%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP269-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 12:33:16 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.42s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 82
% Syntax : Number of formulae : 398 ( 11 unt; 33 def)
% Number of atoms : 1717 ( 509 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 2500 (1181 ~;1286 |; 0 &)
% ( 33 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 35 ( 33 usr; 34 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 95 ( 95 !; 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_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c7) = sk_c6
| multiply(sk_c1,sk_c11) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c6) = sk_c8
| multiply(sk_c1,sk_c11) = sk_c10 ),
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(f24,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( inverse(sk_c7) = sk_c6
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( inverse(sk_c6) = sk_c8
| multiply(sk_c11,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c2,sk_c11) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( inverse(sk_c3) = sk_c11
| multiply(sk_c2,sk_c11) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c2,sk_c11) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c2,sk_c11) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c2,sk_c11) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c11) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c2,sk_c11) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,negated_conjecture,
( inverse(sk_c7) = sk_c6
| multiply(sk_c2,sk_c11) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,negated_conjecture,
( inverse(sk_c6) = sk_c8
| multiply(sk_c2,sk_c11) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
( inverse(sk_c3) = sk_c11
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c11
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c11
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f51,negated_conjecture,
( inverse(sk_c7) = sk_c6
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f52,negated_conjecture,
( inverse(sk_c6) = sk_c8
| inverse(sk_c2) = sk_c11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
! [X3,X4,X1,X2,X5,X6,X7,X8] :
( multiply(X7,X6) != X8
| inverse(X8) != X6
| inverse(X7) != X8
| multiply(X6,sk_c10) != sk_c11
| inverse(X5) != X6
| multiply(X5,X6) != sk_c11
| inverse(X2) != sk_c10
| multiply(X2,sk_c10) != sk_c9
| inverse(X1) != sk_c11
| multiply(X1,sk_c11) != sk_c10
| inverse(X4) != sk_c11
| multiply(X4,sk_c11) != sk_c9
| multiply(sk_c11,sk_c9) != sk_c10
| inverse(X3) != sk_c11
| multiply(X3,sk_c11) != sk_c10 ),
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_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f59,plain,
( inverse(sk_c3) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f60,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f61,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f62,plain,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f63,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f64,plain,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f65,plain,
( inverse(sk_c7) = sk_c6
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f66,plain,
( inverse(sk_c6) = sk_c8
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f68,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f69,plain,
( inverse(sk_c3) = sk_c11
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f70,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f71,plain,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f72,plain,
( multiply(sk_c5,sk_c8) = sk_c11
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f73,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f74,plain,
( multiply(sk_c8,sk_c10) = sk_c11
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f75,plain,
( inverse(sk_c7) = sk_c6
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f76,plain,
( inverse(sk_c6) = sk_c8
| inverse(sk_c1) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f78,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f79,plain,
( inverse(sk_c3) = sk_c11
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f80,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f81,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f82,plain,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f83,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f84,plain,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f85,plain,
( inverse(sk_c7) = sk_c6
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f86,plain,
( inverse(sk_c6) = sk_c8
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f88,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| multiply(sk_c2,sk_c11) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f89,plain,
( inverse(sk_c3) = sk_c11
| multiply(sk_c2,sk_c11) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f90,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c2,sk_c11) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f91,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c2,sk_c11) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f92,plain,
( multiply(sk_c5,sk_c8) = sk_c11
| multiply(sk_c2,sk_c11) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f93,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c11) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f94,plain,
( multiply(sk_c8,sk_c10) = sk_c11
| multiply(sk_c2,sk_c11) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f95,plain,
( inverse(sk_c7) = sk_c6
| multiply(sk_c2,sk_c11) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f96,plain,
( inverse(sk_c6) = sk_c8
| multiply(sk_c2,sk_c11) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f98,plain,
( multiply(sk_c3,sk_c11) = sk_c10
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f99,plain,
( inverse(sk_c3) = sk_c11
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f100,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f101,plain,
( inverse(sk_c4) = sk_c10
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f102,plain,
( multiply(sk_c5,sk_c8) = sk_c11
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f103,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f104,plain,
( multiply(sk_c8,sk_c10) = sk_c11
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f105,plain,
( inverse(sk_c7) = sk_c6
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f106,plain,
( inverse(sk_c6) = sk_c8
| inverse(sk_c2) = sk_c11 ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f108,plain,
! [X6,X7,X8] :
( multiply(X7,X6) != X8
| inverse(X8) != X6
| inverse(X7) != X8
| multiply(X6,sk_c10) != sk_c11
| ! [X5] :
( inverse(X5) != X6
| multiply(X5,X6) != sk_c11
| ! [X2] :
( inverse(X2) != sk_c10
| multiply(X2,sk_c10) != sk_c9
| ! [X1] :
( inverse(X1) != sk_c11
| multiply(X1,sk_c11) != sk_c10
| ! [X4] :
( inverse(X4) != sk_c11
| multiply(X4,sk_c11) != sk_c9
| multiply(sk_c11,sk_c9) != sk_c10
| ! [X3] :
( inverse(X3) != sk_c11
| multiply(X3,sk_c11) != sk_c10 ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f54]) ).
fof(f109,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( multiply(X6,X5) != X7
| inverse(X7) != X5
| inverse(X6) != X7
| multiply(X5,sk_c10) != sk_c11
| inverse(X4) != X5
| multiply(X4,X5) != sk_c11
| inverse(X3) != sk_c10
| multiply(X3,sk_c10) != sk_c9
| inverse(X2) != sk_c11
| multiply(X2,sk_c11) != sk_c10
| inverse(X1) != sk_c11
| multiply(X1,sk_c11) != sk_c9
| multiply(sk_c11,sk_c9) != sk_c10
| inverse(X0) != sk_c11
| multiply(X0,sk_c11) != sk_c10 ),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f110,definition,
( sQ0_spl
<=> multiply(sk_c1,sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f111,plain,
( ~ sQ0_spl
| multiply(sk_c1,sk_c11) = sk_c10 ),
inference(component_clause,[status(thm)],[f110]) ).
fof(f113,definition,
( sQ1_spl
<=> multiply(sk_c3,sk_c11) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f114,plain,
( ~ sQ1_spl
| multiply(sk_c3,sk_c11) = sk_c10 ),
inference(component_clause,[status(thm)],[f113]) ).
fof(f116,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f58,f110,f113]) ).
fof(f117,definition,
( sQ2_spl
<=> inverse(sk_c3) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f118,plain,
( ~ sQ2_spl
| inverse(sk_c3) = sk_c11 ),
inference(component_clause,[status(thm)],[f117]) ).
fof(f119,plain,
( sQ2_spl
| inverse(sk_c3) != sk_c11 ),
inference(component_clause,[status(thm)],[f117]) ).
fof(f120,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f59,f110,f117]) ).
fof(f121,definition,
( sQ3_spl
<=> multiply(sk_c4,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f122,plain,
( ~ sQ3_spl
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(component_clause,[status(thm)],[f121]) ).
fof(f124,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f60,f110,f121]) ).
fof(f125,definition,
( sQ4_spl
<=> inverse(sk_c4) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f126,plain,
( ~ sQ4_spl
| inverse(sk_c4) = sk_c10 ),
inference(component_clause,[status(thm)],[f125]) ).
fof(f128,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f61,f110,f125]) ).
fof(f129,definition,
( sQ5_spl
<=> multiply(sk_c5,sk_c8) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f130,plain,
( ~ sQ5_spl
| multiply(sk_c5,sk_c8) = sk_c11 ),
inference(component_clause,[status(thm)],[f129]) ).
fof(f132,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f62,f110,f129]) ).
fof(f133,definition,
( sQ6_spl
<=> inverse(sk_c5) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f134,plain,
( ~ sQ6_spl
| inverse(sk_c5) = sk_c8 ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,plain,
( sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f63,f110,f133]) ).
fof(f137,definition,
( sQ7_spl
<=> multiply(sk_c8,sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f138,plain,
( ~ sQ7_spl
| multiply(sk_c8,sk_c10) = sk_c11 ),
inference(component_clause,[status(thm)],[f137]) ).
fof(f140,plain,
( sQ7_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f64,f110,f137]) ).
fof(f141,definition,
( sQ8_spl
<=> inverse(sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f142,plain,
( ~ sQ8_spl
| inverse(sk_c7) = sk_c6 ),
inference(component_clause,[status(thm)],[f141]) ).
fof(f144,plain,
( sQ8_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f65,f110,f141]) ).
fof(f145,definition,
( sQ9_spl
<=> inverse(sk_c6) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f146,plain,
( ~ sQ9_spl
| inverse(sk_c6) = sk_c8 ),
inference(component_clause,[status(thm)],[f145]) ).
fof(f148,plain,
( sQ9_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f66,f110,f145]) ).
fof(f153,definition,
( sQ11_spl
<=> inverse(sk_c1) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f154,plain,
( ~ sQ11_spl
| inverse(sk_c1) = sk_c11 ),
inference(component_clause,[status(thm)],[f153]) ).
fof(f156,plain,
( sQ1_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f68,f153,f113]) ).
fof(f157,plain,
( sQ2_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f69,f153,f117]) ).
fof(f158,plain,
( sQ3_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f70,f153,f121]) ).
fof(f159,plain,
( sQ4_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f71,f153,f125]) ).
fof(f160,plain,
( sQ5_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f72,f153,f129]) ).
fof(f161,plain,
( sQ6_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f73,f153,f133]) ).
fof(f162,plain,
( sQ7_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f74,f153,f137]) ).
fof(f163,plain,
( sQ8_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f75,f153,f141]) ).
fof(f164,plain,
( sQ9_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f76,f153,f145]) ).
fof(f166,definition,
( sQ12_spl
<=> multiply(sk_c11,sk_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f167,plain,
( ~ sQ12_spl
| multiply(sk_c11,sk_c9) = sk_c10 ),
inference(component_clause,[status(thm)],[f166]) ).
fof(f168,plain,
( sQ12_spl
| multiply(sk_c11,sk_c9) != sk_c10 ),
inference(component_clause,[status(thm)],[f166]) ).
fof(f169,plain,
( sQ1_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f78,f166,f113]) ).
fof(f170,plain,
( sQ2_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f79,f166,f117]) ).
fof(f171,plain,
( sQ3_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f80,f166,f121]) ).
fof(f172,plain,
( sQ4_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f81,f166,f125]) ).
fof(f173,plain,
( sQ5_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f82,f166,f129]) ).
fof(f174,plain,
( sQ6_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f83,f166,f133]) ).
fof(f175,plain,
( sQ7_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f84,f166,f137]) ).
fof(f176,plain,
( sQ8_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f85,f166,f141]) ).
fof(f177,plain,
( sQ9_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f86,f166,f145]) ).
fof(f179,definition,
( sQ13_spl
<=> multiply(sk_c2,sk_c11) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f180,plain,
( ~ sQ13_spl
| multiply(sk_c2,sk_c11) = sk_c9 ),
inference(component_clause,[status(thm)],[f179]) ).
fof(f182,plain,
( sQ1_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f88,f179,f113]) ).
fof(f183,plain,
( sQ2_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f89,f179,f117]) ).
fof(f184,plain,
( sQ3_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f90,f179,f121]) ).
fof(f185,plain,
( sQ4_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f91,f179,f125]) ).
fof(f186,plain,
( sQ5_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f92,f179,f129]) ).
fof(f187,plain,
( sQ6_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f93,f179,f133]) ).
fof(f188,plain,
( sQ7_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f94,f179,f137]) ).
fof(f189,plain,
( sQ8_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f95,f179,f141]) ).
fof(f190,plain,
( sQ9_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f96,f179,f145]) ).
fof(f192,definition,
( sQ14_spl
<=> inverse(sk_c2) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f193,plain,
( ~ sQ14_spl
| inverse(sk_c2) = sk_c11 ),
inference(component_clause,[status(thm)],[f192]) ).
fof(f195,plain,
( sQ1_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f98,f192,f113]) ).
fof(f196,plain,
( sQ2_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f99,f192,f117]) ).
fof(f197,plain,
( sQ3_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f100,f192,f121]) ).
fof(f198,plain,
( sQ4_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f101,f192,f125]) ).
fof(f199,plain,
( sQ5_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f102,f192,f129]) ).
fof(f200,plain,
( sQ6_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f103,f192,f133]) ).
fof(f201,plain,
( sQ7_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f104,f192,f137]) ).
fof(f202,plain,
( sQ8_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f105,f192,f141]) ).
fof(f203,plain,
( sQ9_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f106,f192,f145]) ).
fof(f205,definition,
! [X0] :
( sQ15_spl
<=> ( inverse(X0) != sk_c11
| multiply(X0,sk_c11) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f206,plain,
! [X0] :
( ~ sQ15_spl
| inverse(X0) != sk_c11
| multiply(X0,sk_c11) != sk_c10 ),
inference(component_clause,[status(thm)],[f205]) ).
fof(f208,definition,
! [X1] :
( sQ16_spl
<=> ( inverse(X1) != sk_c11
| multiply(X1,sk_c11) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f209,plain,
! [X0] :
( ~ sQ16_spl
| inverse(X0) != sk_c11
| multiply(X0,sk_c11) != sk_c9 ),
inference(component_clause,[status(thm)],[f208]) ).
fof(f211,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(f212,plain,
! [X0] :
( ~ sQ17_spl
| inverse(X0) != sk_c10
| multiply(X0,sk_c10) != sk_c9 ),
inference(component_clause,[status(thm)],[f211]) ).
fof(f214,definition,
! [X4,X5,X6,X7] :
( sQ18_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,[sQ18_spl])],[split_symbol_definition]) ).
fof(f215,plain,
! [X0,X1,X2,X3] :
( ~ sQ18_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)],[f214]) ).
fof(f217,plain,
( sQ18_spl
| sQ17_spl
| sQ16_spl
| ~ sQ12_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f109,f205,f166,f208,f211,f214]) ).
fof(f218,plain,
! [X0,X1] :
( ~ sQ18_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)],[f215]) ).
fof(f221,plain,
! [X0] :
( ~ sQ1_spl
| multiply(sk_c10,X0) = multiply(sk_c3,multiply(sk_c11,X0)) ),
inference(paramodulation,[status(thm)],[f114,f57]) ).
fof(f223,plain,
! [X0] :
( ~ sQ5_spl
| multiply(sk_c11,X0) = multiply(sk_c5,multiply(sk_c8,X0)) ),
inference(paramodulation,[status(thm)],[f130,f57]) ).
fof(f233,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ18_spl
| multiply(X0,sk_c8) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c5)
| multiply(inverse(sk_c5),sk_c10) != sk_c11
| multiply(sk_c5,inverse(sk_c5)) != sk_c11 ),
inference(paramodulation,[status(thm)],[f134,f218]) ).
fof(f235,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ18_spl
| multiply(X0,sk_c8) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c6)
| multiply(inverse(sk_c6),sk_c10) != sk_c11
| multiply(sk_c6,inverse(sk_c6)) != sk_c11 ),
inference(paramodulation,[status(thm)],[f146,f218]) ).
fof(f258,definition,
( sQ25_spl
<=> multiply(sk_c5,inverse(sk_c5)) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f260,plain,
( sQ25_spl
| multiply(sk_c5,inverse(sk_c5)) != sk_c11 ),
inference(component_clause,[status(thm)],[f258]) ).
fof(f261,definition,
( sQ26_spl
<=> multiply(inverse(sk_c5),sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f263,plain,
( sQ26_spl
| multiply(inverse(sk_c5),sk_c10) != sk_c11 ),
inference(component_clause,[status(thm)],[f261]) ).
fof(f264,definition,
! [X0] :
( sQ27_spl
<=> ( multiply(X0,sk_c8) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c5) ) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f267,plain,
( ~ sQ6_spl
| ~ sQ18_spl
| sQ27_spl
| ~ sQ26_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f233,f258,f261,f264,f214,f133]) ).
fof(f278,definition,
( sQ31_spl
<=> multiply(sk_c6,inverse(sk_c6)) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f280,plain,
( sQ31_spl
| multiply(sk_c6,inverse(sk_c6)) != sk_c11 ),
inference(component_clause,[status(thm)],[f278]) ).
fof(f281,definition,
( sQ32_spl
<=> multiply(inverse(sk_c6),sk_c10) = sk_c11 ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f283,plain,
( sQ32_spl
| multiply(inverse(sk_c6),sk_c10) != sk_c11 ),
inference(component_clause,[status(thm)],[f281]) ).
fof(f284,definition,
! [X0] :
( sQ33_spl
<=> ( multiply(X0,sk_c8) != inverse(X0)
| inverse(inverse(X0)) != inverse(sk_c6) ) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f287,plain,
( ~ sQ9_spl
| ~ sQ18_spl
| sQ33_spl
| ~ sQ32_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f235,f278,f281,f284,f214,f145]) ).
fof(f318,plain,
( ~ sQ3_spl
| ~ sQ17_spl
| inverse(sk_c4) != sk_c10
| sk_c9 != sk_c9 ),
inference(paramodulation,[status(thm)],[f122,f212]) ).
fof(f320,definition,
( sQ40_spl
<=> sk_c9 = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f322,plain,
( sQ40_spl
| sk_c9 != sk_c9 ),
inference(component_clause,[status(thm)],[f320]) ).
fof(f323,plain,
( ~ sQ3_spl
| ~ sQ17_spl
| ~ sQ4_spl
| ~ sQ40_spl ),
inference(split_clause,[status(thm)],[f318,f320,f125,f211,f121]) ).
fof(f331,plain,
( sQ40_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f322]) ).
fof(f332,plain,
sQ40_spl,
inference(contradiction_clause,[status(thm)],[f331]) ).
fof(f335,plain,
( ~ sQ14_spl
| multiply(sk_c11,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f193,f56]) ).
fof(f336,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f56,f57]) ).
fof(f337,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f55,f336]) ).
fof(f344,plain,
( ~ sQ13_spl
| ~ sQ16_spl
| inverse(sk_c2) != sk_c11 ),
inference(resolution,[status(thm)],[f209,f180]) ).
fof(f348,plain,
( ~ sQ1_spl
| ~ sQ16_spl
| inverse(sk_c3) != sk_c11
| sk_c10 != sk_c9 ),
inference(paramodulation,[status(thm)],[f114,f209]) ).
fof(f351,plain,
( ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ14_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f193,f344]) ).
fof(f352,plain,
( ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ14_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f351]) ).
fof(f353,plain,
( ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f352]) ).
fof(f359,plain,
( ~ sQ1_spl
| ~ sQ15_spl
| inverse(sk_c3) != sk_c11
| sk_c10 != sk_c10 ),
inference(paramodulation,[status(thm)],[f114,f206]) ).
fof(f360,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| inverse(sk_c1) != sk_c11
| sk_c10 != sk_c10 ),
inference(paramodulation,[status(thm)],[f111,f206]) ).
fof(f375,definition,
( sQ47_spl
<=> sk_c10 = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f377,plain,
( sQ47_spl
| sk_c10 != sk_c10 ),
inference(component_clause,[status(thm)],[f375]) ).
fof(f378,plain,
( ~ sQ1_spl
| ~ sQ15_spl
| ~ sQ2_spl
| ~ sQ47_spl ),
inference(split_clause,[status(thm)],[f359,f375,f117,f205,f113]) ).
fof(f379,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ11_spl
| ~ sQ47_spl ),
inference(split_clause,[status(thm)],[f360,f375,f153,f205,f110]) ).
fof(f380,plain,
( sQ47_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f377]) ).
fof(f381,plain,
sQ47_spl,
inference(contradiction_clause,[status(thm)],[f380]) ).
fof(f384,plain,
( ~ sQ8_spl
| multiply(sk_c6,sk_c7) = identity ),
inference(paramodulation,[status(thm)],[f142,f56]) ).
fof(f385,plain,
( sQ31_spl
| ~ sQ9_spl
| multiply(sk_c6,sk_c8) != sk_c11 ),
inference(backward_demodulation,[status(thm)],[f146,f280]) ).
fof(f386,plain,
( sQ32_spl
| ~ sQ9_spl
| multiply(sk_c8,sk_c10) != sk_c11 ),
inference(backward_demodulation,[status(thm)],[f146,f283]) ).
fof(f388,plain,
( sQ32_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f138,f386]) ).
fof(f389,plain,
( sQ32_spl
| ~ sQ9_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f388]) ).
fof(f390,plain,
( sQ32_spl
| ~ sQ9_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f389]) ).
fof(f392,plain,
( ~ sQ4_spl
| multiply(sk_c10,sk_c4) = identity ),
inference(paramodulation,[status(thm)],[f126,f56]) ).
fof(f439,plain,
( sQ26_spl
| ~ sQ6_spl
| multiply(sk_c8,sk_c10) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f134,f263]) ).
fof(f440,plain,
( sQ26_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f138,f439]) ).
fof(f441,plain,
( sQ26_spl
| ~ sQ6_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f440]) ).
fof(f442,plain,
( sQ26_spl
| ~ sQ6_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f441]) ).
fof(f444,plain,
( sQ25_spl
| ~ sQ6_spl
| multiply(sk_c5,sk_c8) != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f134,f260]) ).
fof(f445,plain,
( sQ25_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sk_c11 != sk_c11 ),
inference(forward_demodulation,[status(thm)],[f130,f444]) ).
fof(f446,plain,
( sQ25_spl
| ~ sQ6_spl
| ~ sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f445]) ).
fof(f447,plain,
( sQ25_spl
| ~ sQ6_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f446]) ).
fof(f456,plain,
( ~ sQ8_spl
| sk_c7 = multiply(inverse(sk_c6),identity) ),
inference(paramodulation,[status(thm)],[f384,f337]) ).
fof(f457,plain,
( ~ sQ3_spl
| sk_c10 = multiply(inverse(sk_c4),sk_c9) ),
inference(paramodulation,[status(thm)],[f122,f337]) ).
fof(f468,plain,
( ~ sQ1_spl
| sk_c11 = multiply(inverse(sk_c3),sk_c10) ),
inference(paramodulation,[status(thm)],[f114,f337]) ).
fof(f469,plain,
( ~ sQ5_spl
| sk_c8 = multiply(inverse(sk_c5),sk_c11) ),
inference(paramodulation,[status(thm)],[f130,f337]) ).
fof(f472,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 = multiply(sk_c8,identity) ),
inference(forward_demodulation,[status(thm)],[f146,f456]) ).
fof(f473,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c10 = multiply(sk_c10,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f126,f457]) ).
fof(f475,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c11 = multiply(sk_c11,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f118,f468]) ).
fof(f476,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sk_c8 = multiply(sk_c8,sk_c11) ),
inference(forward_demodulation,[status(thm)],[f134,f469]) ).
fof(f482,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c9 = multiply(inverse(sk_c10),sk_c10) ),
inference(paramodulation,[status(thm)],[f473,f337]) ).
fof(f484,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c9 = identity ),
inference(forward_demodulation,[status(thm)],[f56,f482]) ).
fof(f485,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c7 = multiply(sk_c8,sk_c9) ),
inference(backward_demodulation,[status(thm)],[f484,f472]) ).
fof(f486,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f484,f392]) ).
fof(f492,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| multiply(inverse(X0),X0) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f484,f56]) ).
fof(f493,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c9,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f484,f55]) ).
fof(f501,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c10,sk_c10) = multiply(sk_c3,sk_c11) ),
inference(paramodulation,[status(thm)],[f475,f221]) ).
fof(f504,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c10,sk_c10) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f114,f501]) ).
fof(f518,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c11,sk_c11) = multiply(sk_c5,sk_c8) ),
inference(paramodulation,[status(thm)],[f476,f223]) ).
fof(f522,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c11,sk_c11) = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f130,f518]) ).
fof(f580,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c10 = multiply(inverse(sk_c10),sk_c10) ),
inference(paramodulation,[status(thm)],[f504,f337]) ).
fof(f583,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c10 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f492,f580]) ).
fof(f586,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c9,sk_c4) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f583,f486]) ).
fof(f589,plain,
( sQ12_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c11,sk_c9) != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f583,f168]) ).
fof(f591,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| inverse(sk_c4) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f583,f126]) ).
fof(f593,plain,
( ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c8,sk_c9) = sk_c11 ),
inference(backward_demodulation,[status(thm)],[f583,f138]) ).
fof(f598,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c4 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f493,f586]) ).
fof(f601,plain,
( ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f485,f593]) ).
fof(f611,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| inverse(sk_c9) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f598,f591]) ).
fof(f617,plain,
( sQ12_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c7,sk_c9) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f601,f589]) ).
fof(f633,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c7,sk_c11) = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f601,f522]) ).
fof(f634,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c7,sk_c7) = sk_c11 ),
inference(forward_demodulation,[status(thm)],[f601,f633]) ).
fof(f635,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c7,sk_c7) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f601,f634]) ).
fof(f636,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 = multiply(inverse(sk_c7),sk_c7) ),
inference(paramodulation,[status(thm)],[f635,f337]) ).
fof(f638,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f492,f636]) ).
fof(f641,plain,
( sQ12_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c7,sk_c9) != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f638,f617]) ).
fof(f642,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c9) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f638,f611]) ).
fof(f644,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c10 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f638,f583]) ).
fof(f651,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 = identity ),
inference(backward_demodulation,[status(thm)],[f638,f484]) ).
fof(f652,plain,
( sQ12_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c7,sk_c7) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f638,f641]) ).
fof(f653,plain,
( sQ12_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f635,f652]) ).
fof(f654,plain,
( sQ12_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f653]) ).
fof(f655,plain,
( sQ12_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f654]) ).
fof(f656,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c7) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f638,f642]) ).
fof(f657,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c6 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f142,f656]) ).
fof(f659,plain,
( sQ31_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| multiply(sk_c6,sk_c8) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f601,f385]) ).
fof(f699,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c10) != sk_c11
| multiply(X0,inverse(X0)) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f601,f218]) ).
fof(f700,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c10) != sk_c7
| multiply(X0,inverse(X0)) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f601,f699]) ).
fof(f708,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c6 = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f657,f638]) ).
fof(f712,plain,
( ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c6 = sk_c11 ),
inference(backward_demodulation,[status(thm)],[f657,f601]) ).
fof(f714,plain,
( ~ sQ8_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| inverse(sk_c6) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f657,f142]) ).
fof(f719,plain,
( ~ sQ8_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| sk_c8 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f146,f714]) ).
fof(f721,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c10 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f657,f644]) ).
fof(f722,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f657,f651]) ).
fof(f823,plain,
( ~ sQ0_spl
| sk_c11 = multiply(inverse(sk_c1),sk_c10) ),
inference(paramodulation,[status(thm)],[f111,f337]) ).
fof(f825,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| sk_c11 = multiply(sk_c11,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f154,f823]) ).
fof(f848,plain,
( ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c6 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f601,f712]) ).
fof(f859,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c6,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f722,f55]) ).
fof(f868,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c6) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f708,f611]) ).
fof(f869,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c6) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f708,f868]) ).
fof(f878,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(inverse(X0),X0) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f722,f56]) ).
fof(f909,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c10) != sk_c7
| multiply(X0,inverse(X0)) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f848,f700]) ).
fof(f910,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c6) != sk_c7
| multiply(X0,inverse(X0)) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f721,f909]) ).
fof(f911,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c6) != sk_c6
| multiply(X0,inverse(X0)) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f848,f910]) ).
fof(f912,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ18_spl
| inverse(inverse(sk_c6)) != inverse(sk_c6)
| multiply(inverse(sk_c6),sk_c6) != sk_c6
| multiply(sk_c6,inverse(sk_c6)) != sk_c6 ),
inference(resolution,[status(thm)],[f911,f859]) ).
fof(f917,definition,
( sQ54_spl
<=> multiply(sk_c6,inverse(sk_c6)) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f919,plain,
( sQ54_spl
| multiply(sk_c6,inverse(sk_c6)) != sk_c6 ),
inference(component_clause,[status(thm)],[f917]) ).
fof(f920,definition,
( sQ55_spl
<=> multiply(inverse(sk_c6),sk_c6) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f922,plain,
( sQ55_spl
| multiply(inverse(sk_c6),sk_c6) != sk_c6 ),
inference(component_clause,[status(thm)],[f920]) ).
fof(f923,definition,
( sQ56_spl
<=> inverse(inverse(sk_c6)) = inverse(sk_c6) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f925,plain,
( sQ56_spl
| inverse(inverse(sk_c6)) != inverse(sk_c6) ),
inference(component_clause,[status(thm)],[f923]) ).
fof(f926,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ18_spl
| ~ sQ56_spl
| ~ sQ55_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f912,f917,f920,f923,f214,f145,f141,f117,f113,f137,f133,f129,f125,f121]) ).
fof(f935,plain,
( sQ55_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f878,f922]) ).
fof(f936,plain,
( sQ55_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f935]) ).
fof(f937,plain,
( sQ55_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f936]) ).
fof(f938,plain,
( sQ54_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f859,f919]) ).
fof(f939,plain,
( sQ54_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f869,f938]) ).
fof(f940,plain,
( sQ54_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f939]) ).
fof(f941,plain,
( sQ54_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ8_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f940]) ).
fof(f958,definition,
( sQ59_spl
<=> sk_c10 = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f960,plain,
( sQ59_spl
| sk_c10 != sk_c9 ),
inference(component_clause,[status(thm)],[f958]) ).
fof(f961,plain,
( ~ sQ1_spl
| ~ sQ16_spl
| ~ sQ2_spl
| ~ sQ59_spl ),
inference(split_clause,[status(thm)],[f348,f958,f117,f208,f113]) ).
fof(f1012,plain,
( ~ sQ13_spl
| sk_c11 = multiply(inverse(sk_c2),sk_c9) ),
inference(paramodulation,[status(thm)],[f180,f337]) ).
fof(f1014,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| sk_c11 = multiply(sk_c11,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f193,f1012]) ).
fof(f1015,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| sk_c11 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f167,f1014]) ).
fof(f1020,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| multiply(sk_c2,sk_c10) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f1015,f180]) ).
fof(f1023,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c10) != sk_c10
| multiply(X0,inverse(X0)) != sk_c11 ),
inference(backward_demodulation,[status(thm)],[f1015,f218]) ).
fof(f1025,plain,
( ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| inverse(sk_c2) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f1015,f193]) ).
fof(f1027,plain,
( sQ2_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| inverse(sk_c3) != sk_c10 ),
inference(backward_demodulation,[status(thm)],[f1015,f119]) ).
fof(f1029,plain,
( ~ sQ1_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| multiply(sk_c3,sk_c10) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f1015,f114]) ).
fof(f1030,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c10) != sk_c10
| multiply(X0,inverse(X0)) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1015,f1023]) ).
fof(f1041,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| sk_c10 = multiply(sk_c11,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f1015,f825]) ).
fof(f1042,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| sk_c10 = multiply(sk_c10,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f1015,f1041]) ).
fof(f1043,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| sk_c10 = multiply(inverse(sk_c10),sk_c10) ),
inference(paramodulation,[status(thm)],[f1042,f337]) ).
fof(f1045,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| sk_c10 = identity ),
inference(forward_demodulation,[status(thm)],[f56,f1043]) ).
fof(f1047,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| multiply(inverse(X0),X0) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f1045,f56]) ).
fof(f1049,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| multiply(sk_c10,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f1045,f55]) ).
fof(f1054,plain,
( ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| multiply(sk_c10,sk_c2) = identity ),
inference(forward_demodulation,[status(thm)],[f1015,f335]) ).
fof(f1055,plain,
( ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ11_spl
| sk_c2 = identity ),
inference(forward_demodulation,[status(thm)],[f1049,f1054]) ).
fof(f1056,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| multiply(sk_c2,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f1065,f1049]) ).
fof(f1058,plain,
( sQ2_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ11_spl
| inverse(sk_c3) != sk_c2 ),
inference(backward_demodulation,[status(thm)],[f1065,f1027]) ).
fof(f1060,plain,
( ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ11_spl
| inverse(sk_c2) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f1065,f1025]) ).
fof(f1061,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ11_spl
| multiply(sk_c2,sk_c2) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f1065,f1020]) ).
fof(f1065,plain,
( ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ11_spl
| sk_c2 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1045,f1055]) ).
fof(f1112,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ11_spl
| inverse(X0) != sk_c10
| multiply(X0,sk_c2) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1065,f212]) ).
fof(f1113,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ11_spl
| inverse(X0) != sk_c2
| multiply(X0,sk_c2) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1065,f1112]) ).
fof(f1134,plain,
( ~ sQ1_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ11_spl
| multiply(sk_c3,sk_c2) = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f1065,f1029]) ).
fof(f1135,plain,
( ~ sQ1_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ11_spl
| multiply(sk_c3,sk_c2) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1065,f1134]) ).
fof(f1137,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ11_spl
| multiply(sk_c2,X0) = multiply(sk_c3,multiply(sk_c2,X0)) ),
inference(paramodulation,[status(thm)],[f1135,f57]) ).
fof(f1138,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ11_spl
| X0 = multiply(sk_c3,multiply(sk_c2,X0)) ),
inference(forward_demodulation,[status(thm)],[f1056,f1137]) ).
fof(f1139,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ11_spl
| X0 = multiply(sk_c3,X0) ),
inference(forward_demodulation,[status(thm)],[f1056,f1138]) ).
fof(f1140,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| multiply(inverse(X0),X0) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1065,f1047]) ).
fof(f1145,plain,
( ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ11_spl
| sk_c2 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f1056,f1061]) ).
fof(f1147,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ11_spl
| X0 = multiply(inverse(sk_c3),X0) ),
inference(paramodulation,[status(thm)],[f1139,f337]) ).
fof(f1151,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ11_spl
| inverse(X0) != sk_c2
| multiply(X0,sk_c2) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1145,f1113]) ).
fof(f1152,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ17_spl
| inverse(inverse(sk_c2)) != sk_c2 ),
inference(resolution,[status(thm)],[f1151,f1140]) ).
fof(f1159,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ17_spl
| inverse(sk_c2) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1060,f1152]) ).
fof(f1160,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ17_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1060,f1159]) ).
fof(f1161,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ17_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1160]) ).
fof(f1162,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f1161]) ).
fof(f1212,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ11_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c10) != sk_c10
| multiply(X0,inverse(X0)) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1065,f1030]) ).
fof(f1213,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ11_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c2) != sk_c10
| multiply(X0,inverse(X0)) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1065,f1212]) ).
fof(f1214,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ11_spl
| multiply(X1,inverse(X0)) != inverse(X1)
| inverse(inverse(X1)) != inverse(X0)
| multiply(inverse(X0),sk_c2) != sk_c2
| multiply(X0,inverse(X0)) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1065,f1213]) ).
fof(f1227,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ1_spl
| sk_c3 = sk_c2 ),
inference(paramodulation,[status(thm)],[f1140,f1147]) ).
fof(f1234,plain,
( sQ2_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ1_spl
| inverse(sk_c2) != sk_c2 ),
inference(backward_demodulation,[status(thm)],[f1227,f1058]) ).
fof(f1236,plain,
( sQ2_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ1_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1060,f1234]) ).
fof(f1237,plain,
( sQ2_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1236]) ).
fof(f1238,plain,
( sQ2_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f1237]) ).
fof(f1294,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ18_spl
| inverse(inverse(sk_c2)) != inverse(sk_c2)
| multiply(inverse(sk_c2),sk_c2) != sk_c2
| multiply(sk_c2,inverse(sk_c2)) != sk_c2 ),
inference(resolution,[status(thm)],[f1214,f1056]) ).
fof(f1301,definition,
( sQ63_spl
<=> multiply(sk_c2,inverse(sk_c2)) = sk_c2 ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f1303,plain,
( sQ63_spl
| multiply(sk_c2,inverse(sk_c2)) != sk_c2 ),
inference(component_clause,[status(thm)],[f1301]) ).
fof(f1304,definition,
( sQ64_spl
<=> multiply(inverse(sk_c2),sk_c2) = sk_c2 ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f1306,plain,
( sQ64_spl
| multiply(inverse(sk_c2),sk_c2) != sk_c2 ),
inference(component_clause,[status(thm)],[f1304]) ).
fof(f1307,definition,
( sQ65_spl
<=> inverse(inverse(sk_c2)) = inverse(sk_c2) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f1309,plain,
( sQ65_spl
| inverse(inverse(sk_c2)) != inverse(sk_c2) ),
inference(component_clause,[status(thm)],[f1307]) ).
fof(f1310,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ18_spl
| ~ sQ65_spl
| ~ sQ64_spl
| ~ sQ63_spl ),
inference(split_clause,[status(thm)],[f1294,f1301,f1304,f1307,f214,f166,f192,f179,f153,f110]) ).
fof(f1329,plain,
( sQ64_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1140,f1306]) ).
fof(f1330,plain,
( sQ64_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1329]) ).
fof(f1331,plain,
( sQ64_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f1330]) ).
fof(f1332,plain,
( sQ63_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| inverse(sk_c2) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1056,f1303]) ).
fof(f1333,plain,
( sQ63_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1060,f1332]) ).
fof(f1334,plain,
( sQ63_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1333]) ).
fof(f1335,plain,
( sQ63_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ14_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f1334]) ).
fof(f1338,plain,
( sQ65_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ11_spl
| inverse(sk_c2) != inverse(sk_c2) ),
inference(forward_demodulation,[status(thm)],[f1060,f1309]) ).
fof(f1339,plain,
( sQ65_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ11_spl
| sk_c2 != inverse(sk_c2) ),
inference(forward_demodulation,[status(thm)],[f1060,f1338]) ).
fof(f1340,plain,
( sQ65_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ11_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f1060,f1339]) ).
fof(f1341,plain,
( sQ65_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1340]) ).
fof(f1342,plain,
( sQ65_spl
| ~ sQ14_spl
| ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f1341]) ).
fof(f1478,plain,
( sQ31_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c8 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f859,f659]) ).
fof(f1479,plain,
( sQ31_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c6 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f719,f1478]) ).
fof(f1480,plain,
( sQ31_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f848,f1479]) ).
fof(f1481,plain,
( sQ31_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ5_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1480]) ).
fof(f1482,plain,
( sQ31_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ5_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f1481]) ).
fof(f1586,plain,
( sQ56_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c6) != inverse(sk_c6) ),
inference(forward_demodulation,[status(thm)],[f869,f925]) ).
fof(f1587,plain,
( sQ56_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c6 != inverse(sk_c6) ),
inference(forward_demodulation,[status(thm)],[f869,f1586]) ).
fof(f1588,plain,
( sQ56_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f869,f1587]) ).
fof(f1589,plain,
( sQ56_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1588]) ).
fof(f1590,plain,
( sQ56_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f1589]) ).
fof(f1597,plain,
( sQ59_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c6 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f721,f960]) ).
fof(f1598,plain,
( sQ59_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f708,f1597]) ).
fof(f1599,plain,
( sQ59_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1598]) ).
fof(f1600,plain,
( sQ59_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f1599]) ).
fof(f1601,plain,
$false,
inference(sat_refutation,[status(thm)],[f116,f120,f124,f128,f132,f136,f140,f144,f148,f156,f157,f158,f159,f160,f161,f162,f163,f164,f169,f170,f171,f172,f173,f174,f175,f176,f177,f182,f183,f184,f185,f186,f187,f188,f189,f190,f195,f196,f197,f198,f199,f200,f201,f202,f203,f217,f267,f287,f323,f332,f353,f378,f379,f381,f390,f442,f447,f655,f926,f937,f941,f961,f1162,f1238,f1310,f1331,f1335,f1342,f1482,f1590,f1600]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP269-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n004.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 20:07:34 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.14/0.38 % Drodi V4.1.1
% 0.14/0.42 % Refutation found
% 0.14/0.42 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.45 % Elapsed time: 0.074462 seconds
% 0.14/0.45 % CPU time: 0.347009 seconds
% 0.14/0.45 % Total memory used: 65.409 MB
% 0.14/0.45 % Net memory used: 64.969 MB
%------------------------------------------------------------------------------