%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP296-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 12:33:20 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.40s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 61
% Syntax : Number of formulae : 290 ( 10 unt; 23 def)
% Number of atoms : 1119 ( 355 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 1573 ( 744 ~; 806 |; 0 &)
% ( 23 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 25 ( 23 usr; 24 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 58 ( 58 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( multiply(sk_c8,sk_c4) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c4
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
( multiply(sk_c8,sk_c4) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c4
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
( multiply(sk_c8,sk_c4) = sk_c7
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c4
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c8
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c1) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,negated_conjecture,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
( multiply(sk_c8,sk_c4) = sk_c7
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c4
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c8
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c8,sk_c6) = sk_c7 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
( multiply(sk_c8,sk_c4) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c4
| multiply(sk_c2,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
( inverse(sk_c3) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
( inverse(sk_c5) = sk_c6
| multiply(sk_c2,sk_c8) = sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
( multiply(sk_c8,sk_c4) = sk_c7
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
( multiply(sk_c3,sk_c8) = sk_c4
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
( inverse(sk_c3) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
( multiply(sk_c5,sk_c6) = sk_c8
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
( inverse(sk_c5) = sk_c6
| inverse(sk_c2) = sk_c8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,negated_conjecture,
! [X3,X4,X1,X2,X5] :
( inverse(X5) != sk_c6
| multiply(X5,sk_c6) != sk_c8
| inverse(X2) != sk_c8
| multiply(X2,sk_c8) != X1
| multiply(sk_c8,X1) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(X4) != sk_c8
| multiply(X4,sk_c8) != sk_c6
| multiply(sk_c8,sk_c6) != sk_c7
| inverse(X3) != sk_c8
| multiply(X3,sk_c8) != sk_c7
| multiply(sk_c8,sk_c7) != sk_c6 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f42,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f43,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f44,plain,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f45,plain,
( multiply(sk_c8,sk_c4) = sk_c7
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f46,plain,
( multiply(sk_c3,sk_c8) = sk_c4
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f47,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f48,plain,
( multiply(sk_c5,sk_c6) = sk_c8
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f49,plain,
( inverse(sk_c5) = sk_c6
| multiply(sk_c8,sk_c7) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f50,plain,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f51,plain,
( multiply(sk_c8,sk_c4) = sk_c7
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f52,plain,
( multiply(sk_c3,sk_c8) = sk_c4
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f53,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f54,plain,
( multiply(sk_c5,sk_c6) = sk_c8
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f55,plain,
( inverse(sk_c5) = sk_c6
| multiply(sk_c1,sk_c8) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f56,plain,
( multiply(sk_c6,sk_c8) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f57,plain,
( multiply(sk_c8,sk_c4) = sk_c7
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f58,plain,
( multiply(sk_c3,sk_c8) = sk_c4
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f59,plain,
( inverse(sk_c3) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f60,plain,
( multiply(sk_c5,sk_c6) = sk_c8
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f61,plain,
( inverse(sk_c5) = sk_c6
| inverse(sk_c1) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f62,plain,
( multiply(sk_c6,sk_c8) = sk_c7
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f63,plain,
( multiply(sk_c8,sk_c4) = sk_c7
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f64,plain,
( multiply(sk_c3,sk_c8) = sk_c4
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f65,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f66,plain,
( multiply(sk_c5,sk_c6) = sk_c8
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f67,plain,
( inverse(sk_c5) = sk_c6
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f69,plain,
( multiply(sk_c8,sk_c4) = sk_c7
| multiply(sk_c2,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f70,plain,
( multiply(sk_c3,sk_c8) = sk_c4
| multiply(sk_c2,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f71,plain,
( inverse(sk_c3) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f72,plain,
( multiply(sk_c5,sk_c6) = sk_c8
| multiply(sk_c2,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f73,plain,
( inverse(sk_c5) = sk_c6
| multiply(sk_c2,sk_c8) = sk_c6 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f75,plain,
( multiply(sk_c8,sk_c4) = sk_c7
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f76,plain,
( multiply(sk_c3,sk_c8) = sk_c4
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f77,plain,
( inverse(sk_c3) = sk_c8
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f78,plain,
( multiply(sk_c5,sk_c6) = sk_c8
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f79,plain,
( inverse(sk_c5) = sk_c6
| inverse(sk_c2) = sk_c8 ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f80,plain,
! [X5] :
( inverse(X5) != sk_c6
| multiply(X5,sk_c6) != sk_c8
| ! [X2] :
( inverse(X2) != sk_c8
| ! [X1] :
( multiply(X2,sk_c8) != X1
| multiply(sk_c8,X1) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| ! [X4] :
( inverse(X4) != sk_c8
| multiply(X4,sk_c8) != sk_c6
| multiply(sk_c8,sk_c6) != 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_c6
| multiply(X4,sk_c6) != sk_c8
| inverse(X3) != sk_c8
| multiply(X3,sk_c8) != X2
| multiply(sk_c8,X2) != sk_c7
| multiply(sk_c6,sk_c8) != sk_c7
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c6
| multiply(sk_c8,sk_c6) != 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_c6,sk_c8) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ1_spl
| multiply(sk_c6,sk_c8) = sk_c7 ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f87,plain,
( sQ1_spl
| multiply(sk_c6,sk_c8) != sk_c7 ),
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_c8,sk_c4) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f90,plain,
( ~ sQ2_spl
| multiply(sk_c8,sk_c4) = sk_c7 ),
inference(component_clause,[status(thm)],[f89]) ).
fof(f92,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f45,f82,f89]) ).
fof(f93,definition,
( sQ3_spl
<=> multiply(sk_c3,sk_c8) = sk_c4 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( ~ sQ3_spl
| multiply(sk_c3,sk_c8) = sk_c4 ),
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_c3) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f98,plain,
( ~ sQ4_spl
| inverse(sk_c3) = sk_c8 ),
inference(component_clause,[status(thm)],[f97]) ).
fof(f100,plain,
( sQ4_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f47,f82,f97]) ).
fof(f101,definition,
( sQ5_spl
<=> multiply(sk_c5,sk_c6) = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f102,plain,
( ~ sQ5_spl
| multiply(sk_c5,sk_c6) = sk_c8 ),
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_c6 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f106,plain,
( ~ sQ6_spl
| inverse(sk_c5) = sk_c6 ),
inference(component_clause,[status(thm)],[f105]) ).
fof(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_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f128,plain,
( ~ sQ9_spl
| multiply(sk_c8,sk_c6) = sk_c7 ),
inference(component_clause,[status(thm)],[f127]) ).
fof(f129,plain,
( sQ9_spl
| multiply(sk_c8,sk_c6) != 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_c6 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f137,plain,
( ~ sQ10_spl
| multiply(sk_c2,sk_c8) = sk_c6 ),
inference(component_clause,[status(thm)],[f136]) ).
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(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] :
( sQ13_spl
<=> ( inverse(X1) != sk_c8
| multiply(X1,sk_c8) != sk_c6 ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f158,plain,
! [X0] :
( ~ sQ13_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c8) != sk_c6 ),
inference(component_clause,[status(thm)],[f157]) ).
fof(f160,definition,
! [X2,X3] :
( sQ14_spl
<=> ( inverse(X3) != sk_c8
| multiply(X3,sk_c8) != X2
| multiply(sk_c8,X2) != sk_c7 ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f161,plain,
! [X0,X1] :
( ~ sQ14_spl
| inverse(X1) != sk_c8
| multiply(X1,sk_c8) != X0
| multiply(sk_c8,X0) != sk_c7 ),
inference(component_clause,[status(thm)],[f160]) ).
fof(f163,definition,
! [X4] :
( sQ15_spl
<=> ( inverse(X4) != sk_c6
| multiply(X4,sk_c6) != sk_c8 ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f164,plain,
! [X0] :
( ~ sQ15_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c8 ),
inference(component_clause,[status(thm)],[f163]) ).
fof(f166,plain,
( sQ15_spl
| sQ14_spl
| ~ sQ1_spl
| sQ13_spl
| ~ sQ9_spl
| sQ12_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f81,f82,f154,f127,f157,f85,f160,f163]) ).
fof(f167,plain,
( ~ sQ5_spl
| ~ sQ15_spl
| inverse(sk_c5) != sk_c6 ),
inference(resolution,[status(thm)],[f164,f102]) ).
fof(f170,plain,
( ~ sQ5_spl
| ~ sQ15_spl
| ~ sQ6_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f106,f167]) ).
fof(f171,plain,
( ~ sQ5_spl
| ~ sQ15_spl
| ~ sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f170]) ).
fof(f172,plain,
( ~ sQ5_spl
| ~ sQ15_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f171]) ).
fof(f173,plain,
! [X0] :
( ~ sQ14_spl
| inverse(X0) != sk_c8
| multiply(sk_c8,multiply(X0,sk_c8)) != sk_c7 ),
inference(destructive_equality_resolution,[status(thm)],[f161]) ).
fof(f185,plain,
( ~ sQ7_spl
| ~ sQ14_spl
| inverse(sk_c1) != sk_c8
| multiply(sk_c8,sk_c7) != sk_c7 ),
inference(paramodulation,[status(thm)],[f110,f173]) ).
fof(f186,plain,
( ~ sQ3_spl
| ~ sQ14_spl
| inverse(sk_c3) != sk_c8
| multiply(sk_c8,sk_c4) != sk_c7 ),
inference(paramodulation,[status(thm)],[f94,f173]) ).
fof(f188,definition,
( sQ16_spl
<=> multiply(sk_c8,sk_c7) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f189,plain,
( ~ sQ16_spl
| multiply(sk_c8,sk_c7) = sk_c7 ),
inference(component_clause,[status(thm)],[f188]) ).
fof(f190,plain,
( sQ16_spl
| multiply(sk_c8,sk_c7) != sk_c7 ),
inference(component_clause,[status(thm)],[f188]) ).
fof(f191,plain,
( ~ sQ7_spl
| ~ sQ14_spl
| ~ sQ8_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f185,f188,f118,f160,f109]) ).
fof(f192,plain,
( ~ sQ3_spl
| ~ sQ14_spl
| ~ sQ4_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f186,f89,f97,f160,f93]) ).
fof(f195,plain,
( ~ sQ6_spl
| multiply(sk_c6,sk_c5) = identity ),
inference(paramodulation,[status(thm)],[f106,f42]) ).
fof(f198,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f42,f43]) ).
fof(f199,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f41,f198]) ).
fof(f219,plain,
( ~ sQ3_spl
| sk_c8 = multiply(inverse(sk_c3),sk_c4) ),
inference(paramodulation,[status(thm)],[f94,f199]) ).
fof(f220,plain,
( ~ sQ5_spl
| sk_c6 = multiply(inverse(sk_c5),sk_c8) ),
inference(paramodulation,[status(thm)],[f102,f199]) ).
fof(f221,plain,
( ~ sQ10_spl
| sk_c8 = multiply(inverse(sk_c2),sk_c6) ),
inference(paramodulation,[status(thm)],[f137,f199]) ).
fof(f223,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sk_c8 = multiply(sk_c8,sk_c4) ),
inference(forward_demodulation,[status(thm)],[f98,f219]) ).
fof(f224,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| sk_c8 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f90,f223]) ).
fof(f225,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| sk_c6 = multiply(sk_c6,sk_c8) ),
inference(forward_demodulation,[status(thm)],[f106,f220]) ).
fof(f226,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| sk_c6 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f86,f225]) ).
fof(f227,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| sk_c8 = multiply(sk_c8,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f146,f221]) ).
fof(f231,plain,
( sQ9_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| multiply(sk_c7,sk_c6) != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f224,f129]) ).
fof(f232,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| multiply(sk_c6,sk_c7) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f224,f86]) ).
fof(f233,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c7,sk_c4) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f224,f90]) ).
fof(f239,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| sk_c8 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f226,f224]) ).
fof(f240,plain,
( sQ9_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| multiply(sk_c6,sk_c6) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f226,f231]) ).
fof(f241,plain,
( sQ9_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| multiply(sk_c6,sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f226,f240]) ).
fof(f242,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c6,sk_c6) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f226,f232]) ).
fof(f243,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c6,sk_c6) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f226,f242]) ).
fof(f244,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f243,f241]) ).
fof(f245,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f244]) ).
fof(f246,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c4 = multiply(inverse(sk_c7),sk_c7) ),
inference(paramodulation,[status(thm)],[f233,f199]) ).
fof(f248,plain,
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| sk_c4 = identity ),
inference(forward_demodulation,[status(thm)],[f42,f246]) ).
fof(f282,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c7) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f224,f158]) ).
fof(f283,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c7) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f224,f282]) ).
fof(f299,plain,
( sQ16_spl
| ~ sQ0_spl
| sk_c6 != sk_c7 ),
inference(backward_demodulation,[status(thm)],[f83,f190]) ).
fof(f302,plain,
( ~ sQ7_spl
| sk_c8 = multiply(inverse(sk_c1),sk_c7) ),
inference(paramodulation,[status(thm)],[f110,f199]) ).
fof(f304,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| sk_c8 = multiply(sk_c8,sk_c7) ),
inference(forward_demodulation,[status(thm)],[f119,f302]) ).
fof(f305,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c8 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f83,f304]) ).
fof(f307,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| ~ sQ8_spl
| multiply(sk_c6,sk_c7) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f305,f83]) ).
fof(f308,plain,
( ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| multiply(sk_c6,sk_c6) = sk_c7 ),
inference(backward_demodulation,[status(thm)],[f305,f128]) ).
fof(f310,plain,
( ~ sQ11_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| inverse(sk_c2) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f305,f146]) ).
fof(f311,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| inverse(sk_c1) = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f305,f119]) ).
fof(f313,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c6) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f305,f155]) ).
fof(f314,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f305,f313]) ).
fof(f316,plain,
( ~ sQ11_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ12_spl
| sk_c6 != sk_c6
| multiply(sk_c2,sk_c6) != sk_c7 ),
inference(paramodulation,[status(thm)],[f310,f314]) ).
fof(f317,definition,
( sQ17_spl
<=> multiply(sk_c2,sk_c6) = sk_c7 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f319,plain,
( sQ17_spl
| multiply(sk_c2,sk_c6) != sk_c7 ),
inference(component_clause,[status(thm)],[f317]) ).
fof(f320,definition,
( sQ18_spl
<=> sk_c6 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f322,plain,
( sQ18_spl
| sk_c6 != sk_c6 ),
inference(component_clause,[status(thm)],[f320]) ).
fof(f323,plain,
( ~ sQ11_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ12_spl
| ~ sQ18_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f316,f317,f320,f154,f82,f118,f109,f145]) ).
fof(f324,plain,
( sQ18_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f322]) ).
fof(f325,plain,
sQ18_spl,
inference(contradiction_clause,[status(thm)],[f324]) ).
fof(f326,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f305,f158]) ).
fof(f327,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f305,f326]) ).
fof(f332,plain,
( ~ sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| multiply(sk_c6,sk_c6) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f305,f86]) ).
fof(f337,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c6 = multiply(sk_c8,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f305,f227]) ).
fof(f338,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c6 = multiply(sk_c6,sk_c6) ),
inference(forward_demodulation,[status(thm)],[f305,f337]) ).
fof(f339,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ1_spl
| sk_c6 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f332,f338]) ).
fof(f340,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ1_spl
| sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f339,f299]) ).
fof(f341,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ1_spl
| sQ16_spl ),
inference(contradiction_clause,[status(thm)],[f340]) ).
fof(f378,plain,
( ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| multiply(sk_c2,sk_c6) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f305,f137]) ).
fof(f420,plain,
( sQ17_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c6 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f378,f319]) ).
fof(f427,plain,
( sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| multiply(sk_c6,sk_c6) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f305,f87]) ).
fof(f438,plain,
( sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ9_spl
| sk_c7 != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f308,f427]) ).
fof(f439,plain,
( sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f438]) ).
fof(f440,plain,
( sQ1_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f439]) ).
fof(f443,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ1_spl
| sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f339,f420]) ).
fof(f444,plain,
( ~ sQ10_spl
| ~ sQ11_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ1_spl
| sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f443]) ).
fof(f445,plain,
( ~ sQ16_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| multiply(sk_c6,sk_c7) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f305,f189]) ).
fof(f446,plain,
( ~ sQ16_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c6 = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f307,f445]) ).
fof(f448,plain,
( ~ sQ11_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ13_spl
| multiply(sk_c2,sk_c6) != sk_c6 ),
inference(resolution,[status(thm)],[f327,f310]) ).
fof(f452,plain,
( ~ sQ6_spl
| ~ sQ13_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c6 != sk_c6
| multiply(sk_c5,sk_c6) != sk_c6 ),
inference(paramodulation,[status(thm)],[f106,f327]) ).
fof(f453,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ13_spl
| sk_c6 != sk_c6
| multiply(sk_c1,sk_c6) != sk_c6 ),
inference(paramodulation,[status(thm)],[f311,f327]) ).
fof(f454,plain,
( ~ sQ11_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ10_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f378,f448]) ).
fof(f455,plain,
( ~ sQ11_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f454]) ).
fof(f456,plain,
( ~ sQ11_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f455]) ).
fof(f457,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f305,f164]) ).
fof(f458,definition,
( sQ19_spl
<=> sk_c7 = sk_c8 ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f460,plain,
( sQ19_spl
| sk_c7 != sk_c8 ),
inference(component_clause,[status(thm)],[f458]) ).
fof(f465,plain,
( sQ19_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| sk_c7 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f305,f460]) ).
fof(f470,plain,
( sQ19_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ16_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f446,f465]) ).
fof(f471,plain,
( sQ19_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ16_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f470]) ).
fof(f472,plain,
( sQ19_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ16_spl ),
inference(contradiction_clause,[status(thm)],[f471]) ).
fof(f512,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c4,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f248,f41]) ).
fof(f520,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(inverse(X0),X0) = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f248,f42]) ).
fof(f528,plain,
( ~ sQ11_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ15_spl
| multiply(sk_c2,sk_c6) != sk_c6 ),
inference(resolution,[status(thm)],[f457,f310]) ).
fof(f534,plain,
( ~ sQ11_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ10_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f378,f528]) ).
fof(f535,plain,
( ~ sQ11_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f534]) ).
fof(f536,plain,
( ~ sQ11_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f535]) ).
fof(f538,plain,
( ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| multiply(sk_c6,sk_c5) = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f248,f195]) ).
fof(f539,definition,
( sQ22_spl
<=> multiply(sk_c5,sk_c6) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f541,plain,
( sQ22_spl
| multiply(sk_c5,sk_c6) != sk_c6 ),
inference(component_clause,[status(thm)],[f539]) ).
fof(f542,plain,
( ~ sQ6_spl
| ~ sQ13_spl
| ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| ~ sQ18_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f452,f539,f320,f82,f118,f109,f157,f105]) ).
fof(f545,definition,
( sQ23_spl
<=> multiply(sk_c1,sk_c6) = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f548,plain,
( ~ sQ8_spl
| ~ sQ7_spl
| ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ18_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f453,f545,f320,f157,f82,f109,f118]) ).
fof(f549,definition,
( sQ24_spl
<=> sk_c7 = sk_c6 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f597,plain,
( sQ16_spl
| ~ sQ0_spl
| ~ sQ24_spl ),
inference(split_clause,[status(thm)],[f299,f549,f82,f188]) ).
fof(f598,plain,
( ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f226,f549,f85,f105,f101]) ).
fof(f600,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| sk_c8 = sk_c6 ),
inference(backward_demodulation,[status(thm)],[f601,f224]) ).
fof(f601,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| sk_c7 = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f224,f239]) ).
fof(f606,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| inverse(X0) != sk_c7
| multiply(X0,sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f601,f283]) ).
fof(f607,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f601,f606]) ).
fof(f611,plain,
( ~ sQ6_spl
| ~ sQ13_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ1_spl
| sk_c6 != sk_c6
| multiply(sk_c5,sk_c6) != sk_c6 ),
inference(paramodulation,[status(thm)],[f106,f607]) ).
fof(f616,plain,
( ~ sQ6_spl
| ~ sQ13_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ18_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f611,f539,f320,f85,f101,f89,f97,f93,f157,f105]) ).
fof(f633,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c6,sk_c6) = sk_c7 ),
inference(forward_demodulation,[status(thm)],[f601,f232]) ).
fof(f634,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| multiply(sk_c6,sk_c6) = sk_c6 ),
inference(forward_demodulation,[status(thm)],[f601,f633]) ).
fof(f635,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c6 = multiply(inverse(sk_c6),sk_c6) ),
inference(paramodulation,[status(thm)],[f634,f199]) ).
fof(f637,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c6 = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f520,f635]) ).
fof(f640,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c6) != sk_c7 ),
inference(forward_demodulation,[status(thm)],[f600,f155]) ).
fof(f641,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| inverse(X0) != sk_c8
| multiply(X0,sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f601,f640]) ).
fof(f642,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c6) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f600,f641]) ).
fof(f655,plain,
( ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ5_spl
| multiply(sk_c4,sk_c5) = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f637,f538]) ).
fof(f658,plain,
( ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| inverse(sk_c5) = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f637,f106]) ).
fof(f659,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| sk_c8 = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f637,f600]) ).
fof(f660,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| sk_c7 = sk_c4 ),
inference(backward_demodulation,[status(thm)],[f637,f601]) ).
fof(f664,plain,
( ~ sQ6_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ5_spl
| sk_c5 = sk_c4 ),
inference(forward_demodulation,[status(thm)],[f512,f655]) ).
fof(f665,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| sk_c6 = sk_c5 ),
inference(backward_demodulation,[status(thm)],[f664,f637]) ).
fof(f668,plain,
! [X0] :
( ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ5_spl
| multiply(sk_c5,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f664,f512]) ).
fof(f670,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| sk_c8 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f664,f659]) ).
fof(f674,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| sk_c7 = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f664,f660]) ).
fof(f678,plain,
( ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| inverse(sk_c5) = sk_c5 ),
inference(forward_demodulation,[status(thm)],[f664,f658]) ).
fof(f729,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c5) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f665,f642]) ).
fof(f730,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| inverse(X0) != sk_c6
| multiply(X0,sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f665,f729]) ).
fof(f731,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| inverse(X0) != sk_c5
| multiply(X0,sk_c5) != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f665,f730]) ).
fof(f732,plain,
( ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ12_spl
| multiply(sk_c5,sk_c5) != sk_c5 ),
inference(resolution,[status(thm)],[f731,f678]) ).
fof(f734,plain,
( ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ12_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f668,f732]) ).
fof(f735,plain,
( ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f734]) ).
fof(f736,plain,
( ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f735]) ).
fof(f737,plain,
( sQ22_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ5_spl
| sk_c6 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f668,f541]) ).
fof(f738,plain,
( sQ22_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ5_spl
| sk_c5 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f665,f737]) ).
fof(f739,plain,
( sQ22_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ5_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f665,f738]) ).
fof(f740,plain,
( sQ22_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f739]) ).
fof(f741,plain,
( sQ22_spl
| ~ sQ2_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ1_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f740]) ).
fof(f742,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| multiply(sk_c5,sk_c7) != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f670,f84]) ).
fof(f743,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| sk_c7 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f668,f742]) ).
fof(f744,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| sk_c5 != sk_c6 ),
inference(forward_demodulation,[status(thm)],[f674,f743]) ).
fof(f745,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| sk_c5 != sk_c5 ),
inference(forward_demodulation,[status(thm)],[f665,f744]) ).
fof(f746,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f745]) ).
fof(f747,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ4_spl
| ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ6_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f746]) ).
fof(f748,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,f140,f141,f142,f143,f144,f149,f150,f151,f152,f153,f166,f172,f191,f192,f245,f323,f325,f341,f440,f444,f456,f472,f536,f542,f548,f597,f598,f616,f736,f741,f747]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP296-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n009.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 20 20:08:28 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.12/0.40 % Refutation found
% 0.12/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.42 % Elapsed time: 0.063660 seconds
% 0.12/0.42 % CPU time: 0.203460 seconds
% 0.12/0.42 % Total memory used: 104.871 MB
% 0.12/0.42 % Net memory used: 104.669 MB
%------------------------------------------------------------------------------