%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP337-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 12:33:27 PM UTC 2026
% Result : Unsatisfiable 0.08s 0.39s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 69
% Syntax : Number of formulae : 301 ( 13 unt; 33 def)
% Number of atoms : 915 ( 337 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 1120 ( 506 ~; 581 |; 0 &)
% ( 33 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 35 ( 33 usr; 34 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 51 ( 51 !; 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_c7,sk_c6) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( inverse(sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c2,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c2,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c2,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c2,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( inverse(sk_c8) = sk_c6
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c2) = sk_c3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
( inverse(sk_c4) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( inverse(sk_c8) = sk_c6
| multiply(sk_c3,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
! [X3,X4,X5,X1,X2] :
( inverse(X2) != sk_c6
| multiply(X2,sk_c6) != sk_c7
| inverse(sk_c8) != sk_c6
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| multiply(sk_c7,sk_c6) != sk_c8
| multiply(X5,sk_c8) != sk_c7
| inverse(X4) != X5
| multiply(X4,X5) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| inverse(X3) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f42,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f43,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f44,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f45,plain,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f46,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f47,plain,
( inverse(sk_c8) = sk_c6
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f50,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f51,plain,
( multiply(sk_c4,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f52,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f53,plain,
( inverse(sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f54,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f55,plain,
( inverse(sk_c5) = sk_c6
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f56,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f57,plain,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f58,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f59,plain,
( inverse(sk_c8) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f60,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f61,plain,
( inverse(sk_c5) = sk_c6
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f62,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f63,plain,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c2,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f64,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c2,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f65,plain,
( inverse(sk_c8) = sk_c6
| multiply(sk_c2,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f66,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| multiply(sk_c2,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f67,plain,
( inverse(sk_c5) = sk_c6
| multiply(sk_c2,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f68,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f69,plain,
( multiply(sk_c4,sk_c8) = sk_c7
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f70,plain,
( inverse(sk_c4) = sk_c8
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f71,plain,
( inverse(sk_c8) = sk_c6
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f72,plain,
( multiply(sk_c5,sk_c6) = sk_c7
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f73,plain,
( inverse(sk_c5) = sk_c6
| inverse(sk_c2) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f74,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f75,plain,
( multiply(sk_c4,sk_c8) = sk_c7
| multiply(sk_c3,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f76,plain,
( inverse(sk_c4) = sk_c8
| multiply(sk_c3,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f77,plain,
( inverse(sk_c8) = sk_c6
| multiply(sk_c3,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f80,plain,
! [X2] :
( inverse(X2) != sk_c6
| multiply(X2,sk_c6) != sk_c7
| inverse(sk_c8) != sk_c6
| ! [X1] :
( inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c7
| multiply(sk_c7,sk_c6) != sk_c8
| ! [X5] :
( multiply(X5,sk_c8) != sk_c7
| ! [X4] :
( inverse(X4) != X5
| multiply(X4,X5) != sk_c7
| ! [X3] :
( multiply(X3,sk_c7) != sk_c8
| inverse(X3) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ) ) ) ) ),
inference(miniscoping,[status(thm)],[f40]) ).
fof(f81,plain,
! [X0,X1,X2,X3,X4] :
( inverse(X4) != sk_c6
| multiply(X4,sk_c6) != sk_c7
| inverse(sk_c8) != sk_c6
| inverse(X3) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| multiply(sk_c7,sk_c6) != sk_c8
| multiply(X2,sk_c8) != sk_c7
| inverse(X1) != X2
| multiply(X1,X2) != sk_c7
| multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c8
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f82,definition,
( sQ0_spl
<=> multiply(sk_c7,sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f83,plain,
( ~ sQ0_spl
| multiply(sk_c7,sk_c8) = sk_c6 ),
inference(component_clause,[status(thm)],[f82]) ).
fof(f84,plain,
( sQ0_spl
| multiply(sk_c7,sk_c8) != sk_c6 ),
inference(component_clause,[status(thm)],[f82]) ).
fof(f85,definition,
( sQ1_spl
<=> multiply(sk_c7,sk_c6) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ1_spl
| multiply(sk_c7,sk_c6) = sk_c8 ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f87,plain,
( sQ1_spl
| multiply(sk_c7,sk_c6) != sk_c8 ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f88,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f44,f82,f85]) ).
fof(f89,definition,
( sQ2_spl
<=> multiply(sk_c4,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f90,plain,
( ~ sQ2_spl
| multiply(sk_c4,sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f89]) ).
fof(f92,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f45,f82,f89]) ).
fof(f93,definition,
( sQ3_spl
<=> inverse(sk_c4) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ3_spl
| inverse(sk_c4) = sk_c8 ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f96,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f46,f82,f93]) ).
fof(f97,definition,
( sQ4_spl
<=> inverse(sk_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f98,plain,
( ~ sQ4_spl
| inverse(sk_c8) = sk_c6 ),
inference(component_clause,[status(thm)],[f97]) ).
fof(f99,plain,
( sQ4_spl
| inverse(sk_c8) != sk_c6 ),
inference(component_clause,[status(thm)],[f97]) ).
fof(f100,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f47,f82,f97]) ).
fof(f101,definition,
( sQ5_spl
<=> multiply(sk_c5,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f102,plain,
( ~ sQ5_spl
| multiply(sk_c5,sk_c6) = sk_c7 ),
inference(component_clause,[status(thm)],[f101]) ).
fof(f105,definition,
( sQ6_spl
<=> inverse(sk_c5) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f106,plain,
( ~ sQ6_spl
| inverse(sk_c5) = sk_c6 ),
inference(component_clause,[status(thm)],[f105]) ).
fof(f109,definition,
( sQ7_spl
<=> inverse(sk_c1) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f110,plain,
( ~ sQ7_spl
| inverse(sk_c1) = sk_c8 ),
inference(component_clause,[status(thm)],[f109]) ).
fof(f112,plain,
( sQ1_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f50,f109,f85]) ).
fof(f113,plain,
( sQ2_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f51,f109,f89]) ).
fof(f114,plain,
( sQ3_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f52,f109,f93]) ).
fof(f115,plain,
( sQ4_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f53,f109,f97]) ).
fof(f116,plain,
( sQ5_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f54,f109,f101]) ).
fof(f117,plain,
( sQ6_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f55,f109,f105]) ).
fof(f118,definition,
( sQ8_spl
<=> multiply(sk_c1,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f119,plain,
( ~ sQ8_spl
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f118]) ).
fof(f121,plain,
( sQ1_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f56,f118,f85]) ).
fof(f122,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f57,f118,f89]) ).
fof(f123,plain,
( sQ3_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f58,f118,f93]) ).
fof(f124,plain,
( sQ4_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f59,f118,f97]) ).
fof(f125,plain,
( sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f60,f118,f101]) ).
fof(f126,plain,
( sQ6_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f61,f118,f105]) ).
fof(f127,definition,
( sQ9_spl
<=> multiply(sk_c2,sk_c3) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f128,plain,
( ~ sQ9_spl
| multiply(sk_c2,sk_c3) = sk_c7 ),
inference(component_clause,[status(thm)],[f127]) ).
fof(f130,plain,
( sQ1_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f62,f127,f85]) ).
fof(f131,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f63,f127,f89]) ).
fof(f132,plain,
( sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f64,f127,f93]) ).
fof(f133,plain,
( sQ4_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f65,f127,f97]) ).
fof(f134,plain,
( sQ5_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f66,f127,f101]) ).
fof(f135,plain,
( sQ6_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f67,f127,f105]) ).
fof(f136,definition,
( sQ10_spl
<=> inverse(sk_c2) = sk_c3 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f137,plain,
( ~ sQ10_spl
| inverse(sk_c2) = sk_c3 ),
inference(component_clause,[status(thm)],[f136]) ).
fof(f139,plain,
( sQ1_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f68,f136,f85]) ).
fof(f140,plain,
( sQ2_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f69,f136,f89]) ).
fof(f141,plain,
( sQ3_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f70,f136,f93]) ).
fof(f142,plain,
( sQ4_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f71,f136,f97]) ).
fof(f143,plain,
( sQ5_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f72,f136,f101]) ).
fof(f144,plain,
( sQ6_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f73,f136,f105]) ).
fof(f145,definition,
( sQ11_spl
<=> multiply(sk_c3,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f146,plain,
( ~ sQ11_spl
| multiply(sk_c3,sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f145]) ).
fof(f148,plain,
( sQ1_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f74,f145,f85]) ).
fof(f149,plain,
( sQ2_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f75,f145,f89]) ).
fof(f150,plain,
( sQ3_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f76,f145,f93]) ).
fof(f151,plain,
( sQ4_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f77,f145,f97]) ).
fof(f154,definition,
! [X0] :
( sQ12_spl
<=> ( multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f155,plain,
! [X0] :
( ~ sQ12_spl
| multiply(X0,sk_c7) != sk_c8
| inverse(X0) != sk_c8 ),
inference(component_clause,[status(thm)],[f154]) ).
fof(f157,definition,
! [X1,X2] :
( sQ13_spl
<=> ( multiply(X2,sk_c8) != sk_c7
| inverse(X1) != X2
| multiply(X1,X2) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f158,plain,
! [X0,X1] :
( ~ sQ13_spl
| multiply(X1,sk_c8) != sk_c7
| inverse(X0) != X1
| multiply(X0,X1) != sk_c7 ),
inference(component_clause,[status(thm)],[f157]) ).
fof(f160,definition,
! [X3] :
( sQ14_spl
<=> ( inverse(X3) != sk_c8
| multiply(X3,sk_c8) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f161,plain,
! [X0] :
( ~ sQ14_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f160]) ).
fof(f163,definition,
! [X4] :
( sQ15_spl
<=> ( inverse(X4) != sk_c6
| multiply(X4,sk_c6) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f164,plain,
! [X0] :
( ~ sQ15_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c7 ),
inference(component_clause,[status(thm)],[f163]) ).
fof(f166,plain,
( sQ15_spl
| ~ sQ4_spl
| sQ14_spl
| ~ sQ1_spl
| sQ13_spl
| sQ12_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f81,f82,f154,f157,f85,f160,f97,f163]) ).
fof(f167,plain,
( ~ sQ5_spl
| ~ sQ15_spl
| inverse(sk_c5) != sk_c6 ),
inference(resolution,[status(thm)],[f164,f102]) ).
fof(f169,plain,
( ~ sQ5_spl
| ~ sQ15_spl
| ~ sQ6_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f106,f167]) ).
fof(f170,plain,
( ~ sQ5_spl
| ~ sQ15_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f169]) ).
fof(f171,plain,
( ~ sQ5_spl
| ~ sQ15_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f170]) ).
fof(f172,plain,
! [X0] :
( ~ sQ13_spl
| multiply(inverse(X0),sk_c8) != sk_c7
| multiply(X0,inverse(X0)) != sk_c7 ),
inference(destructive_equality_resolution,[status(thm)],[f158]) ).
fof(f173,plain,
( ~ sQ2_spl
| ~ sQ14_spl
| inverse(sk_c4) != sk_c8 ),
inference(resolution,[status(thm)],[f161,f90]) ).
fof(f177,plain,
( ~ sQ11_spl
| ~ sQ14_spl
| inverse(sk_c3) != sk_c8
| sk_c7 != sk_c7 ),
inference(paramodulation,[status(thm)],[f146,f161]) ).
fof(f178,plain,
( ~ sQ2_spl
| ~ sQ14_spl
| ~ sQ3_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f94,f173]) ).
fof(f179,plain,
( ~ sQ2_spl
| ~ sQ14_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f178]) ).
fof(f180,plain,
( ~ sQ2_spl
| ~ sQ14_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f179]) ).
fof(f187,plain,
! [X0] :
( ~ sQ11_spl
| multiply(sk_c7,X0) = multiply(sk_c3,multiply(sk_c8,X0)) ),
inference(paramodulation,[status(thm)],[f146,f43]) ).
fof(f190,plain,
( ~ sQ7_spl
| ~ sQ13_spl
| multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c1,inverse(sk_c1)) != sk_c7 ),
inference(paramodulation,[status(thm)],[f110,f172]) ).
fof(f191,plain,
( ~ sQ10_spl
| ~ sQ13_spl
| multiply(sk_c3,sk_c8) != sk_c7
| multiply(sk_c2,inverse(sk_c2)) != sk_c7 ),
inference(paramodulation,[status(thm)],[f137,f172]) ).
fof(f192,definition,
( sQ16_spl
<=> multiply(sk_c1,inverse(sk_c1)) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f195,definition,
( sQ17_spl
<=> multiply(sk_c8,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f197,plain,
( sQ17_spl
| multiply(sk_c8,sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f195]) ).
fof(f198,plain,
( ~ sQ7_spl
| ~ sQ13_spl
| ~ sQ17_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f190,f192,f195,f157,f109]) ).
fof(f199,definition,
( sQ18_spl
<=> multiply(sk_c2,inverse(sk_c2)) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f201,plain,
( sQ18_spl
| multiply(sk_c2,inverse(sk_c2)) != sk_c7 ),
inference(component_clause,[status(thm)],[f199]) ).
fof(f202,plain,
( ~ sQ10_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f191,f199,f145,f157,f136]) ).
fof(f203,plain,
( sQ18_spl
| ~ sQ10_spl
| multiply(sk_c2,sk_c3) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f137,f201]) ).
fof(f204,plain,
( sQ18_spl
| ~ sQ10_spl
| ~ sQ9_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f128,f203]) ).
fof(f205,plain,
( sQ18_spl
| ~ sQ10_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f204]) ).
fof(f206,plain,
( sQ18_spl
| ~ sQ10_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f205]) ).
fof(f210,plain,
( ~ sQ7_spl
| multiply(sk_c8,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f110,f42]) ).
fof(f212,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f42,f43]) ).
fof(f213,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f41,f212]) ).
fof(f224,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f41,f213]) ).
fof(f230,plain,
( ~ sQ8_spl
| sk_c7 = multiply(inverse(sk_c1),sk_c8) ),
inference(paramodulation,[status(thm)],[f119,f213]) ).
fof(f231,plain,
( ~ sQ9_spl
| sk_c3 = multiply(inverse(sk_c2),sk_c7) ),
inference(paramodulation,[status(thm)],[f128,f213]) ).
fof(f235,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| sk_c7 = multiply(sk_c8,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f110,f230]) ).
fof(f236,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f235,f197]) ).
fof(f237,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f236]) ).
fof(f238,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| sk_c3 = multiply(sk_c3,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f137,f231]) ).
fof(f246,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| sk_c7 = multiply(inverse(sk_c3),sk_c3) ),
inference(paramodulation,[status(thm)],[f238,f213]) ).
fof(f248,plain,
( ~ sQ9_spl
| ~ sQ10_spl
| sk_c7 = identity ),
inference(forward_demodulation,[status(thm)],[f42,f246]) ).
fof(f252,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ10_spl
| multiply(inverse(X0),X0) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f248,f42]) ).
fof(f253,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c7,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f248,f41]) ).
fof(f254,plain,
( ~ sQ7_spl
| ~ sQ12_spl
| multiply(sk_c1,sk_c7) != sk_c8 ),
inference(resolution,[status(thm)],[f155,f110]) ).
fof(f257,plain,
( ~ sQ7_spl
| ~ sQ12_spl
| ~ sQ8_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f119,f254]) ).
fof(f258,plain,
( ~ sQ7_spl
| ~ sQ12_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f257]) ).
fof(f259,plain,
( ~ sQ7_spl
| ~ sQ12_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f258]) ).
fof(f267,definition,
( sQ21_spl
<=> sk_c7 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f269,plain,
( sQ21_spl
| sk_c7 != sk_c7 ),
inference(component_clause,[status(thm)],[f267]) ).
fof(f271,definition,
( sQ22_spl
<=> inverse(sk_c3) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f273,plain,
( sQ22_spl
| inverse(sk_c3) != sk_c8 ),
inference(component_clause,[status(thm)],[f271]) ).
fof(f274,plain,
( ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ22_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f177,f267,f271,f160,f145]) ).
fof(f275,plain,
( sQ21_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f269]) ).
fof(f276,plain,
sQ21_spl,
inference(contradiction_clause,[status(thm)],[f275]) ).
fof(f281,plain,
! [X0,X1] :
( ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c7,X0) = multiply(inverse(X1),multiply(X1,X0)) ),
inference(paramodulation,[status(thm)],[f252,f43]) ).
fof(f282,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c7,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f213,f281]) ).
fof(f283,plain,
( ~ sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c6 = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f253,f86]) ).
fof(f284,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c8 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f253,f83]) ).
fof(f291,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| inverse(sk_c6) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f283,f98]) ).
fof(f300,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ15_spl
| sk_c6 != sk_c6
| multiply(sk_c6,sk_c6) != sk_c7 ),
inference(paramodulation,[status(thm)],[f291,f164]) ).
fof(f305,definition,
( sQ24_spl
<=> sk_c6 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f307,plain,
( sQ24_spl
| sk_c6 != sk_c6 ),
inference(component_clause,[status(thm)],[f305]) ).
fof(f309,definition,
( sQ25_spl
<=> multiply(sk_c6,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f311,plain,
( sQ25_spl
| multiply(sk_c6,sk_c6) != sk_c7 ),
inference(component_clause,[status(thm)],[f309]) ).
fof(f312,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ15_spl
| ~ sQ24_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f300,f309,f305,f163,f136,f127,f85,f97]) ).
fof(f320,plain,
( sQ24_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f307]) ).
fof(f321,plain,
sQ24_spl,
inference(contradiction_clause,[status(thm)],[f320]) ).
fof(f326,plain,
( ~ sQ2_spl
| sk_c8 = multiply(inverse(sk_c4),sk_c7) ),
inference(paramodulation,[status(thm)],[f90,f213]) ).
fof(f328,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| sk_c8 = multiply(sk_c8,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f94,f326]) ).
fof(f347,plain,
( ~ sQ4_spl
| multiply(sk_c6,sk_c8) = identity ),
inference(paramodulation,[status(thm)],[f98,f42]) ).
fof(f354,plain,
( ~ sQ13_spl
| sk_c8 != sk_c7
| multiply(identity,inverse(identity)) != sk_c7 ),
inference(paramodulation,[status(thm)],[f224,f172]) ).
fof(f355,plain,
( ~ sQ13_spl
| identity != sk_c7
| multiply(sk_c8,inverse(sk_c8)) != sk_c7 ),
inference(paramodulation,[status(thm)],[f42,f172]) ).
fof(f358,plain,
( ~ sQ3_spl
| ~ sQ13_spl
| multiply(sk_c8,sk_c8) != sk_c7
| multiply(sk_c4,inverse(sk_c4)) != sk_c7 ),
inference(paramodulation,[status(thm)],[f94,f172]) ).
fof(f359,plain,
( ~ sQ6_spl
| ~ sQ13_spl
| multiply(sk_c6,sk_c8) != sk_c7
| multiply(sk_c5,inverse(sk_c5)) != sk_c7 ),
inference(paramodulation,[status(thm)],[f106,f172]) ).
fof(f360,definition,
( sQ28_spl
<=> multiply(identity,inverse(identity)) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f363,definition,
( sQ29_spl
<=> sk_c8 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f366,plain,
( ~ sQ13_spl
| ~ sQ29_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f354,f360,f363,f157]) ).
fof(f367,definition,
( sQ30_spl
<=> multiply(sk_c8,inverse(sk_c8)) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f370,definition,
( sQ31_spl
<=> identity = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f372,plain,
( sQ31_spl
| identity != sk_c7 ),
inference(component_clause,[status(thm)],[f370]) ).
fof(f373,plain,
( ~ sQ13_spl
| ~ sQ31_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f355,f367,f370,f157]) ).
fof(f375,definition,
( sQ32_spl
<=> multiply(sk_c6,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f376,plain,
( ~ sQ32_spl
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f375]) ).
fof(f377,plain,
( sQ32_spl
| multiply(sk_c6,sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f375]) ).
fof(f379,definition,
( sQ33_spl
<=> multiply(sk_c4,inverse(sk_c4)) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f381,plain,
( sQ33_spl
| multiply(sk_c4,inverse(sk_c4)) != sk_c7 ),
inference(component_clause,[status(thm)],[f379]) ).
fof(f382,plain,
( ~ sQ3_spl
| ~ sQ13_spl
| ~ sQ17_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f358,f379,f195,f157,f93]) ).
fof(f383,definition,
( sQ34_spl
<=> multiply(sk_c5,inverse(sk_c5)) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f385,plain,
( sQ34_spl
| multiply(sk_c5,inverse(sk_c5)) != sk_c7 ),
inference(component_clause,[status(thm)],[f383]) ).
fof(f386,plain,
( ~ sQ6_spl
| ~ sQ13_spl
| ~ sQ32_spl
| ~ sQ34_spl ),
inference(split_clause,[status(thm)],[f359,f383,f375,f157,f105]) ).
fof(f389,plain,
( sQ33_spl
| ~ sQ3_spl
| multiply(sk_c4,sk_c8) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f94,f381]) ).
fof(f390,plain,
( sQ33_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f90,f389]) ).
fof(f391,plain,
( sQ33_spl
| ~ sQ3_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f390]) ).
fof(f392,plain,
( sQ33_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f391]) ).
fof(f393,plain,
( sQ34_spl
| ~ sQ6_spl
| multiply(sk_c5,sk_c6) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f106,f385]) ).
fof(f394,plain,
( sQ34_spl
| ~ sQ6_spl
| ~ sQ5_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f102,f393]) ).
fof(f395,plain,
( sQ34_spl
| ~ sQ6_spl
| ~ sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f394]) ).
fof(f396,plain,
( sQ34_spl
| ~ sQ6_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f395]) ).
fof(f399,definition,
( sQ35_spl
<=> sk_c8 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f401,plain,
( sQ35_spl
| sk_c8 != sk_c8 ),
inference(component_clause,[status(thm)],[f399]) ).
fof(f413,definition,
( sQ37_spl
<=> sk_c8 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f414,plain,
( ~ sQ37_spl
| sk_c8 = sk_c6 ),
inference(component_clause,[status(thm)],[f413]) ).
fof(f415,plain,
( sQ37_spl
| sk_c8 != sk_c6 ),
inference(component_clause,[status(thm)],[f413]) ).
fof(f525,plain,
( sQ35_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f401]) ).
fof(f526,plain,
sQ35_spl,
inference(contradiction_clause,[status(thm)],[f525]) ).
fof(f547,plain,
( sQ32_spl
| ~ sQ4_spl
| identity != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f347,f377]) ).
fof(f555,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ12_spl
| sk_c8 != sk_c8
| inverse(sk_c8) != sk_c8 ),
inference(paramodulation,[status(thm)],[f328,f155]) ).
fof(f556,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| sk_c7 = multiply(inverse(sk_c8),sk_c8) ),
inference(paramodulation,[status(thm)],[f328,f213]) ).
fof(f559,definition,
( sQ39_spl
<=> inverse(sk_c8) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f561,plain,
( sQ39_spl
| inverse(sk_c8) != sk_c8 ),
inference(component_clause,[status(thm)],[f559]) ).
fof(f562,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ12_spl
| ~ sQ35_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f555,f559,f399,f154,f93,f89]) ).
fof(f563,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c7 = multiply(sk_c6,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f98,f556]) ).
fof(f564,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c7 = identity ),
inference(forward_demodulation,[status(thm)],[f347,f563]) ).
fof(f565,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f564,f372]) ).
fof(f566,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sQ31_spl ),
inference(contradiction_clause,[status(thm)],[f565]) ).
fof(f567,plain,
( sQ39_spl
| ~ sQ4_spl
| sk_c6 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f98,f561]) ).
fof(f568,plain,
( sQ32_spl
| ~ sQ4_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f547,f370,f97,f375]) ).
fof(f569,plain,
( ~ sQ32_spl
| ~ sQ4_spl
| identity = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f347,f376]) ).
fof(f573,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c7,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f564,f41]) ).
fof(f576,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c6 = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f573,f86]) ).
fof(f581,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sQ37_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f576,f415]) ).
fof(f582,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sQ37_spl ),
inference(contradiction_clause,[status(thm)],[f581]) ).
fof(f584,plain,
( sQ39_spl
| ~ sQ4_spl
| ~ sQ37_spl ),
inference(split_clause,[status(thm)],[f567,f413,f97,f559]) ).
fof(f598,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| inverse(sk_c1) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f284,f110]) ).
fof(f600,plain,
( sQ22_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| inverse(sk_c3) != sk_c6 ),
inference(backward_demodulation,[status(thm)],[f284,f273]) ).
fof(f606,plain,
( sQ4_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| inverse(sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f284,f99]) ).
fof(f613,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c1,sk_c7) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f284,f119]) ).
fof(f614,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c7 = multiply(inverse(sk_c1),sk_c6) ),
inference(paramodulation,[status(thm)],[f613,f213]) ).
fof(f616,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ7_spl
| sk_c7 = multiply(sk_c6,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f598,f614]) ).
fof(f617,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ7_spl
| sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f616,f311]) ).
fof(f618,plain,
( ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ7_spl
| sQ25_spl ),
inference(contradiction_clause,[status(thm)],[f617]) ).
fof(f626,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c6,sk_c1) = identity ),
inference(forward_demodulation,[status(thm)],[f284,f210]) ).
fof(f627,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| multiply(sk_c6,sk_c1) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f248,f626]) ).
fof(f633,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c7 = multiply(sk_c6,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f284,f235]) ).
fof(f634,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c7 = multiply(sk_c6,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f284,f633]) ).
fof(f658,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ10_spl
| X0 = multiply(sk_c3,multiply(sk_c8,X0)) ),
inference(forward_demodulation,[status(thm)],[f282,f187]) ).
fof(f659,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ0_spl
| X0 = multiply(sk_c3,multiply(sk_c6,X0)) ),
inference(forward_demodulation,[status(thm)],[f284,f658]) ).
fof(f660,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| sk_c6 = multiply(sk_c3,sk_c7) ),
inference(paramodulation,[status(thm)],[f634,f659]) ).
fof(f661,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| sk_c1 = multiply(sk_c3,sk_c7) ),
inference(paramodulation,[status(thm)],[f627,f659]) ).
fof(f664,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| sk_c6 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f238,f660]) ).
fof(f667,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| sk_c1 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f238,f661]) ).
fof(f671,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| inverse(sk_c3) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f667,f598]) ).
fof(f674,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f671,f600]) ).
fof(f675,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f674]) ).
fof(f688,plain,
( sQ4_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ11_spl
| inverse(sk_c6) != sk_c3 ),
inference(backward_demodulation,[status(thm)],[f664,f606]) ).
fof(f691,plain,
( ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ11_spl
| sk_c8 = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f664,f284]) ).
fof(f697,plain,
( sQ4_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ11_spl
| inverse(sk_c3) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f664,f688]) ).
fof(f702,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ8_spl
| inverse(sk_c3) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f664,f671]) ).
fof(f710,plain,
( sQ4_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ11_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f702,f697]) ).
fof(f711,plain,
( sQ4_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f710]) ).
fof(f712,plain,
( sQ4_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f711]) ).
fof(f747,plain,
( sQ31_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f248,f372]) ).
fof(f748,plain,
( sQ31_spl
| ~ sQ9_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f747]) ).
fof(f749,plain,
( sQ31_spl
| ~ sQ9_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f748]) ).
fof(f750,plain,
( sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| sk_c6 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f282,f87]) ).
fof(f751,plain,
( sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ11_spl
| sk_c3 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f664,f750]) ).
fof(f752,plain,
( sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ11_spl
| sk_c3 != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f691,f751]) ).
fof(f753,plain,
( sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f752]) ).
fof(f754,plain,
( sQ1_spl
| ~ sQ9_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f753]) ).
fof(f760,plain,
! [X0] :
( ~ sQ32_spl
| ~ sQ4_spl
| multiply(sk_c7,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f569,f41]) ).
fof(f777,plain,
( sQ0_spl
| ~ sQ32_spl
| ~ sQ4_spl
| sk_c8 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f760,f84]) ).
fof(f778,plain,
( sQ0_spl
| ~ sQ32_spl
| ~ sQ4_spl
| ~ sQ37_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f414,f777]) ).
fof(f779,plain,
( sQ0_spl
| ~ sQ32_spl
| ~ sQ4_spl
| ~ sQ37_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f778]) ).
fof(f780,plain,
( sQ0_spl
| ~ sQ32_spl
| ~ sQ4_spl
| ~ sQ37_spl ),
inference(contradiction_clause,[status(thm)],[f779]) ).
fof(f781,plain,
$false,
inference(sat_refutation,[status(thm)],[f88,f92,f96,f100,f112,f113,f114,f115,f116,f117,f121,f122,f123,f124,f125,f126,f130,f131,f132,f133,f134,f135,f139,f140,f141,f142,f143,f144,f148,f149,f150,f151,f166,f171,f180,f198,f202,f206,f237,f259,f274,f276,f312,f321,f366,f373,f382,f386,f392,f396,f526,f562,f566,f568,f582,f584,f618,f675,f712,f749,f754,f780]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP337-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n026.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 20:12:07 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.08/0.39 % Refutation found
% 0.08/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.42 % Elapsed time: 0.053883 seconds
% 0.12/0.42 % CPU time: 0.144789 seconds
% 0.12/0.42 % Total memory used: 34.429 MB
% 0.12/0.42 % Net memory used: 34.350 MB
%------------------------------------------------------------------------------