TSTP Solution File: HEN007-4 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : HEN007-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n004.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 12:58:39 EDT 2022
% Result : Unsatisfiable 2.71s 2.89s
% Output : CNFRefutation 2.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 21
% Syntax : Number of clauses : 76 ( 39 unt; 0 nHn; 37 RR)
% Number of literals : 124 ( 62 equ; 49 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 83 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(quotient_less_equal1,axiom,
( ~ less_equal(X,Y)
| divide(X,Y) = zero ) ).
cnf(quotient_less_equal2,axiom,
( divide(X,Y) != zero
| less_equal(X,Y) ) ).
cnf(quotient_property,axiom,
less_equal(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)) ).
cnf(zero_is_smallest,axiom,
less_equal(zero,X) ).
cnf(less_equal_and_equal,axiom,
( ~ less_equal(X,Y)
| ~ less_equal(Y,X)
| X = Y ) ).
cnf(zero_divide_anything_is_zero,axiom,
divide(zero,X) = zero ).
cnf(x_divide_x_is_zero,axiom,
divide(X,X) = zero ).
cnf(property_of_divide1,axiom,
( ~ less_equal(divide(X,Y),Z)
| less_equal(divide(X,Z),Y) ) ).
cnf(a_LE_b,hypothesis,
less_equal(a,b) ).
cnf(prove_c_divide_b_LE_c_divide_a,negated_conjecture,
~ less_equal(divide(c,b),divide(c,a)) ).
cnf(refute_0_0,plain,
( ~ less_equal(divide(X_314,divide(X_314,a)),b)
| less_equal(divide(X_314,b),divide(X_314,a)) ),
inference(subst,[],[property_of_divide1:[bind(X,$fot(X_314)),bind(Y,$fot(divide(X_314,a))),bind(Z,$fot(b))]]) ).
cnf(refute_0_1,plain,
( divide(divide(X_284,divide(X_284,a)),b) != zero
| less_equal(divide(X_284,divide(X_284,a)),b) ),
inference(subst,[],[quotient_less_equal2:[bind(X,$fot(divide(X_284,divide(X_284,a)))),bind(Y,$fot(b))]]) ).
cnf(refute_0_2,plain,
less_equal(zero,X_227),
inference(subst,[],[zero_is_smallest:[bind(X,$fot(X_227))]]) ).
cnf(refute_0_3,plain,
( ~ less_equal(X_227,zero)
| ~ less_equal(zero,X_227)
| zero = X_227 ),
inference(subst,[],[less_equal_and_equal:[bind(X,$fot(zero)),bind(Y,$fot(X_227))]]) ).
cnf(refute_0_4,plain,
( ~ less_equal(X_227,zero)
| zero = X_227 ),
inference(resolve,[$cnf( less_equal(zero,X_227) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ less_equal(divide(divide(X_283,divide(X_283,a)),b),zero)
| zero = divide(divide(X_283,divide(X_283,a)),b) ),
inference(subst,[],[refute_0_4:[bind(X_227,$fot(divide(divide(X_283,divide(X_283,a)),b)))]]) ).
cnf(refute_0_6,plain,
( divide(divide(divide(X_229,divide(X_229,a)),b),zero) != zero
| less_equal(divide(divide(X_229,divide(X_229,a)),b),zero) ),
inference(subst,[],[quotient_less_equal2:[bind(X,$fot(divide(divide(X_229,divide(X_229,a)),b))),bind(Y,$fot(zero))]]) ).
cnf(refute_0_7,plain,
less_equal(divide(divide(X_14,b),divide(a,b)),divide(divide(X_14,a),b)),
inference(subst,[],[quotient_property:[bind(X,$fot(X_14)),bind(Y,$fot(a)),bind(Z,$fot(b))]]) ).
cnf(refute_0_8,plain,
( ~ less_equal(a,b)
| divide(a,b) = zero ),
inference(subst,[],[quotient_less_equal1:[bind(X,$fot(a)),bind(Y,$fot(b))]]) ).
cnf(refute_0_9,plain,
divide(a,b) = zero,
inference(resolve,[$cnf( less_equal(a,b) )],[a_LE_b,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ less_equal(divide(divide(X_14,b),divide(a,b)),divide(divide(X_14,a),b))
| divide(a,b) != zero
| less_equal(divide(divide(X_14,b),zero),divide(divide(X_14,a),b)) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(divide(X_14,b),divide(a,b)),divide(divide(X_14,a),b)) ),[0,1],$fot(zero)]]) ).
cnf(refute_0_11,plain,
( ~ less_equal(divide(divide(X_14,b),divide(a,b)),divide(divide(X_14,a),b))
| less_equal(divide(divide(X_14,b),zero),divide(divide(X_14,a),b)) ),
inference(resolve,[$cnf( $equal(divide(a,b),zero) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
less_equal(divide(divide(X_14,b),zero),divide(divide(X_14,a),b)),
inference(resolve,[$cnf( less_equal(divide(divide(X_14,b),divide(a,b)),divide(divide(X_14,a),b)) )],[refute_0_7,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ less_equal(divide(divide(X_14,b),zero),divide(divide(X_14,a),b))
| less_equal(divide(divide(X_14,b),divide(divide(X_14,a),b)),zero) ),
inference(subst,[],[property_of_divide1:[bind(X,$fot(divide(X_14,b))),bind(Y,$fot(zero)),bind(Z,$fot(divide(divide(X_14,a),b)))]]) ).
cnf(refute_0_14,plain,
less_equal(divide(divide(X_14,b),divide(divide(X_14,a),b)),zero),
inference(resolve,[$cnf( less_equal(divide(divide(X_14,b),zero),divide(divide(X_14,a),b)) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
less_equal(divide(divide(divide(X_103,divide(X_103,a)),b),divide(divide(divide(X_103,divide(X_103,a)),a),b)),zero),
inference(subst,[],[refute_0_14:[bind(X_14,$fot(divide(X_103,divide(X_103,a))))]]) ).
cnf(refute_0_16,plain,
( ~ less_equal(divide(X_103,divide(X_103,X_104)),X_104)
| divide(divide(X_103,divide(X_103,X_104)),X_104) = zero ),
inference(subst,[],[quotient_less_equal1:[bind(X,$fot(divide(X_103,divide(X_103,X_104)))),bind(Y,$fot(X_104))]]) ).
cnf(refute_0_17,plain,
( divide(X_12,X_12) != zero
| less_equal(X_12,X_12) ),
inference(subst,[],[quotient_less_equal2:[bind(X,$fot(X_12)),bind(Y,$fot(X_12))]]) ).
cnf(refute_0_18,plain,
divide(X_12,X_12) = zero,
inference(subst,[],[x_divide_x_is_zero:[bind(X,$fot(X_12))]]) ).
cnf(refute_0_19,plain,
( divide(X_12,X_12) != zero
| zero != zero
| divide(X_12,X_12) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(divide(X_12,X_12),zero) ),[0],$fot(zero)]]) ).
cnf(refute_0_20,plain,
( zero != zero
| divide(X_12,X_12) = zero ),
inference(resolve,[$cnf( $equal(divide(X_12,X_12),zero) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
( zero != zero
| less_equal(X_12,X_12) ),
inference(resolve,[$cnf( $equal(divide(X_12,X_12),zero) )],[refute_0_20,refute_0_17]) ).
cnf(refute_0_22,plain,
zero = zero,
introduced(tautology,[refl,[$fot(zero)]]) ).
cnf(refute_0_23,plain,
less_equal(X_12,X_12),
inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_22,refute_0_21]) ).
cnf(refute_0_24,plain,
less_equal(divide(X_76,X_77),divide(X_76,X_77)),
inference(subst,[],[refute_0_23:[bind(X_12,$fot(divide(X_76,X_77)))]]) ).
cnf(refute_0_25,plain,
( ~ less_equal(divide(X_76,X_77),divide(X_76,X_77))
| less_equal(divide(X_76,divide(X_76,X_77)),X_77) ),
inference(subst,[],[property_of_divide1:[bind(X,$fot(X_76)),bind(Y,$fot(X_77)),bind(Z,$fot(divide(X_76,X_77)))]]) ).
cnf(refute_0_26,plain,
less_equal(divide(X_76,divide(X_76,X_77)),X_77),
inference(resolve,[$cnf( less_equal(divide(X_76,X_77),divide(X_76,X_77)) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
less_equal(divide(X_103,divide(X_103,X_104)),X_104),
inference(subst,[],[refute_0_26:[bind(X_76,$fot(X_103)),bind(X_77,$fot(X_104))]]) ).
cnf(refute_0_28,plain,
divide(divide(X_103,divide(X_103,X_104)),X_104) = zero,
inference(resolve,[$cnf( less_equal(divide(X_103,divide(X_103,X_104)),X_104) )],[refute_0_27,refute_0_16]) ).
cnf(refute_0_29,plain,
divide(divide(X_103,divide(X_103,a)),a) = zero,
inference(subst,[],[refute_0_28:[bind(X_104,$fot(a))]]) ).
cnf(refute_0_30,plain,
( ~ less_equal(divide(divide(divide(X_103,divide(X_103,a)),b),divide(divide(divide(X_103,divide(X_103,a)),a),b)),zero)
| divide(divide(X_103,divide(X_103,a)),a) != zero
| less_equal(divide(divide(divide(X_103,divide(X_103,a)),b),divide(zero,b)),zero) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(divide(divide(X_103,divide(X_103,a)),b),divide(divide(divide(X_103,divide(X_103,a)),a),b)),zero) ),[0,1,0],$fot(zero)]]) ).
cnf(refute_0_31,plain,
( ~ less_equal(divide(divide(divide(X_103,divide(X_103,a)),b),divide(divide(divide(X_103,divide(X_103,a)),a),b)),zero)
| less_equal(divide(divide(divide(X_103,divide(X_103,a)),b),divide(zero,b)),zero) ),
inference(resolve,[$cnf( $equal(divide(divide(X_103,divide(X_103,a)),a),zero) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
less_equal(divide(divide(divide(X_103,divide(X_103,a)),b),divide(zero,b)),zero),
inference(resolve,[$cnf( less_equal(divide(divide(divide(X_103,divide(X_103,a)),b),divide(divide(divide(X_103,divide(X_103,a)),a),b)),zero) )],[refute_0_15,refute_0_31]) ).
cnf(refute_0_33,plain,
divide(zero,b) = zero,
inference(subst,[],[zero_divide_anything_is_zero:[bind(X,$fot(b))]]) ).
cnf(refute_0_34,plain,
divide(divide(divide(X_103,divide(X_103,a)),b),divide(zero,b)) = divide(divide(divide(X_103,divide(X_103,a)),b),divide(zero,b)),
introduced(tautology,[refl,[$fot(divide(divide(divide(X_103,divide(X_103,a)),b),divide(zero,b)))]]) ).
cnf(refute_0_35,plain,
( divide(divide(divide(X_103,divide(X_103,a)),b),divide(zero,b)) != divide(divide(divide(X_103,divide(X_103,a)),b),divide(zero,b))
| divide(zero,b) != zero
| divide(divide(divide(X_103,divide(X_103,a)),b),divide(zero,b)) = divide(divide(divide(X_103,divide(X_103,a)),b),zero) ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(divide(X_103,divide(X_103,a)),b),divide(zero,b)),divide(divide(divide(X_103,divide(X_103,a)),b),divide(zero,b))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_36,plain,
( divide(zero,b) != zero
| divide(divide(divide(X_103,divide(X_103,a)),b),divide(zero,b)) = divide(divide(divide(X_103,divide(X_103,a)),b),zero) ),
inference(resolve,[$cnf( $equal(divide(divide(divide(X_103,divide(X_103,a)),b),divide(zero,b)),divide(divide(divide(X_103,divide(X_103,a)),b),divide(zero,b))) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
divide(divide(divide(X_103,divide(X_103,a)),b),divide(zero,b)) = divide(divide(divide(X_103,divide(X_103,a)),b),zero),
inference(resolve,[$cnf( $equal(divide(zero,b),zero) )],[refute_0_33,refute_0_36]) ).
cnf(refute_0_38,plain,
( ~ less_equal(divide(divide(divide(X_103,divide(X_103,a)),b),divide(zero,b)),zero)
| divide(divide(divide(X_103,divide(X_103,a)),b),divide(zero,b)) != divide(divide(divide(X_103,divide(X_103,a)),b),zero)
| less_equal(divide(divide(divide(X_103,divide(X_103,a)),b),zero),zero) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(divide(divide(X_103,divide(X_103,a)),b),divide(zero,b)),zero) ),[0],$fot(divide(divide(divide(X_103,divide(X_103,a)),b),zero))]]) ).
cnf(refute_0_39,plain,
( ~ less_equal(divide(divide(divide(X_103,divide(X_103,a)),b),divide(zero,b)),zero)
| less_equal(divide(divide(divide(X_103,divide(X_103,a)),b),zero),zero) ),
inference(resolve,[$cnf( $equal(divide(divide(divide(X_103,divide(X_103,a)),b),divide(zero,b)),divide(divide(divide(X_103,divide(X_103,a)),b),zero)) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
less_equal(divide(divide(divide(X_103,divide(X_103,a)),b),zero),zero),
inference(resolve,[$cnf( less_equal(divide(divide(divide(X_103,divide(X_103,a)),b),divide(zero,b)),zero) )],[refute_0_32,refute_0_39]) ).
cnf(refute_0_41,plain,
( ~ less_equal(divide(divide(divide(X_103,divide(X_103,a)),b),zero),zero)
| ~ less_equal(zero,divide(divide(divide(X_103,divide(X_103,a)),b),zero))
| divide(divide(divide(X_103,divide(X_103,a)),b),zero) = zero ),
inference(subst,[],[less_equal_and_equal:[bind(X,$fot(divide(divide(divide(X_103,divide(X_103,a)),b),zero))),bind(Y,$fot(zero))]]) ).
cnf(refute_0_42,plain,
( ~ less_equal(zero,divide(divide(divide(X_103,divide(X_103,a)),b),zero))
| divide(divide(divide(X_103,divide(X_103,a)),b),zero) = zero ),
inference(resolve,[$cnf( less_equal(divide(divide(divide(X_103,divide(X_103,a)),b),zero),zero) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
less_equal(zero,divide(divide(divide(X_103,divide(X_103,a)),b),zero)),
inference(subst,[],[zero_is_smallest:[bind(X,$fot(divide(divide(divide(X_103,divide(X_103,a)),b),zero)))]]) ).
cnf(refute_0_44,plain,
divide(divide(divide(X_103,divide(X_103,a)),b),zero) = zero,
inference(resolve,[$cnf( less_equal(zero,divide(divide(divide(X_103,divide(X_103,a)),b),zero)) )],[refute_0_43,refute_0_42]) ).
cnf(refute_0_45,plain,
divide(divide(divide(X_229,divide(X_229,a)),b),zero) = zero,
inference(subst,[],[refute_0_44:[bind(X_103,$fot(X_229))]]) ).
cnf(refute_0_46,plain,
( divide(divide(divide(X_229,divide(X_229,a)),b),zero) != zero
| zero != zero
| divide(divide(divide(X_229,divide(X_229,a)),b),zero) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(divide(divide(divide(X_229,divide(X_229,a)),b),zero),zero) ),[0],$fot(zero)]]) ).
cnf(refute_0_47,plain,
( zero != zero
| divide(divide(divide(X_229,divide(X_229,a)),b),zero) = zero ),
inference(resolve,[$cnf( $equal(divide(divide(divide(X_229,divide(X_229,a)),b),zero),zero) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
( zero != zero
| less_equal(divide(divide(X_229,divide(X_229,a)),b),zero) ),
inference(resolve,[$cnf( $equal(divide(divide(divide(X_229,divide(X_229,a)),b),zero),zero) )],[refute_0_47,refute_0_6]) ).
cnf(refute_0_49,plain,
less_equal(divide(divide(X_229,divide(X_229,a)),b),zero),
inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_22,refute_0_48]) ).
cnf(refute_0_50,plain,
less_equal(divide(divide(X_283,divide(X_283,a)),b),zero),
inference(subst,[],[refute_0_49:[bind(X_229,$fot(X_283))]]) ).
cnf(refute_0_51,plain,
zero = divide(divide(X_283,divide(X_283,a)),b),
inference(resolve,[$cnf( less_equal(divide(divide(X_283,divide(X_283,a)),b),zero) )],[refute_0_50,refute_0_5]) ).
cnf(refute_0_52,plain,
zero = divide(divide(X_284,divide(X_284,a)),b),
inference(subst,[],[refute_0_51:[bind(X_283,$fot(X_284))]]) ).
cnf(refute_0_53,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_54,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_55,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
( zero != divide(divide(X_284,divide(X_284,a)),b)
| divide(divide(X_284,divide(X_284,a)),b) = zero ),
inference(subst,[],[refute_0_55:[bind(X0,$fot(zero)),bind(Y0,$fot(divide(divide(X_284,divide(X_284,a)),b)))]]) ).
cnf(refute_0_57,plain,
divide(divide(X_284,divide(X_284,a)),b) = zero,
inference(resolve,[$cnf( $equal(zero,divide(divide(X_284,divide(X_284,a)),b)) )],[refute_0_52,refute_0_56]) ).
cnf(refute_0_58,plain,
( divide(divide(X_284,divide(X_284,a)),b) != zero
| zero != zero
| divide(divide(X_284,divide(X_284,a)),b) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(divide(divide(X_284,divide(X_284,a)),b),zero) ),[0],$fot(zero)]]) ).
cnf(refute_0_59,plain,
( zero != zero
| divide(divide(X_284,divide(X_284,a)),b) = zero ),
inference(resolve,[$cnf( $equal(divide(divide(X_284,divide(X_284,a)),b),zero) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
( zero != zero
| less_equal(divide(X_284,divide(X_284,a)),b) ),
inference(resolve,[$cnf( $equal(divide(divide(X_284,divide(X_284,a)),b),zero) )],[refute_0_59,refute_0_1]) ).
cnf(refute_0_61,plain,
less_equal(divide(X_284,divide(X_284,a)),b),
inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_22,refute_0_60]) ).
cnf(refute_0_62,plain,
less_equal(divide(X_314,divide(X_314,a)),b),
inference(subst,[],[refute_0_61:[bind(X_284,$fot(X_314))]]) ).
cnf(refute_0_63,plain,
less_equal(divide(X_314,b),divide(X_314,a)),
inference(resolve,[$cnf( less_equal(divide(X_314,divide(X_314,a)),b) )],[refute_0_62,refute_0_0]) ).
cnf(refute_0_64,plain,
less_equal(divide(c,b),divide(c,a)),
inference(subst,[],[refute_0_63:[bind(X_314,$fot(c))]]) ).
cnf(refute_0_65,plain,
$false,
inference(resolve,[$cnf( less_equal(divide(c,b),divide(c,a)) )],[refute_0_64,prove_c_divide_b_LE_c_divide_a]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : HEN007-4 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n004.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 : Fri Jul 1 12:58:38 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2.71/2.89 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.71/2.89
% 2.71/2.89 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.73/2.90
%------------------------------------------------------------------------------