TSTP Solution File: GRP175-4 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GRP175-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n026.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 0.60s 0.81s
% Output : CNFRefutation 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 24
% Syntax : Number of clauses : 64 ( 37 unt; 0 nHn; 44 RR)
% Number of literals : 104 ( 103 equ; 43 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 65 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(left_identity,axiom,
multiply(identity,X) = X ).
cnf(left_inverse,axiom,
multiply(inverse(X),X) = identity ).
cnf(symmetry_of_glb,axiom,
greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X) ).
cnf(symmetry_of_lub,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X) ).
cnf(lub_absorbtion,axiom,
least_upper_bound(X,greatest_lower_bound(X,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(p06d_1,hypothesis,
greatest_lower_bound(identity,b) = identity ).
cnf(prove_p06d,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_66),least_upper_bound(X_66,X_67)) = least_upper_bound(multiply(inverse(X_66),X_66),multiply(inverse(X_66),X_67)),
inference(subst,[],[monotony_lub1:[bind(X,$fot(inverse(X_66))),bind(Y,$fot(X_66)),bind(Z,$fot(X_67))]]) ).
cnf(refute_0_1,plain,
multiply(inverse(X_66),X_66) = identity,
inference(subst,[],[left_inverse:[bind(X,$fot(X_66))]]) ).
cnf(refute_0_2,plain,
( multiply(inverse(X_66),X_66) != identity
| multiply(inverse(X_66),least_upper_bound(X_66,X_67)) != least_upper_bound(multiply(inverse(X_66),X_66),multiply(inverse(X_66),X_67))
| multiply(inverse(X_66),least_upper_bound(X_66,X_67)) = least_upper_bound(identity,multiply(inverse(X_66),X_67)) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(inverse(X_66),least_upper_bound(X_66,X_67)),least_upper_bound(multiply(inverse(X_66),X_66),multiply(inverse(X_66),X_67))) ),[1,0],$fot(identity)]]) ).
cnf(refute_0_3,plain,
( multiply(inverse(X_66),least_upper_bound(X_66,X_67)) != least_upper_bound(multiply(inverse(X_66),X_66),multiply(inverse(X_66),X_67))
| multiply(inverse(X_66),least_upper_bound(X_66,X_67)) = least_upper_bound(identity,multiply(inverse(X_66),X_67)) ),
inference(resolve,[$cnf( $equal(multiply(inverse(X_66),X_66),identity) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
multiply(inverse(X_66),least_upper_bound(X_66,X_67)) = least_upper_bound(identity,multiply(inverse(X_66),X_67)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_66),least_upper_bound(X_66,X_67)),least_upper_bound(multiply(inverse(X_66),X_66),multiply(inverse(X_66),X_67))) )],[refute_0_0,refute_0_3]) ).
cnf(refute_0_5,plain,
X0 = X0,
introduced(tautology,[refl,[$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( $equal(X0,X0) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( multiply(inverse(X_66),least_upper_bound(X_66,X_67)) != least_upper_bound(identity,multiply(inverse(X_66),X_67))
| least_upper_bound(identity,multiply(inverse(X_66),X_67)) = multiply(inverse(X_66),least_upper_bound(X_66,X_67)) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(multiply(inverse(X_66),least_upper_bound(X_66,X_67)))),bind(Y0,$fot(least_upper_bound(identity,multiply(inverse(X_66),X_67))))]]) ).
cnf(refute_0_9,plain,
least_upper_bound(identity,multiply(inverse(X_66),X_67)) = multiply(inverse(X_66),least_upper_bound(X_66,X_67)),
inference(resolve,[$cnf( $equal(multiply(inverse(X_66),least_upper_bound(X_66,X_67)),least_upper_bound(identity,multiply(inverse(X_66),X_67))) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
least_upper_bound(identity,multiply(inverse(a),multiply(b,a))) = multiply(inverse(a),least_upper_bound(a,multiply(b,a))),
inference(subst,[],[refute_0_9:[bind(X_66,$fot(a)),bind(X_67,$fot(multiply(b,a)))]]) ).
cnf(refute_0_11,plain,
( multiply(inverse(a),least_upper_bound(a,multiply(b,a))) != multiply(inverse(a),multiply(b,a))
| least_upper_bound(identity,multiply(inverse(a),multiply(b,a))) != multiply(inverse(a),least_upper_bound(a,multiply(b,a)))
| least_upper_bound(identity,multiply(inverse(a),multiply(b,a))) = multiply(inverse(a),multiply(b,a)) ),
introduced(tautology,[equality,[$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( $equal(least_upper_bound(identity,multiply(inverse(a),multiply(b,a))),multiply(inverse(a),multiply(b,a))) )],[refute_0_12,prove_p06d]) ).
cnf(refute_0_14,plain,
least_upper_bound(b,greatest_lower_bound(b,identity)) = b,
inference(subst,[],[lub_absorbtion:[bind(X,$fot(b)),bind(Y,$fot(identity))]]) ).
cnf(refute_0_15,plain,
( greatest_lower_bound(X,Y) != greatest_lower_bound(Y,X)
| greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(greatest_lower_bound(X,Y))),bind(Y0,$fot(greatest_lower_bound(Y,X)))]]) ).
cnf(refute_0_16,plain,
greatest_lower_bound(Y,X) = greatest_lower_bound(X,Y),
inference(resolve,[$cnf( $equal(greatest_lower_bound(X,Y),greatest_lower_bound(Y,X)) )],[symmetry_of_glb,refute_0_15]) ).
cnf(refute_0_17,plain,
greatest_lower_bound(identity,b) = greatest_lower_bound(b,identity),
inference(subst,[],[refute_0_16:[bind(X,$fot(b)),bind(Y,$fot(identity))]]) ).
cnf(refute_0_18,plain,
( greatest_lower_bound(identity,b) != greatest_lower_bound(b,identity)
| greatest_lower_bound(identity,b) != identity
| greatest_lower_bound(b,identity) = identity ),
introduced(tautology,[equality,[$cnf( $equal(greatest_lower_bound(identity,b),identity) ),[0],$fot(greatest_lower_bound(b,identity))]]) ).
cnf(refute_0_19,plain,
( greatest_lower_bound(identity,b) != identity
| greatest_lower_bound(b,identity) = identity ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,b),greatest_lower_bound(b,identity)) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
greatest_lower_bound(b,identity) = identity,
inference(resolve,[$cnf( $equal(greatest_lower_bound(identity,b),identity) )],[p06d_1,refute_0_19]) ).
cnf(refute_0_21,plain,
( greatest_lower_bound(b,identity) != identity
| least_upper_bound(b,greatest_lower_bound(b,identity)) != b
| least_upper_bound(b,identity) = b ),
introduced(tautology,[equality,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(b,identity)),b) ),[0,1],$fot(identity)]]) ).
cnf(refute_0_22,plain,
( least_upper_bound(b,greatest_lower_bound(b,identity)) != b
| least_upper_bound(b,identity) = b ),
inference(resolve,[$cnf( $equal(greatest_lower_bound(b,identity),identity) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
least_upper_bound(b,identity) = b,
inference(resolve,[$cnf( $equal(least_upper_bound(b,greatest_lower_bound(b,identity)),b) )],[refute_0_14,refute_0_22]) ).
cnf(refute_0_24,plain,
multiply(least_upper_bound(b,identity),a) = multiply(least_upper_bound(b,identity),a),
introduced(tautology,[refl,[$fot(multiply(least_upper_bound(b,identity),a))]]) ).
cnf(refute_0_25,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_26,plain,
( least_upper_bound(b,identity) != b
| multiply(least_upper_bound(b,identity),a) = multiply(b,a) ),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,identity),a),multiply(least_upper_bound(b,identity),a)) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
multiply(least_upper_bound(b,identity),a) = multiply(b,a),
inference(resolve,[$cnf( $equal(least_upper_bound(b,identity),b) )],[refute_0_23,refute_0_26]) ).
cnf(refute_0_28,plain,
multiply(least_upper_bound(X_86,identity),X_85) = least_upper_bound(multiply(X_86,X_85),multiply(identity,X_85)),
inference(subst,[],[monotony_lub2:[bind(X,$fot(X_85)),bind(Y,$fot(X_86)),bind(Z,$fot(identity))]]) ).
cnf(refute_0_29,plain,
multiply(identity,X_85) = X_85,
inference(subst,[],[left_identity:[bind(X,$fot(X_85))]]) ).
cnf(refute_0_30,plain,
( multiply(identity,X_85) != X_85
| multiply(least_upper_bound(X_86,identity),X_85) != least_upper_bound(multiply(X_86,X_85),multiply(identity,X_85))
| multiply(least_upper_bound(X_86,identity),X_85) = least_upper_bound(multiply(X_86,X_85),X_85) ),
introduced(tautology,[equality,[$cnf( $equal(multiply(least_upper_bound(X_86,identity),X_85),least_upper_bound(multiply(X_86,X_85),multiply(identity,X_85))) ),[1,1],$fot(X_85)]]) ).
cnf(refute_0_31,plain,
( multiply(least_upper_bound(X_86,identity),X_85) != least_upper_bound(multiply(X_86,X_85),multiply(identity,X_85))
| multiply(least_upper_bound(X_86,identity),X_85) = least_upper_bound(multiply(X_86,X_85),X_85) ),
inference(resolve,[$cnf( $equal(multiply(identity,X_85),X_85) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
multiply(least_upper_bound(X_86,identity),X_85) = least_upper_bound(multiply(X_86,X_85),X_85),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_86,identity),X_85),least_upper_bound(multiply(X_86,X_85),multiply(identity,X_85))) )],[refute_0_28,refute_0_31]) ).
cnf(refute_0_33,plain,
least_upper_bound(X_18,X_17) = least_upper_bound(X_17,X_18),
inference(subst,[],[symmetry_of_lub:[bind(X,$fot(X_18)),bind(Y,$fot(X_17))]]) ).
cnf(refute_0_34,plain,
least_upper_bound(multiply(X_86,X_85),X_85) = least_upper_bound(X_85,multiply(X_86,X_85)),
inference(subst,[],[refute_0_33:[bind(X_17,$fot(X_85)),bind(X_18,$fot(multiply(X_86,X_85)))]]) ).
cnf(refute_0_35,plain,
( multiply(least_upper_bound(X_86,identity),X_85) != least_upper_bound(multiply(X_86,X_85),X_85)
| least_upper_bound(multiply(X_86,X_85),X_85) != least_upper_bound(X_85,multiply(X_86,X_85))
| multiply(least_upper_bound(X_86,identity),X_85) = least_upper_bound(X_85,multiply(X_86,X_85)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiply(least_upper_bound(X_86,identity),X_85),least_upper_bound(X_85,multiply(X_86,X_85))) ),[0],$fot(least_upper_bound(multiply(X_86,X_85),X_85))]]) ).
cnf(refute_0_36,plain,
( multiply(least_upper_bound(X_86,identity),X_85) != least_upper_bound(multiply(X_86,X_85),X_85)
| multiply(least_upper_bound(X_86,identity),X_85) = least_upper_bound(X_85,multiply(X_86,X_85)) ),
inference(resolve,[$cnf( $equal(least_upper_bound(multiply(X_86,X_85),X_85),least_upper_bound(X_85,multiply(X_86,X_85))) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
multiply(least_upper_bound(X_86,identity),X_85) = least_upper_bound(X_85,multiply(X_86,X_85)),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_86,identity),X_85),least_upper_bound(multiply(X_86,X_85),X_85)) )],[refute_0_32,refute_0_36]) ).
cnf(refute_0_38,plain,
( multiply(least_upper_bound(X_86,identity),X_85) != least_upper_bound(X_85,multiply(X_86,X_85))
| least_upper_bound(X_85,multiply(X_86,X_85)) = multiply(least_upper_bound(X_86,identity),X_85) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(multiply(least_upper_bound(X_86,identity),X_85))),bind(Y0,$fot(least_upper_bound(X_85,multiply(X_86,X_85))))]]) ).
cnf(refute_0_39,plain,
least_upper_bound(X_85,multiply(X_86,X_85)) = multiply(least_upper_bound(X_86,identity),X_85),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(X_86,identity),X_85),least_upper_bound(X_85,multiply(X_86,X_85))) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
least_upper_bound(a,multiply(b,a)) = multiply(least_upper_bound(b,identity),a),
inference(subst,[],[refute_0_39:[bind(X_85,$fot(a)),bind(X_86,$fot(b))]]) ).
cnf(refute_0_41,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_42,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_7,refute_0_41]) ).
cnf(refute_0_43,plain,
( multiply(least_upper_bound(b,identity),a) != multiply(b,a)
| least_upper_bound(a,multiply(b,a)) != multiply(least_upper_bound(b,identity),a)
| least_upper_bound(a,multiply(b,a)) = multiply(b,a) ),
inference(subst,[],[refute_0_42:[bind(X0,$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_44,plain,
( multiply(least_upper_bound(b,identity),a) != multiply(b,a)
| least_upper_bound(a,multiply(b,a)) = multiply(b,a) ),
inference(resolve,[$cnf( $equal(least_upper_bound(a,multiply(b,a)),multiply(least_upper_bound(b,identity),a)) )],[refute_0_40,refute_0_43]) ).
cnf(refute_0_45,plain,
least_upper_bound(a,multiply(b,a)) = multiply(b,a),
inference(resolve,[$cnf( $equal(multiply(least_upper_bound(b,identity),a),multiply(b,a)) )],[refute_0_27,refute_0_44]) ).
cnf(refute_0_46,plain,
multiply(inverse(a),least_upper_bound(a,multiply(b,a))) = multiply(inverse(a),least_upper_bound(a,multiply(b,a))),
introduced(tautology,[refl,[$fot(multiply(inverse(a),least_upper_bound(a,multiply(b,a))))]]) ).
cnf(refute_0_47,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_48,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( $equal(multiply(inverse(a),least_upper_bound(a,multiply(b,a))),multiply(inverse(a),least_upper_bound(a,multiply(b,a)))) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
multiply(inverse(a),least_upper_bound(a,multiply(b,a))) = multiply(inverse(a),multiply(b,a)),
inference(resolve,[$cnf( $equal(least_upper_bound(a,multiply(b,a)),multiply(b,a)) )],[refute_0_45,refute_0_48]) ).
cnf(refute_0_50,plain,
( multiply(inverse(a),multiply(b,a)) != multiply(inverse(a),multiply(b,a))
| multiply(inverse(a),least_upper_bound(a,multiply(b,a))) != multiply(inverse(a),multiply(b,a))
| multiply(inverse(a),least_upper_bound(a,multiply(b,a))) = multiply(inverse(a),multiply(b,a)) ),
introduced(tautology,[equality,[$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_51,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( $equal(multiply(inverse(a),least_upper_bound(a,multiply(b,a))),multiply(inverse(a),multiply(b,a))) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
multiply(inverse(a),multiply(b,a)) != multiply(inverse(a),multiply(b,a)),
inference(resolve,[$cnf( $equal(multiply(inverse(a),least_upper_bound(a,multiply(b,a))),multiply(inverse(a),multiply(b,a))) )],[refute_0_51,refute_0_13]) ).
cnf(refute_0_53,plain,
multiply(inverse(a),multiply(b,a)) = multiply(inverse(a),multiply(b,a)),
introduced(tautology,[refl,[$fot(multiply(inverse(a),multiply(b,a)))]]) ).
cnf(refute_0_54,plain,
$false,
inference(resolve,[$cnf( $equal(multiply(inverse(a),multiply(b,a)),multiply(inverse(a),multiply(b,a))) )],[refute_0_53,refute_0_52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP175-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Mon Jun 13 05:17:50 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.60/0.81 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.60/0.81
% 0.60/0.81 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.60/0.82
%------------------------------------------------------------------------------