%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP340-1 : 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 12:33:27 PM UTC 2026
% Result : Unsatisfiable 0.07s 0.48s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 90
% Syntax : Number of formulae : 481 ( 13 unt; 41 def)
% Number of atoms : 1767 ( 541 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 2411 (1125 ~;1245 |; 0 &)
% ( 41 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 43 ( 41 usr; 42 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 121 ( 121 !; 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(f12,negated_conjecture,
( inverse(sk_c6) = sk_c8
| multiply(sk_c10,sk_c11) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| 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
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c3) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c7) = sk_c6
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( inverse(sk_c6) = sk_c8
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( inverse(sk_c6) = sk_c8
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c1,sk_c10) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( inverse(sk_c3) = sk_c11
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,negated_conjecture,
( inverse(sk_c6) = sk_c8
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f52,negated_conjecture,
( inverse(sk_c6) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f53,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c2,sk_c9) = sk_c10 ),
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
| multiply(X4,sk_c9) != sk_c10
| inverse(X4) != sk_c10
| multiply(X3,sk_c10) != sk_c11
| inverse(X3) != 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(f66,plain,
( inverse(sk_c6) = sk_c8
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f67,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c10,sk_c11) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f68,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f69,plain,
( inverse(sk_c3) = sk_c11
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f70,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f71,plain,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f72,plain,
( multiply(sk_c5,sk_c8) = sk_c11
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f73,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f74,plain,
( multiply(sk_c8,sk_c10) = sk_c11
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f75,plain,
( inverse(sk_c7) = sk_c6
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f76,plain,
( inverse(sk_c6) = sk_c8
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f77,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f78,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f79,plain,
( inverse(sk_c3) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f80,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f81,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f82,plain,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f83,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f84,plain,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f86,plain,
( inverse(sk_c6) = sk_c8
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f87,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f88,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f89,plain,
( inverse(sk_c3) = sk_c11
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f90,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f91,plain,
( inverse(sk_c4) = sk_c10
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f92,plain,
( multiply(sk_c5,sk_c8) = sk_c11
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f93,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f94,plain,
( multiply(sk_c8,sk_c10) = sk_c11
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f96,plain,
( inverse(sk_c6) = sk_c8
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f97,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f98,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f99,plain,
( inverse(sk_c3) = sk_c11
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f100,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f101,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f102,plain,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f103,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f104,plain,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f106,plain,
( inverse(sk_c6) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f107,plain,
( multiply(sk_c7,sk_c8) = sk_c6
| multiply(sk_c2,sk_c9) = sk_c10 ),
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] :
( multiply(X4,sk_c9) != sk_c10
| inverse(X4) != sk_c10
| ! [X3] :
( multiply(X3,sk_c10) != sk_c11
| inverse(X3) != 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
| multiply(X1,sk_c9) != sk_c10
| inverse(X1) != sk_c10
| multiply(X0,sk_c10) != sk_c11
| inverse(X0) != 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(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(f152,plain,
( sQ10_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f67,f110,f149]) ).
fof(f153,definition,
( sQ11_spl
<=> inverse(sk_c1) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f154,plain,
( ~ sQ11_spl
| inverse(sk_c1) = sk_c11 ),
inference(component_clause,[status(thm)],[f153]) ).
fof(f156,plain,
( sQ1_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f68,f153,f113]) ).
fof(f157,plain,
( sQ2_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f69,f153,f117]) ).
fof(f158,plain,
( sQ3_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f70,f153,f121]) ).
fof(f159,plain,
( sQ4_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f71,f153,f125]) ).
fof(f160,plain,
( sQ5_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f72,f153,f129]) ).
fof(f161,plain,
( sQ6_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f73,f153,f133]) ).
fof(f162,plain,
( sQ7_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f74,f153,f137]) ).
fof(f163,plain,
( sQ8_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f75,f153,f141]) ).
fof(f164,plain,
( sQ9_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f76,f153,f145]) ).
fof(f165,plain,
( sQ10_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f77,f153,f149]) ).
fof(f166,definition,
( sQ12_spl
<=> multiply(sk_c1,sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f167,plain,
( ~ sQ12_spl
| multiply(sk_c1,sk_c10) = sk_c11 ),
inference(component_clause,[status(thm)],[f166]) ).
fof(f168,plain,
( sQ12_spl
| multiply(sk_c1,sk_c10) != sk_c11 ),
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(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
<=> inverse(sk_c2) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f180,plain,
( ~ sQ13_spl
| inverse(sk_c2) = sk_c10 ),
inference(component_clause,[status(thm)],[f179]) ).
fof(f182,plain,
( sQ1_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f88,f179,f113]) ).
fof(f183,plain,
( sQ2_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f89,f179,f117]) ).
fof(f184,plain,
( sQ3_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f90,f179,f121]) ).
fof(f185,plain,
( sQ4_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f91,f179,f125]) ).
fof(f186,plain,
( sQ5_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f92,f179,f129]) ).
fof(f187,plain,
( sQ6_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f93,f179,f133]) ).
fof(f188,plain,
( sQ7_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f94,f179,f137]) ).
fof(f190,plain,
( sQ9_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f96,f179,f145]) ).
fof(f191,plain,
( sQ10_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f97,f179,f149]) ).
fof(f192,definition,
( sQ14_spl
<=> multiply(sk_c2,sk_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f193,plain,
( ~ sQ14_spl
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(component_clause,[status(thm)],[f192]) ).
fof(f194,plain,
( sQ14_spl
| multiply(sk_c2,sk_c9) != sk_c10 ),
inference(component_clause,[status(thm)],[f192]) ).
fof(f195,plain,
( sQ1_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f98,f192,f113]) ).
fof(f196,plain,
( sQ2_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f99,f192,f117]) ).
fof(f197,plain,
( sQ3_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f100,f192,f121]) ).
fof(f198,plain,
( sQ4_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f101,f192,f125]) ).
fof(f199,plain,
( sQ5_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f102,f192,f129]) ).
fof(f200,plain,
( sQ6_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f103,f192,f133]) ).
fof(f201,plain,
( sQ7_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f104,f192,f137]) ).
fof(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
<=> ( multiply(X0,sk_c10) != sk_c11
| inverse(X0) != sk_c11 ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f206,plain,
! [X0] :
( ~ sQ15_spl
| multiply(X0,sk_c10) != sk_c11
| inverse(X0) != sk_c11 ),
inference(component_clause,[status(thm)],[f205]) ).
fof(f208,definition,
! [X1] :
( sQ16_spl
<=> ( multiply(X1,sk_c9) != sk_c10
| inverse(X1) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f209,plain,
! [X0] :
( ~ sQ16_spl
| multiply(X0,sk_c9) != sk_c10
| inverse(X0) != 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(f223,plain,
! [X0] :
( ~ sQ14_spl
| multiply(sk_c10,X0) = multiply(sk_c2,multiply(sk_c9,X0)) ),
inference(paramodulation,[status(thm)],[f193,f57]) ).
fof(f226,plain,
! [X0] :
( ~ sQ12_spl
| multiply(sk_c11,X0) = multiply(sk_c1,multiply(sk_c10,X0)) ),
inference(paramodulation,[status(thm)],[f167,f57]) ).
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,
( ~ sQ11_spl
| multiply(sk_c11,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f154,f56]) ).
fof(f232,plain,
( ~ sQ13_spl
| multiply(sk_c10,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f180,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(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(f250,plain,
! [X0] :
( ~ sQ11_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_c11) != sk_c11 ),
inference(paramodulation,[status(thm)],[f154,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(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(f263,plain,
( ~ sQ23_spl
| inverse(identity) = sk_c11 ),
inference(component_clause,[status(thm)],[f262]) ).
fof(f264,plain,
( sQ23_spl
| inverse(identity) != sk_c11 ),
inference(component_clause,[status(thm)],[f262]) ).
fof(f316,definition,
( sQ39_spl
<=> multiply(sk_c1,sk_c11) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f318,plain,
( sQ39_spl
| multiply(sk_c1,sk_c11) != sk_c11 ),
inference(component_clause,[status(thm)],[f316]) ).
fof(f319,definition,
( sQ40_spl
<=> multiply(inverse(sk_c1),sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f321,plain,
( sQ40_spl
| multiply(inverse(sk_c1),sk_c10) != sk_c11 ),
inference(component_clause,[status(thm)],[f319]) ).
fof(f322,definition,
! [X0] :
( sQ41_spl
<=> ( multiply(X0,inverse(sk_c1)) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c1) ) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f323,plain,
! [X0] :
( ~ sQ41_spl
| multiply(X0,inverse(sk_c1)) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c1) ),
inference(component_clause,[status(thm)],[f322]) ).
fof(f325,plain,
( ~ sQ11_spl
| ~ sQ19_spl
| sQ41_spl
| ~ sQ40_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f250,f316,f319,f322,f217,f153]) ).
fof(f344,plain,
( sQ20_spl
| inverse(identity) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f55,f254]) ).
fof(f345,plain,
! [X0] :
( ~ sQ0_spl
| multiply(sk_c9,X0) = multiply(sk_c10,multiply(sk_c11,X0)) ),
inference(paramodulation,[status(thm)],[f111,f57]) ).
fof(f347,plain,
( ~ sQ3_spl
| ~ sQ18_spl
| inverse(sk_c4) != sk_c10
| sk_c9 != sk_c9 ),
inference(paramodulation,[status(thm)],[f122,f215]) ).
fof(f351,plain,
( ~ sQ12_spl
| ~ sQ18_spl
| inverse(sk_c1) != sk_c10
| sk_c11 != sk_c9 ),
inference(paramodulation,[status(thm)],[f167,f215]) ).
fof(f353,definition,
( sQ45_spl
<=> sk_c9 = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f355,plain,
( sQ45_spl
| sk_c9 != sk_c9 ),
inference(component_clause,[status(thm)],[f353]) ).
fof(f356,plain,
( ~ sQ3_spl
| ~ sQ18_spl
| ~ sQ4_spl
| ~ sQ45_spl ),
inference(split_clause,[status(thm)],[f347,f353,f125,f214,f121]) ).
fof(f357,definition,
( sQ46_spl
<=> sk_c11 = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f358,plain,
( ~ sQ46_spl
| sk_c11 = sk_c9 ),
inference(component_clause,[status(thm)],[f357]) ).
fof(f359,plain,
( sQ46_spl
| sk_c11 != sk_c9 ),
inference(component_clause,[status(thm)],[f357]) ).
fof(f371,definition,
( sQ50_spl
<=> sk_c10 = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f373,plain,
( sQ50_spl
| sk_c10 != sk_c9 ),
inference(component_clause,[status(thm)],[f371]) ).
fof(f374,definition,
( sQ51_spl
<=> inverse(identity) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f376,plain,
( sQ51_spl
| inverse(identity) != sk_c10 ),
inference(component_clause,[status(thm)],[f374]) ).
fof(f378,definition,
( sQ52_spl
<=> inverse(sk_c1) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f379,plain,
( ~ sQ52_spl
| inverse(sk_c1) = sk_c10 ),
inference(component_clause,[status(thm)],[f378]) ).
fof(f380,plain,
( sQ52_spl
| inverse(sk_c1) != sk_c10 ),
inference(component_clause,[status(thm)],[f378]) ).
fof(f381,plain,
( ~ sQ12_spl
| ~ sQ18_spl
| ~ sQ52_spl
| ~ sQ46_spl ),
inference(split_clause,[status(thm)],[f351,f357,f378,f214,f166]) ).
fof(f383,plain,
( sQ45_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f355]) ).
fof(f384,plain,
sQ45_spl,
inference(contradiction_clause,[status(thm)],[f383]) ).
fof(f385,plain,
! [X0] :
( ~ sQ11_spl
| multiply(identity,X0) = multiply(sk_c11,multiply(sk_c1,X0)) ),
inference(paramodulation,[status(thm)],[f231,f57]) ).
fof(f386,plain,
! [X0] :
( ~ sQ11_spl
| X0 = multiply(sk_c11,multiply(sk_c1,X0)) ),
inference(forward_demodulation,[status(thm)],[f55,f385]) ).
fof(f389,plain,
( ~ sQ1_spl
| ~ sQ17_spl
| inverse(sk_c3) != sk_c11
| sk_c10 != sk_c10 ),
inference(paramodulation,[status(thm)],[f114,f212]) ).
fof(f391,plain,
( ~ sQ17_spl
| inverse(identity) != sk_c11
| sk_c11 != sk_c10 ),
inference(paramodulation,[status(thm)],[f55,f212]) ).
fof(f397,definition,
( sQ54_spl
<=> sk_c10 = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f399,plain,
( sQ54_spl
| sk_c10 != sk_c10 ),
inference(component_clause,[status(thm)],[f397]) ).
fof(f400,plain,
( ~ sQ1_spl
| ~ sQ17_spl
| ~ sQ2_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f389,f397,f117,f211,f113]) ).
fof(f408,definition,
( sQ57_spl
<=> sk_c11 = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f409,plain,
( ~ sQ57_spl
| sk_c11 = sk_c10 ),
inference(component_clause,[status(thm)],[f408]) ).
fof(f410,plain,
( sQ57_spl
| sk_c11 != sk_c10 ),
inference(component_clause,[status(thm)],[f408]) ).
fof(f411,plain,
( ~ sQ17_spl
| ~ sQ23_spl
| ~ sQ57_spl ),
inference(split_clause,[status(thm)],[f391,f408,f262,f211]) ).
fof(f412,plain,
( sQ54_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f399]) ).
fof(f413,plain,
sQ54_spl,
inference(contradiction_clause,[status(thm)],[f412]) ).
fof(f414,plain,
( ~ sQ14_spl
| ~ sQ16_spl
| inverse(sk_c2) != sk_c10 ),
inference(resolution,[status(thm)],[f209,f193]) ).
fof(f416,plain,
( ~ sQ16_spl
| sk_c9 != sk_c10
| inverse(identity) != sk_c10 ),
inference(paramodulation,[status(thm)],[f55,f209]) ).
fof(f419,plain,
( ~ sQ14_spl
| ~ sQ16_spl
| ~ sQ13_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f180,f414]) ).
fof(f420,plain,
( ~ sQ14_spl
| ~ sQ16_spl
| ~ sQ13_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f419]) ).
fof(f421,plain,
( ~ sQ14_spl
| ~ sQ16_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f420]) ).
fof(f457,plain,
! [X0] :
( ~ sQ41_spl
| ~ sQ11_spl
| multiply(X0,sk_c11) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c1) ),
inference(backward_demodulation,[status(thm)],[f154,f323]) ).
fof(f458,plain,
( sQ40_spl
| ~ sQ11_spl
| multiply(sk_c11,sk_c10) != sk_c11 ),
inference(backward_demodulation,[status(thm)],[f154,f321]) ).
fof(f459,plain,
( sQ52_spl
| ~ sQ11_spl
| sk_c11 != sk_c10 ),
inference(backward_demodulation,[status(thm)],[f154,f380]) ).
fof(f460,plain,
! [X0] :
( ~ sQ41_spl
| ~ sQ11_spl
| multiply(X0,sk_c11) != inverse(X0)
| inverse(inverse(X0)) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f154,f457]) ).
fof(f471,plain,
( ~ sQ7_spl
| ~ sQ15_spl
| sk_c11 != sk_c11
| inverse(sk_c8) != sk_c11 ),
inference(paramodulation,[status(thm)],[f138,f206]) ).
fof(f473,definition,
( sQ61_spl
<=> inverse(sk_c8) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f475,plain,
( sQ61_spl
| inverse(sk_c8) != sk_c11 ),
inference(component_clause,[status(thm)],[f473]) ).
fof(f476,definition,
( sQ62_spl
<=> sk_c11 = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f478,plain,
( sQ62_spl
| sk_c11 != sk_c11 ),
inference(component_clause,[status(thm)],[f476]) ).
fof(f479,plain,
( ~ sQ7_spl
| ~ sQ15_spl
| ~ sQ62_spl
| ~ sQ61_spl ),
inference(split_clause,[status(thm)],[f471,f473,f476,f205,f137]) ).
fof(f480,plain,
( sQ62_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f478]) ).
fof(f481,plain,
sQ62_spl,
inference(contradiction_clause,[status(thm)],[f480]) ).
fof(f486,plain,
! [X0] :
( ~ sQ6_spl
| multiply(identity,X0) = multiply(sk_c8,multiply(sk_c5,X0)) ),
inference(paramodulation,[status(thm)],[f228,f57]) ).
fof(f487,plain,
! [X0] :
( ~ sQ6_spl
| X0 = multiply(sk_c8,multiply(sk_c5,X0)) ),
inference(forward_demodulation,[status(thm)],[f55,f486]) ).
fof(f488,plain,
! [X0] :
( ~ sQ8_spl
| multiply(identity,X0) = multiply(sk_c6,multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f229,f57]) ).
fof(f489,plain,
! [X0] :
( ~ sQ8_spl
| X0 = multiply(sk_c6,multiply(sk_c7,X0)) ),
inference(forward_demodulation,[status(thm)],[f55,f488]) ).
fof(f490,plain,
! [X0] :
( ~ sQ9_spl
| multiply(identity,X0) = multiply(sk_c8,multiply(sk_c6,X0)) ),
inference(paramodulation,[status(thm)],[f230,f57]) ).
fof(f491,plain,
! [X0] :
( ~ sQ9_spl
| X0 = multiply(sk_c8,multiply(sk_c6,X0)) ),
inference(forward_demodulation,[status(thm)],[f55,f490]) ).
fof(f492,plain,
! [X0] :
( ~ sQ2_spl
| multiply(identity,X0) = multiply(sk_c11,multiply(sk_c3,X0)) ),
inference(paramodulation,[status(thm)],[f238,f57]) ).
fof(f493,plain,
! [X0] :
( ~ sQ2_spl
| X0 = multiply(sk_c11,multiply(sk_c3,X0)) ),
inference(forward_demodulation,[status(thm)],[f55,f492]) ).
fof(f494,plain,
! [X0] :
( ~ sQ4_spl
| multiply(identity,X0) = multiply(sk_c10,multiply(sk_c4,X0)) ),
inference(paramodulation,[status(thm)],[f237,f57]) ).
fof(f495,plain,
! [X0] :
( ~ sQ4_spl
| X0 = multiply(sk_c10,multiply(sk_c4,X0)) ),
inference(forward_demodulation,[status(thm)],[f55,f494]) ).
fof(f496,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sk_c8 = multiply(sk_c8,sk_c11) ),
inference(paramodulation,[status(thm)],[f130,f487]) ).
fof(f503,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| multiply(sk_c6,sk_c11) = multiply(sk_c7,sk_c8) ),
inference(paramodulation,[status(thm)],[f496,f235]) ).
fof(f507,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| multiply(sk_c6,sk_c10) = multiply(sk_c7,sk_c11) ),
inference(paramodulation,[status(thm)],[f138,f235]) ).
fof(f509,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| multiply(sk_c6,sk_c11) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f150,f503]) ).
fof(f513,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| multiply(sk_c10,sk_c3) = multiply(sk_c3,identity) ),
inference(paramodulation,[status(thm)],[f238,f241]) ).
fof(f532,plain,
( ~ sQ4_spl
| ~ sQ7_spl
| multiply(sk_c11,sk_c4) = multiply(sk_c8,identity) ),
inference(paramodulation,[status(thm)],[f237,f236]) ).
fof(f546,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c7,X0) = multiply(sk_c8,X0) ),
inference(paramodulation,[status(thm)],[f489,f491]) ).
fof(f547,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 = multiply(sk_c8,identity) ),
inference(paramodulation,[status(thm)],[f229,f491]) ).
fof(f555,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c6,sk_c10) = multiply(sk_c8,sk_c11) ),
inference(backward_demodulation,[status(thm)],[f546,f507]) ).
fof(f558,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ4_spl
| ~ sQ7_spl
| sk_c7 = multiply(sk_c11,sk_c4) ),
inference(forward_demodulation,[status(thm)],[f532,f547]) ).
fof(f562,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c6,sk_c10) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f496,f555]) ).
fof(f588,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c11 = multiply(sk_c11,sk_c10) ),
inference(paramodulation,[status(thm)],[f114,f493]) ).
fof(f597,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c10 = multiply(sk_c10,sk_c9) ),
inference(paramodulation,[status(thm)],[f122,f495]) ).
fof(f598,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ7_spl
| multiply(sk_c11,multiply(sk_c4,X0)) = multiply(sk_c8,X0) ),
inference(paramodulation,[status(thm)],[f495,f236]) ).
fof(f602,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| sk_c11 = multiply(sk_c8,sk_c6) ),
inference(paramodulation,[status(thm)],[f509,f491]) ).
fof(f610,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| multiply(sk_c11,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f616,f55]) ).
fof(f615,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| multiply(sk_c10,sk_c3) = multiply(sk_c3,sk_c11) ),
inference(backward_demodulation,[status(thm)],[f616,f513]) ).
fof(f616,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| sk_c11 = identity ),
inference(forward_demodulation,[status(thm)],[f230,f602]) ).
fof(f623,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| X0 = multiply(sk_c3,X0) ),
inference(backward_demodulation,[status(thm)],[f610,f493]) ).
fof(f626,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| multiply(sk_c10,X0) = multiply(sk_c3,X0) ),
inference(backward_demodulation,[status(thm)],[f610,f241]) ).
fof(f628,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| sk_c7 = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f610,f558]) ).
fof(f629,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| sk_c11 = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f610,f588]) ).
fof(f632,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| multiply(sk_c4,X0) = multiply(sk_c8,X0) ),
inference(backward_demodulation,[status(thm)],[f610,f598]) ).
fof(f641,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| multiply(sk_c10,sk_c3) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f114,f615]) ).
fof(f646,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ2_spl
| X0 = multiply(sk_c4,X0) ),
inference(backward_demodulation,[status(thm)],[f654,f495]) ).
fof(f647,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ2_spl
| sk_c11 != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f654,f112]) ).
fof(f650,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ2_spl
| sk_c10 = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f654,f597]) ).
fof(f651,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| sk_c3 = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f654,f641]) ).
fof(f654,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ2_spl
| multiply(sk_c10,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f623,f626]) ).
fof(f656,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| inverse(sk_c4) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f628,f142]) ).
fof(f658,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ9_spl
| multiply(sk_c6,sk_c10) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f629,f509]) ).
fof(f660,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| inverse(sk_c3) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f629,f118]) ).
fof(f666,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c10 = identity ),
inference(backward_demodulation,[status(thm)],[f629,f616]) ).
fof(f672,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| multiply(sk_c8,sk_c10) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f632,f122]) ).
fof(f683,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ2_spl
| ~ sQ7_spl
| X0 = multiply(sk_c8,X0) ),
inference(forward_demodulation,[status(thm)],[f632,f646]) ).
fof(f684,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ2_spl
| sk_c10 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f629,f647]) ).
fof(f688,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ2_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f650,f684]) ).
fof(f689,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ2_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f688]) ).
fof(f698,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| sk_c10 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f126,f656]) ).
fof(f700,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c8 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f562,f658]) ).
fof(f702,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ4_spl
| sk_c8 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f698,f700]) ).
fof(f704,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| inverse(sk_c10) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f651,f660]) ).
fof(f720,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c10 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f683,f672]) ).
fof(f726,plain,
( sQ23_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c10) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f666,f264]) ).
fof(f727,plain,
( sQ23_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c10 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f704,f726]) ).
fof(f728,plain,
( sQ23_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f629,f727]) ).
fof(f729,plain,
( sQ23_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f728]) ).
fof(f730,plain,
( sQ23_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f729]) ).
fof(f731,plain,
( sQ46_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| sk_c10 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f629,f359]) ).
fof(f732,plain,
( sQ46_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f720,f731]) ).
fof(f733,plain,
( sQ46_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f732]) ).
fof(f734,plain,
( sQ46_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f733]) ).
fof(f735,plain,
( sQ61_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ4_spl
| inverse(sk_c10) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f702,f475]) ).
fof(f736,plain,
( sQ61_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ4_spl
| sk_c10 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f704,f735]) ).
fof(f737,plain,
( sQ61_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ4_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f629,f736]) ).
fof(f738,plain,
( sQ61_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f737]) ).
fof(f739,plain,
( sQ61_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f738]) ).
fof(f753,plain,
( sQ21_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(inverse(sk_c10),sk_c10) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f666,f257]) ).
fof(f754,plain,
( sQ21_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c10,sk_c10) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f704,f753]) ).
fof(f755,plain,
( sQ21_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c10 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f654,f754]) ).
fof(f756,plain,
( sQ21_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f629,f755]) ).
fof(f757,plain,
( sQ21_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f756]) ).
fof(f758,plain,
( sQ21_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f757]) ).
fof(f774,plain,
( ~ sQ16_spl
| ~ sQ50_spl
| ~ sQ51_spl ),
inference(split_clause,[status(thm)],[f416,f374,f371,f208]) ).
fof(f777,plain,
( sQ50_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f720,f373]) ).
fof(f778,plain,
( sQ50_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f777]) ).
fof(f779,plain,
( sQ50_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f778]) ).
fof(f783,plain,
( sQ51_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c10) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f666,f376]) ).
fof(f784,plain,
( sQ51_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f704,f783]) ).
fof(f785,plain,
( sQ51_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f784]) ).
fof(f786,plain,
( sQ51_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ1_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f785]) ).
fof(f787,plain,
( sQ57_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f629,f410]) ).
fof(f788,plain,
( sQ57_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f787]) ).
fof(f789,plain,
( sQ57_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f788]) ).
fof(f796,plain,
( sQ20_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f344,f262,f252]) ).
fof(f813,plain,
( ~ sQ12_spl
| ~ sQ15_spl
| inverse(sk_c1) != sk_c11 ),
inference(resolution,[status(thm)],[f206,f167]) ).
fof(f816,plain,
( ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ11_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f154,f813]) ).
fof(f817,plain,
( ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f816]) ).
fof(f818,plain,
( ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f817]) ).
fof(f825,plain,
( ~ sQ11_spl
| ~ sQ41_spl
| multiply(sk_c1,sk_c11) != inverse(sk_c1)
| inverse(sk_c11) != sk_c11 ),
inference(paramodulation,[status(thm)],[f154,f460]) ).
fof(f830,definition,
( sQ65_spl
<=> inverse(sk_c11) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f832,plain,
( sQ65_spl
| inverse(sk_c11) != sk_c11 ),
inference(component_clause,[status(thm)],[f830]) ).
fof(f833,definition,
( sQ66_spl
<=> multiply(sk_c1,sk_c11) = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f835,plain,
( sQ66_spl
| multiply(sk_c1,sk_c11) != inverse(sk_c1) ),
inference(component_clause,[status(thm)],[f833]) ).
fof(f836,plain,
( ~ sQ11_spl
| ~ sQ41_spl
| ~ sQ66_spl
| ~ sQ65_spl ),
inference(split_clause,[status(thm)],[f825,f830,f833,f322,f153]) ).
fof(f837,plain,
( sQ66_spl
| ~ sQ11_spl
| multiply(sk_c1,sk_c11) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f154,f835]) ).
fof(f845,plain,
( ~ sQ13_spl
| ~ sQ12_spl
| multiply(sk_c11,sk_c2) = multiply(sk_c1,identity) ),
inference(paramodulation,[status(thm)],[f232,f226]) ).
fof(f846,plain,
! [X0] :
( ~ sQ13_spl
| multiply(identity,X0) = multiply(sk_c10,multiply(sk_c2,X0)) ),
inference(paramodulation,[status(thm)],[f232,f57]) ).
fof(f847,plain,
! [X0] :
( ~ sQ13_spl
| X0 = multiply(sk_c10,multiply(sk_c2,X0)) ),
inference(forward_demodulation,[status(thm)],[f55,f846]) ).
fof(f848,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ11_spl
| multiply(sk_c10,X0) = multiply(sk_c11,multiply(sk_c11,X0)) ),
inference(paramodulation,[status(thm)],[f226,f386]) ).
fof(f849,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| sk_c10 = multiply(sk_c11,sk_c11) ),
inference(paramodulation,[status(thm)],[f167,f386]) ).
fof(f855,plain,
( ~ sQ14_spl
| ~ sQ13_spl
| sk_c9 = multiply(sk_c10,sk_c10) ),
inference(paramodulation,[status(thm)],[f193,f847]) ).
fof(f856,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ12_spl
| multiply(sk_c11,multiply(sk_c2,X0)) = multiply(sk_c1,X0) ),
inference(paramodulation,[status(thm)],[f847,f226]) ).
fof(f864,definition,
( sQ67_spl
<=> inverse(sk_c10) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f866,plain,
( sQ67_spl
| inverse(sk_c10) != sk_c10 ),
inference(component_clause,[status(thm)],[f864]) ).
fof(f882,definition,
( sQ70_spl
<=> multiply(sk_c1,sk_c10) = inverse(sk_c1) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f883,plain,
( ~ sQ70_spl
| multiply(sk_c1,sk_c10) = inverse(sk_c1) ),
inference(component_clause,[status(thm)],[f882]) ).
fof(f884,plain,
( sQ70_spl
| multiply(sk_c1,sk_c10) != inverse(sk_c1) ),
inference(component_clause,[status(thm)],[f882]) ).
fof(f886,plain,
( sQ70_spl
| ~ sQ12_spl
| sk_c11 != inverse(sk_c1) ),
inference(forward_demodulation,[status(thm)],[f167,f884]) ).
fof(f887,plain,
( sQ70_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f154,f886]) ).
fof(f888,plain,
( sQ70_spl
| ~ sQ12_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f887]) ).
fof(f889,plain,
( sQ70_spl
| ~ sQ12_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f888]) ).
fof(f894,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ0_spl
| multiply(sk_c9,multiply(sk_c1,X0)) = multiply(sk_c10,X0) ),
inference(paramodulation,[status(thm)],[f386,f345]) ).
fof(f896,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ12_spl
| multiply(sk_c11,multiply(sk_c11,X0)) = multiply(sk_c1,multiply(sk_c9,X0)) ),
inference(paramodulation,[status(thm)],[f345,f226]) ).
fof(f899,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| multiply(sk_c10,X0) = multiply(sk_c1,multiply(sk_c9,X0)) ),
inference(forward_demodulation,[status(thm)],[f848,f896]) ).
fof(f994,definition,
( sQ87_spl
<=> multiply(inverse(multiply(sk_c1,sk_c10)),sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f996,plain,
( sQ87_spl
| multiply(inverse(multiply(sk_c1,sk_c10)),sk_c10) != sk_c11 ),
inference(component_clause,[status(thm)],[f994]) ).
fof(f1085,plain,
( sQ87_spl
| ~ sQ12_spl
| multiply(inverse(sk_c11),sk_c10) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f167,f996]) ).
fof(f1146,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f234,f234]) ).
fof(f1149,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| sk_c11 = multiply(inverse(sk_c11),sk_c10) ),
inference(paramodulation,[status(thm)],[f849,f234]) ).
fof(f1150,plain,
! [X0] :
( ~ sQ11_spl
| multiply(sk_c1,X0) = multiply(inverse(sk_c11),X0) ),
inference(paramodulation,[status(thm)],[f386,f234]) ).
fof(f1151,plain,
( ~ sQ11_spl
| sk_c1 = multiply(inverse(sk_c11),identity) ),
inference(paramodulation,[status(thm)],[f231,f234]) ).
fof(f1154,plain,
( ~ sQ14_spl
| ~ sQ13_spl
| sk_c10 = multiply(inverse(sk_c10),sk_c9) ),
inference(paramodulation,[status(thm)],[f855,f234]) ).
fof(f1155,plain,
! [X0] :
( ~ sQ0_spl
| multiply(sk_c11,X0) = multiply(inverse(sk_c10),multiply(sk_c9,X0)) ),
inference(paramodulation,[status(thm)],[f345,f234]) ).
fof(f1156,plain,
! [X0] :
( ~ sQ13_spl
| multiply(sk_c2,X0) = multiply(inverse(sk_c10),X0) ),
inference(paramodulation,[status(thm)],[f847,f234]) ).
fof(f1158,plain,
( ~ sQ0_spl
| sk_c11 = multiply(inverse(sk_c10),sk_c9) ),
inference(paramodulation,[status(thm)],[f111,f234]) ).
fof(f1168,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| sQ87_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1149,f1085]) ).
fof(f1169,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| sQ87_spl ),
inference(contradiction_clause,[status(thm)],[f1168]) ).
fof(f1170,plain,
( ~ sQ11_spl
| sk_c1 = multiply(sk_c1,identity) ),
inference(forward_demodulation,[status(thm)],[f1150,f1151]) ).
fof(f1175,plain,
( ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ12_spl
| sk_c1 = multiply(sk_c11,sk_c2) ),
inference(forward_demodulation,[status(thm)],[f845,f1170]) ).
fof(f1178,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ13_spl
| multiply(sk_c11,X0) = multiply(sk_c2,multiply(sk_c9,X0)) ),
inference(backward_demodulation,[status(thm)],[f1156,f1155]) ).
fof(f1181,plain,
( ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ13_spl
| sk_c11 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1154,f1158]) ).
fof(f1182,plain,
( ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ13_spl
| sQ52_spl
| ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1181,f459]) ).
fof(f1183,plain,
( ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ13_spl
| sQ52_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f1182]) ).
fof(f1211,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sk_c10 = multiply(sk_c10,sk_c11) ),
inference(backward_demodulation,[status(thm)],[f1224,f849]) ).
fof(f1213,plain,
( sQ40_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| multiply(sk_c10,sk_c10) != sk_c11 ),
inference(backward_demodulation,[status(thm)],[f1224,f458]) ).
fof(f1217,plain,
( ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ14_spl
| sk_c1 = multiply(sk_c10,sk_c2) ),
inference(backward_demodulation,[status(thm)],[f1224,f1175]) ).
fof(f1220,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ14_spl
| multiply(sk_c10,multiply(sk_c2,X0)) = multiply(sk_c1,X0) ),
inference(backward_demodulation,[status(thm)],[f1224,f856]) ).
fof(f1224,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| multiply(sk_c11,X0) = multiply(sk_c10,X0) ),
inference(forward_demodulation,[status(thm)],[f223,f1178]) ).
fof(f1233,plain,
( sQ65_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ13_spl
| inverse(sk_c11) != sk_c10 ),
inference(backward_demodulation,[status(thm)],[f1181,f832]) ).
fof(f1235,plain,
( sQ39_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ13_spl
| multiply(sk_c1,sk_c11) != sk_c10 ),
inference(backward_demodulation,[status(thm)],[f1181,f318]) ).
fof(f1239,plain,
( sQ23_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ13_spl
| inverse(identity) != sk_c10 ),
inference(backward_demodulation,[status(thm)],[f1181,f264]) ).
fof(f1267,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sk_c10 = multiply(sk_c10,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f1181,f1211]) ).
fof(f1280,plain,
( ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sk_c10 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f855,f1267]) ).
fof(f1284,plain,
( sQ40_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sk_c9 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f855,f1213]) ).
fof(f1285,plain,
( sQ40_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| sk_c10 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1280,f1284]) ).
fof(f1286,plain,
( sQ40_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1181,f1285]) ).
fof(f1287,plain,
( sQ40_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1286]) ).
fof(f1288,plain,
( sQ40_spl
| ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f1287]) ).
fof(f1298,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ14_spl
| multiply(inverse(X0),X0) = sk_c1 ),
inference(backward_demodulation,[status(thm)],[f1299,f56]) ).
fof(f1299,plain,
( ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ14_spl
| sk_c1 = identity ),
inference(forward_demodulation,[status(thm)],[f232,f1217]) ).
fof(f1305,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ14_spl
| X0 = multiply(sk_c1,X0) ),
inference(forward_demodulation,[status(thm)],[f847,f1220]) ).
fof(f1312,plain,
( sQ65_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ13_spl
| inverse(sk_c10) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1181,f1233]) ).
fof(f1313,plain,
( sQ39_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| sk_c11 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1305,f1235]) ).
fof(f1314,plain,
( sQ39_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1181,f1313]) ).
fof(f1315,plain,
( sQ39_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1314]) ).
fof(f1316,plain,
( sQ39_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f1315]) ).
fof(f1318,plain,
( sQ23_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ12_spl
| inverse(sk_c1) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1299,f1239]) ).
fof(f1319,plain,
( sQ23_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ52_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f379,f1318]) ).
fof(f1320,plain,
( sQ23_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ52_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1319]) ).
fof(f1321,plain,
( sQ23_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ52_spl ),
inference(contradiction_clause,[status(thm)],[f1320]) ).
fof(f1375,plain,
( sQ46_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ13_spl
| sk_c10 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1181,f359]) ).
fof(f1376,plain,
( sQ46_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1280,f1375]) ).
fof(f1377,plain,
( sQ46_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1376]) ).
fof(f1378,plain,
( sQ46_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f1377]) ).
fof(f1380,plain,
( sQ66_spl
| ~ sQ11_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f837,f316,f153,f833]) ).
fof(f1471,plain,
( sQ57_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ13_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1181,f410]) ).
fof(f1472,plain,
( sQ57_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ13_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1471]) ).
fof(f1473,plain,
( sQ57_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f1472]) ).
fof(f1488,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ14_spl
| X0 = multiply(inverse(inverse(X0)),sk_c1) ),
inference(paramodulation,[status(thm)],[f1298,f234]) ).
fof(f1525,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ14_spl
| X0 = multiply(X0,sk_c1) ),
inference(forward_demodulation,[status(thm)],[f1146,f1488]) ).
fof(f1551,plain,
( ~ sQ46_spl
| ~ sQ57_spl
| sk_c10 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f409,f358]) ).
fof(f1556,plain,
( ~ sQ23_spl
| ~ sQ57_spl
| inverse(identity) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f409,f263]) ).
fof(f1559,plain,
( sQ22_spl
| ~ sQ23_spl
| ~ sQ57_spl
| inverse(sk_c10) != inverse(identity) ),
inference(forward_demodulation,[status(thm)],[f1556,f260]) ).
fof(f1560,plain,
( sQ22_spl
| ~ sQ23_spl
| ~ sQ57_spl
| inverse(sk_c10) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1556,f1559]) ).
fof(f1568,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ46_spl
| ~ sQ57_spl
| multiply(sk_c10,multiply(sk_c1,X0)) = multiply(sk_c10,X0) ),
inference(forward_demodulation,[status(thm)],[f1551,f894]) ).
fof(f1575,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ57_spl
| X0 = multiply(sk_c10,multiply(sk_c1,X0)) ),
inference(forward_demodulation,[status(thm)],[f409,f386]) ).
fof(f1582,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ57_spl
| ~ sQ0_spl
| ~ sQ46_spl
| X0 = multiply(sk_c10,X0) ),
inference(forward_demodulation,[status(thm)],[f1568,f1575]) ).
fof(f1583,plain,
( ~ sQ11_spl
| ~ sQ57_spl
| multiply(sk_c10,sk_c1) = identity ),
inference(forward_demodulation,[status(thm)],[f409,f231]) ).
fof(f1585,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ57_spl
| ~ sQ0_spl
| ~ sQ46_spl
| multiply(inverse(X0),X0) = sk_c1 ),
inference(backward_demodulation,[status(thm)],[f1588,f56]) ).
fof(f1588,plain,
( ~ sQ11_spl
| ~ sQ57_spl
| ~ sQ0_spl
| ~ sQ46_spl
| sk_c1 = identity ),
inference(forward_demodulation,[status(thm)],[f1582,f1583]) ).
fof(f1624,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ57_spl
| multiply(sk_c1,X0) = multiply(inverse(sk_c10),X0) ),
inference(forward_demodulation,[status(thm)],[f409,f1150]) ).
fof(f1635,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ57_spl
| multiply(sk_c10,X0) = multiply(inverse(sk_c10),multiply(sk_c9,X0)) ),
inference(forward_demodulation,[status(thm)],[f409,f1155]) ).
fof(f1636,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ57_spl
| ~ sQ11_spl
| ~ sQ46_spl
| X0 = multiply(inverse(sk_c10),multiply(sk_c9,X0)) ),
inference(forward_demodulation,[status(thm)],[f1582,f1635]) ).
fof(f1637,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ57_spl
| ~ sQ11_spl
| ~ sQ46_spl
| X0 = multiply(sk_c1,multiply(sk_c9,X0)) ),
inference(forward_demodulation,[status(thm)],[f1624,f1636]) ).
fof(f1638,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ57_spl
| ~ sQ11_spl
| ~ sQ46_spl
| X0 = multiply(sk_c1,multiply(sk_c10,X0)) ),
inference(forward_demodulation,[status(thm)],[f1551,f1637]) ).
fof(f1641,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ57_spl
| ~ sQ11_spl
| ~ sQ46_spl
| X0 = multiply(sk_c1,X0) ),
inference(forward_demodulation,[status(thm)],[f1582,f1638]) ).
fof(f1689,plain,
( sQ12_spl
| ~ sQ0_spl
| ~ sQ57_spl
| ~ sQ11_spl
| ~ sQ46_spl
| sk_c10 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f1641,f168]) ).
fof(f1690,plain,
( sQ12_spl
| ~ sQ0_spl
| ~ sQ57_spl
| ~ sQ11_spl
| ~ sQ46_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f409,f1689]) ).
fof(f1691,plain,
( sQ12_spl
| ~ sQ0_spl
| ~ sQ57_spl
| ~ sQ11_spl
| ~ sQ46_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1690]) ).
fof(f1692,plain,
( sQ12_spl
| ~ sQ0_spl
| ~ sQ57_spl
| ~ sQ11_spl
| ~ sQ46_spl ),
inference(contradiction_clause,[status(thm)],[f1691]) ).
fof(f1711,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| sQ67_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f704,f866]) ).
fof(f1712,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl
| sQ67_spl ),
inference(contradiction_clause,[status(thm)],[f1711]) ).
fof(f2121,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ57_spl
| ~ sQ0_spl
| ~ sQ46_spl
| X0 = multiply(sk_c2,X0) ),
inference(forward_demodulation,[status(thm)],[f1582,f847]) ).
fof(f2146,plain,
( sQ14_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ57_spl
| ~ sQ0_spl
| ~ sQ46_spl
| sk_c9 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f2121,f194]) ).
fof(f2147,plain,
( sQ14_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ57_spl
| ~ sQ0_spl
| ~ sQ46_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1551,f2146]) ).
fof(f2148,plain,
( sQ14_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ57_spl
| ~ sQ0_spl
| ~ sQ46_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f2147]) ).
fof(f2149,plain,
( sQ14_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ57_spl
| ~ sQ0_spl
| ~ sQ46_spl ),
inference(contradiction_clause,[status(thm)],[f2148]) ).
fof(f2150,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ57_spl
| ~ sQ46_spl
| X0 = multiply(sk_c1,multiply(sk_c9,X0)) ),
inference(forward_demodulation,[status(thm)],[f1582,f899]) ).
fof(f2151,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ57_spl
| ~ sQ46_spl
| X0 = multiply(sk_c1,multiply(sk_c10,X0)) ),
inference(forward_demodulation,[status(thm)],[f1551,f2150]) ).
fof(f2152,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ57_spl
| ~ sQ46_spl
| X0 = multiply(sk_c1,X0) ),
inference(forward_demodulation,[status(thm)],[f1582,f2151]) ).
fof(f2174,plain,
( ~ sQ70_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ57_spl
| ~ sQ46_spl
| sk_c10 = inverse(sk_c1) ),
inference(forward_demodulation,[status(thm)],[f2152,f883]) ).
fof(f2382,plain,
( ~ sQ11_spl
| ~ sQ57_spl
| ~ sQ0_spl
| ~ sQ46_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ14_spl
| inverse(sk_c1) = sk_c1 ),
inference(paramodulation,[status(thm)],[f1585,f1525]) ).
fof(f2393,plain,
( ~ sQ70_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ57_spl
| ~ sQ46_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sk_c10 = inverse(sk_c10) ),
inference(backward_demodulation,[status(thm)],[f2403,f2174]) ).
fof(f2403,plain,
( ~ sQ11_spl
| ~ sQ57_spl
| ~ sQ0_spl
| ~ sQ46_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ14_spl
| ~ sQ70_spl
| sk_c10 = sk_c1 ),
inference(forward_demodulation,[status(thm)],[f2174,f2382]) ).
fof(f2417,plain,
( ~ sQ70_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ57_spl
| ~ sQ46_spl
| ~ sQ13_spl
| ~ sQ14_spl
| sQ67_spl ),
inference(split_clause,[status(thm)],[f2393,f864,f192,f179,f357,f408,f153,f166,f110,f882]) ).
fof(f2437,plain,
( sQ65_spl
| ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ67_spl ),
inference(split_clause,[status(thm)],[f1312,f864,f179,f192,f110,f830]) ).
fof(f2448,plain,
( sQ22_spl
| ~ sQ23_spl
| ~ sQ57_spl
| ~ sQ67_spl ),
inference(split_clause,[status(thm)],[f1560,f864,f408,f262,f258]) ).
fof(f2461,plain,
$false,
inference(sat_refutation,[status(thm)],[f116,f120,f124,f128,f132,f136,f148,f152,f156,f157,f158,f159,f160,f161,f162,f163,f164,f165,f169,f170,f171,f172,f173,f174,f175,f177,f178,f182,f183,f184,f185,f186,f187,f188,f190,f191,f195,f196,f197,f198,f199,f200,f201,f203,f204,f220,f261,f325,f356,f381,f384,f400,f411,f413,f421,f479,f481,f689,f730,f734,f739,f758,f774,f779,f786,f789,f796,f818,f836,f889,f1169,f1183,f1288,f1316,f1321,f1378,f1380,f1473,f1692,f1712,f2149,f2417,f2437,f2448]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP340-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n011.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Sun Sep 20 20:09:25 UTC 2026
% 0.07/0.36 % CPUTime :
% 0.07/0.37 % Drodi V4.1.1
% 0.07/0.48 % Refutation found
% 0.07/0.48 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.07/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.52 % Elapsed time: 0.144927 seconds
% 0.14/0.52 % CPU time: 0.832725 seconds
% 0.14/0.52 % Total memory used: 116.993 MB
% 0.14/0.52 % Net memory used: 116.417 MB
%------------------------------------------------------------------------------