TSTP Solution File: HEN012-3 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : HEN012-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n013.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 12:58:50 EDT 2022
% Result : Unsatisfiable 0.12s 0.36s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 14
% Syntax : Number of clauses : 49 ( 26 unt; 0 nHn; 23 RR)
% Number of literals : 80 ( 41 equ; 32 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 65 ( 9 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_smaller_than_numerator,axiom,
less_equal(divide(X,Y),X) ).
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(prove_a_LE_a,negated_conjecture,
~ less_equal(a,a) ).
cnf(refute_0_0,plain,
( divide(Y,Y) != zero
| less_equal(Y,Y) ),
inference(subst,[],[quotient_less_equal2:[bind(X,$fot(Y))]]) ).
cnf(refute_0_1,plain,
( ~ less_equal(divide(X_32,X_32),zero)
| ~ less_equal(zero,divide(X_32,X_32))
| zero = divide(X_32,X_32) ),
inference(subst,[],[less_equal_and_equal:[bind(X,$fot(zero)),bind(Y,$fot(divide(X_32,X_32)))]]) ).
cnf(refute_0_2,plain,
( divide(divide(X_31,X_31),zero) != zero
| less_equal(divide(X_31,X_31),zero) ),
inference(subst,[],[quotient_less_equal2:[bind(X,$fot(divide(X_31,X_31))),bind(Y,$fot(zero))]]) ).
cnf(refute_0_3,plain,
less_equal(divide(divide(X_14,X_14),divide(X_13,X_14)),divide(divide(X_14,X_13),X_14)),
inference(subst,[],[quotient_property:[bind(X,$fot(X_14)),bind(Y,$fot(X_13)),bind(Z,$fot(X_14))]]) ).
cnf(refute_0_4,plain,
less_equal(divide(X_5,Y),X_5),
inference(subst,[],[quotient_smaller_than_numerator:[bind(X,$fot(X_5))]]) ).
cnf(refute_0_5,plain,
( ~ less_equal(divide(X_5,Y),X_5)
| divide(divide(X_5,Y),X_5) = zero ),
inference(subst,[],[quotient_less_equal1:[bind(X,$fot(divide(X_5,Y))),bind(Y,$fot(X_5))]]) ).
cnf(refute_0_6,plain,
divide(divide(X_5,Y),X_5) = zero,
inference(resolve,[$cnf( less_equal(divide(X_5,Y),X_5) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
divide(divide(X_14,X_13),X_14) = zero,
inference(subst,[],[refute_0_6:[bind(Y,$fot(X_13)),bind(X_5,$fot(X_14))]]) ).
cnf(refute_0_8,plain,
( ~ less_equal(divide(divide(X_14,X_14),divide(X_13,X_14)),divide(divide(X_14,X_13),X_14))
| divide(divide(X_14,X_13),X_14) != zero
| less_equal(divide(divide(X_14,X_14),divide(X_13,X_14)),zero) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(divide(X_14,X_14),divide(X_13,X_14)),divide(divide(X_14,X_13),X_14)) ),[1],$fot(zero)]]) ).
cnf(refute_0_9,plain,
( ~ less_equal(divide(divide(X_14,X_14),divide(X_13,X_14)),divide(divide(X_14,X_13),X_14))
| less_equal(divide(divide(X_14,X_14),divide(X_13,X_14)),zero) ),
inference(resolve,[$cnf( $equal(divide(divide(X_14,X_13),X_14),zero) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
less_equal(divide(divide(X_14,X_14),divide(X_13,X_14)),zero),
inference(resolve,[$cnf( less_equal(divide(divide(X_14,X_14),divide(X_13,X_14)),divide(divide(X_14,X_13),X_14)) )],[refute_0_3,refute_0_9]) ).
cnf(refute_0_11,plain,
less_equal(divide(divide(X_18,X_18),divide(divide(X_18,Y),X_18)),zero),
inference(subst,[],[refute_0_10:[bind(X_13,$fot(divide(X_18,Y))),bind(X_14,$fot(X_18))]]) ).
cnf(refute_0_12,plain,
divide(divide(X_18,Y),X_18) = zero,
inference(subst,[],[refute_0_6:[bind(X_5,$fot(X_18))]]) ).
cnf(refute_0_13,plain,
( ~ less_equal(divide(divide(X_18,X_18),divide(divide(X_18,Y),X_18)),zero)
| divide(divide(X_18,Y),X_18) != zero
| less_equal(divide(divide(X_18,X_18),zero),zero) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(divide(X_18,X_18),divide(divide(X_18,Y),X_18)),zero) ),[0,1],$fot(zero)]]) ).
cnf(refute_0_14,plain,
( ~ less_equal(divide(divide(X_18,X_18),divide(divide(X_18,Y),X_18)),zero)
| less_equal(divide(divide(X_18,X_18),zero),zero) ),
inference(resolve,[$cnf( $equal(divide(divide(X_18,Y),X_18),zero) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
less_equal(divide(divide(X_18,X_18),zero),zero),
inference(resolve,[$cnf( less_equal(divide(divide(X_18,X_18),divide(divide(X_18,Y),X_18)),zero) )],[refute_0_11,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ less_equal(divide(divide(X_18,X_18),zero),zero)
| ~ less_equal(zero,divide(divide(X_18,X_18),zero))
| divide(divide(X_18,X_18),zero) = zero ),
inference(subst,[],[less_equal_and_equal:[bind(X,$fot(divide(divide(X_18,X_18),zero))),bind(Y,$fot(zero))]]) ).
cnf(refute_0_17,plain,
( ~ less_equal(zero,divide(divide(X_18,X_18),zero))
| divide(divide(X_18,X_18),zero) = zero ),
inference(resolve,[$cnf( less_equal(divide(divide(X_18,X_18),zero),zero) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
less_equal(zero,divide(divide(X_18,X_18),zero)),
inference(subst,[],[zero_is_smallest:[bind(X,$fot(divide(divide(X_18,X_18),zero)))]]) ).
cnf(refute_0_19,plain,
divide(divide(X_18,X_18),zero) = zero,
inference(resolve,[$cnf( less_equal(zero,divide(divide(X_18,X_18),zero)) )],[refute_0_18,refute_0_17]) ).
cnf(refute_0_20,plain,
divide(divide(X_31,X_31),zero) = zero,
inference(subst,[],[refute_0_19:[bind(X_18,$fot(X_31))]]) ).
cnf(refute_0_21,plain,
( divide(divide(X_31,X_31),zero) != zero
| zero != zero
| divide(divide(X_31,X_31),zero) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(divide(divide(X_31,X_31),zero),zero) ),[0],$fot(zero)]]) ).
cnf(refute_0_22,plain,
( zero != zero
| divide(divide(X_31,X_31),zero) = zero ),
inference(resolve,[$cnf( $equal(divide(divide(X_31,X_31),zero),zero) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
( zero != zero
| less_equal(divide(X_31,X_31),zero) ),
inference(resolve,[$cnf( $equal(divide(divide(X_31,X_31),zero),zero) )],[refute_0_22,refute_0_2]) ).
cnf(refute_0_24,plain,
zero = zero,
introduced(tautology,[refl,[$fot(zero)]]) ).
cnf(refute_0_25,plain,
less_equal(divide(X_31,X_31),zero),
inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_24,refute_0_23]) ).
cnf(refute_0_26,plain,
less_equal(divide(X_32,X_32),zero),
inference(subst,[],[refute_0_25:[bind(X_31,$fot(X_32))]]) ).
cnf(refute_0_27,plain,
( ~ less_equal(zero,divide(X_32,X_32))
| zero = divide(X_32,X_32) ),
inference(resolve,[$cnf( less_equal(divide(X_32,X_32),zero) )],[refute_0_26,refute_0_1]) ).
cnf(refute_0_28,plain,
less_equal(zero,divide(X_32,X_32)),
inference(subst,[],[zero_is_smallest:[bind(X,$fot(divide(X_32,X_32)))]]) ).
cnf(refute_0_29,plain,
zero = divide(X_32,X_32),
inference(resolve,[$cnf( less_equal(zero,divide(X_32,X_32)) )],[refute_0_28,refute_0_27]) ).
cnf(refute_0_30,plain,
zero = divide(Y,Y),
inference(subst,[],[refute_0_29:[bind(X_32,$fot(Y))]]) ).
cnf(refute_0_31,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_32,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_33,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
( zero != divide(Y,Y)
| divide(Y,Y) = zero ),
inference(subst,[],[refute_0_33:[bind(X0,$fot(zero)),bind(Y0,$fot(divide(Y,Y)))]]) ).
cnf(refute_0_35,plain,
divide(Y,Y) = zero,
inference(resolve,[$cnf( $equal(zero,divide(Y,Y)) )],[refute_0_30,refute_0_34]) ).
cnf(refute_0_36,plain,
( divide(Y,Y) != zero
| zero != zero
| divide(Y,Y) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(divide(Y,Y),zero) ),[0],$fot(zero)]]) ).
cnf(refute_0_37,plain,
( zero != zero
| divide(Y,Y) = zero ),
inference(resolve,[$cnf( $equal(divide(Y,Y),zero) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
( zero != zero
| less_equal(Y,Y) ),
inference(resolve,[$cnf( $equal(divide(Y,Y),zero) )],[refute_0_37,refute_0_0]) ).
cnf(refute_0_39,plain,
less_equal(Y,Y),
inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_24,refute_0_38]) ).
cnf(refute_0_40,plain,
less_equal(a,a),
inference(subst,[],[refute_0_39:[bind(Y,$fot(a))]]) ).
cnf(refute_0_41,plain,
$false,
inference(resolve,[$cnf( less_equal(a,a) )],[refute_0_40,prove_a_LE_a]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : HEN012-3 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Fri Jul 1 12:56:14 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.36 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.36
% 0.12/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.37
%------------------------------------------------------------------------------