%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP175-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 10:37:19 EDT 2022
% Result : Unsatisfiable 0.19s 0.52s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 21
% Syntax : Number of clauses : 57 ( 32 unt; 0 nHn; 40 RR)
% Number of literals : 94 ( 93 equ; 40 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 59 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
multiply(identity,X) = X ).
cnf(left_inverse,axiom,
multiply(inverse(X),X) = identity ).
cnf(symmetry_of_lub,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X) ).
cnf(monotony_lub1,axiom,
multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)) ).
cnf(monotony_lub2,axiom,
multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)) ).
cnf(p06a_1,hypothesis,
least_upper_bound(identity,b) = b ).
cnf(prove_p06a,negated_conjecture,
least_upper_bound(identity,multiply(inverse(a),multiply(b,a))) != multiply(inverse(a),multiply(b,a)) ).
cnf(refute_0_0,plain,
multiply(inverse(X_37),least_upper_bound(X_37,X_38)) = least_upper_bound(multiply(inverse(X_37),X_37),multiply(inverse(X_37),X_38)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(inverse(X_37))),bind(Y,$fot(X_37)),bind(Z,$fot(X_38))]]) ).
cnf(refute_0_1,plain,
multiply(inverse(X_37),X_37) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_37))]]) ).
cnf(refute_0_2,plain,
( multiply(inverse(X_37),X_37) != identity
| multiply(inverse(X_37),least_upper_bound(X_37,X_38)) != least_upper_bound(multiply(inverse(X_37),X_37),multiply(inverse(X_37),X_38))
| multiply(inverse(X_37),least_upper_bound(X_37,X_38)) = least_upper_bound(identity,multiply(inverse(X_37),X_38)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_37),least_upper_bound(X_37,X_38)),least_upper_bound(multiply(inverse(X_37),X_37),multiply(inverse(X_37),X_38))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_3,plain,
( multiply(inverse(X_37),least_upper_bound(X_37,X_38)) != least_upper_bound(multiply(inverse(X_37),X_37),multiply(inverse(X_37),X_38))
| multiply(inverse(X_37),least_upper_bound(X_37,X_38)) = least_upper_bound(identity,multiply(inverse(X_37),X_38)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_37),X_37),identity) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
multiply(inverse(X_37),least_upper_bound(X_37,X_38)) = least_upper_bound(identity,multiply(inverse(X_37),X_38)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_37),least_upper_bound(X_37,X_38)),least_upper_bound(multiply(inverse(X_37),X_37),multiply(inverse(X_37),X_38))) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_6,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_7,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( multiply(inverse(X_37),least_upper_bound(X_37,X_38)) != least_upper_bound(identity,multiply(inverse(X_37),X_38))
| least_upper_bound(identity,multiply(inverse(X_37),X_38)) = multiply(inverse(X_37),least_upper_bound(X_37,X_38)) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(multiply(inverse(X_37),least_upper_bound(X_37,X_38)))),bind(Y0,$fot(least_upper_bound(identity,multiply(inverse(X_37),X_38))))]]) ).
cnf(refute_0_9,plain,
least_upper_bound(identity,multiply(inverse(X_37),X_38)) = multiply(inverse(X_37),least_upper_bound(X_37,X_38)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_37),least_upper_bound(X_37,X_38)),least_upper_bound(identity,multiply(inverse(X_37),X_38))) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
least_upper_bound(identity,multiply(inverse(a),multiply(b,a))) = multiply(inverse(a),least_upper_bound(a,multiply(b,a))),
inference(subst,[],[refute_0_9:[bind(X_37,$fot(a)),bind(X_38,$fot(multiply(b,a)))]]) ).
cnf(refute_0_11,plain,
( multiply(inverse(a),least_upper_bound(a,multiply(b,a))) != multiply(inverse(a),multiply(b,a))
| least_upper_bound(identity,multiply(inverse(a),multiply(b,a))) != multiply(inverse(a),least_upper_bound(a,multiply(b,a)))
| least_upper_bound(identity,multiply(inverse(a),multiply(b,a))) = multiply(inverse(a),multiply(b,a)) ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(a),multiply(b,a))),multiply(inverse(a),least_upper_bound(a,multiply(b,a)))) ),[1],$fot(multiply(inverse(a),multiply(b,a)))]]) ).
cnf(refute_0_12,plain,
( multiply(inverse(a),least_upper_bound(a,multiply(b,a))) != multiply(inverse(a),multiply(b,a))
| least_upper_bound(identity,multiply(inverse(a),multiply(b,a))) = multiply(inverse(a),multiply(b,a)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(a),multiply(b,a))),multiply(inverse(a),least_upper_bound(a,multiply(b,a)))) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
multiply(inverse(a),least_upper_bound(a,multiply(b,a))) != multiply(inverse(a),multiply(b,a)),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,multiply(inverse(a),multiply(b,a))),multiply(inverse(a),multiply(b,a))) )],[refute_0_12,prove_p06a]) ).
cnf(refute_0_14,plain,
( least_upper_bound(X,Y) != least_upper_bound(Y,X)
| least_upper_bound(Y,X) = least_upper_bound(X,Y) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(least_upper_bound(X,Y))),bind(Y0,$fot(least_upper_bound(Y,X)))]]) ).
cnf(refute_0_15,plain,
least_upper_bound(Y,X) = least_upper_bound(X,Y),
inference(resolve,[$cnf( $equal(least_upper_bound(X,Y),least_upper_bound(Y,X)) )],[symmetry_of_lub,refute_0_14]) ).
cnf(refute_0_16,plain,
least_upper_bound(identity,b) = least_upper_bound(b,identity),
inference(subst,[],[refute_0_15:[bind(X,$fot(b)),bind(Y,$fot(identity))]]) ).
cnf(refute_0_17,plain,
( least_upper_bound(identity,b) != b
| least_upper_bound(identity,b) != least_upper_bound(b,identity)
| least_upper_bound(b,identity) = b ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(identity,b),b) ),[0],$fot(least_upper_bound(b,identity))]]) ).
cnf(refute_0_18,plain,
( least_upper_bound(identity,b) != b
| least_upper_bound(b,identity) = b ),
inference(resolve,[$cnf( $equal(least_upper_bound(identity,b),least_upper_bound(b,identity)) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
least_upper_bound(b,identity) = b,
inference(resolve,[$cnf( $equal(least_upper_bound(identity,b),b) )],[p06a_1,refute_0_18]) ).
cnf(refute_0_20,plain,
multiply(least_upper_bound(b,identity),a) = multiply(least_upper_bound(b,identity),a),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(b,identity),a))]]) ).
cnf(refute_0_21,plain,
( multiply(least_upper_bound(b,identity),a) != multiply(least_upper_bound(b,identity),a)
| least_upper_bound(b,identity) != b
| multiply(least_upper_bound(b,identity),a) = multiply(b,a) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(b,identity),a),multiply(least_upper_bound(b,identity),a)) ),[1,0],$fot(b)]]) ).
cnf(refute_0_22,plain,
( least_upper_bound(b,identity) != b
| multiply(least_upper_bound(b,identity),a) = multiply(b,a) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,identity),a),multiply(least_upper_bound(b,identity),a)) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
multiply(least_upper_bound(b,identity),a) = multiply(b,a),
inference(resolve,[$cnf( $equal(least_upper_bound(b,identity),b) )],[refute_0_19,refute_0_22]) ).
cnf(refute_0_24,plain,
multiply(least_upper_bound(X_51,identity),X_50) = least_upper_bound(multiply(X_51,X_50),multiply(identity,X_50)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_50)),bind(Y,$fot(X_51)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_25,plain,
multiply(identity,X_50) = X_50,
inference(subst,[],[left_identity:[bind(X,$fot(X_50))]]) ).
cnf(refute_0_26,plain,
( multiply(identity,X_50) != X_50
| multiply(least_upper_bound(X_51,identity),X_50) != least_upper_bound(multiply(X_51,X_50),multiply(identity,X_50))
| multiply(least_upper_bound(X_51,identity),X_50) = least_upper_bound(multiply(X_51,X_50),X_50) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_51,identity),X_50),least_upper_bound(multiply(X_51,X_50),multiply(identity,X_50))) ),[1,1],$fot(X_50)]]) ).
cnf(refute_0_27,plain,
( multiply(least_upper_bound(X_51,identity),X_50) != least_upper_bound(multiply(X_51,X_50),multiply(identity,X_50))
| multiply(least_upper_bound(X_51,identity),X_50) = least_upper_bound(multiply(X_51,X_50),X_50) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_50),X_50) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
multiply(least_upper_bound(X_51,identity),X_50) = least_upper_bound(multiply(X_51,X_50),X_50),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_51,identity),X_50),least_upper_bound(multiply(X_51,X_50),multiply(identity,X_50))) )],[refute_0_24,refute_0_27]) ).
cnf(refute_0_29,plain,
least_upper_bound(multiply(X_51,X_50),X_50) = least_upper_bound(X_50,multiply(X_51,X_50)),
inference(subst,[],[refute_0_15:[bind(X,$fot(X_50)),bind(Y,$fot(multiply(X_51,X_50)))]]) ).
cnf(refute_0_30,plain,
( multiply(least_upper_bound(X_51,identity),X_50) != least_upper_bound(multiply(X_51,X_50),X_50)
| least_upper_bound(multiply(X_51,X_50),X_50) != least_upper_bound(X_50,multiply(X_51,X_50))
| multiply(least_upper_bound(X_51,identity),X_50) = least_upper_bound(X_50,multiply(X_51,X_50)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_51,identity),X_50),least_upper_bound(X_50,multiply(X_51,X_50))) ),[0],$fot(least_upper_bound(multiply(X_51,X_50),X_50))]]) ).
cnf(refute_0_31,plain,
( multiply(least_upper_bound(X_51,identity),X_50) != least_upper_bound(multiply(X_51,X_50),X_50)
| multiply(least_upper_bound(X_51,identity),X_50) = least_upper_bound(X_50,multiply(X_51,X_50)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_51,X_50),X_50),least_upper_bound(X_50,multiply(X_51,X_50))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
multiply(least_upper_bound(X_51,identity),X_50) = least_upper_bound(X_50,multiply(X_51,X_50)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_51,identity),X_50),least_upper_bound(multiply(X_51,X_50),X_50)) )],[refute_0_28,refute_0_31]) ).
cnf(refute_0_33,plain,
( multiply(least_upper_bound(X_51,identity),X_50) != least_upper_bound(X_50,multiply(X_51,X_50))
| least_upper_bound(X_50,multiply(X_51,X_50)) = multiply(least_upper_bound(X_51,identity),X_50) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(multiply(least_upper_bound(X_51,identity),X_50))),bind(Y0,$fot(least_upper_bound(X_50,multiply(X_51,X_50))))]]) ).
cnf(refute_0_34,plain,
least_upper_bound(X_50,multiply(X_51,X_50)) = multiply(least_upper_bound(X_51,identity),X_50),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_51,identity),X_50),least_upper_bound(X_50,multiply(X_51,X_50))) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
least_upper_bound(a,multiply(b,a)) = multiply(least_upper_bound(b,identity),a),
inference(subst,[],[refute_0_34:[bind(X_50,$fot(a)),bind(X_51,$fot(b))]]) ).
cnf(refute_0_36,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_37,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_7,refute_0_36]) ).
cnf(refute_0_38,plain,
( multiply(least_upper_bound(b,identity),a) != multiply(b,a)
| least_upper_bound(a,multiply(b,a)) != multiply(least_upper_bound(b,identity),a)
| least_upper_bound(a,multiply(b,a)) = multiply(b,a) ),
inference(subst,[],[refute_0_37:[bind(X0,$fot(least_upper_bound(a,multiply(b,a)))),bind(Y0,$fot(multiply(least_upper_bound(b,identity),a))),bind(Z0,$fot(multiply(b,a)))]]) ).
cnf(refute_0_39,plain,
( multiply(least_upper_bound(b,identity),a) != multiply(b,a)
| least_upper_bound(a,multiply(b,a)) = multiply(b,a) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,multiply(b,a)),multiply(least_upper_bound(b,identity),a)) )],[refute_0_35,refute_0_38]) ).
cnf(refute_0_40,plain,
least_upper_bound(a,multiply(b,a)) = multiply(b,a),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,identity),a),multiply(b,a)) )],[refute_0_23,refute_0_39]) ).
cnf(refute_0_41,plain,
multiply(inverse(a),least_upper_bound(a,multiply(b,a))) = multiply(inverse(a),least_upper_bound(a,multiply(b,a))),
introduced(tautology,[refl,[$fot(multiply(inverse(a),least_upper_bound(a,multiply(b,a))))]]) ).
cnf(refute_0_42,plain,
( multiply(inverse(a),least_upper_bound(a,multiply(b,a))) != multiply(inverse(a),least_upper_bound(a,multiply(b,a)))
| least_upper_bound(a,multiply(b,a)) != multiply(b,a)
| multiply(inverse(a),least_upper_bound(a,multiply(b,a))) = multiply(inverse(a),multiply(b,a)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(a),least_upper_bound(a,multiply(b,a))),multiply(inverse(a),least_upper_bound(a,multiply(b,a)))) ),[1,1],$fot(multiply(b,a))]]) ).
cnf(refute_0_43,plain,
( least_upper_bound(a,multiply(b,a)) != multiply(b,a)
| multiply(inverse(a),least_upper_bound(a,multiply(b,a))) = multiply(inverse(a),multiply(b,a)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(a),least_upper_bound(a,multiply(b,a))),multiply(inverse(a),least_upper_bound(a,multiply(b,a)))) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
multiply(inverse(a),least_upper_bound(a,multiply(b,a))) = multiply(inverse(a),multiply(b,a)),
inference(resolve,[$cnf( $equal(least_upper_bound(a,multiply(b,a)),multiply(b,a)) )],[refute_0_40,refute_0_43]) ).
cnf(refute_0_45,plain,
( multiply(inverse(a),multiply(b,a)) != multiply(inverse(a),multiply(b,a))
| multiply(inverse(a),least_upper_bound(a,multiply(b,a))) != multiply(inverse(a),multiply(b,a))
| multiply(inverse(a),least_upper_bound(a,multiply(b,a))) = multiply(inverse(a),multiply(b,a)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(a),least_upper_bound(a,multiply(b,a))),multiply(inverse(a),multiply(b,a))) ),[1],$fot(multiply(inverse(a),multiply(b,a)))]]) ).
cnf(refute_0_46,plain,
( multiply(inverse(a),multiply(b,a)) != multiply(inverse(a),multiply(b,a))
| multiply(inverse(a),least_upper_bound(a,multiply(b,a))) = multiply(inverse(a),multiply(b,a)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(a),least_upper_bound(a,multiply(b,a))),multiply(inverse(a),multiply(b,a))) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
multiply(inverse(a),multiply(b,a)) != multiply(inverse(a),multiply(b,a)),
inference(resolve,[$cnf( $equal(multiply(inverse(a),least_upper_bound(a,multiply(b,a))),multiply(inverse(a),multiply(b,a))) )],[refute_0_46,refute_0_13]) ).
cnf(refute_0_48,plain,
multiply(inverse(a),multiply(b,a)) = multiply(inverse(a),multiply(b,a)),
introduced(tautology,[refl,[$fot(multiply(inverse(a),multiply(b,a)))]]) ).
cnf(refute_0_49,plain,
$false,
inference(resolve,[$cnf( $equal(multiply(inverse(a),multiply(b,a)),multiply(inverse(a),multiply(b,a))) )],[refute_0_48,refute_0_47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP175-1 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jun 13 11:23:24 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.52 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.52
% 0.19/0.52 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.52
%------------------------------------------------------------------------------