%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP332-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 12:33:26 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 55
% Syntax : Number of formulae : 282 ( 13 unt; 21 def)
% Number of atoms : 1141 ( 339 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 1640 ( 781 ~; 838 |; 0 &)
% ( 21 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 23 ( 21 usr; 22 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 63 ( 63 !; 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_c8,sk_c7) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
! [X3,X4,X1,X2,X5] :
( inverse(X5) != sk_c8
| multiply(X5,sk_c8) != X2
| multiply(sk_c8,X2) != sk_c7
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| multiply(X4,sk_c6) != sk_c7
| inverse(X4) != sk_c7
| inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ),
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_c8,sk_c7) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f39,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f40,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f41,plain,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f42,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f43,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f44,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f45,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f46,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f47,plain,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f48,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f49,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f50,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f51,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f52,plain,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f53,plain,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f54,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f55,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f56,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f57,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f58,plain,
( inverse(sk_c3) = sk_c8
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f59,plain,
( multiply(sk_c8,sk_c5) = sk_c7
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f60,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f61,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f62,plain,
( multiply(sk_c8,sk_c7) = sk_c6
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f63,plain,
( multiply(sk_c3,sk_c8) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f64,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f65,plain,
( multiply(sk_c8,sk_c5) = sk_c7
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f66,plain,
( multiply(sk_c4,sk_c8) = sk_c5
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f67,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f68,plain,
! [X5] :
( inverse(X5) != sk_c8
| ! [X2] :
( multiply(X5,sk_c8) != X2
| multiply(sk_c8,X2) != sk_c7
| ! [X1] :
( inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| ! [X4] :
( multiply(X4,sk_c6) != sk_c7
| inverse(X4) != sk_c7
| ! [X3] :
( inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ) ) ) ) ),
inference(miniscoping,[status(thm)],[f34]) ).
fof(f69,plain,
! [X0,X1,X2,X3,X4] :
( inverse(X4) != sk_c8
| multiply(X4,sk_c8) != X3
| multiply(sk_c8,X3) != sk_c7
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6
| multiply(X1,sk_c6) != sk_c7
| inverse(X1) != sk_c7
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(cnf_transformation,[status(thm)],[f68]) ).
fof(f70,definition,
( sQ0_spl
<=> multiply(sk_c7,sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f71,plain,
( ~ sQ0_spl
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f72,plain,
( sQ0_spl
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f73,definition,
( sQ1_spl
<=> multiply(sk_c8,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f74,plain,
( ~ sQ1_spl
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f75,plain,
( sQ1_spl
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f76,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f38,f70,f73]) ).
fof(f77,definition,
( sQ2_spl
<=> multiply(sk_c3,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f78,plain,
( ~ sQ2_spl
| multiply(sk_c3,sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f77]) ).
fof(f80,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f39,f70,f77]) ).
fof(f81,definition,
( sQ3_spl
<=> inverse(sk_c3) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f82,plain,
( ~ sQ3_spl
| inverse(sk_c3) = sk_c8 ),
inference(component_clause,[status(thm)],[f81]) ).
fof(f84,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f40,f70,f81]) ).
fof(f85,definition,
( sQ4_spl
<=> multiply(sk_c8,sk_c5) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ4_spl
| multiply(sk_c8,sk_c5) = 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_c8) = sk_c5 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f90,plain,
( ~ sQ5_spl
| multiply(sk_c4,sk_c8) = 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_c8 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ6_spl
| inverse(sk_c4) = sk_c8 ),
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
<=> multiply(sk_c1,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f98,plain,
( ~ sQ7_spl
| multiply(sk_c1,sk_c7) = sk_c8 ),
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
<=> inverse(sk_c1) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f107,plain,
( ~ sQ8_spl
| inverse(sk_c1) = 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_c7 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f116,plain,
( ~ sQ9_spl
| inverse(sk_c2) = sk_c7 ),
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_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f125,plain,
( ~ sQ10_spl
| multiply(sk_c2,sk_c6) = 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] :
( sQ11_spl
<=> ( inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f134,plain,
! [X0] :
( ~ sQ11_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c8 ),
inference(component_clause,[status(thm)],[f133]) ).
fof(f136,definition,
! [X1] :
( sQ12_spl
<=> ( multiply(X1,sk_c6) != sk_c7
| inverse(X1) != 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,
! [X2] :
( sQ13_spl
<=> ( inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f140,plain,
! [X0] :
( ~ sQ13_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f139]) ).
fof(f142,definition,
! [X3,X4] :
( sQ14_spl
<=> ( inverse(X4) != sk_c8
| multiply(X4,sk_c8) != X3
| multiply(sk_c8,X3) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f143,plain,
! [X0,X1] :
( ~ sQ14_spl
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != X0
| multiply(sk_c8,X0) != sk_c7 ),
inference(component_clause,[status(thm)],[f142]) ).
fof(f145,plain,
( sQ14_spl
| sQ13_spl
| ~ sQ1_spl
| sQ12_spl
| sQ11_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f69,f70,f133,f136,f73,f139,f142]) ).
fof(f146,plain,
! [X0] :
( ~ sQ14_spl
| inverse(X0) != sk_c8
| multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ),
inference(destructive_equality_resolution,[status(thm)],[f143]) ).
fof(f165,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| inverse(sk_c4) != sk_c8
| multiply(sk_c8,sk_c5) != sk_c7 ),
inference(paramodulation,[status(thm)],[f90,f146]) ).
fof(f177,plain,
( ~ sQ5_spl
| ~ sQ14_spl
| ~ sQ6_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f165,f85,f93,f142,f89]) ).
fof(f179,plain,
( ~ sQ6_spl
| ~ sQ13_spl
| sk_c8 != sk_c8
| multiply(sk_c4,sk_c8) != sk_c7 ),
inference(paramodulation,[status(thm)],[f94,f140]) ).
fof(f183,definition,
( sQ18_spl
<=> multiply(sk_c4,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f185,plain,
( sQ18_spl
| multiply(sk_c4,sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f183]) ).
fof(f186,definition,
( sQ19_spl
<=> sk_c8 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f188,plain,
( sQ19_spl
| sk_c8 != sk_c8 ),
inference(component_clause,[status(thm)],[f186]) ).
fof(f189,plain,
( ~ sQ6_spl
| ~ sQ13_spl
| ~ sQ19_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f179,f183,f186,f139,f93]) ).
fof(f193,definition,
( sQ21_spl
<=> sk_c7 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f195,plain,
( sQ21_spl
| sk_c7 != sk_c8 ),
inference(component_clause,[status(thm)],[f193]) ).
fof(f201,plain,
( sQ19_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f188]) ).
fof(f202,plain,
sQ19_spl,
inference(contradiction_clause,[status(thm)],[f201]) ).
fof(f203,plain,
( sQ18_spl
| ~ sQ5_spl
| sk_c5 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f90,f185]) ).
fof(f205,plain,
( ~ sQ8_spl
| multiply(sk_c7,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f107,f36]) ).
fof(f207,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f36,f37]) ).
fof(f208,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f35,f207]) ).
fof(f214,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| multiply(sk_c2,sk_c6) != sk_c7 ),
inference(resolution,[status(thm)],[f137,f116]) ).
fof(f217,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ10_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f125,f214]) ).
fof(f218,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f217]) ).
fof(f219,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f218]) ).
fof(f220,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| sk_c8 != sk_c7
| multiply(sk_c3,sk_c7) != sk_c8 ),
inference(paramodulation,[status(thm)],[f82,f134]) ).
fof(f222,definition,
( sQ23_spl
<=> multiply(sk_c3,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f224,plain,
( sQ23_spl
| multiply(sk_c3,sk_c7) != sk_c8 ),
inference(component_clause,[status(thm)],[f222]) ).
fof(f225,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| ~ sQ21_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f220,f222,f193,f133,f81]) ).
fof(f232,plain,
( ~ sQ11_spl
| ~ sQ8_spl
| multiply(sk_c1,sk_c7) != sk_c8 ),
inference(resolution,[status(thm)],[f107,f134]) ).
fof(f235,plain,
( ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ7_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f98,f232]) ).
fof(f236,plain,
( ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f235]) ).
fof(f237,plain,
( ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f236]) ).
fof(f248,plain,
( ~ sQ0_spl
| sk_c8 = multiply(inverse(sk_c7),sk_c6) ),
inference(paramodulation,[status(thm)],[f71,f208]) ).
fof(f249,plain,
( ~ sQ2_spl
| sk_c8 = multiply(inverse(sk_c3),sk_c7) ),
inference(paramodulation,[status(thm)],[f78,f208]) ).
fof(f256,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f35,f208]) ).
fof(f258,plain,
( ~ sQ5_spl
| sk_c8 = multiply(inverse(sk_c4),sk_c5) ),
inference(paramodulation,[status(thm)],[f90,f208]) ).
fof(f259,plain,
( ~ sQ7_spl
| sk_c7 = multiply(inverse(sk_c1),sk_c8) ),
inference(paramodulation,[status(thm)],[f98,f208]) ).
fof(f262,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| sk_c8 = multiply(sk_c8,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f82,f249]) ).
fof(f263,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c8 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f74,f262]) ).
fof(f264,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sk_c8 = multiply(sk_c8,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f94,f258]) ).
fof(f265,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sk_c8 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f86,f264]) ).
fof(f266,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f265,f195]) ).
fof(f267,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sQ21_spl ),
inference(contradiction_clause,[status(thm)],[f266]) ).
fof(f279,plain,
( sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(sk_c7,sk_c6) != sk_c6 ),
inference(backward_demodulation,[status(thm)],[f263,f72]) ).
fof(f282,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(sk_c3,sk_c6) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f263,f78]) ).
fof(f284,plain,
( ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| inverse(sk_c4) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f263,f94]) ).
fof(f285,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| inverse(sk_c3) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f263,f82]) ).
fof(f286,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(sk_c6,sk_c5) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f263,f86]) ).
fof(f290,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c6 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f263,f265]) ).
fof(f300,plain,
! [X0] : X0 = multiply(inverse(inverse(identity)),X0),
inference(paramodulation,[status(thm)],[f256,f208]) ).
fof(f302,plain,
( sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| multiply(sk_c6,sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f290,f279]) ).
fof(f309,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| multiply(sk_c3,sk_c6) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f290,f282]) ).
fof(f310,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sk_c6 = multiply(inverse(sk_c3),sk_c6) ),
inference(paramodulation,[status(thm)],[f309,f208]) ).
fof(f312,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sk_c6 = multiply(sk_c6,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f285,f310]) ).
fof(f313,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f312,f302]) ).
fof(f314,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f313]) ).
fof(f315,plain,
( sQ18_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c5 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f290,f203]) ).
fof(f328,plain,
( ~ sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c6 = multiply(inverse(sk_c7),sk_c6) ),
inference(forward_demodulation,[status(thm)],[f263,f248]) ).
fof(f329,plain,
( ~ sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sk_c6 = multiply(inverse(sk_c6),sk_c6) ),
inference(forward_demodulation,[status(thm)],[f290,f328]) ).
fof(f330,plain,
( ~ sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f36,f329]) ).
fof(f340,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c6,sk_c5) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f290,f286]) ).
fof(f341,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c5 = multiply(inverse(sk_c6),sk_c6) ),
inference(paramodulation,[status(thm)],[f340,f208]) ).
fof(f343,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c5 = identity ),
inference(forward_demodulation,[status(thm)],[f36,f341]) ).
fof(f350,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| multiply(inverse(X0),X0) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f330,f36]) ).
fof(f351,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| multiply(sk_c6,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f330,f35]) ).
fof(f352,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ0_spl
| sk_c5 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f330,f343]) ).
fof(f353,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ0_spl
| sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f352,f315]) ).
fof(f354,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ0_spl
| sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f353]) ).
fof(f355,plain,
( sQ23_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(sk_c3,sk_c6) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f290,f224]) ).
fof(f356,plain,
( sQ23_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c6 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f309,f355]) ).
fof(f357,plain,
( sQ23_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f263,f356]) ).
fof(f358,plain,
( sQ23_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f357]) ).
fof(f359,plain,
( sQ23_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f358]) ).
fof(f365,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(X0,sk_c6) != sk_c7
| inverse(X0) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f290,f137]) ).
fof(f366,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| multiply(X0,sk_c6) != sk_c6
| inverse(X0) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f290,f365]) ).
fof(f376,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ0_spl
| inverse(sk_c3) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f352,f285]) ).
fof(f377,plain,
( ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ0_spl
| inverse(sk_c4) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f352,f284]) ).
fof(f385,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| multiply(sk_c5,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f352,f351]) ).
fof(f388,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ0_spl
| X0 = multiply(sk_c5,multiply(sk_c3,X0)) ),
inference(paramodulation,[status(thm)],[f376,f208]) ).
fof(f389,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ0_spl
| X0 = multiply(sk_c3,X0) ),
inference(forward_demodulation,[status(thm)],[f385,f388]) ).
fof(f391,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| multiply(inverse(X0),X0) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f352,f350]) ).
fof(f392,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ0_spl
| multiply(sk_c5,sk_c3) = sk_c5 ),
inference(paramodulation,[status(thm)],[f376,f391]) ).
fof(f395,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ0_spl
| sk_c3 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f385,f392]) ).
fof(f397,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ0_spl
| inverse(sk_c5) = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f395,f376]) ).
fof(f398,plain,
( ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ0_spl
| multiply(sk_c5,sk_c4) = sk_c5 ),
inference(paramodulation,[status(thm)],[f377,f391]) ).
fof(f400,plain,
( ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ0_spl
| sk_c4 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f385,f398]) ).
fof(f403,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ0_spl
| sk_c3 = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f400,f395]) ).
fof(f410,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ0_spl
| sk_c4 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f400,f352]) ).
fof(f411,plain,
! [X0] :
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ0_spl
| X0 = multiply(sk_c4,X0) ),
inference(forward_demodulation,[status(thm)],[f403,f389]) ).
fof(f414,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ0_spl
| inverse(sk_c4) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f400,f397]) ).
fof(f415,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ0_spl
| inverse(sk_c4) = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f400,f414]) ).
fof(f418,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ0_spl
| multiply(X0,sk_c6) != sk_c6
| inverse(X0) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f410,f366]) ).
fof(f419,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ0_spl
| multiply(X0,sk_c4) != sk_c6
| inverse(X0) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f410,f418]) ).
fof(f420,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ0_spl
| multiply(X0,sk_c4) != sk_c4
| inverse(X0) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f410,f419]) ).
fof(f421,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ12_spl
| multiply(sk_c4,sk_c4) != sk_c4 ),
inference(resolution,[status(thm)],[f420,f415]) ).
fof(f423,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ12_spl
| sk_c4 != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f411,f421]) ).
fof(f424,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f423]) ).
fof(f425,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ0_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f424]) ).
fof(f440,plain,
( ~ sQ10_spl
| sk_c6 = multiply(inverse(sk_c2),sk_c7) ),
inference(paramodulation,[status(thm)],[f125,f208]) ).
fof(f442,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| sk_c6 = multiply(sk_c7,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f116,f440]) ).
fof(f466,plain,
inverse(identity) = identity,
inference(paramodulation,[status(thm)],[f36,f300]) ).
fof(f503,definition,
( sQ30_spl
<=> inverse(inverse(sk_c8)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f505,plain,
( sQ30_spl
| inverse(inverse(sk_c8)) != sk_c8 ),
inference(component_clause,[status(thm)],[f503]) ).
fof(f528,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| sk_c7 = multiply(sk_c7,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f107,f259]) ).
fof(f534,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c6 ),
inference(backward_demodulation,[status(thm)],[f549,f140]) ).
fof(f535,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c6 = multiply(sk_c7,sk_c6) ),
inference(backward_demodulation,[status(thm)],[f549,f442]) ).
fof(f538,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| multiply(sk_c6,sk_c1) = identity ),
inference(backward_demodulation,[status(thm)],[f549,f205]) ).
fof(f548,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| multiply(sk_c1,sk_c6) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f549,f98]) ).
fof(f549,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c7 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f71,f528]) ).
fof(f550,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c6 = multiply(sk_c6,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f549,f535]) ).
fof(f558,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c6 = multiply(inverse(sk_c6),sk_c6) ),
inference(paramodulation,[status(thm)],[f550,f208]) ).
fof(f560,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f36,f558]) ).
fof(f562,plain,
( ~ sQ13_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| inverse(inverse(sk_c8)) != sk_c8
| identity != sk_c6 ),
inference(paramodulation,[status(thm)],[f36,f534]) ).
fof(f568,definition,
( sQ32_spl
<=> identity = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f570,plain,
( sQ32_spl
| identity != sk_c6 ),
inference(component_clause,[status(thm)],[f568]) ).
fof(f571,plain,
( ~ sQ13_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ30_spl
| ~ sQ32_spl ),
inference(split_clause,[status(thm)],[f562,f568,f503,f70,f106,f97,f139]) ).
fof(f573,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| inverse(X0) != sk_c8
| multiply(sk_c8,multiply(X0,sk_c8)) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f549,f146]) ).
fof(f580,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| inverse(identity) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f560,f466]) ).
fof(f583,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| multiply(sk_c6,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f560,f35]) ).
fof(f584,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| inverse(sk_c6) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f560,f580]) ).
fof(f585,plain,
( sQ32_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f560,f570]) ).
fof(f586,plain,
( sQ32_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f585]) ).
fof(f587,plain,
( sQ32_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f586]) ).
fof(f594,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| sk_c1 = identity ),
inference(forward_demodulation,[status(thm)],[f583,f538]) ).
fof(f596,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| multiply(sk_c1,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f605,f583]) ).
fof(f597,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| inverse(sk_c6) = sk_c1 ),
inference(backward_demodulation,[status(thm)],[f605,f584]) ).
fof(f604,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| sk_c7 = sk_c1 ),
inference(backward_demodulation,[status(thm)],[f605,f549]) ).
fof(f605,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| sk_c1 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f560,f594]) ).
fof(f607,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| inverse(sk_c1) = sk_c1 ),
inference(forward_demodulation,[status(thm)],[f605,f597]) ).
fof(f626,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| sk_c6 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f596,f548]) ).
fof(f627,plain,
( sQ30_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| inverse(inverse(sk_c8)) != sk_c1 ),
inference(backward_demodulation,[status(thm)],[f629,f505]) ).
fof(f629,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| sk_c1 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f605,f626]) ).
fof(f630,plain,
( sQ30_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| inverse(inverse(sk_c1)) != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f629,f627]) ).
fof(f631,plain,
( sQ30_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| inverse(sk_c1) != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f607,f630]) ).
fof(f632,plain,
( sQ30_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| sk_c1 != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f607,f631]) ).
fof(f633,plain,
( sQ30_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f632]) ).
fof(f634,plain,
( sQ30_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f633]) ).
fof(f638,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| inverse(X0) != sk_c8
| multiply(sk_c1,multiply(X0,sk_c8)) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f629,f573]) ).
fof(f639,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f596,f638]) ).
fof(f640,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c1) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f629,f639]) ).
fof(f641,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c1) != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f605,f640]) ).
fof(f642,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| inverse(X0) != sk_c1
| multiply(X0,sk_c1) != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f629,f641]) ).
fof(f643,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ14_spl
| inverse(sk_c1) != sk_c1 ),
inference(resolution,[status(thm)],[f642,f596]) ).
fof(f646,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ14_spl
| sk_c1 != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f607,f643]) ).
fof(f647,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ14_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f646]) ).
fof(f648,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f647]) ).
fof(f649,plain,
( sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| multiply(sk_c1,sk_c7) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f629,f75]) ).
fof(f650,plain,
( sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| sk_c7 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f596,f649]) ).
fof(f651,plain,
( sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| sk_c1 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f604,f650]) ).
fof(f652,plain,
( sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| sk_c1 != sk_c1 ),
inference(forward_demodulation,[status(thm)],[f605,f651]) ).
fof(f653,plain,
( sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f652]) ).
fof(f654,plain,
( sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f653]) ).
fof(f655,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,f177,f189,f202,f219,f225,f237,f267,f314,f354,f359,f425,f571,f587,f634,f648,f654]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP332-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n002.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 20:12:17 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.13/0.41 % Refutation found
% 0.13/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.46 % Elapsed time: 0.082279 seconds
% 0.13/0.46 % CPU time: 0.264175 seconds
% 0.13/0.46 % Total memory used: 97.995 MB
% 0.13/0.46 % Net memory used: 97.782 MB
%------------------------------------------------------------------------------