%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP280-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 12:33:18 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.40s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 66
% Syntax : Number of formulae : 337 ( 13 unt; 26 def)
% Number of atoms : 1311 ( 407 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 1857 ( 883 ~; 948 |; 0 &)
% ( 26 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 28 ( 26 usr; 27 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 72 ( 72 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c9,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c9
| multiply(sk_c9,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c9,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c9,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c9,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c9,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( inverse(sk_c4) = sk_c5
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c1) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( inverse(sk_c4) = sk_c5
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( inverse(sk_c6) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( multiply(sk_c4,sk_c5) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
( inverse(sk_c4) = sk_c5
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
( inverse(sk_c6) = sk_c9
| inverse(sk_c2) = sk_c9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
! [X4,X5,X6,X2,X1,X3] :
( inverse(X3) != sk_c9
| multiply(X3,sk_c9) != sk_c7
| multiply(X1,sk_c8) != sk_c9
| inverse(X2) != X1
| multiply(X2,X1) != sk_c9
| multiply(sk_c9,sk_c7) != sk_c8
| inverse(X6) != sk_c9
| multiply(X6,sk_c9) != X5
| multiply(sk_c9,X5) != sk_c8
| inverse(X4) != sk_c9
| multiply(X4,sk_c9) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c7 ),
file('/export/starexec/sandbox/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_c9,sk_c7) = sk_c8
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f45,plain,
( multiply(sk_c4,sk_c5) = sk_c9
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f46,plain,
( inverse(sk_c4) = sk_c5
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f47,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f48,plain,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f49,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f50,plain,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f51,plain,
( multiply(sk_c4,sk_c5) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f52,plain,
( inverse(sk_c4) = sk_c5
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f53,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f54,plain,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f55,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c1,sk_c9) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f56,plain,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f57,plain,
( multiply(sk_c4,sk_c5) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f58,plain,
( inverse(sk_c4) = sk_c5
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f59,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f60,plain,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f61,plain,
( inverse(sk_c6) = sk_c9
| inverse(sk_c1) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f62,plain,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f63,plain,
( multiply(sk_c4,sk_c5) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f64,plain,
( inverse(sk_c4) = sk_c5
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f65,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f66,plain,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f67,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c9,sk_c3) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f68,plain,
( multiply(sk_c9,sk_c7) = sk_c8
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f69,plain,
( multiply(sk_c4,sk_c5) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f70,plain,
( inverse(sk_c4) = sk_c5
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f71,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f72,plain,
( multiply(sk_c6,sk_c9) = sk_c7
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f73,plain,
( inverse(sk_c6) = sk_c9
| multiply(sk_c2,sk_c9) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f74,plain,
( multiply(sk_c9,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f75,plain,
( multiply(sk_c4,sk_c5) = sk_c9
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f76,plain,
( inverse(sk_c4) = sk_c5
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f77,plain,
( multiply(sk_c5,sk_c8) = sk_c9
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f78,plain,
( multiply(sk_c6,sk_c9) = sk_c7
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f79,plain,
( inverse(sk_c6) = sk_c9
| inverse(sk_c2) = sk_c9 ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f80,plain,
! [X3] :
( inverse(X3) != sk_c9
| multiply(X3,sk_c9) != sk_c7
| ! [X1] :
( multiply(X1,sk_c8) != sk_c9
| ! [X2] :
( inverse(X2) != X1
| multiply(X2,X1) != sk_c9
| multiply(sk_c9,sk_c7) != sk_c8
| ! [X6] :
( inverse(X6) != sk_c9
| ! [X5] :
( multiply(X6,sk_c9) != X5
| multiply(sk_c9,X5) != sk_c8
| ! [X4] :
( inverse(X4) != sk_c9
| multiply(X4,sk_c9) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c7 ) ) ) ) ) ),
inference(miniscoping,[status(thm)],[f40]) ).
fof(f81,plain,
! [X0,X1,X2,X3,X4,X5] :
( inverse(X5) != sk_c9
| multiply(X5,sk_c9) != sk_c7
| multiply(X4,sk_c8) != sk_c9
| inverse(X3) != X4
| multiply(X3,X4) != sk_c9
| multiply(sk_c9,sk_c7) != sk_c8
| inverse(X2) != sk_c9
| multiply(X2,sk_c9) != X1
| multiply(sk_c9,X1) != sk_c8
| inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c8
| multiply(sk_c9,sk_c8) != sk_c7 ),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f82,definition,
( sQ0_spl
<=> multiply(sk_c9,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f83,plain,
( ~ sQ0_spl
| multiply(sk_c9,sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f82]) ).
fof(f84,plain,
( sQ0_spl
| multiply(sk_c9,sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f82]) ).
fof(f85,definition,
( sQ1_spl
<=> multiply(sk_c9,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ1_spl
| multiply(sk_c9,sk_c7) = sk_c8 ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f87,plain,
( sQ1_spl
| multiply(sk_c9,sk_c7) != 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_c5) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f90,plain,
( ~ sQ2_spl
| multiply(sk_c4,sk_c5) = sk_c9 ),
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_c5 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ3_spl
| inverse(sk_c4) = sk_c5 ),
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
<=> multiply(sk_c5,sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f98,plain,
( ~ sQ4_spl
| multiply(sk_c5,sk_c8) = sk_c9 ),
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_c6,sk_c9) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f102,plain,
( ~ sQ5_spl
| multiply(sk_c6,sk_c9) = sk_c7 ),
inference(component_clause,[status(thm)],[f101]) ).
fof(f104,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f48,f82,f101]) ).
fof(f105,definition,
( sQ6_spl
<=> inverse(sk_c6) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f106,plain,
( ~ sQ6_spl
| inverse(sk_c6) = sk_c9 ),
inference(component_clause,[status(thm)],[f105]) ).
fof(f108,plain,
( sQ6_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f49,f82,f105]) ).
fof(f109,definition,
( sQ7_spl
<=> multiply(sk_c1,sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f110,plain,
( ~ sQ7_spl
| multiply(sk_c1,sk_c9) = 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
<=> inverse(sk_c1) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f119,plain,
( ~ sQ8_spl
| inverse(sk_c1) = sk_c9 ),
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_c9,sk_c3) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f128,plain,
( ~ sQ9_spl
| multiply(sk_c9,sk_c3) = sk_c8 ),
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
<=> multiply(sk_c2,sk_c9) = sk_c3 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f137,plain,
( ~ sQ10_spl
| multiply(sk_c2,sk_c9) = 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
<=> inverse(sk_c2) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f146,plain,
( ~ sQ11_spl
| inverse(sk_c2) = sk_c9 ),
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(f152,plain,
( sQ5_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f78,f145,f101]) ).
fof(f153,plain,
( sQ6_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f79,f145,f105]) ).
fof(f154,definition,
! [X0] :
( sQ12_spl
<=> ( inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f155,plain,
! [X0] :
( ~ sQ12_spl
| inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c8 ),
inference(component_clause,[status(thm)],[f154]) ).
fof(f157,definition,
! [X1,X2] :
( sQ13_spl
<=> ( inverse(X2) != sk_c9
| multiply(X2,sk_c9) != X1
| multiply(sk_c9,X1) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f158,plain,
! [X0,X1] :
( ~ sQ13_spl
| inverse(X1) != sk_c9
| multiply(X1,sk_c9) != X0
| multiply(sk_c9,X0) != sk_c8 ),
inference(component_clause,[status(thm)],[f157]) ).
fof(f160,definition,
! [X3,X4] :
( sQ14_spl
<=> ( multiply(X4,sk_c8) != sk_c9
| inverse(X3) != X4
| multiply(X3,X4) != sk_c9 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f161,plain,
! [X0,X1] :
( ~ sQ14_spl
| multiply(X1,sk_c8) != sk_c9
| inverse(X0) != X1
| multiply(X0,X1) != sk_c9 ),
inference(component_clause,[status(thm)],[f160]) ).
fof(f163,definition,
! [X5] :
( sQ15_spl
<=> ( inverse(X5) != sk_c9
| multiply(X5,sk_c9) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f164,plain,
! [X0] :
( ~ sQ15_spl
| inverse(X0) != sk_c9
| multiply(X0,sk_c9) != sk_c7 ),
inference(component_clause,[status(thm)],[f163]) ).
fof(f166,plain,
( sQ15_spl
| sQ14_spl
| ~ sQ1_spl
| sQ13_spl
| sQ12_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f81,f82,f154,f157,f85,f160,f163]) ).
fof(f167,plain,
( ~ sQ5_spl
| ~ sQ15_spl
| inverse(sk_c6) != sk_c9 ),
inference(resolution,[status(thm)],[f164,f102]) ).
fof(f169,plain,
( ~ sQ7_spl
| ~ sQ15_spl
| inverse(sk_c1) != sk_c9
| sk_c8 != sk_c7 ),
inference(paramodulation,[status(thm)],[f110,f164]) ).
fof(f171,plain,
( ~ sQ5_spl
| ~ sQ15_spl
| ~ sQ6_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f106,f167]) ).
fof(f172,plain,
( ~ sQ5_spl
| ~ sQ15_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f171]) ).
fof(f173,plain,
( ~ sQ5_spl
| ~ sQ15_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f172]) ).
fof(f174,plain,
! [X0] :
( ~ sQ14_spl
| multiply(inverse(X0),sk_c8) != sk_c9
| multiply(X0,inverse(X0)) != sk_c9 ),
inference(destructive_equality_resolution,[status(thm)],[f161]) ).
fof(f175,plain,
! [X0] :
( ~ sQ13_spl
| inverse(X0) != sk_c9
| multiply(sk_c9,multiply(X0,sk_c9)) != sk_c8 ),
inference(destructive_equality_resolution,[status(thm)],[f158]) ).
fof(f186,plain,
( ~ sQ3_spl
| ~ sQ14_spl
| multiply(sk_c5,sk_c8) != sk_c9
| multiply(sk_c4,inverse(sk_c4)) != sk_c9 ),
inference(paramodulation,[status(thm)],[f94,f174]) ).
fof(f187,plain,
( ~ sQ8_spl
| ~ sQ14_spl
| multiply(sk_c9,sk_c8) != sk_c9
| multiply(sk_c1,inverse(sk_c1)) != sk_c9 ),
inference(paramodulation,[status(thm)],[f119,f174]) ).
fof(f189,definition,
( sQ16_spl
<=> multiply(sk_c4,inverse(sk_c4)) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f191,plain,
( sQ16_spl
| multiply(sk_c4,inverse(sk_c4)) != sk_c9 ),
inference(component_clause,[status(thm)],[f189]) ).
fof(f192,plain,
( ~ sQ3_spl
| ~ sQ14_spl
| ~ sQ4_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f186,f189,f97,f160,f93]) ).
fof(f193,definition,
( sQ17_spl
<=> multiply(sk_c1,inverse(sk_c1)) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f194,plain,
( ~ sQ17_spl
| multiply(sk_c1,inverse(sk_c1)) = sk_c9 ),
inference(component_clause,[status(thm)],[f193]) ).
fof(f195,plain,
( sQ17_spl
| multiply(sk_c1,inverse(sk_c1)) != sk_c9 ),
inference(component_clause,[status(thm)],[f193]) ).
fof(f196,definition,
( sQ18_spl
<=> multiply(sk_c9,sk_c8) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f198,plain,
( sQ18_spl
| multiply(sk_c9,sk_c8) != sk_c9 ),
inference(component_clause,[status(thm)],[f196]) ).
fof(f199,plain,
( ~ sQ8_spl
| ~ sQ14_spl
| ~ sQ18_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f187,f193,f196,f160,f118]) ).
fof(f204,plain,
( sQ18_spl
| ~ sQ0_spl
| sk_c7 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f83,f198]) ).
fof(f207,plain,
( sQ17_spl
| ~ sQ8_spl
| multiply(sk_c1,sk_c9) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f119,f195]) ).
fof(f208,plain,
( sQ17_spl
| ~ sQ8_spl
| ~ sQ7_spl
| sk_c8 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f110,f207]) ).
fof(f209,plain,
( sQ16_spl
| ~ sQ3_spl
| multiply(sk_c4,sk_c5) != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f94,f191]) ).
fof(f210,plain,
( sQ16_spl
| ~ sQ3_spl
| ~ sQ2_spl
| sk_c9 != sk_c9 ),
inference(forward_demodulation,[status(thm)],[f90,f209]) ).
fof(f211,plain,
( sQ16_spl
| ~ sQ3_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f210]) ).
fof(f212,plain,
( sQ16_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f211]) ).
fof(f214,plain,
( ~ sQ8_spl
| multiply(sk_c9,sk_c1) = identity ),
inference(paramodulation,[status(thm)],[f119,f42]) ).
fof(f215,plain,
( ~ sQ11_spl
| multiply(sk_c9,sk_c2) = identity ),
inference(paramodulation,[status(thm)],[f146,f42]) ).
fof(f216,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f42,f43]) ).
fof(f217,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f41,f216]) ).
fof(f226,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f41,f217]) ).
fof(f231,plain,
( ~ sQ7_spl
| sk_c9 = multiply(inverse(sk_c1),sk_c8) ),
inference(paramodulation,[status(thm)],[f110,f217]) ).
fof(f236,plain,
( ~ sQ10_spl
| sk_c9 = multiply(inverse(sk_c2),sk_c3) ),
inference(paramodulation,[status(thm)],[f137,f217]) ).
fof(f238,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| sk_c9 = multiply(sk_c9,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f119,f231]) ).
fof(f239,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c9 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f83,f238]) ).
fof(f240,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f239,f204]) ).
fof(f241,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f240]) ).
fof(f242,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| sk_c9 = multiply(sk_c9,sk_c3) ),
inference(forward_demodulation,[status(thm)],[f146,f236]) ).
fof(f243,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sk_c9 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f128,f242]) ).
fof(f244,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sQ17_spl
| ~ sQ8_spl
| ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f243,f208]) ).
fof(f245,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sQ17_spl
| ~ sQ8_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f244]) ).
fof(f248,plain,
( ~ sQ17_spl
| ~ sQ8_spl
| multiply(sk_c1,sk_c9) = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f119,f194]) ).
fof(f249,plain,
( ~ sQ17_spl
| ~ sQ8_spl
| ~ sQ7_spl
| sk_c8 = sk_c9 ),
inference(forward_demodulation,[status(thm)],[f110,f248]) ).
fof(f250,plain,
( ~ sQ11_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| multiply(sk_c7,sk_c2) = identity ),
inference(backward_demodulation,[status(thm)],[f239,f215]) ).
fof(f251,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| multiply(sk_c7,sk_c1) = identity ),
inference(backward_demodulation,[status(thm)],[f239,f214]) ).
fof(f254,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| multiply(sk_c7,sk_c8) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f239,f83]) ).
fof(f258,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| multiply(sk_c1,sk_c7) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f239,f110]) ).
fof(f261,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| inverse(sk_c1) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f239,f119]) ).
fof(f263,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c7 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f239,f243]) ).
fof(f264,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| inverse(X0) != sk_c9
| multiply(sk_c7,multiply(X0,sk_c9)) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f239,f175]) ).
fof(f265,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| inverse(X0) != sk_c9
| multiply(sk_c7,multiply(X0,sk_c7)) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f239,f264]) ).
fof(f266,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| inverse(X0) != sk_c9
| multiply(sk_c7,multiply(X0,sk_c7)) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f263,f265]) ).
fof(f267,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| inverse(X0) != sk_c7
| multiply(sk_c7,multiply(X0,sk_c7)) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f239,f266]) ).
fof(f268,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| inverse(X0) != sk_c9
| multiply(X0,sk_c7) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f239,f155]) ).
fof(f269,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| inverse(X0) != sk_c9
| multiply(X0,sk_c7) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f263,f268]) ).
fof(f270,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f239,f269]) ).
fof(f271,plain,
( ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| multiply(sk_c7,sk_c7) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f239,f86]) ).
fof(f272,plain,
( ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| multiply(sk_c7,sk_c7) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f263,f271]) ).
fof(f273,plain,
( ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sk_c7 = multiply(inverse(sk_c7),sk_c7) ),
inference(paramodulation,[status(thm)],[f272,f217]) ).
fof(f275,plain,
( ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sk_c7 = identity ),
inference(forward_demodulation,[status(thm)],[f42,f273]) ).
fof(f278,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| multiply(sk_c7,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f275,f41]) ).
fof(f281,plain,
( ~ sQ13_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| multiply(sk_c7,multiply(sk_c1,sk_c7)) != sk_c7 ),
inference(resolution,[status(thm)],[f261,f267]) ).
fof(f282,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sk_c7 != sk_c7
| multiply(sk_c1,sk_c7) != sk_c7 ),
inference(paramodulation,[status(thm)],[f261,f270]) ).
fof(f285,definition,
( sQ20_spl
<=> multiply(sk_c1,sk_c7) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f287,plain,
( sQ20_spl
| multiply(sk_c1,sk_c7) != sk_c7 ),
inference(component_clause,[status(thm)],[f285]) ).
fof(f288,definition,
( sQ21_spl
<=> sk_c7 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f290,plain,
( sQ21_spl
| sk_c7 != sk_c7 ),
inference(component_clause,[status(thm)],[f288]) ).
fof(f291,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ21_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f282,f285,f288,f127,f145,f136,f154,f82,f109,f118]) ).
fof(f296,plain,
( sQ21_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f290]) ).
fof(f297,plain,
sQ21_spl,
inference(contradiction_clause,[status(thm)],[f296]) ).
fof(f313,plain,
( ~ sQ11_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ10_spl
| ~ sQ9_spl
| sk_c2 = identity ),
inference(forward_demodulation,[status(thm)],[f278,f250]) ).
fof(f315,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| multiply(sk_c2,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f323,f278]) ).
fof(f319,plain,
( ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sk_c2 = identity ),
inference(backward_demodulation,[status(thm)],[f323,f275]) ).
fof(f323,plain,
( ~ sQ11_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ10_spl
| ~ sQ9_spl
| sk_c2 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f275,f313]) ).
fof(f340,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ10_spl
| ~ sQ9_spl
| multiply(sk_c2,sk_c1) = identity ),
inference(forward_demodulation,[status(thm)],[f323,f251]) ).
fof(f341,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ10_spl
| ~ sQ9_spl
| sk_c1 = identity ),
inference(forward_demodulation,[status(thm)],[f315,f340]) ).
fof(f344,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ11_spl
| ~ sQ1_spl
| ~ sQ10_spl
| ~ sQ9_spl
| sk_c1 = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f319,f341]) ).
fof(f384,plain,
( ~ sQ13_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ1_spl
| multiply(sk_c2,multiply(sk_c1,sk_c7)) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f323,f281]) ).
fof(f385,plain,
( ~ sQ13_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ1_spl
| multiply(sk_c1,sk_c7) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f315,f384]) ).
fof(f386,plain,
( ~ sQ13_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ1_spl
| multiply(sk_c2,sk_c7) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f344,f385]) ).
fof(f387,plain,
( ~ sQ13_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ1_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f315,f386]) ).
fof(f388,plain,
( ~ sQ13_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ1_spl
| sk_c2 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f323,f387]) ).
fof(f389,plain,
( ~ sQ13_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ1_spl
| sk_c2 != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f323,f388]) ).
fof(f390,plain,
( ~ sQ13_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f389]) ).
fof(f391,plain,
( ~ sQ13_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f390]) ).
fof(f397,plain,
! [X0] : multiply(identity,X0) = X0,
inference(paramodulation,[status(thm)],[f217,f226]) ).
fof(f399,plain,
( ~ sQ13_spl
| inverse(inverse(identity)) != sk_c9
| multiply(sk_c9,sk_c9) != sk_c8 ),
inference(paramodulation,[status(thm)],[f226,f175]) ).
fof(f402,definition,
( sQ24_spl
<=> multiply(sk_c9,sk_c9) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f404,plain,
( sQ24_spl
| multiply(sk_c9,sk_c9) != sk_c8 ),
inference(component_clause,[status(thm)],[f402]) ).
fof(f405,definition,
( sQ25_spl
<=> inverse(inverse(identity)) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f408,plain,
( ~ sQ13_spl
| ~ sQ25_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f399,f402,f405,f157]) ).
fof(f409,plain,
( ~ sQ13_spl
| inverse(identity) != sk_c9
| multiply(sk_c9,sk_c9) != sk_c8 ),
inference(paramodulation,[status(thm)],[f397,f175]) ).
fof(f412,definition,
( sQ26_spl
<=> inverse(identity) = sk_c9 ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f415,plain,
( ~ sQ13_spl
| ~ sQ26_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f409,f402,f412,f157]) ).
fof(f418,plain,
( ~ sQ2_spl
| sk_c5 = multiply(inverse(sk_c4),sk_c9) ),
inference(paramodulation,[status(thm)],[f90,f217]) ).
fof(f420,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| sk_c5 = multiply(sk_c5,sk_c9) ),
inference(forward_demodulation,[status(thm)],[f94,f418]) ).
fof(f423,plain,
( ~ sQ5_spl
| ~ sQ13_spl
| inverse(sk_c6) != sk_c9
| multiply(sk_c9,sk_c7) != sk_c8 ),
inference(paramodulation,[status(thm)],[f102,f175]) ).
fof(f424,plain,
( ~ sQ5_spl
| sk_c9 = multiply(inverse(sk_c6),sk_c7) ),
inference(paramodulation,[status(thm)],[f102,f217]) ).
fof(f426,plain,
( ~ sQ5_spl
| ~ sQ13_spl
| ~ sQ6_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f423,f85,f105,f157,f101]) ).
fof(f427,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sk_c9 = multiply(sk_c9,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f106,f424]) ).
fof(f428,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| sk_c9 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f86,f427]) ).
fof(f429,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f428,f102]) ).
fof(f430,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| multiply(sk_c5,sk_c8) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f428,f98]) ).
fof(f431,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| multiply(sk_c4,sk_c5) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f428,f90]) ).
fof(f435,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ1_spl
| inverse(sk_c6) = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f428,f106]) ).
fof(f439,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| inverse(X0) != sk_c9
| multiply(X0,sk_c8) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f428,f155]) ).
fof(f440,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f428,f439]) ).
fof(f455,definition,
( sQ30_spl
<=> sk_c8 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f457,plain,
( sQ30_spl
| sk_c8 != sk_c8 ),
inference(component_clause,[status(thm)],[f455]) ).
fof(f460,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ1_spl
| multiply(sk_c8,sk_c6) = identity ),
inference(paramodulation,[status(thm)],[f435,f42]) ).
fof(f466,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| sk_c5 = multiply(sk_c5,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f428,f420]) ).
fof(f467,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| sk_c8 = multiply(inverse(sk_c5),sk_c5) ),
inference(paramodulation,[status(thm)],[f466,f217]) ).
fof(f469,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| sk_c8 = identity ),
inference(forward_demodulation,[status(thm)],[f42,f467]) ).
fof(f471,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| multiply(sk_c8,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f469,f397]) ).
fof(f475,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| sk_c8 = multiply(inverse(sk_c6),sk_c7) ),
inference(paramodulation,[status(thm)],[f429,f217]) ).
fof(f477,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| sk_c8 = multiply(sk_c8,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f435,f475]) ).
fof(f478,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c8 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f471,f477]) ).
fof(f481,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| multiply(sk_c7,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f478,f471]) ).
fof(f482,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| sk_c7 = identity ),
inference(backward_demodulation,[status(thm)],[f478,f469]) ).
fof(f484,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| inverse(sk_c6) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f478,f435]) ).
fof(f486,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c8) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f478,f440]) ).
fof(f488,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c9 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f478,f428]) ).
fof(f489,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f478,f486]) ).
fof(f490,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f478,f489]) ).
fof(f494,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| multiply(sk_c5,sk_c7) = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f478,f430]) ).
fof(f495,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| multiply(sk_c5,sk_c7) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f478,f494]) ).
fof(f497,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| multiply(sk_c7,X0) = multiply(sk_c5,multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f495,f43]) ).
fof(f498,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| X0 = multiply(sk_c5,multiply(sk_c7,X0)) ),
inference(forward_demodulation,[status(thm)],[f481,f497]) ).
fof(f499,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| X0 = multiply(sk_c5,X0) ),
inference(forward_demodulation,[status(thm)],[f481,f498]) ).
fof(f500,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ3_spl
| multiply(sk_c4,sk_c5) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f478,f431]) ).
fof(f501,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ3_spl
| sk_c5 = multiply(inverse(sk_c4),sk_c7) ),
inference(paramodulation,[status(thm)],[f500,f217]) ).
fof(f503,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ3_spl
| sk_c5 = multiply(sk_c5,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f94,f501]) ).
fof(f504,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c5 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f495,f503]) ).
fof(f511,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c9 = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f504,f488]) ).
fof(f512,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ4_spl
| sk_c5 = identity ),
inference(backward_demodulation,[status(thm)],[f504,f482]) ).
fof(f513,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c8 = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f504,f478]) ).
fof(f520,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| inverse(sk_c6) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f504,f484]) ).
fof(f532,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c5,sk_c6) = identity ),
inference(forward_demodulation,[status(thm)],[f513,f460]) ).
fof(f533,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f499,f532]) ).
fof(f536,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| X0 = multiply(sk_c6,X0) ),
inference(backward_demodulation,[status(thm)],[f544,f499]) ).
fof(f538,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| inverse(sk_c6) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f544,f520]) ).
fof(f539,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c8 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f544,f513]) ).
fof(f540,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ4_spl
| sk_c6 = identity ),
inference(backward_demodulation,[status(thm)],[f544,f512]) ).
fof(f541,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c9 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f544,f511]) ).
fof(f542,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c6 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f544,f504]) ).
fof(f544,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c6 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f512,f533]) ).
fof(f572,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c6) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f542,f490]) ).
fof(f573,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f542,f572]) ).
fof(f574,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f542,f573]) ).
fof(f575,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ12_spl
| multiply(sk_c6,sk_c6) != sk_c6 ),
inference(resolution,[status(thm)],[f574,f538]) ).
fof(f577,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ12_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f536,f575]) ).
fof(f578,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f577]) ).
fof(f579,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f578]) ).
fof(f584,definition,
( sQ32_spl
<=> sk_c8 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f586,plain,
( sQ32_spl
| sk_c8 != sk_c7 ),
inference(component_clause,[status(thm)],[f584]) ).
fof(f587,plain,
( ~ sQ7_spl
| ~ sQ15_spl
| ~ sQ8_spl
| ~ sQ32_spl ),
inference(split_clause,[status(thm)],[f169,f584,f118,f163,f109]) ).
fof(f588,plain,
( sQ30_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f457]) ).
fof(f589,plain,
sQ30_spl,
inference(contradiction_clause,[status(thm)],[f588]) ).
fof(f595,plain,
( ~ sQ17_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c8 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f239,f249]) ).
fof(f597,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ17_spl
| multiply(sk_c1,sk_c7) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f595,f258]) ).
fof(f600,plain,
( sQ32_spl
| ~ sQ17_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f595,f586]) ).
fof(f601,plain,
( sQ32_spl
| ~ sQ17_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f600]) ).
fof(f602,plain,
( sQ32_spl
| ~ sQ17_spl
| ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f601]) ).
fof(f610,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ17_spl
| multiply(sk_c7,sk_c7) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f595,f254]) ).
fof(f654,plain,
( sQ24_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| multiply(sk_c7,sk_c9) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f239,f404]) ).
fof(f655,plain,
( sQ24_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| multiply(sk_c7,sk_c7) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f239,f654]) ).
fof(f656,plain,
( sQ24_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ17_spl
| sk_c7 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f610,f655]) ).
fof(f657,plain,
( sQ24_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ17_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f595,f656]) ).
fof(f658,plain,
( sQ24_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ17_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f657]) ).
fof(f659,plain,
( sQ24_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f658]) ).
fof(f675,plain,
( sQ20_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ17_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f597,f287]) ).
fof(f676,plain,
( sQ20_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ17_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f675]) ).
fof(f677,plain,
( sQ20_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f676]) ).
fof(f678,plain,
( sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| multiply(sk_c7,sk_c7) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f239,f87]) ).
fof(f679,plain,
( sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ17_spl
| sk_c7 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f610,f678]) ).
fof(f680,plain,
( sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ17_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f595,f679]) ).
fof(f681,plain,
( sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ17_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f680]) ).
fof(f682,plain,
( sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f681]) ).
fof(f698,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ4_spl
| multiply(sk_c6,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f540,f397]) ).
fof(f710,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c6,sk_c8) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f541,f84]) ).
fof(f711,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c8 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f698,f710]) ).
fof(f712,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c6 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f539,f711]) ).
fof(f713,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f542,f712]) ).
fof(f714,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f713]) ).
fof(f715,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f714]) ).
fof(f716,plain,
$false,
inference(sat_refutation,[status(thm)],[f88,f92,f96,f100,f104,f108,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,f152,f153,f166,f173,f192,f199,f212,f241,f245,f291,f297,f391,f408,f415,f426,f579,f587,f589,f602,f659,f677,f682,f715]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP280-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n019.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 20:08:21 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
% 0.09/0.44 % Elapsed time: 0.063090 seconds
% 0.09/0.44 % CPU time: 0.197275 seconds
% 0.09/0.44 % Total memory used: 104.775 MB
% 0.09/0.44 % Net memory used: 104.561 MB
%------------------------------------------------------------------------------