%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP301-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:33:21 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 51
% Syntax : Number of formulae : 297 ( 13 unt; 20 def)
% Number of atoms : 1151 ( 337 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1636 ( 782 ~; 834 |; 0 &)
% ( 20 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 21 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 63 ( 63 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
! [X3,X4,X1,X2] :
( multiply(X2,sk_c5) != sk_c6
| inverse(X2) != sk_c6
| multiply(X1,sk_c6) != sk_c7
| inverse(X1) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(X4) != sk_c6
| multiply(X4,sk_c6) != sk_c5
| inverse(sk_c7) != sk_c5
| inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c5 ),
file('/export/starexec/sandbox2/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_c6,sk_c7) = sk_c5
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f39,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f40,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f41,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f42,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f43,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f44,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f45,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f46,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f47,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f48,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f49,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f50,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f51,plain,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f52,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f54,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f55,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f56,plain,
( inverse(sk_c4) = sk_c6
| inverse(sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f57,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f59,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f60,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f61,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f62,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f64,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f65,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f66,plain,
( inverse(sk_c4) = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f67,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f68,plain,
! [X2] :
( multiply(X2,sk_c5) != sk_c6
| inverse(X2) != sk_c6
| ! [X1] :
( multiply(X1,sk_c6) != sk_c7
| inverse(X1) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| ! [X4] :
( inverse(X4) != sk_c6
| multiply(X4,sk_c6) != sk_c5
| inverse(sk_c7) != sk_c5
| ! [X3] :
( inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c5 ) ) ) ),
inference(miniscoping,[status(thm)],[f34]) ).
fof(f69,plain,
! [X0,X1,X2,X3] :
( multiply(X3,sk_c5) != sk_c6
| inverse(X3) != sk_c6
| multiply(X2,sk_c6) != sk_c7
| inverse(X2) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(X1) != sk_c6
| multiply(X1,sk_c6) != sk_c5
| inverse(sk_c7) != sk_c5
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c5 ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f70,definition,
( sQ0_spl
<=> multiply(sk_c7,sk_c6) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f71,plain,
( ~ sQ0_spl
| multiply(sk_c7,sk_c6) = sk_c5 ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f72,plain,
( sQ0_spl
| multiply(sk_c7,sk_c6) != sk_c5 ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f73,definition,
( sQ1_spl
<=> multiply(sk_c6,sk_c7) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f74,plain,
( ~ sQ1_spl
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f75,plain,
( sQ1_spl
| multiply(sk_c6,sk_c7) != sk_c5 ),
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
<=> inverse(sk_c3) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f78,plain,
( ~ sQ2_spl
| inverse(sk_c3) = sk_c7 ),
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_c3,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f82,plain,
( ~ sQ3_spl
| multiply(sk_c3,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
<=> inverse(sk_c4) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ4_spl
| inverse(sk_c4) = 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
<=> multiply(sk_c4,sk_c5) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f90,plain,
( ~ sQ5_spl
| multiply(sk_c4,sk_c5) = sk_c6 ),
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_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ6_spl
| multiply(sk_c1,sk_c7) = sk_c6 ),
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_c7 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f102,plain,
( ~ sQ7_spl
| inverse(sk_c1) = sk_c7 ),
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
<=> inverse(sk_c7) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f110,plain,
( ~ sQ8_spl
| inverse(sk_c7) = sk_c5 ),
inference(component_clause,[status(thm)],[f109]) ).
fof(f111,plain,
( sQ8_spl
| inverse(sk_c7) != sk_c5 ),
inference(component_clause,[status(thm)],[f109]) ).
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
<=> multiply(sk_c2,sk_c6) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f118,plain,
( ~ sQ9_spl
| multiply(sk_c2,sk_c6) = sk_c5 ),
inference(component_clause,[status(thm)],[f117]) ).
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(f125,definition,
( sQ10_spl
<=> inverse(sk_c2) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f126,plain,
( ~ sQ10_spl
| inverse(sk_c2) = sk_c6 ),
inference(component_clause,[status(thm)],[f125]) ).
fof(f129,plain,
( sQ2_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f64,f125,f77]) ).
fof(f130,plain,
( sQ3_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f65,f125,f81]) ).
fof(f131,plain,
( sQ4_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f66,f125,f85]) ).
fof(f132,plain,
( sQ5_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f67,f125,f89]) ).
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_c6
| multiply(X1,sk_c6) != sk_c5 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f137,plain,
! [X0] :
( ~ sQ12_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c5 ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f139,definition,
! [X2] :
( sQ13_spl
<=> ( multiply(X2,sk_c6) != sk_c7
| inverse(X2) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f140,plain,
! [X0] :
( ~ sQ13_spl
| multiply(X0,sk_c6) != sk_c7
| inverse(X0) != sk_c7 ),
inference(component_clause,[status(thm)],[f139]) ).
fof(f142,definition,
! [X3] :
( sQ14_spl
<=> ( multiply(X3,sk_c5) != sk_c6
| inverse(X3) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f143,plain,
! [X0] :
( ~ sQ14_spl
| multiply(X0,sk_c5) != sk_c6
| inverse(X0) != sk_c6 ),
inference(component_clause,[status(thm)],[f142]) ).
fof(f145,plain,
( sQ14_spl
| sQ13_spl
| ~ sQ1_spl
| sQ12_spl
| ~ sQ8_spl
| sQ11_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f69,f70,f133,f109,f136,f73,f139,f142]) ).
fof(f146,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| inverse(sk_c4) != sk_c6 ),
inference(resolution,[status(thm)],[f143,f90]) ).
fof(f148,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| ~ sQ4_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f86,f146]) ).
fof(f149,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f148]) ).
fof(f150,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f149]) ).
fof(f151,plain,
( ~ sQ3_spl
| ~ sQ13_spl
| inverse(sk_c3) != sk_c7 ),
inference(resolution,[status(thm)],[f140,f82]) ).
fof(f152,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| sk_c5 != sk_c7
| inverse(sk_c7) != sk_c7 ),
inference(paramodulation,[status(thm)],[f71,f140]) ).
fof(f155,plain,
( ~ sQ3_spl
| ~ sQ13_spl
| ~ sQ2_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f78,f151]) ).
fof(f156,plain,
( ~ sQ3_spl
| ~ sQ13_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f155]) ).
fof(f157,plain,
( ~ sQ3_spl
| ~ sQ13_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f156]) ).
fof(f159,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| inverse(sk_c2) != sk_c6 ),
inference(resolution,[status(thm)],[f137,f118]) ).
fof(f160,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| inverse(sk_c7) != sk_c6
| sk_c5 != sk_c5 ),
inference(paramodulation,[status(thm)],[f71,f137]) ).
fof(f164,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ10_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f126,f159]) ).
fof(f165,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f164]) ).
fof(f166,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f165]) ).
fof(f172,plain,
! [X0] :
( ~ sQ5_spl
| multiply(sk_c6,X0) = multiply(sk_c4,multiply(sk_c5,X0)) ),
inference(paramodulation,[status(thm)],[f90,f37]) ).
fof(f175,plain,
( ~ sQ6_spl
| ~ sQ11_spl
| inverse(sk_c1) != sk_c7 ),
inference(resolution,[status(thm)],[f134,f94]) ).
fof(f178,plain,
( ~ sQ6_spl
| ~ sQ11_spl
| ~ sQ7_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f102,f175]) ).
fof(f179,plain,
( ~ sQ6_spl
| ~ sQ11_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f178]) ).
fof(f180,plain,
( ~ sQ6_spl
| ~ sQ11_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f179]) ).
fof(f181,definition,
( sQ15_spl
<=> inverse(sk_c7) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f183,plain,
( sQ15_spl
| inverse(sk_c7) != sk_c7 ),
inference(component_clause,[status(thm)],[f181]) ).
fof(f184,definition,
( sQ16_spl
<=> sk_c5 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f185,plain,
( ~ sQ16_spl
| sk_c5 = sk_c7 ),
inference(component_clause,[status(thm)],[f184]) ).
fof(f186,plain,
( sQ16_spl
| sk_c5 != sk_c7 ),
inference(component_clause,[status(thm)],[f184]) ).
fof(f187,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f152,f181,f184,f139,f70]) ).
fof(f197,plain,
( sQ15_spl
| ~ sQ8_spl
| sk_c5 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f110,f183]) ).
fof(f199,plain,
( ~ sQ8_spl
| multiply(sk_c5,sk_c7) = identity ),
inference(paramodulation,[status(thm)],[f110,f36]) ).
fof(f200,plain,
( ~ sQ7_spl
| multiply(sk_c7,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f102,f36]) ).
fof(f202,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f36,f37]) ).
fof(f203,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f35,f202]) ).
fof(f204,plain,
! [X0] :
( ~ sQ1_spl
| multiply(sk_c5,X0) = multiply(sk_c6,multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f74,f37]) ).
fof(f221,plain,
( ~ sQ7_spl
| sk_c1 = multiply(inverse(sk_c7),identity) ),
inference(paramodulation,[status(thm)],[f200,f203]) ).
fof(f223,plain,
( ~ sQ6_spl
| sk_c7 = multiply(inverse(sk_c1),sk_c6) ),
inference(paramodulation,[status(thm)],[f94,f203]) ).
fof(f224,plain,
( ~ sQ9_spl
| sk_c6 = multiply(inverse(sk_c2),sk_c5) ),
inference(paramodulation,[status(thm)],[f118,f203]) ).
fof(f228,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| sk_c1 = multiply(sk_c5,identity) ),
inference(forward_demodulation,[status(thm)],[f110,f221]) ).
fof(f230,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| sk_c7 = multiply(sk_c7,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f102,f223]) ).
fof(f231,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c7 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f71,f230]) ).
fof(f232,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f231,f186]) ).
fof(f233,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sQ16_spl ),
inference(contradiction_clause,[status(thm)],[f232]) ).
fof(f234,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| sk_c6 = multiply(sk_c6,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f126,f224]) ).
fof(f238,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(sk_c5,sk_c6) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f231,f71]) ).
fof(f252,plain,
( sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| multiply(sk_c6,sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f231,f75]) ).
fof(f253,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c6 = multiply(inverse(sk_c5),sk_c5) ),
inference(paramodulation,[status(thm)],[f238,f203]) ).
fof(f255,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f36,f253]) ).
fof(f261,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(inverse(X0),X0) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f255,f36]) ).
fof(f262,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(sk_c6,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f255,f35]) ).
fof(f263,plain,
( sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c5 != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f262,f252]) ).
fof(f266,plain,
( sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f263]) ).
fof(f267,plain,
( sQ1_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f266]) ).
fof(f268,plain,
( sQ15_spl
| ~ sQ8_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f197,f184,f109,f181]) ).
fof(f278,definition,
( sQ19_spl
<=> sk_c6 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f280,plain,
( sQ19_spl
| sk_c6 != sk_c6 ),
inference(component_clause,[status(thm)],[f278]) ).
fof(f282,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c1 = multiply(sk_c5,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f255,f228]) ).
fof(f290,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| sk_c1 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f238,f282]) ).
fof(f295,plain,
( ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(sk_c6,sk_c2) = sk_c6 ),
inference(paramodulation,[status(thm)],[f126,f261]) ).
fof(f298,plain,
( ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c2 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f262,f295]) ).
fof(f301,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ10_spl
| multiply(sk_c2,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f298,f262]) ).
fof(f304,plain,
( ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| inverse(sk_c2) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f298,f126]) ).
fof(f316,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c2 = multiply(sk_c6,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f298,f234]) ).
fof(f317,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c2 = multiply(sk_c2,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f298,f316]) ).
fof(f318,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sk_c2 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f301,f317]) ).
fof(f322,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c2 = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f323,f290]) ).
fof(f323,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c2 = sk_c1 ),
inference(forward_demodulation,[status(thm)],[f290,f318]) ).
fof(f326,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(X0,sk_c5) != sk_c6
| inverse(X0) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f298,f143]) ).
fof(f327,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(X0,sk_c2) != sk_c6
| inverse(X0) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f322,f326]) ).
fof(f328,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ9_spl
| multiply(X0,sk_c2) != sk_c2
| inverse(X0) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f298,f327]) ).
fof(f329,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ14_spl
| ~ sQ8_spl
| ~ sQ9_spl
| inverse(sk_c2) != sk_c2 ),
inference(resolution,[status(thm)],[f328,f301]) ).
fof(f332,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ14_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f304,f329]) ).
fof(f333,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ14_spl
| ~ sQ8_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f332]) ).
fof(f334,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ14_spl
| ~ sQ8_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f333]) ).
fof(f336,plain,
( sQ19_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f280]) ).
fof(f337,plain,
sQ19_spl,
inference(contradiction_clause,[status(thm)],[f336]) ).
fof(f344,plain,
( ~ sQ3_spl
| sk_c6 = multiply(inverse(sk_c3),sk_c7) ),
inference(paramodulation,[status(thm)],[f82,f203]) ).
fof(f346,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| sk_c6 = multiply(sk_c7,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f78,f344]) ).
fof(f347,plain,
( ~ sQ5_spl
| sk_c5 = multiply(inverse(sk_c4),sk_c6) ),
inference(paramodulation,[status(thm)],[f90,f203]) ).
fof(f349,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 = multiply(sk_c6,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f86,f347]) ).
fof(f351,plain,
! [X0] :
( ~ sQ1_spl
| multiply(sk_c5,X0) = multiply(sk_c6,multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f74,f37]) ).
fof(f362,plain,
( ~ sQ2_spl
| multiply(sk_c7,sk_c3) = identity ),
inference(paramodulation,[status(thm)],[f78,f36]) ).
fof(f363,plain,
( ~ sQ4_spl
| multiply(sk_c6,sk_c4) = identity ),
inference(paramodulation,[status(thm)],[f86,f36]) ).
fof(f371,plain,
( ~ sQ8_spl
| ~ sQ5_spl
| multiply(sk_c6,sk_c7) = multiply(sk_c4,identity) ),
inference(paramodulation,[status(thm)],[f199,f172]) ).
fof(f374,plain,
( ~ sQ8_spl
| ~ sQ5_spl
| ~ sQ1_spl
| sk_c5 = multiply(sk_c4,identity) ),
inference(forward_demodulation,[status(thm)],[f74,f371]) ).
fof(f390,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| multiply(sk_c5,sk_c7) = multiply(sk_c6,sk_c6) ),
inference(paramodulation,[status(thm)],[f346,f204]) ).
fof(f393,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ8_spl
| identity = multiply(sk_c6,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f199,f390]) ).
fof(f411,plain,
( ~ sQ8_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ4_spl
| sk_c5 = multiply(sk_c4,sk_c5) ),
inference(backward_demodulation,[status(thm)],[f419,f374]) ).
fof(f419,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ5_spl
| ~ sQ4_spl
| identity = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f349,f393]) ).
fof(f420,plain,
( ~ sQ8_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ4_spl
| sk_c5 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f90,f411]) ).
fof(f426,plain,
( sQ0_spl
| ~ sQ8_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ4_spl
| multiply(sk_c7,sk_c5) != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f420,f72]) ).
fof(f460,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f35,f203]) ).
fof(f462,plain,
( sQ8_spl
| ~ sQ16_spl
| inverse(sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f185,f111]) ).
fof(f466,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ16_spl
| sk_c6 = multiply(sk_c5,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f185,f346]) ).
fof(f467,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ16_spl
| sk_c6 = multiply(sk_c5,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f185,f466]) ).
fof(f477,plain,
( ~ sQ2_spl
| ~ sQ16_spl
| multiply(sk_c5,sk_c3) = identity ),
inference(forward_demodulation,[status(thm)],[f185,f362]) ).
fof(f500,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ16_spl
| multiply(sk_c5,X0) = multiply(sk_c6,multiply(sk_c5,X0)) ),
inference(forward_demodulation,[status(thm)],[f185,f351]) ).
fof(f501,plain,
( ~ sQ2_spl
| ~ sQ16_spl
| ~ sQ1_spl
| multiply(sk_c5,sk_c3) = multiply(sk_c6,identity) ),
inference(paramodulation,[status(thm)],[f477,f500]) ).
fof(f502,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ16_spl
| ~ sQ1_spl
| multiply(sk_c5,sk_c5) = multiply(sk_c6,sk_c6) ),
inference(paramodulation,[status(thm)],[f467,f500]) ).
fof(f505,plain,
( ~ sQ2_spl
| ~ sQ16_spl
| ~ sQ1_spl
| identity = multiply(sk_c6,identity) ),
inference(forward_demodulation,[status(thm)],[f477,f501]) ).
fof(f506,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ16_spl
| ~ sQ1_spl
| sk_c6 = multiply(sk_c6,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f467,f502]) ).
fof(f507,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ16_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c6 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f349,f506]) ).
fof(f515,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ16_spl
| ~ sQ1_spl
| ~ sQ5_spl
| multiply(sk_c5,sk_c4) = identity ),
inference(backward_demodulation,[status(thm)],[f507,f363]) ).
fof(f519,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ16_spl
| ~ sQ1_spl
| ~ sQ5_spl
| inverse(sk_c4) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f507,f86]) ).
fof(f529,plain,
( ~ sQ2_spl
| ~ sQ16_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ4_spl
| identity = multiply(sk_c5,identity) ),
inference(forward_demodulation,[status(thm)],[f507,f505]) ).
fof(f531,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ16_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(identity,X0) = multiply(sk_c5,multiply(identity,X0)) ),
inference(paramodulation,[status(thm)],[f529,f37]) ).
fof(f532,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ16_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ4_spl
| X0 = multiply(sk_c5,multiply(identity,X0)) ),
inference(forward_demodulation,[status(thm)],[f35,f531]) ).
fof(f533,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ16_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ4_spl
| X0 = multiply(sk_c5,X0) ),
inference(forward_demodulation,[status(thm)],[f35,f532]) ).
fof(f538,plain,
( ~ sQ2_spl
| ~ sQ16_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c3 = identity ),
inference(backward_demodulation,[status(thm)],[f533,f477]) ).
fof(f539,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ16_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ4_spl
| X0 = multiply(inverse(sk_c5),X0) ),
inference(paramodulation,[status(thm)],[f533,f203]) ).
fof(f541,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ16_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(inverse(X0),X0) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f538,f36]) ).
fof(f542,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ16_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c3,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f538,f35]) ).
fof(f550,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ16_spl
| ~ sQ1_spl
| ~ sQ5_spl
| sk_c4 = identity ),
inference(forward_demodulation,[status(thm)],[f533,f515]) ).
fof(f551,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ16_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c4,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f554,f542]) ).
fof(f554,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ16_spl
| ~ sQ1_spl
| ~ sQ5_spl
| sk_c4 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f538,f550]) ).
fof(f560,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ16_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(inverse(X0),X0) = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f554,f541]) ).
fof(f567,plain,
( ~ sQ2_spl
| ~ sQ16_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 = sk_c4 ),
inference(paramodulation,[status(thm)],[f560,f539]) ).
fof(f575,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ16_spl
| ~ sQ1_spl
| ~ sQ5_spl
| inverse(sk_c4) = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f567,f519]) ).
fof(f577,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ16_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c6 = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f567,f507]) ).
fof(f578,plain,
( sQ8_spl
| ~ sQ16_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(sk_c5) != sk_c4 ),
inference(backward_demodulation,[status(thm)],[f567,f462]) ).
fof(f579,plain,
( ~ sQ16_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c4 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f567,f185]) ).
fof(f581,plain,
( sQ8_spl
| ~ sQ16_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(sk_c4) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f567,f578]) ).
fof(f585,plain,
( sQ8_spl
| ~ sQ16_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c4 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f575,f581]) ).
fof(f586,plain,
( sQ8_spl
| ~ sQ16_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f585]) ).
fof(f587,plain,
( sQ8_spl
| ~ sQ16_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f586]) ).
fof(f649,plain,
( sQ0_spl
| ~ sQ8_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ16_spl
| multiply(sk_c4,sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f579,f426]) ).
fof(f650,plain,
( sQ0_spl
| ~ sQ8_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ16_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f551,f649]) ).
fof(f651,plain,
( sQ0_spl
| ~ sQ8_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ16_spl
| sk_c4 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f567,f650]) ).
fof(f652,plain,
( sQ0_spl
| ~ sQ8_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ16_spl
| sk_c4 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f567,f651]) ).
fof(f653,plain,
( sQ0_spl
| ~ sQ8_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ16_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f652]) ).
fof(f654,plain,
( sQ0_spl
| ~ sQ8_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ16_spl ),
inference(contradiction_clause,[status(thm)],[f653]) ).
fof(f683,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ16_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c4) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f579,f134]) ).
fof(f684,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ16_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c4) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f577,f683]) ).
fof(f685,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ16_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(X0) != sk_c4
| multiply(X0,sk_c4) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f579,f684]) ).
fof(f696,plain,
( ~ sQ2_spl
| ~ sQ16_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ11_spl
| inverse(inverse(sk_c4)) != sk_c4 ),
inference(resolution,[status(thm)],[f685,f560]) ).
fof(f703,plain,
( ~ sQ2_spl
| ~ sQ16_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ11_spl
| inverse(sk_c4) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f575,f696]) ).
fof(f704,plain,
( ~ sQ2_spl
| ~ sQ16_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ11_spl
| sk_c4 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f575,f703]) ).
fof(f705,plain,
( ~ sQ2_spl
| ~ sQ16_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f704]) ).
fof(f706,plain,
( ~ sQ2_spl
| ~ sQ16_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f705]) ).
fof(f718,definition,
( sQ20_spl
<=> sk_c5 = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f720,plain,
( sQ20_spl
| sk_c5 != sk_c5 ),
inference(component_clause,[status(thm)],[f718]) ).
fof(f721,definition,
( sQ21_spl
<=> inverse(sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f723,plain,
( sQ21_spl
| inverse(sk_c7) != sk_c6 ),
inference(component_clause,[status(thm)],[f721]) ).
fof(f724,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ21_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f160,f718,f721,f136,f70]) ).
fof(f733,plain,
( sQ20_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f720]) ).
fof(f734,plain,
sQ20_spl,
inference(contradiction_clause,[status(thm)],[f733]) ).
fof(f744,plain,
! [X0] : multiply(identity,X0) = X0,
inference(paramodulation,[status(thm)],[f203,f460]) ).
fof(f765,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| multiply(sk_c5,sk_c7) = multiply(sk_c6,sk_c6) ),
inference(paramodulation,[status(thm)],[f346,f204]) ).
fof(f770,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c5,sk_c7) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f349,f765]) ).
fof(f791,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c7 = multiply(inverse(sk_c5),sk_c5) ),
inference(paramodulation,[status(thm)],[f770,f203]) ).
fof(f793,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c7 = identity ),
inference(forward_demodulation,[status(thm)],[f36,f791]) ).
fof(f794,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(inverse(X0),X0) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f793,f36]) ).
fof(f797,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c7,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f793,f744]) ).
fof(f799,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c6 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f797,f346]) ).
fof(f805,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c6,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f799,f797]) ).
fof(f810,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(sk_c3) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f799,f78]) ).
fof(f812,plain,
( sQ16_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 != sk_c6 ),
inference(backward_demodulation,[status(thm)],[f799,f186]) ).
fof(f823,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| X0 = multiply(sk_c6,multiply(sk_c3,X0)) ),
inference(paramodulation,[status(thm)],[f810,f203]) ).
fof(f824,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| X0 = multiply(sk_c3,X0) ),
inference(forward_demodulation,[status(thm)],[f805,f823]) ).
fof(f825,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(inverse(X0),X0) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f799,f794]) ).
fof(f826,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c6,sk_c3) = sk_c6 ),
inference(paramodulation,[status(thm)],[f810,f825]) ).
fof(f829,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c3 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f805,f826]) ).
fof(f839,plain,
( ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ4_spl
| multiply(sk_c4,sk_c5) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f829,f90]) ).
fof(f843,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(sk_c3) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f829,f810]) ).
fof(f845,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c3 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f829,f799]) ).
fof(f846,plain,
( sQ16_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 != sk_c3 ),
inference(backward_demodulation,[status(thm)],[f829,f812]) ).
fof(f849,plain,
( sQ21_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(sk_c3) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f845,f723]) ).
fof(f850,plain,
( sQ21_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(sk_c3) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f829,f849]) ).
fof(f851,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| inverse(sk_c4) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f829,f86]) ).
fof(f858,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f843,f850]) ).
fof(f859,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sQ21_spl ),
inference(contradiction_clause,[status(thm)],[f858]) ).
fof(f872,plain,
( ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ4_spl
| sk_c5 = multiply(inverse(sk_c4),sk_c3) ),
inference(paramodulation,[status(thm)],[f839,f203]) ).
fof(f874,plain,
( ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ4_spl
| sk_c5 = multiply(sk_c3,sk_c3) ),
inference(forward_demodulation,[status(thm)],[f851,f872]) ).
fof(f875,plain,
( ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ4_spl
| sk_c5 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f824,f874]) ).
fof(f876,plain,
( ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ4_spl
| sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f875,f846]) ).
fof(f877,plain,
( ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ4_spl
| sQ16_spl ),
inference(contradiction_clause,[status(thm)],[f876]) ).
fof(f878,plain,
$false,
inference(sat_refutation,[status(thm)],[f76,f80,f84,f88,f92,f96,f97,f98,f99,f100,f104,f105,f106,f107,f108,f113,f114,f115,f116,f121,f122,f123,f124,f129,f130,f131,f132,f145,f150,f157,f166,f180,f187,f233,f267,f268,f334,f337,f587,f654,f706,f724,f734,f859,f877]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP301-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n010.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 20:09:10 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.10/0.39 % Refutation found
% 0.10/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.42 % Elapsed time: 0.055644 seconds
% 0.14/0.42 % CPU time: 0.135460 seconds
% 0.14/0.42 % Total memory used: 27.854 MB
% 0.14/0.42 % Net memory used: 27.748 MB
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