%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP283-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 : 22
% Number of leaves : 66
% Syntax : Number of formulae : 358 ( 14 unt; 26 def)
% Number of atoms : 1297 ( 403 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 1763 ( 824 ~; 913 |; 0 &)
% ( 26 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 28 ( 26 usr; 27 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 58 ( 58 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/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_c7,sk_c6) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( inverse(sk_c7) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( inverse(sk_c7) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( inverse(sk_c7) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c4) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( inverse(sk_c7) = sk_c6
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c8,sk_c3) = sk_c7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( inverse(sk_c7) = sk_c6
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( inverse(sk_c4) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,negated_conjecture,
( multiply(sk_c7,sk_c6) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( inverse(sk_c7) = sk_c6
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( inverse(sk_c4) = sk_c7
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
! [X3,X4,X5,X1,X2] :
( inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c6
| inverse(X1) != sk_c7
| multiply(X1,sk_c7) != sk_c8
| inverse(sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c8
| inverse(X5) != sk_c8
| multiply(X5,sk_c8) != X4
| multiply(sk_c8,X4) != sk_c7
| inverse(X3) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
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_c7,sk_c6) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f45,plain,
( inverse(sk_c7) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f46,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f47,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f48,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f49,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f50,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f51,plain,
( inverse(sk_c7) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f52,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f53,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f54,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f55,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f56,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f57,plain,
( inverse(sk_c7) = sk_c6
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f58,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f59,plain,
( inverse(sk_c4) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f60,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f61,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f62,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f63,plain,
( inverse(sk_c7) = sk_c6
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f64,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f65,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f66,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f67,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c8,sk_c3) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f68,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f69,plain,
( inverse(sk_c7) = sk_c6
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f70,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f71,plain,
( inverse(sk_c4) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f72,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f73,plain,
( inverse(sk_c5) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c3 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f74,plain,
( multiply(sk_c7,sk_c6) = sk_c8
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f75,plain,
( inverse(sk_c7) = sk_c6
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f76,plain,
( multiply(sk_c4,sk_c7) = sk_c8
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f77,plain,
( inverse(sk_c4) = sk_c7
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f78,plain,
( multiply(sk_c5,sk_c8) = sk_c6
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f79,plain,
( inverse(sk_c5) = sk_c8
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f80,plain,
! [X2] :
( inverse(X2) != sk_c8
| multiply(X2,sk_c8) != sk_c6
| ! [X1] :
( inverse(X1) != sk_c7
| multiply(X1,sk_c7) != sk_c8
| inverse(sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c8
| ! [X5] :
( inverse(X5) != sk_c8
| ! [X4] :
( multiply(X5,sk_c8) != X4
| multiply(sk_c8,X4) != sk_c7
| ! [X3] :
( inverse(X3) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ) ) ) ) ),
inference(miniscoping,[status(thm)],[f40]) ).
fof(f81,plain,
! [X0,X1,X2,X3,X4] :
( inverse(X4) != sk_c8
| multiply(X4,sk_c8) != sk_c6
| inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c8
| inverse(sk_c7) != sk_c6
| multiply(sk_c7,sk_c6) != sk_c8
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != X1
| multiply(sk_c8,X1) != sk_c7
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f82,definition,
( sQ0_spl
<=> multiply(sk_c8,sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f83,plain,
( ~ sQ0_spl
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(component_clause,[status(thm)],[f82]) ).
fof(f84,plain,
( sQ0_spl
| multiply(sk_c8,sk_c7) != 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
<=> inverse(sk_c7) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f90,plain,
( ~ sQ2_spl
| inverse(sk_c7) = sk_c6 ),
inference(component_clause,[status(thm)],[f89]) ).
fof(f91,plain,
( sQ2_spl
| inverse(sk_c7) != sk_c6 ),
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
<=> multiply(sk_c4,sk_c7) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ3_spl
| multiply(sk_c4,sk_c7) = 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_c4) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f98,plain,
( ~ sQ4_spl
| inverse(sk_c4) = sk_c7 ),
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_c8) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f102,plain,
( ~ sQ5_spl
| multiply(sk_c5,sk_c8) = sk_c6 ),
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_c5) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f106,plain,
( ~ sQ6_spl
| inverse(sk_c5) = sk_c8 ),
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_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f110,plain,
( ~ sQ7_spl
| multiply(sk_c1,sk_c8) = sk_c7 ),
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_c8 ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f119,plain,
( ~ sQ8_spl
| inverse(sk_c1) = 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_c8,sk_c3) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f128,plain,
( ~ sQ9_spl
| multiply(sk_c8,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
<=> multiply(sk_c2,sk_c8) = sk_c3 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f137,plain,
( ~ sQ10_spl
| multiply(sk_c2,sk_c8) = 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_c8 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f146,plain,
( ~ sQ11_spl
| inverse(sk_c2) = sk_c8 ),
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_c8
| multiply(X0,sk_c8) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f155,plain,
! [X0] :
( ~ sQ12_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f154]) ).
fof(f157,definition,
! [X1,X2] :
( sQ13_spl
<=> ( inverse(X2) != sk_c8
| multiply(X2,sk_c8) != X1
| multiply(sk_c8,X1) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f158,plain,
! [X0,X1] :
( ~ sQ13_spl
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != X0
| multiply(sk_c8,X0) != sk_c7 ),
inference(component_clause,[status(thm)],[f157]) ).
fof(f160,definition,
! [X3] :
( sQ14_spl
<=> ( inverse(X3) != sk_c7
| multiply(X3,sk_c7) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f161,plain,
! [X0] :
( ~ sQ14_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c8 ),
inference(component_clause,[status(thm)],[f160]) ).
fof(f163,definition,
! [X4] :
( sQ15_spl
<=> ( inverse(X4) != sk_c8
| multiply(X4,sk_c8) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f164,plain,
! [X0] :
( ~ sQ15_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c6 ),
inference(component_clause,[status(thm)],[f163]) ).
fof(f166,plain,
( sQ15_spl
| sQ14_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sQ13_spl
| sQ12_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f81,f82,f154,f157,f85,f89,f160,f163]) ).
fof(f167,plain,
( ~ sQ5_spl
| ~ sQ15_spl
| inverse(sk_c5) != sk_c8 ),
inference(resolution,[status(thm)],[f164,f102]) ).
fof(f169,plain,
( ~ sQ7_spl
| ~ sQ15_spl
| inverse(sk_c1) != sk_c8
| sk_c7 != sk_c6 ),
inference(paramodulation,[status(thm)],[f110,f164]) ).
fof(f170,plain,
( ~ sQ10_spl
| ~ sQ15_spl
| inverse(sk_c2) != sk_c8
| sk_c3 != sk_c6 ),
inference(paramodulation,[status(thm)],[f137,f164]) ).
fof(f171,plain,
( ~ sQ5_spl
| ~ sQ15_spl
| ~ sQ6_spl
| sk_c8 != sk_c8 ),
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] :
( ~ sQ13_spl
| inverse(X0) != sk_c8
| multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ),
inference(destructive_equality_resolution,[status(thm)],[f158]) ).
fof(f175,plain,
( ~ sQ3_spl
| ~ sQ14_spl
| inverse(sk_c4) != sk_c7 ),
inference(resolution,[status(thm)],[f161,f94]) ).
fof(f177,plain,
( ~ sQ0_spl
| ~ sQ14_spl
| inverse(sk_c8) != sk_c7
| sk_c6 != sk_c8 ),
inference(paramodulation,[status(thm)],[f83,f161]) ).
fof(f178,plain,
( ~ sQ3_spl
| ~ sQ14_spl
| ~ sQ4_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f98,f175]) ).
fof(f179,plain,
( ~ sQ3_spl
| ~ sQ14_spl
| ~ sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f178]) ).
fof(f180,plain,
( ~ sQ3_spl
| ~ sQ14_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f179]) ).
fof(f181,plain,
( ~ sQ7_spl
| ~ sQ12_spl
| inverse(sk_c1) != sk_c8 ),
inference(resolution,[status(thm)],[f155,f110]) ).
fof(f182,plain,
( ~ sQ5_spl
| ~ sQ12_spl
| inverse(sk_c5) != sk_c8
| sk_c6 != sk_c7 ),
inference(paramodulation,[status(thm)],[f102,f155]) ).
fof(f185,plain,
( ~ sQ7_spl
| ~ sQ12_spl
| ~ sQ8_spl
| sk_c8 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f119,f181]) ).
fof(f186,plain,
( ~ sQ7_spl
| ~ sQ12_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f185]) ).
fof(f187,plain,
( ~ sQ7_spl
| ~ sQ12_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f186]) ).
fof(f192,plain,
! [X0] :
( ~ sQ10_spl
| multiply(sk_c3,X0) = multiply(sk_c2,multiply(sk_c8,X0)) ),
inference(paramodulation,[status(thm)],[f137,f43]) ).
fof(f196,plain,
( ~ sQ5_spl
| ~ sQ13_spl
| inverse(sk_c5) != sk_c8
| multiply(sk_c8,sk_c6) != sk_c7 ),
inference(paramodulation,[status(thm)],[f102,f174]) ).
fof(f197,plain,
( ~ sQ10_spl
| ~ sQ13_spl
| inverse(sk_c2) != sk_c8
| multiply(sk_c8,sk_c3) != sk_c7 ),
inference(paramodulation,[status(thm)],[f137,f174]) ).
fof(f198,definition,
( sQ16_spl
<=> multiply(sk_c8,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f199,plain,
( ~ sQ16_spl
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(component_clause,[status(thm)],[f198]) ).
fof(f200,plain,
( sQ16_spl
| multiply(sk_c8,sk_c6) != sk_c7 ),
inference(component_clause,[status(thm)],[f198]) ).
fof(f201,plain,
( ~ sQ5_spl
| ~ sQ13_spl
| ~ sQ6_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f196,f198,f105,f157,f101]) ).
fof(f202,plain,
( ~ sQ10_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f197,f127,f145,f157,f136]) ).
fof(f203,plain,
( ~ sQ13_spl
| inverse(identity) != sk_c8
| multiply(sk_c8,sk_c8) != sk_c7 ),
inference(paramodulation,[status(thm)],[f41,f174]) ).
fof(f205,definition,
( sQ17_spl
<=> multiply(sk_c8,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f208,definition,
( sQ18_spl
<=> inverse(identity) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f210,plain,
( sQ18_spl
| inverse(identity) != sk_c8 ),
inference(component_clause,[status(thm)],[f208]) ).
fof(f211,plain,
( ~ sQ13_spl
| ~ sQ18_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f203,f205,f208,f157]) ).
fof(f212,plain,
( ~ sQ6_spl
| multiply(sk_c8,sk_c5) = identity ),
inference(paramodulation,[status(thm)],[f106,f42]) ).
fof(f213,plain,
( ~ sQ4_spl
| multiply(sk_c7,sk_c4) = identity ),
inference(paramodulation,[status(thm)],[f98,f42]) ).
fof(f217,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f42,f43]) ).
fof(f218,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f41,f217]) ).
fof(f220,plain,
! [X0] :
( ~ sQ6_spl
| multiply(identity,X0) = multiply(sk_c8,multiply(sk_c5,X0)) ),
inference(paramodulation,[status(thm)],[f212,f43]) ).
fof(f221,plain,
! [X0] :
( ~ sQ6_spl
| X0 = multiply(sk_c8,multiply(sk_c5,X0)) ),
inference(forward_demodulation,[status(thm)],[f41,f220]) ).
fof(f248,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sk_c8 = multiply(sk_c8,sk_c6) ),
inference(paramodulation,[status(thm)],[f102,f221]) ).
fof(f253,plain,
( sQ16_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c8 != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f248,f200]) ).
fof(f254,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| multiply(sk_c3,sk_c6) = multiply(sk_c2,sk_c8) ),
inference(paramodulation,[status(thm)],[f248,f192]) ).
fof(f257,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| multiply(sk_c3,sk_c6) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f137,f254]) ).
fof(f273,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| sk_c6 = multiply(inverse(sk_c3),sk_c3) ),
inference(paramodulation,[status(thm)],[f257,f218]) ).
fof(f276,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sk_c6 = multiply(inverse(sk_c8),sk_c8) ),
inference(paramodulation,[status(thm)],[f248,f218]) ).
fof(f282,plain,
( ~ sQ4_spl
| sk_c4 = multiply(inverse(sk_c7),identity) ),
inference(paramodulation,[status(thm)],[f213,f218]) ).
fof(f283,plain,
( ~ sQ1_spl
| sk_c6 = multiply(inverse(sk_c7),sk_c8) ),
inference(paramodulation,[status(thm)],[f86,f218]) ).
fof(f286,plain,
! [X0] : X0 = multiply(inverse(identity),X0),
inference(paramodulation,[status(thm)],[f41,f218]) ).
fof(f293,plain,
( ~ sQ10_spl
| sk_c8 = multiply(inverse(sk_c2),sk_c3) ),
inference(paramodulation,[status(thm)],[f137,f218]) ).
fof(f295,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f42,f273]) ).
fof(f297,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sk_c6 = identity ),
inference(forward_demodulation,[status(thm)],[f42,f276]) ).
fof(f299,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| sk_c4 = multiply(sk_c6,identity) ),
inference(forward_demodulation,[status(thm)],[f90,f282]) ).
fof(f300,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sk_c6 = multiply(sk_c6,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f90,f283]) ).
fof(f306,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| sk_c8 = multiply(sk_c8,sk_c3) ),
inference(forward_demodulation,[status(thm)],[f146,f293]) ).
fof(f314,plain,
( sQ18_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| inverse(sk_c6) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f295,f210]) ).
fof(f315,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| multiply(sk_c6,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f295,f41]) ).
fof(f321,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| sk_c4 = identity ),
inference(forward_demodulation,[status(thm)],[f315,f299]) ).
fof(f322,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ4_spl
| ~ sQ2_spl
| multiply(sk_c4,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f331,f315]) ).
fof(f323,plain,
( sQ18_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ4_spl
| ~ sQ2_spl
| inverse(sk_c4) != sk_c8 ),
inference(backward_demodulation,[status(thm)],[f331,f314]) ).
fof(f331,plain,
( ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| sk_c4 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f295,f321]) ).
fof(f332,plain,
( sQ18_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ4_spl
| ~ sQ2_spl
| sk_c7 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f98,f323]) ).
fof(f334,plain,
( ~ sQ3_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ4_spl
| ~ sQ2_spl
| sk_c7 = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f322,f94]) ).
fof(f360,plain,
( sQ18_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f334,f332]) ).
fof(f361,plain,
( sQ18_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f360]) ).
fof(f362,plain,
( sQ18_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ10_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f361]) ).
fof(f366,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c6,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f297,f41]) ).
fof(f370,plain,
( ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| inverse(sk_c5) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f373,f106]) ).
fof(f372,plain,
( sQ16_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c6 != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f373,f253]) ).
fof(f373,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c6 = sk_c8 ),
inference(forward_demodulation,[status(thm)],[f366,f300]) ).
fof(f376,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| X0 = multiply(sk_c6,multiply(sk_c5,X0)) ),
inference(paramodulation,[status(thm)],[f370,f218]) ).
fof(f377,plain,
! [X0] :
( ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| X0 = multiply(sk_c5,X0) ),
inference(forward_demodulation,[status(thm)],[f366,f376]) ).
fof(f378,plain,
( ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c6,sk_c7) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f373,f83]) ).
fof(f379,plain,
( ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c7 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f366,f378]) ).
fof(f380,plain,
( ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f379,f372]) ).
fof(f381,plain,
( ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sQ16_spl ),
inference(contradiction_clause,[status(thm)],[f380]) ).
fof(f382,plain,
( ~ sQ16_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c6,sk_c6) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f373,f199]) ).
fof(f383,plain,
( ~ sQ16_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c6 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f366,f382]) ).
fof(f386,definition,
( sQ19_spl
<=> sk_c6 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f387,plain,
( ~ sQ19_spl
| sk_c6 = sk_c7 ),
inference(component_clause,[status(thm)],[f386]) ).
fof(f388,plain,
( sQ19_spl
| sk_c6 != sk_c7 ),
inference(component_clause,[status(thm)],[f386]) ).
fof(f389,plain,
( ~ sQ5_spl
| ~ sQ12_spl
| ~ sQ6_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f182,f386,f105,f154,f101]) ).
fof(f390,definition,
( sQ20_spl
<=> sk_c7 = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f392,plain,
( sQ20_spl
| sk_c7 != sk_c7 ),
inference(component_clause,[status(thm)],[f390]) ).
fof(f399,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c4,sk_c7) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f373,f94]) ).
fof(f411,plain,
( sQ20_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f392]) ).
fof(f412,plain,
sQ20_spl,
inference(contradiction_clause,[status(thm)],[f411]) ).
fof(f413,definition,
( sQ21_spl
<=> sk_c8 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f415,plain,
( sQ21_spl
| sk_c8 != sk_c8 ),
inference(component_clause,[status(thm)],[f413]) ).
fof(f417,definition,
( sQ22_spl
<=> sk_c6 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f418,plain,
( ~ sQ22_spl
| sk_c6 = sk_c8 ),
inference(component_clause,[status(thm)],[f417]) ).
fof(f419,plain,
( sQ22_spl
| sk_c6 != sk_c8 ),
inference(component_clause,[status(thm)],[f417]) ).
fof(f420,definition,
( sQ23_spl
<=> inverse(sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f421,plain,
( ~ sQ23_spl
| inverse(sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f420]) ).
fof(f422,plain,
( sQ23_spl
| inverse(sk_c8) != sk_c7 ),
inference(component_clause,[status(thm)],[f420]) ).
fof(f423,plain,
( ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ23_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f177,f417,f420,f160,f82]) ).
fof(f424,plain,
( sQ21_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f415]) ).
fof(f425,plain,
sQ21_spl,
inference(contradiction_clause,[status(thm)],[f424]) ).
fof(f430,plain,
! [X0] : multiply(identity,X0) = X0,
inference(paramodulation,[status(thm)],[f218,f286]) ).
fof(f441,plain,
( ~ sQ10_spl
| sk_c8 = multiply(inverse(sk_c2),sk_c3) ),
inference(paramodulation,[status(thm)],[f137,f218]) ).
fof(f443,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| sk_c8 = multiply(sk_c8,sk_c3) ),
inference(forward_demodulation,[status(thm)],[f146,f441]) ).
fof(f444,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sk_c8 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f128,f443]) ).
fof(f452,plain,
( sQ23_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| inverse(sk_c7) != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f444,f422]) ).
fof(f453,plain,
( ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ9_spl
| inverse(sk_c2) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f444,f146]) ).
fof(f454,plain,
( ~ sQ1_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| multiply(sk_c7,sk_c6) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f444,f86]) ).
fof(f455,plain,
( ~ sQ8_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| inverse(sk_c1) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f444,f119]) ).
fof(f456,plain,
( sQ22_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sk_c6 != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f444,f419]) ).
fof(f471,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sk_c7 = multiply(sk_c8,sk_c3) ),
inference(forward_demodulation,[status(thm)],[f444,f306]) ).
fof(f472,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sk_c7 = multiply(sk_c7,sk_c3) ),
inference(forward_demodulation,[status(thm)],[f444,f471]) ).
fof(f473,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sk_c3 = multiply(inverse(sk_c7),sk_c7) ),
inference(paramodulation,[status(thm)],[f472,f218]) ).
fof(f475,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sk_c3 = identity ),
inference(forward_demodulation,[status(thm)],[f42,f473]) ).
fof(f482,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| multiply(sk_c1,sk_c7) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f444,f110]) ).
fof(f483,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sk_c7 = multiply(inverse(sk_c1),sk_c7) ),
inference(paramodulation,[status(thm)],[f482,f218]) ).
fof(f485,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| sk_c7 = multiply(sk_c7,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f455,f483]) ).
fof(f486,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| multiply(sk_c7,sk_c7) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f444,f83]) ).
fof(f519,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c7 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f486,f485]) ).
fof(f520,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f519,f456]) ).
fof(f521,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f520]) ).
fof(f529,plain,
( ~ sQ22_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sk_c6 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f444,f418]) ).
fof(f567,definition,
( sQ24_spl
<=> sk_c6 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f569,plain,
( sQ24_spl
| sk_c6 != sk_c6 ),
inference(component_clause,[status(thm)],[f567]) ).
fof(f571,plain,
( ~ sQ7_spl
| ~ sQ15_spl
| ~ sQ8_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f169,f386,f118,f163,f109]) ).
fof(f572,definition,
( sQ25_spl
<=> sk_c3 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f574,plain,
( sQ25_spl
| sk_c3 != sk_c6 ),
inference(component_clause,[status(thm)],[f572]) ).
fof(f575,plain,
( ~ sQ10_spl
| ~ sQ15_spl
| ~ sQ11_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f170,f572,f145,f163,f136]) ).
fof(f577,plain,
( ~ sQ16_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f383,f388]) ).
fof(f578,plain,
( ~ sQ16_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sQ19_spl ),
inference(contradiction_clause,[status(thm)],[f577]) ).
fof(f579,plain,
( sQ24_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f569]) ).
fof(f580,plain,
sQ24_spl,
inference(contradiction_clause,[status(thm)],[f579]) ).
fof(f586,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ22_spl
| sk_c8 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f529,f444]) ).
fof(f587,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| multiply(sk_c3,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f475,f430]) ).
fof(f590,plain,
( sQ23_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ22_spl
| inverse(sk_c6) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f529,f452]) ).
fof(f591,plain,
( sQ23_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ22_spl
| inverse(sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f529,f590]) ).
fof(f596,plain,
( ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ22_spl
| inverse(sk_c2) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f529,f453]) ).
fof(f600,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| multiply(inverse(X0),X0) = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f475,f42]) ).
fof(f606,plain,
( ~ sQ1_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ22_spl
| multiply(sk_c6,sk_c6) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f529,f454]) ).
fof(f607,plain,
( ~ sQ1_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ22_spl
| multiply(sk_c6,sk_c6) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f529,f606]) ).
fof(f608,plain,
( ~ sQ1_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ22_spl
| sk_c6 = multiply(inverse(sk_c6),sk_c6) ),
inference(paramodulation,[status(thm)],[f607,f218]) ).
fof(f610,plain,
( ~ sQ1_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ22_spl
| sk_c6 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f600,f608]) ).
fof(f611,plain,
( ~ sQ1_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ22_spl
| sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f610,f574]) ).
fof(f612,plain,
( ~ sQ1_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ22_spl
| sQ25_spl ),
inference(contradiction_clause,[status(thm)],[f611]) ).
fof(f615,plain,
( ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ22_spl
| ~ sQ1_spl
| inverse(sk_c2) = sk_c3 ),
inference(backward_demodulation,[status(thm)],[f610,f596]) ).
fof(f617,plain,
( sQ23_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ22_spl
| ~ sQ1_spl
| inverse(sk_c6) != sk_c3 ),
inference(backward_demodulation,[status(thm)],[f610,f591]) ).
fof(f619,plain,
( ~ sQ22_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ1_spl
| sk_c3 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f610,f529]) ).
fof(f622,plain,
( sQ23_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ22_spl
| ~ sQ1_spl
| inverse(sk_c3) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f610,f617]) ).
fof(f628,plain,
( ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ22_spl
| ~ sQ1_spl
| multiply(sk_c3,sk_c2) = sk_c3 ),
inference(paramodulation,[status(thm)],[f615,f600]) ).
fof(f630,plain,
( ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ22_spl
| ~ sQ1_spl
| sk_c2 = sk_c3 ),
inference(forward_demodulation,[status(thm)],[f587,f628]) ).
fof(f632,plain,
( ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ22_spl
| ~ sQ1_spl
| inverse(sk_c2) = sk_c2 ),
inference(backward_demodulation,[status(thm)],[f630,f615]) ).
fof(f635,plain,
( ~ sQ22_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ1_spl
| sk_c2 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f630,f619]) ).
fof(f644,plain,
( sQ23_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ22_spl
| ~ sQ1_spl
| inverse(sk_c2) != sk_c3 ),
inference(forward_demodulation,[status(thm)],[f630,f622]) ).
fof(f645,plain,
( sQ23_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ22_spl
| ~ sQ1_spl
| inverse(sk_c2) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f630,f644]) ).
fof(f657,plain,
( ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ22_spl
| ~ sQ1_spl
| sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f632,f645]) ).
fof(f658,plain,
( ~ sQ11_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ22_spl
| ~ sQ1_spl
| sQ23_spl ),
inference(contradiction_clause,[status(thm)],[f657]) ).
fof(f691,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ22_spl
| sk_c6 = multiply(sk_c7,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f529,f485]) ).
fof(f692,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ22_spl
| sk_c6 = multiply(sk_c6,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f529,f691]) ).
fof(f693,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ22_spl
| sk_c6 = multiply(sk_c6,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f529,f692]) ).
fof(f728,plain,
( sQ1_spl
| ~ sQ22_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| multiply(sk_c6,sk_c6) != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f529,f87]) ).
fof(f729,plain,
( sQ1_spl
| ~ sQ22_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c6 != sk_c8 ),
inference(forward_demodulation,[status(thm)],[f693,f728]) ).
fof(f730,plain,
( sQ1_spl
| ~ sQ22_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f586,f729]) ).
fof(f731,plain,
( sQ1_spl
| ~ sQ22_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f730]) ).
fof(f732,plain,
( sQ1_spl
| ~ sQ22_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f731]) ).
fof(f758,plain,
( ~ sQ22_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ1_spl
| sk_c2 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f529,f635]) ).
fof(f775,plain,
( sQ2_spl
| ~ sQ22_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| inverse(sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f529,f91]) ).
fof(f776,plain,
( ~ sQ23_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ22_spl
| inverse(sk_c6) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f586,f421]) ).
fof(f777,plain,
( ~ sQ23_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ22_spl
| inverse(sk_c6) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f529,f776]) ).
fof(f822,plain,
( sQ2_spl
| ~ sQ22_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ1_spl
| inverse(sk_c2) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f758,f775]) ).
fof(f823,plain,
( sQ2_spl
| ~ sQ22_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ1_spl
| inverse(sk_c2) != sk_c2 ),
inference(forward_demodulation,[status(thm)],[f758,f822]) ).
fof(f824,plain,
( ~ sQ23_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ22_spl
| ~ sQ1_spl
| inverse(sk_c2) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f758,f777]) ).
fof(f825,plain,
( ~ sQ23_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ22_spl
| ~ sQ1_spl
| inverse(sk_c2) = sk_c2 ),
inference(forward_demodulation,[status(thm)],[f758,f824]) ).
fof(f826,plain,
( ~ sQ23_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ22_spl
| ~ sQ1_spl
| sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f825,f823]) ).
fof(f827,plain,
( ~ sQ23_spl
| ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ9_spl
| ~ sQ22_spl
| ~ sQ1_spl
| sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f826]) ).
fof(f834,plain,
( ~ sQ4_spl
| ~ sQ19_spl
| inverse(sk_c4) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f387,f98]) ).
fof(f835,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c6,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f297,f430]) ).
fof(f847,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ19_spl
| X0 = multiply(sk_c6,multiply(sk_c4,X0)) ),
inference(paramodulation,[status(thm)],[f834,f218]) ).
fof(f848,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ19_spl
| ~ sQ5_spl
| ~ sQ6_spl
| X0 = multiply(sk_c4,X0) ),
inference(forward_demodulation,[status(thm)],[f835,f847]) ).
fof(f852,plain,
( ~ sQ4_spl
| ~ sQ19_spl
| multiply(sk_c6,sk_c4) = identity ),
inference(forward_demodulation,[status(thm)],[f387,f213]) ).
fof(f853,plain,
( ~ sQ4_spl
| ~ sQ19_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c4 = identity ),
inference(forward_demodulation,[status(thm)],[f835,f852]) ).
fof(f856,plain,
( ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ19_spl
| inverse(sk_c5) = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f861,f370]) ).
fof(f858,plain,
( ~ sQ19_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c4 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f861,f387]) ).
fof(f859,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ19_spl
| sk_c4 = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f861,f373]) ).
fof(f860,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ19_spl
| sk_c4 = identity ),
inference(backward_demodulation,[status(thm)],[f861,f297]) ).
fof(f861,plain,
( ~ sQ4_spl
| ~ sQ19_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c4 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f297,f853]) ).
fof(f865,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ19_spl
| multiply(inverse(X0),X0) = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f860,f42]) ).
fof(f874,plain,
( ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ19_spl
| multiply(sk_c4,sk_c5) = sk_c4 ),
inference(paramodulation,[status(thm)],[f856,f865]) ).
fof(f876,plain,
( ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ19_spl
| sk_c5 = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f848,f874]) ).
fof(f883,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ19_spl
| sk_c5 = sk_c8 ),
inference(backward_demodulation,[status(thm)],[f876,f859]) ).
fof(f884,plain,
( ~ sQ19_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c5 = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f876,f858]) ).
fof(f888,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sk_c8 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f377,f102]) ).
fof(f889,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ4_spl
| ~ sQ19_spl
| sk_c5 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f883,f888]) ).
fof(f906,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ19_spl
| multiply(sk_c5,sk_c7) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f883,f84]) ).
fof(f907,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ19_spl
| sk_c7 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f377,f906]) ).
fof(f908,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ19_spl
| sk_c5 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f884,f907]) ).
fof(f909,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ19_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f889,f908]) ).
fof(f910,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ19_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f909]) ).
fof(f911,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ19_spl ),
inference(contradiction_clause,[status(thm)],[f910]) ).
fof(f912,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f888,f417,f89,f85,f105,f101]) ).
fof(f920,plain,
! [X0] :
( ~ sQ2_spl
| X0 = multiply(sk_c6,multiply(sk_c7,X0)) ),
inference(paramodulation,[status(thm)],[f90,f218]) ).
fof(f921,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| X0 = multiply(sk_c7,X0) ),
inference(forward_demodulation,[status(thm)],[f835,f920]) ).
fof(f926,plain,
( ~ sQ6_spl
| ~ sQ22_spl
| multiply(sk_c6,sk_c5) = identity ),
inference(forward_demodulation,[status(thm)],[f418,f212]) ).
fof(f927,plain,
( ~ sQ6_spl
| ~ sQ22_spl
| ~ sQ5_spl
| sk_c5 = identity ),
inference(forward_demodulation,[status(thm)],[f835,f926]) ).
fof(f932,plain,
( sQ19_spl
| ~ sQ6_spl
| ~ sQ22_spl
| ~ sQ5_spl
| sk_c5 != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f934,f388]) ).
fof(f934,plain,
( ~ sQ6_spl
| ~ sQ22_spl
| ~ sQ5_spl
| sk_c5 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f297,f927]) ).
fof(f935,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ22_spl
| multiply(sk_c4,sk_c7) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f934,f399]) ).
fof(f936,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ22_spl
| sk_c7 = multiply(inverse(sk_c4),sk_c5) ),
inference(paramodulation,[status(thm)],[f935,f218]) ).
fof(f938,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ22_spl
| ~ sQ4_spl
| sk_c7 = multiply(sk_c7,sk_c5) ),
inference(forward_demodulation,[status(thm)],[f98,f936]) ).
fof(f939,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ22_spl
| ~ sQ4_spl
| sk_c7 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f921,f938]) ).
fof(f940,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ22_spl
| ~ sQ4_spl
| sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f939,f932]) ).
fof(f941,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ22_spl
| ~ sQ4_spl
| sQ19_spl ),
inference(contradiction_clause,[status(thm)],[f940]) ).
fof(f942,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,f180,f187,f201,f202,f211,f362,f381,f389,f412,f423,f425,f521,f571,f575,f578,f580,f612,f658,f732,f827,f911,f912,f941]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP283-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n005.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 20 20:08:32 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % 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: 0.057860 seconds
% 0.09/0.44 % CPU time: 0.222110 seconds
% 0.09/0.44 % Total memory used: 105.935 MB
% 0.09/0.44 % Net memory used: 105.628 MB
%------------------------------------------------------------------------------