%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP361-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 12:33:31 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 50
% Syntax : Number of formulae : 235 ( 10 unt; 18 def)
% Number of atoms : 809 ( 281 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1064 ( 490 ~; 556 |; 0 &)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 20 ( 18 usr; 19 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 40 ( 40 !; 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(f5,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c7
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c6,sk_c5) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c7
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c4) = sk_c5
| inverse(sk_c7) = sk_c5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c7,sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| multiply(sk_c7,sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c7,sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c7,sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c7
| multiply(sk_c7,sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c7,sk_c2) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( inverse(sk_c4) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
! [X3,X4,X1,X2] :
( inverse(X2) != sk_c5
| multiply(X2,sk_c5) != sk_c7
| multiply(X1,sk_c6) != sk_c7
| inverse(X1) != sk_c7
| multiply(sk_c5,sk_c7) != sk_c6
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(X4) != sk_c7
| multiply(X4,sk_c7) != X3
| multiply(sk_c7,X3) != sk_c6
| inverse(sk_c7) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c7 ),
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(f39,plain,
( multiply(sk_c5,sk_c7) = sk_c6
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f40,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f41,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f42,plain,
( multiply(sk_c4,sk_c5) = sk_c7
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f43,plain,
( inverse(sk_c4) = sk_c5
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f45,plain,
( multiply(sk_c5,sk_c7) = sk_c6
| inverse(sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f46,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f47,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f48,plain,
( multiply(sk_c4,sk_c5) = sk_c7
| inverse(sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f49,plain,
( inverse(sk_c4) = sk_c5
| inverse(sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f50,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c7,sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f51,plain,
( multiply(sk_c5,sk_c7) = sk_c6
| multiply(sk_c7,sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f52,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c7,sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f53,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c7,sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f54,plain,
( multiply(sk_c4,sk_c5) = sk_c7
| multiply(sk_c7,sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f55,plain,
( inverse(sk_c4) = sk_c5
| multiply(sk_c7,sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f56,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f57,plain,
( multiply(sk_c5,sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f58,plain,
( inverse(sk_c3) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f59,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f60,plain,
( multiply(sk_c4,sk_c5) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f61,plain,
( inverse(sk_c4) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c2 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f62,plain,
( multiply(sk_c6,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f63,plain,
( multiply(sk_c5,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f64,plain,
( inverse(sk_c3) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f65,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f66,plain,
( multiply(sk_c4,sk_c5) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f67,plain,
( inverse(sk_c4) = sk_c5
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f68,plain,
! [X2] :
( inverse(X2) != sk_c5
| multiply(X2,sk_c5) != sk_c7
| ! [X1] :
( multiply(X1,sk_c6) != sk_c7
| inverse(X1) != sk_c7
| multiply(sk_c5,sk_c7) != sk_c6
| multiply(sk_c6,sk_c7) != sk_c5
| ! [X4] :
( inverse(X4) != sk_c7
| ! [X3] :
( multiply(X4,sk_c7) != X3
| multiply(sk_c7,X3) != sk_c6
| inverse(sk_c7) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c7 ) ) ) ),
inference(miniscoping,[status(thm)],[f34]) ).
fof(f69,plain,
! [X0,X1,X2,X3] :
( inverse(X3) != sk_c5
| multiply(X3,sk_c5) != sk_c7
| multiply(X2,sk_c6) != sk_c7
| inverse(X2) != sk_c7
| multiply(sk_c5,sk_c7) != sk_c6
| multiply(sk_c6,sk_c7) != sk_c5
| inverse(X1) != sk_c7
| multiply(X1,sk_c7) != X0
| multiply(sk_c7,X0) != sk_c6
| inverse(sk_c7) != sk_c5
| multiply(sk_c6,sk_c5) != sk_c7 ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f70,definition,
( sQ0_spl
<=> multiply(sk_c6,sk_c5) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f71,plain,
( ~ sQ0_spl
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f72,plain,
( sQ0_spl
| multiply(sk_c6,sk_c5) != sk_c7 ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f73,definition,
( sQ1_spl
<=> multiply(sk_c6,sk_c7) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f75,plain,
( sQ1_spl
| multiply(sk_c6,sk_c7) != sk_c5 ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f77,definition,
( sQ2_spl
<=> multiply(sk_c5,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f78,plain,
( ~ sQ2_spl
| multiply(sk_c5,sk_c7) = sk_c6 ),
inference(component_clause,[status(thm)],[f77]) ).
fof(f79,plain,
( sQ2_spl
| multiply(sk_c5,sk_c7) != sk_c6 ),
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_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(f84,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f40,f70,f81]) ).
fof(f85,definition,
( sQ4_spl
<=> multiply(sk_c3,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ4_spl
| multiply(sk_c3,sk_c6) = 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
<=> multiply(sk_c4,sk_c5) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f90,plain,
( ~ sQ5_spl
| multiply(sk_c4,sk_c5) = sk_c7 ),
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_c5 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ6_spl
| inverse(sk_c4) = sk_c5 ),
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_c7) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f98,plain,
( ~ sQ7_spl
| inverse(sk_c7) = sk_c5 ),
inference(component_clause,[status(thm)],[f97]) ).
fof(f99,plain,
( sQ7_spl
| inverse(sk_c7) != sk_c5 ),
inference(component_clause,[status(thm)],[f97]) ).
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_c7,sk_c2) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f107,plain,
( ~ sQ8_spl
| multiply(sk_c7,sk_c2) = sk_c6 ),
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_c7) = sk_c2 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f116,plain,
( ~ sQ9_spl
| multiply(sk_c1,sk_c7) = 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_c7 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f125,plain,
( ~ sQ10_spl
| inverse(sk_c1) = sk_c7 ),
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_c7
| multiply(X1,sk_c7) != X0
| multiply(sk_c7,X0) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f134,plain,
! [X0,X1] :
( ~ sQ11_spl
| inverse(X1) != sk_c7
| multiply(X1,sk_c7) != X0
| multiply(sk_c7,X0) != sk_c6 ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,definition,
! [X2] :
( sQ12_spl
<=> ( multiply(X2,sk_c6) != sk_c7
| inverse(X2) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f137,plain,
! [X0] :
( ~ sQ12_spl
| multiply(X0,sk_c6) != sk_c7
| inverse(X0) != sk_c7 ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f139,definition,
! [X3] :
( sQ13_spl
<=> ( inverse(X3) != sk_c5
| multiply(X3,sk_c5) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f140,plain,
! [X0] :
( ~ sQ13_spl
| inverse(X0) != sk_c5
| multiply(X0,sk_c5) != sk_c7 ),
inference(component_clause,[status(thm)],[f139]) ).
fof(f142,plain,
( sQ13_spl
| sQ12_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sQ11_spl
| ~ sQ7_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f69,f70,f97,f133,f73,f77,f136,f139]) ).
fof(f161,plain,
( ~ sQ7_spl
| multiply(sk_c5,sk_c7) = identity ),
inference(paramodulation,[status(thm)],[f98,f36]) ).
fof(f162,plain,
( ~ sQ3_spl
| multiply(sk_c7,sk_c3) = identity ),
inference(paramodulation,[status(thm)],[f82,f36]) ).
fof(f166,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f36,f37]) ).
fof(f167,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f35,f166]) ).
fof(f174,plain,
! [X0] :
( ~ sQ3_spl
| multiply(identity,X0) = multiply(sk_c7,multiply(sk_c3,X0)) ),
inference(paramodulation,[status(thm)],[f162,f37]) ).
fof(f175,plain,
! [X0] :
( ~ sQ3_spl
| X0 = multiply(sk_c7,multiply(sk_c3,X0)) ),
inference(forward_demodulation,[status(thm)],[f35,f174]) ).
fof(f180,plain,
( ~ sQ5_spl
| ~ sQ13_spl
| inverse(sk_c4) != sk_c5 ),
inference(resolution,[status(thm)],[f140,f90]) ).
fof(f181,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| inverse(sk_c6) != sk_c5
| sk_c7 != sk_c7 ),
inference(paramodulation,[status(thm)],[f71,f140]) ).
fof(f186,plain,
( ~ sQ5_spl
| ~ sQ13_spl
| ~ sQ6_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f94,f180]) ).
fof(f187,plain,
( ~ sQ5_spl
| ~ sQ13_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f186]) ).
fof(f188,plain,
( ~ sQ5_spl
| ~ sQ13_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f187]) ).
fof(f189,plain,
! [X0] :
( ~ sQ11_spl
| inverse(X0) != sk_c7
| multiply(sk_c7,multiply(X0,sk_c7)) != sk_c6 ),
inference(destructive_equality_resolution,[status(thm)],[f134]) ).
fof(f190,plain,
( ~ sQ4_spl
| ~ sQ12_spl
| inverse(sk_c3) != sk_c7 ),
inference(resolution,[status(thm)],[f137,f86]) ).
fof(f195,plain,
( ~ sQ4_spl
| ~ sQ12_spl
| ~ sQ3_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f82,f190]) ).
fof(f196,plain,
( ~ sQ4_spl
| ~ sQ12_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f195]) ).
fof(f197,plain,
( ~ sQ4_spl
| ~ sQ12_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f196]) ).
fof(f200,plain,
( ~ sQ11_spl
| inverse(identity) != sk_c7
| multiply(sk_c7,sk_c7) != sk_c6 ),
inference(paramodulation,[status(thm)],[f35,f189]) ).
fof(f202,plain,
( ~ sQ9_spl
| ~ sQ11_spl
| inverse(sk_c1) != sk_c7
| multiply(sk_c7,sk_c2) != sk_c6 ),
inference(paramodulation,[status(thm)],[f116,f189]) ).
fof(f214,definition,
( sQ17_spl
<=> multiply(sk_c7,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f216,plain,
( sQ17_spl
| multiply(sk_c7,sk_c7) != sk_c6 ),
inference(component_clause,[status(thm)],[f214]) ).
fof(f217,definition,
( sQ18_spl
<=> inverse(identity) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f219,plain,
( sQ18_spl
| inverse(identity) != sk_c7 ),
inference(component_clause,[status(thm)],[f217]) ).
fof(f220,plain,
( ~ sQ11_spl
| ~ sQ18_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f200,f214,f217,f133]) ).
fof(f221,plain,
( ~ sQ9_spl
| ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f202,f106,f124,f133,f115]) ).
fof(f395,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| sk_c6 = multiply(sk_c7,sk_c7) ),
inference(paramodulation,[status(thm)],[f86,f175]) ).
fof(f404,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f395,f216]) ).
fof(f405,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f404]) ).
fof(f432,plain,
( ~ sQ5_spl
| sk_c5 = multiply(inverse(sk_c4),sk_c7) ),
inference(paramodulation,[status(thm)],[f90,f167]) ).
fof(f433,plain,
( ~ sQ9_spl
| sk_c7 = multiply(inverse(sk_c1),sk_c2) ),
inference(paramodulation,[status(thm)],[f116,f167]) ).
fof(f447,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sk_c5 = multiply(sk_c5,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f94,f432]) ).
fof(f448,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ2_spl
| sk_c5 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f78,f447]) ).
fof(f449,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| sk_c7 = multiply(sk_c7,sk_c2) ),
inference(forward_demodulation,[status(thm)],[f125,f433]) ).
fof(f451,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ2_spl
| multiply(sk_c6,sk_c6) != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f448,f72]) ).
fof(f454,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c6,sk_c7) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f448,f78]) ).
fof(f458,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c7 = multiply(inverse(sk_c6),sk_c6) ),
inference(paramodulation,[status(thm)],[f454,f167]) ).
fof(f465,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c7 = identity ),
inference(forward_demodulation,[status(thm)],[f36,f458]) ).
fof(f467,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ2_spl
| multiply(sk_c6,sk_c6) != identity ),
inference(backward_demodulation,[status(thm)],[f465,f451]) ).
fof(f468,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c6 = multiply(sk_c7,identity) ),
inference(backward_demodulation,[status(thm)],[f465,f395]) ).
fof(f470,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(identity,sk_c3) = identity ),
inference(backward_demodulation,[status(thm)],[f465,f162]) ).
fof(f472,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| inverse(sk_c3) = identity ),
inference(backward_demodulation,[status(thm)],[f465,f82]) ).
fof(f477,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c6 = multiply(identity,identity) ),
inference(forward_demodulation,[status(thm)],[f465,f468]) ).
fof(f478,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f35,f477]) ).
fof(f480,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c3 = identity ),
inference(forward_demodulation,[status(thm)],[f35,f470]) ).
fof(f483,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sk_c5 = identity ),
inference(backward_demodulation,[status(thm)],[f478,f448]) ).
fof(f513,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| inverse(identity) = identity ),
inference(forward_demodulation,[status(thm)],[f480,f472]) ).
fof(f520,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ3_spl
| multiply(identity,sk_c6) != identity ),
inference(forward_demodulation,[status(thm)],[f478,f467]) ).
fof(f521,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ3_spl
| sk_c6 != identity ),
inference(forward_demodulation,[status(thm)],[f35,f520]) ).
fof(f522,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ3_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f478,f521]) ).
fof(f523,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f522]) ).
fof(f524,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f523]) ).
fof(f550,plain,
( sQ7_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| inverse(identity) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f465,f99]) ).
fof(f551,plain,
( sQ7_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| identity != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f513,f550]) ).
fof(f552,plain,
( sQ7_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f483,f551]) ).
fof(f553,plain,
( sQ7_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f552]) ).
fof(f554,plain,
( sQ7_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f553]) ).
fof(f560,plain,
( sQ18_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| identity != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f513,f219]) ).
fof(f561,plain,
( sQ18_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f465,f560]) ).
fof(f562,plain,
( sQ18_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f561]) ).
fof(f563,plain,
( sQ18_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f562]) ).
fof(f575,definition,
( sQ22_spl
<=> sk_c7 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f577,plain,
( sQ22_spl
| sk_c7 != sk_c7 ),
inference(component_clause,[status(thm)],[f575]) ).
fof(f605,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c7 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f107,f449]) ).
fof(f617,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| multiply(sk_c1,sk_c6) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f605,f116]) ).
fof(f620,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| multiply(sk_c6,sk_c5) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f605,f71]) ).
fof(f621,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c6,sk_c2) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f605,f107]) ).
fof(f622,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| inverse(sk_c1) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f605,f125]) ).
fof(f626,plain,
( ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| inverse(sk_c6) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f605,f98]) ).
fof(f664,plain,
( sQ2_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| multiply(sk_c5,sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f605,f79]) ).
fof(f680,plain,
( sQ2_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| identity != sk_c6 ),
inference(backward_demodulation,[status(thm)],[f681,f664]) ).
fof(f681,plain,
( ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| multiply(sk_c5,sk_c6) = identity ),
inference(forward_demodulation,[status(thm)],[f605,f161]) ).
fof(f694,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c5 = multiply(inverse(sk_c6),sk_c6) ),
inference(paramodulation,[status(thm)],[f620,f167]) ).
fof(f701,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c5 = identity ),
inference(forward_demodulation,[status(thm)],[f36,f694]) ).
fof(f703,plain,
( ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| multiply(identity,sk_c6) = identity ),
inference(backward_demodulation,[status(thm)],[f701,f681]) ).
fof(f704,plain,
( ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| inverse(sk_c6) = identity ),
inference(backward_demodulation,[status(thm)],[f701,f626]) ).
fof(f709,plain,
( ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f35,f703]) ).
fof(f714,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| multiply(sk_c1,identity) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f709,f617]) ).
fof(f716,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| inverse(sk_c1) = identity ),
inference(backward_demodulation,[status(thm)],[f709,f622]) ).
fof(f718,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c7 = identity ),
inference(backward_demodulation,[status(thm)],[f709,f605]) ).
fof(f720,plain,
( sQ2_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f709,f680]) ).
fof(f721,plain,
( sQ2_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f720]) ).
fof(f722,plain,
( sQ2_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f721]) ).
fof(f748,definition,
( sQ23_spl
<=> inverse(sk_c6) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f750,plain,
( sQ23_spl
| inverse(sk_c6) != sk_c5 ),
inference(component_clause,[status(thm)],[f748]) ).
fof(f751,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ23_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f181,f575,f748,f139,f70]) ).
fof(f769,plain,
( sQ22_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f577]) ).
fof(f770,plain,
sQ22_spl,
inference(contradiction_clause,[status(thm)],[f769]) ).
fof(f771,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| multiply(X0,identity) != sk_c7
| inverse(X0) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f709,f137]) ).
fof(f773,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ0_spl
| multiply(identity,sk_c2) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f709,f621]) ).
fof(f774,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c2 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f35,f773]) ).
fof(f775,plain,
( ~ sQ8_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c2 = identity ),
inference(forward_demodulation,[status(thm)],[f709,f774]) ).
fof(f779,plain,
( ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| inverse(identity) = identity ),
inference(forward_demodulation,[status(thm)],[f709,f704]) ).
fof(f789,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| multiply(sk_c1,identity) = identity ),
inference(forward_demodulation,[status(thm)],[f775,f714]) ).
fof(f803,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| multiply(X0,identity) != sk_c7
| inverse(X0) != identity ),
inference(forward_demodulation,[status(thm)],[f718,f771]) ).
fof(f804,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| multiply(X0,identity) != identity
| inverse(X0) != identity ),
inference(forward_demodulation,[status(thm)],[f718,f803]) ).
fof(f805,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ12_spl
| inverse(sk_c1) != identity ),
inference(resolution,[status(thm)],[f804,f789]) ).
fof(f814,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ12_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f716,f805]) ).
fof(f815,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f814]) ).
fof(f816,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f815]) ).
fof(f817,plain,
( sQ23_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| inverse(identity) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f709,f750]) ).
fof(f818,plain,
( sQ23_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| identity != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f779,f817]) ).
fof(f819,plain,
( sQ23_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f701,f818]) ).
fof(f820,plain,
( sQ23_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f819]) ).
fof(f821,plain,
( sQ23_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f820]) ).
fof(f842,plain,
( sQ1_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| multiply(identity,sk_c7) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f709,f75]) ).
fof(f843,plain,
( sQ1_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c7 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f35,f842]) ).
fof(f844,plain,
( sQ1_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| identity != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f718,f843]) ).
fof(f845,plain,
( sQ1_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f701,f844]) ).
fof(f846,plain,
( sQ1_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f845]) ).
fof(f847,plain,
( sQ1_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f846]) ).
fof(f848,plain,
$false,
inference(sat_refutation,[status(thm)],[f80,f84,f88,f92,f96,f101,f102,f103,f104,f105,f109,f110,f111,f112,f113,f114,f118,f119,f120,f121,f122,f123,f127,f128,f129,f130,f131,f132,f142,f188,f197,f220,f221,f405,f524,f554,f563,f722,f751,f770,f816,f821,f847]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP361-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 20:13:35 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.13/0.40 % Refutation found
% 0.13/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.42 % Elapsed time: 0.056285 seconds
% 0.13/0.42 % CPU time: 0.234244 seconds
% 0.13/0.42 % Total memory used: 105.609 MB
% 0.13/0.42 % Net memory used: 105.294 MB
%------------------------------------------------------------------------------