%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP358-1 : 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 12:33:30 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 56
% Syntax : Number of formulae : 267 ( 12 unt; 22 def)
% Number of atoms : 927 ( 315 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1230 ( 570 ~; 638 |; 0 &)
% ( 22 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 24 ( 22 usr; 23 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 53 ( 53 !; 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_c3,sk_c8) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c6
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( inverse(sk_c4) = sk_c7
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c8,sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c8,sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c6
| multiply(sk_c8,sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c8,sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c8,sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c8,sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( inverse(sk_c4) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
! [X3,X4,X1,X2,X5] :
( multiply(X5,sk_c8) != sk_c6
| inverse(X5) != sk_c6
| inverse(X2) != sk_c7
| multiply(X2,sk_c7) != sk_c6
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| inverse(X4) != sk_c8
| multiply(X4,sk_c8) != X3
| multiply(sk_c8,X3) != sk_c7
| inverse(sk_c8) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c8 ),
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_c3,sk_c8) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f39,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f40,plain,
( multiply(sk_c4,sk_c7) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f41,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f42,plain,
( inverse(sk_c5) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f43,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f44,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f45,plain,
( inverse(sk_c3) = sk_c8
| inverse(sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f46,plain,
( multiply(sk_c4,sk_c7) = sk_c6
| inverse(sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f47,plain,
( inverse(sk_c4) = sk_c7
| inverse(sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f48,plain,
( inverse(sk_c5) = sk_c6
| inverse(sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f49,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f50,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c8,sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f51,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c8,sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f52,plain,
( multiply(sk_c4,sk_c7) = sk_c6
| multiply(sk_c8,sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f53,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c8,sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f54,plain,
( inverse(sk_c5) = sk_c6
| multiply(sk_c8,sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f55,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c8,sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f56,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f57,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f58,plain,
( multiply(sk_c4,sk_c7) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f59,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f60,plain,
( inverse(sk_c5) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f61,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f62,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f63,plain,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f64,plain,
( multiply(sk_c4,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f65,plain,
( inverse(sk_c4) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f66,plain,
( inverse(sk_c5) = sk_c6
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f67,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f68,plain,
! [X5] :
( multiply(X5,sk_c8) != sk_c6
| inverse(X5) != sk_c6
| ! [X2] :
( inverse(X2) != sk_c7
| multiply(X2,sk_c7) != sk_c6
| ! [X1] :
( inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| ! [X4] :
( inverse(X4) != sk_c8
| ! [X3] :
( multiply(X4,sk_c8) != X3
| multiply(sk_c8,X3) != sk_c7
| inverse(sk_c8) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c8 ) ) ) ) ),
inference(miniscoping,[status(thm)],[f34]) ).
fof(f69,plain,
! [X0,X1,X2,X3,X4] :
( multiply(X4,sk_c8) != sk_c6
| inverse(X4) != sk_c6
| inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c6
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c7
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != X0
| multiply(sk_c8,X0) != sk_c7
| inverse(sk_c8) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c8 ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f70,definition,
( sQ0_spl
<=> multiply(sk_c7,sk_c6) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f71,plain,
( ~ sQ0_spl
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f72,plain,
( sQ0_spl
| multiply(sk_c7,sk_c6) != sk_c8 ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f73,definition,
( sQ1_spl
<=> multiply(sk_c3,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f74,plain,
( ~ sQ1_spl
| multiply(sk_c3,sk_c8) = sk_c7 ),
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_c8 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f78,plain,
( ~ sQ2_spl
| inverse(sk_c3) = sk_c8 ),
inference(component_clause,[status(thm)],[f77]) ).
fof(f80,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f39,f70,f77]) ).
fof(f81,definition,
( sQ3_spl
<=> multiply(sk_c4,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f82,plain,
( ~ sQ3_spl
| multiply(sk_c4,sk_c7) = sk_c6 ),
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_c7 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ4_spl
| inverse(sk_c4) = sk_c7 ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f88,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f41,f70,f85]) ).
fof(f89,definition,
( sQ5_spl
<=> inverse(sk_c5) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f90,plain,
( ~ sQ5_spl
| inverse(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_c5,sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ6_spl
| multiply(sk_c5,sk_c8) = sk_c6 ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f96,plain,
( sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f43,f70,f93]) ).
fof(f97,definition,
( sQ7_spl
<=> inverse(sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f98,plain,
( ~ sQ7_spl
| inverse(sk_c8) = sk_c6 ),
inference(component_clause,[status(thm)],[f97]) ).
fof(f99,plain,
( sQ7_spl
| inverse(sk_c8) != sk_c6 ),
inference(component_clause,[status(thm)],[f97]) ).
fof(f100,plain,
( sQ1_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f44,f97,f73]) ).
fof(f101,plain,
( sQ2_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f45,f97,f77]) ).
fof(f102,plain,
( sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f46,f97,f81]) ).
fof(f103,plain,
( sQ4_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f47,f97,f85]) ).
fof(f104,plain,
( sQ5_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f48,f97,f89]) ).
fof(f105,plain,
( sQ6_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f49,f97,f93]) ).
fof(f106,definition,
( sQ8_spl
<=> multiply(sk_c8,sk_c2) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f107,plain,
( ~ sQ8_spl
| multiply(sk_c8,sk_c2) = sk_c7 ),
inference(component_clause,[status(thm)],[f106]) ).
fof(f109,plain,
( sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f50,f106,f73]) ).
fof(f110,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f51,f106,f77]) ).
fof(f111,plain,
( sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f52,f106,f81]) ).
fof(f112,plain,
( sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f53,f106,f85]) ).
fof(f113,plain,
( sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f54,f106,f89]) ).
fof(f114,plain,
( sQ6_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f55,f106,f93]) ).
fof(f115,definition,
( sQ9_spl
<=> multiply(sk_c1,sk_c8) = sk_c2 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f116,plain,
( ~ sQ9_spl
| multiply(sk_c1,sk_c8) = sk_c2 ),
inference(component_clause,[status(thm)],[f115]) ).
fof(f118,plain,
( sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f56,f115,f73]) ).
fof(f119,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f57,f115,f77]) ).
fof(f120,plain,
( sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f58,f115,f81]) ).
fof(f121,plain,
( sQ4_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f59,f115,f85]) ).
fof(f122,plain,
( sQ5_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f60,f115,f89]) ).
fof(f123,plain,
( sQ6_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f61,f115,f93]) ).
fof(f124,definition,
( sQ10_spl
<=> inverse(sk_c1) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f125,plain,
( ~ sQ10_spl
| inverse(sk_c1) = sk_c8 ),
inference(component_clause,[status(thm)],[f124]) ).
fof(f127,plain,
( sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f62,f124,f73]) ).
fof(f128,plain,
( sQ2_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f63,f124,f77]) ).
fof(f129,plain,
( sQ3_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f64,f124,f81]) ).
fof(f130,plain,
( sQ4_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f65,f124,f85]) ).
fof(f131,plain,
( sQ5_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f66,f124,f89]) ).
fof(f132,plain,
( sQ6_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f67,f124,f93]) ).
fof(f133,definition,
! [X0,X1] :
( sQ11_spl
<=> ( inverse(X1) != sk_c8
| multiply(X1,sk_c8) != X0
| multiply(sk_c8,X0) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f134,plain,
! [X0,X1] :
( ~ sQ11_spl
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != X0
| multiply(sk_c8,X0) != sk_c7 ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,definition,
! [X2] :
( sQ12_spl
<=> ( inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f137,plain,
! [X0] :
( ~ sQ12_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f139,definition,
! [X3] :
( sQ13_spl
<=> ( inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f140,plain,
! [X0] :
( ~ sQ13_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6 ),
inference(component_clause,[status(thm)],[f139]) ).
fof(f142,definition,
! [X4] :
( sQ14_spl
<=> ( multiply(X4,sk_c8) != sk_c6
| inverse(X4) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f143,plain,
! [X0] :
( ~ sQ14_spl
| multiply(X0,sk_c8) != sk_c6
| inverse(X0) != sk_c6 ),
inference(component_clause,[status(thm)],[f142]) ).
fof(f145,plain,
( sQ14_spl
| sQ13_spl
| sQ12_spl
| sQ11_spl
| ~ sQ7_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f69,f70,f97,f133,f136,f139,f142]) ).
fof(f146,plain,
( ~ sQ6_spl
| ~ sQ14_spl
| inverse(sk_c5) != sk_c6 ),
inference(resolution,[status(thm)],[f143,f94]) ).
fof(f149,plain,
( ~ sQ9_spl
| ~ sQ14_spl
| sk_c2 != sk_c6
| inverse(sk_c1) != sk_c6 ),
inference(paramodulation,[status(thm)],[f116,f143]) ).
fof(f150,plain,
( ~ sQ6_spl
| ~ sQ14_spl
| ~ sQ5_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f90,f146]) ).
fof(f151,plain,
( ~ sQ6_spl
| ~ sQ14_spl
| ~ sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f150]) ).
fof(f152,plain,
( ~ sQ6_spl
| ~ sQ14_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f151]) ).
fof(f153,plain,
! [X0] :
( ~ sQ11_spl
| inverse(X0) != sk_c8
| multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ),
inference(destructive_equality_resolution,[status(thm)],[f134]) ).
fof(f154,plain,
( ~ sQ3_spl
| ~ sQ13_spl
| inverse(sk_c4) != sk_c7 ),
inference(resolution,[status(thm)],[f140,f82]) ).
fof(f156,plain,
( ~ sQ3_spl
| ~ sQ13_spl
| ~ sQ4_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f86,f154]) ).
fof(f157,plain,
( ~ sQ3_spl
| ~ sQ13_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f156]) ).
fof(f158,plain,
( ~ sQ3_spl
| ~ sQ13_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f157]) ).
fof(f159,plain,
( ~ sQ1_spl
| ~ sQ12_spl
| inverse(sk_c3) != sk_c8 ),
inference(resolution,[status(thm)],[f137,f74]) ).
fof(f163,plain,
( ~ sQ1_spl
| ~ sQ12_spl
| ~ sQ2_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f78,f159]) ).
fof(f164,plain,
( ~ sQ1_spl
| ~ sQ12_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f163]) ).
fof(f165,plain,
( ~ sQ1_spl
| ~ sQ12_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f164]) ).
fof(f176,plain,
( ~ sQ1_spl
| ~ sQ11_spl
| inverse(sk_c3) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c7 ),
inference(paramodulation,[status(thm)],[f74,f153]) ).
fof(f178,plain,
( ~ sQ9_spl
| ~ sQ11_spl
| inverse(sk_c1) != sk_c8
| multiply(sk_c8,sk_c2) != sk_c7 ),
inference(paramodulation,[status(thm)],[f116,f153]) ).
fof(f179,definition,
( sQ15_spl
<=> multiply(sk_c8,sk_c7) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f181,plain,
( sQ15_spl
| multiply(sk_c8,sk_c7) != sk_c7 ),
inference(component_clause,[status(thm)],[f179]) ).
fof(f182,plain,
( ~ sQ1_spl
| ~ sQ11_spl
| ~ sQ2_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f176,f179,f77,f133,f73]) ).
fof(f183,definition,
( sQ16_spl
<=> multiply(sk_c8,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f185,plain,
( sQ16_spl
| multiply(sk_c8,sk_c6) != sk_c7 ),
inference(component_clause,[status(thm)],[f183]) ).
fof(f190,plain,
( ~ sQ9_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f178,f106,f124,f133,f115]) ).
fof(f195,plain,
( ~ sQ10_spl
| multiply(sk_c8,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f125,f36]) ).
fof(f196,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f36,f37]) ).
fof(f197,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f35,f196]) ).
fof(f216,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f35,f197]) ).
fof(f218,plain,
( ~ sQ1_spl
| sk_c8 = multiply(inverse(sk_c3),sk_c7) ),
inference(paramodulation,[status(thm)],[f74,f197]) ).
fof(f219,plain,
( ~ sQ3_spl
| sk_c7 = multiply(inverse(sk_c4),sk_c6) ),
inference(paramodulation,[status(thm)],[f82,f197]) ).
fof(f220,plain,
( ~ sQ6_spl
| sk_c8 = multiply(inverse(sk_c5),sk_c6) ),
inference(paramodulation,[status(thm)],[f94,f197]) ).
fof(f221,plain,
( ~ sQ9_spl
| sk_c8 = multiply(inverse(sk_c1),sk_c2) ),
inference(paramodulation,[status(thm)],[f116,f197]) ).
fof(f223,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 = multiply(sk_c8,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f78,f218]) ).
fof(f224,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c7 = multiply(sk_c7,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f86,f219]) ).
fof(f225,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| sk_c8 = multiply(sk_c6,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f90,f220]) ).
fof(f226,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| sk_c8 = multiply(sk_c8,sk_c2) ),
inference(forward_demodulation,[status(thm)],[f125,f221]) ).
fof(f234,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c7 = multiply(inverse(sk_c8),sk_c8) ),
inference(paramodulation,[status(thm)],[f223,f197]) ).
fof(f236,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c7 = identity ),
inference(forward_demodulation,[status(thm)],[f36,f234]) ).
fof(f242,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(inverse(X0),X0) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f236,f36]) ).
fof(f243,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c7,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f236,f35]) ).
fof(f251,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c6 != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f243,f72]) ).
fof(f254,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c6,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f262,f243]) ).
fof(f255,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(inverse(X0),X0) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f262,f242]) ).
fof(f259,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c4) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f262,f86]) ).
fof(f262,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c7 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f243,f224]) ).
fof(f265,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| X0 = multiply(sk_c6,multiply(sk_c4,X0)) ),
inference(paramodulation,[status(thm)],[f259,f197]) ).
fof(f266,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| X0 = multiply(sk_c4,X0) ),
inference(forward_demodulation,[status(thm)],[f254,f265]) ).
fof(f267,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c6,sk_c4) = sk_c6 ),
inference(paramodulation,[status(thm)],[f259,f255]) ).
fof(f269,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c6,sk_c5) = sk_c6 ),
inference(paramodulation,[status(thm)],[f90,f255]) ).
fof(f273,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c4 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f254,f267]) ).
fof(f274,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c5 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f254,f269]) ).
fof(f277,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c4) = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f273,f259]) ).
fof(f280,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c7 = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f273,f262]) ).
fof(f281,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sk_c4 != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f273,f251]) ).
fof(f284,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| sk_c5 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f285,f273]) ).
fof(f285,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c5 = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f273,f274]) ).
fof(f287,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| sk_c7 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f285,f280]) ).
fof(f288,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ5_spl
| sk_c5 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f285,f281]) ).
fof(f289,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| X0 = multiply(sk_c5,X0) ),
inference(forward_demodulation,[status(thm)],[f285,f266]) ).
fof(f292,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| inverse(sk_c5) = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f285,f277]) ).
fof(f293,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| inverse(sk_c5) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f285,f292]) ).
fof(f304,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 = multiply(sk_c5,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f284,f225]) ).
fof(f305,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f289,f304]) ).
fof(f306,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f284,f305]) ).
fof(f307,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f306,f288]) ).
fof(f308,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f307]) ).
fof(f316,plain,
( sQ7_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| inverse(sk_c8) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f284,f99]) ).
fof(f324,plain,
( sQ7_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| inverse(sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f306,f316]) ).
fof(f325,plain,
( sQ7_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f293,f324]) ).
fof(f326,plain,
( sQ7_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f325]) ).
fof(f327,plain,
( sQ7_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f326]) ).
fof(f328,plain,
( sQ15_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c5,sk_c7) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f306,f181]) ).
fof(f329,plain,
( sQ15_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f289,f328]) ).
fof(f330,plain,
( sQ15_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c5 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f287,f329]) ).
fof(f331,plain,
( sQ15_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f287,f330]) ).
fof(f332,plain,
( sQ15_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f331]) ).
fof(f333,plain,
( sQ15_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f332]) ).
fof(f338,definition,
( sQ19_spl
<=> sk_c6 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f340,plain,
( sQ19_spl
| sk_c6 != sk_c6 ),
inference(component_clause,[status(thm)],[f338]) ).
fof(f342,plain,
( sQ19_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f340]) ).
fof(f343,plain,
sQ19_spl,
inference(contradiction_clause,[status(thm)],[f342]) ).
fof(f350,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| sk_c2 = multiply(inverse(sk_c8),sk_c8) ),
inference(paramodulation,[status(thm)],[f226,f197]) ).
fof(f352,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ7_spl
| sk_c2 = multiply(sk_c6,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f98,f350]) ).
fof(f355,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c8 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f226,f107]) ).
fof(f359,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c8,sk_c6) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f355,f71]) ).
fof(f360,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c6 = multiply(inverse(sk_c8),sk_c8) ),
inference(paramodulation,[status(thm)],[f359,f197]) ).
fof(f362,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ7_spl
| sk_c6 = multiply(sk_c6,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f98,f360]) ).
fof(f363,plain,
( sQ16_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c8 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f359,f185]) ).
fof(f364,plain,
( sQ16_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f355,f363]) ).
fof(f365,plain,
( sQ16_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f364]) ).
fof(f366,plain,
( sQ16_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f365]) ).
fof(f368,plain,
( ~ sQ10_spl
| sk_c1 = multiply(inverse(sk_c8),identity) ),
inference(paramodulation,[status(thm)],[f195,f197]) ).
fof(f370,plain,
( ~ sQ10_spl
| ~ sQ7_spl
| sk_c1 = multiply(sk_c6,identity) ),
inference(forward_demodulation,[status(thm)],[f98,f368]) ).
fof(f375,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c8) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f355,f140]) ).
fof(f376,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f355,f375]) ).
fof(f377,plain,
( ~ sQ9_spl
| ~ sQ13_spl
| ~ sQ8_spl
| ~ sQ10_spl
| inverse(sk_c1) != sk_c8
| sk_c2 != sk_c6 ),
inference(paramodulation,[status(thm)],[f116,f376]) ).
fof(f380,definition,
( sQ20_spl
<=> sk_c2 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f382,plain,
( sQ20_spl
| sk_c2 != sk_c6 ),
inference(component_clause,[status(thm)],[f380]) ).
fof(f383,plain,
( ~ sQ9_spl
| ~ sQ13_spl
| ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f377,f380,f124,f106,f139,f115]) ).
fof(f391,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f355,f137]) ).
fof(f398,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ7_spl
| sk_c6 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f352,f362]) ).
fof(f399,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ7_spl
| sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f398,f382]) ).
fof(f400,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ7_spl
| sQ20_spl ),
inference(contradiction_clause,[status(thm)],[f399]) ).
fof(f401,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sk_c2 = multiply(sk_c2,sk_c8) ),
inference(backward_demodulation,[status(thm)],[f398,f352]) ).
fof(f406,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| inverse(sk_c8) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f398,f98]) ).
fof(f412,plain,
( ~ sQ12_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| inverse(inverse(identity)) != sk_c8
| sk_c8 != sk_c8 ),
inference(paramodulation,[status(thm)],[f216,f391]) ).
fof(f418,definition,
( sQ24_spl
<=> sk_c8 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f420,plain,
( sQ24_spl
| sk_c8 != sk_c8 ),
inference(component_clause,[status(thm)],[f418]) ).
fof(f422,definition,
( sQ25_spl
<=> inverse(inverse(identity)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f424,plain,
( sQ25_spl
| inverse(inverse(identity)) != sk_c8 ),
inference(component_clause,[status(thm)],[f422]) ).
fof(f425,plain,
( ~ sQ12_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ25_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f412,f418,f422,f124,f115,f106,f136]) ).
fof(f426,plain,
( sQ24_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f420]) ).
fof(f427,plain,
sQ24_spl,
inference(contradiction_clause,[status(thm)],[f426]) ).
fof(f446,plain,
( ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c1 = multiply(sk_c2,identity) ),
inference(forward_demodulation,[status(thm)],[f398,f370]) ).
fof(f451,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sk_c8 = multiply(inverse(sk_c2),sk_c2) ),
inference(paramodulation,[status(thm)],[f401,f197]) ).
fof(f457,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sk_c8 = identity ),
inference(forward_demodulation,[status(thm)],[f36,f451]) ).
fof(f463,definition,
( sQ29_spl
<=> inverse(sk_c1) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f465,plain,
( sQ29_spl
| inverse(sk_c1) != sk_c6 ),
inference(component_clause,[status(thm)],[f463]) ).
fof(f466,plain,
( ~ sQ9_spl
| ~ sQ14_spl
| ~ sQ20_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f149,f463,f380,f142,f115]) ).
fof(f467,plain,
( sQ29_spl
| ~ sQ10_spl
| sk_c8 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f125,f465]) ).
fof(f468,plain,
( sQ29_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sk_c8 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f398,f467]) ).
fof(f469,plain,
( ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c1 = multiply(sk_c2,sk_c8) ),
inference(backward_demodulation,[status(thm)],[f457,f446]) ).
fof(f470,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| multiply(inverse(X0),X0) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f457,f36]) ).
fof(f473,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| multiply(sk_c8,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f457,f35]) ).
fof(f474,plain,
( ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| sk_c1 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f401,f469]) ).
fof(f476,plain,
( sQ29_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ7_spl
| sk_c8 != sk_c1 ),
inference(backward_demodulation,[status(thm)],[f474,f468]) ).
fof(f478,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| inverse(sk_c8) = sk_c1 ),
inference(backward_demodulation,[status(thm)],[f474,f406]) ).
fof(f509,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| multiply(sk_c8,sk_c1) = sk_c8 ),
inference(paramodulation,[status(thm)],[f125,f470]) ).
fof(f513,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sk_c1 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f473,f509]) ).
fof(f514,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f513,f476]) ).
fof(f515,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sQ29_spl ),
inference(contradiction_clause,[status(thm)],[f514]) ).
fof(f521,plain,
( sQ25_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| inverse(inverse(sk_c8)) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f457,f424]) ).
fof(f522,plain,
( sQ25_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| inverse(sk_c1) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f478,f521]) ).
fof(f523,plain,
( sQ25_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f125,f522]) ).
fof(f524,plain,
( sQ25_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f523]) ).
fof(f525,plain,
( sQ25_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f524]) ).
fof(f526,plain,
$false,
inference(sat_refutation,[status(thm)],[f76,f80,f84,f88,f92,f96,f100,f101,f102,f103,f104,f105,f109,f110,f111,f112,f113,f114,f118,f119,f120,f121,f122,f123,f127,f128,f129,f130,f131,f132,f145,f152,f158,f165,f182,f190,f308,f327,f333,f343,f366,f383,f400,f425,f427,f466,f515,f525]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP358-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n009.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 20:10:27 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.12/0.38 % Refutation found
% 0.12/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.41 % Elapsed time: 0.052816 seconds
% 0.12/0.41 % CPU time: 0.170952 seconds
% 0.12/0.41 % Total memory used: 103.847 MB
% 0.12/0.41 % Net memory used: 103.634 MB
%------------------------------------------------------------------------------