%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP232-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 12:33:10 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 59
% Syntax : Number of formulae : 282 ( 14 unt; 30 def)
% Number of atoms : 812 ( 317 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 988 ( 458 ~; 500 |; 0 &)
% ( 30 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 32 ( 30 usr; 31 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 58 ( 58 !; 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_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c2,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c2,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
! [X4,X5,X6,X1,X2,X3] :
( inverse(X3) != sk_c8
| multiply(X3,sk_c8) != X2
| multiply(sk_c8,X2) != sk_c7
| multiply(X1,sk_c7) != sk_c8
| inverse(X1) != sk_c8
| multiply(X6,sk_c7) != sk_c8
| inverse(X5) != X6
| multiply(X5,X6) != sk_c8
| inverse(X4) != sk_c8
| multiply(X4,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c7 ),
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,
( inverse(sk_c4) = sk_c8
| inverse(sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f39,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f40,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f41,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f42,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f43,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f44,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f45,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f46,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f47,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f48,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f49,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f50,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f51,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f52,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f53,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f54,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f55,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| multiply(sk_c2,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f56,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c2,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f57,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f58,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f59,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f60,plain,
( multiply(sk_c8,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f61,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f62,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f68,plain,
! [X3] :
( inverse(X3) != sk_c8
| ! [X2] :
( multiply(X3,sk_c8) != X2
| multiply(sk_c8,X2) != sk_c7
| ! [X1] :
( multiply(X1,sk_c7) != sk_c8
| inverse(X1) != sk_c8
| ! [X6] :
( multiply(X6,sk_c7) != sk_c8
| ! [X5] :
( inverse(X5) != X6
| multiply(X5,X6) != sk_c8
| ! [X4] :
( inverse(X4) != sk_c8
| multiply(X4,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c7 ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f34]) ).
fof(f69,plain,
! [X0,X1,X2,X3,X4,X5] :
( inverse(X5) != sk_c8
| multiply(X5,sk_c8) != X4
| multiply(sk_c8,X4) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| inverse(X3) != sk_c8
| multiply(X2,sk_c7) != sk_c8
| inverse(X1) != X2
| multiply(X1,X2) != sk_c8
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7
| inverse(sk_c8) != sk_c7 ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f70,definition,
( sQ0_spl
<=> inverse(sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f71,plain,
( ~ sQ0_spl
| inverse(sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f72,plain,
( sQ0_spl
| inverse(sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f73,definition,
( sQ1_spl
<=> inverse(sk_c4) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f74,plain,
( ~ sQ1_spl
| inverse(sk_c4) = sk_c8 ),
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_c4,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f78,plain,
( ~ sQ2_spl
| multiply(sk_c4,sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f77]) ).
fof(f80,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f39,f70,f77]) ).
fof(f81,definition,
( sQ3_spl
<=> multiply(sk_c8,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f82,plain,
( ~ sQ3_spl
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(component_clause,[status(thm)],[f81]) ).
fof(f84,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f40,f70,f81]) ).
fof(f85,definition,
( sQ4_spl
<=> multiply(sk_c5,sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ4_spl
| multiply(sk_c5,sk_c8) = sk_c6 ),
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
<=> inverse(sk_c5) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f90,plain,
( ~ sQ5_spl
| inverse(sk_c5) = sk_c8 ),
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
<=> multiply(sk_c1,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ6_spl
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f96,plain,
( sQ1_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f43,f93,f73]) ).
fof(f97,plain,
( sQ2_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f44,f93,f77]) ).
fof(f98,plain,
( sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f45,f93,f81]) ).
fof(f99,plain,
( sQ4_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f46,f93,f85]) ).
fof(f100,plain,
( sQ5_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f47,f93,f89]) ).
fof(f101,definition,
( sQ7_spl
<=> inverse(sk_c1) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f102,plain,
( ~ sQ7_spl
| inverse(sk_c1) = sk_c8 ),
inference(component_clause,[status(thm)],[f101]) ).
fof(f104,plain,
( sQ1_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f48,f101,f73]) ).
fof(f105,plain,
( sQ2_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f49,f101,f77]) ).
fof(f106,plain,
( sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f50,f101,f81]) ).
fof(f107,plain,
( sQ4_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f51,f101,f85]) ).
fof(f108,plain,
( sQ5_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f52,f101,f89]) ).
fof(f109,definition,
( sQ8_spl
<=> multiply(sk_c2,sk_c3) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f110,plain,
( ~ sQ8_spl
| multiply(sk_c2,sk_c3) = sk_c8 ),
inference(component_clause,[status(thm)],[f109]) ).
fof(f112,plain,
( sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f53,f109,f73]) ).
fof(f113,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f54,f109,f77]) ).
fof(f114,plain,
( sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f55,f109,f81]) ).
fof(f115,plain,
( sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f56,f109,f85]) ).
fof(f116,plain,
( sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f57,f109,f89]) ).
fof(f117,definition,
( sQ9_spl
<=> inverse(sk_c2) = sk_c3 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f118,plain,
( ~ sQ9_spl
| inverse(sk_c2) = sk_c3 ),
inference(component_clause,[status(thm)],[f117]) ).
fof(f120,plain,
( sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f58,f117,f73]) ).
fof(f121,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f59,f117,f77]) ).
fof(f122,plain,
( sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f60,f117,f81]) ).
fof(f123,plain,
( sQ4_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f61,f117,f85]) ).
fof(f124,plain,
( sQ5_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f62,f117,f89]) ).
fof(f133,definition,
! [X0] :
( sQ11_spl
<=> ( inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f134,plain,
! [X0] :
( ~ sQ11_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,definition,
! [X1,X2] :
( sQ12_spl
<=> ( multiply(X2,sk_c7) != sk_c8
| inverse(X1) != X2
| multiply(X1,X2) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f137,plain,
! [X0,X1] :
( ~ sQ12_spl
| multiply(X1,sk_c7) != sk_c8
| inverse(X0) != X1
| multiply(X0,X1) != sk_c8 ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f139,definition,
! [X3] :
( sQ13_spl
<=> ( multiply(X3,sk_c7) != sk_c8
| inverse(X3) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f140,plain,
! [X0] :
( ~ sQ13_spl
| multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c8 ),
inference(component_clause,[status(thm)],[f139]) ).
fof(f142,definition,
! [X4,X5] :
( sQ14_spl
<=> ( inverse(X5) != sk_c8
| multiply(X5,sk_c8) != X4
| multiply(sk_c8,X4) != 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
| sQ12_spl
| sQ11_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f69,f70,f133,f136,f139,f142]) ).
fof(f146,plain,
! [X0] :
( ~ sQ14_spl
| inverse(X0) != sk_c8
| multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ),
inference(destructive_equality_resolution,[status(thm)],[f143]) ).
fof(f148,plain,
! [X0] :
( ~ sQ4_spl
| multiply(sk_c6,X0) = multiply(sk_c5,multiply(sk_c8,X0)) ),
inference(paramodulation,[status(thm)],[f86,f37]) ).
fof(f153,plain,
( ~ sQ7_spl
| multiply(sk_c8,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f102,f36]) ).
fof(f154,plain,
( ~ sQ9_spl
| multiply(sk_c3,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f118,f36]) ).
fof(f155,plain,
( ~ sQ1_spl
| multiply(sk_c8,sk_c4) = identity ),
inference(paramodulation,[status(thm)],[f74,f36]) ).
fof(f156,plain,
( ~ sQ5_spl
| multiply(sk_c8,sk_c5) = identity ),
inference(paramodulation,[status(thm)],[f90,f36]) ).
fof(f157,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f36,f37]) ).
fof(f158,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f35,f157]) ).
fof(f161,plain,
! [X0] :
( ~ sQ8_spl
| multiply(sk_c8,X0) = multiply(sk_c2,multiply(sk_c3,X0)) ),
inference(paramodulation,[status(thm)],[f110,f37]) ).
fof(f162,plain,
! [X0] :
( ~ sQ6_spl
| multiply(sk_c7,X0) = multiply(sk_c1,multiply(sk_c8,X0)) ),
inference(paramodulation,[status(thm)],[f94,f37]) ).
fof(f163,plain,
! [X0] :
( ~ sQ7_spl
| multiply(identity,X0) = multiply(sk_c8,multiply(sk_c1,X0)) ),
inference(paramodulation,[status(thm)],[f153,f37]) ).
fof(f164,plain,
! [X0] :
( ~ sQ7_spl
| X0 = multiply(sk_c8,multiply(sk_c1,X0)) ),
inference(forward_demodulation,[status(thm)],[f35,f163]) ).
fof(f170,plain,
( ~ sQ14_spl
| inverse(inverse(sk_c8)) != sk_c8
| multiply(sk_c8,identity) != sk_c7 ),
inference(paramodulation,[status(thm)],[f36,f146]) ).
fof(f171,plain,
( ~ sQ14_spl
| inverse(identity) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7 ),
inference(paramodulation,[status(thm)],[f35,f146]) ).
fof(f173,plain,
( ~ sQ4_spl
| ~ sQ14_spl
| inverse(sk_c5) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7 ),
inference(paramodulation,[status(thm)],[f86,f146]) ).
fof(f178,definition,
( sQ16_spl
<=> multiply(sk_c8,identity) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f180,plain,
( sQ16_spl
| multiply(sk_c8,identity) != sk_c7 ),
inference(component_clause,[status(thm)],[f178]) ).
fof(f181,definition,
( sQ17_spl
<=> inverse(inverse(sk_c8)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f183,plain,
( sQ17_spl
| inverse(inverse(sk_c8)) != sk_c8 ),
inference(component_clause,[status(thm)],[f181]) ).
fof(f184,plain,
( ~ sQ14_spl
| ~ sQ17_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f170,f178,f181,f142]) ).
fof(f185,definition,
( sQ18_spl
<=> multiply(sk_c8,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f187,plain,
( sQ18_spl
| multiply(sk_c8,sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f185]) ).
fof(f188,definition,
( sQ19_spl
<=> inverse(identity) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f190,plain,
( sQ19_spl
| inverse(identity) != sk_c8 ),
inference(component_clause,[status(thm)],[f188]) ).
fof(f191,plain,
( ~ sQ14_spl
| ~ sQ19_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f171,f185,f188,f142]) ).
fof(f192,plain,
( ~ sQ4_spl
| ~ sQ14_spl
| ~ sQ5_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f173,f81,f89,f142,f85]) ).
fof(f195,plain,
( ~ sQ2_spl
| ~ sQ13_spl
| inverse(sk_c4) != sk_c8 ),
inference(resolution,[status(thm)],[f140,f78]) ).
fof(f201,plain,
( ~ sQ2_spl
| ~ sQ13_spl
| ~ sQ1_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f74,f195]) ).
fof(f202,plain,
( ~ sQ2_spl
| ~ sQ13_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f201]) ).
fof(f203,plain,
( ~ sQ2_spl
| ~ sQ13_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f202]) ).
fof(f204,plain,
! [X0] :
( ~ sQ12_spl
| multiply(inverse(X0),sk_c7) != sk_c8
| multiply(X0,inverse(X0)) != sk_c8 ),
inference(destructive_equality_resolution,[status(thm)],[f137]) ).
fof(f205,plain,
( ~ sQ0_spl
| multiply(sk_c7,sk_c8) = identity ),
inference(paramodulation,[status(thm)],[f71,f36]) ).
fof(f210,plain,
( ~ sQ12_spl
| multiply(inverse(identity),sk_c7) != sk_c8
| inverse(identity) != sk_c8 ),
inference(paramodulation,[status(thm)],[f35,f204]) ).
fof(f212,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| multiply(inverse(sk_c8),sk_c7) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c8 ),
inference(paramodulation,[status(thm)],[f71,f204]) ).
fof(f216,definition,
( sQ20_spl
<=> multiply(inverse(identity),sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f218,plain,
( sQ20_spl
| multiply(inverse(identity),sk_c7) != sk_c8 ),
inference(component_clause,[status(thm)],[f216]) ).
fof(f219,plain,
( ~ sQ12_spl
| ~ sQ20_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f210,f188,f216,f136]) ).
fof(f220,definition,
( sQ21_spl
<=> multiply(sk_c8,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f222,plain,
( sQ21_spl
| multiply(sk_c8,sk_c7) != sk_c8 ),
inference(component_clause,[status(thm)],[f220]) ).
fof(f223,definition,
( sQ22_spl
<=> multiply(inverse(sk_c8),sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f225,plain,
( sQ22_spl
| multiply(inverse(sk_c8),sk_c7) != sk_c8 ),
inference(component_clause,[status(thm)],[f223]) ).
fof(f226,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ22_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f212,f220,f223,f136,f70]) ).
fof(f255,plain,
( ~ sQ6_spl
| ~ sQ11_spl
| inverse(sk_c1) != sk_c8 ),
inference(resolution,[status(thm)],[f134,f94]) ).
fof(f258,plain,
( ~ sQ11_spl
| inverse(inverse(sk_c8)) != sk_c8
| identity != sk_c7 ),
inference(paramodulation,[status(thm)],[f36,f134]) ).
fof(f259,plain,
( ~ sQ11_spl
| inverse(identity) != sk_c8
| sk_c8 != sk_c7 ),
inference(paramodulation,[status(thm)],[f35,f134]) ).
fof(f261,plain,
( ~ sQ4_spl
| ~ sQ11_spl
| inverse(sk_c5) != sk_c8
| sk_c6 != sk_c7 ),
inference(paramodulation,[status(thm)],[f86,f134]) ).
fof(f262,plain,
( ~ sQ6_spl
| ~ sQ11_spl
| ~ sQ7_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f102,f255]) ).
fof(f263,plain,
( ~ sQ6_spl
| ~ sQ11_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f262]) ).
fof(f264,plain,
( ~ sQ6_spl
| ~ sQ11_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f263]) ).
fof(f271,definition,
( sQ28_spl
<=> inverse(sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f273,plain,
( sQ28_spl
| inverse(sk_c7) != sk_c8 ),
inference(component_clause,[status(thm)],[f271]) ).
fof(f279,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c6,sk_c5) = multiply(sk_c5,identity) ),
inference(paramodulation,[status(thm)],[f156,f148]) ).
fof(f306,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| sk_c8 = multiply(sk_c8,sk_c7) ),
inference(paramodulation,[status(thm)],[f94,f164]) ).
fof(f307,plain,
( ~ sQ7_spl
| ~ sQ14_spl
| inverse(sk_c1) != sk_c8
| sk_c8 != sk_c7 ),
inference(paramodulation,[status(thm)],[f164,f146]) ).
fof(f314,definition,
( sQ29_spl
<=> sk_c8 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f315,plain,
( ~ sQ29_spl
| sk_c8 = sk_c7 ),
inference(component_clause,[status(thm)],[f314]) ).
fof(f316,plain,
( sQ29_spl
| sk_c8 != sk_c7 ),
inference(component_clause,[status(thm)],[f314]) ).
fof(f317,plain,
( ~ sQ14_spl
| ~ sQ7_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f307,f314,f101,f142]) ).
fof(f321,plain,
( sQ21_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f306,f222]) ).
fof(f322,plain,
( sQ21_spl
| ~ sQ6_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f321]) ).
fof(f323,plain,
( sQ21_spl
| ~ sQ6_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f322]) ).
fof(f327,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| multiply(sk_c7,sk_c7) = multiply(sk_c1,sk_c8) ),
inference(paramodulation,[status(thm)],[f306,f162]) ).
fof(f331,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| multiply(sk_c7,sk_c7) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f94,f327]) ).
fof(f342,definition,
( sQ32_spl
<=> sk_c8 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f344,plain,
( sQ32_spl
| sk_c8 != sk_c8 ),
inference(component_clause,[status(thm)],[f342]) ).
fof(f346,definition,
( sQ33_spl
<=> inverse(inverse(sk_c7)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f348,plain,
( sQ33_spl
| inverse(inverse(sk_c7)) != sk_c8 ),
inference(component_clause,[status(thm)],[f346]) ).
fof(f363,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ13_spl
| inverse(sk_c8) != sk_c8 ),
inference(resolution,[status(thm)],[f140,f306]) ).
fof(f365,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ13_spl
| sk_c7 != sk_c8
| inverse(sk_c7) != sk_c8 ),
inference(paramodulation,[status(thm)],[f331,f140]) ).
fof(f369,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ13_spl
| sk_c8 != sk_c8
| inverse(sk_c8) != sk_c8 ),
inference(paramodulation,[status(thm)],[f306,f140]) ).
fof(f371,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ13_spl
| ~ sQ0_spl
| sk_c7 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f71,f363]) ).
fof(f372,definition,
( sQ35_spl
<=> inverse(sk_c6) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f374,plain,
( sQ35_spl
| inverse(sk_c6) != sk_c8 ),
inference(component_clause,[status(thm)],[f372]) ).
fof(f375,definition,
( sQ36_spl
<=> sk_c6 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f377,plain,
( sQ36_spl
| sk_c6 != sk_c8 ),
inference(component_clause,[status(thm)],[f375]) ).
fof(f379,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ13_spl
| ~ sQ29_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f365,f271,f314,f139,f101,f93]) ).
fof(f383,definition,
( sQ37_spl
<=> inverse(sk_c8) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f385,plain,
( sQ37_spl
| inverse(sk_c8) != sk_c8 ),
inference(component_clause,[status(thm)],[f383]) ).
fof(f386,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ13_spl
| ~ sQ32_spl
| ~ sQ37_spl ),
inference(split_clause,[status(thm)],[f369,f383,f342,f139,f101,f93]) ).
fof(f387,plain,
( sQ32_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f344]) ).
fof(f388,plain,
sQ32_spl,
inference(contradiction_clause,[status(thm)],[f387]) ).
fof(f404,plain,
( ~ sQ2_spl
| sk_c7 = multiply(inverse(sk_c4),sk_c8) ),
inference(paramodulation,[status(thm)],[f78,f158]) ).
fof(f407,plain,
( ~ sQ9_spl
| sk_c2 = multiply(inverse(sk_c3),identity) ),
inference(paramodulation,[status(thm)],[f154,f158]) ).
fof(f408,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f158,f158]) ).
fof(f409,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f36,f158]) ).
fof(f410,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f35,f158]) ).
fof(f411,plain,
( ~ sQ1_spl
| sk_c4 = multiply(inverse(sk_c8),identity) ),
inference(paramodulation,[status(thm)],[f155,f158]) ).
fof(f413,plain,
( ~ sQ3_spl
| sk_c6 = multiply(inverse(sk_c8),sk_c7) ),
inference(paramodulation,[status(thm)],[f82,f158]) ).
fof(f414,plain,
( ~ sQ5_spl
| sk_c5 = multiply(inverse(sk_c8),identity) ),
inference(paramodulation,[status(thm)],[f156,f158]) ).
fof(f417,plain,
( ~ sQ4_spl
| sk_c8 = multiply(inverse(sk_c5),sk_c6) ),
inference(paramodulation,[status(thm)],[f86,f158]) ).
fof(f419,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sk_c7 = multiply(sk_c8,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f74,f404]) ).
fof(f420,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f419,f187]) ).
fof(f421,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f420]) ).
fof(f424,plain,
( sQ16_spl
| sk_c8 != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f427,f180]) ).
fof(f426,plain,
( ~ sQ9_spl
| sk_c2 = inverse(sk_c3) ),
inference(backward_demodulation,[status(thm)],[f427,f407]) ).
fof(f427,plain,
! [X0] : X0 = multiply(X0,identity),
inference(forward_demodulation,[status(thm)],[f408,f409]) ).
fof(f428,plain,
( sQ20_spl
| sk_c7 != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f410,f218]) ).
fof(f429,plain,
( sQ0_spl
| ~ sQ1_spl
| sk_c4 != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f433,f72]) ).
fof(f430,plain,
( sQ17_spl
| ~ sQ1_spl
| inverse(sk_c4) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f433,f183]) ).
fof(f431,plain,
( sQ22_spl
| ~ sQ1_spl
| multiply(sk_c4,sk_c7) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f433,f225]) ).
fof(f433,plain,
( ~ sQ1_spl
| sk_c4 = inverse(sk_c8) ),
inference(forward_demodulation,[status(thm)],[f427,f411]) ).
fof(f441,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| sk_c6 = multiply(sk_c4,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f433,f413]) ).
fof(f442,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c6 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f78,f441]) ).
fof(f443,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sQ36_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f442,f377]) ).
fof(f444,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sQ36_spl ),
inference(contradiction_clause,[status(thm)],[f443]) ).
fof(f445,plain,
( ~ sQ5_spl
| sk_c5 = inverse(sk_c8) ),
inference(forward_demodulation,[status(thm)],[f427,f414]) ).
fof(f450,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| sk_c5 = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f433,f445]) ).
fof(f453,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| sk_c8 = multiply(sk_c8,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f90,f417]) ).
fof(f454,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c8 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f82,f453]) ).
fof(f455,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f454,f316]) ).
fof(f456,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sQ29_spl ),
inference(contradiction_clause,[status(thm)],[f455]) ).
fof(f458,plain,
( sQ16_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f424,f314,f178]) ).
fof(f459,plain,
( sQ20_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f428,f314,f216]) ).
fof(f460,plain,
( sQ17_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f430,f73,f181]) ).
fof(f461,plain,
( sQ22_spl
| ~ sQ1_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f431,f77,f73,f223]) ).
fof(f482,plain,
( sQ35_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c8) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f442,f374]) ).
fof(f501,plain,
( sQ37_spl
| ~ sQ0_spl
| sk_c7 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f71,f385]) ).
fof(f502,plain,
( ~ sQ3_spl
| ~ sQ0_spl
| sk_c6 = multiply(sk_c7,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f71,f413]) ).
fof(f513,plain,
( ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(sk_c8,sk_c7) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f518,f82]) ).
fof(f518,plain,
( ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c6 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f331,f502]) ).
fof(f551,plain,
( ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c8 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f306,f513]) ).
fof(f552,plain,
( ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f551,f371]) ).
fof(f553,plain,
( ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f552]) ).
fof(f555,plain,
( sQ37_spl
| ~ sQ0_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f501,f314,f70,f383]) ).
fof(f557,plain,
( ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ29_spl
| sk_c6 = multiply(sk_c7,sk_c8) ),
inference(backward_demodulation,[status(thm)],[f315,f502]) ).
fof(f564,plain,
( ~ sQ3_spl
| ~ sQ29_spl
| multiply(sk_c8,sk_c6) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f315,f82]) ).
fof(f568,plain,
( sQ28_spl
| ~ sQ29_spl
| inverse(sk_c8) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f315,f273]) ).
fof(f569,plain,
( sQ33_spl
| ~ sQ29_spl
| inverse(inverse(sk_c8)) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f315,f348]) ).
fof(f574,plain,
( sQ35_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| sk_c7 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f71,f482]) ).
fof(f575,plain,
( sQ35_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ29_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f315,f574]) ).
fof(f576,plain,
( sQ35_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ29_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f575]) ).
fof(f577,plain,
( sQ35_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ29_spl ),
inference(contradiction_clause,[status(thm)],[f576]) ).
fof(f595,plain,
! [X0] :
( ~ sQ9_spl
| X0 = multiply(sk_c2,multiply(sk_c3,X0)) ),
inference(paramodulation,[status(thm)],[f426,f158]) ).
fof(f599,plain,
( ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ8_spl
| sk_c1 = identity ),
inference(backward_demodulation,[status(thm)],[f610,f153]) ).
fof(f603,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ8_spl
| sk_c8 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f610,f306]) ).
fof(f610,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ8_spl
| X0 = multiply(sk_c8,X0) ),
inference(forward_demodulation,[status(thm)],[f161,f595]) ).
fof(f614,plain,
( sQ19_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ8_spl
| inverse(sk_c1) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f599,f190]) ).
fof(f629,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ8_spl
| sQ29_spl ),
inference(split_clause,[status(thm)],[f603,f314,f109,f117,f101,f93]) ).
fof(f644,plain,
( sQ19_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f614,f101,f109,f117,f188]) ).
fof(f656,plain,
( sQ19_spl
| ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ29_spl
| inverse(sk_c6) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f657,f190]) ).
fof(f657,plain,
( ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ29_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f205,f557]) ).
fof(f659,plain,
( sQ28_spl
| ~ sQ29_spl
| ~ sQ37_spl ),
inference(split_clause,[status(thm)],[f568,f383,f314,f271]) ).
fof(f660,plain,
( sQ33_spl
| ~ sQ29_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f569,f181,f314,f346]) ).
fof(f675,plain,
( ~ sQ3_spl
| ~ sQ29_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c8,sk_c8) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f442,f564]) ).
fof(f721,definition,
( sQ38_spl
<=> sk_c6 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f723,plain,
( sQ38_spl
| sk_c6 != sk_c7 ),
inference(component_clause,[status(thm)],[f721]) ).
fof(f724,plain,
( ~ sQ4_spl
| ~ sQ11_spl
| ~ sQ5_spl
| ~ sQ38_spl ),
inference(split_clause,[status(thm)],[f261,f721,f89,f133,f85]) ).
fof(f740,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c8,sk_c5) = multiply(sk_c5,identity) ),
inference(forward_demodulation,[status(thm)],[f442,f279]) ).
fof(f770,definition,
( sQ39_spl
<=> identity = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f774,plain,
( ~ sQ11_spl
| ~ sQ17_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f258,f770,f181,f133]) ).
fof(f775,plain,
( ~ sQ11_spl
| ~ sQ19_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f259,f314,f188,f133]) ).
fof(f812,plain,
( sQ19_spl
| ~ sQ3_spl
| ~ sQ0_spl
| ~ sQ29_spl
| ~ sQ35_spl ),
inference(split_clause,[status(thm)],[f656,f372,f314,f70,f81,f188]) ).
fof(f832,plain,
( sQ38_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f442,f723]) ).
fof(f835,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c8,sk_c8) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f442,f82]) ).
fof(f836,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ29_spl
| sk_c8 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f675,f835]) ).
fof(f837,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ29_spl
| sQ38_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f836,f832]) ).
fof(f838,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ29_spl
| sQ38_spl ),
inference(contradiction_clause,[status(thm)],[f837]) ).
fof(f844,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| identity = multiply(sk_c5,identity) ),
inference(forward_demodulation,[status(thm)],[f156,f740]) ).
fof(f872,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| identity = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f427,f844]) ).
fof(f895,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 = multiply(inverse(sk_c8),sk_c7) ),
inference(forward_demodulation,[status(thm)],[f442,f413]) ).
fof(f896,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sk_c8 = multiply(inverse(sk_c8),sk_c8) ),
inference(forward_demodulation,[status(thm)],[f454,f895]) ).
fof(f902,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sk_c8 = identity ),
inference(forward_demodulation,[status(thm)],[f36,f896]) ).
fof(f903,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ3_spl
| sk_c4 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f454,f429]) ).
fof(f927,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f902,f872]) ).
fof(f928,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f450,f927]) ).
fof(f929,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f928,f903]) ).
fof(f930,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f929]) ).
fof(f931,plain,
$false,
inference(sat_refutation,[status(thm)],[f76,f80,f84,f88,f92,f96,f97,f98,f99,f100,f104,f105,f106,f107,f108,f112,f113,f114,f115,f116,f120,f121,f122,f123,f124,f145,f184,f191,f192,f203,f219,f226,f264,f317,f323,f379,f386,f388,f421,f444,f456,f458,f459,f460,f461,f553,f555,f577,f629,f644,f659,f660,f724,f774,f775,f812,f838,f930]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP232-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n011.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
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 20 20:07:25 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.14/0.36 % Drodi V4.1.1
% 0.14/0.40 % Refutation found
% 0.14/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.42 % Elapsed time: 0.063407 seconds
% 0.14/0.42 % CPU time: 0.249791 seconds
% 0.14/0.42 % Total memory used: 105.745 MB
% 0.14/0.42 % Net memory used: 105.488 MB
%------------------------------------------------------------------------------