%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP225-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 12:33:09 PM UTC 2026
% Result : Unsatisfiable 0.16s 0.51s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 65
% Syntax : Number of formulae : 284 ( 12 unt; 29 def)
% Number of atoms : 924 ( 346 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 1204 ( 564 ~; 611 |; 0 &)
% ( 29 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 31 ( 29 usr; 30 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 68 ( 68 !; 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_c4) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c7,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( multiply(sk_c7,sk_c9) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c7,sk_c9) = sk_c8
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c4) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( inverse(sk_c6) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( multiply(sk_c7,sk_c9) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( inverse(sk_c4) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( inverse(sk_c6) = sk_c7
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
( multiply(sk_c7,sk_c9) = sk_c8
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
! [X4,X5,X6,X1,X2,X7,X3] :
( multiply(X3,sk_c9) != sk_c8
| inverse(X7) != X3
| multiply(X7,X3) != sk_c8
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c9
| multiply(X1,sk_c8) != sk_c9
| inverse(X1) != sk_c9
| inverse(X6) != sk_c9
| multiply(X6,sk_c9) != X5
| multiply(sk_c9,X5) != sk_c8
| multiply(X4,sk_c8) != sk_c9
| inverse(X4) != sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f41,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f42,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f43,plain,
( inverse(sk_c4) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f44,plain,
( multiply(sk_c4,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f45,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f46,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f47,plain,
( multiply(sk_c6,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f48,plain,
( inverse(sk_c6) = sk_c7
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f49,plain,
( multiply(sk_c7,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f50,plain,
( inverse(sk_c4) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f51,plain,
( multiply(sk_c4,sk_c8) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f52,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f53,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f54,plain,
( multiply(sk_c6,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f55,plain,
( inverse(sk_c6) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f56,plain,
( multiply(sk_c7,sk_c9) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f57,plain,
( inverse(sk_c4) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f59,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f60,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f61,plain,
( multiply(sk_c6,sk_c7) = sk_c8
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f62,plain,
( inverse(sk_c6) = sk_c7
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f63,plain,
( multiply(sk_c7,sk_c9) = sk_c8
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f64,plain,
( inverse(sk_c4) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f66,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f67,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f68,plain,
( multiply(sk_c6,sk_c7) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f69,plain,
( inverse(sk_c6) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f70,plain,
( multiply(sk_c7,sk_c9) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f71,plain,
( inverse(sk_c4) = sk_c9
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f73,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f74,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f75,plain,
( multiply(sk_c6,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f76,plain,
( inverse(sk_c6) = sk_c7
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f77,plain,
( multiply(sk_c7,sk_c9) = sk_c8
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f78,plain,
! [X3] :
( multiply(X3,sk_c9) != sk_c8
| ! [X7] :
( inverse(X7) != X3
| multiply(X7,X3) != sk_c8
| ! [X2] :
( inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c9
| ! [X1] :
( multiply(X1,sk_c8) != sk_c9
| inverse(X1) != sk_c9
| ! [X6] :
( inverse(X6) != sk_c9
| ! [X5] :
( multiply(X6,sk_c9) != X5
| multiply(sk_c9,X5) != sk_c8
| ! [X4] :
( multiply(X4,sk_c8) != sk_c9
| inverse(X4) != sk_c9 ) ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f39]) ).
fof(f79,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( multiply(X6,sk_c9) != sk_c8
| inverse(X5) != X6
| multiply(X5,X6) != sk_c8
| inverse(X4) != sk_c8
| multiply(X4,sk_c8) != sk_c9
| multiply(X3,sk_c8) != sk_c9
| inverse(X3) != sk_c9
| inverse(X2) != sk_c9
| multiply(X2,sk_c9) != X1
| multiply(sk_c9,X1) != sk_c8
| multiply(X0,sk_c8) != sk_c9
| inverse(X0) != sk_c9 ),
inference(cnf_transformation,[status(thm)],[f78]) ).
fof(f80,definition,
( sQ0_spl
<=> inverse(sk_c1) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f81,plain,
( ~ sQ0_spl
| inverse(sk_c1) = sk_c9 ),
inference(component_clause,[status(thm)],[f80]) ).
fof(f83,definition,
( sQ1_spl
<=> inverse(sk_c4) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f84,plain,
( ~ sQ1_spl
| inverse(sk_c4) = sk_c9 ),
inference(component_clause,[status(thm)],[f83]) ).
fof(f86,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f43,f80,f83]) ).
fof(f87,definition,
( sQ2_spl
<=> multiply(sk_c4,sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f88,plain,
( ~ sQ2_spl
| multiply(sk_c4,sk_c8) = sk_c9 ),
inference(component_clause,[status(thm)],[f87]) ).
fof(f90,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f44,f80,f87]) ).
fof(f91,definition,
( sQ3_spl
<=> multiply(sk_c5,sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f92,plain,
( ~ sQ3_spl
| multiply(sk_c5,sk_c8) = sk_c9 ),
inference(component_clause,[status(thm)],[f91]) ).
fof(f94,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f45,f80,f91]) ).
fof(f95,definition,
( sQ4_spl
<=> inverse(sk_c5) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f96,plain,
( ~ sQ4_spl
| inverse(sk_c5) = sk_c8 ),
inference(component_clause,[status(thm)],[f95]) ).
fof(f98,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f46,f80,f95]) ).
fof(f99,definition,
( sQ5_spl
<=> multiply(sk_c6,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f100,plain,
( ~ sQ5_spl
| multiply(sk_c6,sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f99]) ).
fof(f102,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f47,f80,f99]) ).
fof(f103,definition,
( sQ6_spl
<=> inverse(sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f104,plain,
( ~ sQ6_spl
| inverse(sk_c6) = sk_c7 ),
inference(component_clause,[status(thm)],[f103]) ).
fof(f106,plain,
( sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f48,f80,f103]) ).
fof(f107,definition,
( sQ7_spl
<=> multiply(sk_c7,sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f110,plain,
( sQ7_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f49,f80,f107]) ).
fof(f111,definition,
( sQ8_spl
<=> multiply(sk_c1,sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f112,plain,
( ~ sQ8_spl
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(component_clause,[status(thm)],[f111]) ).
fof(f114,plain,
( sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f50,f111,f83]) ).
fof(f115,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f51,f111,f87]) ).
fof(f116,plain,
( sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f52,f111,f91]) ).
fof(f117,plain,
( sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f53,f111,f95]) ).
fof(f118,plain,
( sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f54,f111,f99]) ).
fof(f119,plain,
( sQ6_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f55,f111,f103]) ).
fof(f120,plain,
( sQ7_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f56,f111,f107]) ).
fof(f121,definition,
( sQ9_spl
<=> multiply(sk_c9,sk_c3) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f122,plain,
( ~ sQ9_spl
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(component_clause,[status(thm)],[f121]) ).
fof(f124,plain,
( sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f57,f121,f83]) ).
fof(f126,plain,
( sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f59,f121,f91]) ).
fof(f127,plain,
( sQ4_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f60,f121,f95]) ).
fof(f128,plain,
( sQ5_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f61,f121,f99]) ).
fof(f129,plain,
( sQ6_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f62,f121,f103]) ).
fof(f130,plain,
( sQ7_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f63,f121,f107]) ).
fof(f131,definition,
( sQ10_spl
<=> multiply(sk_c2,sk_c9) = sk_c3 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f132,plain,
( ~ sQ10_spl
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(component_clause,[status(thm)],[f131]) ).
fof(f134,plain,
( sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f64,f131,f83]) ).
fof(f136,plain,
( sQ3_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f66,f131,f91]) ).
fof(f137,plain,
( sQ4_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f67,f131,f95]) ).
fof(f138,plain,
( sQ5_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f68,f131,f99]) ).
fof(f139,plain,
( sQ6_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f69,f131,f103]) ).
fof(f140,plain,
( sQ7_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f70,f131,f107]) ).
fof(f141,definition,
( sQ11_spl
<=> inverse(sk_c2) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f142,plain,
( ~ sQ11_spl
| inverse(sk_c2) = sk_c9 ),
inference(component_clause,[status(thm)],[f141]) ).
fof(f144,plain,
( sQ1_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f71,f141,f83]) ).
fof(f146,plain,
( sQ3_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f73,f141,f91]) ).
fof(f147,plain,
( sQ4_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f74,f141,f95]) ).
fof(f148,plain,
( sQ5_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f75,f141,f99]) ).
fof(f149,plain,
( sQ6_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f76,f141,f103]) ).
fof(f150,plain,
( sQ7_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f77,f141,f107]) ).
fof(f151,definition,
! [X0] :
( sQ12_spl
<=> ( multiply(X0,sk_c8) != sk_c9
| inverse(X0) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f152,plain,
! [X0] :
( ~ sQ12_spl
| multiply(X0,sk_c8) != sk_c9
| inverse(X0) != sk_c9 ),
inference(component_clause,[status(thm)],[f151]) ).
fof(f154,definition,
! [X1,X2] :
( sQ13_spl
<=> ( inverse(X2) != sk_c9
| multiply(X2,sk_c9) != X1
| multiply(sk_c9,X1) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f155,plain,
! [X0,X1] :
( ~ sQ13_spl
| inverse(X1) != sk_c9
| multiply(X1,sk_c9) != X0
| multiply(sk_c9,X0) != sk_c8 ),
inference(component_clause,[status(thm)],[f154]) ).
fof(f157,definition,
! [X4] :
( sQ14_spl
<=> ( inverse(X4) != sk_c8
| multiply(X4,sk_c8) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f158,plain,
! [X0] :
( ~ sQ14_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c9 ),
inference(component_clause,[status(thm)],[f157]) ).
fof(f160,definition,
! [X5,X6] :
( sQ15_spl
<=> ( multiply(X6,sk_c9) != sk_c8
| inverse(X5) != X6
| multiply(X5,X6) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f161,plain,
! [X0,X1] :
( ~ sQ15_spl
| multiply(X1,sk_c9) != sk_c8
| inverse(X0) != X1
| multiply(X0,X1) != sk_c8 ),
inference(component_clause,[status(thm)],[f160]) ).
fof(f163,plain,
( sQ15_spl
| sQ14_spl
| sQ13_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f79,f151,f154,f157,f160]) ).
fof(f164,plain,
! [X0] :
( ~ sQ15_spl
| multiply(inverse(X0),sk_c9) != sk_c8
| multiply(X0,inverse(X0)) != sk_c8 ),
inference(destructive_equality_resolution,[status(thm)],[f161]) ).
fof(f175,plain,
( ~ sQ1_spl
| ~ sQ15_spl
| multiply(sk_c9,sk_c9) != sk_c8
| multiply(sk_c4,inverse(sk_c4)) != sk_c8 ),
inference(paramodulation,[status(thm)],[f84,f164]) ).
fof(f177,plain,
( ~ sQ6_spl
| ~ sQ15_spl
| multiply(sk_c7,sk_c9) != sk_c8
| multiply(sk_c6,inverse(sk_c6)) != sk_c8 ),
inference(paramodulation,[status(thm)],[f104,f164]) ).
fof(f178,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| multiply(sk_c9,sk_c9) != sk_c8
| multiply(sk_c1,inverse(sk_c1)) != sk_c8 ),
inference(paramodulation,[status(thm)],[f81,f164]) ).
fof(f179,plain,
( ~ sQ11_spl
| ~ sQ15_spl
| multiply(sk_c9,sk_c9) != sk_c8
| multiply(sk_c2,inverse(sk_c2)) != sk_c8 ),
inference(paramodulation,[status(thm)],[f142,f164]) ).
fof(f180,definition,
( sQ16_spl
<=> multiply(sk_c4,inverse(sk_c4)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f183,definition,
( sQ17_spl
<=> multiply(sk_c9,sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f184,plain,
( ~ sQ17_spl
| multiply(sk_c9,sk_c9) = sk_c8 ),
inference(component_clause,[status(thm)],[f183]) ).
fof(f185,plain,
( sQ17_spl
| multiply(sk_c9,sk_c9) != sk_c8 ),
inference(component_clause,[status(thm)],[f183]) ).
fof(f186,plain,
( ~ sQ1_spl
| ~ sQ15_spl
| ~ sQ17_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f175,f180,f183,f160,f83]) ).
fof(f194,definition,
( sQ20_spl
<=> multiply(sk_c6,inverse(sk_c6)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f196,plain,
( sQ20_spl
| multiply(sk_c6,inverse(sk_c6)) != sk_c8 ),
inference(component_clause,[status(thm)],[f194]) ).
fof(f197,plain,
( ~ sQ6_spl
| ~ sQ15_spl
| ~ sQ7_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f177,f194,f107,f160,f103]) ).
fof(f198,definition,
( sQ21_spl
<=> multiply(sk_c1,inverse(sk_c1)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f200,plain,
( sQ21_spl
| multiply(sk_c1,inverse(sk_c1)) != sk_c8 ),
inference(component_clause,[status(thm)],[f198]) ).
fof(f201,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ17_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f178,f198,f183,f160,f80]) ).
fof(f202,definition,
( sQ22_spl
<=> multiply(sk_c2,inverse(sk_c2)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f205,plain,
( ~ sQ11_spl
| ~ sQ15_spl
| ~ sQ17_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f179,f202,f183,f160,f141]) ).
fof(f209,plain,
( ~ sQ0_spl
| ~ sQ14_spl
| sk_c9 != sk_c8
| multiply(sk_c1,sk_c8) != sk_c9 ),
inference(paramodulation,[status(thm)],[f81,f158]) ).
fof(f211,definition,
( sQ23_spl
<=> sk_c9 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f213,plain,
( sQ23_spl
| sk_c9 != sk_c8 ),
inference(component_clause,[status(thm)],[f211]) ).
fof(f214,plain,
( ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ23_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f209,f111,f211,f157,f80]) ).
fof(f215,definition,
( sQ24_spl
<=> multiply(sk_c2,sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f219,plain,
! [X0] :
( ~ sQ13_spl
| inverse(X0) != sk_c9
| multiply(sk_c9,multiply(X0,sk_c9)) != sk_c8 ),
inference(destructive_equality_resolution,[status(thm)],[f155]) ).
fof(f223,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f41,f42]) ).
fof(f224,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f40,f223]) ).
fof(f229,plain,
( ~ sQ13_spl
| inverse(inverse(sk_c9)) != sk_c9
| multiply(sk_c9,identity) != sk_c8 ),
inference(paramodulation,[status(thm)],[f41,f219]) ).
fof(f230,plain,
( ~ sQ13_spl
| inverse(identity) != sk_c9
| multiply(sk_c9,sk_c9) != sk_c8 ),
inference(paramodulation,[status(thm)],[f40,f219]) ).
fof(f232,plain,
( ~ sQ10_spl
| ~ sQ13_spl
| inverse(sk_c2) != sk_c9
| multiply(sk_c9,sk_c3) != sk_c8 ),
inference(paramodulation,[status(thm)],[f132,f219]) ).
fof(f233,definition,
( sQ25_spl
<=> multiply(sk_c9,identity) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f235,plain,
( sQ25_spl
| multiply(sk_c9,identity) != sk_c8 ),
inference(component_clause,[status(thm)],[f233]) ).
fof(f236,definition,
( sQ26_spl
<=> inverse(inverse(sk_c9)) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f239,plain,
( ~ sQ13_spl
| ~ sQ26_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f229,f233,f236,f154]) ).
fof(f240,definition,
( sQ27_spl
<=> inverse(identity) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f242,plain,
( sQ27_spl
| inverse(identity) != sk_c9 ),
inference(component_clause,[status(thm)],[f240]) ).
fof(f243,plain,
( ~ sQ13_spl
| ~ sQ27_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f230,f183,f240,f154]) ).
fof(f244,plain,
( ~ sQ10_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f232,f121,f141,f154,f131]) ).
fof(f246,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| multiply(sk_c2,sk_c8) != sk_c9
| sk_c9 != sk_c9 ),
inference(paramodulation,[status(thm)],[f142,f152]) ).
fof(f247,definition,
( sQ28_spl
<=> sk_c9 = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f249,plain,
( sQ28_spl
| sk_c9 != sk_c9 ),
inference(component_clause,[status(thm)],[f247]) ).
fof(f250,plain,
( ~ sQ11_spl
| ~ sQ12_spl
| ~ sQ24_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f246,f247,f215,f151,f141]) ).
fof(f251,plain,
( sQ28_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f249]) ).
fof(f252,plain,
sQ28_spl,
inference(contradiction_clause,[status(thm)],[f251]) ).
fof(f253,plain,
( ~ sQ1_spl
| multiply(sk_c9,sk_c4) = identity ),
inference(paramodulation,[status(thm)],[f84,f41]) ).
fof(f257,plain,
( sQ20_spl
| ~ sQ6_spl
| multiply(sk_c6,sk_c7) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f104,f196]) ).
fof(f259,plain,
( sQ20_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f100,f257]) ).
fof(f260,plain,
( sQ20_spl
| ~ sQ6_spl
| ~ sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f259]) ).
fof(f261,plain,
( sQ20_spl
| ~ sQ6_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f260]) ).
fof(f271,plain,
( ~ sQ4_spl
| ~ sQ14_spl
| multiply(sk_c5,sk_c8) != sk_c9 ),
inference(resolution,[status(thm)],[f158,f96]) ).
fof(f276,plain,
( ~ sQ4_spl
| ~ sQ14_spl
| ~ sQ3_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f92,f271]) ).
fof(f277,plain,
( ~ sQ4_spl
| ~ sQ14_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f276]) ).
fof(f278,plain,
( ~ sQ4_spl
| ~ sQ14_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f277]) ).
fof(f303,plain,
( ~ sQ8_spl
| sk_c8 = multiply(inverse(sk_c1),sk_c9) ),
inference(paramodulation,[status(thm)],[f112,f224]) ).
fof(f311,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f40,f224]) ).
fof(f313,plain,
( ~ sQ2_spl
| sk_c8 = multiply(inverse(sk_c4),sk_c9) ),
inference(paramodulation,[status(thm)],[f88,f224]) ).
fof(f314,plain,
( ~ sQ3_spl
| sk_c8 = multiply(inverse(sk_c5),sk_c9) ),
inference(paramodulation,[status(thm)],[f92,f224]) ).
fof(f318,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| sk_c8 = multiply(sk_c9,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f81,f303]) ).
fof(f319,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f318,f185]) ).
fof(f320,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f319]) ).
fof(f321,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sk_c8 = multiply(sk_c9,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f84,f313]) ).
fof(f322,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f321,f185]) ).
fof(f323,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f322]) ).
fof(f324,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c8 = multiply(sk_c8,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f96,f314]) ).
fof(f327,plain,
( sQ21_spl
| ~ sQ0_spl
| multiply(sk_c1,sk_c9) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f81,f200]) ).
fof(f333,plain,
( ~ sQ13_spl
| inverse(inverse(identity)) != sk_c9
| multiply(sk_c9,sk_c9) != sk_c8 ),
inference(paramodulation,[status(thm)],[f311,f219]) ).
fof(f336,definition,
( sQ31_spl
<=> inverse(inverse(identity)) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f339,plain,
( ~ sQ13_spl
| ~ sQ31_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f333,f183,f336,f154]) ).
fof(f341,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c9 = multiply(inverse(sk_c8),sk_c8) ),
inference(paramodulation,[status(thm)],[f324,f224]) ).
fof(f347,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c9 = identity ),
inference(forward_demodulation,[status(thm)],[f41,f341]) ).
fof(f352,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c9,sk_c4) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f347,f253]) ).
fof(f354,plain,
( sQ25_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c9,sk_c9) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f347,f235]) ).
fof(f355,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| multiply(inverse(X0),X0) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f347,f41]) ).
fof(f356,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c9,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f347,f40]) ).
fof(f357,plain,
( sQ25_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f354,f183,f95,f91,f233]) ).
fof(f370,plain,
( ~ sQ10_spl
| sk_c9 = multiply(inverse(sk_c2),sk_c3) ),
inference(paramodulation,[status(thm)],[f132,f224]) ).
fof(f372,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| sk_c9 = multiply(sk_c9,sk_c3) ),
inference(forward_demodulation,[status(thm)],[f142,f370]) ).
fof(f373,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sk_c9 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f122,f372]) ).
fof(f374,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f373,f213]) ).
fof(f375,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sQ23_spl ),
inference(contradiction_clause,[status(thm)],[f374]) ).
fof(f378,plain,
( ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c3 = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f356,f122]) ).
fof(f385,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c1,sk_c3) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f378,f112]) ).
fof(f386,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c3 = multiply(inverse(sk_c1),sk_c9) ),
inference(paramodulation,[status(thm)],[f385,f224]) ).
fof(f388,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sk_c3 = multiply(sk_c9,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f81,f386]) ).
fof(f389,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sk_c3 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f356,f388]) ).
fof(f400,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| sk_c3 = identity ),
inference(backward_demodulation,[status(thm)],[f389,f347]) ).
fof(f402,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ4_spl
| inverse(sk_c1) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f389,f81]) ).
fof(f403,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| multiply(sk_c3,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f400,f40]) ).
fof(f424,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| multiply(inverse(X0),X0) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f400,f41]) ).
fof(f425,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c3,sk_c1) = sk_c3 ),
inference(paramodulation,[status(thm)],[f402,f424]) ).
fof(f431,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c1 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f403,f425]) ).
fof(f444,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ4_spl
| inverse(sk_c3) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f431,f402]) ).
fof(f450,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ0_spl
| multiply(X0,sk_c8) != sk_c9
| inverse(X0) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f389,f152]) ).
fof(f451,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ0_spl
| multiply(X0,sk_c3) != sk_c9
| inverse(X0) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f378,f450]) ).
fof(f452,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ0_spl
| multiply(X0,sk_c3) != sk_c3
| inverse(X0) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f389,f451]) ).
fof(f461,plain,
( ~ sQ12_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ0_spl
| multiply(sk_c3,sk_c3) != sk_c3 ),
inference(resolution,[status(thm)],[f444,f452]) ).
fof(f465,plain,
( ~ sQ12_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f403,f461]) ).
fof(f466,plain,
( ~ sQ12_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f465]) ).
fof(f467,plain,
( ~ sQ12_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f466]) ).
fof(f471,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| multiply(X0,sk_c8) != sk_c9
| inverse(X0) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f373,f152]) ).
fof(f472,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| multiply(X0,sk_c8) != sk_c8
| inverse(X0) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f373,f471]) ).
fof(f483,definition,
( sQ36_spl
<=> sk_c8 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f485,plain,
( sQ36_spl
| sk_c8 != sk_c8 ),
inference(component_clause,[status(thm)],[f483]) ).
fof(f487,plain,
( sQ36_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f485]) ).
fof(f488,plain,
sQ36_spl,
inference(contradiction_clause,[status(thm)],[f487]) ).
fof(f489,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| inverse(sk_c1) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f373,f81]) ).
fof(f550,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| identity = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f41,f355]) ).
fof(f566,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ17_spl
| multiply(sk_c8,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f573,f356]) ).
fof(f569,plain,
( ~ sQ1_spl
| ~ sQ17_spl
| ~ sQ3_spl
| ~ sQ4_spl
| inverse(sk_c4) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f573,f84]) ).
fof(f571,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ17_spl
| identity = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f573,f550]) ).
fof(f573,plain,
( ~ sQ17_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c9 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f356,f184]) ).
fof(f576,plain,
( ~ sQ3_spl
| ~ sQ17_spl
| ~ sQ4_spl
| multiply(sk_c5,sk_c8) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f573,f92]) ).
fof(f582,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ17_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(X0,sk_c8) != sk_c9
| inverse(X0) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f573,f152]) ).
fof(f583,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ17_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(X0,sk_c8) != sk_c8
| inverse(X0) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f573,f582]) ).
fof(f584,plain,
( ~ sQ4_spl
| ~ sQ12_spl
| ~ sQ17_spl
| ~ sQ3_spl
| multiply(sk_c5,sk_c8) != sk_c8 ),
inference(resolution,[status(thm)],[f583,f96]) ).
fof(f587,plain,
( ~ sQ4_spl
| ~ sQ12_spl
| ~ sQ17_spl
| ~ sQ3_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f576,f584]) ).
fof(f588,plain,
( ~ sQ4_spl
| ~ sQ12_spl
| ~ sQ17_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f587]) ).
fof(f589,plain,
( ~ sQ4_spl
| ~ sQ12_spl
| ~ sQ17_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f588]) ).
fof(f624,plain,
( ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| multiply(sk_c1,sk_c8) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f373,f112]) ).
fof(f625,plain,
( ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| inverse(sk_c1) != sk_c8 ),
inference(resolution,[status(thm)],[f624,f472]) ).
fof(f629,plain,
( ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f489,f625]) ).
fof(f630,plain,
( ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f629]) ).
fof(f631,plain,
( ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f630]) ).
fof(f641,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ0_spl
| multiply(sk_c3,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f400,f40]) ).
fof(f650,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ0_spl
| inverse(X0) != sk_c9
| multiply(sk_c3,multiply(X0,sk_c9)) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f389,f219]) ).
fof(f651,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ0_spl
| inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f641,f650]) ).
fof(f652,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ0_spl
| inverse(X0) != sk_c9
| multiply(X0,sk_c3) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f389,f651]) ).
fof(f653,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ0_spl
| inverse(X0) != sk_c9
| multiply(X0,sk_c3) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f378,f652]) ).
fof(f654,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ0_spl
| inverse(X0) != sk_c3
| multiply(X0,sk_c3) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f389,f653]) ).
fof(f655,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ4_spl
| inverse(sk_c3) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f431,f81]) ).
fof(f656,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ4_spl
| inverse(sk_c3) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f389,f655]) ).
fof(f657,plain,
( ~ sQ13_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ0_spl
| multiply(sk_c3,sk_c3) != sk_c3 ),
inference(resolution,[status(thm)],[f656,f654]) ).
fof(f661,plain,
( ~ sQ13_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ0_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f641,f657]) ).
fof(f662,plain,
( ~ sQ13_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f661]) ).
fof(f663,plain,
( ~ sQ13_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f662]) ).
fof(f672,plain,
( sQ27_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ17_spl
| inverse(sk_c8) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f571,f242]) ).
fof(f673,plain,
( sQ27_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ17_spl
| inverse(sk_c8) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f573,f672]) ).
fof(f708,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ17_spl
| multiply(sk_c8,sk_c4) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f573,f352]) ).
fof(f709,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ17_spl
| sk_c4 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f566,f708]) ).
fof(f711,plain,
( ~ sQ1_spl
| ~ sQ17_spl
| ~ sQ3_spl
| ~ sQ4_spl
| inverse(sk_c8) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f712,f569]) ).
fof(f712,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ17_spl
| sk_c4 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f573,f709]) ).
fof(f713,plain,
( ~ sQ1_spl
| ~ sQ17_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sQ27_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f711,f673]) ).
fof(f714,plain,
( ~ sQ1_spl
| ~ sQ17_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sQ27_spl ),
inference(contradiction_clause,[status(thm)],[f713]) ).
fof(f809,plain,
( sQ21_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| multiply(sk_c1,sk_c8) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f373,f327]) ).
fof(f810,plain,
( sQ21_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f624,f809]) ).
fof(f811,plain,
( sQ21_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f810]) ).
fof(f812,plain,
( sQ21_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f811]) ).
fof(f813,plain,
$false,
inference(sat_refutation,[status(thm)],[f86,f90,f94,f98,f102,f106,f110,f114,f115,f116,f117,f118,f119,f120,f124,f126,f127,f128,f129,f130,f134,f136,f137,f138,f139,f140,f144,f146,f147,f148,f149,f150,f163,f186,f197,f201,f205,f214,f239,f243,f244,f250,f252,f261,f278,f320,f323,f339,f357,f375,f467,f488,f589,f631,f663,f714,f812]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP225-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.44 % Computer : n010.cluster.edu
% 0.16/0.44 % Model : x86_64 x86_64
% 0.16/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.44 % Memory : 8046.5625MB
% 0.16/0.44 % OS : Linux 6.8.0-71-generic
% 0.16/0.44 % CPULimit : 300
% 0.16/0.44 % WCLimit : 300
% 0.16/0.44 % DateTime : Sun Sep 20 20:07:09 UTC 2026
% 0.16/0.45 % CPUTime :
% 0.16/0.48 % Drodi V4.1.1
% 0.16/0.51 % Refutation found
% 0.16/0.51 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.16/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.56 % Elapsed time: 0.105090 seconds
% 0.16/0.56 % CPU time: 0.255676 seconds
% 0.16/0.56 % Total memory used: 41.415 MB
% 0.16/0.56 % Net memory used: 41.345 MB
%------------------------------------------------------------------------------