%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP323-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : 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 12:33:25 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.40s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 60
% Syntax : Number of formulae : 319 ( 12 unt; 26 def)
% Number of atoms : 1336 ( 371 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 1949 ( 932 ~; 991 |; 0 &)
% ( 26 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 28 ( 26 usr; 27 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 66 ( 66 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
! [X3,X4,X5,X1,X2] :
( inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c6
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| inverse(X5) != sk_c8
| multiply(X5,sk_c8) != X4
| multiply(sk_c8,X4) != sk_c7
| inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f36,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f37,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f38,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f39,plain,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f40,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f41,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f42,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f43,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f44,plain,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f45,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f46,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f47,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f48,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f49,plain,
( multiply(sk_c4,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f50,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f51,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f52,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f53,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f54,plain,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f55,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f56,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f57,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f58,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f59,plain,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f60,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f61,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f62,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f63,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f64,plain,
( multiply(sk_c4,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f65,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f66,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f67,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f68,plain,
! [X2] :
( inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c6
| ! [X1] :
( inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| ! [X5] :
( inverse(X5) != sk_c8
| ! [X4] :
( multiply(X5,sk_c8) != X4
| multiply(sk_c8,X4) != sk_c7
| ! [X3] :
( inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ) ) ) ) ),
inference(miniscoping,[status(thm)],[f34]) ).
fof(f69,plain,
! [X0,X1,X2,X3,X4] :
( inverse(X4) != sk_c8
| multiply(X4,sk_c8) != sk_c6
| inverse(X3) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != X1
| multiply(sk_c8,X1) != sk_c7
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f70,definition,
( sQ0_spl
<=> multiply(sk_c7,sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f71,plain,
( ~ sQ0_spl
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f72,plain,
( sQ0_spl
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f73,definition,
( sQ1_spl
<=> multiply(sk_c8,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f74,plain,
( ~ sQ1_spl
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f75,plain,
( sQ1_spl
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f76,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f38,f70,f73]) ).
fof(f77,definition,
( sQ2_spl
<=> multiply(sk_c4,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f78,plain,
( ~ sQ2_spl
| multiply(sk_c4,sk_c8) = 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
<=> inverse(sk_c4) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f82,plain,
( ~ sQ3_spl
| inverse(sk_c4) = sk_c8 ),
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_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ6_spl
| multiply(sk_c1,sk_c7) = sk_c8 ),
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
<=> multiply(sk_c8,sk_c3) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f110,plain,
( ~ sQ8_spl
| multiply(sk_c8,sk_c3) = 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_c8) = sk_c3 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f118,plain,
( ~ sQ9_spl
| multiply(sk_c2,sk_c8) = 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(f125,definition,
( sQ10_spl
<=> inverse(sk_c2) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f126,plain,
( ~ sQ10_spl
| inverse(sk_c2) = sk_c8 ),
inference(component_clause,[status(thm)],[f125]) ).
fof(f128,plain,
( sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f63,f125,f73]) ).
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_c8 ) ),
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_c8 ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,definition,
! [X1,X2] :
( sQ12_spl
<=> ( inverse(X2) != sk_c8
| multiply(X2,sk_c8) != X1
| multiply(sk_c8,X1) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f137,plain,
! [X0,X1] :
( ~ sQ12_spl
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != X0
| multiply(sk_c8,X0) != sk_c7 ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f139,definition,
! [X3] :
( sQ13_spl
<=> ( inverse(X3) != sk_c8
| multiply(X3,sk_c8) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f140,plain,
! [X0] :
( ~ sQ13_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f139]) ).
fof(f142,definition,
! [X4] :
( sQ14_spl
<=> ( inverse(X4) != sk_c8
| multiply(X4,sk_c8) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f143,plain,
! [X0] :
( ~ sQ14_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c6 ),
inference(component_clause,[status(thm)],[f142]) ).
fof(f145,plain,
( sQ14_spl
| sQ13_spl
| ~ sQ1_spl
| sQ12_spl
| sQ11_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f69,f70,f133,f136,f73,f139,f142]) ).
fof(f146,plain,
( ~ sQ4_spl
| ~ sQ14_spl
| inverse(sk_c5) != sk_c8 ),
inference(resolution,[status(thm)],[f143,f86]) ).
fof(f147,plain,
( ~ sQ9_spl
| ~ sQ14_spl
| inverse(sk_c2) != sk_c8
| sk_c3 != sk_c6 ),
inference(paramodulation,[status(thm)],[f118,f143]) ).
fof(f150,plain,
( ~ sQ4_spl
| ~ sQ14_spl
| ~ sQ5_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f90,f146]) ).
fof(f151,plain,
( ~ sQ4_spl
| ~ sQ14_spl
| ~ sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f150]) ).
fof(f152,plain,
( ~ sQ4_spl
| ~ sQ14_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f151]) ).
fof(f161,plain,
( ~ sQ2_spl
| ~ sQ13_spl
| inverse(sk_c4) != sk_c8 ),
inference(resolution,[status(thm)],[f140,f78]) ).
fof(f163,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| inverse(sk_c7) != sk_c8
| sk_c6 != sk_c7 ),
inference(paramodulation,[status(thm)],[f71,f140]) ).
fof(f164,plain,
( ~ sQ9_spl
| ~ sQ13_spl
| inverse(sk_c2) != sk_c8
| sk_c3 != sk_c7 ),
inference(paramodulation,[status(thm)],[f118,f140]) ).
fof(f166,plain,
( ~ sQ2_spl
| ~ sQ13_spl
| ~ sQ3_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f82,f161]) ).
fof(f167,plain,
( ~ sQ2_spl
| ~ sQ13_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f166]) ).
fof(f168,plain,
( ~ sQ2_spl
| ~ sQ13_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f167]) ).
fof(f169,plain,
! [X0] :
( ~ sQ12_spl
| inverse(X0) != sk_c8
| multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ),
inference(destructive_equality_resolution,[status(thm)],[f137]) ).
fof(f171,plain,
( ~ sQ7_spl
| multiply(sk_c7,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f102,f36]) ).
fof(f174,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f36,f37]) ).
fof(f175,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f35,f174]) ).
fof(f191,plain,
( ~ sQ6_spl
| sk_c7 = multiply(inverse(sk_c1),sk_c8) ),
inference(paramodulation,[status(thm)],[f94,f175]) ).
fof(f195,plain,
( ~ sQ9_spl
| sk_c8 = multiply(inverse(sk_c2),sk_c3) ),
inference(paramodulation,[status(thm)],[f118,f175]) ).
fof(f198,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| sk_c7 = multiply(sk_c7,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f102,f191]) ).
fof(f199,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c7 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f71,f198]) ).
fof(f200,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| sk_c8 = multiply(sk_c8,sk_c3) ),
inference(forward_demodulation,[status(thm)],[f126,f195]) ).
fof(f201,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c8 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f110,f200]) ).
fof(f203,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| multiply(sk_c6,sk_c1) = identity ),
inference(backward_demodulation,[status(thm)],[f199,f171]) ).
fof(f204,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(sk_c6,sk_c8) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f199,f71]) ).
fof(f206,plain,
( ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| multiply(sk_c8,sk_c3) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f199,f110]) ).
fof(f208,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| inverse(sk_c1) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f199,f102]) ).
fof(f214,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| inverse(sk_c2) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f216,f126]) ).
fof(f216,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c8 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f199,f201]) ).
fof(f221,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| inverse(X0) != sk_c8
| multiply(sk_c6,multiply(X0,sk_c8)) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f216,f169]) ).
fof(f222,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| inverse(X0) != sk_c8
| multiply(sk_c6,multiply(X0,sk_c6)) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f216,f221]) ).
fof(f223,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| inverse(X0) != sk_c8
| multiply(sk_c6,multiply(X0,sk_c6)) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f199,f222]) ).
fof(f224,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| inverse(X0) != sk_c6
| multiply(sk_c6,multiply(X0,sk_c6)) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f216,f223]) ).
fof(f225,plain,
( ~ sQ12_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| inverse(inverse(sk_c6)) != sk_c6
| multiply(sk_c6,identity) != sk_c6 ),
inference(paramodulation,[status(thm)],[f36,f224]) ).
fof(f228,definition,
( sQ15_spl
<=> multiply(sk_c6,identity) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f230,plain,
( sQ15_spl
| multiply(sk_c6,identity) != sk_c6 ),
inference(component_clause,[status(thm)],[f228]) ).
fof(f231,definition,
( sQ16_spl
<=> inverse(inverse(sk_c6)) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f233,plain,
( sQ16_spl
| inverse(inverse(sk_c6)) != sk_c6 ),
inference(component_clause,[status(thm)],[f231]) ).
fof(f234,plain,
( ~ sQ12_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f225,f228,f231,f70,f101,f93,f109,f125,f117,f136]) ).
fof(f238,definition,
( sQ18_spl
<=> inverse(identity) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f240,plain,
( sQ18_spl
| inverse(identity) != sk_c6 ),
inference(component_clause,[status(thm)],[f238]) ).
fof(f242,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c6) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f199,f134]) ).
fof(f243,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f216,f242]) ).
fof(f244,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f199,f243]) ).
fof(f247,plain,
( ~ sQ11_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| inverse(identity) != sk_c6
| sk_c6 != sk_c6 ),
inference(paramodulation,[status(thm)],[f35,f244]) ).
fof(f253,definition,
( sQ20_spl
<=> sk_c6 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f255,plain,
( sQ20_spl
| sk_c6 != sk_c6 ),
inference(component_clause,[status(thm)],[f253]) ).
fof(f256,plain,
( ~ sQ11_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ18_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f247,f253,f238,f109,f125,f117,f70,f101,f93,f133]) ).
fof(f257,plain,
( sQ20_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f255]) ).
fof(f258,plain,
sQ20_spl,
inference(contradiction_clause,[status(thm)],[f257]) ).
fof(f267,definition,
( sQ21_spl
<=> sk_c6 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f269,plain,
( sQ21_spl
| sk_c6 != sk_c7 ),
inference(component_clause,[status(thm)],[f267]) ).
fof(f270,definition,
( sQ22_spl
<=> inverse(sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f273,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ22_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f163,f267,f270,f139,f70]) ).
fof(f274,definition,
( sQ23_spl
<=> sk_c3 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f276,plain,
( sQ23_spl
| sk_c3 != sk_c7 ),
inference(component_clause,[status(thm)],[f274]) ).
fof(f277,plain,
( ~ sQ9_spl
| ~ sQ13_spl
| ~ sQ10_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f164,f274,f125,f139,f117]) ).
fof(f278,definition,
( sQ24_spl
<=> sk_c7 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f280,plain,
( sQ24_spl
| sk_c7 != sk_c7 ),
inference(component_clause,[status(thm)],[f278]) ).
fof(f283,plain,
( sQ24_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c6 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f199,f280]) ).
fof(f284,plain,
( sQ24_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f199,f283]) ).
fof(f285,plain,
( sQ24_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f284]) ).
fof(f286,plain,
( sQ24_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f285]) ).
fof(f287,plain,
( sQ23_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c3 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f199,f276]) ).
fof(f290,plain,
( sQ21_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f199,f269]) ).
fof(f291,plain,
( sQ21_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f290]) ).
fof(f292,plain,
( sQ21_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f291]) ).
fof(f294,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| multiply(sk_c6,sk_c6) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f216,f204]) ).
fof(f295,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c6 = multiply(inverse(sk_c6),sk_c6) ),
inference(paramodulation,[status(thm)],[f294,f175]) ).
fof(f297,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f36,f295]) ).
fof(f300,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| multiply(inverse(X0),X0) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f297,f36]) ).
fof(f301,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| multiply(sk_c6,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f297,f35]) ).
fof(f307,plain,
( sQ18_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| inverse(sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f297,f240]) ).
fof(f317,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c1 = identity ),
inference(forward_demodulation,[status(thm)],[f301,f203]) ).
fof(f319,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| multiply(sk_c1,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f330,f301]) ).
fof(f321,plain,
( sQ18_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| inverse(sk_c6) != sk_c1 ),
inference(backward_demodulation,[status(thm)],[f330,f307]) ).
fof(f324,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c1 = identity ),
inference(backward_demodulation,[status(thm)],[f330,f297]) ).
fof(f325,plain,
( sQ23_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c3 != sk_c1 ),
inference(backward_demodulation,[status(thm)],[f330,f287]) ).
fof(f326,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| inverse(sk_c2) = sk_c1 ),
inference(backward_demodulation,[status(thm)],[f330,f214]) ).
fof(f327,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| inverse(sk_c1) = sk_c1 ),
inference(backward_demodulation,[status(thm)],[f330,f208]) ).
fof(f328,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c8 = sk_c1 ),
inference(backward_demodulation,[status(thm)],[f330,f216]) ).
fof(f329,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c7 = sk_c1 ),
inference(backward_demodulation,[status(thm)],[f330,f199]) ).
fof(f330,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c1 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f297,f317]) ).
fof(f331,plain,
( sQ18_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| inverse(sk_c1) != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f330,f321]) ).
fof(f333,plain,
( ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c8,sk_c3) = sk_c1 ),
inference(forward_demodulation,[status(thm)],[f330,f206]) ).
fof(f340,plain,
( ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c1,sk_c3) = sk_c1 ),
inference(backward_demodulation,[status(thm)],[f328,f333]) ).
fof(f347,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| X0 = multiply(sk_c1,multiply(sk_c2,X0)) ),
inference(paramodulation,[status(thm)],[f326,f175]) ).
fof(f348,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| X0 = multiply(sk_c2,X0) ),
inference(forward_demodulation,[status(thm)],[f319,f347]) ).
fof(f349,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f327,f331]) ).
fof(f350,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f349]) ).
fof(f369,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f36,f37]) ).
fof(f370,plain,
! [X0] : multiply(identity,X0) = X0,
inference(forward_demodulation,[status(thm)],[f175,f369]) ).
fof(f377,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| sk_c8 != sk_c7
| multiply(sk_c5,sk_c7) != sk_c8 ),
inference(paramodulation,[status(thm)],[f90,f134]) ).
fof(f379,definition,
( sQ25_spl
<=> multiply(sk_c5,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f381,plain,
( sQ25_spl
| multiply(sk_c5,sk_c7) != sk_c8 ),
inference(component_clause,[status(thm)],[f379]) ).
fof(f382,definition,
( sQ26_spl
<=> sk_c8 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f384,plain,
( sQ26_spl
| sk_c8 != sk_c7 ),
inference(component_clause,[status(thm)],[f382]) ).
fof(f385,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| ~ sQ26_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f377,f379,f382,f133,f89]) ).
fof(f405,plain,
( ~ sQ2_spl
| sk_c8 = multiply(inverse(sk_c4),sk_c7) ),
inference(paramodulation,[status(thm)],[f78,f175]) ).
fof(f407,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| sk_c8 = multiply(sk_c8,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f82,f405]) ).
fof(f408,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c8 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f74,f407]) ).
fof(f413,plain,
( sQ26_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c6 != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f408,f384]) ).
fof(f415,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| multiply(sk_c6,sk_c7) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f408,f74]) ).
fof(f416,plain,
( ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| inverse(sk_c5) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f408,f90]) ).
fof(f417,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| inverse(sk_c4) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f408,f82]) ).
fof(f418,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(sk_c5,sk_c6) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f408,f86]) ).
fof(f437,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c7 = multiply(inverse(sk_c6),sk_c6) ),
inference(paramodulation,[status(thm)],[f415,f175]) ).
fof(f439,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c7 = identity ),
inference(forward_demodulation,[status(thm)],[f36,f437]) ).
fof(f443,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| multiply(sk_c7,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f439,f370]) ).
fof(f444,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| multiply(inverse(X0),X0) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f439,f36]) ).
fof(f458,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c6 = multiply(inverse(sk_c5),sk_c6) ),
inference(paramodulation,[status(thm)],[f418,f175]) ).
fof(f460,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| sk_c6 = multiply(sk_c6,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f416,f458]) ).
fof(f481,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| sk_c6 = multiply(inverse(sk_c6),sk_c6) ),
inference(paramodulation,[status(thm)],[f460,f175]) ).
fof(f483,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| sk_c6 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f444,f481]) ).
fof(f484,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f483,f413]) ).
fof(f485,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| sQ26_spl ),
inference(contradiction_clause,[status(thm)],[f484]) ).
fof(f487,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| inverse(X0) != sk_c8
| multiply(sk_c6,multiply(X0,sk_c8)) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f408,f169]) ).
fof(f488,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| inverse(X0) != sk_c8
| multiply(sk_c6,multiply(X0,sk_c6)) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f408,f487]) ).
fof(f489,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| inverse(X0) != sk_c6
| multiply(sk_c6,multiply(X0,sk_c6)) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f408,f488]) ).
fof(f494,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| multiply(sk_c6,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f483,f443]) ).
fof(f495,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sk_c6 = identity ),
inference(backward_demodulation,[status(thm)],[f483,f439]) ).
fof(f503,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f494,f489]) ).
fof(f504,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f483,f503]) ).
fof(f506,plain,
( ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ12_spl
| ~ sQ4_spl
| multiply(sk_c5,sk_c6) != sk_c6 ),
inference(resolution,[status(thm)],[f504,f416]) ).
fof(f509,plain,
( ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ12_spl
| ~ sQ4_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f418,f506]) ).
fof(f510,plain,
( ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ12_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f509]) ).
fof(f511,plain,
( ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ12_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f510]) ).
fof(f512,plain,
( sQ25_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| multiply(sk_c5,sk_c6) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f483,f381]) ).
fof(f513,plain,
( sQ25_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| sk_c6 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f418,f512]) ).
fof(f514,plain,
( sQ25_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f408,f513]) ).
fof(f515,plain,
( sQ25_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f514]) ).
fof(f516,plain,
( sQ25_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f515]) ).
fof(f530,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| multiply(inverse(X0),X0) = sk_c1 ),
inference(forward_demodulation,[status(thm)],[f330,f300]) ).
fof(f532,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| multiply(sk_c1,sk_c2) = sk_c1 ),
inference(paramodulation,[status(thm)],[f326,f530]) ).
fof(f535,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c2 = sk_c1 ),
inference(forward_demodulation,[status(thm)],[f319,f532]) ).
fof(f541,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c7 = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f545,f329]) ).
fof(f542,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c8 = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f545,f328]) ).
fof(f543,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c3 = identity ),
inference(backward_demodulation,[status(thm)],[f545,f324]) ).
fof(f544,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c3 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f545,f330]) ).
fof(f545,plain,
( ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c3 = sk_c1 ),
inference(forward_demodulation,[status(thm)],[f319,f340]) ).
fof(f547,plain,
( ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c2 = sk_c1 ),
inference(backward_demodulation,[status(thm)],[f548,f545]) ).
fof(f548,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c2 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f545,f535]) ).
fof(f549,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c7 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f548,f541]) ).
fof(f550,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c8 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f548,f542]) ).
fof(f551,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c2 = identity ),
inference(forward_demodulation,[status(thm)],[f548,f543]) ).
fof(f557,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c2 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f548,f544]) ).
fof(f560,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| inverse(sk_c2) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f547,f208]) ).
fof(f561,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| inverse(sk_c2) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f557,f560]) ).
fof(f622,plain,
( sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| multiply(sk_c2,sk_c7) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f550,f75]) ).
fof(f623,plain,
( sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c7 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f348,f622]) ).
fof(f624,plain,
( sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c2 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f549,f623]) ).
fof(f625,plain,
( sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f557,f624]) ).
fof(f626,plain,
( sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f625]) ).
fof(f627,plain,
( sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f626]) ).
fof(f628,plain,
( sQ16_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| inverse(inverse(sk_c2)) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f557,f233]) ).
fof(f629,plain,
( sQ16_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| inverse(sk_c2) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f561,f628]) ).
fof(f630,plain,
( sQ16_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c2 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f561,f629]) ).
fof(f631,plain,
( sQ16_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f557,f630]) ).
fof(f632,plain,
( sQ16_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f631]) ).
fof(f633,plain,
( sQ16_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f632]) ).
fof(f657,definition,
( sQ30_spl
<=> sk_c3 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f659,plain,
( sQ30_spl
| sk_c3 != sk_c6 ),
inference(component_clause,[status(thm)],[f657]) ).
fof(f660,plain,
( ~ sQ9_spl
| ~ sQ14_spl
| ~ sQ10_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f147,f657,f125,f142,f117]) ).
fof(f661,plain,
( sQ30_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c2 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f548,f659]) ).
fof(f662,plain,
( sQ30_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f557,f661]) ).
fof(f663,plain,
( sQ30_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f662]) ).
fof(f664,plain,
( sQ30_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f663]) ).
fof(f665,plain,
( sQ15_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| multiply(sk_c2,identity) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f557,f230]) ).
fof(f666,plain,
( sQ15_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| identity != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f348,f665]) ).
fof(f667,plain,
( sQ15_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c2 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f551,f666]) ).
fof(f668,plain,
( sQ15_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f557,f667]) ).
fof(f669,plain,
( sQ15_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f668]) ).
fof(f670,plain,
( sQ15_spl
| ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f669]) ).
fof(f671,plain,
( sQ23_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c2 != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f548,f325]) ).
fof(f672,plain,
( sQ23_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f547,f671]) ).
fof(f673,plain,
( sQ23_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f672]) ).
fof(f674,plain,
( sQ23_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f673]) ).
fof(f677,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| multiply(sk_c6,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f495,f370]) ).
fof(f707,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| multiply(inverse(X0),X0) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f495,f36]) ).
fof(f709,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| multiply(sk_c6,sk_c4) = sk_c6 ),
inference(paramodulation,[status(thm)],[f417,f707]) ).
fof(f710,plain,
( ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ4_spl
| multiply(sk_c6,sk_c5) = sk_c6 ),
inference(paramodulation,[status(thm)],[f416,f707]) ).
fof(f714,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| sk_c4 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f677,f709]) ).
fof(f715,plain,
( ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ4_spl
| sk_c5 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f677,f710]) ).
fof(f723,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| sk_c4 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f714,f483]) ).
fof(f727,plain,
( ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ4_spl
| sk_c5 = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f714,f715]) ).
fof(f732,plain,
( sQ0_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| multiply(sk_c5,sk_c8) != sk_c6 ),
inference(backward_demodulation,[status(thm)],[f733,f72]) ).
fof(f733,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| sk_c5 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f727,f723]) ).
fof(f734,plain,
( sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f732,f85,f89,f73,f81,f77,f70]) ).
fof(f735,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,f128,f129,f130,f131,f132,f145,f152,f168,f234,f256,f258,f273,f277,f286,f292,f350,f385,f485,f511,f516,f627,f633,f660,f664,f670,f674,f734]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP323-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n010.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 20 20:09:55 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.40 % Refutation found
% 0.09/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.43 % Elapsed time: 0.052311 seconds
% 0.09/0.43 % CPU time: 0.168857 seconds
% 0.09/0.43 % Total memory used: 84.477 MB
% 0.09/0.43 % Net memory used: 84.318 MB
%------------------------------------------------------------------------------