%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP347-1 : 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 12:33:29 PM UTC 2026
% Result : Unsatisfiable 0.08s 0.41s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 54
% Syntax : Number of formulae : 271 ( 15 unt; 20 def)
% Number of atoms : 884 ( 320 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1149 ( 536 ~; 593 |; 0 &)
% ( 20 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 21 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 54 ( 54 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c6) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c3) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c6) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( inverse(sk_c3) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c4) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c6) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c3) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( inverse(sk_c6) = sk_c5
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c3) = sk_c6
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c5
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c4) = sk_c7
| inverse(sk_c2) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( inverse(sk_c6) = sk_c5
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( inverse(sk_c3) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c5
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c2,sk_c5) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
! [X3,X4,X1,X2] :
( inverse(X2) != sk_c7
| multiply(X2,sk_c7) != sk_c5
| inverse(X1) != sk_c6
| multiply(X1,sk_c6) != sk_c7
| inverse(sk_c6) != sk_c5
| 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/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f36,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f37,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f38,plain,
( multiply(sk_c6,sk_c5) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f39,plain,
( inverse(sk_c6) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f40,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f41,plain,
( inverse(sk_c3) = sk_c6
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f42,plain,
( multiply(sk_c4,sk_c7) = sk_c5
| multiply(sk_c6,sk_c7) = sk_c5 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f43,plain,
( inverse(sk_c4) = sk_c7
| 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,
( inverse(sk_c6) = sk_c5
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f46,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f47,plain,
( inverse(sk_c3) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f48,plain,
( multiply(sk_c4,sk_c7) = sk_c5
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f49,plain,
( inverse(sk_c4) = sk_c7
| 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,
( inverse(sk_c6) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f52,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f53,plain,
( inverse(sk_c3) = sk_c6
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f54,plain,
( multiply(sk_c4,sk_c7) = sk_c5
| multiply(sk_c1,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f55,plain,
( inverse(sk_c4) = sk_c7
| 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,
( inverse(sk_c6) = sk_c5
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f58,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f59,plain,
( inverse(sk_c3) = sk_c6
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f60,plain,
( multiply(sk_c4,sk_c7) = sk_c5
| inverse(sk_c2) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f61,plain,
( inverse(sk_c4) = sk_c7
| 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,
( inverse(sk_c6) = sk_c5
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f64,plain,
( multiply(sk_c3,sk_c6) = sk_c7
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f65,plain,
( inverse(sk_c3) = sk_c6
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f66,plain,
( multiply(sk_c4,sk_c7) = sk_c5
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f67,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c2,sk_c5) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f68,plain,
! [X2] :
( inverse(X2) != sk_c7
| multiply(X2,sk_c7) != sk_c5
| ! [X1] :
( inverse(X1) != sk_c6
| multiply(X1,sk_c6) != sk_c7
| inverse(sk_c6) != sk_c5
| 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_c7
| multiply(X3,sk_c7) != sk_c5
| inverse(X2) != sk_c6
| multiply(X2,sk_c6) != sk_c7
| inverse(sk_c6) != sk_c5
| 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
<=> inverse(sk_c6) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f78,plain,
( ~ sQ2_spl
| inverse(sk_c6) = sk_c5 ),
inference(component_clause,[status(thm)],[f77]) ).
fof(f79,plain,
( sQ2_spl
| inverse(sk_c6) != sk_c5 ),
inference(component_clause,[status(thm)],[f77]) ).
fof(f80,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f39,f70,f77]) ).
fof(f81,definition,
( sQ3_spl
<=> multiply(sk_c3,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f82,plain,
( ~ sQ3_spl
| multiply(sk_c3,sk_c6) = sk_c7 ),
inference(component_clause,[status(thm)],[f81]) ).
fof(f84,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f40,f70,f81]) ).
fof(f85,definition,
( sQ4_spl
<=> inverse(sk_c3) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ4_spl
| inverse(sk_c3) = sk_c6 ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f88,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f41,f70,f85]) ).
fof(f89,definition,
( sQ5_spl
<=> multiply(sk_c4,sk_c7) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f90,plain,
( ~ sQ5_spl
| multiply(sk_c4,sk_c7) = 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_c7 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ6_spl
| inverse(sk_c4) = sk_c7 ),
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_c6
| multiply(X2,sk_c6) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f140,plain,
! [X0] :
( ~ sQ13_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c7 ),
inference(component_clause,[status(thm)],[f139]) ).
fof(f142,definition,
! [X3] :
( sQ14_spl
<=> ( inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c5 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f143,plain,
! [X0] :
( ~ sQ14_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c5 ),
inference(component_clause,[status(thm)],[f142]) ).
fof(f145,plain,
( sQ14_spl
| sQ13_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sQ12_spl
| sQ11_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f69,f70,f133,f136,f73,f77,f139,f142]) ).
fof(f147,plain,
! [X0] :
( ~ sQ5_spl
| multiply(sk_c5,X0) = multiply(sk_c4,multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f90,f37]) ).
fof(f149,plain,
! [X0] :
( ~ sQ10_spl
| multiply(sk_c6,X0) = multiply(sk_c2,multiply(sk_c5,X0)) ),
inference(paramodulation,[status(thm)],[f125,f37]) ).
fof(f154,plain,
( ~ sQ4_spl
| multiply(sk_c6,sk_c3) = identity ),
inference(paramodulation,[status(thm)],[f86,f36]) ).
fof(f155,plain,
( ~ sQ6_spl
| multiply(sk_c7,sk_c4) = identity ),
inference(paramodulation,[status(thm)],[f94,f36]) ).
fof(f157,plain,
( ~ sQ9_spl
| multiply(sk_c6,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f116,f36]) ).
fof(f158,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f36,f37]) ).
fof(f159,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f35,f158]) ).
fof(f168,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| inverse(sk_c4) != sk_c7 ),
inference(resolution,[status(thm)],[f143,f90]) ).
fof(f174,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| ~ sQ6_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f94,f168]) ).
fof(f175,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f174]) ).
fof(f176,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f175]) ).
fof(f177,plain,
( ~ sQ4_spl
| ~ sQ13_spl
| multiply(sk_c3,sk_c6) != sk_c7 ),
inference(resolution,[status(thm)],[f140,f86]) ).
fof(f180,plain,
( ~ sQ7_spl
| ~ sQ13_spl
| sk_c7 != sk_c6
| multiply(sk_c1,sk_c6) != sk_c7 ),
inference(paramodulation,[status(thm)],[f98,f140]) ).
fof(f181,plain,
( ~ sQ9_spl
| ~ sQ13_spl
| sk_c6 != sk_c6
| multiply(sk_c2,sk_c6) != sk_c7 ),
inference(paramodulation,[status(thm)],[f116,f140]) ).
fof(f182,plain,
( ~ sQ4_spl
| ~ sQ13_spl
| ~ sQ3_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f82,f177]) ).
fof(f183,plain,
( ~ sQ4_spl
| ~ sQ13_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f182]) ).
fof(f184,plain,
( ~ sQ4_spl
| ~ sQ13_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f183]) ).
fof(f186,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| multiply(sk_c2,sk_c5) != sk_c6 ),
inference(resolution,[status(thm)],[f137,f116]) ).
fof(f190,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ10_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f125,f186]) ).
fof(f191,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f190]) ).
fof(f192,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f191]) ).
fof(f193,plain,
( ~ sQ2_spl
| multiply(sk_c5,sk_c6) = identity ),
inference(paramodulation,[status(thm)],[f78,f36]) ).
fof(f194,plain,
( ~ sQ7_spl
| ~ sQ11_spl
| multiply(sk_c1,sk_c6) != sk_c7 ),
inference(resolution,[status(thm)],[f134,f98]) ).
fof(f196,plain,
( ~ sQ4_spl
| ~ sQ11_spl
| multiply(sk_c3,sk_c6) != sk_c7
| sk_c6 != sk_c7 ),
inference(paramodulation,[status(thm)],[f86,f134]) ).
fof(f198,plain,
( ~ sQ7_spl
| ~ sQ11_spl
| ~ sQ8_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f107,f194]) ).
fof(f199,plain,
( ~ sQ7_spl
| ~ sQ11_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f198]) ).
fof(f200,plain,
( ~ sQ7_spl
| ~ sQ11_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f199]) ).
fof(f201,definition,
( sQ15_spl
<=> sk_c5 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f202,plain,
( ~ sQ15_spl
| sk_c5 = sk_c7 ),
inference(component_clause,[status(thm)],[f201]) ).
fof(f203,plain,
( sQ15_spl
| sk_c5 != sk_c7 ),
inference(component_clause,[status(thm)],[f201]) ).
fof(f208,definition,
( sQ17_spl
<=> sk_c6 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f210,plain,
( sQ17_spl
| sk_c6 != sk_c7 ),
inference(component_clause,[status(thm)],[f208]) ).
fof(f211,plain,
( ~ sQ4_spl
| ~ sQ11_spl
| ~ sQ3_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f196,f208,f81,f133,f85]) ).
fof(f212,definition,
( sQ18_spl
<=> sk_c7 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f214,plain,
( sQ18_spl
| sk_c7 != sk_c7 ),
inference(component_clause,[status(thm)],[f212]) ).
fof(f221,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| multiply(sk_c5,sk_c4) = multiply(sk_c4,identity) ),
inference(paramodulation,[status(thm)],[f155,f147]) ).
fof(f232,plain,
( ~ sQ3_spl
| sk_c6 = multiply(inverse(sk_c3),sk_c7) ),
inference(paramodulation,[status(thm)],[f82,f159]) ).
fof(f233,plain,
( ~ sQ1_spl
| sk_c5 = multiply(inverse(sk_c6),sk_c7) ),
inference(paramodulation,[status(thm)],[f74,f159]) ).
fof(f234,plain,
( ~ sQ4_spl
| sk_c3 = multiply(inverse(sk_c6),identity) ),
inference(paramodulation,[status(thm)],[f154,f159]) ).
fof(f235,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f159,f159]) ).
fof(f236,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f36,f159]) ).
fof(f241,plain,
( ~ sQ10_spl
| sk_c5 = multiply(inverse(sk_c2),sk_c6) ),
inference(paramodulation,[status(thm)],[f125,f159]) ).
fof(f243,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c6 != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f244,f72]) ).
fof(f244,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c6 = multiply(sk_c6,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f86,f232]) ).
fof(f246,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| sk_c3 = multiply(sk_c5,identity) ),
inference(forward_demodulation,[status(thm)],[f78,f234]) ).
fof(f249,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| multiply(sk_c5,sk_c4) = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f251,f221]) ).
fof(f250,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| sk_c3 = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f251,f246]) ).
fof(f251,plain,
! [X0] : X0 = multiply(X0,identity),
inference(forward_demodulation,[status(thm)],[f235,f236]) ).
fof(f255,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f250,f82]) ).
fof(f261,plain,
( ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| multiply(identity,sk_c4) = identity ),
inference(backward_demodulation,[status(thm)],[f272,f155]) ).
fof(f264,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| multiply(sk_c4,identity) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f272,f90]) ).
fof(f272,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| identity = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f193,f255]) ).
fof(f281,plain,
( ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| sk_c4 = identity ),
inference(forward_demodulation,[status(thm)],[f35,f261]) ).
fof(f284,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ6_spl
| multiply(sk_c5,sk_c4) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f221,f264]) ).
fof(f285,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ6_spl
| sk_c4 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f249,f284]) ).
fof(f286,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| multiply(identity,sk_c6) = identity ),
inference(backward_demodulation,[status(thm)],[f295,f193]) ).
fof(f291,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ6_spl
| sk_c6 != identity ),
inference(backward_demodulation,[status(thm)],[f295,f243]) ).
fof(f295,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ6_spl
| identity = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f281,f285]) ).
fof(f315,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f35,f286]) ).
fof(f321,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ6_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f315,f291]) ).
fof(f322,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f321]) ).
fof(f323,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ2_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f322]) ).
fof(f337,plain,
( sQ17_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| identity != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f315,f210]) ).
fof(f338,plain,
( sQ17_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f272,f337]) ).
fof(f339,plain,
( sQ17_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f338]) ).
fof(f340,plain,
( sQ17_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f339]) ).
fof(f341,plain,
( sQ18_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f214]) ).
fof(f342,plain,
sQ18_spl,
inference(contradiction_clause,[status(thm)],[f341]) ).
fof(f344,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| sk_c5 = multiply(sk_c6,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f116,f241]) ).
fof(f345,plain,
( ~ sQ7_spl
| ~ sQ13_spl
| ~ sQ17_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f180,f106,f208,f139,f97]) ).
fof(f346,definition,
( sQ19_spl
<=> multiply(sk_c2,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f348,plain,
( sQ19_spl
| multiply(sk_c2,sk_c6) != sk_c7 ),
inference(component_clause,[status(thm)],[f346]) ).
fof(f349,definition,
( sQ20_spl
<=> sk_c6 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f351,plain,
( sQ20_spl
| sk_c6 != sk_c6 ),
inference(component_clause,[status(thm)],[f349]) ).
fof(f352,plain,
( ~ sQ9_spl
| ~ sQ13_spl
| ~ sQ20_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f181,f346,f349,f139,f115]) ).
fof(f353,plain,
( sQ20_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f351]) ).
fof(f354,plain,
sQ20_spl,
inference(contradiction_clause,[status(thm)],[f353]) ).
fof(f355,plain,
inverse(identity) = identity,
inference(paramodulation,[status(thm)],[f36,f251]) ).
fof(f368,plain,
( ~ sQ0_spl
| sk_c7 = multiply(inverse(sk_c6),sk_c5) ),
inference(paramodulation,[status(thm)],[f71,f159]) ).
fof(f370,plain,
( ~ sQ8_spl
| sk_c6 = multiply(inverse(sk_c1),sk_c7) ),
inference(paramodulation,[status(thm)],[f107,f159]) ).
fof(f372,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| sk_c6 = multiply(sk_c7,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f98,f370]) ).
fof(f381,plain,
( ~ sQ9_spl
| sk_c2 = multiply(inverse(sk_c6),identity) ),
inference(paramodulation,[status(thm)],[f157,f159]) ).
fof(f383,plain,
( sQ2_spl
| ~ sQ9_spl
| sk_c2 != sk_c5 ),
inference(backward_demodulation,[status(thm)],[f386,f79]) ).
fof(f384,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| sk_c7 = multiply(sk_c2,sk_c5) ),
inference(backward_demodulation,[status(thm)],[f386,f368]) ).
fof(f385,plain,
( ~ sQ1_spl
| ~ sQ9_spl
| sk_c5 = multiply(sk_c2,sk_c7) ),
inference(backward_demodulation,[status(thm)],[f386,f233]) ).
fof(f386,plain,
( ~ sQ9_spl
| sk_c2 = inverse(sk_c6) ),
inference(forward_demodulation,[status(thm)],[f251,f381]) ).
fof(f393,plain,
( sQ15_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c5 != sk_c6 ),
inference(backward_demodulation,[status(thm)],[f405,f203]) ).
fof(f394,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c6 = multiply(sk_c7,sk_c6) ),
inference(backward_demodulation,[status(thm)],[f405,f372]) ).
fof(f395,plain,
( sQ19_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c2,sk_c6) != sk_c6 ),
inference(backward_demodulation,[status(thm)],[f405,f348]) ).
fof(f405,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c7 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f125,f384]) ).
fof(f406,plain,
( ~ sQ1_spl
| ~ sQ9_spl
| ~ sQ0_spl
| ~ sQ10_spl
| sk_c5 = multiply(sk_c2,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f405,f385]) ).
fof(f410,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c6 = multiply(sk_c6,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f405,f394]) ).
fof(f411,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c6 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f344,f410]) ).
fof(f412,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f411,f393]) ).
fof(f413,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sQ15_spl ),
inference(contradiction_clause,[status(thm)],[f412]) ).
fof(f414,plain,
( sQ19_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ1_spl
| sk_c5 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f406,f395]) ).
fof(f415,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sQ19_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f411,f414]) ).
fof(f416,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sQ19_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f415]) ).
fof(f426,plain,
( sQ2_spl
| ~ sQ9_spl
| ~ sQ15_spl
| ~ sQ0_spl
| ~ sQ10_spl
| sk_c2 != sk_c6 ),
inference(backward_demodulation,[status(thm)],[f429,f383]) ).
fof(f427,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ15_spl
| ~ sQ0_spl
| ~ sQ9_spl
| multiply(sk_c6,X0) = multiply(sk_c2,multiply(sk_c6,X0)) ),
inference(backward_demodulation,[status(thm)],[f429,f149]) ).
fof(f429,plain,
( ~ sQ15_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c5 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f405,f202]) ).
fof(f440,plain,
! [X0] :
( ~ sQ9_spl
| X0 = multiply(sk_c2,multiply(sk_c6,X0)) ),
inference(paramodulation,[status(thm)],[f386,f159]) ).
fof(f441,plain,
( ~ sQ9_spl
| multiply(sk_c2,sk_c6) = identity ),
inference(paramodulation,[status(thm)],[f386,f36]) ).
fof(f442,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ15_spl
| ~ sQ0_spl
| sk_c2 = identity ),
inference(backward_demodulation,[status(thm)],[f450,f157]) ).
fof(f450,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ15_spl
| ~ sQ0_spl
| X0 = multiply(sk_c6,X0) ),
inference(forward_demodulation,[status(thm)],[f427,f440]) ).
fof(f452,plain,
( sQ2_spl
| ~ sQ9_spl
| ~ sQ15_spl
| ~ sQ0_spl
| ~ sQ10_spl
| identity != sk_c6 ),
inference(backward_demodulation,[status(thm)],[f442,f426]) ).
fof(f453,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ15_spl
| ~ sQ0_spl
| inverse(identity) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f442,f116]) ).
fof(f454,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ15_spl
| ~ sQ0_spl
| multiply(identity,sk_c6) = identity ),
inference(backward_demodulation,[status(thm)],[f442,f441]) ).
fof(f464,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ15_spl
| ~ sQ0_spl
| identity = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f355,f453]) ).
fof(f465,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ15_spl
| ~ sQ0_spl
| sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f464,f452]) ).
fof(f466,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ15_spl
| ~ sQ0_spl
| sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f465]) ).
fof(f468,plain,
( ~ sQ15_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c5 = identity ),
inference(backward_demodulation,[status(thm)],[f471,f429]) ).
fof(f469,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ15_spl
| sk_c7 = identity ),
inference(backward_demodulation,[status(thm)],[f471,f405]) ).
fof(f471,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ15_spl
| ~ sQ0_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f35,f454]) ).
fof(f487,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c6) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f405,f143]) ).
fof(f488,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ15_spl
| inverse(X0) != sk_c7
| multiply(X0,identity) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f471,f487]) ).
fof(f489,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ15_spl
| inverse(X0) != sk_c7
| X0 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f251,f488]) ).
fof(f490,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ15_spl
| inverse(X0) != sk_c7
| X0 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f429,f489]) ).
fof(f491,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ15_spl
| inverse(X0) != sk_c7
| X0 != identity ),
inference(forward_demodulation,[status(thm)],[f471,f490]) ).
fof(f492,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ15_spl
| inverse(X0) != sk_c6
| X0 != identity ),
inference(forward_demodulation,[status(thm)],[f405,f491]) ).
fof(f493,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ15_spl
| inverse(X0) != identity
| X0 != identity ),
inference(forward_demodulation,[status(thm)],[f471,f492]) ).
fof(f494,plain,
( ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ15_spl
| inverse(identity) != identity ),
inference(destructive_equality_resolution,[status(thm)],[f493]) ).
fof(f495,plain,
( ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f494,f355]) ).
fof(f496,plain,
( ~ sQ14_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ15_spl ),
inference(contradiction_clause,[status(thm)],[f495]) ).
fof(f534,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| multiply(X0,sk_c5) != sk_c6
| inverse(X0) != identity ),
inference(forward_demodulation,[status(thm)],[f315,f137]) ).
fof(f535,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| multiply(X0,identity) != sk_c6
| inverse(X0) != identity ),
inference(forward_demodulation,[status(thm)],[f295,f534]) ).
fof(f536,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| X0 != sk_c6
| inverse(X0) != identity ),
inference(forward_demodulation,[status(thm)],[f251,f535]) ).
fof(f537,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| X0 != identity
| inverse(X0) != identity ),
inference(forward_demodulation,[status(thm)],[f315,f536]) ).
fof(f538,plain,
( ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| inverse(identity) != identity ),
inference(destructive_equality_resolution,[status(thm)],[f537]) ).
fof(f539,plain,
( ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f538,f355]) ).
fof(f540,plain,
( ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f539]) ).
fof(f542,plain,
( sQ1_spl
| ~ sQ15_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c6,identity) != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f468,f75]) ).
fof(f639,plain,
( sQ1_spl
| ~ sQ15_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c6 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f251,f542]) ).
fof(f640,plain,
( sQ1_spl
| ~ sQ15_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| identity != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f471,f639]) ).
fof(f641,plain,
( sQ1_spl
| ~ sQ15_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| identity != identity ),
inference(forward_demodulation,[status(thm)],[f469,f640]) ).
fof(f642,plain,
( sQ1_spl
| ~ sQ15_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f641]) ).
fof(f643,plain,
( sQ1_spl
| ~ sQ15_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f642]) ).
fof(f644,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,f176,f184,f192,f200,f211,f323,f340,f342,f345,f352,f354,f413,f416,f466,f496,f540,f643]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP347-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n009.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 20 20:09:59 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.08/0.41 % Refutation found
% 0.08/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.42 % Elapsed time: 0.057604 seconds
% 0.08/0.42 % CPU time: 0.232763 seconds
% 0.08/0.42 % Total memory used: 102.192 MB
% 0.08/0.42 % Net memory used: 101.983 MB
%------------------------------------------------------------------------------