sk_c9 = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f290,plain,
( sQ32_spl
| sk_c9 != sk_c9 ),
inference(component_clause,[status(thm)],[f288]) ).
fof(f291,plain,
( ~ sQ6_spl
| ~ sQ18_spl
| ~ sQ32_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f273,f121,f288,f201,f125]) ).
fof(f292,plain,
( sQ32_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f290]) ).
fof(f293,plain,
sQ32_spl,
inference(contradiction_clause,[status(thm)],[f292]) ).
fof(f294,plain,
! [X0] :
( ~ sQ16_spl
| inverse(X0) != sk_c10
| multiply(sk_c10,multiply(X0,sk_c10)) != sk_c9 ),
inference(destructive_equality_resolution,[status(thm)],[f196]) ).
fof(f295,plain,
( sQ14_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f54,f191]) ).
fof(f296,plain,
( sQ14_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f295]) ).
fof(f297,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f296]) ).
fof(f299,plain,
( ~ sQ10_spl
| ~ sQ17_spl
| sk_c9 != sk_c10
| multiply(sk_c1,sk_c10) != sk_c9 ),
inference(paramodulation,[status(thm)],[f142,f199]) ).
fof(f302,definition,
( sQ33_spl
<=> multiply(sk_c1,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f304,plain,
( sQ33_spl
| multiply(sk_c1,sk_c10) != sk_c9 ),
inference(component_clause,[status(thm)],[f302]) ).
fof(f305,definition,
( sQ34_spl
<=> sk_c9 = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f307,plain,
( sQ34_spl
| sk_c9 != sk_c10 ),
inference(component_clause,[status(thm)],[f305]) ).
fof(f308,plain,
( ~ sQ10_spl
| ~ sQ17_spl
| ~ sQ34_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f299,f302,f305,f198,f141]) ).
fof(f312,definition,
( sQ36_spl
<=> sk_c10 = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f314,plain,
( sQ36_spl
| sk_c10 != sk_c10 ),
inference(component_clause,[status(thm)],[f312]) ).
fof(f316,plain,
( sQ36_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f314]) ).
fof(f317,plain,
sQ36_spl,
inference(contradiction_clause,[status(thm)],[f316]) ).
fof(f319,plain,
( ~ sQ16_spl
| inverse(inverse(sk_c10)) != sk_c10
| multiply(sk_c10,identity) != sk_c9 ),
inference(paramodulation,[status(thm)],[f52,f294]) ).
fof(f320,plain,
( ~ sQ16_spl
| inverse(identity) != sk_c10
| multiply(sk_c10,sk_c10) != sk_c9 ),
inference(paramodulation,[status(thm)],[f51,f294]) ).
fof(f322,plain,
( ~ sQ1_spl
| ~ sQ16_spl
| inverse(sk_c4) != sk_c10
| multiply(sk_c10,sk_c9) != sk_c9 ),
inference(paramodulation,[status(thm)],[f106,f294]) ).
fof(f324,plain,
( ~ sQ12_spl
| ~ sQ16_spl
| inverse(sk_c2) != sk_c10
| multiply(sk_c10,sk_c3) != sk_c9 ),
inference(paramodulation,[status(thm)],[f166,f294]) ).
fof(f325,plain,
( ~ sQ16_spl
| inverse(sk_c9) != sk_c10
| multiply(sk_c10,sk_c8) != sk_c9 ),
inference(paramodulation,[status(thm)],[f54,f294]) ).
fof(f326,definition,
( sQ37_spl
<=> multiply(sk_c10,identity) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f329,definition,
( sQ38_spl
<=> inverse(inverse(sk_c10)) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f332,plain,
( ~ sQ16_spl
| ~ sQ38_spl
| ~ sQ37_spl ),
inference(split_clause,[status(thm)],[f319,f326,f329,f195]) ).
fof(f333,definition,
( sQ39_spl
<=> multiply(sk_c10,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f336,definition,
( sQ40_spl
<=> inverse(identity) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f339,plain,
( ~ sQ16_spl
| ~ sQ40_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f320,f333,f336,f195]) ).
fof(f340,definition,
( sQ41_spl
<=> multiply(sk_c10,sk_c9) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f343,plain,
( ~ sQ1_spl
| ~ sQ16_spl
| ~ sQ2_spl
| ~ sQ41_spl ),
inference(split_clause,[status(thm)],[f322,f340,f109,f195,f105]) ).
fof(f344,definition,
( sQ42_spl
<=> multiply(sk_c10,sk_c6) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f346,plain,
( sQ42_spl
| multiply(sk_c10,sk_c6) != sk_c9 ),
inference(component_clause,[status(thm)],[f344]) ).
fof(f351,plain,
( ~ sQ12_spl
| ~ sQ16_spl
| ~ sQ13_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f324,f153,f177,f195,f165]) ).
fof(f352,plain,
( ~ sQ16_spl
| ~ sQ22_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f325,f117,f232,f195]) ).
fof(f353,plain,
( ~ sQ13_spl
| ~ sQ15_spl
| sk_c10 != sk_c9
| multiply(sk_c2,sk_c9) != sk_c10 ),
inference(paramodulation,[status(thm)],[f178,f193]) ).
fof(f354,definition,
( sQ44_spl
<=> multiply(sk_c2,sk_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f356,plain,
( sQ44_spl
| multiply(sk_c2,sk_c9) != sk_c10 ),
inference(component_clause,[status(thm)],[f354]) ).
fof(f357,plain,
( ~ sQ13_spl
| ~ sQ15_spl
| ~ sQ34_spl
| ~ sQ44_spl ),
inference(split_clause,[status(thm)],[f353,f354,f305,f192,f177]) ).
fof(f358,plain,
( sQ22_spl
| ~ sQ3_spl
| sk_c8 != sk_c10 ),
inference(backward_demodulation,[status(thm)],[f114,f234]) ).
fof(f363,plain,
( ~ sQ8_spl
| multiply(sk_c10,sk_c6) = identity ),
inference(paramodulation,[status(thm)],[f134,f52]) ).
fof(f366,plain,
( ~ sQ1_spl
| ~ sQ17_spl
| inverse(sk_c4) != sk_c10 ),
inference(resolution,[status(thm)],[f199,f106]) ).
fof(f374,plain,
( ~ sQ1_spl
| ~ sQ17_spl
| ~ sQ2_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f110,f366]) ).
fof(f375,plain,
( ~ sQ1_spl
| ~ sQ17_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f374]) ).
fof(f376,plain,
( ~ sQ1_spl
| ~ sQ17_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f375]) ).
fof(f387,plain,
( sQ42_spl
| ~ sQ8_spl
| identity != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f363,f346]) ).
fof(f396,plain,
( ~ sQ6_spl
| sk_c8 = multiply(inverse(sk_c5),sk_c9) ),
inference(paramodulation,[status(thm)],[f126,f264]) ).
fof(f401,plain,
( ~ sQ1_spl
| sk_c10 = multiply(inverse(sk_c4),sk_c9) ),
inference(paramodulation,[status(thm)],[f106,f264]) ).
fof(f408,plain,
( ~ sQ12_spl
| sk_c10 = multiply(inverse(sk_c2),sk_c3) ),
inference(paramodulation,[status(thm)],[f166,f264]) ).
fof(f413,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| sk_c8 = multiply(sk_c9,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f122,f396]) ).
fof(f414,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c10 = multiply(sk_c10,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f110,f401]) ).
fof(f416,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| sk_c10 = multiply(sk_c10,sk_c3) ),
inference(forward_demodulation,[status(thm)],[f178,f408]) ).
fof(f462,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c9,sk_c9) = multiply(sk_c4,sk_c10) ),
inference(paramodulation,[status(thm)],[f414,f210]) ).
fof(f463,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c9 = multiply(inverse(sk_c10),sk_c10) ),
inference(paramodulation,[status(thm)],[f414,f264]) ).
fof(f466,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sk_c8 = multiply(sk_c4,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f413,f462]) ).
fof(f467,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sk_c8 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f106,f466]) ).
fof(f468,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c9 = identity ),
inference(forward_demodulation,[status(thm)],[f52,f463]) ).
fof(f469,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sQ42_spl
| ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f468,f387]) ).
fof(f470,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sQ42_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f469]) ).
fof(f471,plain,
( sQ24_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f130,f258]) ).
fof(f472,plain,
( sQ24_spl
| ~ sQ9_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f471]) ).
fof(f473,plain,
( sQ24_spl
| ~ sQ9_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f472]) ).
fof(f482,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| multiply(sk_c10,sk_c8) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f467,f118]) ).
fof(f485,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| inverse(sk_c5) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f467,f122]) ).
fof(f498,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| multiply(sk_c8,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f499,f51]) ).
fof(f499,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sk_c8 = identity ),
inference(forward_demodulation,[status(thm)],[f467,f468]) ).
fof(f522,definition,
( sQ48_spl
<=> inverse(sk_c8) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f523,plain,
( ~ sQ48_spl
| inverse(sk_c8) = sk_c10 ),
inference(component_clause,[status(thm)],[f522]) ).
fof(f524,plain,
( sQ48_spl
| inverse(sk_c8) != sk_c10 ),
inference(component_clause,[status(thm)],[f522]) ).
fof(f534,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| multiply(sk_c8,X0) = multiply(sk_c10,multiply(sk_c8,X0)) ),
inference(paramodulation,[status(thm)],[f482,f53]) ).
fof(f535,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| X0 = multiply(sk_c10,multiply(sk_c8,X0)) ),
inference(forward_demodulation,[status(thm)],[f498,f534]) ).
fof(f536,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| X0 = multiply(sk_c10,X0) ),
inference(forward_demodulation,[status(thm)],[f498,f535]) ).
fof(f585,plain,
( ~ sQ12_spl
| sk_c10 = multiply(inverse(sk_c2),sk_c3) ),
inference(paramodulation,[status(thm)],[f166,f264]) ).
fof(f587,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| sk_c10 = multiply(sk_c10,sk_c3) ),
inference(forward_demodulation,[status(thm)],[f178,f585]) ).
fof(f588,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| sk_c10 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f154,f587]) ).
fof(f589,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| sQ34_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f588,f307]) ).
fof(f590,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| sQ34_spl ),
inference(contradiction_clause,[status(thm)],[f589]) ).
fof(f595,plain,
( ~ sQ10_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| inverse(sk_c1) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f588,f142]) ).
fof(f597,plain,
( sQ31_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| sk_c8 != sk_c10 ),
inference(backward_demodulation,[status(thm)],[f588,f286]) ).
fof(f617,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| multiply(sk_c1,sk_c10) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f588,f103]) ).
fof(f618,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| sk_c10 = multiply(inverse(sk_c1),sk_c10) ),
inference(paramodulation,[status(thm)],[f617,f264]) ).
fof(f620,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ10_spl
| sk_c10 = multiply(sk_c10,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f595,f618]) ).
fof(f632,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| multiply(sk_c10,sk_c10) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f588,f54]) ).
fof(f650,plain,
( sQ44_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| multiply(sk_c2,sk_c10) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f588,f356]) ).
fof(f651,plain,
( sQ44_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| sk_c3 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f166,f650]) ).
fof(f653,plain,
( sQ33_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| sk_c10 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f617,f304]) ).
fof(f654,plain,
( sQ33_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f588,f653]) ).
fof(f655,plain,
( sQ33_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f654]) ).
fof(f656,plain,
( sQ33_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f655]) ).
fof(f659,plain,
( sQ26_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| sk_c10 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f617,f257]) ).
fof(f660,plain,
( sQ26_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f588,f659]) ).
fof(f661,plain,
( sQ26_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f660]) ).
fof(f662,plain,
( sQ26_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f661]) ).
fof(f670,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| sk_c3 = multiply(inverse(sk_c10),sk_c10) ),
inference(paramodulation,[status(thm)],[f416,f264]) ).
fof(f672,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| sk_c3 = identity ),
inference(forward_demodulation,[status(thm)],[f52,f670]) ).
fof(f674,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ13_spl
| multiply(inverse(X0),X0) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f672,f52]) ).
fof(f675,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ13_spl
| multiply(sk_c3,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f672,f51]) ).
fof(f683,plain,
( sQ4_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| multiply(sk_c10,sk_c8) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f588,f119]) ).
fof(f738,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ10_spl
| sk_c10 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f632,f620]) ).
fof(f739,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ10_spl
| sQ22_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f738,f358]) ).
fof(f740,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ10_spl
| sQ22_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f739]) ).
fof(f743,plain,
( sQ3_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| inverse(sk_c10) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f588,f115]) ).
fof(f744,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ10_spl
| multiply(sk_c10,sk_c8) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f738,f632]) ).
fof(f754,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ10_spl
| multiply(sk_c1,sk_c10) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f738,f617]) ).
fof(f755,plain,
( ~ sQ10_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ0_spl
| inverse(sk_c1) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f738,f595]) ).
fof(f756,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ10_spl
| sk_c8 = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f738,f588]) ).
fof(f757,plain,
( ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ10_spl
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f738,f166]) ).
fof(f758,plain,
( ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl
| inverse(sk_c2) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f738,f178]) ).
fof(f759,plain,
( sQ48_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ10_spl
| inverse(sk_c8) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f738,f524]) ).
fof(f762,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ10_spl
| multiply(sk_c8,sk_c8) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f738,f744]) ).
fof(f765,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ10_spl
| multiply(sk_c1,sk_c8) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f738,f754]) ).
fof(f770,plain,
( sQ3_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ10_spl
| inverse(sk_c8) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f738,f743]) ).
fof(f775,plain,
( sQ31_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ10_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f738,f597]) ).
fof(f776,plain,
( sQ31_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f775]) ).
fof(f777,plain,
( sQ31_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f776]) ).
fof(f780,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ10_spl
| sk_c8 = multiply(inverse(sk_c8),sk_c8) ),
inference(paramodulation,[status(thm)],[f762,f264]) ).
fof(f782,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ10_spl
| sk_c8 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f674,f780]) ).
fof(f785,plain,
( sQ44_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ10_spl
| sk_c3 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f738,f651]) ).
fof(f794,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ10_spl
| sk_c3 = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f782,f756]) ).
fof(f795,plain,
( sQ3_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ10_spl
| inverse(sk_c8) != sk_c3 ),
inference(backward_demodulation,[status(thm)],[f782,f770]) ).
fof(f796,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ10_spl
| sk_c10 = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f782,f738]) ).
fof(f800,plain,
( sQ3_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ10_spl
| inverse(sk_c3) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f782,f795]) ).
fof(f801,plain,
( sQ44_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ10_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f782,f785]) ).
fof(f802,plain,
( sQ44_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f801]) ).
fof(f803,plain,
( sQ44_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f802]) ).
fof(f808,plain,
( ~ sQ10_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ0_spl
| inverse(sk_c1) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f782,f755]) ).
fof(f809,plain,
( ~ sQ10_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ0_spl
| multiply(sk_c3,sk_c1) = sk_c3 ),
inference(paramodulation,[status(thm)],[f808,f674]) ).
fof(f810,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ0_spl
| X0 = multiply(sk_c3,multiply(sk_c1,X0)) ),
inference(paramodulation,[status(thm)],[f808,f264]) ).
fof(f811,plain,
( ~ sQ10_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ0_spl
| sk_c1 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f675,f809]) ).
fof(f812,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ0_spl
| X0 = multiply(sk_c1,X0) ),
inference(forward_demodulation,[status(thm)],[f675,f810]) ).
fof(f813,plain,
( ~ sQ10_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ0_spl
| inverse(sk_c3) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f811,f808]) ).
fof(f814,plain,
( ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl
| inverse(sk_c2) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f782,f758]) ).
fof(f815,plain,
( ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl
| multiply(sk_c3,sk_c2) = sk_c3 ),
inference(paramodulation,[status(thm)],[f814,f674]) ).
fof(f817,plain,
( ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl
| sk_c2 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f675,f815]) ).
fof(f819,plain,
( ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ10_spl
| inverse(sk_c2) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f817,f814]) ).
fof(f820,plain,
( ~ sQ10_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ0_spl
| sk_c1 = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f817,f811]) ).
fof(f822,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ10_spl
| sk_c10 = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f817,f796]) ).
fof(f823,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ10_spl
| sk_c2 = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f817,f794]) ).
fof(f830,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ10_spl
| sk_c2 = identity ),
inference(backward_demodulation,[status(thm)],[f817,f672]) ).
fof(f831,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ10_spl
| multiply(sk_c2,sk_c8) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f820,f765]) ).
fof(f834,plain,
( ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ10_spl
| sk_c8 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f831,f757]) ).
fof(f837,plain,
( ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ10_spl
| sk_c8 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f817,f834]) ).
fof(f843,plain,
( sQ48_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ10_spl
| inverse(sk_c2) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f837,f759]) ).
fof(f844,plain,
( sQ48_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ10_spl
| inverse(sk_c2) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f837,f843]) ).
fof(f847,plain,
( sQ3_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ10_spl
| inverse(sk_c2) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f817,f800]) ).
fof(f848,plain,
( sQ3_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ10_spl
| inverse(sk_c2) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f817,f847]) ).
fof(f849,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ0_spl
| X0 = multiply(sk_c2,X0) ),
inference(forward_demodulation,[status(thm)],[f820,f812]) ).
fof(f852,plain,
( ~ sQ10_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ0_spl
| inverse(sk_c2) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f817,f813]) ).
fof(f853,plain,
( ~ sQ10_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ0_spl
| inverse(sk_c2) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f817,f852]) ).
fof(f854,plain,
( ~ sQ10_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ0_spl
| sQ48_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f853,f844]) ).
fof(f855,plain,
( ~ sQ10_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ0_spl
| sQ48_spl ),
inference(contradiction_clause,[status(thm)],[f854]) ).
fof(f856,plain,
( ~ sQ48_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ10_spl
| inverse(sk_c2) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f837,f523]) ).
fof(f857,plain,
( ~ sQ48_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ10_spl
| inverse(sk_c2) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f822,f856]) ).
fof(f865,plain,
( sQ3_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ10_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f819,f848]) ).
fof(f866,plain,
( sQ3_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f865]) ).
fof(f867,plain,
( sQ3_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f866]) ).
fof(f879,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| multiply(inverse(X0),X0) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f499,f52]) ).
fof(f884,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| multiply(sk_c8,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f499,f51]) ).
fof(f898,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| multiply(sk_c8,sk_c10) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f467,f54]) ).
fof(f899,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sk_c10 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f884,f898]) ).
fof(f900,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sQ22_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f899,f358]) ).
fof(f901,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sQ22_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f900]) ).
fof(f919,plain,
( sQ30_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ10_spl
| inverse(sk_c2) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f830,f283]) ).
fof(f920,plain,
( sQ30_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ10_spl
| inverse(sk_c2) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f823,f919]) ).
fof(f924,plain,
( ~ sQ48_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ10_spl
| sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f857,f920]) ).
fof(f925,plain,
( ~ sQ48_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ10_spl
| sQ30_spl ),
inference(contradiction_clause,[status(thm)],[f924]) ).
fof(f1145,plain,
( sQ4_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ10_spl
| multiply(sk_c2,sk_c8) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f822,f683]) ).
fof(f1146,plain,
( sQ4_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ10_spl
| sk_c8 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f849,f1145]) ).
fof(f1147,plain,
( sQ4_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ10_spl
| sk_c2 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f837,f1146]) ).
fof(f1148,plain,
( sQ4_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ10_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f822,f1147]) ).
fof(f1149,plain,
( sQ4_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1148]) ).
fof(f1150,plain,
( sQ4_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f1149]) ).
fof(f1157,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| multiply(sk_c8,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f499,f51]) ).
fof(f1166,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| multiply(inverse(X0),X0) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f499,f52]) ).
fof(f1174,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| multiply(sk_c8,sk_c5) = sk_c8 ),
inference(paramodulation,[status(thm)],[f485,f1166]) ).
fof(f1175,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| X0 = multiply(sk_c8,multiply(sk_c5,X0)) ),
inference(paramodulation,[status(thm)],[f485,f264]) ).
fof(f1176,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| sk_c5 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f1157,f1174]) ).
fof(f1177,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| X0 = multiply(sk_c5,X0) ),
inference(forward_demodulation,[status(thm)],[f1157,f1175]) ).
fof(f1180,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| inverse(sk_c5) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f1176,f485]) ).
fof(f1186,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sk_c5 = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f1176,f467]) ).
fof(f1188,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sk_c10 = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f1176,f899]) ).
fof(f1190,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| X0 = multiply(sk_c5,X0) ),
inference(forward_demodulation,[status(thm)],[f1188,f536]) ).
fof(f1196,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| multiply(inverse(X0),X0) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f1176,f879]) ).
fof(f1216,plain,
( ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| inverse(sk_c6) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f1188,f134]) ).
fof(f1217,plain,
( ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| multiply(sk_c5,sk_c6) = sk_c5 ),
inference(paramodulation,[status(thm)],[f1216,f1196]) ).
fof(f1219,plain,
( ~ sQ8_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c6 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f1190,f1217]) ).
fof(f1230,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ4_spl
| sk_c10 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f1219,f1188]) ).
fof(f1232,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ4_spl
| sk_c6 = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f1219,f1186]) ).
fof(f1235,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ4_spl
| X0 = multiply(sk_c6,X0) ),
inference(forward_demodulation,[status(thm)],[f1219,f1177]) ).
fof(f1250,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ4_spl
| inverse(sk_c6) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f1219,f1180]) ).
fof(f1251,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ4_spl
| inverse(sk_c6) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f1219,f1250]) ).
fof(f1317,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ4_spl
| inverse(X0) != sk_c9
| multiply(X0,sk_c6) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1232,f193]) ).
fof(f1318,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ4_spl
| inverse(X0) != sk_c9
| multiply(X0,sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f1230,f1317]) ).
fof(f1319,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ8_spl
| ~ sQ4_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f1232,f1318]) ).
fof(f1320,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ4_spl
| ~ sQ15_spl
| multiply(sk_c6,sk_c6) != sk_c6 ),
inference(resolution,[status(thm)],[f1319,f1251]) ).
fof(f1322,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ4_spl
| ~ sQ15_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f1235,f1320]) ).
fof(f1323,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ4_spl
| ~ sQ15_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1322]) ).
fof(f1324,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ4_spl
| ~ sQ15_spl ),
inference(contradiction_clause,[status(thm)],[f1323]) ).
fof(f1325,plain,
$false,
inference(sat_refutation,[status(thm)],[f108,f112,f116,f120,f124,f128,f132,f136,f140,f144,f145,f146,f147,f148,f149,f150,f151,f152,f156,f157,f158,f159,f160,f161,f162,f163,f164,f168,f169,f170,f171,f172,f173,f174,f175,f176,f180,f181,f182,f183,f184,f185,f186,f187,f188,f207,f242,f250,f287,f291,f293,f297,f308,f317,f332,f339,f343,f351,f352,f357,f376,f470,f473,f590,f656,f662,f740,f777,f803,f855,f867,f901,f925,f1150,f1324]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP325-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n020.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 20 20:10:33 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.15/0.39 % Drodi V4.1.1
% 0.15/0.46 % Refutation found
% 0.15/0.46 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.49 % Elapsed time: 0.114430 seconds
% 0.15/0.49 % CPU time: 0.499957 seconds
% 0.15/0.49 % Total memory used: 109.494 MB
% 0.15/0.49 % Net memory used: 109.157 MB
%------------------------------------------------------------------------------