%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP381-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 12:33:34 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.41s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 51
% Syntax : Number of formulae : 240 ( 10 unt; 19 def)
% Number of atoms : 801 ( 281 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1054 ( 493 ~; 542 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 20 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 42 ( 42 !; 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
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c7 ),
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_c7
| inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| inverse(sk_c7) != sk_c6 ),
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
| inverse(sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f39,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f40,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f41,plain,
( inverse(sk_c4) = sk_c6
| inverse(sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f42,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f43,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f44,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f45,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f46,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f47,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f48,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f49,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f50,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f51,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f52,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f53,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f54,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f55,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f56,plain,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f57,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f59,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f60,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f61,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f62,plain,
( multiply(sk_c4,sk_c5) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c7 ),
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_c7
| ! [X3] :
( inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| inverse(sk_c7) != sk_c6 ) ) ) ),
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_c7
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| inverse(sk_c7) != sk_c6 ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f70,definition,
( sQ0_spl
<=> inverse(sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f71,plain,
( ~ sQ0_spl
| inverse(sk_c7) = sk_c6 ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f72,plain,
( sQ0_spl
| inverse(sk_c7) != sk_c6 ),
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_c6,sk_c5) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ6_spl
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f95,plain,
( sQ6_spl
| multiply(sk_c6,sk_c5) != 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
<=> multiply(sk_c1,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f102,plain,
( ~ sQ7_spl
| multiply(sk_c1,sk_c7) = sk_c6 ),
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_c1) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f110,plain,
( ~ sQ8_spl
| inverse(sk_c1) = sk_c7 ),
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
<=> multiply(sk_c2,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f118,plain,
( ~ sQ9_spl
| multiply(sk_c2,sk_c6) = sk_c7 ),
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_c7 ) ),
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_c7 ),
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
| sQ11_spl
| ~ sQ6_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f69,f70,f93,f133,f136,f73,f139,f142]) ).
fof(f147,plain,
! [X0] :
( ~ sQ5_spl
| multiply(sk_c6,X0) = multiply(sk_c4,multiply(sk_c5,X0)) ),
inference(paramodulation,[status(thm)],[f90,f37]) ).
fof(f150,plain,
! [X0] :
( ~ sQ3_spl
| multiply(sk_c7,X0) = multiply(sk_c3,multiply(sk_c6,X0)) ),
inference(paramodulation,[status(thm)],[f82,f37]) ).
fof(f152,plain,
( ~ sQ8_spl
| multiply(sk_c7,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f110,f36]) ).
fof(f154,plain,
( ~ sQ2_spl
| multiply(sk_c7,sk_c3) = identity ),
inference(paramodulation,[status(thm)],[f78,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(f160,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| inverse(sk_c4) != sk_c6 ),
inference(resolution,[status(thm)],[f143,f90]) ).
fof(f165,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| ~ sQ4_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f86,f160]) ).
fof(f166,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f165]) ).
fof(f167,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f166]) ).
fof(f168,plain,
( ~ sQ9_spl
| ~ sQ13_spl
| inverse(sk_c2) != sk_c7 ),
inference(resolution,[status(thm)],[f140,f118]) ).
fof(f169,plain,
( ~ sQ3_spl
| ~ sQ13_spl
| inverse(sk_c3) != sk_c7 ),
inference(resolution,[status(thm)],[f140,f82]) ).
fof(f175,plain,
( ~ sQ9_spl
| ~ sQ13_spl
| ~ sQ10_spl
| sk_c6 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f126,f168]) ).
fof(f176,plain,
( ~ sQ3_spl
| ~ sQ13_spl
| ~ sQ2_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f78,f169]) ).
fof(f177,plain,
( ~ sQ3_spl
| ~ sQ13_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f176]) ).
fof(f178,plain,
( ~ sQ3_spl
| ~ sQ13_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f177]) ).
fof(f179,plain,
( ~ sQ0_spl
| multiply(sk_c6,sk_c7) = identity ),
inference(paramodulation,[status(thm)],[f71,f36]) ).
fof(f181,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| inverse(sk_c2) != sk_c6 ),
inference(resolution,[status(thm)],[f137,f118]) ).
fof(f182,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| inverse(sk_c3) != sk_c6 ),
inference(resolution,[status(thm)],[f137,f82]) ).
fof(f186,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| inverse(sk_c3) != sk_c6
| sk_c7 != sk_c7 ),
inference(paramodulation,[status(thm)],[f82,f137]) ).
fof(f188,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ10_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f126,f181]) ).
fof(f189,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f188]) ).
fof(f190,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f189]) ).
fof(f191,plain,
! [X0] :
( ~ sQ8_spl
| multiply(identity,X0) = multiply(sk_c7,multiply(sk_c1,X0)) ),
inference(paramodulation,[status(thm)],[f152,f37]) ).
fof(f192,plain,
! [X0] :
( ~ sQ8_spl
| X0 = multiply(sk_c7,multiply(sk_c1,X0)) ),
inference(forward_demodulation,[status(thm)],[f35,f191]) ).
fof(f197,plain,
( ~ sQ7_spl
| ~ sQ11_spl
| inverse(sk_c1) != sk_c7 ),
inference(resolution,[status(thm)],[f134,f102]) ).
fof(f201,plain,
( ~ sQ11_spl
| inverse(identity) != sk_c7
| sk_c7 != sk_c6 ),
inference(paramodulation,[status(thm)],[f35,f134]) ).
fof(f203,plain,
( ~ sQ7_spl
| ~ sQ11_spl
| ~ sQ8_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f110,f197]) ).
fof(f204,plain,
( ~ sQ7_spl
| ~ sQ11_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f203]) ).
fof(f205,plain,
( ~ sQ7_spl
| ~ sQ11_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f204]) ).
fof(f206,plain,
( ~ sQ1_spl
| ~ sQ0_spl
| identity = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f179,f74]) ).
fof(f210,definition,
( sQ16_spl
<=> sk_c7 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f212,plain,
( sQ16_spl
| sk_c7 != sk_c7 ),
inference(component_clause,[status(thm)],[f210]) ).
fof(f221,definition,
( sQ19_spl
<=> inverse(identity) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f223,plain,
( sQ19_spl
| inverse(identity) != sk_c7 ),
inference(component_clause,[status(thm)],[f221]) ).
fof(f224,definition,
( sQ20_spl
<=> sk_c6 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f226,plain,
( sQ20_spl
| sk_c6 != sk_c7 ),
inference(component_clause,[status(thm)],[f224]) ).
fof(f229,plain,
( sQ16_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f212]) ).
fof(f230,plain,
sQ16_spl,
inference(contradiction_clause,[status(thm)],[f229]) ).
fof(f231,plain,
( sQ1_spl
| ~ sQ0_spl
| identity != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f179,f75]) ).
fof(f235,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| sk_c7 = multiply(sk_c7,sk_c6) ),
inference(paramodulation,[status(thm)],[f102,f192]) ).
fof(f248,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| sk_c6 = multiply(inverse(sk_c7),sk_c7) ),
inference(paramodulation,[status(thm)],[f235,f157]) ).
fof(f264,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f36,f248]) ).
fof(f292,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| multiply(identity,sk_c7) = identity ),
inference(backward_demodulation,[status(thm)],[f264,f179]) ).
fof(f294,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| multiply(identity,sk_c5) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f264,f94]) ).
fof(f295,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| inverse(sk_c7) = identity ),
inference(backward_demodulation,[status(thm)],[f264,f71]) ).
fof(f305,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c7 = identity ),
inference(forward_demodulation,[status(thm)],[f35,f292]) ).
fof(f307,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c5 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f35,f294]) ).
fof(f313,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c5 = identity ),
inference(forward_demodulation,[status(thm)],[f305,f307]) ).
fof(f314,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f313,f231]) ).
fof(f315,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f314]) ).
fof(f327,plain,
( ~ sQ9_spl
| ~ sQ13_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| identity != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f264,f175]) ).
fof(f328,plain,
( ~ sQ9_spl
| ~ sQ13_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f305,f327]) ).
fof(f329,plain,
( ~ sQ9_spl
| ~ sQ13_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f328]) ).
fof(f330,plain,
( ~ sQ9_spl
| ~ sQ13_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f329]) ).
fof(f331,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ7_spl
| ~ sQ8_spl
| multiply(X0,sk_c5) != sk_c6
| inverse(X0) != identity ),
inference(forward_demodulation,[status(thm)],[f264,f143]) ).
fof(f332,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ7_spl
| ~ sQ8_spl
| multiply(X0,sk_c5) != identity
| inverse(X0) != identity ),
inference(forward_demodulation,[status(thm)],[f264,f331]) ).
fof(f356,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| inverse(identity) = identity ),
inference(forward_demodulation,[status(thm)],[f305,f295]) ).
fof(f376,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ0_spl
| multiply(X0,identity) != identity
| inverse(X0) != identity ),
inference(forward_demodulation,[status(thm)],[f313,f332]) ).
fof(f378,plain,
( ~ sQ14_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ0_spl
| inverse(inverse(identity)) != identity ),
inference(resolution,[status(thm)],[f376,f36]) ).
fof(f384,plain,
( ~ sQ14_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ0_spl
| inverse(identity) != identity ),
inference(forward_demodulation,[status(thm)],[f356,f378]) ).
fof(f385,plain,
( ~ sQ14_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ0_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f356,f384]) ).
fof(f386,plain,
( ~ sQ14_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f385]) ).
fof(f387,plain,
( ~ sQ14_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f386]) ).
fof(f396,plain,
( ~ sQ11_spl
| ~ sQ19_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f201,f224,f221,f133]) ).
fof(f401,plain,
( ~ sQ3_spl
| sk_c6 = multiply(inverse(sk_c3),sk_c7) ),
inference(paramodulation,[status(thm)],[f82,f157]) ).
fof(f403,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| sk_c6 = multiply(sk_c7,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f78,f401]) ).
fof(f408,plain,
( ~ sQ5_spl
| sk_c5 = multiply(inverse(sk_c4),sk_c6) ),
inference(paramodulation,[status(thm)],[f90,f157]) ).
fof(f410,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 = multiply(sk_c6,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f86,f408]) ).
fof(f413,plain,
! [X0] :
( ~ sQ1_spl
| multiply(sk_c5,X0) = multiply(sk_c6,multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f74,f37]) ).
fof(f453,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| multiply(sk_c5,sk_c7) = multiply(sk_c6,sk_c6) ),
inference(paramodulation,[status(thm)],[f403,f413]) ).
fof(f458,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c5,sk_c7) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f410,f453]) ).
fof(f465,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c6,sk_c7) = multiply(sk_c4,sk_c5) ),
inference(paramodulation,[status(thm)],[f458,f147]) ).
fof(f467,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c7 = multiply(inverse(sk_c5),sk_c5) ),
inference(paramodulation,[status(thm)],[f458,f157]) ).
fof(f469,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 = multiply(sk_c4,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f74,f465]) ).
fof(f470,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f90,f469]) ).
fof(f477,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c7 = identity ),
inference(forward_demodulation,[status(thm)],[f36,f467]) ).
fof(f487,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c6,sk_c7) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f470,f74]) ).
fof(f493,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(sk_c7,sk_c7) = multiply(sk_c3,sk_c6) ),
inference(paramodulation,[status(thm)],[f487,f150]) ).
fof(f496,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c6 = multiply(sk_c3,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f403,f493]) ).
fof(f497,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c6 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f82,f496]) ).
fof(f517,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(identity,sk_c3) = identity ),
inference(backward_demodulation,[status(thm)],[f477,f154]) ).
fof(f518,plain,
( sQ19_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(identity) != identity ),
inference(backward_demodulation,[status(thm)],[f477,f223]) ).
fof(f519,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(sk_c3) = identity ),
inference(backward_demodulation,[status(thm)],[f477,f78]) ).
fof(f521,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c3 = identity ),
inference(forward_demodulation,[status(thm)],[f35,f517]) ).
fof(f537,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f477,f497]) ).
fof(f566,plain,
( sQ20_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| identity != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f537,f226]) ).
fof(f567,plain,
( sQ20_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f477,f566]) ).
fof(f568,plain,
( sQ20_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f567]) ).
fof(f569,plain,
( sQ20_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f568]) ).
fof(f626,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(identity) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f521,f182]) ).
fof(f627,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(identity) != identity ),
inference(forward_demodulation,[status(thm)],[f537,f626]) ).
fof(f633,definition,
( sQ29_spl
<=> inverse(sk_c3) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f636,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| ~ sQ29_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f186,f210,f633,f136,f81]) ).
fof(f654,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(identity) = identity ),
inference(forward_demodulation,[status(thm)],[f521,f519]) ).
fof(f665,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f654,f627]) ).
fof(f666,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f665]) ).
fof(f667,plain,
( ~ sQ3_spl
| ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f666]) ).
fof(f668,plain,
( sQ19_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f654,f518]) ).
fof(f669,plain,
( sQ19_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f668]) ).
fof(f670,plain,
( sQ19_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f669]) ).
fof(f678,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| inverse(identity) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f477,f72]) ).
fof(f679,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| identity != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f654,f678]) ).
fof(f680,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f537,f679]) ).
fof(f681,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f680]) ).
fof(f682,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f681]) ).
fof(f739,plain,
( sQ6_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| multiply(identity,sk_c5) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f537,f95]) ).
fof(f740,plain,
( sQ6_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f35,f739]) ).
fof(f741,plain,
( sQ6_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| sk_c5 != identity ),
inference(forward_demodulation,[status(thm)],[f477,f740]) ).
fof(f757,plain,
( sQ6_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f206,f741]) ).
fof(f758,plain,
( sQ6_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f757]) ).
fof(f759,plain,
( sQ6_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f758]) ).
fof(f760,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,f121,f122,f123,f124,f129,f130,f131,f132,f145,f167,f178,f190,f205,f230,f315,f330,f387,f396,f569,f636,f667,f670,f682,f759]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP381-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 20:10:43 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.41 % Refutation found
% 0.10/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.44 % Elapsed time: 0.055299 seconds
% 0.10/0.44 % CPU time: 0.208255 seconds
% 0.10/0.44 % Total memory used: 104.833 MB
% 0.10/0.44 % Net memory used: 104.540 MB
%------------------------------------------------------------------------------