%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP335-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 12:33:27 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.40s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 58
% Syntax : Number of formulae : 295 ( 13 unt; 29 def)
% Number of atoms : 1043 ( 342 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1430 ( 682 ~; 719 |; 0 &)
% ( 29 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 31 ( 29 usr; 30 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 77 ( 77 !; 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_c8,sk_c7) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
! [X3,X4,X1,X2,X5] :
( inverse(X5) != sk_c8
| multiply(X5,sk_c8) != X2
| multiply(sk_c8,X2) != sk_c7
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| inverse(X4) != sk_c7
| multiply(X4,sk_c7) != sk_c8
| inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c6
| multiply(sk_c7,sk_c8) != sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f36,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f37,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f38,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f41,plain,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f42,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f43,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f45,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f46,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f47,plain,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f48,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f49,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f51,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f52,plain,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f53,plain,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f54,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f55,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f57,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f58,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f59,plain,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f60,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f61,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f62,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f63,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f64,plain,
( inverse(sk_c3) = sk_c8
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f65,plain,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f66,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f67,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f68,plain,
! [X5] :
( inverse(X5) != sk_c8
| ! [X2] :
( multiply(X5,sk_c8) != X2
| multiply(sk_c8,X2) != sk_c7
| ! [X1] :
( inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| ! [X4] :
( inverse(X4) != sk_c7
| multiply(X4,sk_c7) != sk_c8
| ! [X3] :
( inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c6
| multiply(sk_c7,sk_c8) != sk_c6 ) ) ) ) ),
inference(miniscoping,[status(thm)],[f34]) ).
fof(f69,plain,
! [X0,X1,X2,X3,X4] :
( inverse(X4) != sk_c8
| multiply(X4,sk_c8) != X3
| multiply(sk_c8,X3) != sk_c7
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| inverse(X1) != sk_c7
| multiply(X1,sk_c7) != sk_c8
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f70,definition,
( sQ0_spl
<=> multiply(sk_c7,sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f71,plain,
( ~ sQ0_spl
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f72,plain,
( sQ0_spl
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f73,definition,
( sQ1_spl
<=> multiply(sk_c8,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f74,plain,
( ~ sQ1_spl
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f75,plain,
( sQ1_spl
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f76,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f38,f70,f73]) ).
fof(f77,definition,
( sQ2_spl
<=> multiply(sk_c3,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f78,plain,
( ~ sQ2_spl
| multiply(sk_c3,sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f77]) ).
fof(f81,definition,
( sQ3_spl
<=> inverse(sk_c3) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f82,plain,
( ~ sQ3_spl
| inverse(sk_c3) = sk_c8 ),
inference(component_clause,[status(thm)],[f81]) ).
fof(f85,definition,
( sQ4_spl
<=> multiply(sk_c8,sk_c5) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ4_spl
| multiply(sk_c8,sk_c5) = sk_c7 ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f88,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f41,f70,f85]) ).
fof(f89,definition,
( sQ5_spl
<=> multiply(sk_c4,sk_c8) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f90,plain,
( ~ sQ5_spl
| multiply(sk_c4,sk_c8) = sk_c5 ),
inference(component_clause,[status(thm)],[f89]) ).
fof(f92,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f42,f70,f89]) ).
fof(f93,definition,
( sQ6_spl
<=> inverse(sk_c4) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ6_spl
| inverse(sk_c4) = sk_c8 ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f96,plain,
( sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f43,f70,f93]) ).
fof(f97,definition,
( sQ7_spl
<=> multiply(sk_c1,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f98,plain,
( ~ sQ7_spl
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(component_clause,[status(thm)],[f97]) ).
fof(f101,plain,
( sQ2_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f45,f97,f77]) ).
fof(f102,plain,
( sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f46,f97,f81]) ).
fof(f103,plain,
( sQ4_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f47,f97,f85]) ).
fof(f104,plain,
( sQ5_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f48,f97,f89]) ).
fof(f105,plain,
( sQ6_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f49,f97,f93]) ).
fof(f106,definition,
( sQ8_spl
<=> inverse(sk_c1) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f107,plain,
( ~ sQ8_spl
| inverse(sk_c1) = sk_c7 ),
inference(component_clause,[status(thm)],[f106]) ).
fof(f110,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f51,f106,f77]) ).
fof(f111,plain,
( sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f52,f106,f81]) ).
fof(f112,plain,
( sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f53,f106,f85]) ).
fof(f113,plain,
( sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f54,f106,f89]) ).
fof(f114,plain,
( sQ6_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f55,f106,f93]) ).
fof(f115,definition,
( sQ9_spl
<=> multiply(sk_c2,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f116,plain,
( ~ sQ9_spl
| multiply(sk_c2,sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f115]) ).
fof(f117,plain,
( sQ9_spl
| multiply(sk_c2,sk_c7) != sk_c8 ),
inference(component_clause,[status(thm)],[f115]) ).
fof(f119,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f57,f115,f77]) ).
fof(f120,plain,
( sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f58,f115,f81]) ).
fof(f121,plain,
( sQ4_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f59,f115,f85]) ).
fof(f122,plain,
( sQ5_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f60,f115,f89]) ).
fof(f123,plain,
( sQ6_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f61,f115,f93]) ).
fof(f124,definition,
( sQ10_spl
<=> inverse(sk_c2) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f125,plain,
( ~ sQ10_spl
| inverse(sk_c2) = sk_c7 ),
inference(component_clause,[status(thm)],[f124]) ).
fof(f127,plain,
( sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f62,f124,f73]) ).
fof(f128,plain,
( sQ2_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f63,f124,f77]) ).
fof(f129,plain,
( sQ3_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f64,f124,f81]) ).
fof(f130,plain,
( sQ4_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f65,f124,f85]) ).
fof(f131,plain,
( sQ5_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f66,f124,f89]) ).
fof(f132,plain,
( sQ6_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f67,f124,f93]) ).
fof(f133,definition,
! [X0] :
( sQ11_spl
<=> ( inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f134,plain,
! [X0] :
( ~ sQ11_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6 ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,definition,
! [X1] :
( sQ12_spl
<=> ( inverse(X1) != sk_c7
| multiply(X1,sk_c7) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f137,plain,
! [X0] :
( ~ sQ12_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c8 ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f139,definition,
! [X2] :
( sQ13_spl
<=> ( inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f140,plain,
! [X0] :
( ~ sQ13_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f139]) ).
fof(f142,definition,
! [X3,X4] :
( sQ14_spl
<=> ( inverse(X4) != sk_c8
| multiply(X4,sk_c8) != X3
| multiply(sk_c8,X3) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f143,plain,
! [X0,X1] :
( ~ sQ14_spl
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != X0
| multiply(sk_c8,X0) != sk_c7 ),
inference(component_clause,[status(thm)],[f142]) ).
fof(f145,plain,
( sQ14_spl
| sQ13_spl
| ~ sQ1_spl
| sQ12_spl
| sQ11_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f69,f70,f133,f136,f73,f139,f142]) ).
fof(f150,plain,
! [X0] :
( ~ sQ7_spl
| multiply(sk_c6,X0) = multiply(sk_c1,multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f98,f37]) ).
fof(f152,plain,
( ~ sQ3_spl
| multiply(sk_c8,sk_c3) = identity ),
inference(paramodulation,[status(thm)],[f82,f36]) ).
fof(f154,plain,
( ~ sQ8_spl
| multiply(sk_c7,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f107,f36]) ).
fof(f155,plain,
( ~ sQ10_spl
| multiply(sk_c7,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f125,f36]) ).
fof(f156,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f36,f37]) ).
fof(f157,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f35,f156]) ).
fof(f158,plain,
! [X0] :
( ~ sQ5_spl
| multiply(sk_c5,X0) = multiply(sk_c4,multiply(sk_c8,X0)) ),
inference(paramodulation,[status(thm)],[f90,f37]) ).
fof(f163,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ14_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c5
| sk_c7 != sk_c7 ),
inference(paramodulation,[status(thm)],[f86,f143]) ).
fof(f164,definition,
( sQ15_spl
<=> sk_c7 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f166,plain,
( sQ15_spl
| sk_c7 != sk_c7 ),
inference(component_clause,[status(thm)],[f164]) ).
fof(f167,definition,
! [X0] :
( sQ16_spl
<=> ( inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c5 ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f168,plain,
! [X0] :
( ~ sQ16_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c5 ),
inference(component_clause,[status(thm)],[f167]) ).
fof(f170,plain,
( ~ sQ4_spl
| ~ sQ14_spl
| sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f163,f164,f167,f142,f85]) ).
fof(f171,plain,
( sQ15_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f166]) ).
fof(f172,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f171]) ).
fof(f177,plain,
( ~ sQ2_spl
| ~ sQ13_spl
| inverse(sk_c3) != sk_c8 ),
inference(resolution,[status(thm)],[f140,f78]) ).
fof(f184,plain,
( ~ sQ2_spl
| ~ sQ13_spl
| ~ sQ3_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f82,f177]) ).
fof(f185,plain,
( ~ sQ2_spl
| ~ sQ13_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f184]) ).
fof(f186,plain,
( ~ sQ2_spl
| ~ sQ13_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f185]) ).
fof(f187,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| inverse(sk_c2) != sk_c7 ),
inference(resolution,[status(thm)],[f137,f116]) ).
fof(f193,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ10_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f125,f187]) ).
fof(f194,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f193]) ).
fof(f195,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f194]) ).
fof(f199,plain,
! [X0] :
( ~ sQ10_spl
| multiply(identity,X0) = multiply(sk_c7,multiply(sk_c2,X0)) ),
inference(paramodulation,[status(thm)],[f155,f37]) ).
fof(f200,plain,
! [X0] :
( ~ sQ10_spl
| X0 = multiply(sk_c7,multiply(sk_c2,X0)) ),
inference(forward_demodulation,[status(thm)],[f35,f199]) ).
fof(f201,plain,
( ~ sQ7_spl
| ~ sQ11_spl
| inverse(sk_c1) != sk_c7 ),
inference(resolution,[status(thm)],[f134,f98]) ).
fof(f203,plain,
( ~ sQ11_spl
| inverse(identity) != sk_c7
| sk_c7 != sk_c6 ),
inference(paramodulation,[status(thm)],[f35,f134]) ).
fof(f206,plain,
( ~ sQ7_spl
| ~ sQ11_spl
| ~ sQ8_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f107,f201]) ).
fof(f207,plain,
( ~ sQ7_spl
| ~ sQ11_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f206]) ).
fof(f208,plain,
( ~ sQ7_spl
| ~ sQ11_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f207]) ).
fof(f209,definition,
( sQ17_spl
<=> identity = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f211,plain,
( sQ17_spl
| identity != sk_c6 ),
inference(component_clause,[status(thm)],[f209]) ).
fof(f216,definition,
( sQ19_spl
<=> sk_c7 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f217,plain,
( ~ sQ19_spl
| sk_c7 = sk_c6 ),
inference(component_clause,[status(thm)],[f216]) ).
fof(f218,plain,
( sQ19_spl
| sk_c7 != sk_c6 ),
inference(component_clause,[status(thm)],[f216]) ).
fof(f219,definition,
( sQ20_spl
<=> inverse(identity) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f221,plain,
( sQ20_spl
| inverse(identity) != sk_c7 ),
inference(component_clause,[status(thm)],[f219]) ).
fof(f222,plain,
( ~ sQ11_spl
| ~ sQ20_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f203,f216,f219,f133]) ).
fof(f223,definition,
( sQ21_spl
<=> sk_c6 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f225,plain,
( sQ21_spl
| sk_c6 != sk_c6 ),
inference(component_clause,[status(thm)],[f223]) ).
fof(f227,plain,
( sQ21_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f225]) ).
fof(f228,plain,
sQ21_spl,
inference(contradiction_clause,[status(thm)],[f227]) ).
fof(f229,definition,
( sQ22_spl
<=> identity = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f231,plain,
( sQ22_spl
| identity != sk_c8 ),
inference(component_clause,[status(thm)],[f229]) ).
fof(f237,definition,
( sQ24_spl
<=> sk_c6 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f239,plain,
( sQ24_spl
| sk_c6 != sk_c8 ),
inference(component_clause,[status(thm)],[f237]) ).
fof(f246,plain,
( ~ sQ1_spl
| ~ sQ11_spl
| inverse(sk_c8) != sk_c7
| sk_c6 != sk_c6 ),
inference(paramodulation,[status(thm)],[f74,f134]) ).
fof(f251,definition,
( sQ25_spl
<=> inverse(sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f253,plain,
( sQ25_spl
| inverse(sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f251]) ).
fof(f254,plain,
( ~ sQ1_spl
| ~ sQ11_spl
| ~ sQ25_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f246,f223,f251,f133,f73]) ).
fof(f273,plain,
( ~ sQ2_spl
| sk_c8 = multiply(inverse(sk_c3),sk_c7) ),
inference(paramodulation,[status(thm)],[f78,f157]) ).
fof(f274,plain,
( ~ sQ5_spl
| sk_c8 = multiply(inverse(sk_c4),sk_c5) ),
inference(paramodulation,[status(thm)],[f90,f157]) ).
fof(f280,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| sk_c8 = multiply(sk_c8,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f82,f273]) ).
fof(f281,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sk_c8 = multiply(sk_c8,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f94,f274]) ).
fof(f282,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sk_c8 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f86,f281]) ).
fof(f286,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c7,sk_c5) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f282,f86]) ).
fof(f287,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| multiply(sk_c7,sk_c7) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f282,f74]) ).
fof(f288,plain,
( sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| multiply(sk_c2,sk_c7) != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f282,f117]) ).
fof(f289,plain,
( ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| inverse(sk_c3) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f282,f82]) ).
fof(f291,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| multiply(sk_c3,sk_c7) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f282,f78]) ).
fof(f292,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| multiply(sk_c4,sk_c7) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f282,f90]) ).
fof(f293,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(sk_c4) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f282,f94]) ).
fof(f294,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| multiply(sk_c7,sk_c7) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f282,f72]) ).
fof(f297,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c5 = multiply(inverse(sk_c7),sk_c7) ),
inference(paramodulation,[status(thm)],[f286,f157]) ).
fof(f299,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c5 = identity ),
inference(forward_demodulation,[status(thm)],[f36,f297]) ).
fof(f300,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f287,f294]) ).
fof(f301,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f300]) ).
fof(f314,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| multiply(sk_c4,sk_c7) = identity ),
inference(forward_demodulation,[status(thm)],[f299,f292]) ).
fof(f323,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ11_spl
| inverse(sk_c3) != sk_c7
| sk_c7 != sk_c6 ),
inference(paramodulation,[status(thm)],[f291,f134]) ).
fof(f332,definition,
( sQ27_spl
<=> inverse(sk_c3) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f334,plain,
( sQ27_spl
| inverse(sk_c3) != sk_c7 ),
inference(component_clause,[status(thm)],[f332]) ).
fof(f335,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ11_spl
| ~ sQ27_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f323,f216,f332,f133,f85,f93,f89,f77]) ).
fof(f342,plain,
( ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| multiply(sk_c7,sk_c3) = identity ),
inference(forward_demodulation,[status(thm)],[f282,f152]) ).
fof(f348,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ6_spl
| multiply(identity,X0) = multiply(sk_c4,multiply(sk_c8,X0)) ),
inference(forward_demodulation,[status(thm)],[f299,f158]) ).
fof(f349,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ6_spl
| X0 = multiply(sk_c4,multiply(sk_c8,X0)) ),
inference(forward_demodulation,[status(thm)],[f35,f348]) ).
fof(f350,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ6_spl
| X0 = multiply(sk_c4,multiply(sk_c7,X0)) ),
inference(forward_demodulation,[status(thm)],[f282,f349]) ).
fof(f373,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c7) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f282,f168]) ).
fof(f374,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c7) != identity ),
inference(forward_demodulation,[status(thm)],[f299,f373]) ).
fof(f375,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != identity ),
inference(forward_demodulation,[status(thm)],[f282,f374]) ).
fof(f376,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ16_spl
| inverse(sk_c4) != sk_c7 ),
inference(resolution,[status(thm)],[f375,f314]) ).
fof(f384,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ16_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f293,f376]) ).
fof(f385,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ16_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f384]) ).
fof(f386,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ16_spl ),
inference(contradiction_clause,[status(thm)],[f385]) ).
fof(f387,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sk_c7 = multiply(sk_c8,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f282,f280]) ).
fof(f388,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c7 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f389,f287]) ).
fof(f389,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sk_c7 = multiply(sk_c7,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f282,f387]) ).
fof(f391,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sk_c7 = multiply(sk_c4,sk_c7) ),
inference(paramodulation,[status(thm)],[f389,f350]) ).
fof(f395,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f388,f218]) ).
fof(f396,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sQ19_spl ),
inference(contradiction_clause,[status(thm)],[f395]) ).
fof(f398,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sk_c7 = identity ),
inference(forward_demodulation,[status(thm)],[f314,f391]) ).
fof(f402,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f282,f137]) ).
fof(f408,plain,
( ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ2_spl
| multiply(identity,sk_c3) = identity ),
inference(backward_demodulation,[status(thm)],[f398,f342]) ).
fof(f411,plain,
( sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| multiply(sk_c2,sk_c7) != identity ),
inference(backward_demodulation,[status(thm)],[f398,f288]) ).
fof(f413,plain,
( ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ2_spl
| inverse(sk_c3) = identity ),
inference(backward_demodulation,[status(thm)],[f398,f289]) ).
fof(f415,plain,
( ~ sQ10_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| multiply(identity,sk_c2) = identity ),
inference(backward_demodulation,[status(thm)],[f398,f155]) ).
fof(f424,plain,
( ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ2_spl
| sk_c3 = identity ),
inference(forward_demodulation,[status(thm)],[f35,f408]) ).
fof(f426,plain,
( sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| multiply(sk_c2,identity) != identity ),
inference(forward_demodulation,[status(thm)],[f398,f411]) ).
fof(f427,plain,
( ~ sQ10_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sk_c2 = identity ),
inference(forward_demodulation,[status(thm)],[f35,f415]) ).
fof(f428,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| inverse(X0) != sk_c7
| multiply(X0,identity) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f398,f402]) ).
fof(f429,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| inverse(X0) != sk_c7
| multiply(X0,identity) != identity ),
inference(forward_demodulation,[status(thm)],[f398,f428]) ).
fof(f430,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| inverse(X0) != identity
| multiply(X0,identity) != identity ),
inference(forward_demodulation,[status(thm)],[f398,f429]) ).
fof(f434,plain,
( ~ sQ12_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| inverse(identity) != identity
| identity != identity ),
inference(paramodulation,[status(thm)],[f35,f430]) ).
fof(f436,definition,
( sQ29_spl
<=> identity = identity ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f438,plain,
( sQ29_spl
| identity != identity ),
inference(component_clause,[status(thm)],[f436]) ).
fof(f443,definition,
( sQ31_spl
<=> inverse(identity) = identity ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f445,plain,
( sQ31_spl
| inverse(identity) != identity ),
inference(component_clause,[status(thm)],[f443]) ).
fof(f446,plain,
( ~ sQ12_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ31_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f434,f436,f443,f81,f77,f85,f93,f89,f136]) ).
fof(f447,plain,
( sQ29_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f438]) ).
fof(f448,plain,
sQ29_spl,
inference(contradiction_clause,[status(thm)],[f447]) ).
fof(f457,plain,
( sQ27_spl
| ~ sQ3_spl
| sk_c8 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f82,f334]) ).
fof(f505,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| sk_c7 = multiply(sk_c7,sk_c8) ),
inference(paramodulation,[status(thm)],[f116,f200]) ).
fof(f511,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c7 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f505,f71]) ).
fof(f514,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| sk_c8 = multiply(inverse(sk_c7),sk_c7) ),
inference(paramodulation,[status(thm)],[f505,f157]) ).
fof(f518,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| sk_c8 = identity ),
inference(forward_demodulation,[status(thm)],[f36,f514]) ).
fof(f519,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f518,f231]) ).
fof(f520,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f519]) ).
fof(f522,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sQ27_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f282,f457]) ).
fof(f523,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sQ27_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f522]) ).
fof(f525,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f511,f216,f124,f115,f70]) ).
fof(f530,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c7,identity) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f518,f71]) ).
fof(f531,plain,
( sQ24_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c6 != identity ),
inference(backward_demodulation,[status(thm)],[f518,f239]) ).
fof(f533,plain,
( sQ25_spl
| ~ sQ9_spl
| ~ sQ10_spl
| inverse(identity) != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f518,f253]) ).
fof(f537,plain,
( sQ17_spl
| ~ sQ19_spl
| identity != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f217,f211]) ).
fof(f549,plain,
( sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(identity,sk_c7) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f518,f75]) ).
fof(f550,plain,
( sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c7 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f35,f549]) ).
fof(f551,plain,
( sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ19_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f217,f550]) ).
fof(f552,plain,
( sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ19_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f551]) ).
fof(f553,plain,
( sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ19_spl ),
inference(contradiction_clause,[status(thm)],[f552]) ).
fof(f561,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ9_spl
| ~ sQ10_spl
| inverse(X0) != sk_c8
| multiply(X0,identity) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f518,f140]) ).
fof(f562,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ9_spl
| ~ sQ10_spl
| inverse(X0) != identity
| multiply(X0,identity) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f518,f561]) ).
fof(f567,definition,
( sQ33_spl
<=> identity = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f569,plain,
( sQ33_spl
| identity != sk_c7 ),
inference(component_clause,[status(thm)],[f567]) ).
fof(f585,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ19_spl
| multiply(sk_c7,identity) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f217,f530]) ).
fof(f592,plain,
( ~ sQ13_spl
| ~ sQ9_spl
| ~ sQ10_spl
| inverse(identity) != identity
| identity != sk_c7 ),
inference(paramodulation,[status(thm)],[f35,f562]) ).
fof(f600,plain,
( ~ sQ13_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ31_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f592,f567,f443,f124,f115,f139]) ).
fof(f615,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ19_spl
| multiply(sk_c7,X0) = multiply(sk_c1,multiply(sk_c7,X0)) ),
inference(forward_demodulation,[status(thm)],[f217,f150]) ).
fof(f617,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ19_spl
| multiply(sk_c7,multiply(sk_c2,X0)) = multiply(sk_c1,X0) ),
inference(paramodulation,[status(thm)],[f200,f615]) ).
fof(f622,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ19_spl
| X0 = multiply(sk_c1,X0) ),
inference(forward_demodulation,[status(thm)],[f200,f617]) ).
fof(f636,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ19_spl
| X0 = multiply(inverse(sk_c1),X0) ),
inference(paramodulation,[status(thm)],[f622,f157]) ).
fof(f642,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ19_spl
| ~ sQ8_spl
| X0 = multiply(sk_c7,X0) ),
inference(forward_demodulation,[status(thm)],[f107,f636]) ).
fof(f644,plain,
( ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ19_spl
| sk_c1 = identity ),
inference(backward_demodulation,[status(thm)],[f642,f154]) ).
fof(f645,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ19_spl
| ~ sQ7_spl
| ~ sQ8_spl
| identity = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f642,f585]) ).
fof(f652,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ19_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f645,f537]) ).
fof(f653,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ19_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f652]) ).
fof(f655,plain,
( sQ24_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f531,f209,f124,f115,f237]) ).
fof(f659,plain,
( ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ19_spl
| inverse(identity) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f644,f107]) ).
fof(f660,plain,
( ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ19_spl
| sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f659,f221]) ).
fof(f661,plain,
( ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ19_spl
| sQ20_spl ),
inference(contradiction_clause,[status(thm)],[f660]) ).
fof(f662,plain,
( sQ25_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f533,f219,f124,f115,f251]) ).
fof(f669,plain,
! [X0,X1] :
( ~ sQ14_spl
| ~ sQ9_spl
| ~ sQ10_spl
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != X0
| multiply(identity,X0) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f518,f143]) ).
fof(f670,plain,
! [X0,X1] :
( ~ sQ14_spl
| ~ sQ9_spl
| ~ sQ10_spl
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != X0
| X0 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f35,f669]) ).
fof(f671,plain,
! [X0,X1] :
( ~ sQ14_spl
| ~ sQ9_spl
| ~ sQ10_spl
| inverse(X1) != sk_c8
| multiply(X1,identity) != X0
| X0 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f518,f670]) ).
fof(f672,plain,
! [X0,X1] :
( ~ sQ14_spl
| ~ sQ9_spl
| ~ sQ10_spl
| inverse(X1) != identity
| multiply(X1,identity) != X0
| X0 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f518,f671]) ).
fof(f679,plain,
( ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ19_spl
| ~ sQ0_spl
| ~ sQ9_spl
| inverse(identity) = identity ),
inference(forward_demodulation,[status(thm)],[f645,f659]) ).
fof(f688,plain,
! [X0,X1] :
( ~ sQ14_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ19_spl
| ~ sQ7_spl
| ~ sQ8_spl
| inverse(X1) != identity
| multiply(X1,identity) != X0
| X0 != identity ),
inference(forward_demodulation,[status(thm)],[f645,f672]) ).
fof(f697,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ19_spl
| ~ sQ7_spl
| ~ sQ8_spl
| inverse(identity) != identity
| identity != X0
| X0 != identity ),
inference(paramodulation,[status(thm)],[f35,f688]) ).
fof(f708,definition,
! [X0] :
( sQ39_spl
<=> ( identity != X0
| X0 != identity ) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f709,plain,
! [X0] :
( ~ sQ39_spl
| identity != X0
| X0 != identity ),
inference(component_clause,[status(thm)],[f708]) ).
fof(f713,plain,
( ~ sQ14_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ19_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ31_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f697,f708,f443,f106,f97,f216,f70,f124,f115,f142]) ).
fof(f738,plain,
( sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ10_spl
| multiply(identity,identity) != identity ),
inference(backward_demodulation,[status(thm)],[f427,f426]) ).
fof(f739,plain,
( sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ10_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f35,f738]) ).
fof(f740,plain,
( sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f739]) ).
fof(f741,plain,
( sQ9_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f740]) ).
fof(f742,plain,
! [X0] :
( ~ sQ39_spl
| X0 != identity ),
inference(duplicate_literals_removal,[status(thm)],[f709]) ).
fof(f743,plain,
( ~ sQ39_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f36,f742]) ).
fof(f747,plain,
~ sQ39_spl,
inference(contradiction_clause,[status(thm)],[f743]) ).
fof(f749,plain,
( sQ33_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ19_spl
| ~ sQ7_spl
| ~ sQ8_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f645,f569]) ).
fof(f750,plain,
( sQ33_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ19_spl
| ~ sQ7_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f749]) ).
fof(f751,plain,
( sQ33_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ19_spl
| ~ sQ7_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f750]) ).
fof(f784,plain,
( sQ31_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ19_spl
| ~ sQ0_spl
| ~ sQ9_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f679,f445]) ).
fof(f785,plain,
( sQ31_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ19_spl
| ~ sQ0_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f784]) ).
fof(f786,plain,
( sQ31_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ19_spl
| ~ sQ0_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f785]) ).
fof(f828,plain,
( ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ2_spl
| inverse(identity) = identity ),
inference(forward_demodulation,[status(thm)],[f424,f413]) ).
fof(f841,plain,
( sQ31_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ2_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f828,f445]) ).
fof(f842,plain,
( sQ31_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f841]) ).
fof(f843,plain,
( sQ31_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f842]) ).
fof(f844,plain,
$false,
inference(sat_refutation,[status(thm)],[f76,f88,f92,f96,f101,f102,f103,f104,f105,f110,f111,f112,f113,f114,f119,f120,f121,f122,f123,f127,f128,f129,f130,f131,f132,f145,f170,f172,f186,f195,f208,f222,f228,f254,f301,f335,f386,f396,f446,f448,f520,f523,f525,f553,f600,f653,f655,f661,f662,f713,f741,f747,f751,f786,f843]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP335-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n017.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 20:04:41 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.10/0.40 % Refutation found
% 0.10/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.44 % Elapsed time: 0.057215 seconds
% 0.10/0.44 % CPU time: 0.204743 seconds
% 0.10/0.44 % Total memory used: 104.325 MB
% 0.10/0.44 % Net memory used: 104.084 MB
%------------------------------------------------------------------------------