%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP345-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 12:33:28 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.41s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 54
% Syntax : Number of formulae : 269 ( 13 unt; 22 def)
% Number of atoms : 894 ( 307 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1168 ( 543 ~; 603 |; 0 &)
% ( 22 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 24 ( 22 usr; 23 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 45 ( 45 !; 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_c6,sk_c5) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c6) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( inverse(sk_c6) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c6) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c6) = sk_c5
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c5
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c4) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( multiply(sk_c3,sk_c7) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( inverse(sk_c6) = sk_c5
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( multiply(sk_c4,sk_c6) = sk_c5
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
! [X3,X4,X1,X2] :
( inverse(X2) != sk_c6
| multiply(X2,sk_c6) != sk_c5
| inverse(sk_c6) != sk_c5
| inverse(X1) != sk_c7
| multiply(X1,sk_c7) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| multiply(X4,sk_c5) != sk_c6
| inverse(X4) != sk_c6
| multiply(X3,sk_c6) != sk_c7
| inverse(X3) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5 ),
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_c6,sk_c5) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f41,plain,
( inverse(sk_c6) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f42,plain,
( multiply(sk_c4,sk_c6) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f43,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f44,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f45,plain,
( multiply(sk_c3,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f46,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f47,plain,
( inverse(sk_c6) = sk_c5
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f48,plain,
( multiply(sk_c4,sk_c6) = sk_c5
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f49,plain,
( inverse(sk_c4) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f50,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f51,plain,
( multiply(sk_c3,sk_c7) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f52,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f53,plain,
( inverse(sk_c6) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f54,plain,
( multiply(sk_c4,sk_c6) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f55,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f56,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f57,plain,
( multiply(sk_c3,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f58,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f59,plain,
( inverse(sk_c6) = sk_c5
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f60,plain,
( multiply(sk_c4,sk_c6) = sk_c5
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f61,plain,
( inverse(sk_c4) = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f62,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f63,plain,
( multiply(sk_c3,sk_c7) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f64,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f65,plain,
( inverse(sk_c6) = sk_c5
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f66,plain,
( multiply(sk_c4,sk_c6) = sk_c5
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f67,plain,
( inverse(sk_c4) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f68,plain,
! [X2] :
( inverse(X2) != sk_c6
| multiply(X2,sk_c6) != sk_c5
| inverse(sk_c6) != sk_c5
| ! [X1] :
( inverse(X1) != sk_c7
| multiply(X1,sk_c7) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| ! [X4] :
( multiply(X4,sk_c5) != sk_c6
| inverse(X4) != sk_c6
| ! [X3] :
( multiply(X3,sk_c6) != sk_c7
| inverse(X3) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5 ) ) ) ),
inference(miniscoping,[status(thm)],[f34]) ).
fof(f69,plain,
! [X0,X1,X2,X3] :
( inverse(X3) != sk_c6
| multiply(X3,sk_c6) != sk_c5
| inverse(sk_c6) != sk_c5
| inverse(X2) != sk_c7
| multiply(X2,sk_c7) != sk_c6
| multiply(sk_c6,sk_c5) != sk_c7
| multiply(X1,sk_c5) != sk_c6
| inverse(X1) != sk_c6
| multiply(X0,sk_c6) != sk_c7
| inverse(X0) != sk_c7
| multiply(sk_c6,sk_c7) != sk_c5 ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f70,definition,
( sQ0_spl
<=> multiply(sk_c6,sk_c7) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f71,plain,
( ~ sQ0_spl
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f72,plain,
( sQ0_spl
| multiply(sk_c6,sk_c7) != sk_c5 ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f73,definition,
( sQ1_spl
<=> multiply(sk_c6,sk_c5) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f74,plain,
( ~ sQ1_spl
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f75,plain,
( sQ1_spl
| multiply(sk_c6,sk_c5) != 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
<=> multiply(sk_c3,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f78,plain,
( ~ sQ2_spl
| multiply(sk_c3,sk_c7) = sk_c6 ),
inference(component_clause,[status(thm)],[f77]) ).
fof(f81,definition,
( sQ3_spl
<=> inverse(sk_c3) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f82,plain,
( ~ sQ3_spl
| inverse(sk_c3) = sk_c7 ),
inference(component_clause,[status(thm)],[f81]) ).
fof(f85,definition,
( sQ4_spl
<=> inverse(sk_c6) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ4_spl
| inverse(sk_c6) = sk_c5 ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f87,plain,
( sQ4_spl
| inverse(sk_c6) != sk_c5 ),
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_c6) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f90,plain,
( ~ sQ5_spl
| multiply(sk_c4,sk_c6) = sk_c5 ),
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
<=> inverse(sk_c4) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ6_spl
| inverse(sk_c4) = 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_c1) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f98,plain,
( ~ sQ7_spl
| inverse(sk_c1) = sk_c7 ),
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_c1,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f107,plain,
( ~ sQ8_spl
| multiply(sk_c1,sk_c6) = 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
<=> inverse(sk_c2) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f116,plain,
( ~ sQ9_spl
| inverse(sk_c2) = sk_c6 ),
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
<=> multiply(sk_c2,sk_c5) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f125,plain,
( ~ sQ10_spl
| multiply(sk_c2,sk_c5) = sk_c6 ),
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] :
( sQ11_spl
<=> ( multiply(X0,sk_c6) != sk_c7
| inverse(X0) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f134,plain,
! [X0] :
( ~ sQ11_spl
| multiply(X0,sk_c6) != sk_c7
| inverse(X0) != sk_c7 ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,definition,
! [X1] :
( sQ12_spl
<=> ( multiply(X1,sk_c5) != sk_c6
| inverse(X1) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f137,plain,
! [X0] :
( ~ sQ12_spl
| multiply(X0,sk_c5) != sk_c6
| inverse(X0) != sk_c6 ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f139,definition,
! [X2] :
( sQ13_spl
<=> ( inverse(X2) != sk_c7
| multiply(X2,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,
! [X3] :
( sQ14_spl
<=> ( inverse(X3) != sk_c6
| multiply(X3,sk_c6) != sk_c5 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f143,plain,
! [X0] :
( ~ sQ14_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c5 ),
inference(component_clause,[status(thm)],[f142]) ).
fof(f145,plain,
( sQ14_spl
| ~ sQ4_spl
| sQ13_spl
| ~ sQ1_spl
| sQ12_spl
| sQ11_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f69,f70,f133,f136,f73,f139,f85,f142]) ).
fof(f146,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| inverse(sk_c4) != sk_c6 ),
inference(resolution,[status(thm)],[f143,f90]) ).
fof(f148,plain,
( ~ sQ8_spl
| ~ sQ14_spl
| inverse(sk_c1) != sk_c6
| sk_c7 != sk_c5 ),
inference(paramodulation,[status(thm)],[f107,f143]) ).
fof(f149,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| ~ sQ6_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f94,f146]) ).
fof(f150,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f149]) ).
fof(f151,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f150]) ).
fof(f152,plain,
( ~ sQ2_spl
| ~ sQ13_spl
| inverse(sk_c3) != sk_c7 ),
inference(resolution,[status(thm)],[f140,f78]) ).
fof(f153,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| inverse(sk_c6) != sk_c7
| sk_c5 != sk_c6 ),
inference(paramodulation,[status(thm)],[f71,f140]) ).
fof(f155,plain,
( ~ sQ2_spl
| ~ sQ13_spl
| ~ sQ3_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f82,f152]) ).
fof(f156,plain,
( ~ sQ2_spl
| ~ sQ13_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f155]) ).
fof(f157,plain,
( ~ sQ2_spl
| ~ sQ13_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f156]) ).
fof(f158,plain,
( ~ sQ10_spl
| ~ sQ12_spl
| inverse(sk_c2) != sk_c6 ),
inference(resolution,[status(thm)],[f137,f125]) ).
fof(f160,plain,
( ~ sQ10_spl
| ~ sQ12_spl
| ~ sQ9_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f116,f158]) ).
fof(f161,plain,
( ~ sQ10_spl
| ~ sQ12_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f160]) ).
fof(f162,plain,
( ~ sQ10_spl
| ~ sQ12_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f161]) ).
fof(f170,plain,
( ~ sQ8_spl
| ~ sQ11_spl
| inverse(sk_c1) != sk_c7 ),
inference(resolution,[status(thm)],[f134,f107]) ).
fof(f174,plain,
( ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ7_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f98,f170]) ).
fof(f175,plain,
( ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f174]) ).
fof(f176,plain,
( ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f175]) ).
fof(f180,definition,
( sQ16_spl
<=> sk_c5 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f182,plain,
( sQ16_spl
| sk_c5 != sk_c7 ),
inference(component_clause,[status(thm)],[f180]) ).
fof(f188,plain,
( ~ sQ11_spl
| sk_c6 != sk_c7
| inverse(identity) != sk_c7 ),
inference(paramodulation,[status(thm)],[f35,f134]) ).
fof(f190,definition,
( sQ18_spl
<=> inverse(identity) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f192,plain,
( sQ18_spl
| inverse(identity) != sk_c7 ),
inference(component_clause,[status(thm)],[f190]) ).
fof(f193,definition,
( sQ19_spl
<=> sk_c6 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f195,plain,
( sQ19_spl
| sk_c6 != sk_c7 ),
inference(component_clause,[status(thm)],[f193]) ).
fof(f196,plain,
( ~ sQ11_spl
| ~ sQ19_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f188,f190,f193,f133]) ).
fof(f198,plain,
( ~ sQ6_spl
| multiply(sk_c6,sk_c4) = identity ),
inference(paramodulation,[status(thm)],[f94,f36]) ).
fof(f202,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f36,f37]) ).
fof(f210,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f35,f202]) ).
fof(f214,plain,
! [X0] :
( ~ sQ6_spl
| multiply(identity,X0) = multiply(sk_c6,multiply(sk_c4,X0)) ),
inference(paramodulation,[status(thm)],[f198,f37]) ).
fof(f215,plain,
! [X0] :
( ~ sQ6_spl
| X0 = multiply(sk_c6,multiply(sk_c4,X0)) ),
inference(forward_demodulation,[status(thm)],[f35,f214]) ).
fof(f242,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sk_c6 = multiply(sk_c6,sk_c5) ),
inference(paramodulation,[status(thm)],[f90,f215]) ).
fof(f246,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| sk_c6 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f74,f242]) ).
fof(f247,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f246,f195]) ).
fof(f248,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| sQ19_spl ),
inference(contradiction_clause,[status(thm)],[f247]) ).
fof(f254,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ1_spl
| multiply(sk_c7,sk_c4) = identity ),
inference(backward_demodulation,[status(thm)],[f246,f198]) ).
fof(f255,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c7,sk_c5) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f246,f74]) ).
fof(f256,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ1_spl
| inverse(sk_c4) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f246,f94]) ).
fof(f257,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| inverse(sk_c7) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f246,f86]) ).
fof(f262,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| multiply(sk_c7,sk_c7) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f246,f72]) ).
fof(f264,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| multiply(sk_c5,sk_c7) = identity ),
inference(paramodulation,[status(thm)],[f257,f36]) ).
fof(f286,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c5 = multiply(inverse(sk_c7),sk_c7) ),
inference(paramodulation,[status(thm)],[f255,f210]) ).
fof(f287,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ1_spl
| sk_c4 = multiply(inverse(sk_c7),identity) ),
inference(paramodulation,[status(thm)],[f254,f210]) ).
fof(f291,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f35,f210]) ).
fof(f296,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c5 = identity ),
inference(forward_demodulation,[status(thm)],[f36,f286]) ).
fof(f297,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ4_spl
| sk_c4 = multiply(sk_c5,identity) ),
inference(forward_demodulation,[status(thm)],[f257,f287]) ).
fof(f303,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(inverse(X0),X0) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f296,f36]) ).
fof(f304,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c5,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f296,f35]) ).
fof(f308,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| sk_c7 = identity ),
inference(forward_demodulation,[status(thm)],[f304,f264]) ).
fof(f315,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ4_spl
| inverse(sk_c4) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f319,f256]) ).
fof(f316,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ4_spl
| multiply(sk_c7,sk_c5) != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f319,f262]) ).
fof(f317,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ4_spl
| sk_c6 = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f319,f246]) ).
fof(f319,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| sk_c7 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f296,f308]) ).
fof(f322,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ4_spl
| multiply(sk_c5,sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f319,f316]) ).
fof(f323,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ4_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f304,f322]) ).
fof(f324,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f323]) ).
fof(f325,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f324]) ).
fof(f337,definition,
( sQ23_spl
<=> sk_c6 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f339,plain,
( sQ23_spl
| sk_c6 != sk_c6 ),
inference(component_clause,[status(thm)],[f337]) ).
fof(f358,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ4_spl
| sk_c4 = identity ),
inference(forward_demodulation,[status(thm)],[f304,f297]) ).
fof(f360,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ4_spl
| inverse(sk_c4) = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f367,f315]) ).
fof(f363,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ4_spl
| sk_c6 = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f367,f317]) ).
fof(f364,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| sk_c7 = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f367,f319]) ).
fof(f366,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sk_c4 = identity ),
inference(backward_demodulation,[status(thm)],[f367,f296]) ).
fof(f367,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ4_spl
| sk_c4 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f296,f358]) ).
fof(f369,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| multiply(inverse(X0),X0) = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f367,f303]) ).
fof(f408,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ4_spl
| multiply(X0,sk_c5) != sk_c6
| inverse(X0) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f363,f137]) ).
fof(f409,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ4_spl
| multiply(X0,sk_c4) != sk_c6
| inverse(X0) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f367,f408]) ).
fof(f410,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ4_spl
| multiply(X0,sk_c4) != sk_c4
| inverse(X0) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f363,f409]) ).
fof(f411,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ12_spl
| inverse(inverse(sk_c4)) != sk_c4 ),
inference(resolution,[status(thm)],[f410,f369]) ).
fof(f418,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ12_spl
| inverse(sk_c4) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f360,f411]) ).
fof(f419,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ12_spl
| sk_c4 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f360,f418]) ).
fof(f420,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f419]) ).
fof(f421,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f420]) ).
fof(f422,plain,
( sQ18_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| inverse(sk_c4) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f366,f192]) ).
fof(f423,plain,
( sQ18_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sk_c4 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f360,f422]) ).
fof(f424,plain,
( sQ18_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sk_c4 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f364,f423]) ).
fof(f425,plain,
( sQ18_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f424]) ).
fof(f426,plain,
( sQ18_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f425]) ).
fof(f431,plain,
( ~ sQ8_spl
| sk_c6 = multiply(inverse(sk_c1),sk_c7) ),
inference(paramodulation,[status(thm)],[f107,f210]) ).
fof(f433,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| sk_c6 = multiply(sk_c7,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f98,f431]) ).
fof(f436,plain,
! [X0] : X0 = multiply(inverse(inverse(identity)),X0),
inference(paramodulation,[status(thm)],[f291,f210]) ).
fof(f438,plain,
( ~ sQ0_spl
| sk_c7 = multiply(inverse(sk_c6),sk_c5) ),
inference(paramodulation,[status(thm)],[f71,f210]) ).
fof(f441,plain,
( ~ sQ7_spl
| multiply(sk_c7,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f98,f36]) ).
fof(f442,plain,
( ~ sQ9_spl
| multiply(sk_c6,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f116,f36]) ).
fof(f449,plain,
( ~ sQ10_spl
| sk_c5 = multiply(inverse(sk_c2),sk_c6) ),
inference(paramodulation,[status(thm)],[f125,f210]) ).
fof(f451,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| sk_c5 = multiply(sk_c6,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f116,f449]) ).
fof(f469,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| sk_c7 = multiply(inverse(sk_c7),sk_c6) ),
inference(paramodulation,[status(thm)],[f433,f210]) ).
fof(f472,plain,
( ~ sQ7_spl
| sk_c1 = multiply(inverse(sk_c7),identity) ),
inference(paramodulation,[status(thm)],[f441,f210]) ).
fof(f476,plain,
( ~ sQ9_spl
| sk_c2 = multiply(inverse(sk_c6),identity) ),
inference(paramodulation,[status(thm)],[f442,f210]) ).
fof(f480,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| sk_c6 = multiply(inverse(sk_c6),sk_c5) ),
inference(paramodulation,[status(thm)],[f451,f210]) ).
fof(f511,plain,
inverse(identity) = identity,
inference(paramodulation,[status(thm)],[f36,f436]) ).
fof(f536,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| sk_c2 = multiply(inverse(sk_c7),identity) ),
inference(backward_demodulation,[status(thm)],[f557,f476]) ).
fof(f537,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| sk_c7 = multiply(inverse(sk_c7),sk_c7) ),
inference(backward_demodulation,[status(thm)],[f557,f469]) ).
fof(f543,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| sk_c5 = multiply(sk_c6,sk_c7) ),
inference(backward_demodulation,[status(thm)],[f557,f451]) ).
fof(f550,plain,
( sQ1_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| multiply(sk_c7,sk_c5) != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f557,f75]) ).
fof(f552,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| multiply(sk_c2,sk_c5) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f557,f125]) ).
fof(f556,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| inverse(sk_c2) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f557,f116]) ).
fof(f557,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| sk_c6 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f438,f480]) ).
fof(f558,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| sk_c2 = sk_c1 ),
inference(forward_demodulation,[status(thm)],[f472,f536]) ).
fof(f559,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| sk_c7 = identity ),
inference(forward_demodulation,[status(thm)],[f36,f537]) ).
fof(f560,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| sk_c5 = multiply(sk_c7,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f557,f543]) ).
fof(f565,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| inverse(identity) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f559,f511]) ).
fof(f568,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| multiply(sk_c7,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f559,f35]) ).
fof(f569,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| inverse(sk_c7) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f559,f565]) ).
fof(f578,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl
| sk_c5 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f568,f560]) ).
fof(f579,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl
| sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f578,f182]) ).
fof(f580,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl
| sQ16_spl ),
inference(contradiction_clause,[status(thm)],[f579]) ).
fof(f581,plain,
( sQ1_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl
| sk_c5 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f568,f550]) ).
fof(f582,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| sk_c5 = multiply(inverse(sk_c2),sk_c7) ),
inference(paramodulation,[status(thm)],[f552,f210]) ).
fof(f584,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| sk_c5 = multiply(sk_c7,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f556,f582]) ).
fof(f585,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl
| sk_c5 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f568,f584]) ).
fof(f586,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f585,f581]) ).
fof(f587,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f586]) ).
fof(f589,plain,
( sQ4_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| inverse(sk_c7) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f557,f87]) ).
fof(f590,plain,
( sQ4_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl
| sk_c7 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f569,f589]) ).
fof(f603,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl
| inverse(sk_c2) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f578,f556]) ).
fof(f605,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl
| sk_c6 = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f578,f557]) ).
fof(f610,plain,
( sQ4_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f578,f590]) ).
fof(f611,plain,
( sQ4_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f610]) ).
fof(f612,plain,
( sQ4_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f611]) ).
fof(f616,definition,
( sQ24_spl
<=> sk_c5 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f618,plain,
( sQ24_spl
| sk_c5 != sk_c6 ),
inference(component_clause,[status(thm)],[f616]) ).
fof(f619,definition,
( sQ25_spl
<=> inverse(sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f621,plain,
( sQ25_spl
| inverse(sk_c6) != sk_c7 ),
inference(component_clause,[status(thm)],[f619]) ).
fof(f622,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ25_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f153,f616,f619,f139,f70]) ).
fof(f625,plain,
( sQ23_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f339]) ).
fof(f626,plain,
sQ23_spl,
inference(contradiction_clause,[status(thm)],[f625]) ).
fof(f627,plain,
( sQ25_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl
| inverse(sk_c6) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f578,f621]) ).
fof(f632,plain,
( sQ24_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f605,f618]) ).
fof(f633,plain,
( sQ24_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f632]) ).
fof(f634,plain,
( sQ24_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f633]) ).
fof(f637,definition,
( sQ26_spl
<=> inverse(sk_c1) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f639,plain,
( sQ26_spl
| inverse(sk_c1) != sk_c6 ),
inference(component_clause,[status(thm)],[f637]) ).
fof(f640,plain,
( ~ sQ8_spl
| ~ sQ14_spl
| ~ sQ26_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f148,f180,f637,f142,f106]) ).
fof(f641,plain,
( sQ26_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| inverse(sk_c2) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f558,f639]) ).
fof(f642,plain,
( sQ26_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| inverse(sk_c2) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f605,f641]) ).
fof(f650,plain,
( sQ26_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f603,f642]) ).
fof(f651,plain,
( sQ26_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f650]) ).
fof(f652,plain,
( sQ26_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f651]) ).
fof(f653,plain,
( sQ25_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f627,f85,f97,f106,f70,f115,f124,f619]) ).
fof(f660,plain,
$false,
inference(sat_refutation,[status(thm)],[f76,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,f151,f157,f162,f176,f196,f248,f325,f421,f426,f580,f587,f612,f622,f626,f634,f640,f652,f653]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP345-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n020.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 20 20:10:48 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.14/0.37 % Drodi V4.1.1
% 0.14/0.41 % Refutation found
% 0.14/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.43 % Elapsed time: 0.065062 seconds
% 0.14/0.43 % CPU time: 0.214517 seconds
% 0.14/0.43 % Total memory used: 104.626 MB
% 0.14/0.43 % Net memory used: 104.347 MB
%------------------------------------------------------------------------------