%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP329-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 12:33:26 PM UTC 2026
% Result : Unsatisfiable 0.08s 0.33s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 66
% Syntax : Number of formulae : 297 ( 11 unt; 22 def)
% Number of atoms : 1003 ( 362 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 1299 ( 593 ~; 684 |; 0 &)
% ( 22 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 24 ( 22 usr; 23 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 54 ( 54 !; 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,
( inverse(sk_c8) = sk_c7
| multiply(sk_c8,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c8,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c8,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c8,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c8,sk_c9) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( inverse(sk_c8) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
( inverse(sk_c8) = sk_c7
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,negated_conjecture,
! [X4,X5,X6,X1,X2,X3] :
( inverse(X3) != sk_c9
| multiply(X3,sk_c9) != sk_c7
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c9
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c7
| inverse(X6) != sk_c9
| multiply(X6,sk_c9) != X5
| multiply(sk_c9,X5) != sk_c8
| inverse(X4) != sk_c8
| multiply(X4,sk_c8) != sk_c9
| multiply(sk_c8,sk_c9) != sk_c7 ),
file('/export/starexec/sandbox/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_c8) = sk_c7
| multiply(sk_c8,sk_c9) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f51,plain,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c8,sk_c9) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f52,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c8,sk_c9) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f53,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c8,sk_c9) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f54,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c8,sk_c9) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f57,plain,
( inverse(sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f58,plain,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f59,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f60,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f61,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f62,plain,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f63,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f64,plain,
( inverse(sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f65,plain,
( multiply(sk_c4,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f66,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f67,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f68,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f69,plain,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f70,plain,
( inverse(sk_c6) = sk_c9
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f71,plain,
( inverse(sk_c8) = sk_c7
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f72,plain,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f73,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f74,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f75,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f76,plain,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f77,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f78,plain,
( inverse(sk_c8) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f79,plain,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f80,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f81,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f82,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f83,plain,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f84,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f85,plain,
( inverse(sk_c8) = sk_c7
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f86,plain,
( multiply(sk_c4,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f87,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f88,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f89,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f90,plain,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f91,plain,
( inverse(sk_c6) = sk_c9
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f92,plain,
! [X3] :
( inverse(X3) != sk_c9
| multiply(X3,sk_c9) != sk_c7
| ! [X2] :
( inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c9
| ! [X1] :
( inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c7
| ! [X6] :
( inverse(X6) != sk_c9
| ! [X5] :
( multiply(X6,sk_c9) != X5
| multiply(sk_c9,X5) != sk_c8
| ! [X4] :
( inverse(X4) != sk_c8
| multiply(X4,sk_c8) != sk_c9
| multiply(sk_c8,sk_c9) != sk_c7 ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f46]) ).
fof(f93,plain,
! [X0,X1,X2,X3,X4,X5] :
( inverse(X5) != sk_c9
| multiply(X5,sk_c9) != sk_c7
| inverse(X4) != sk_c8
| multiply(X4,sk_c8) != sk_c9
| inverse(X3) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c7
| inverse(X2) != sk_c9
| multiply(X2,sk_c9) != X1
| multiply(sk_c9,X1) != sk_c8
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c9
| multiply(sk_c8,sk_c9) != sk_c7 ),
inference(cnf_transformation,[status(thm)],[f92]) ).
fof(f94,definition,
( sQ0_spl
<=> multiply(sk_c8,sk_c9) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f95,plain,
( ~ sQ0_spl
| multiply(sk_c8,sk_c9) = sk_c7 ),
inference(component_clause,[status(thm)],[f94]) ).
fof(f96,plain,
( sQ0_spl
| multiply(sk_c8,sk_c9) != sk_c7 ),
inference(component_clause,[status(thm)],[f94]) ).
fof(f97,definition,
( sQ1_spl
<=> inverse(sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f98,plain,
( ~ sQ1_spl
| inverse(sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f97]) ).
fof(f99,plain,
( sQ1_spl
| inverse(sk_c8) != sk_c7 ),
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_c4,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f102,plain,
( ~ sQ2_spl
| multiply(sk_c4,sk_c8) = sk_c7 ),
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
<=> inverse(sk_c4) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f106,plain,
( ~ sQ3_spl
| inverse(sk_c4) = sk_c8 ),
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
<=> multiply(sk_c5,sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f110,plain,
( ~ sQ4_spl
| multiply(sk_c5,sk_c8) = 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
<=> inverse(sk_c5) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f114,plain,
( ~ sQ5_spl
| inverse(sk_c5) = sk_c8 ),
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
<=> multiply(sk_c6,sk_c9) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f118,plain,
( ~ sQ6_spl
| multiply(sk_c6,sk_c9) = sk_c7 ),
inference(component_clause,[status(thm)],[f117]) ).
fof(f121,definition,
( sQ7_spl
<=> inverse(sk_c6) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f122,plain,
( ~ sQ7_spl
| inverse(sk_c6) = sk_c9 ),
inference(component_clause,[status(thm)],[f121]) ).
fof(f125,definition,
( sQ8_spl
<=> multiply(sk_c1,sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f126,plain,
( ~ sQ8_spl
| multiply(sk_c1,sk_c8) = sk_c9 ),
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
<=> inverse(sk_c1) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f136,plain,
( ~ sQ9_spl
| inverse(sk_c1) = sk_c8 ),
inference(component_clause,[status(thm)],[f135]) ).
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_c9,sk_c3) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f146,plain,
( ~ sQ10_spl
| multiply(sk_c9,sk_c3) = sk_c8 ),
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_c2,sk_c9) = sk_c3 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f156,plain,
( ~ sQ11_spl
| multiply(sk_c2,sk_c9) = sk_c3 ),
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_c2) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f166,plain,
( ~ sQ12_spl
| inverse(sk_c2) = sk_c9 ),
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] :
( sQ13_spl
<=> ( inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f176,plain,
! [X0] :
( ~ sQ13_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c9 ),
inference(component_clause,[status(thm)],[f175]) ).
fof(f178,definition,
! [X1,X2] :
( sQ14_spl
<=> ( inverse(X2) != sk_c9
| multiply(X2,sk_c9) != X1
| multiply(sk_c9,X1) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f179,plain,
! [X0,X1] :
( ~ sQ14_spl
| inverse(X1) != sk_c9
| multiply(X1,sk_c9) != X0
| multiply(sk_c9,X0) != sk_c8 ),
inference(component_clause,[status(thm)],[f178]) ).
fof(f181,definition,
! [X3] :
( sQ15_spl
<=> ( inverse(X3) != sk_c8
| multiply(X3,sk_c8) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f182,plain,
! [X0] :
( ~ sQ15_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f181]) ).
fof(f184,definition,
! [X5] :
( sQ16_spl
<=> ( inverse(X5) != sk_c9
| multiply(X5,sk_c9) != sk_c7 ) ),
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_c7 ),
inference(component_clause,[status(thm)],[f184]) ).
fof(f187,plain,
( sQ16_spl
| sQ15_spl
| ~ sQ1_spl
| sQ14_spl
| sQ13_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f93,f94,f175,f178,f97,f181,f184]) ).
fof(f188,plain,
( ~ sQ0_spl
| ~ sQ16_spl
| inverse(sk_c8) != sk_c9 ),
inference(resolution,[status(thm)],[f185,f95]) ).
fof(f189,plain,
( ~ sQ6_spl
| ~ sQ16_spl
| inverse(sk_c6) != sk_c9 ),
inference(resolution,[status(thm)],[f185,f118]) ).
fof(f190,plain,
( ~ sQ0_spl
| ~ sQ16_spl
| inverse(sk_c8) != sk_c9
| sk_c7 != sk_c7 ),
inference(paramodulation,[status(thm)],[f95,f185]) ).
fof(f193,plain,
( ~ sQ6_spl
| ~ sQ16_spl
| ~ sQ7_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f122,f189]) ).
fof(f194,plain,
( ~ sQ6_spl
| ~ sQ16_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f193]) ).
fof(f195,plain,
( ~ sQ6_spl
| ~ sQ16_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f194]) ).
fof(f196,plain,
! [X0] :
( ~ sQ14_spl
| inverse(X0) != sk_c9
| multiply(sk_c9,multiply(X0,sk_c9)) != sk_c8 ),
inference(destructive_equality_resolution,[status(thm)],[f179]) ).
fof(f197,plain,
( ~ sQ2_spl
| ~ sQ15_spl
| inverse(sk_c4) != sk_c8 ),
inference(resolution,[status(thm)],[f182,f102]) ).
fof(f200,plain,
( ~ sQ8_spl
| ~ sQ15_spl
| inverse(sk_c1) != sk_c8
| sk_c9 != sk_c7 ),
inference(paramodulation,[status(thm)],[f126,f182]) ).
fof(f201,plain,
( ~ sQ2_spl
| ~ sQ15_spl
| ~ sQ3_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f106,f197]) ).
fof(f202,plain,
( ~ sQ2_spl
| ~ sQ15_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f201]) ).
fof(f203,plain,
( ~ sQ2_spl
| ~ sQ15_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f202]) ).
fof(f206,plain,
! [X0] :
( ~ sQ2_spl
| multiply(sk_c7,X0) = multiply(sk_c4,multiply(sk_c8,X0)) ),
inference(paramodulation,[status(thm)],[f102,f49]) ).
fof(f215,plain,
( ~ sQ0_spl
| ~ sQ14_spl
| inverse(sk_c8) != sk_c9
| multiply(sk_c9,sk_c7) != sk_c8 ),
inference(paramodulation,[status(thm)],[f95,f196]) ).
fof(f216,plain,
( ~ sQ6_spl
| ~ sQ14_spl
| inverse(sk_c6) != sk_c9
| multiply(sk_c9,sk_c7) != sk_c8 ),
inference(paramodulation,[status(thm)],[f118,f196]) ).
fof(f217,plain,
( ~ sQ11_spl
| ~ sQ14_spl
| inverse(sk_c2) != sk_c9
| multiply(sk_c9,sk_c3) != sk_c8 ),
inference(paramodulation,[status(thm)],[f156,f196]) ).
fof(f218,definition,
( sQ17_spl
<=> multiply(sk_c9,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f220,plain,
( sQ17_spl
| multiply(sk_c9,sk_c7) != sk_c8 ),
inference(component_clause,[status(thm)],[f218]) ).
fof(f221,definition,
( sQ18_spl
<=> inverse(sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f224,plain,
( ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ18_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f215,f218,f221,f178,f94]) ).
fof(f225,plain,
( ~ sQ6_spl
| ~ sQ14_spl
| ~ sQ7_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f216,f218,f121,f178,f117]) ).
fof(f226,plain,
( ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f217,f145,f165,f178,f155]) ).
fof(f229,plain,
( ~ sQ7_spl
| multiply(sk_c9,sk_c6) = identity ),
inference(paramodulation,[status(thm)],[f122,f48]) ).
fof(f230,plain,
( ~ sQ3_spl
| multiply(sk_c8,sk_c4) = identity ),
inference(paramodulation,[status(thm)],[f106,f48]) ).
fof(f232,plain,
( ~ sQ5_spl
| multiply(sk_c8,sk_c5) = identity ),
inference(paramodulation,[status(thm)],[f114,f48]) ).
fof(f235,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f48,f49]) ).
fof(f236,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f47,f235]) ).
fof(f237,plain,
! [X0] :
( ~ sQ7_spl
| multiply(identity,X0) = multiply(sk_c9,multiply(sk_c6,X0)) ),
inference(paramodulation,[status(thm)],[f229,f49]) ).
fof(f238,plain,
! [X0] :
( ~ sQ7_spl
| X0 = multiply(sk_c9,multiply(sk_c6,X0)) ),
inference(forward_demodulation,[status(thm)],[f47,f237]) ).
fof(f239,plain,
! [X0] :
( ~ sQ3_spl
| multiply(identity,X0) = multiply(sk_c8,multiply(sk_c4,X0)) ),
inference(paramodulation,[status(thm)],[f230,f49]) ).
fof(f240,plain,
! [X0] :
( ~ sQ3_spl
| X0 = multiply(sk_c8,multiply(sk_c4,X0)) ),
inference(forward_demodulation,[status(thm)],[f47,f239]) ).
fof(f249,plain,
( ~ sQ4_spl
| ~ sQ13_spl
| inverse(sk_c5) != sk_c8 ),
inference(resolution,[status(thm)],[f176,f110]) ).
fof(f257,plain,
( ~ sQ8_spl
| ~ sQ13_spl
| inverse(sk_c1) != sk_c8
| sk_c9 != sk_c9 ),
inference(paramodulation,[status(thm)],[f126,f176]) ).
fof(f258,plain,
( ~ sQ4_spl
| ~ sQ13_spl
| ~ sQ5_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f114,f249]) ).
fof(f259,plain,
( ~ sQ4_spl
| ~ sQ13_spl
| ~ sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f258]) ).
fof(f260,plain,
( ~ sQ4_spl
| ~ sQ13_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f259]) ).
fof(f266,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| sk_c9 = multiply(sk_c9,sk_c7) ),
inference(paramodulation,[status(thm)],[f118,f238]) ).
fof(f269,plain,
( sQ17_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c9 != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f266,f220]) ).
fof(f272,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| sk_c8 = multiply(sk_c8,sk_c7) ),
inference(paramodulation,[status(thm)],[f102,f240]) ).
fof(f276,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| multiply(sk_c7,sk_c7) = multiply(sk_c4,sk_c8) ),
inference(paramodulation,[status(thm)],[f272,f206]) ).
fof(f278,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| multiply(sk_c7,sk_c7) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f102,f276]) ).
fof(f293,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| sk_c7 = multiply(inverse(sk_c7),sk_c7) ),
inference(paramodulation,[status(thm)],[f278,f236]) ).
fof(f297,plain,
( ~ sQ5_spl
| sk_c5 = multiply(inverse(sk_c8),identity) ),
inference(paramodulation,[status(thm)],[f232,f236]) ).
fof(f312,plain,
( ~ sQ11_spl
| sk_c9 = multiply(inverse(sk_c2),sk_c3) ),
inference(paramodulation,[status(thm)],[f156,f236]) ).
fof(f314,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| sk_c7 = identity ),
inference(forward_demodulation,[status(thm)],[f48,f293]) ).
fof(f317,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| sk_c5 = multiply(sk_c7,identity) ),
inference(forward_demodulation,[status(thm)],[f98,f297]) ).
fof(f325,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| sk_c9 = multiply(sk_c9,sk_c3) ),
inference(forward_demodulation,[status(thm)],[f166,f312]) ).
fof(f332,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ3_spl
| multiply(inverse(X0),X0) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f314,f48]) ).
fof(f333,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ3_spl
| multiply(sk_c7,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f314,f47]) ).
fof(f338,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c5 = identity ),
inference(forward_demodulation,[status(thm)],[f333,f317]) ).
fof(f339,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ1_spl
| multiply(sk_c5,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f347,f333]) ).
fof(f343,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| multiply(sk_c8,sk_c9) != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f347,f96]) ).
fof(f344,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| inverse(sk_c8) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f347,f98]) ).
fof(f347,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c5 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f314,f338]) ).
fof(f349,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ1_spl
| sk_c8 = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f339,f110]) ).
fof(f352,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ1_spl
| sQ17_spl
| ~ sQ6_spl
| ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f349,f269]) ).
fof(f353,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ1_spl
| sQ17_spl
| ~ sQ6_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f352]) ).
fof(f360,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ1_spl
| multiply(inverse(X0),X0) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f347,f332]) ).
fof(f366,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c9,sk_c9) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f349,f343]) ).
fof(f367,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| inverse(sk_c9) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f349,f344]) ).
fof(f368,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c5,sk_c9) = sk_c5 ),
inference(paramodulation,[status(thm)],[f367,f360]) ).
fof(f370,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c9 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f339,f368]) ).
fof(f373,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c9,sk_c5) != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f370,f366]) ).
fof(f379,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c5,sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f370,f373]) ).
fof(f380,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f339,f379]) ).
fof(f381,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f380]) ).
fof(f382,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f381]) ).
fof(f383,definition,
( sQ19_spl
<=> sk_c9 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f385,plain,
( sQ19_spl
| sk_c9 != sk_c7 ),
inference(component_clause,[status(thm)],[f383]) ).
fof(f386,plain,
( ~ sQ8_spl
| ~ sQ15_spl
| ~ sQ9_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f200,f383,f135,f181,f125]) ).
fof(f387,definition,
( sQ20_spl
<=> sk_c7 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f389,plain,
( sQ20_spl
| sk_c7 != sk_c7 ),
inference(component_clause,[status(thm)],[f387]) ).
fof(f392,plain,
( sQ20_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f389]) ).
fof(f393,plain,
sQ20_spl,
inference(contradiction_clause,[status(thm)],[f392]) ).
fof(f412,definition,
( sQ26_spl
<=> sk_c9 = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f414,plain,
( sQ26_spl
| sk_c9 != sk_c9 ),
inference(component_clause,[status(thm)],[f412]) ).
fof(f415,plain,
( ~ sQ8_spl
| ~ sQ13_spl
| ~ sQ9_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f257,f412,f135,f175,f125]) ).
fof(f416,plain,
( sQ26_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f414]) ).
fof(f417,plain,
sQ26_spl,
inference(contradiction_clause,[status(thm)],[f416]) ).
fof(f428,plain,
( ~ sQ8_spl
| sk_c8 = multiply(inverse(sk_c1),sk_c9) ),
inference(paramodulation,[status(thm)],[f126,f236]) ).
fof(f430,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c8 = multiply(sk_c8,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f136,f428]) ).
fof(f431,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sk_c9 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f325,f146]) ).
fof(f436,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| multiply(sk_c9,sk_c9) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f431,f95]) ).
fof(f438,plain,
( sQ1_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| inverse(sk_c9) != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f431,f99]) ).
fof(f442,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| inverse(sk_c1) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f431,f136]) ).
fof(f458,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sk_c9 = multiply(sk_c8,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f431,f430]) ).
fof(f459,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sk_c9 = multiply(sk_c9,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f431,f458]) ).
fof(f462,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c9 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f459,f436]) ).
fof(f463,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f462,f385]) ).
fof(f464,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sQ19_spl ),
inference(contradiction_clause,[status(thm)],[f463]) ).
fof(f465,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| sk_c9 = multiply(sk_c9,sk_c7) ),
inference(backward_demodulation,[status(thm)],[f462,f459]) ).
fof(f470,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ8_spl
| inverse(sk_c1) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f462,f442]) ).
fof(f472,plain,
( ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ12_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c2,sk_c7) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f462,f156]) ).
fof(f475,plain,
( sQ1_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c7) != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f462,f438]) ).
fof(f476,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f462,f431]) ).
fof(f479,plain,
( ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c2) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f462,f166]) ).
fof(f481,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| sk_c7 = multiply(sk_c9,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f462,f465]) ).
fof(f482,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| sk_c7 = multiply(sk_c7,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f462,f481]) ).
fof(f501,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| sk_c7 = multiply(inverse(sk_c7),sk_c7) ),
inference(paramodulation,[status(thm)],[f482,f236]) ).
fof(f503,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| sk_c7 = identity ),
inference(forward_demodulation,[status(thm)],[f48,f501]) ).
fof(f507,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| multiply(inverse(X0),X0) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f503,f48]) ).
fof(f510,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| multiply(sk_c7,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f503,f47]) ).
fof(f514,plain,
( ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ12_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 = multiply(inverse(sk_c2),sk_c3) ),
inference(paramodulation,[status(thm)],[f472,f236]) ).
fof(f516,plain,
( ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ12_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 = multiply(sk_c7,sk_c3) ),
inference(forward_demodulation,[status(thm)],[f479,f514]) ).
fof(f517,plain,
( ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ12_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f510,f516]) ).
fof(f519,plain,
( ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c7,sk_c2) = sk_c7 ),
inference(paramodulation,[status(thm)],[f479,f507]) ).
fof(f520,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ8_spl
| multiply(sk_c7,sk_c1) = sk_c7 ),
inference(paramodulation,[status(thm)],[f470,f507]) ).
fof(f523,plain,
( ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c2 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f510,f519]) ).
fof(f524,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sk_c1 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f510,f520]) ).
fof(f536,plain,
( ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c2) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f517,f479]) ).
fof(f540,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c3 = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f517,f476]) ).
fof(f542,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c9 = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f517,f462]) ).
fof(f545,plain,
( ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ12_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c7 = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f546,f517]) ).
fof(f546,plain,
( ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c2 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f517,f523]) ).
fof(f548,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c2 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f546,f540]) ).
fof(f553,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c9 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f546,f542]) ).
fof(f554,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sk_c2 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f555,f524]) ).
fof(f555,plain,
( ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ12_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c1 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f524,f545]) ).
fof(f559,plain,
( ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c2) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f546,f536]) ).
fof(f688,plain,
( ~ sQ0_spl
| ~ sQ16_spl
| ~ sQ18_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f190,f387,f221,f184,f94]) ).
fof(f693,plain,
( ~ sQ0_spl
| ~ sQ16_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c2) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f548,f188]) ).
fof(f694,plain,
( ~ sQ0_spl
| ~ sQ16_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c2 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f559,f693]) ).
fof(f695,plain,
( ~ sQ0_spl
| ~ sQ16_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f553,f694]) ).
fof(f696,plain,
( ~ sQ0_spl
| ~ sQ16_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ8_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f695]) ).
fof(f697,plain,
( ~ sQ0_spl
| ~ sQ16_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ8_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f696]) ).
fof(f700,plain,
( sQ1_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c2) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f554,f475]) ).
fof(f701,plain,
( sQ1_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c2 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f559,f700]) ).
fof(f702,plain,
( sQ1_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f554,f701]) ).
fof(f703,plain,
( sQ1_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f702]) ).
fof(f704,plain,
( sQ1_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f703]) ).
fof(f705,plain,
$false,
inference(sat_refutation,[status(thm)],[f100,f104,f108,f112,f116,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,f187,f195,f203,f224,f225,f226,f260,f353,f382,f386,f393,f415,f417,f464,f688,f697,f704]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP329-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.02/0.30 % Computer : n012.cluster.edu
% 0.02/0.30 % Model : x86_64 x86_64
% 0.02/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.30 % Memory : 8046.5625MB
% 0.02/0.30 % OS : Linux 6.8.0-71-generic
% 0.02/0.30 % CPULimit : 300
% 0.02/0.30 % WCLimit : 300
% 0.02/0.30 % DateTime : Sun Sep 20 20:09:24 UTC 2026
% 0.02/0.30 % CPUTime :
% 0.02/0.30 % Drodi V4.1.1
% 0.08/0.33 % Refutation found
% 0.08/0.33 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/0.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.34 % Elapsed time: 0.041618 seconds
% 0.08/0.34 % CPU time: 0.101000 seconds
% 0.08/0.34 % Total memory used: 104.283 MB
% 0.08/0.34 % Net memory used: 104.152 MB
%------------------------------------------------------------------------------