%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP209-1 : 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 12:33:06 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.41s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 77
% Syntax : Number of formulae : 324 ( 11 unt; 31 def)
% Number of atoms : 976 ( 395 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 1173 ( 521 ~; 621 |; 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 : 70 ( 70 !; 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,
( inverse(sk_c5) = sk_c10
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c10
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c10
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c9
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c7) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c9
| multiply(sk_c1,sk_c2) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c5) = sk_c10
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c10
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c10
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( inverse(sk_c7) = sk_c8
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( inverse(sk_c5) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( inverse(sk_c7) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c5) = sk_c10
| multiply(sk_c10,sk_c4) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c10
| multiply(sk_c10,sk_c4) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c10
| multiply(sk_c10,sk_c4) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c10,sk_c4) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c9
| multiply(sk_c10,sk_c4) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( inverse(sk_c7) = sk_c8
| multiply(sk_c10,sk_c4) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c9
| multiply(sk_c10,sk_c4) = sk_c9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( inverse(sk_c5) = sk_c10
| multiply(sk_c3,sk_c10) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c10
| multiply(sk_c3,sk_c10) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c10
| multiply(sk_c3,sk_c10) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c3,sk_c10) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c9
| multiply(sk_c3,sk_c10) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( inverse(sk_c7) = sk_c8
| multiply(sk_c3,sk_c10) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c9
| multiply(sk_c3,sk_c10) = sk_c4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
( inverse(sk_c5) = sk_c10
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c10
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c10
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,negated_conjecture,
( multiply(sk_c7,sk_c8) = sk_c9
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
( inverse(sk_c7) = sk_c8
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
( multiply(sk_c8,sk_c10) = sk_c9
| inverse(sk_c3) = sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,negated_conjecture,
! [X5,X6,X7,X8,X1,X2,X4,X3] :
( multiply(X3,sk_c10) != sk_c9
| inverse(X4) != X3
| multiply(X4,X3) != sk_c9
| inverse(X2) != sk_c9
| multiply(X2,sk_c9) != sk_c10
| multiply(X1,sk_c9) != sk_c10
| inverse(X1) != sk_c10
| inverse(X8) != sk_c10
| multiply(X8,sk_c10) != X7
| multiply(sk_c10,X7) != sk_c9
| multiply(X6,sk_c9) != sk_c10
| inverse(X5) != X6
| multiply(X5,X6) != sk_c10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f48,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f49,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f50,plain,
( inverse(sk_c5) = sk_c10
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f51,plain,
( multiply(sk_c5,sk_c9) = sk_c10
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f52,plain,
( multiply(sk_c6,sk_c9) = sk_c10
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f53,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f54,plain,
( multiply(sk_c7,sk_c8) = sk_c9
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f55,plain,
( inverse(sk_c7) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f56,plain,
( multiply(sk_c8,sk_c10) = sk_c9
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f57,plain,
( inverse(sk_c5) = sk_c10
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f58,plain,
( multiply(sk_c5,sk_c9) = sk_c10
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f59,plain,
( multiply(sk_c6,sk_c9) = sk_c10
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f60,plain,
( inverse(sk_c6) = sk_c9
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f61,plain,
( multiply(sk_c7,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f62,plain,
( inverse(sk_c7) = sk_c8
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f63,plain,
( multiply(sk_c8,sk_c10) = sk_c9
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f64,plain,
( inverse(sk_c5) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f65,plain,
( multiply(sk_c5,sk_c9) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f66,plain,
( multiply(sk_c6,sk_c9) = sk_c10
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f67,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f68,plain,
( multiply(sk_c7,sk_c8) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f69,plain,
( inverse(sk_c7) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f70,plain,
( multiply(sk_c8,sk_c10) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f71,plain,
( inverse(sk_c5) = sk_c10
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f72,plain,
( multiply(sk_c5,sk_c9) = sk_c10
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f73,plain,
( multiply(sk_c6,sk_c9) = sk_c10
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f74,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f75,plain,
( multiply(sk_c7,sk_c8) = sk_c9
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f76,plain,
( inverse(sk_c7) = sk_c8
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f77,plain,
( multiply(sk_c8,sk_c10) = sk_c9
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f78,plain,
( inverse(sk_c5) = sk_c10
| multiply(sk_c3,sk_c10) = sk_c4 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f79,plain,
( multiply(sk_c5,sk_c9) = sk_c10
| multiply(sk_c3,sk_c10) = sk_c4 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f80,plain,
( multiply(sk_c6,sk_c9) = sk_c10
| multiply(sk_c3,sk_c10) = sk_c4 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f81,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c3,sk_c10) = sk_c4 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f82,plain,
( multiply(sk_c7,sk_c8) = sk_c9
| multiply(sk_c3,sk_c10) = sk_c4 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f83,plain,
( inverse(sk_c7) = sk_c8
| multiply(sk_c3,sk_c10) = sk_c4 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f84,plain,
( multiply(sk_c8,sk_c10) = sk_c9
| multiply(sk_c3,sk_c10) = sk_c4 ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f85,plain,
( inverse(sk_c5) = sk_c10
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f86,plain,
( multiply(sk_c5,sk_c9) = sk_c10
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f87,plain,
( multiply(sk_c6,sk_c9) = sk_c10
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f88,plain,
( inverse(sk_c6) = sk_c9
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f89,plain,
( multiply(sk_c7,sk_c8) = sk_c9
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f90,plain,
( inverse(sk_c7) = sk_c8
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f91,plain,
( multiply(sk_c8,sk_c10) = sk_c9
| inverse(sk_c3) = sk_c10 ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f92,plain,
! [X3] :
( multiply(X3,sk_c10) != sk_c9
| ! [X4] :
( inverse(X4) != X3
| multiply(X4,X3) != sk_c9
| ! [X2] :
( inverse(X2) != sk_c9
| multiply(X2,sk_c9) != sk_c10
| ! [X1] :
( multiply(X1,sk_c9) != sk_c10
| inverse(X1) != sk_c10
| ! [X8] :
( inverse(X8) != sk_c10
| ! [X7] :
( multiply(X8,sk_c10) != X7
| multiply(sk_c10,X7) != sk_c9
| ! [X6] :
( multiply(X6,sk_c9) != sk_c10
| ! [X5] :
( inverse(X5) != X6
| multiply(X5,X6) != sk_c10 ) ) ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f46]) ).
fof(f93,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( multiply(X7,sk_c10) != sk_c9
| inverse(X6) != X7
| multiply(X6,X7) != sk_c9
| inverse(X5) != sk_c9
| multiply(X5,sk_c9) != sk_c10
| multiply(X4,sk_c9) != sk_c10
| inverse(X4) != sk_c10
| inverse(X3) != sk_c10
| multiply(X3,sk_c10) != X2
| multiply(sk_c10,X2) != sk_c9
| multiply(X1,sk_c9) != sk_c10
| inverse(X0) != X1
| multiply(X0,X1) != sk_c10 ),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f94,definition,
( sQ0_spl
<=> multiply(sk_c1,sk_c2) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f95,plain,
( ~ sQ0_spl
| multiply(sk_c1,sk_c2) = sk_c10 ),
inference(component_clause,[status(thm)],[f94]) ).
fof(f97,definition,
( sQ1_spl
<=> inverse(sk_c5) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f98,plain,
( ~ sQ1_spl
| inverse(sk_c5) = sk_c10 ),
inference(component_clause,[status(thm)],[f97]) ).
fof(f100,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f50,f94,f97]) ).
fof(f101,definition,
( sQ2_spl
<=> multiply(sk_c5,sk_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f102,plain,
( ~ sQ2_spl
| multiply(sk_c5,sk_c9) = sk_c10 ),
inference(component_clause,[status(thm)],[f101]) ).
fof(f104,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f51,f94,f101]) ).
fof(f105,definition,
( sQ3_spl
<=> multiply(sk_c6,sk_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f106,plain,
( ~ sQ3_spl
| multiply(sk_c6,sk_c9) = sk_c10 ),
inference(component_clause,[status(thm)],[f105]) ).
fof(f108,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f52,f94,f105]) ).
fof(f109,definition,
( sQ4_spl
<=> inverse(sk_c6) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f110,plain,
( ~ sQ4_spl
| inverse(sk_c6) = sk_c9 ),
inference(component_clause,[status(thm)],[f109]) ).
fof(f112,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f53,f94,f109]) ).
fof(f113,definition,
( sQ5_spl
<=> multiply(sk_c7,sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f114,plain,
( ~ sQ5_spl
| multiply(sk_c7,sk_c8) = sk_c9 ),
inference(component_clause,[status(thm)],[f113]) ).
fof(f116,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f54,f94,f113]) ).
fof(f117,definition,
( sQ6_spl
<=> inverse(sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f118,plain,
( ~ sQ6_spl
| inverse(sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f117]) ).
fof(f120,plain,
( sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f55,f94,f117]) ).
fof(f121,definition,
( sQ7_spl
<=> multiply(sk_c8,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f122,plain,
( ~ sQ7_spl
| multiply(sk_c8,sk_c10) = sk_c9 ),
inference(component_clause,[status(thm)],[f121]) ).
fof(f124,plain,
( sQ7_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f56,f94,f121]) ).
fof(f125,definition,
( sQ8_spl
<=> inverse(sk_c1) = sk_c2 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f126,plain,
( ~ sQ8_spl
| inverse(sk_c1) = sk_c2 ),
inference(component_clause,[status(thm)],[f125]) ).
fof(f128,plain,
( sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f57,f125,f97]) ).
fof(f129,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f58,f125,f101]) ).
fof(f130,plain,
( sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f59,f125,f105]) ).
fof(f131,plain,
( sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f60,f125,f109]) ).
fof(f132,plain,
( sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f61,f125,f113]) ).
fof(f133,plain,
( sQ6_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f62,f125,f117]) ).
fof(f134,plain,
( sQ7_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f63,f125,f121]) ).
fof(f135,definition,
( sQ9_spl
<=> multiply(sk_c2,sk_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f138,plain,
( sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f64,f135,f97]) ).
fof(f139,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f65,f135,f101]) ).
fof(f140,plain,
( sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f66,f135,f105]) ).
fof(f141,plain,
( sQ4_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f67,f135,f109]) ).
fof(f142,plain,
( sQ5_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f68,f135,f113]) ).
fof(f143,plain,
( sQ6_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f69,f135,f117]) ).
fof(f144,plain,
( sQ7_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f70,f135,f121]) ).
fof(f145,definition,
( sQ10_spl
<=> multiply(sk_c10,sk_c4) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f146,plain,
( ~ sQ10_spl
| multiply(sk_c10,sk_c4) = sk_c9 ),
inference(component_clause,[status(thm)],[f145]) ).
fof(f148,plain,
( sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f71,f145,f97]) ).
fof(f149,plain,
( sQ2_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f72,f145,f101]) ).
fof(f150,plain,
( sQ3_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f73,f145,f105]) ).
fof(f151,plain,
( sQ4_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f74,f145,f109]) ).
fof(f152,plain,
( sQ5_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f75,f145,f113]) ).
fof(f153,plain,
( sQ6_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f76,f145,f117]) ).
fof(f154,plain,
( sQ7_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f77,f145,f121]) ).
fof(f155,definition,
( sQ11_spl
<=> multiply(sk_c3,sk_c10) = sk_c4 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f156,plain,
( ~ sQ11_spl
| multiply(sk_c3,sk_c10) = sk_c4 ),
inference(component_clause,[status(thm)],[f155]) ).
fof(f158,plain,
( sQ1_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f78,f155,f97]) ).
fof(f159,plain,
( sQ2_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f79,f155,f101]) ).
fof(f160,plain,
( sQ3_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f80,f155,f105]) ).
fof(f161,plain,
( sQ4_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f81,f155,f109]) ).
fof(f162,plain,
( sQ5_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f82,f155,f113]) ).
fof(f163,plain,
( sQ6_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f83,f155,f117]) ).
fof(f164,plain,
( sQ7_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f84,f155,f121]) ).
fof(f165,definition,
( sQ12_spl
<=> inverse(sk_c3) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f166,plain,
( ~ sQ12_spl
| inverse(sk_c3) = sk_c10 ),
inference(component_clause,[status(thm)],[f165]) ).
fof(f168,plain,
( sQ1_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f85,f165,f97]) ).
fof(f169,plain,
( sQ2_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f86,f165,f101]) ).
fof(f170,plain,
( sQ3_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f87,f165,f105]) ).
fof(f171,plain,
( sQ4_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f88,f165,f109]) ).
fof(f172,plain,
( sQ5_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f89,f165,f113]) ).
fof(f173,plain,
( sQ6_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f90,f165,f117]) ).
fof(f174,plain,
( sQ7_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f91,f165,f121]) ).
fof(f175,definition,
! [X0,X1] :
( sQ13_spl
<=> ( multiply(X1,sk_c9) != sk_c10
| inverse(X0) != X1
| multiply(X0,X1) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f176,plain,
! [X0,X1] :
( ~ sQ13_spl
| multiply(X1,sk_c9) != sk_c10
| inverse(X0) != X1
| multiply(X0,X1) != sk_c10 ),
inference(component_clause,[status(thm)],[f175]) ).
fof(f178,definition,
! [X2,X3] :
( sQ14_spl
<=> ( inverse(X3) != sk_c10
| multiply(X3,sk_c10) != X2
| multiply(sk_c10,X2) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f179,plain,
! [X0,X1] :
( ~ sQ14_spl
| inverse(X1) != sk_c10
| multiply(X1,sk_c10) != X0
| multiply(sk_c10,X0) != sk_c9 ),
inference(component_clause,[status(thm)],[f178]) ).
fof(f181,definition,
! [X4] :
( sQ15_spl
<=> ( multiply(X4,sk_c9) != sk_c10
| inverse(X4) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f182,plain,
! [X0] :
( ~ sQ15_spl
| multiply(X0,sk_c9) != sk_c10
| inverse(X0) != sk_c10 ),
inference(component_clause,[status(thm)],[f181]) ).
fof(f184,definition,
! [X5] :
( sQ16_spl
<=> ( inverse(X5) != sk_c9
| multiply(X5,sk_c9) != sk_c10 ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f185,plain,
! [X0] :
( ~ sQ16_spl
| inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c10 ),
inference(component_clause,[status(thm)],[f184]) ).
fof(f187,definition,
! [X6,X7] :
( sQ17_spl
<=> ( multiply(X7,sk_c10) != sk_c9
| inverse(X6) != X7
| multiply(X6,X7) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f188,plain,
! [X0,X1] :
( ~ sQ17_spl
| multiply(X1,sk_c10) != sk_c9
| inverse(X0) != X1
| multiply(X0,X1) != sk_c9 ),
inference(component_clause,[status(thm)],[f187]) ).
fof(f190,plain,
( sQ17_spl
| sQ16_spl
| sQ15_spl
| sQ14_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f93,f175,f178,f181,f184,f187]) ).
fof(f191,plain,
! [X0] :
( ~ sQ17_spl
| multiply(inverse(X0),sk_c10) != sk_c9
| multiply(X0,inverse(X0)) != sk_c9 ),
inference(destructive_equality_resolution,[status(thm)],[f188]) ).
fof(f197,plain,
! [X0] :
( ~ sQ0_spl
| multiply(sk_c10,X0) = multiply(sk_c1,multiply(sk_c2,X0)) ),
inference(paramodulation,[status(thm)],[f95,f49]) ).
fof(f204,plain,
( ~ sQ4_spl
| ~ sQ17_spl
| multiply(sk_c9,sk_c10) != sk_c9
| multiply(sk_c6,inverse(sk_c6)) != sk_c9 ),
inference(paramodulation,[status(thm)],[f110,f191]) ).
fof(f207,plain,
( ~ sQ12_spl
| ~ sQ17_spl
| multiply(sk_c10,sk_c10) != sk_c9
| multiply(sk_c3,inverse(sk_c3)) != sk_c9 ),
inference(paramodulation,[status(thm)],[f166,f191]) ).
fof(f211,definition,
( sQ19_spl
<=> multiply(sk_c10,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f212,plain,
( ~ sQ19_spl
| multiply(sk_c10,sk_c10) = sk_c9 ),
inference(component_clause,[status(thm)],[f211]) ).
fof(f213,plain,
( sQ19_spl
| multiply(sk_c10,sk_c10) != sk_c9 ),
inference(component_clause,[status(thm)],[f211]) ).
fof(f215,definition,
( sQ20_spl
<=> multiply(sk_c6,inverse(sk_c6)) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f217,plain,
( sQ20_spl
| multiply(sk_c6,inverse(sk_c6)) != sk_c9 ),
inference(component_clause,[status(thm)],[f215]) ).
fof(f218,definition,
( sQ21_spl
<=> multiply(sk_c9,sk_c10) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f220,plain,
( sQ21_spl
| multiply(sk_c9,sk_c10) != sk_c9 ),
inference(component_clause,[status(thm)],[f218]) ).
fof(f221,plain,
( ~ sQ4_spl
| ~ sQ17_spl
| ~ sQ21_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f204,f215,f218,f187,f109]) ).
fof(f233,definition,
( sQ25_spl
<=> multiply(sk_c3,inverse(sk_c3)) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f235,plain,
( sQ25_spl
| multiply(sk_c3,inverse(sk_c3)) != sk_c9 ),
inference(component_clause,[status(thm)],[f233]) ).
fof(f236,plain,
( ~ sQ12_spl
| ~ sQ17_spl
| ~ sQ19_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f207,f233,f211,f187,f165]) ).
fof(f237,plain,
( sQ25_spl
| ~ sQ12_spl
| multiply(sk_c3,sk_c10) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f166,f235]) ).
fof(f238,plain,
( sQ25_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sk_c4 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f156,f237]) ).
fof(f244,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f48,f49]) ).
fof(f245,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f47,f244]) ).
fof(f251,plain,
( ~ sQ12_spl
| ~ sQ16_spl
| sk_c10 != sk_c9
| multiply(sk_c3,sk_c9) != sk_c10 ),
inference(paramodulation,[status(thm)],[f166,f185]) ).
fof(f259,definition,
( sQ28_spl
<=> multiply(sk_c3,sk_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f261,plain,
( sQ28_spl
| multiply(sk_c3,sk_c9) != sk_c10 ),
inference(component_clause,[status(thm)],[f259]) ).
fof(f262,definition,
( sQ29_spl
<=> sk_c10 = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f265,plain,
( ~ sQ12_spl
| ~ sQ16_spl
| ~ sQ29_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f251,f259,f262,f184,f165]) ).
fof(f268,plain,
( ~ sQ12_spl
| ~ sQ15_spl
| multiply(sk_c3,sk_c9) != sk_c10
| sk_c10 != sk_c10 ),
inference(paramodulation,[status(thm)],[f166,f182]) ).
fof(f273,definition,
( sQ31_spl
<=> sk_c10 = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f275,plain,
( sQ31_spl
| sk_c10 != sk_c10 ),
inference(component_clause,[status(thm)],[f273]) ).
fof(f276,plain,
( ~ sQ12_spl
| ~ sQ15_spl
| ~ sQ28_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f268,f273,f259,f181,f165]) ).
fof(f277,plain,
( sQ31_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f275]) ).
fof(f278,plain,
sQ31_spl,
inference(contradiction_clause,[status(thm)],[f277]) ).
fof(f279,plain,
! [X0] :
( ~ sQ14_spl
| inverse(X0) != sk_c10
| multiply(sk_c10,multiply(X0,sk_c10)) != sk_c9 ),
inference(destructive_equality_resolution,[status(thm)],[f179]) ).
fof(f281,plain,
( ~ sQ14_spl
| inverse(identity) != sk_c10
| multiply(sk_c10,sk_c10) != sk_c9 ),
inference(paramodulation,[status(thm)],[f47,f279]) ).
fof(f283,plain,
( ~ sQ11_spl
| ~ sQ14_spl
| inverse(sk_c3) != sk_c10
| multiply(sk_c10,sk_c4) != sk_c9 ),
inference(paramodulation,[status(thm)],[f156,f279]) ).
fof(f291,definition,
( sQ34_spl
<=> inverse(identity) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f293,plain,
( sQ34_spl
| inverse(identity) != sk_c10 ),
inference(component_clause,[status(thm)],[f291]) ).
fof(f294,plain,
( ~ sQ14_spl
| ~ sQ34_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f281,f211,f291,f178]) ).
fof(f295,plain,
( ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f283,f145,f165,f178,f155]) ).
fof(f296,plain,
! [X0] :
( ~ sQ13_spl
| multiply(inverse(X0),sk_c9) != sk_c10
| multiply(X0,inverse(X0)) != sk_c10 ),
inference(destructive_equality_resolution,[status(thm)],[f176]) ).
fof(f311,plain,
( ~ sQ8_spl
| ~ sQ13_spl
| multiply(sk_c2,sk_c9) != sk_c10
| multiply(sk_c1,inverse(sk_c1)) != sk_c10 ),
inference(paramodulation,[status(thm)],[f126,f296]) ).
fof(f312,plain,
( ~ sQ4_spl
| ~ sQ13_spl
| multiply(sk_c9,sk_c9) != sk_c10
| multiply(sk_c6,inverse(sk_c6)) != sk_c10 ),
inference(paramodulation,[status(thm)],[f110,f296]) ).
fof(f328,definition,
( sQ39_spl
<=> multiply(sk_c1,inverse(sk_c1)) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f330,plain,
( sQ39_spl
| multiply(sk_c1,inverse(sk_c1)) != sk_c10 ),
inference(component_clause,[status(thm)],[f328]) ).
fof(f331,plain,
( ~ sQ8_spl
| ~ sQ13_spl
| ~ sQ9_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f311,f328,f135,f175,f125]) ).
fof(f332,definition,
( sQ40_spl
<=> multiply(sk_c6,inverse(sk_c6)) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f334,plain,
( sQ40_spl
| multiply(sk_c6,inverse(sk_c6)) != sk_c10 ),
inference(component_clause,[status(thm)],[f332]) ).
fof(f335,definition,
( sQ41_spl
<=> multiply(sk_c9,sk_c9) = sk_c10 ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f337,plain,
( sQ41_spl
| multiply(sk_c9,sk_c9) != sk_c10 ),
inference(component_clause,[status(thm)],[f335]) ).
fof(f338,plain,
( ~ sQ4_spl
| ~ sQ13_spl
| ~ sQ41_spl
| ~ sQ40_spl ),
inference(split_clause,[status(thm)],[f312,f332,f335,f175,f109]) ).
fof(f344,plain,
( sQ40_spl
| ~ sQ4_spl
| multiply(sk_c6,sk_c9) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f110,f334]) ).
fof(f345,plain,
( sQ40_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f106,f344]) ).
fof(f346,plain,
( sQ40_spl
| ~ sQ4_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f345]) ).
fof(f347,plain,
( sQ40_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f346]) ).
fof(f348,plain,
( sQ39_spl
| ~ sQ8_spl
| multiply(sk_c1,sk_c2) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f126,f330]) ).
fof(f349,plain,
( sQ39_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f95,f348]) ).
fof(f350,plain,
( sQ39_spl
| ~ sQ8_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f349]) ).
fof(f351,plain,
( sQ39_spl
| ~ sQ8_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f350]) ).
fof(f357,plain,
( ~ sQ1_spl
| ~ sQ15_spl
| multiply(sk_c5,sk_c9) != sk_c10 ),
inference(resolution,[status(thm)],[f182,f98]) ).
fof(f361,plain,
( ~ sQ1_spl
| ~ sQ15_spl
| ~ sQ2_spl
| sk_c10 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f102,f357]) ).
fof(f362,plain,
( ~ sQ1_spl
| ~ sQ15_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f361]) ).
fof(f363,plain,
( ~ sQ1_spl
| ~ sQ15_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f362]) ).
fof(f368,definition,
( sQ43_spl
<=> multiply(sk_c10,sk_c9) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f370,plain,
( sQ43_spl
| multiply(sk_c10,sk_c9) != sk_c9 ),
inference(component_clause,[status(thm)],[f368]) ).
fof(f396,plain,
( ~ sQ2_spl
| sk_c9 = multiply(inverse(sk_c5),sk_c10) ),
inference(paramodulation,[status(thm)],[f102,f245]) ).
fof(f397,plain,
( ~ sQ3_spl
| sk_c9 = multiply(inverse(sk_c6),sk_c10) ),
inference(paramodulation,[status(thm)],[f106,f245]) ).
fof(f398,plain,
( ~ sQ5_spl
| sk_c8 = multiply(inverse(sk_c7),sk_c9) ),
inference(paramodulation,[status(thm)],[f114,f245]) ).
fof(f399,plain,
( ~ sQ0_spl
| sk_c2 = multiply(inverse(sk_c1),sk_c10) ),
inference(paramodulation,[status(thm)],[f95,f245]) ).
fof(f405,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sk_c9 = multiply(sk_c10,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f98,f396]) ).
fof(f406,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f405,f213]) ).
fof(f407,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sQ19_spl ),
inference(contradiction_clause,[status(thm)],[f406]) ).
fof(f408,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c9 = multiply(sk_c9,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f110,f397]) ).
fof(f409,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f408,f220]) ).
fof(f410,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sQ21_spl ),
inference(contradiction_clause,[status(thm)],[f409]) ).
fof(f411,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sk_c8 = multiply(sk_c8,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f118,f398]) ).
fof(f424,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sk_c9 = multiply(inverse(sk_c8),sk_c8) ),
inference(paramodulation,[status(thm)],[f411,f245]) ).
fof(f426,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sk_c9 = identity ),
inference(forward_demodulation,[status(thm)],[f48,f424]) ).
fof(f433,plain,
( sQ34_spl
| ~ sQ5_spl
| ~ sQ6_spl
| inverse(sk_c9) != sk_c10 ),
inference(backward_demodulation,[status(thm)],[f426,f293]) ).
fof(f434,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ6_spl
| multiply(inverse(X0),X0) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f426,f48]) ).
fof(f435,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c9,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f426,f47]) ).
fof(f436,plain,
( sQ41_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c9 != sk_c10 ),
inference(backward_demodulation,[status(thm)],[f435,f337]) ).
fof(f445,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c9,sk_c6) = sk_c9 ),
inference(paramodulation,[status(thm)],[f110,f434]) ).
fof(f450,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c6 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f435,f445]) ).
fof(f468,plain,
( sQ41_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sk_c6 != sk_c10 ),
inference(backward_demodulation,[status(thm)],[f450,f436]) ).
fof(f471,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| multiply(sk_c6,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f450,f435]) ).
fof(f473,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sk_c8 = multiply(sk_c8,sk_c6) ),
inference(backward_demodulation,[status(thm)],[f450,f411]) ).
fof(f475,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| inverse(sk_c6) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f450,f110]) ).
fof(f476,plain,
( ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c8,sk_c10) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f450,f122]) ).
fof(f478,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c6,sk_c6) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f450,f106]) ).
fof(f479,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ6_spl
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f450,f114]) ).
fof(f491,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c6 = multiply(sk_c9,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f450,f408]) ).
fof(f492,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c6 = multiply(sk_c6,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f450,f491]) ).
fof(f493,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c6 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f471,f492]) ).
fof(f498,plain,
( sQ34_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| inverse(sk_c6) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f450,f433]) ).
fof(f499,plain,
( sQ34_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sk_c6 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f475,f498]) ).
fof(f515,plain,
( sQ20_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| inverse(sk_c6) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f471,f217]) ).
fof(f516,plain,
( sQ20_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sk_c6 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f475,f515]) ).
fof(f517,plain,
( sQ20_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f450,f516]) ).
fof(f518,plain,
( sQ20_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f517]) ).
fof(f519,plain,
( sQ20_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f518]) ).
fof(f549,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c6 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f471,f478]) ).
fof(f550,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sQ34_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f549,f499]) ).
fof(f551,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sQ34_spl ),
inference(contradiction_clause,[status(thm)],[f550]) ).
fof(f555,plain,
( ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| multiply(sk_c8,sk_c6) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f493,f476]) ).
fof(f560,plain,
( sQ41_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f493,f468]) ).
fof(f561,plain,
( sQ41_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f560]) ).
fof(f562,plain,
( sQ41_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f561]) ).
fof(f563,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| inverse(X0) != sk_c9
| multiply(X0,sk_c6) != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f450,f185]) ).
fof(f564,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| inverse(X0) != sk_c9
| multiply(X0,sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f493,f563]) ).
fof(f565,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f450,f564]) ).
fof(f607,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ3_spl
| multiply(sk_c7,sk_c8) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f615,f479]) ).
fof(f615,plain,
( ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| sk_c8 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f473,f555]) ).
fof(f621,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ7_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c8) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f615,f565]) ).
fof(f622,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ7_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c8) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f615,f621]) ).
fof(f623,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ7_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f615,f622]) ).
fof(f625,plain,
( ~ sQ16_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ7_spl
| inverse(sk_c7) != sk_c8 ),
inference(resolution,[status(thm)],[f607,f623]) ).
fof(f629,plain,
( ~ sQ16_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f625,f117,f121,f105,f113,f109,f184]) ).
fof(f630,definition,
( sQ49_spl
<=> sk_c8 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f632,plain,
( sQ49_spl
| sk_c8 != sk_c8 ),
inference(component_clause,[status(thm)],[f630]) ).
fof(f635,plain,
( sQ49_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f632]) ).
fof(f636,plain,
sQ49_spl,
inference(contradiction_clause,[status(thm)],[f635]) ).
fof(f700,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| sk_c2 = multiply(sk_c2,sk_c10) ),
inference(forward_demodulation,[status(thm)],[f126,f399]) ).
fof(f701,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| multiply(sk_c10,sk_c10) = multiply(sk_c1,sk_c2) ),
inference(paramodulation,[status(thm)],[f700,f197]) ).
fof(f702,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| sk_c10 = multiply(inverse(sk_c2),sk_c2) ),
inference(paramodulation,[status(thm)],[f700,f245]) ).
fof(f704,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ19_spl
| sk_c9 = multiply(sk_c1,sk_c2) ),
inference(forward_demodulation,[status(thm)],[f212,f701]) ).
fof(f705,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ19_spl
| sk_c9 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f95,f704]) ).
fof(f708,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| sk_c10 = identity ),
inference(forward_demodulation,[status(thm)],[f48,f702]) ).
fof(f716,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| multiply(inverse(X0),X0) = sk_c10 ),
inference(backward_demodulation,[status(thm)],[f708,f48]) ).
fof(f718,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| multiply(sk_c10,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f708,f47]) ).
fof(f720,plain,
( sQ43_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sk_c9 != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f718,f370]) ).
fof(f721,plain,
( ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sk_c4 = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f718,f146]) ).
fof(f725,plain,
( sQ43_spl
| ~ sQ0_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f720]) ).
fof(f726,plain,
( sQ43_spl
| ~ sQ0_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f725]) ).
fof(f727,plain,
( ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sQ25_spl
| ~ sQ12_spl
| ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f721,f238]) ).
fof(f728,plain,
( ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sQ25_spl
| ~ sQ12_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f727]) ).
fof(f734,plain,
( sQ28_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| multiply(sk_c3,sk_c4) != sk_c10 ),
inference(backward_demodulation,[status(thm)],[f721,f261]) ).
fof(f744,plain,
( ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ8_spl
| multiply(sk_c10,sk_c3) = sk_c10 ),
inference(paramodulation,[status(thm)],[f166,f716]) ).
fof(f748,plain,
( ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sk_c3 = sk_c10 ),
inference(forward_demodulation,[status(thm)],[f718,f744]) ).
fof(f779,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ12_spl
| multiply(sk_c3,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f748,f718]) ).
fof(f785,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ8_spl
| multiply(sk_c3,sk_c3) = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f748,f156]) ).
fof(f831,plain,
( sQ19_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ8_spl
| multiply(sk_c3,sk_c10) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f748,f213]) ).
fof(f832,plain,
( sQ19_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sk_c10 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f779,f831]) ).
fof(f833,plain,
( sQ19_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sk_c3 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f748,f832]) ).
fof(f834,plain,
( sQ19_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ10_spl
| sk_c3 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f721,f833]) ).
fof(f849,plain,
( sQ28_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ12_spl
| sk_c4 != sk_c10 ),
inference(forward_demodulation,[status(thm)],[f779,f734]) ).
fof(f850,plain,
( sQ28_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ12_spl
| sk_c4 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f748,f849]) ).
fof(f855,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sk_c3 = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f779,f785]) ).
fof(f879,plain,
( sQ28_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ11_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f855,f850]) ).
fof(f880,plain,
( sQ28_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f879]) ).
fof(f881,plain,
( sQ28_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f880]) ).
fof(f896,plain,
( sQ19_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ11_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f855,f834]) ).
fof(f897,plain,
( sQ19_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f896]) ).
fof(f898,plain,
( sQ19_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f897]) ).
fof(f912,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ19_spl
| sQ29_spl ),
inference(split_clause,[status(thm)],[f705,f262,f211,f125,f94]) ).
fof(f918,plain,
$false,
inference(sat_refutation,[status(thm)],[f100,f104,f108,f112,f116,f120,f124,f128,f129,f130,f131,f132,f133,f134,f138,f139,f140,f141,f142,f143,f144,f148,f149,f150,f151,f152,f153,f154,f158,f159,f160,f161,f162,f163,f164,f168,f169,f170,f171,f172,f173,f174,f190,f221,f236,f265,f276,f278,f294,f295,f331,f338,f347,f351,f363,f407,f410,f519,f551,f562,f629,f636,f726,f728,f881,f898,f912]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP209-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n004.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 20 20:06:05 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.39 % Drodi V4.1.1
% 0.15/0.41 % Refutation found
% 0.15/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.46 % Elapsed time: 0.068920 seconds
% 0.15/0.46 % CPU time: 0.221507 seconds
% 0.15/0.46 % Total memory used: 104.392 MB
% 0.15/0.46 % Net memory used: 104.284 MB
%------------------------------------------------------------------------------