%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP370-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 12:33:32 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.41s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 65
% Syntax : Number of formulae : 297 ( 19 unt; 35 def)
% Number of atoms : 877 ( 339 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 1091 ( 511 ~; 545 |; 0 &)
% ( 35 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 37 ( 35 usr; 36 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 73 ( 73 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c3) = sk_c9
| multiply(sk_c7,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c9,sk_c6) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( inverse(sk_c5) = sk_c9
| multiply(sk_c7,sk_c8) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c3) = sk_c9
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( multiply(sk_c9,sk_c6) = sk_c7
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c6
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c5) = sk_c9
| multiply(sk_c1,sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c3) = sk_c9
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c4) = sk_c7
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c9,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c6
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( inverse(sk_c5) = sk_c9
| inverse(sk_c1) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( multiply(sk_c3,sk_c9) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( inverse(sk_c3) = sk_c9
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( multiply(sk_c9,sk_c6) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( multiply(sk_c5,sk_c9) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( inverse(sk_c5) = sk_c9
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
! [X3,X4,X1,X2,X5,X6] :
( inverse(X6) != sk_c9
| multiply(X6,sk_c9) != X5
| multiply(sk_c9,X5) != sk_c7
| inverse(X2) != sk_c7
| multiply(X2,sk_c7) != sk_c8
| inverse(X1) != sk_c9
| multiply(X1,sk_c9) != sk_c8
| multiply(X4,sk_c7) != sk_c8
| inverse(X3) != X4
| multiply(X3,X4) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f34,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f35,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f36,plain,
( multiply(sk_c3,sk_c9) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f37,plain,
( inverse(sk_c3) = sk_c9
| multiply(sk_c7,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f40,plain,
( multiply(sk_c9,sk_c6) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f41,plain,
( multiply(sk_c5,sk_c9) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f42,plain,
( inverse(sk_c5) = sk_c9
| multiply(sk_c7,sk_c8) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f43,plain,
( multiply(sk_c3,sk_c9) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f44,plain,
( inverse(sk_c3) = sk_c9
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f45,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f46,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f47,plain,
( multiply(sk_c9,sk_c6) = sk_c7
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f48,plain,
( multiply(sk_c5,sk_c9) = sk_c6
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f49,plain,
( inverse(sk_c5) = sk_c9
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f50,plain,
( multiply(sk_c3,sk_c9) = sk_c8
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f51,plain,
( inverse(sk_c3) = sk_c9
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f52,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f53,plain,
( inverse(sk_c4) = sk_c7
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f54,plain,
( multiply(sk_c9,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f55,plain,
( multiply(sk_c5,sk_c9) = sk_c6
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f56,plain,
( inverse(sk_c5) = sk_c9
| inverse(sk_c1) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f57,plain,
( multiply(sk_c3,sk_c9) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f58,plain,
( inverse(sk_c3) = sk_c9
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f59,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f60,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f61,plain,
( multiply(sk_c9,sk_c6) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f62,plain,
( multiply(sk_c5,sk_c9) = sk_c6
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f63,plain,
( inverse(sk_c5) = sk_c9
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f64,plain,
! [X6] :
( inverse(X6) != sk_c9
| ! [X5] :
( multiply(X6,sk_c9) != X5
| multiply(sk_c9,X5) != sk_c7
| ! [X2] :
( inverse(X2) != sk_c7
| multiply(X2,sk_c7) != sk_c8
| ! [X1] :
( inverse(X1) != sk_c9
| multiply(X1,sk_c9) != sk_c8
| ! [X4] :
( multiply(X4,sk_c7) != sk_c8
| ! [X3] :
( inverse(X3) != X4
| multiply(X3,X4) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c9 ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f32]) ).
fof(f65,plain,
! [X0,X1,X2,X3,X4,X5] :
( inverse(X5) != sk_c9
| multiply(X5,sk_c9) != X4
| multiply(sk_c9,X4) != sk_c7
| inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| inverse(X2) != sk_c9
| multiply(X2,sk_c9) != sk_c8
| multiply(X1,sk_c7) != sk_c8
| inverse(X0) != X1
| multiply(X0,X1) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c9 ),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f66,definition,
( sQ0_spl
<=> multiply(sk_c7,sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f67,plain,
( ~ sQ0_spl
| multiply(sk_c7,sk_c8) = sk_c9 ),
inference(component_clause,[status(thm)],[f66]) ).
fof(f68,plain,
( sQ0_spl
| multiply(sk_c7,sk_c8) != sk_c9 ),
inference(component_clause,[status(thm)],[f66]) ).
fof(f69,definition,
( sQ1_spl
<=> multiply(sk_c3,sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f70,plain,
( ~ sQ1_spl
| multiply(sk_c3,sk_c9) = sk_c8 ),
inference(component_clause,[status(thm)],[f69]) ).
fof(f72,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f36,f66,f69]) ).
fof(f73,definition,
( sQ2_spl
<=> inverse(sk_c3) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f74,plain,
( ~ sQ2_spl
| inverse(sk_c3) = sk_c9 ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f76,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f37,f66,f73]) ).
fof(f77,definition,
( sQ3_spl
<=> multiply(sk_c4,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f78,plain,
( ~ sQ3_spl
| multiply(sk_c4,sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f77]) ).
fof(f81,definition,
( sQ4_spl
<=> inverse(sk_c4) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f82,plain,
( ~ sQ4_spl
| inverse(sk_c4) = sk_c7 ),
inference(component_clause,[status(thm)],[f81]) ).
fof(f85,definition,
( sQ5_spl
<=> multiply(sk_c9,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ5_spl
| multiply(sk_c9,sk_c6) = sk_c7 ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f88,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f40,f66,f85]) ).
fof(f89,definition,
( sQ6_spl
<=> multiply(sk_c5,sk_c9) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f90,plain,
( ~ sQ6_spl
| multiply(sk_c5,sk_c9) = sk_c6 ),
inference(component_clause,[status(thm)],[f89]) ).
fof(f92,plain,
( sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f41,f66,f89]) ).
fof(f93,definition,
( sQ7_spl
<=> inverse(sk_c5) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ7_spl
| inverse(sk_c5) = sk_c9 ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f96,plain,
( sQ7_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f42,f66,f93]) ).
fof(f97,definition,
( sQ8_spl
<=> multiply(sk_c1,sk_c2) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f98,plain,
( ~ sQ8_spl
| multiply(sk_c1,sk_c2) = sk_c8 ),
inference(component_clause,[status(thm)],[f97]) ).
fof(f100,plain,
( sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f43,f97,f69]) ).
fof(f101,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f44,f97,f73]) ).
fof(f102,plain,
( sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f45,f97,f77]) ).
fof(f103,plain,
( sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f46,f97,f81]) ).
fof(f104,plain,
( sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f47,f97,f85]) ).
fof(f105,plain,
( sQ6_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f48,f97,f89]) ).
fof(f106,plain,
( sQ7_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f49,f97,f93]) ).
fof(f107,definition,
( sQ9_spl
<=> inverse(sk_c1) = sk_c2 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f108,plain,
( ~ sQ9_spl
| inverse(sk_c1) = sk_c2 ),
inference(component_clause,[status(thm)],[f107]) ).
fof(f110,plain,
( sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f50,f107,f69]) ).
fof(f111,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f51,f107,f73]) ).
fof(f112,plain,
( sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f52,f107,f77]) ).
fof(f113,plain,
( sQ4_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f53,f107,f81]) ).
fof(f114,plain,
( sQ5_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f54,f107,f85]) ).
fof(f115,plain,
( sQ6_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f55,f107,f89]) ).
fof(f116,plain,
( sQ7_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f56,f107,f93]) ).
fof(f117,definition,
( sQ10_spl
<=> multiply(sk_c2,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f118,plain,
( ~ sQ10_spl
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f117]) ).
fof(f120,plain,
( sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f57,f117,f69]) ).
fof(f121,plain,
( sQ2_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f58,f117,f73]) ).
fof(f122,plain,
( sQ3_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f59,f117,f77]) ).
fof(f123,plain,
( sQ4_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f60,f117,f81]) ).
fof(f124,plain,
( sQ5_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f61,f117,f85]) ).
fof(f125,plain,
( sQ6_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f62,f117,f89]) ).
fof(f126,plain,
( sQ7_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f63,f117,f93]) ).
fof(f127,definition,
! [X0,X1] :
( sQ11_spl
<=> ( multiply(X1,sk_c7) != sk_c8
| inverse(X0) != X1
| multiply(X0,X1) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f128,plain,
! [X0,X1] :
( ~ sQ11_spl
| multiply(X1,sk_c7) != sk_c8
| inverse(X0) != X1
| multiply(X0,X1) != sk_c8 ),
inference(component_clause,[status(thm)],[f127]) ).
fof(f130,definition,
! [X2] :
( sQ12_spl
<=> ( inverse(X2) != sk_c9
| multiply(X2,sk_c9) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f131,plain,
! [X0] :
( ~ sQ12_spl
| inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c8 ),
inference(component_clause,[status(thm)],[f130]) ).
fof(f133,definition,
! [X3] :
( sQ13_spl
<=> ( inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f134,plain,
! [X0] :
( ~ sQ13_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c8 ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,definition,
! [X4,X5] :
( sQ14_spl
<=> ( inverse(X5) != sk_c9
| multiply(X5,sk_c9) != X4
| multiply(sk_c9,X4) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f137,plain,
! [X0,X1] :
( ~ sQ14_spl
| inverse(X1) != sk_c9
| multiply(X1,sk_c9) != X0
| multiply(sk_c9,X0) != sk_c7 ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f139,plain,
( sQ14_spl
| sQ13_spl
| sQ12_spl
| sQ11_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f65,f66,f127,f130,f133,f136]) ).
fof(f140,plain,
! [X0] :
( ~ sQ14_spl
| inverse(X0) != sk_c9
| multiply(sk_c9,multiply(X0,sk_c9)) != sk_c7 ),
inference(destructive_equality_resolution,[status(thm)],[f137]) ).
fof(f142,plain,
! [X0] :
( ~ sQ0_spl
| multiply(sk_c9,X0) = multiply(sk_c7,multiply(sk_c8,X0)) ),
inference(paramodulation,[status(thm)],[f67,f35]) ).
fof(f147,plain,
! [X0] :
( ~ sQ8_spl
| multiply(sk_c8,X0) = multiply(sk_c1,multiply(sk_c2,X0)) ),
inference(paramodulation,[status(thm)],[f98,f35]) ).
fof(f155,plain,
( ~ sQ1_spl
| ~ sQ14_spl
| inverse(sk_c3) != sk_c9
| multiply(sk_c9,sk_c8) != sk_c7 ),
inference(paramodulation,[status(thm)],[f70,f140]) ).
fof(f156,plain,
( ~ sQ6_spl
| ~ sQ14_spl
| inverse(sk_c5) != sk_c9
| multiply(sk_c9,sk_c6) != sk_c7 ),
inference(paramodulation,[status(thm)],[f90,f140]) ).
fof(f157,definition,
( sQ15_spl
<=> multiply(sk_c9,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f159,plain,
( sQ15_spl
| multiply(sk_c9,sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f157]) ).
fof(f160,plain,
( ~ sQ1_spl
| ~ sQ14_spl
| ~ sQ2_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f155,f157,f73,f136,f69]) ).
fof(f161,plain,
( ~ sQ6_spl
| ~ sQ14_spl
| ~ sQ7_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f156,f85,f93,f136,f89]) ).
fof(f162,plain,
! [X0] :
( ~ sQ11_spl
| multiply(inverse(X0),sk_c7) != sk_c8
| multiply(X0,inverse(X0)) != sk_c8 ),
inference(destructive_equality_resolution,[status(thm)],[f128]) ).
fof(f163,plain,
( ~ sQ4_spl
| ~ sQ13_spl
| multiply(sk_c4,sk_c7) != sk_c8 ),
inference(resolution,[status(thm)],[f134,f82]) ).
fof(f167,plain,
( ~ sQ4_spl
| ~ sQ13_spl
| ~ sQ3_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f78,f163]) ).
fof(f168,plain,
( ~ sQ4_spl
| ~ sQ13_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f167]) ).
fof(f169,plain,
( ~ sQ4_spl
| ~ sQ13_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f168]) ).
fof(f173,plain,
( ~ sQ9_spl
| multiply(sk_c2,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f108,f34]) ).
fof(f174,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f34,f35]) ).
fof(f175,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f33,f174]) ).
fof(f186,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f175,f175]) ).
fof(f188,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f33,f175]) ).
fof(f192,plain,
( ~ sQ0_spl
| sk_c8 = multiply(inverse(sk_c7),sk_c9) ),
inference(paramodulation,[status(thm)],[f67,f175]) ).
fof(f193,plain,
( ~ sQ6_spl
| sk_c9 = multiply(inverse(sk_c5),sk_c6) ),
inference(paramodulation,[status(thm)],[f90,f175]) ).
fof(f194,plain,
( ~ sQ8_spl
| sk_c2 = multiply(inverse(sk_c1),sk_c8) ),
inference(paramodulation,[status(thm)],[f98,f175]) ).
fof(f195,plain,
( ~ sQ9_spl
| sk_c1 = multiply(inverse(sk_c2),identity) ),
inference(paramodulation,[status(thm)],[f173,f175]) ).
fof(f196,plain,
( ~ sQ10_spl
| sk_c7 = multiply(inverse(sk_c2),sk_c8) ),
inference(paramodulation,[status(thm)],[f118,f175]) ).
fof(f198,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| sk_c9 = multiply(sk_c9,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f94,f193]) ).
fof(f199,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c2 = multiply(sk_c2,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f108,f194]) ).
fof(f205,plain,
! [X0] : X0 = multiply(inverse(inverse(identity)),X0),
inference(paramodulation,[status(thm)],[f188,f175]) ).
fof(f208,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| sk_c6 = multiply(inverse(sk_c9),sk_c9) ),
inference(paramodulation,[status(thm)],[f198,f175]) ).
fof(f210,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f34,f208]) ).
fof(f213,plain,
( ~ sQ7_spl
| ~ sQ12_spl
| sk_c9 != sk_c9
| multiply(sk_c5,sk_c9) != sk_c8 ),
inference(paramodulation,[status(thm)],[f94,f131]) ).
fof(f223,definition,
( sQ18_spl
<=> multiply(sk_c5,sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f225,plain,
( sQ18_spl
| multiply(sk_c5,sk_c9) != sk_c8 ),
inference(component_clause,[status(thm)],[f223]) ).
fof(f226,definition,
( sQ19_spl
<=> sk_c9 = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f228,plain,
( sQ19_spl
| sk_c9 != sk_c9 ),
inference(component_clause,[status(thm)],[f226]) ).
fof(f229,plain,
( ~ sQ7_spl
| ~ sQ12_spl
| ~ sQ19_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f213,f223,f226,f130,f93]) ).
fof(f237,plain,
( sQ19_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f228]) ).
fof(f238,plain,
sQ19_spl,
inference(contradiction_clause,[status(thm)],[f237]) ).
fof(f239,plain,
( sQ18_spl
| ~ sQ6_spl
| sk_c6 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f90,f225]) ).
fof(f240,plain,
( ~ sQ11_spl
| sk_c7 != sk_c8
| multiply(identity,inverse(identity)) != sk_c8 ),
inference(paramodulation,[status(thm)],[f188,f162]) ).
fof(f241,plain,
( ~ sQ11_spl
| identity != sk_c8
| multiply(sk_c7,inverse(sk_c7)) != sk_c8 ),
inference(paramodulation,[status(thm)],[f34,f162]) ).
fof(f242,plain,
( ~ sQ9_spl
| ~ sQ11_spl
| multiply(sk_c2,sk_c7) != sk_c8
| multiply(sk_c1,inverse(sk_c1)) != sk_c8 ),
inference(paramodulation,[status(thm)],[f108,f162]) ).
fof(f243,definition,
( sQ22_spl
<=> multiply(identity,inverse(identity)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f244,plain,
( ~ sQ22_spl
| multiply(identity,inverse(identity)) = sk_c8 ),
inference(component_clause,[status(thm)],[f243]) ).
fof(f245,plain,
( sQ22_spl
| multiply(identity,inverse(identity)) != sk_c8 ),
inference(component_clause,[status(thm)],[f243]) ).
fof(f246,definition,
( sQ23_spl
<=> sk_c7 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f249,plain,
( ~ sQ11_spl
| ~ sQ23_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f240,f243,f246,f127]) ).
fof(f250,definition,
( sQ24_spl
<=> multiply(sk_c7,inverse(sk_c7)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f253,definition,
( sQ25_spl
<=> identity = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f255,plain,
( sQ25_spl
| identity != sk_c8 ),
inference(component_clause,[status(thm)],[f253]) ).
fof(f256,plain,
( ~ sQ11_spl
| ~ sQ25_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f241,f250,f253,f127]) ).
fof(f257,definition,
( sQ26_spl
<=> multiply(sk_c1,inverse(sk_c1)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f259,plain,
( sQ26_spl
| multiply(sk_c1,inverse(sk_c1)) != sk_c8 ),
inference(component_clause,[status(thm)],[f257]) ).
fof(f260,plain,
( ~ sQ9_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f242,f257,f117,f127,f107]) ).
fof(f261,plain,
( sQ26_spl
| ~ sQ9_spl
| multiply(sk_c1,sk_c2) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f108,f259]) ).
fof(f262,plain,
( sQ26_spl
| ~ sQ9_spl
| ~ sQ8_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f98,f261]) ).
fof(f263,plain,
( sQ26_spl
| ~ sQ9_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f262]) ).
fof(f264,plain,
( sQ26_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f263]) ).
fof(f269,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ7_spl
| multiply(inverse(X0),X0) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f210,f34]) ).
fof(f278,plain,
( ~ sQ1_spl
| sk_c9 = multiply(inverse(sk_c3),sk_c8) ),
inference(paramodulation,[status(thm)],[f70,f175]) ).
fof(f280,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c9 = multiply(sk_c9,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f74,f278]) ).
fof(f290,plain,
( sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| multiply(sk_c9,sk_c8) != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f295,f68]) ).
fof(f295,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| sk_c9 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f86,f198]) ).
fof(f313,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f280,f290]) ).
fof(f314,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f313]) ).
fof(f319,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| sk_c8 = multiply(inverse(sk_c9),sk_c9) ),
inference(forward_demodulation,[status(thm)],[f295,f192]) ).
fof(f320,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| sk_c8 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f269,f319]) ).
fof(f321,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f320,f239]) ).
fof(f322,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ5_spl
| sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f321]) ).
fof(f329,plain,
( ~ sQ14_spl
| inverse(identity) != sk_c9
| multiply(sk_c9,sk_c9) != sk_c7 ),
inference(paramodulation,[status(thm)],[f33,f140]) ).
fof(f332,definition,
( sQ27_spl
<=> multiply(sk_c9,sk_c9) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f335,definition,
( sQ28_spl
<=> inverse(identity) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f338,plain,
( ~ sQ14_spl
| ~ sQ28_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f329,f332,f335,f136]) ).
fof(f342,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 = multiply(inverse(sk_c9),sk_c9) ),
inference(paramodulation,[status(thm)],[f280,f175]) ).
fof(f347,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c8 = multiply(inverse(sk_c2),sk_c2) ),
inference(paramodulation,[status(thm)],[f199,f175]) ).
fof(f351,plain,
( ~ sQ10_spl
| sk_c7 = multiply(inverse(sk_c2),sk_c8) ),
inference(paramodulation,[status(thm)],[f118,f175]) ).
fof(f360,plain,
( ~ sQ2_spl
| ~ sQ12_spl
| multiply(sk_c3,sk_c9) != sk_c8 ),
inference(resolution,[status(thm)],[f131,f74]) ).
fof(f363,plain,
( ~ sQ2_spl
| ~ sQ12_spl
| ~ sQ1_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f70,f360]) ).
fof(f364,plain,
( ~ sQ2_spl
| ~ sQ12_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f363]) ).
fof(f365,plain,
( ~ sQ2_spl
| ~ sQ12_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f364]) ).
fof(f368,plain,
( ~ sQ14_spl
| inverse(inverse(identity)) != sk_c9
| multiply(sk_c9,sk_c9) != sk_c7 ),
inference(paramodulation,[status(thm)],[f188,f140]) ).
fof(f372,definition,
( sQ29_spl
<=> inverse(inverse(identity)) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f375,plain,
( ~ sQ14_spl
| ~ sQ29_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f368,f332,f372,f136]) ).
fof(f380,plain,
( ~ sQ14_spl
| inverse(inverse(sk_c9)) != sk_c9
| multiply(sk_c9,identity) != sk_c7 ),
inference(paramodulation,[status(thm)],[f34,f140]) ).
fof(f381,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f34,f175]) ).
fof(f383,definition,
( sQ30_spl
<=> multiply(sk_c9,identity) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f386,definition,
( sQ31_spl
<=> inverse(inverse(sk_c9)) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f389,plain,
( ~ sQ14_spl
| ~ sQ31_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f380,f383,f386,f136]) ).
fof(f398,plain,
( ~ sQ12_spl
| inverse(inverse(sk_c9)) != sk_c9
| identity != sk_c8 ),
inference(paramodulation,[status(thm)],[f34,f131]) ).
fof(f405,plain,
( ~ sQ12_spl
| ~ sQ31_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f398,f253,f386,f130]) ).
fof(f406,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 = identity ),
inference(forward_demodulation,[status(thm)],[f34,f342]) ).
fof(f407,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f406,f255]) ).
fof(f408,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sQ25_spl ),
inference(contradiction_clause,[status(thm)],[f407]) ).
fof(f436,plain,
inverse(identity) = identity,
inference(paramodulation,[status(thm)],[f34,f205]) ).
fof(f440,plain,
( ~ sQ14_spl
| inverse(inverse(inverse(identity))) != sk_c9
| multiply(sk_c9,sk_c9) != sk_c7 ),
inference(paramodulation,[status(thm)],[f205,f140]) ).
fof(f443,definition,
( sQ33_spl
<=> inverse(inverse(inverse(identity))) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f446,plain,
( ~ sQ14_spl
| ~ sQ33_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f440,f332,f443,f136]) ).
fof(f480,plain,
( sQ22_spl
| inverse(identity) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f33,f245]) ).
fof(f481,plain,
( sQ22_spl
| identity != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f436,f480]) ).
fof(f482,plain,
( ~ sQ0_spl
| ~ sQ14_spl
| inverse(inverse(sk_c7)) != sk_c9
| multiply(sk_c9,sk_c8) != sk_c7 ),
inference(paramodulation,[status(thm)],[f192,f140]) ).
fof(f485,definition,
( sQ36_spl
<=> inverse(inverse(sk_c7)) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f487,plain,
( sQ36_spl
| inverse(inverse(sk_c7)) != sk_c9 ),
inference(component_clause,[status(thm)],[f485]) ).
fof(f488,plain,
( ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ36_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f482,f157,f485,f136,f66]) ).
fof(f491,plain,
( ~ sQ6_spl
| ~ sQ12_spl
| inverse(sk_c5) != sk_c9
| sk_c6 != sk_c8 ),
inference(paramodulation,[status(thm)],[f90,f131]) ).
fof(f493,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| inverse(inverse(sk_c7)) != sk_c9
| sk_c8 != sk_c8 ),
inference(paramodulation,[status(thm)],[f192,f131]) ).
fof(f496,definition,
( sQ37_spl
<=> sk_c6 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f499,plain,
( ~ sQ6_spl
| ~ sQ12_spl
| ~ sQ7_spl
| ~ sQ37_spl ),
inference(split_clause,[status(thm)],[f491,f496,f93,f130,f89]) ).
fof(f501,definition,
( sQ38_spl
<=> sk_c8 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f503,plain,
( sQ38_spl
| sk_c8 != sk_c8 ),
inference(component_clause,[status(thm)],[f501]) ).
fof(f504,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ36_spl
| ~ sQ38_spl ),
inference(split_clause,[status(thm)],[f493,f501,f485,f130,f66]) ).
fof(f506,plain,
( sQ38_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f503]) ).
fof(f507,plain,
sQ38_spl,
inference(contradiction_clause,[status(thm)],[f506]) ).
fof(f515,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sk_c8 = identity ),
inference(forward_demodulation,[status(thm)],[f34,f347]) ).
fof(f516,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f515,f255]) ).
fof(f517,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| sQ25_spl ),
inference(contradiction_clause,[status(thm)],[f516]) ).
fof(f518,plain,
( sQ22_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f481,f253,f243]) ).
fof(f519,plain,
( ~ sQ22_spl
| inverse(identity) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f33,f244]) ).
fof(f520,plain,
( ~ sQ22_spl
| identity = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f436,f519]) ).
fof(f524,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| sk_c1 = multiply(inverse(sk_c2),sk_c8) ),
inference(backward_demodulation,[status(thm)],[f515,f195]) ).
fof(f526,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| multiply(inverse(X0),X0) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f515,f34]) ).
fof(f528,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| multiply(sk_c8,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f515,f33]) ).
fof(f530,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ10_spl
| sk_c1 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f196,f524]) ).
fof(f532,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ14_spl
| inverse(inverse(sk_c9)) != sk_c9
| multiply(sk_c9,sk_c8) != sk_c7 ),
inference(paramodulation,[status(thm)],[f526,f140]) ).
fof(f535,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ14_spl
| ~ sQ31_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f532,f157,f386,f136,f107,f97]) ).
fof(f538,plain,
( sQ36_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ10_spl
| inverse(inverse(sk_c1)) != sk_c9 ),
inference(backward_demodulation,[status(thm)],[f530,f487]) ).
fof(f546,plain,
( sQ15_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ10_spl
| multiply(sk_c9,sk_c8) != sk_c1 ),
inference(backward_demodulation,[status(thm)],[f530,f159]) ).
fof(f548,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| multiply(sk_c2,sk_c1) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f530,f118]) ).
fof(f550,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ10_spl
| multiply(sk_c1,sk_c8) = sk_c9 ),
inference(backward_demodulation,[status(thm)],[f530,f67]) ).
fof(f554,plain,
( sQ36_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ10_spl
| inverse(sk_c2) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f108,f538]) ).
fof(f631,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| sk_c1 = multiply(inverse(sk_c2),sk_c8) ),
inference(forward_demodulation,[status(thm)],[f530,f351]) ).
fof(f639,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| X0 = multiply(inverse(inverse(X0)),sk_c8) ),
inference(forward_demodulation,[status(thm)],[f515,f381]) ).
fof(f649,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| X0 = multiply(sk_c1,multiply(sk_c2,X0)) ),
inference(forward_demodulation,[status(thm)],[f528,f147]) ).
fof(f651,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| sk_c1 = multiply(sk_c1,sk_c8) ),
inference(paramodulation,[status(thm)],[f548,f649]) ).
fof(f657,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c1 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f550,f651]) ).
fof(f662,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ10_spl
| multiply(sk_c9,X0) = multiply(sk_c1,multiply(sk_c8,X0)) ),
inference(forward_demodulation,[status(thm)],[f530,f142]) ).
fof(f664,plain,
( sQ15_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ0_spl
| multiply(sk_c1,sk_c8) != sk_c1 ),
inference(backward_demodulation,[status(thm)],[f666,f546]) ).
fof(f666,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ10_spl
| multiply(sk_c9,X0) = multiply(sk_c1,X0) ),
inference(forward_demodulation,[status(thm)],[f528,f662]) ).
fof(f669,plain,
( sQ15_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ0_spl
| sk_c9 != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f550,f664]) ).
fof(f675,plain,
( sQ36_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ0_spl
| inverse(sk_c2) != sk_c1 ),
inference(backward_demodulation,[status(thm)],[f657,f554]) ).
fof(f684,plain,
( sQ15_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ0_spl
| sk_c1 != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f657,f669]) ).
fof(f685,plain,
( sQ15_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f684]) ).
fof(f686,plain,
( sQ15_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f685]) ).
fof(f706,definition,
( sQ43_spl
<=> sk_c1 = sk_c1 ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f708,plain,
( sQ43_spl
| sk_c1 != sk_c1 ),
inference(component_clause,[status(thm)],[f706]) ).
fof(f733,plain,
( sQ43_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f708]) ).
fof(f734,plain,
sQ43_spl,
inference(contradiction_clause,[status(thm)],[f733]) ).
fof(f747,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| X0 = multiply(X0,sk_c8) ),
inference(backward_demodulation,[status(thm)],[f186,f639]) ).
fof(f748,plain,
! [X0,X1] : multiply(X0,multiply(inverse(X0),X1)) = X1,
inference(paramodulation,[status(thm)],[f175,f186]) ).
fof(f763,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| sk_c1 = inverse(sk_c2) ),
inference(backward_demodulation,[status(thm)],[f747,f631]) ).
fof(f765,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| inverse(inverse(X0)) = multiply(X0,sk_c8) ),
inference(paramodulation,[status(thm)],[f186,f747]) ).
fof(f776,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| sQ36_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f763,f675]) ).
fof(f777,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| sQ36_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f776]) ).
fof(f778,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ9_spl
| inverse(inverse(X0)) = X0 ),
inference(forward_demodulation,[status(thm)],[f747,f765]) ).
fof(f784,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ10_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c1) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f530,f134]) ).
fof(f785,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ10_spl
| inverse(X0) != sk_c1
| multiply(X0,sk_c1) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f530,f784]) ).
fof(f802,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ13_spl
| ~ sQ10_spl
| inverse(inverse(sk_c1)) != sk_c1 ),
inference(resolution,[status(thm)],[f785,f526]) ).
fof(f807,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ13_spl
| ~ sQ10_spl
| sk_c1 != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f778,f802]) ).
fof(f808,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ13_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f807]) ).
fof(f809,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ13_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f808]) ).
fof(f814,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ22_spl
| sk_c6 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f520,f210]) ).
fof(f816,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ22_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f814,f406]) ).
fof(f834,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ22_spl
| multiply(inverse(X0),X0) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f816,f34]) ).
fof(f856,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ22_spl
| multiply(inverse(X0),sk_c7) != sk_c8
| multiply(X0,inverse(X0)) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f814,f162]) ).
fof(f857,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ22_spl
| ~ sQ5_spl
| multiply(inverse(X0),sk_c9) != sk_c8
| multiply(X0,inverse(X0)) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f295,f856]) ).
fof(f858,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ22_spl
| ~ sQ5_spl
| multiply(inverse(X0),sk_c9) != sk_c6
| multiply(X0,inverse(X0)) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f814,f857]) ).
fof(f860,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ22_spl
| ~ sQ11_spl
| ~ sQ5_spl
| sk_c6 != sk_c6
| multiply(sk_c9,inverse(sk_c9)) != sk_c6 ),
inference(paramodulation,[status(thm)],[f834,f858]) ).
fof(f865,definition,
( sQ51_spl
<=> multiply(sk_c9,inverse(sk_c9)) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f867,plain,
( sQ51_spl
| multiply(sk_c9,inverse(sk_c9)) != sk_c6 ),
inference(component_clause,[status(thm)],[f865]) ).
fof(f868,definition,
( sQ52_spl
<=> sk_c6 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f870,plain,
( sQ52_spl
| sk_c6 != sk_c6 ),
inference(component_clause,[status(thm)],[f868]) ).
fof(f871,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ22_spl
| ~ sQ11_spl
| ~ sQ5_spl
| ~ sQ52_spl
| ~ sQ51_spl ),
inference(split_clause,[status(thm)],[f860,f865,f868,f85,f127,f243,f93,f89,f73,f69]) ).
fof(f936,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ22_spl
| multiply(X0,sk_c6) = X0 ),
inference(paramodulation,[status(thm)],[f834,f748]) ).
fof(f957,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ22_spl
| multiply(X0,inverse(X0)) = sk_c6 ),
inference(paramodulation,[status(thm)],[f936,f748]) ).
fof(f982,plain,
( sQ52_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f870]) ).
fof(f983,plain,
sQ52_spl,
inference(contradiction_clause,[status(thm)],[f982]) ).
fof(f984,plain,
( sQ51_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ22_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f957,f867]) ).
fof(f985,plain,
( sQ51_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ22_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f984]) ).
fof(f986,plain,
( sQ51_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f985]) ).
fof(f987,plain,
$false,
inference(sat_refutation,[status(thm)],[f72,f76,f88,f92,f96,f100,f101,f102,f103,f104,f105,f106,f110,f111,f112,f113,f114,f115,f116,f120,f121,f122,f123,f124,f125,f126,f139,f160,f161,f169,f229,f238,f249,f256,f260,f264,f314,f322,f338,f365,f375,f389,f405,f408,f446,f488,f499,f504,f507,f517,f518,f535,f686,f734,f777,f809,f871,f983,f986]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP370-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n018.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 20:12:13 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.10/0.41 % Refutation found
% 0.10/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.45 % Elapsed time: 0.082221 seconds
% 0.10/0.45 % CPU time: 0.339021 seconds
% 0.10/0.45 % Total memory used: 106.114 MB
% 0.10/0.45 % Net memory used: 105.845 MB
%------------------------------------------------------------------------------