%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP313-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : 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 12:33:23 PM UTC 2026
% Result : Unsatisfiable 0.02s 0.41s
% Output : CNFRefutation 0.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 69
% Syntax : Number of formulae : 247 ( 10 unt; 20 def)
% Number of atoms : 650 ( 317 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 677 ( 274 ~; 383 |; 0 &)
% ( 20 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 21 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 41 ( 41 !; 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_c9) = sk_c8
| multiply(sk_c8,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c8,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c7
| multiply(sk_c8,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c8,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c7,sk_c9) = sk_c8
| multiply(sk_c8,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c9
| multiply(sk_c8,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c8,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( multiply(sk_c7,sk_c9) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c4) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c7,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c2,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( multiply(sk_c7,sk_c9) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c9
| multiply(sk_c2,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( inverse(sk_c4) = sk_c9
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
( multiply(sk_c7,sk_c9) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c9
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c3,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,negated_conjecture,
( multiply(sk_c7,sk_c9) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c9
| multiply(sk_c3,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,negated_conjecture,
( multiply(sk_c4,sk_c9) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,negated_conjecture,
( inverse(sk_c4) = sk_c9
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c7
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f50,negated_conjecture,
( multiply(sk_c7,sk_c9) = sk_c8
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f51,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c9
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f52,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f53,negated_conjecture,
! [X4,X5,X6,X1,X2,X3] :
( inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c9
| multiply(sk_c7,sk_c9) != sk_c8
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c7
| inverse(X1) != sk_c9
| multiply(X1,sk_c9) != sk_c8
| inverse(X6) != sk_c8
| multiply(X6,sk_c8) != sk_c9
| inverse(X5) != sk_c8
| multiply(X5,sk_c8) != sk_c7
| inverse(X4) != sk_c9
| multiply(X4,sk_c9) != sk_c8
| multiply(sk_c8,sk_c9) != sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f54,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f55,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f56,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f57,plain,
( multiply(sk_c4,sk_c9) = sk_c8
| multiply(sk_c8,sk_c9) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f58,plain,
( inverse(sk_c4) = sk_c9
| multiply(sk_c8,sk_c9) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f59,plain,
( multiply(sk_c5,sk_c8) = sk_c7
| multiply(sk_c8,sk_c9) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f60,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c8,sk_c9) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f61,plain,
( multiply(sk_c7,sk_c9) = sk_c8
| multiply(sk_c8,sk_c9) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f62,plain,
( multiply(sk_c6,sk_c7) = sk_c9
| multiply(sk_c8,sk_c9) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f63,plain,
( inverse(sk_c6) = sk_c7
| multiply(sk_c8,sk_c9) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f64,plain,
( multiply(sk_c4,sk_c9) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f65,plain,
( inverse(sk_c4) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f68,plain,
( multiply(sk_c7,sk_c9) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f69,plain,
( multiply(sk_c6,sk_c7) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f70,plain,
( inverse(sk_c6) = sk_c7
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f71,plain,
( multiply(sk_c4,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f72,plain,
( inverse(sk_c4) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f75,plain,
( multiply(sk_c7,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f76,plain,
( multiply(sk_c6,sk_c7) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f77,plain,
( inverse(sk_c6) = sk_c7
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f78,plain,
( multiply(sk_c4,sk_c9) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f79,plain,
( inverse(sk_c4) = sk_c9
| multiply(sk_c2,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f80,plain,
( multiply(sk_c5,sk_c8) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f81,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f82,plain,
( multiply(sk_c7,sk_c9) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f83,plain,
( multiply(sk_c6,sk_c7) = sk_c9
| multiply(sk_c2,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f84,plain,
( inverse(sk_c6) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f85,plain,
( multiply(sk_c4,sk_c9) = sk_c8
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f86,plain,
( inverse(sk_c4) = sk_c9
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f87,plain,
( multiply(sk_c5,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f88,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f89,plain,
( multiply(sk_c7,sk_c9) = sk_c8
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f90,plain,
( multiply(sk_c6,sk_c7) = sk_c9
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f91,plain,
( inverse(sk_c6) = sk_c7
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f92,plain,
( multiply(sk_c4,sk_c9) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f93,plain,
( inverse(sk_c4) = sk_c9
| multiply(sk_c3,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f94,plain,
( multiply(sk_c5,sk_c8) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f95,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f96,plain,
( multiply(sk_c7,sk_c9) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f97,plain,
( multiply(sk_c6,sk_c7) = sk_c9
| multiply(sk_c3,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f98,plain,
( inverse(sk_c6) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f99,plain,
( multiply(sk_c4,sk_c9) = sk_c8
| inverse(sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f100,plain,
( inverse(sk_c4) = sk_c9
| inverse(sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f101,plain,
( multiply(sk_c5,sk_c8) = sk_c7
| inverse(sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f102,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f103,plain,
( multiply(sk_c7,sk_c9) = sk_c8
| inverse(sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f104,plain,
( multiply(sk_c6,sk_c7) = sk_c9
| inverse(sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f105,plain,
( inverse(sk_c6) = sk_c7
| inverse(sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f106,plain,
! [X3] :
( inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c9
| multiply(sk_c7,sk_c9) != sk_c8
| ! [X2] :
( inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c7
| ! [X1] :
( inverse(X1) != sk_c9
| multiply(X1,sk_c9) != sk_c8
| ! [X6] :
( inverse(X6) != sk_c8
| multiply(X6,sk_c8) != sk_c9
| ! [X5] :
( inverse(X5) != sk_c8
| multiply(X5,sk_c8) != sk_c7
| ! [X4] :
( inverse(X4) != sk_c9
| multiply(X4,sk_c9) != sk_c8
| multiply(sk_c8,sk_c9) != sk_c7 ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f53]) ).
fof(f107,plain,
! [X0,X1,X2,X3,X4,X5] :
( inverse(X5) != sk_c7
| multiply(X5,sk_c7) != sk_c9
| multiply(sk_c7,sk_c9) != sk_c8
| inverse(X4) != sk_c8
| multiply(X4,sk_c8) != sk_c7
| inverse(X3) != sk_c9
| multiply(X3,sk_c9) != sk_c8
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c9
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c8
| multiply(sk_c8,sk_c9) != sk_c7 ),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f108,definition,
( sQ0_spl
<=> multiply(sk_c8,sk_c9) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f109,plain,
( ~ sQ0_spl
| multiply(sk_c8,sk_c9) = sk_c7 ),
inference(component_clause,[status(thm)],[f108]) ).
fof(f110,plain,
( sQ0_spl
| multiply(sk_c8,sk_c9) != sk_c7 ),
inference(component_clause,[status(thm)],[f108]) ).
fof(f111,definition,
( sQ1_spl
<=> multiply(sk_c4,sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f112,plain,
( ~ sQ1_spl
| multiply(sk_c4,sk_c9) = sk_c8 ),
inference(component_clause,[status(thm)],[f111]) ).
fof(f114,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f57,f108,f111]) ).
fof(f115,definition,
( sQ2_spl
<=> inverse(sk_c4) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f116,plain,
( ~ sQ2_spl
| inverse(sk_c4) = sk_c9 ),
inference(component_clause,[status(thm)],[f115]) ).
fof(f118,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f58,f108,f115]) ).
fof(f119,definition,
( sQ3_spl
<=> multiply(sk_c5,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f120,plain,
( ~ sQ3_spl
| multiply(sk_c5,sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f119]) ).
fof(f122,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f59,f108,f119]) ).
fof(f123,definition,
( sQ4_spl
<=> inverse(sk_c5) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f124,plain,
( ~ sQ4_spl
| inverse(sk_c5) = sk_c8 ),
inference(component_clause,[status(thm)],[f123]) ).
fof(f126,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f60,f108,f123]) ).
fof(f127,definition,
( sQ5_spl
<=> multiply(sk_c7,sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f128,plain,
( ~ sQ5_spl
| multiply(sk_c7,sk_c9) = sk_c8 ),
inference(component_clause,[status(thm)],[f127]) ).
fof(f129,plain,
( sQ5_spl
| multiply(sk_c7,sk_c9) != sk_c8 ),
inference(component_clause,[status(thm)],[f127]) ).
fof(f130,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f61,f108,f127]) ).
fof(f131,definition,
( sQ6_spl
<=> multiply(sk_c6,sk_c7) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f132,plain,
( ~ sQ6_spl
| multiply(sk_c6,sk_c7) = sk_c9 ),
inference(component_clause,[status(thm)],[f131]) ).
fof(f134,plain,
( sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f62,f108,f131]) ).
fof(f135,definition,
( sQ7_spl
<=> inverse(sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f136,plain,
( ~ sQ7_spl
| inverse(sk_c6) = sk_c7 ),
inference(component_clause,[status(thm)],[f135]) ).
fof(f138,plain,
( sQ7_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f63,f108,f135]) ).
fof(f139,definition,
( sQ8_spl
<=> multiply(sk_c1,sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f140,plain,
( ~ sQ8_spl
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(component_clause,[status(thm)],[f139]) ).
fof(f142,plain,
( sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f64,f139,f111]) ).
fof(f143,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f65,f139,f115]) ).
fof(f146,plain,
( sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f68,f139,f127]) ).
fof(f147,plain,
( sQ6_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f69,f139,f131]) ).
fof(f148,plain,
( sQ7_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f70,f139,f135]) ).
fof(f149,definition,
( sQ9_spl
<=> inverse(sk_c1) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f150,plain,
( ~ sQ9_spl
| inverse(sk_c1) = sk_c9 ),
inference(component_clause,[status(thm)],[f149]) ).
fof(f152,plain,
( sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f71,f149,f111]) ).
fof(f153,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f72,f149,f115]) ).
fof(f156,plain,
( sQ5_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f75,f149,f127]) ).
fof(f157,plain,
( sQ6_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f76,f149,f131]) ).
fof(f158,plain,
( sQ7_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f77,f149,f135]) ).
fof(f159,definition,
( sQ10_spl
<=> multiply(sk_c2,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f160,plain,
( ~ sQ10_spl
| multiply(sk_c2,sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f159]) ).
fof(f162,plain,
( sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f78,f159,f111]) ).
fof(f163,plain,
( sQ2_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f79,f159,f115]) ).
fof(f164,plain,
( sQ3_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f80,f159,f119]) ).
fof(f165,plain,
( sQ4_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f81,f159,f123]) ).
fof(f166,plain,
( sQ5_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f82,f159,f127]) ).
fof(f167,plain,
( sQ6_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f83,f159,f131]) ).
fof(f168,plain,
( sQ7_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f84,f159,f135]) ).
fof(f169,definition,
( sQ11_spl
<=> inverse(sk_c2) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f172,plain,
( sQ1_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f85,f169,f111]) ).
fof(f173,plain,
( sQ2_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f86,f169,f115]) ).
fof(f174,plain,
( sQ3_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f87,f169,f119]) ).
fof(f175,plain,
( sQ4_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f88,f169,f123]) ).
fof(f176,plain,
( sQ5_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f89,f169,f127]) ).
fof(f177,plain,
( sQ6_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f90,f169,f131]) ).
fof(f178,plain,
( sQ7_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f91,f169,f135]) ).
fof(f179,definition,
( sQ12_spl
<=> multiply(sk_c3,sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f180,plain,
( ~ sQ12_spl
| multiply(sk_c3,sk_c8) = sk_c9 ),
inference(component_clause,[status(thm)],[f179]) ).
fof(f182,plain,
( sQ1_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f92,f179,f111]) ).
fof(f183,plain,
( sQ2_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f93,f179,f115]) ).
fof(f184,plain,
( sQ3_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f94,f179,f119]) ).
fof(f185,plain,
( sQ4_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f95,f179,f123]) ).
fof(f186,plain,
( sQ5_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f96,f179,f127]) ).
fof(f187,plain,
( sQ6_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f97,f179,f131]) ).
fof(f188,plain,
( sQ7_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f98,f179,f135]) ).
fof(f189,definition,
( sQ13_spl
<=> inverse(sk_c3) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f190,plain,
( ~ sQ13_spl
| inverse(sk_c3) = sk_c8 ),
inference(component_clause,[status(thm)],[f189]) ).
fof(f192,plain,
( sQ1_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f99,f189,f111]) ).
fof(f193,plain,
( sQ2_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f100,f189,f115]) ).
fof(f194,plain,
( sQ3_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f101,f189,f119]) ).
fof(f195,plain,
( sQ4_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f102,f189,f123]) ).
fof(f196,plain,
( sQ5_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f103,f189,f127]) ).
fof(f197,plain,
( sQ6_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f104,f189,f131]) ).
fof(f198,plain,
( sQ7_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f105,f189,f135]) ).
fof(f199,definition,
! [X0] :
( sQ14_spl
<=> ( inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f200,plain,
! [X0] :
( ~ sQ14_spl
| inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c8 ),
inference(component_clause,[status(thm)],[f199]) ).
fof(f202,definition,
! [X1] :
( sQ15_spl
<=> ( inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f203,plain,
! [X0] :
( ~ sQ15_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f202]) ).
fof(f205,definition,
! [X2] :
( sQ16_spl
<=> ( inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f206,plain,
! [X0] :
( ~ sQ16_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c9 ),
inference(component_clause,[status(thm)],[f205]) ).
fof(f208,definition,
! [X5] :
( sQ17_spl
<=> ( inverse(X5) != sk_c7
| multiply(X5,sk_c7) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f209,plain,
! [X0] :
( ~ sQ17_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c9 ),
inference(component_clause,[status(thm)],[f208]) ).
fof(f211,plain,
( sQ17_spl
| ~ sQ5_spl
| sQ16_spl
| sQ15_spl
| sQ14_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f107,f108,f199,f202,f205,f127,f208]) ).
fof(f212,plain,
( ~ sQ6_spl
| ~ sQ17_spl
| inverse(sk_c6) != sk_c7 ),
inference(resolution,[status(thm)],[f209,f132]) ).
fof(f214,plain,
( ~ sQ6_spl
| ~ sQ17_spl
| ~ sQ7_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f136,f212]) ).
fof(f215,plain,
( ~ sQ6_spl
| ~ sQ17_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f214]) ).
fof(f216,plain,
( ~ sQ6_spl
| ~ sQ17_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f215]) ).
fof(f217,plain,
( ~ sQ12_spl
| ~ sQ16_spl
| inverse(sk_c3) != sk_c8 ),
inference(resolution,[status(thm)],[f206,f180]) ).
fof(f218,plain,
( ~ sQ3_spl
| ~ sQ16_spl
| inverse(sk_c5) != sk_c8
| sk_c7 != sk_c9 ),
inference(paramodulation,[status(thm)],[f120,f206]) ).
fof(f221,plain,
( ~ sQ12_spl
| ~ sQ16_spl
| ~ sQ13_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f190,f217]) ).
fof(f222,plain,
( ~ sQ12_spl
| ~ sQ16_spl
| ~ sQ13_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f221]) ).
fof(f223,plain,
( ~ sQ12_spl
| ~ sQ16_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f222]) ).
fof(f232,plain,
( ~ sQ3_spl
| ~ sQ15_spl
| inverse(sk_c5) != sk_c8 ),
inference(resolution,[status(thm)],[f203,f120]) ).
fof(f236,plain,
( ~ sQ10_spl
| ~ sQ15_spl
| inverse(sk_c2) != sk_c8
| sk_c7 != sk_c7 ),
inference(paramodulation,[status(thm)],[f160,f203]) ).
fof(f237,plain,
( ~ sQ3_spl
| ~ sQ15_spl
| ~ sQ4_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f124,f232]) ).
fof(f238,plain,
( ~ sQ3_spl
| ~ sQ15_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f237]) ).
fof(f239,plain,
( ~ sQ3_spl
| ~ sQ15_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f238]) ).
fof(f246,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f55,f56]) ).
fof(f247,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f54,f246]) ).
fof(f278,plain,
( ~ sQ1_spl
| sk_c9 = multiply(inverse(sk_c4),sk_c8) ),
inference(paramodulation,[status(thm)],[f112,f247]) ).
fof(f280,plain,
( ~ sQ6_spl
| sk_c7 = multiply(inverse(sk_c6),sk_c9) ),
inference(paramodulation,[status(thm)],[f132,f247]) ).
fof(f284,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c9 = multiply(sk_c9,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f116,f278]) ).
fof(f286,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| sk_c7 = multiply(sk_c7,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f136,f280]) ).
fof(f287,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| sk_c7 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f128,f286]) ).
fof(f294,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| multiply(sk_c7,sk_c9) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f287,f109]) ).
fof(f314,definition,
( sQ20_spl
<=> sk_c9 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f316,plain,
( sQ20_spl
| sk_c9 != sk_c7 ),
inference(component_clause,[status(thm)],[f314]) ).
fof(f325,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| sk_c9 = multiply(inverse(sk_c7),sk_c7) ),
inference(paramodulation,[status(thm)],[f294,f247]) ).
fof(f327,definition,
( sQ22_spl
<=> sk_c7 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f329,plain,
( sQ22_spl
| sk_c7 != sk_c7 ),
inference(component_clause,[status(thm)],[f327]) ).
fof(f334,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| sk_c9 = identity ),
inference(forward_demodulation,[status(thm)],[f55,f325]) ).
fof(f335,plain,
( sQ22_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f329]) ).
fof(f336,plain,
sQ22_spl,
inference(contradiction_clause,[status(thm)],[f335]) ).
fof(f338,plain,
( ~ sQ10_spl
| ~ sQ15_spl
| ~ sQ11_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f236,f327,f169,f202,f159]) ).
fof(f343,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| multiply(sk_c9,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f334,f54]) ).
fof(f364,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| sk_c9 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f343,f284]) ).
fof(f365,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| sk_c9 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f287,f364]) ).
fof(f366,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f365,f316]) ).
fof(f367,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| sQ20_spl ),
inference(contradiction_clause,[status(thm)],[f366]) ).
fof(f387,plain,
( ~ sQ8_spl
| ~ sQ14_spl
| inverse(sk_c1) != sk_c9 ),
inference(resolution,[status(thm)],[f200,f140]) ).
fof(f388,plain,
( ~ sQ1_spl
| ~ sQ14_spl
| inverse(sk_c4) != sk_c9 ),
inference(resolution,[status(thm)],[f200,f112]) ).
fof(f393,plain,
( ~ sQ8_spl
| ~ sQ14_spl
| ~ sQ9_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f150,f387]) ).
fof(f394,plain,
( ~ sQ8_spl
| ~ sQ14_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f393]) ).
fof(f395,plain,
( ~ sQ8_spl
| ~ sQ14_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f394]) ).
fof(f398,plain,
( ~ sQ12_spl
| sk_c8 = multiply(inverse(sk_c3),sk_c9) ),
inference(paramodulation,[status(thm)],[f180,f247]) ).
fof(f400,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| sk_c8 = multiply(sk_c8,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f190,f398]) ).
fof(f401,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| sk_c8 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f109,f400]) ).
fof(f402,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| multiply(sk_c3,sk_c7) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f401,f180]) ).
fof(f411,plain,
( ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ0_spl
| inverse(sk_c3) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f401,f190]) ).
fof(f420,plain,
( sQ5_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| multiply(sk_c7,sk_c9) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f401,f129]) ).
fof(f438,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| sk_c7 = multiply(inverse(sk_c3),sk_c9) ),
inference(paramodulation,[status(thm)],[f402,f247]) ).
fof(f440,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| sk_c7 = multiply(sk_c7,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f411,f438]) ).
fof(f441,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f440,f420]) ).
fof(f442,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f441]) ).
fof(f502,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ17_spl
| inverse(sk_c3) != sk_c7 ),
inference(resolution,[status(thm)],[f209,f402]) ).
fof(f509,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ17_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f411,f502]) ).
fof(f510,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ17_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f509]) ).
fof(f511,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ0_spl
| ~ sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f510]) ).
fof(f512,plain,
( ~ sQ3_spl
| ~ sQ16_spl
| ~ sQ4_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f218,f314,f123,f205,f119]) ).
fof(f516,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(sk_c7,sk_c9) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f287,f128]) ).
fof(f584,plain,
( sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| multiply(sk_c7,sk_c9) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f287,f110]) ).
fof(f585,plain,
( sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f516,f584]) ).
fof(f586,plain,
( sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f585]) ).
fof(f587,plain,
( sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f586]) ).
fof(f600,plain,
( ~ sQ1_spl
| ~ sQ14_spl
| ~ sQ2_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f116,f388]) ).
fof(f601,plain,
( ~ sQ1_spl
| ~ sQ14_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f600]) ).
fof(f602,plain,
( ~ sQ1_spl
| ~ sQ14_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f601]) ).
fof(f603,plain,
$false,
inference(sat_refutation,[status(thm)],[f114,f118,f122,f126,f130,f134,f138,f142,f143,f146,f147,f148,f152,f153,f156,f157,f158,f162,f163,f164,f165,f166,f167,f168,f172,f173,f174,f175,f176,f177,f178,f182,f183,f184,f185,f186,f187,f188,f192,f193,f194,f195,f196,f197,f198,f211,f216,f223,f239,f336,f338,f367,f395,f442,f511,f512,f587,f602]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP313-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % 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 20:09:05 UTC 2026
% 0.02/0.37 % CPUTime :
% 0.02/0.38 % Drodi V4.1.1
% 0.02/0.41 % Refutation found
% 0.02/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.02/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.02/0.44 % Elapsed time: 0.063618 seconds
% 0.02/0.44 % CPU time: 0.180044 seconds
% 0.02/0.44 % Total memory used: 103.986 MB
% 0.02/0.44 % Net memory used: 103.892 MB
%------------------------------------------------------------------------------