%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP336-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 0.10s 0.57s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 79
% Syntax : Number of formulae : 360 ( 13 unt; 31 def)
% Number of atoms : 1202 ( 424 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 1543 ( 701 ~; 811 |; 0 &)
% ( 31 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 33 ( 31 usr; 32 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 64 ( 64 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c9,sk_c10) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c9,sk_c10) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c9,sk_c10) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c5) = sk_c10
| multiply(sk_c9,sk_c10) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c10
| multiply(sk_c9,sk_c10) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c9
| multiply(sk_c9,sk_c10) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c9,sk_c10) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c9
| multiply(sk_c9,sk_c10) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c5) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c10
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c9
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( inverse(sk_c5) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c2,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c2,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c2,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( inverse(sk_c5) = sk_c10
| multiply(sk_c2,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c10
| multiply(sk_c2,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c9
| multiply(sk_c2,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c2,sk_c3) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( inverse(sk_c4) = sk_c10
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
( inverse(sk_c5) = sk_c10
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c10
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c9
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c3,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
( inverse(sk_c4) = sk_c10
| multiply(sk_c3,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,negated_conjecture,
( inverse(sk_c5) = sk_c10
| multiply(sk_c3,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c10
| multiply(sk_c3,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c9
| multiply(sk_c3,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f50,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c3,sk_c10) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f52,negated_conjecture,
! [X4,X5,X6,X1,X2,X7,X3] :
( multiply(X3,sk_c8) != sk_c9
| inverse(X7) != X3
| multiply(X7,X3) != sk_c9
| multiply(X2,sk_c9) != sk_c10
| inverse(X2) != sk_c10
| multiply(sk_c10,sk_c8) != sk_c9
| inverse(X1) != sk_c10
| multiply(X1,sk_c10) != sk_c9
| multiply(X6,sk_c10) != sk_c9
| inverse(X5) != X6
| multiply(X5,X6) != sk_c9
| multiply(X4,sk_c9) != sk_c10
| inverse(X4) != sk_c10
| multiply(sk_c9,sk_c10) != sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f53,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f54,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f55,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f56,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c9,sk_c10) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f57,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c9,sk_c10) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f58,plain,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c9,sk_c10) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f59,plain,
( inverse(sk_c5) = sk_c10
| multiply(sk_c9,sk_c10) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f60,plain,
( multiply(sk_c5,sk_c9) = sk_c10
| multiply(sk_c9,sk_c10) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f61,plain,
( multiply(sk_c6,sk_c7) = sk_c9
| multiply(sk_c9,sk_c10) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f62,plain,
( inverse(sk_c6) = sk_c7
| multiply(sk_c9,sk_c10) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f63,plain,
( multiply(sk_c7,sk_c8) = sk_c9
| multiply(sk_c9,sk_c10) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f64,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f65,plain,
( inverse(sk_c4) = sk_c10
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f66,plain,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f67,plain,
( inverse(sk_c5) = sk_c10
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f68,plain,
( multiply(sk_c5,sk_c9) = sk_c10
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f69,plain,
( multiply(sk_c6,sk_c7) = sk_c9
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f70,plain,
( inverse(sk_c6) = sk_c7
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f71,plain,
( multiply(sk_c7,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f72,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f73,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f74,plain,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f75,plain,
( inverse(sk_c5) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f76,plain,
( multiply(sk_c5,sk_c9) = sk_c10
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f77,plain,
( multiply(sk_c6,sk_c7) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f78,plain,
( inverse(sk_c6) = sk_c7
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f79,plain,
( multiply(sk_c7,sk_c8) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f80,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c2,sk_c3) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f81,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c2,sk_c3) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f82,plain,
( multiply(sk_c10,sk_c8) = sk_c9
| multiply(sk_c2,sk_c3) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f83,plain,
( inverse(sk_c5) = sk_c10
| multiply(sk_c2,sk_c3) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f84,plain,
( multiply(sk_c5,sk_c9) = sk_c10
| multiply(sk_c2,sk_c3) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f85,plain,
( multiply(sk_c6,sk_c7) = sk_c9
| multiply(sk_c2,sk_c3) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f86,plain,
( inverse(sk_c6) = sk_c7
| multiply(sk_c2,sk_c3) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f88,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f89,plain,
( inverse(sk_c4) = sk_c10
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f90,plain,
( multiply(sk_c10,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f91,plain,
( inverse(sk_c5) = sk_c10
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f92,plain,
( multiply(sk_c5,sk_c9) = sk_c10
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f93,plain,
( multiply(sk_c6,sk_c7) = sk_c9
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f94,plain,
( inverse(sk_c6) = sk_c7
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f96,plain,
( multiply(sk_c4,sk_c10) = sk_c9
| multiply(sk_c3,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f97,plain,
( inverse(sk_c4) = sk_c10
| multiply(sk_c3,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f99,plain,
( inverse(sk_c5) = sk_c10
| multiply(sk_c3,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f100,plain,
( multiply(sk_c5,sk_c9) = sk_c10
| multiply(sk_c3,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f101,plain,
( multiply(sk_c6,sk_c7) = sk_c9
| multiply(sk_c3,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f102,plain,
( inverse(sk_c6) = sk_c7
| multiply(sk_c3,sk_c10) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f104,plain,
! [X3] :
( multiply(X3,sk_c8) != sk_c9
| ! [X7] :
( inverse(X7) != X3
| multiply(X7,X3) != sk_c9
| ! [X2] :
( multiply(X2,sk_c9) != sk_c10
| inverse(X2) != sk_c10
| multiply(sk_c10,sk_c8) != sk_c9
| ! [X1] :
( inverse(X1) != sk_c10
| multiply(X1,sk_c10) != sk_c9
| ! [X6] :
( multiply(X6,sk_c10) != sk_c9
| ! [X5] :
( inverse(X5) != X6
| multiply(X5,X6) != sk_c9
| ! [X4] :
( multiply(X4,sk_c9) != sk_c10
| inverse(X4) != sk_c10
| multiply(sk_c9,sk_c10) != sk_c8 ) ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f52]) ).
fof(f105,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( multiply(X6,sk_c8) != sk_c9
| inverse(X5) != X6
| multiply(X5,X6) != sk_c9
| multiply(X4,sk_c9) != sk_c10
| inverse(X4) != sk_c10
| multiply(sk_c10,sk_c8) != sk_c9
| inverse(X3) != sk_c10
| multiply(X3,sk_c10) != sk_c9
| multiply(X2,sk_c10) != sk_c9
| inverse(X1) != X2
| multiply(X1,X2) != sk_c9
| multiply(X0,sk_c9) != sk_c10
| inverse(X0) != sk_c10
| multiply(sk_c9,sk_c10) != sk_c8 ),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f106,definition,
( sQ0_spl
<=> multiply(sk_c9,sk_c10) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f107,plain,
( ~ sQ0_spl
| multiply(sk_c9,sk_c10) = sk_c8 ),
inference(component_clause,[status(thm)],[f106]) ).
fof(f108,plain,
( sQ0_spl
| multiply(sk_c9,sk_c10) != sk_c8 ),
inference(component_clause,[status(thm)],[f106]) ).
fof(f109,definition,
( sQ1_spl
<=> multiply(sk_c4,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f110,plain,
( ~ sQ1_spl
| multiply(sk_c4,sk_c10) = sk_c9 ),
inference(component_clause,[status(thm)],[f109]) ).
fof(f112,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f56,f106,f109]) ).
fof(f113,definition,
( sQ2_spl
<=> inverse(sk_c4) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f114,plain,
( ~ sQ2_spl
| inverse(sk_c4) = sk_c10 ),
inference(component_clause,[status(thm)],[f113]) ).
fof(f116,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f57,f106,f113]) ).
fof(f117,definition,
( sQ3_spl
<=> multiply(sk_c10,sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f118,plain,
( ~ sQ3_spl
| multiply(sk_c10,sk_c8) = sk_c9 ),
inference(component_clause,[status(thm)],[f117]) ).
fof(f119,plain,
( sQ3_spl
| multiply(sk_c10,sk_c8) != sk_c9 ),
inference(component_clause,[status(thm)],[f117]) ).
fof(f120,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f58,f106,f117]) ).
fof(f121,definition,
( sQ4_spl
<=> inverse(sk_c5) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f122,plain,
( ~ sQ4_spl
| inverse(sk_c5) = sk_c10 ),
inference(component_clause,[status(thm)],[f121]) ).
fof(f124,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f59,f106,f121]) ).
fof(f125,definition,
( sQ5_spl
<=> multiply(sk_c5,sk_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f126,plain,
( ~ sQ5_spl
| multiply(sk_c5,sk_c9) = sk_c10 ),
inference(component_clause,[status(thm)],[f125]) ).
fof(f128,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f60,f106,f125]) ).
fof(f129,definition,
( sQ6_spl
<=> multiply(sk_c6,sk_c7) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f130,plain,
( ~ sQ6_spl
| multiply(sk_c6,sk_c7) = sk_c9 ),
inference(component_clause,[status(thm)],[f129]) ).
fof(f132,plain,
( sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f61,f106,f129]) ).
fof(f133,definition,
( sQ7_spl
<=> inverse(sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f134,plain,
( ~ sQ7_spl
| inverse(sk_c6) = sk_c7 ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,plain,
( sQ7_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f62,f106,f133]) ).
fof(f137,definition,
( sQ8_spl
<=> multiply(sk_c7,sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f138,plain,
( ~ sQ8_spl
| multiply(sk_c7,sk_c8) = sk_c9 ),
inference(component_clause,[status(thm)],[f137]) ).
fof(f140,plain,
( sQ8_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f63,f106,f137]) ).
fof(f141,definition,
( sQ9_spl
<=> inverse(sk_c1) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f142,plain,
( ~ sQ9_spl
| inverse(sk_c1) = sk_c10 ),
inference(component_clause,[status(thm)],[f141]) ).
fof(f144,plain,
( sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f64,f141,f109]) ).
fof(f145,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f65,f141,f113]) ).
fof(f146,plain,
( sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f66,f141,f117]) ).
fof(f147,plain,
( sQ4_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f67,f141,f121]) ).
fof(f148,plain,
( sQ5_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f68,f141,f125]) ).
fof(f149,plain,
( sQ6_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f69,f141,f129]) ).
fof(f150,plain,
( sQ7_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f70,f141,f133]) ).
fof(f151,plain,
( sQ8_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f71,f141,f137]) ).
fof(f152,definition,
( sQ10_spl
<=> multiply(sk_c1,sk_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f153,plain,
( ~ sQ10_spl
| multiply(sk_c1,sk_c9) = sk_c10 ),
inference(component_clause,[status(thm)],[f152]) ).
fof(f155,plain,
( sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f72,f152,f109]) ).
fof(f156,plain,
( sQ2_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f73,f152,f113]) ).
fof(f157,plain,
( sQ3_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f74,f152,f117]) ).
fof(f158,plain,
( sQ4_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f75,f152,f121]) ).
fof(f159,plain,
( sQ5_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f76,f152,f125]) ).
fof(f160,plain,
( sQ6_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f77,f152,f129]) ).
fof(f161,plain,
( sQ7_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f78,f152,f133]) ).
fof(f162,plain,
( sQ8_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f79,f152,f137]) ).
fof(f163,definition,
( sQ11_spl
<=> multiply(sk_c2,sk_c3) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f164,plain,
( ~ sQ11_spl
| multiply(sk_c2,sk_c3) = sk_c9 ),
inference(component_clause,[status(thm)],[f163]) ).
fof(f166,plain,
( sQ1_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f80,f163,f109]) ).
fof(f167,plain,
( sQ2_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f81,f163,f113]) ).
fof(f168,plain,
( sQ3_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f82,f163,f117]) ).
fof(f169,plain,
( sQ4_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f83,f163,f121]) ).
fof(f170,plain,
( sQ5_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f84,f163,f125]) ).
fof(f171,plain,
( sQ6_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f85,f163,f129]) ).
fof(f172,plain,
( sQ7_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f86,f163,f133]) ).
fof(f174,definition,
( sQ12_spl
<=> inverse(sk_c2) = sk_c3 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f175,plain,
( ~ sQ12_spl
| inverse(sk_c2) = sk_c3 ),
inference(component_clause,[status(thm)],[f174]) ).
fof(f177,plain,
( sQ1_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f88,f174,f109]) ).
fof(f178,plain,
( sQ2_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f89,f174,f113]) ).
fof(f179,plain,
( sQ3_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f90,f174,f117]) ).
fof(f180,plain,
( sQ4_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f91,f174,f121]) ).
fof(f181,plain,
( sQ5_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f92,f174,f125]) ).
fof(f182,plain,
( sQ6_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f93,f174,f129]) ).
fof(f183,plain,
( sQ7_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f94,f174,f133]) ).
fof(f185,definition,
( sQ13_spl
<=> multiply(sk_c3,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f186,plain,
( ~ sQ13_spl
| multiply(sk_c3,sk_c10) = sk_c9 ),
inference(component_clause,[status(thm)],[f185]) ).
fof(f188,plain,
( sQ1_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f96,f185,f109]) ).
fof(f189,plain,
( sQ2_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f97,f185,f113]) ).
fof(f191,plain,
( sQ4_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f99,f185,f121]) ).
fof(f192,plain,
( sQ5_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f100,f185,f125]) ).
fof(f193,plain,
( sQ6_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f101,f185,f129]) ).
fof(f194,plain,
( sQ7_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f102,f185,f133]) ).
fof(f196,definition,
! [X0] :
( sQ14_spl
<=> ( multiply(X0,sk_c9) != sk_c10
| inverse(X0) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f197,plain,
! [X0] :
( ~ sQ14_spl
| multiply(X0,sk_c9) != sk_c10
| inverse(X0) != sk_c10 ),
inference(component_clause,[status(thm)],[f196]) ).
fof(f199,definition,
! [X1,X2] :
( sQ15_spl
<=> ( multiply(X2,sk_c10) != sk_c9
| inverse(X1) != X2
| multiply(X1,X2) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f200,plain,
! [X0,X1] :
( ~ sQ15_spl
| multiply(X1,sk_c10) != sk_c9
| inverse(X0) != X1
| multiply(X0,X1) != sk_c9 ),
inference(component_clause,[status(thm)],[f199]) ).
fof(f202,definition,
! [X3] :
( sQ16_spl
<=> ( inverse(X3) != sk_c10
| multiply(X3,sk_c10) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f203,plain,
! [X0] :
( ~ sQ16_spl
| inverse(X0) != sk_c10
| multiply(X0,sk_c10) != sk_c9 ),
inference(component_clause,[status(thm)],[f202]) ).
fof(f205,definition,
! [X5,X6] :
( sQ17_spl
<=> ( multiply(X6,sk_c8) != sk_c9
| inverse(X5) != X6
| multiply(X5,X6) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f206,plain,
! [X0,X1] :
( ~ sQ17_spl
| multiply(X1,sk_c8) != sk_c9
| inverse(X0) != X1
| multiply(X0,X1) != sk_c9 ),
inference(component_clause,[status(thm)],[f205]) ).
fof(f208,plain,
( sQ17_spl
| ~ sQ3_spl
| sQ16_spl
| sQ15_spl
| sQ14_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f105,f106,f196,f199,f202,f117,f205]) ).
fof(f209,plain,
! [X0] :
( ~ sQ17_spl
| multiply(inverse(X0),sk_c8) != sk_c9
| multiply(X0,inverse(X0)) != sk_c9 ),
inference(destructive_equality_resolution,[status(thm)],[f206]) ).
fof(f213,plain,
! [X0] :
( ~ sQ5_spl
| multiply(sk_c10,X0) = multiply(sk_c5,multiply(sk_c9,X0)) ),
inference(paramodulation,[status(thm)],[f126,f55]) ).
fof(f214,plain,
! [X0] :
( ~ sQ6_spl
| multiply(sk_c9,X0) = multiply(sk_c6,multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f130,f55]) ).
fof(f218,plain,
! [X0] :
( ~ sQ13_spl
| multiply(sk_c9,X0) = multiply(sk_c3,multiply(sk_c10,X0)) ),
inference(paramodulation,[status(thm)],[f186,f55]) ).
fof(f221,plain,
( ~ sQ2_spl
| ~ sQ17_spl
| multiply(sk_c10,sk_c8) != sk_c9
| multiply(sk_c4,inverse(sk_c4)) != sk_c9 ),
inference(paramodulation,[status(thm)],[f114,f209]) ).
fof(f222,plain,
( ~ sQ4_spl
| ~ sQ17_spl
| multiply(sk_c10,sk_c8) != sk_c9
| multiply(sk_c5,inverse(sk_c5)) != sk_c9 ),
inference(paramodulation,[status(thm)],[f122,f209]) ).
fof(f225,plain,
( ~ sQ12_spl
| ~ sQ17_spl
| multiply(sk_c3,sk_c8) != sk_c9
| multiply(sk_c2,inverse(sk_c2)) != sk_c9 ),
inference(paramodulation,[status(thm)],[f175,f209]) ).
fof(f226,definition,
( sQ18_spl
<=> multiply(sk_c4,inverse(sk_c4)) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f229,plain,
( ~ sQ2_spl
| ~ sQ17_spl
| ~ sQ3_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f221,f226,f117,f205,f113]) ).
fof(f230,definition,
( sQ19_spl
<=> multiply(sk_c5,inverse(sk_c5)) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f232,plain,
( sQ19_spl
| multiply(sk_c5,inverse(sk_c5)) != sk_c9 ),
inference(component_clause,[status(thm)],[f230]) ).
fof(f233,plain,
( ~ sQ4_spl
| ~ sQ17_spl
| ~ sQ3_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f222,f230,f117,f205,f121]) ).
fof(f234,definition,
( sQ20_spl
<=> multiply(sk_c6,inverse(sk_c6)) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f236,plain,
( sQ20_spl
| multiply(sk_c6,inverse(sk_c6)) != sk_c9 ),
inference(component_clause,[status(thm)],[f234]) ).
fof(f242,definition,
( sQ22_spl
<=> multiply(sk_c2,inverse(sk_c2)) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f244,plain,
( sQ22_spl
| multiply(sk_c2,inverse(sk_c2)) != sk_c9 ),
inference(component_clause,[status(thm)],[f242]) ).
fof(f245,definition,
( sQ23_spl
<=> multiply(sk_c3,sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f247,plain,
( sQ23_spl
| multiply(sk_c3,sk_c8) != sk_c9 ),
inference(component_clause,[status(thm)],[f245]) ).
fof(f248,plain,
( ~ sQ12_spl
| ~ sQ17_spl
| ~ sQ23_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f225,f242,f245,f205,f174]) ).
fof(f249,plain,
( sQ22_spl
| ~ sQ12_spl
| multiply(sk_c2,sk_c3) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f175,f244]) ).
fof(f250,plain,
( sQ22_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f164,f249]) ).
fof(f251,plain,
( sQ22_spl
| ~ sQ12_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f250]) ).
fof(f252,plain,
( sQ22_spl
| ~ sQ12_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f251]) ).
fof(f254,plain,
( ~ sQ7_spl
| multiply(sk_c7,sk_c6) = identity ),
inference(paramodulation,[status(thm)],[f134,f54]) ).
fof(f255,plain,
( ~ sQ4_spl
| multiply(sk_c10,sk_c5) = identity ),
inference(paramodulation,[status(thm)],[f122,f54]) ).
fof(f256,plain,
( ~ sQ2_spl
| multiply(sk_c10,sk_c4) = identity ),
inference(paramodulation,[status(thm)],[f114,f54]) ).
fof(f258,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f54,f55]) ).
fof(f259,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f53,f258]) ).
fof(f262,plain,
! [X0] :
( ~ sQ7_spl
| multiply(identity,X0) = multiply(sk_c7,multiply(sk_c6,X0)) ),
inference(paramodulation,[status(thm)],[f254,f55]) ).
fof(f263,plain,
! [X0] :
( ~ sQ7_spl
| X0 = multiply(sk_c7,multiply(sk_c6,X0)) ),
inference(forward_demodulation,[status(thm)],[f53,f262]) ).
fof(f268,plain,
( ~ sQ1_spl
| ~ sQ16_spl
| inverse(sk_c4) != sk_c10 ),
inference(resolution,[status(thm)],[f203,f110]) ).
fof(f274,plain,
( ~ sQ13_spl
| ~ sQ16_spl
| inverse(sk_c3) != sk_c10
| sk_c9 != sk_c9 ),
inference(paramodulation,[status(thm)],[f186,f203]) ).
fof(f275,plain,
( ~ sQ1_spl
| ~ sQ16_spl
| ~ sQ2_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f114,f268]) ).
fof(f276,plain,
( ~ sQ1_spl
| ~ sQ16_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f275]) ).
fof(f277,plain,
( ~ sQ1_spl
| ~ sQ16_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f276]) ).
fof(f278,plain,
! [X0] :
( ~ sQ15_spl
| multiply(inverse(X0),sk_c10) != sk_c9
| multiply(X0,inverse(X0)) != sk_c9 ),
inference(destructive_equality_resolution,[status(thm)],[f200]) ).
fof(f279,plain,
( ~ sQ15_spl
| identity != sk_c9
| multiply(sk_c10,inverse(sk_c10)) != sk_c9 ),
inference(paramodulation,[status(thm)],[f54,f278]) ).
fof(f280,plain,
( ~ sQ7_spl
| ~ sQ15_spl
| multiply(sk_c7,sk_c10) != sk_c9
| multiply(sk_c6,inverse(sk_c6)) != sk_c9 ),
inference(paramodulation,[status(thm)],[f134,f278]) ).
fof(f283,plain,
( ~ sQ12_spl
| ~ sQ15_spl
| multiply(sk_c3,sk_c10) != sk_c9
| multiply(sk_c2,inverse(sk_c2)) != sk_c9 ),
inference(paramodulation,[status(thm)],[f175,f278]) ).
fof(f284,definition,
( sQ24_spl
<=> multiply(sk_c10,inverse(sk_c10)) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f286,plain,
( sQ24_spl
| multiply(sk_c10,inverse(sk_c10)) != sk_c9 ),
inference(component_clause,[status(thm)],[f284]) ).
fof(f287,definition,
( sQ25_spl
<=> identity = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f288,plain,
( ~ sQ25_spl
| identity = sk_c9 ),
inference(component_clause,[status(thm)],[f287]) ).
fof(f289,plain,
( sQ25_spl
| identity != sk_c9 ),
inference(component_clause,[status(thm)],[f287]) ).
fof(f290,plain,
( ~ sQ15_spl
| ~ sQ25_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f279,f284,f287,f199]) ).
fof(f291,definition,
( sQ26_spl
<=> multiply(sk_c7,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f294,plain,
( ~ sQ7_spl
| ~ sQ15_spl
| ~ sQ26_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f280,f234,f291,f199,f133]) ).
fof(f300,plain,
( ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ13_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f283,f242,f185,f199,f174]) ).
fof(f303,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| sk_c7 = multiply(sk_c7,sk_c9) ),
inference(paramodulation,[status(thm)],[f130,f263]) ).
fof(f328,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| sk_c9 = multiply(inverse(sk_c7),sk_c7) ),
inference(paramodulation,[status(thm)],[f303,f259]) ).
fof(f343,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| sk_c9 = identity ),
inference(forward_demodulation,[status(thm)],[f54,f328]) ).
fof(f350,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f343,f256]) ).
fof(f351,plain,
( ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(sk_c10,sk_c5) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f343,f255]) ).
fof(f352,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| multiply(sk_c7,sk_c6) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f343,f254]) ).
fof(f353,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ7_spl
| multiply(inverse(X0),X0) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f343,f54]) ).
fof(f354,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ7_spl
| multiply(sk_c9,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f343,f53]) ).
fof(f355,plain,
( sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c10 != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f354,f108]) ).
fof(f372,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(paramodulation,[status(thm)],[f114,f353]) ).
fof(f381,plain,
( ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(sk_c5,sk_c8) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f382,f118]) ).
fof(f382,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(sk_c10,X0) = multiply(sk_c5,X0) ),
inference(forward_demodulation,[status(thm)],[f354,f213]) ).
fof(f386,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| multiply(sk_c5,sk_c4) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f382,f350]) ).
fof(f387,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| sk_c4 = multiply(inverse(sk_c5),sk_c9) ),
inference(paramodulation,[status(thm)],[f386,f259]) ).
fof(f389,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c4 = multiply(sk_c10,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f122,f387]) ).
fof(f390,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c4 = multiply(sk_c5,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f382,f389]) ).
fof(f391,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c4 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f126,f390]) ).
fof(f394,plain,
( sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c4 != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f391,f355]) ).
fof(f395,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| inverse(sk_c5) = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f391,f122]) ).
fof(f396,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(sk_c4) = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f391,f114]) ).
fof(f398,plain,
( ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ4_spl
| multiply(sk_c5,sk_c9) = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f391,f126]) ).
fof(f404,plain,
( ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ5_spl
| multiply(sk_c4,sk_c5) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f391,f351]) ).
fof(f405,plain,
( ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ5_spl
| sk_c5 = multiply(inverse(sk_c4),sk_c9) ),
inference(paramodulation,[status(thm)],[f404,f259]) ).
fof(f407,plain,
( ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ5_spl
| sk_c5 = multiply(sk_c4,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f396,f405]) ).
fof(f413,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c4,sk_c4) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f391,f372]) ).
fof(f414,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c4 = multiply(inverse(sk_c4),sk_c9) ),
inference(paramodulation,[status(thm)],[f413,f259]) ).
fof(f416,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c4 = multiply(sk_c4,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f396,f414]) ).
fof(f419,plain,
( ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c8 = multiply(inverse(sk_c5),sk_c9) ),
inference(paramodulation,[status(thm)],[f381,f259]) ).
fof(f421,plain,
( ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ2_spl
| sk_c8 = multiply(sk_c4,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f395,f419]) ).
fof(f434,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ7_spl
| X0 = multiply(sk_c6,multiply(sk_c7,X0)) ),
inference(forward_demodulation,[status(thm)],[f354,f214]) ).
fof(f435,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| sk_c6 = multiply(sk_c6,sk_c9) ),
inference(paramodulation,[status(thm)],[f352,f434]) ).
fof(f438,plain,
( ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c8 = multiply(sk_c6,sk_c9) ),
inference(paramodulation,[status(thm)],[f138,f434]) ).
fof(f445,plain,
( ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ4_spl
| multiply(sk_c5,sk_c9) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f453,f398]) ).
fof(f446,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c4,sk_c5) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f453,f413]) ).
fof(f448,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(sk_c4) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f453,f396]) ).
fof(f450,plain,
( sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f453,f394]) ).
fof(f451,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f453,f391]) ).
fof(f453,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c4 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f407,f416]) ).
fof(f454,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c5,sk_c5) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f453,f446]) ).
fof(f455,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(sk_c5) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f453,f448]) ).
fof(f458,plain,
( ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ2_spl
| sk_c8 = multiply(sk_c5,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f453,f421]) ).
fof(f466,plain,
( ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ8_spl
| sk_c6 = multiply(sk_c5,sk_c9) ),
inference(backward_demodulation,[status(thm)],[f470,f458]) ).
fof(f467,plain,
( sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ8_spl
| sk_c5 != sk_c6 ),
inference(backward_demodulation,[status(thm)],[f470,f450]) ).
fof(f470,plain,
( ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c8 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f435,f438]) ).
fof(f480,plain,
( ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ8_spl
| sk_c6 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f445,f466]) ).
fof(f481,plain,
( ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ8_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f480,f467]) ).
fof(f482,plain,
( ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ8_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f481]) ).
fof(f483,plain,
( sQ20_spl
| ~ sQ7_spl
| multiply(sk_c6,sk_c7) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f134,f236]) ).
fof(f484,plain,
( sQ20_spl
| ~ sQ7_spl
| ~ sQ6_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f130,f483]) ).
fof(f485,plain,
( sQ20_spl
| ~ sQ7_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f484]) ).
fof(f486,plain,
( sQ20_spl
| ~ sQ7_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f485]) ).
fof(f487,plain,
( sQ19_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c5,sk_c5) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f455,f232]) ).
fof(f488,plain,
( sQ19_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f454,f487]) ).
fof(f489,plain,
( sQ19_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f488]) ).
fof(f490,plain,
( sQ19_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f489]) ).
fof(f491,plain,
( sQ24_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c5,inverse(sk_c10)) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f451,f286]) ).
fof(f492,plain,
( sQ24_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c5,inverse(sk_c5)) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f451,f491]) ).
fof(f493,plain,
( sQ24_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c5,sk_c5) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f455,f492]) ).
fof(f494,plain,
( sQ24_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f454,f493]) ).
fof(f495,plain,
( sQ24_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f494]) ).
fof(f496,plain,
( sQ24_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f495]) ).
fof(f522,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ8_spl
| inverse(sk_c5) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f480,f455]) ).
fof(f523,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ8_spl
| sk_c6 = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f480,f451]) ).
fof(f527,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ8_spl
| inverse(sk_c6) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f480,f522]) ).
fof(f528,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ8_spl
| sk_c7 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f134,f527]) ).
fof(f529,plain,
( ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ8_spl
| sk_c7 = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f528,f480]) ).
fof(f535,plain,
( ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ8_spl
| inverse(sk_c7) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f528,f134]) ).
fof(f538,plain,
( ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ8_spl
| sk_c7 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f528,f523]) ).
fof(f556,plain,
( ~ sQ11_spl
| sk_c3 = multiply(inverse(sk_c2),sk_c9) ),
inference(paramodulation,[status(thm)],[f164,f259]) ).
fof(f558,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| sk_c3 = multiply(sk_c3,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f175,f556]) ).
fof(f565,plain,
( ~ sQ9_spl
| ~ sQ14_spl
| multiply(sk_c1,sk_c9) != sk_c10 ),
inference(resolution,[status(thm)],[f197,f142]) ).
fof(f568,plain,
( ~ sQ9_spl
| ~ sQ14_spl
| ~ sQ10_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f153,f565]) ).
fof(f569,plain,
( ~ sQ9_spl
| ~ sQ14_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f568]) ).
fof(f570,plain,
( ~ sQ9_spl
| ~ sQ14_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f569]) ).
fof(f571,definition,
( sQ30_spl
<=> sk_c10 = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f573,plain,
( sQ30_spl
| sk_c10 != sk_c10 ),
inference(component_clause,[status(thm)],[f571]) ).
fof(f575,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f343,f289]) ).
fof(f576,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| sQ25_spl ),
inference(contradiction_clause,[status(thm)],[f575]) ).
fof(f577,plain,
( sQ30_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f573]) ).
fof(f578,plain,
sQ30_spl,
inference(contradiction_clause,[status(thm)],[f577]) ).
fof(f581,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ8_spl
| multiply(sk_c7,sk_c9) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f529,f126]) ).
fof(f586,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ8_spl
| multiply(X0,sk_c9) != sk_c7
| inverse(X0) != sk_c10 ),
inference(backward_demodulation,[status(thm)],[f538,f197]) ).
fof(f591,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ8_spl
| multiply(X0,sk_c9) != sk_c7
| inverse(X0) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f538,f586]) ).
fof(f638,definition,
( sQ31_spl
<=> sk_c7 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f640,plain,
( sQ31_spl
| sk_c7 != sk_c7 ),
inference(component_clause,[status(thm)],[f638]) ).
fof(f649,plain,
( sQ31_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f640]) ).
fof(f650,plain,
sQ31_spl,
inference(contradiction_clause,[status(thm)],[f649]) ).
fof(f656,plain,
( ~ sQ10_spl
| sk_c9 = multiply(inverse(sk_c1),sk_c10) ),
inference(paramodulation,[status(thm)],[f153,f259]) ).
fof(f658,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| sk_c9 = multiply(sk_c10,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f142,f656]) ).
fof(f665,plain,
( ~ sQ9_spl
| multiply(sk_c10,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f142,f54]) ).
fof(f679,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| sk_c9 = multiply(inverse(sk_c3),sk_c3) ),
inference(paramodulation,[status(thm)],[f558,f259]) ).
fof(f681,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| sk_c9 = identity ),
inference(forward_demodulation,[status(thm)],[f54,f679]) ).
fof(f685,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ12_spl
| multiply(sk_c9,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f681,f53]) ).
fof(f686,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sk_c10 = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f685,f107]) ).
fof(f689,plain,
( sQ3_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| multiply(sk_c8,sk_c8) != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f686,f119]) ).
fof(f692,plain,
( ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| multiply(sk_c3,sk_c8) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f686,f186]) ).
fof(f697,plain,
( ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f692,f247]) ).
fof(f698,plain,
( ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sQ23_spl ),
inference(contradiction_clause,[status(thm)],[f697]) ).
fof(f712,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sk_c9 = multiply(sk_c8,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f686,f658]) ).
fof(f713,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sk_c9 = multiply(sk_c8,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f686,f712]) ).
fof(f714,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f713,f689]) ).
fof(f715,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f714]) ).
fof(f737,definition,
( sQ37_spl
<=> sk_c9 = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f739,plain,
( sQ37_spl
| sk_c9 != sk_c9 ),
inference(component_clause,[status(thm)],[f737]) ).
fof(f741,definition,
( sQ38_spl
<=> inverse(sk_c3) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f743,plain,
( sQ38_spl
| inverse(sk_c3) != sk_c10 ),
inference(component_clause,[status(thm)],[f741]) ).
fof(f744,plain,
( ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ38_spl
| ~ sQ37_spl ),
inference(split_clause,[status(thm)],[f274,f737,f741,f202,f185]) ).
fof(f746,plain,
( sQ37_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f739]) ).
fof(f747,plain,
sQ37_spl,
inference(contradiction_clause,[status(thm)],[f746]) ).
fof(f753,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ8_spl
| multiply(sk_c7,sk_c9) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f538,f581]) ).
fof(f767,plain,
( ~ sQ14_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ8_spl
| multiply(sk_c7,sk_c9) != sk_c7 ),
inference(resolution,[status(thm)],[f535,f591]) ).
fof(f770,plain,
( ~ sQ14_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ8_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f753,f767]) ).
fof(f771,plain,
( ~ sQ14_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f770]) ).
fof(f772,plain,
( ~ sQ14_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f771]) ).
fof(f773,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| sQ25_spl ),
inference(split_clause,[status(thm)],[f681,f287,f174,f163]) ).
fof(f782,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| inverse(sk_c1) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f686,f142]) ).
fof(f784,plain,
! [X0] :
( ~ sQ25_spl
| multiply(sk_c9,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f288,f53]) ).
fof(f787,plain,
( sQ38_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| inverse(sk_c3) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f686,f743]) ).
fof(f805,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| multiply(sk_c8,sk_c1) = identity ),
inference(forward_demodulation,[status(thm)],[f686,f665]) ).
fof(f806,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ25_spl
| multiply(sk_c8,sk_c1) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f288,f805]) ).
fof(f839,definition,
( sQ42_spl
<=> sk_c8 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f841,plain,
( sQ42_spl
| sk_c8 != sk_c8 ),
inference(component_clause,[status(thm)],[f839]) ).
fof(f843,plain,
( sQ42_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f841]) ).
fof(f844,plain,
sQ42_spl,
inference(contradiction_clause,[status(thm)],[f843]) ).
fof(f850,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ25_spl
| X0 = multiply(sk_c3,multiply(sk_c10,X0)) ),
inference(forward_demodulation,[status(thm)],[f784,f218]) ).
fof(f851,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ25_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| X0 = multiply(sk_c3,multiply(sk_c8,X0)) ),
inference(forward_demodulation,[status(thm)],[f686,f850]) ).
fof(f852,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ13_spl
| sk_c1 = multiply(sk_c3,sk_c9) ),
inference(paramodulation,[status(thm)],[f806,f851]) ).
fof(f856,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ13_spl
| sk_c1 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f558,f852]) ).
fof(f872,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ13_spl
| inverse(sk_c3) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f856,f782]) ).
fof(f874,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ13_spl
| sQ38_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f872,f787]) ).
fof(f875,plain,
( ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ13_spl
| sQ38_spl ),
inference(contradiction_clause,[status(thm)],[f874]) ).
fof(f876,plain,
$false,
inference(sat_refutation,[status(thm)],[f112,f116,f120,f124,f128,f132,f136,f140,f144,f145,f146,f147,f148,f149,f150,f151,f155,f156,f157,f158,f159,f160,f161,f162,f166,f167,f168,f169,f170,f171,f172,f177,f178,f179,f180,f181,f182,f183,f188,f189,f191,f192,f193,f194,f208,f229,f233,f248,f252,f277,f290,f294,f300,f482,f486,f490,f496,f570,f576,f578,f650,f698,f715,f744,f747,f772,f773,f844,f875]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP336-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.52 % Computer : n016.cluster.edu
% 0.10/0.52 % Model : x86_64 x86_64
% 0.10/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.52 % Memory : 8046.5625MB
% 0.10/0.52 % OS : Linux 6.8.0-71-generic
% 0.10/0.52 % CPULimit : 300
% 0.10/0.52 % WCLimit : 300
% 0.10/0.52 % DateTime : Sun Sep 20 20:14:08 UTC 2026
% 0.10/0.52 % CPUTime :
% 0.10/0.54 % Drodi V4.1.1
% 0.10/0.57 % Refutation found
% 0.10/0.57 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.61 % Elapsed time: 0.065049 seconds
% 0.16/0.61 % CPU time: 0.215479 seconds
% 0.16/0.61 % Total memory used: 105.594 MB
% 0.16/0.61 % Net memory used: 105.490 MB
%------------------------------------------------------------------------------