%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP321-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 12:33:24 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.40s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 62
% Syntax : Number of formulae : 277 ( 14 unt; 28 def)
% Number of atoms : 939 ( 323 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1243 ( 581 ~; 634 |; 0 &)
% ( 28 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 30 ( 28 usr; 29 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 58 ( 58 !; 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_c4,sk_c8) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c5) = sk_c7
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c5) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( multiply(sk_c5,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( inverse(sk_c5) = sk_c7
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( multiply(sk_c6,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
! [X3,X4,X5,X1,X2] :
( multiply(sk_c6,sk_c7) != sk_c8
| inverse(X2) != sk_c7
| multiply(X2,sk_c7) != sk_c6
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| inverse(X5) != sk_c8
| multiply(X5,sk_c8) != X4
| multiply(sk_c8,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_c4,sk_c8) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f39,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f40,plain,
( multiply(sk_c5,sk_c7) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f41,plain,
( inverse(sk_c5) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f42,plain,
( multiply(sk_c6,sk_c7) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f43,plain,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f44,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f45,plain,
( multiply(sk_c5,sk_c7) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f46,plain,
( inverse(sk_c5) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f47,plain,
( multiply(sk_c6,sk_c7) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f48,plain,
( multiply(sk_c4,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f49,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f50,plain,
( multiply(sk_c5,sk_c7) = sk_c6
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f51,plain,
( inverse(sk_c5) = sk_c7
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f52,plain,
( multiply(sk_c6,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f53,plain,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f54,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f55,plain,
( multiply(sk_c5,sk_c7) = sk_c6
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f56,plain,
( inverse(sk_c5) = sk_c7
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f57,plain,
( multiply(sk_c6,sk_c7) = sk_c8
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f58,plain,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f59,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f60,plain,
( multiply(sk_c5,sk_c7) = sk_c6
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f61,plain,
( inverse(sk_c5) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f62,plain,
( multiply(sk_c6,sk_c7) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f63,plain,
( multiply(sk_c4,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f64,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f65,plain,
( multiply(sk_c5,sk_c7) = sk_c6
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f66,plain,
( inverse(sk_c5) = sk_c7
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f67,plain,
( multiply(sk_c6,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f68,plain,
( multiply(sk_c6,sk_c7) != sk_c8
| ! [X2] :
( inverse(X2) != sk_c7
| multiply(X2,sk_c7) != sk_c6
| ! [X1] :
( inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| ! [X5] :
( inverse(X5) != sk_c8
| ! [X4] :
( multiply(X5,sk_c8) != X4
| multiply(sk_c8,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] :
( multiply(sk_c6,sk_c7) != sk_c8
| inverse(X4) != sk_c7
| multiply(X4,sk_c7) != sk_c6
| inverse(X3) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != X1
| multiply(sk_c8,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_c4,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f74,plain,
( ~ sQ1_spl
| multiply(sk_c4,sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f76,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f38,f70,f73]) ).
fof(f77,definition,
( sQ2_spl
<=> inverse(sk_c4) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f78,plain,
( ~ sQ2_spl
| inverse(sk_c4) = sk_c8 ),
inference(component_clause,[status(thm)],[f77]) ).
fof(f80,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f39,f70,f77]) ).
fof(f81,definition,
( sQ3_spl
<=> multiply(sk_c5,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f82,plain,
( ~ sQ3_spl
| multiply(sk_c5,sk_c7) = sk_c6 ),
inference(component_clause,[status(thm)],[f81]) ).
fof(f84,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f40,f70,f81]) ).
fof(f85,definition,
( sQ4_spl
<=> inverse(sk_c5) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ4_spl
| inverse(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_c6,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f90,plain,
( ~ sQ5_spl
| multiply(sk_c6,sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f89]) ).
fof(f91,plain,
( sQ5_spl
| multiply(sk_c6,sk_c7) != sk_c8 ),
inference(component_clause,[status(thm)],[f89]) ).
fof(f92,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f42,f70,f89]) ).
fof(f93,definition,
( sQ6_spl
<=> multiply(sk_c1,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ6_spl
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f96,plain,
( sQ1_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f43,f93,f73]) ).
fof(f97,plain,
( sQ2_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f44,f93,f77]) ).
fof(f98,plain,
( sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f45,f93,f81]) ).
fof(f99,plain,
( sQ4_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f46,f93,f85]) ).
fof(f100,plain,
( sQ5_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f47,f93,f89]) ).
fof(f101,definition,
( sQ7_spl
<=> inverse(sk_c1) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f102,plain,
( ~ sQ7_spl
| inverse(sk_c1) = sk_c7 ),
inference(component_clause,[status(thm)],[f101]) ).
fof(f104,plain,
( sQ1_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f48,f101,f73]) ).
fof(f105,plain,
( sQ2_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f49,f101,f77]) ).
fof(f106,plain,
( sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f50,f101,f81]) ).
fof(f107,plain,
( sQ4_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f51,f101,f85]) ).
fof(f108,plain,
( sQ5_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f52,f101,f89]) ).
fof(f109,definition,
( sQ8_spl
<=> multiply(sk_c8,sk_c3) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f110,plain,
( ~ sQ8_spl
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(component_clause,[status(thm)],[f109]) ).
fof(f112,plain,
( sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f53,f109,f73]) ).
fof(f113,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f54,f109,f77]) ).
fof(f114,plain,
( sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f55,f109,f81]) ).
fof(f115,plain,
( sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f56,f109,f85]) ).
fof(f116,plain,
( sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f57,f109,f89]) ).
fof(f117,definition,
( sQ9_spl
<=> multiply(sk_c2,sk_c8) = sk_c3 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f118,plain,
( ~ sQ9_spl
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(component_clause,[status(thm)],[f117]) ).
fof(f120,plain,
( sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f58,f117,f73]) ).
fof(f121,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f59,f117,f77]) ).
fof(f122,plain,
( sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f60,f117,f81]) ).
fof(f123,plain,
( sQ4_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f61,f117,f85]) ).
fof(f124,plain,
( sQ5_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f62,f117,f89]) ).
fof(f125,definition,
( sQ10_spl
<=> inverse(sk_c2) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f126,plain,
( ~ sQ10_spl
| inverse(sk_c2) = sk_c8 ),
inference(component_clause,[status(thm)],[f125]) ).
fof(f128,plain,
( sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f63,f125,f73]) ).
fof(f129,plain,
( sQ2_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f64,f125,f77]) ).
fof(f130,plain,
( sQ3_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f65,f125,f81]) ).
fof(f131,plain,
( sQ4_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f66,f125,f85]) ).
fof(f132,plain,
( sQ5_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f67,f125,f89]) ).
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,X2] :
( sQ12_spl
<=> ( inverse(X2) != sk_c8
| multiply(X2,sk_c8) != X1
| multiply(sk_c8,X1) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f137,plain,
! [X0,X1] :
( ~ sQ12_spl
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != X0
| multiply(sk_c8,X0) != sk_c7 ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f139,definition,
! [X3] :
( sQ13_spl
<=> ( inverse(X3) != sk_c8
| multiply(X3,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,
! [X4] :
( sQ14_spl
<=> ( inverse(X4) != sk_c7
| multiply(X4,sk_c7) != sk_c6 ) ),
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_c6 ),
inference(component_clause,[status(thm)],[f142]) ).
fof(f145,plain,
( ~ sQ5_spl
| sQ14_spl
| sQ13_spl
| sQ12_spl
| sQ11_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f69,f70,f133,f136,f139,f142,f89]) ).
fof(f146,plain,
( ~ sQ3_spl
| ~ sQ14_spl
| inverse(sk_c5) != sk_c7 ),
inference(resolution,[status(thm)],[f143,f82]) ).
fof(f148,plain,
( ~ sQ6_spl
| ~ sQ14_spl
| inverse(sk_c1) != sk_c7
| sk_c8 != sk_c6 ),
inference(paramodulation,[status(thm)],[f94,f143]) ).
fof(f150,plain,
( ~ sQ3_spl
| ~ sQ14_spl
| ~ sQ4_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f86,f146]) ).
fof(f151,plain,
( ~ sQ3_spl
| ~ sQ14_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f150]) ).
fof(f152,plain,
( ~ sQ3_spl
| ~ sQ14_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f151]) ).
fof(f153,plain,
( ~ sQ1_spl
| ~ sQ13_spl
| inverse(sk_c4) != sk_c8 ),
inference(resolution,[status(thm)],[f140,f74]) ).
fof(f154,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| inverse(sk_c7) != sk_c8
| sk_c6 != sk_c7 ),
inference(paramodulation,[status(thm)],[f71,f140]) ).
fof(f157,plain,
( ~ sQ1_spl
| ~ sQ13_spl
| ~ sQ2_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f78,f153]) ).
fof(f158,plain,
( ~ sQ1_spl
| ~ sQ13_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f157]) ).
fof(f159,plain,
( ~ sQ1_spl
| ~ sQ13_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f158]) ).
fof(f160,plain,
! [X0] :
( ~ sQ12_spl
| inverse(X0) != sk_c8
| multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ),
inference(destructive_equality_resolution,[status(thm)],[f137]) ).
fof(f161,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| inverse(sk_c6) != sk_c7 ),
inference(resolution,[status(thm)],[f134,f90]) ).
fof(f162,plain,
( ~ sQ6_spl
| ~ sQ11_spl
| inverse(sk_c1) != sk_c7 ),
inference(resolution,[status(thm)],[f134,f94]) ).
fof(f165,plain,
( ~ sQ6_spl
| ~ sQ11_spl
| ~ sQ7_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f102,f162]) ).
fof(f166,plain,
( ~ sQ6_spl
| ~ sQ11_spl
| ~ sQ7_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f165]) ).
fof(f167,plain,
( ~ sQ6_spl
| ~ sQ11_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f166]) ).
fof(f169,plain,
! [X0] :
( ~ sQ0_spl
| multiply(sk_c6,X0) = multiply(sk_c7,multiply(sk_c8,X0)) ),
inference(paramodulation,[status(thm)],[f71,f37]) ).
fof(f178,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| inverse(sk_c7) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7 ),
inference(paramodulation,[status(thm)],[f71,f160]) ).
fof(f179,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| inverse(sk_c2) != sk_c8
| multiply(sk_c8,sk_c3) != sk_c7 ),
inference(paramodulation,[status(thm)],[f118,f160]) ).
fof(f180,plain,
( ~ sQ1_spl
| ~ sQ12_spl
| inverse(sk_c4) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c7 ),
inference(paramodulation,[status(thm)],[f74,f160]) ).
fof(f181,definition,
( sQ15_spl
<=> multiply(sk_c8,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f184,definition,
( sQ16_spl
<=> inverse(sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f187,plain,
( ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f178,f181,f184,f136,f70]) ).
fof(f188,plain,
( ~ sQ9_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f179,f109,f125,f136,f117]) ).
fof(f189,definition,
( sQ17_spl
<=> multiply(sk_c8,sk_c7) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f191,plain,
( sQ17_spl
| multiply(sk_c8,sk_c7) != sk_c7 ),
inference(component_clause,[status(thm)],[f189]) ).
fof(f192,plain,
( ~ sQ1_spl
| ~ sQ12_spl
| ~ sQ2_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f180,f189,f77,f136,f73]) ).
fof(f193,definition,
( sQ18_spl
<=> sk_c6 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f194,plain,
( ~ sQ18_spl
| sk_c6 = sk_c7 ),
inference(component_clause,[status(thm)],[f193]) ).
fof(f195,plain,
( sQ18_spl
| sk_c6 != sk_c7 ),
inference(component_clause,[status(thm)],[f193]) ).
fof(f196,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ16_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f154,f193,f184,f139,f70]) ).
fof(f201,definition,
( sQ20_spl
<=> sk_c7 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f203,plain,
( sQ20_spl
| sk_c7 != sk_c7 ),
inference(component_clause,[status(thm)],[f201]) ).
fof(f205,plain,
( sQ20_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f203]) ).
fof(f206,plain,
sQ20_spl,
inference(contradiction_clause,[status(thm)],[f205]) ).
fof(f211,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f36,f37]) ).
fof(f212,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f35,f211]) ).
fof(f224,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f35,f212]) ).
fof(f229,plain,
( ~ sQ6_spl
| sk_c7 = multiply(inverse(sk_c1),sk_c8) ),
inference(paramodulation,[status(thm)],[f94,f212]) ).
fof(f232,plain,
( ~ sQ9_spl
| sk_c8 = multiply(inverse(sk_c2),sk_c3) ),
inference(paramodulation,[status(thm)],[f118,f212]) ).
fof(f235,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| sk_c7 = multiply(sk_c7,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f102,f229]) ).
fof(f236,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c7 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f71,f235]) ).
fof(f237,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f236,f195]) ).
fof(f238,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f237]) ).
fof(f239,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| sk_c8 = multiply(sk_c8,sk_c3) ),
inference(forward_demodulation,[status(thm)],[f126,f232]) ).
fof(f240,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c8 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f110,f239]) ).
fof(f244,plain,
( sQ5_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| multiply(sk_c6,sk_c8) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f240,f91]) ).
fof(f249,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| multiply(sk_c8,sk_c8) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f240,f71]) ).
fof(f251,plain,
( ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| multiply(sk_c1,sk_c8) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f240,f94]) ).
fof(f254,plain,
( ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| inverse(sk_c1) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f240,f102]) ).
fof(f262,plain,
( ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c8 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f240,f236]) ).
fof(f263,plain,
( sQ5_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| multiply(sk_c6,sk_c6) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f262,f244]) ).
fof(f264,plain,
( sQ5_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| multiply(sk_c6,sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f262,f263]) ).
fof(f265,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(sk_c6,sk_c8) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f262,f249]) ).
fof(f266,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| multiply(sk_c6,sk_c6) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f262,f265]) ).
fof(f267,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f266,f264]) ).
fof(f268,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f267]) ).
fof(f273,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c6) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f262,f140]) ).
fof(f274,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ18_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f194,f273]) ).
fof(f275,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ18_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f262,f274]) ).
fof(f280,plain,
( ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ0_spl
| inverse(sk_c1) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f262,f254]) ).
fof(f286,plain,
( ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| multiply(sk_c1,sk_c6) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f262,f251]) ).
fof(f287,plain,
( ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| multiply(sk_c1,sk_c6) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f262,f286]) ).
fof(f372,plain,
( ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ18_spl
| inverse(sk_c1) != sk_c6 ),
inference(resolution,[status(thm)],[f275,f287]) ).
fof(f382,plain,
( ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ18_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f280,f372]) ).
fof(f383,plain,
( ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ18_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f382]) ).
fof(f384,plain,
( ~ sQ6_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f383]) ).
fof(f386,definition,
( sQ21_spl
<=> sk_c6 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f388,plain,
( sQ21_spl
| sk_c6 != sk_c6 ),
inference(component_clause,[status(thm)],[f386]) ).
fof(f395,definition,
( sQ22_spl
<=> sk_c8 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f397,plain,
( sQ22_spl
| sk_c8 != sk_c6 ),
inference(component_clause,[status(thm)],[f395]) ).
fof(f402,plain,
( ~ sQ6_spl
| ~ sQ14_spl
| ~ sQ7_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f148,f395,f101,f142,f93]) ).
fof(f403,plain,
( sQ22_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f262,f397]) ).
fof(f404,plain,
( sQ22_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f403]) ).
fof(f405,plain,
( sQ22_spl
| ~ sQ6_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f404]) ).
fof(f406,plain,
( sQ21_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f388]) ).
fof(f407,plain,
sQ21_spl,
inference(contradiction_clause,[status(thm)],[f406]) ).
fof(f409,plain,
( ~ sQ2_spl
| multiply(sk_c8,sk_c4) = identity ),
inference(paramodulation,[status(thm)],[f78,f36]) ).
fof(f411,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f36,f37]) ).
fof(f412,plain,
! [X0] : multiply(identity,X0) = X0,
inference(forward_demodulation,[status(thm)],[f212,f411]) ).
fof(f415,plain,
( ~ sQ12_spl
| inverse(inverse(sk_c8)) != sk_c8
| multiply(sk_c8,identity) != sk_c7 ),
inference(paramodulation,[status(thm)],[f36,f160]) ).
fof(f417,definition,
( sQ24_spl
<=> multiply(sk_c8,identity) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f420,definition,
( sQ25_spl
<=> inverse(inverse(sk_c8)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f423,plain,
( ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f415,f417,f420,f136]) ).
fof(f424,plain,
( ~ sQ12_spl
| inverse(identity) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7 ),
inference(paramodulation,[status(thm)],[f412,f160]) ).
fof(f427,definition,
( sQ26_spl
<=> multiply(sk_c8,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f430,definition,
( sQ27_spl
<=> inverse(identity) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f433,plain,
( ~ sQ12_spl
| ~ sQ27_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f424,f427,f430,f136]) ).
fof(f438,plain,
( ~ sQ12_spl
| inverse(inverse(identity)) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7 ),
inference(paramodulation,[status(thm)],[f224,f160]) ).
fof(f441,definition,
( sQ28_spl
<=> inverse(inverse(identity)) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f444,plain,
( ~ sQ12_spl
| ~ sQ28_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f438,f427,f441,f136]) ).
fof(f455,plain,
( ~ sQ1_spl
| sk_c8 = multiply(inverse(sk_c4),sk_c7) ),
inference(paramodulation,[status(thm)],[f74,f212]) ).
fof(f458,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 = multiply(sk_c8,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f78,f455]) ).
fof(f459,plain,
( ~ sQ3_spl
| sk_c7 = multiply(inverse(sk_c5),sk_c6) ),
inference(paramodulation,[status(thm)],[f82,f212]) ).
fof(f461,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c7 = multiply(sk_c7,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f86,f459]) ).
fof(f472,plain,
( sQ17_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f458,f191]) ).
fof(f473,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| multiply(sk_c6,sk_c7) = multiply(sk_c7,sk_c8) ),
inference(paramodulation,[status(thm)],[f458,f169]) ).
fof(f474,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c7 = multiply(inverse(sk_c8),sk_c8) ),
inference(paramodulation,[status(thm)],[f458,f212]) ).
fof(f476,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ5_spl
| sk_c8 = multiply(sk_c7,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f90,f473]) ).
fof(f477,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ5_spl
| sk_c8 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f71,f476]) ).
fof(f478,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c7 = identity ),
inference(forward_demodulation,[status(thm)],[f36,f474]) ).
fof(f479,plain,
( sQ17_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ5_spl
| sk_c6 != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f477,f472]) ).
fof(f485,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl
| ~ sQ5_spl
| multiply(sk_c6,sk_c4) = identity ),
inference(backward_demodulation,[status(thm)],[f477,f409]) ).
fof(f495,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl
| ~ sQ5_spl
| inverse(sk_c4) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f477,f78]) ).
fof(f503,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c7,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f478,f412]) ).
fof(f504,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(inverse(X0),X0) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f478,f36]) ).
fof(f513,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c7 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f503,f461]) ).
fof(f514,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sQ17_spl
| ~ sQ0_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f513,f479]) ).
fof(f515,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sQ17_spl
| ~ sQ0_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f514]) ).
fof(f519,definition,
( sQ29_spl
<=> sk_c8 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f521,plain,
( sQ29_spl
| sk_c8 != sk_c8 ),
inference(component_clause,[status(thm)],[f519]) ).
fof(f524,plain,
( sQ29_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ5_spl
| sk_c6 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f477,f521]) ).
fof(f525,plain,
( sQ29_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ5_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f477,f524]) ).
fof(f526,plain,
( sQ29_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f525]) ).
fof(f527,plain,
( sQ29_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f526]) ).
fof(f528,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c6,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f513,f503]) ).
fof(f531,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c6 = identity ),
inference(backward_demodulation,[status(thm)],[f513,f478]) ).
fof(f533,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c5) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f513,f86]) ).
fof(f538,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| inverse(sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f513,f161]) ).
fof(f542,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| X0 = multiply(sk_c6,multiply(sk_c5,X0)) ),
inference(paramodulation,[status(thm)],[f533,f212]) ).
fof(f543,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| X0 = multiply(sk_c5,X0) ),
inference(forward_demodulation,[status(thm)],[f528,f542]) ).
fof(f548,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c4 = identity ),
inference(forward_demodulation,[status(thm)],[f528,f485]) ).
fof(f552,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| inverse(sk_c6) != sk_c4 ),
inference(backward_demodulation,[status(thm)],[f558,f538]) ).
fof(f556,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| inverse(sk_c4) = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f558,f495]) ).
fof(f558,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c4 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f531,f548]) ).
fof(f559,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ0_spl
| inverse(sk_c4) != sk_c4 ),
inference(forward_demodulation,[status(thm)],[f558,f552]) ).
fof(f566,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c7,X0) = multiply(inverse(X1),multiply(X1,X0)) ),
inference(paramodulation,[status(thm)],[f504,f37]) ).
fof(f567,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c7,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f212,f566]) ).
fof(f574,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f556,f559]) ).
fof(f575,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f574]) ).
fof(f577,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c6,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f513,f567]) ).
fof(f583,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(inverse(X0),X0) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f513,f504]) ).
fof(f584,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c6,sk_c5) = sk_c6 ),
inference(paramodulation,[status(thm)],[f533,f583]) ).
fof(f587,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c5 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f577,f584]) ).
fof(f589,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c7 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f577,f90]) ).
fof(f591,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c6 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f513,f589]) ).
fof(f592,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c5 = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f587,f591]) ).
fof(f597,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c7 = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f587,f513]) ).
fof(f634,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| multiply(sk_c5,sk_c8) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f597,f72]) ).
fof(f635,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f543,f634]) ).
fof(f636,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| sk_c5 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f592,f635]) ).
fof(f637,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f587,f636]) ).
fof(f638,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f637]) ).
fof(f639,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f638]) ).
fof(f640,plain,
$false,
inference(sat_refutation,[status(thm)],[f76,f80,f84,f88,f92,f96,f97,f98,f99,f100,f104,f105,f106,f107,f108,f112,f113,f114,f115,f116,f120,f121,f122,f123,f124,f128,f129,f130,f131,f132,f145,f152,f159,f167,f187,f188,f192,f196,f206,f238,f268,f384,f402,f405,f407,f423,f433,f444,f515,f527,f575,f639]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP321-1 : 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 : n008.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 20:09:54 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.40 % Refutation found
% 0.09/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.43 % Elapsed time: 0.063880 seconds
% 0.09/0.43 % CPU time: 0.211865 seconds
% 0.09/0.43 % Total memory used: 104.364 MB
% 0.09/0.43 % Net memory used: 104.119 MB
%------------------------------------------------------------------------------