TSTP Solution File: HEN008-4 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : HEN008-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n029.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 12:58:41 EDT 2022
% Result : Unsatisfiable 0.61s 0.79s
% Output : CNFRefutation 0.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of clauses : 31 ( 17 unt; 0 nHn; 18 RR)
% Number of literals : 50 ( 21 equ; 20 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 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 : 29 ( 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(a_LE_b,hypothesis,
less_equal(a,b) ).
cnf(prove_a_divide_c_LE_b_divide_c,negated_conjecture,
~ less_equal(divide(a,c),divide(b,c)) ).
cnf(refute_0_0,plain,
( divide(divide(a,X_207),divide(b,X_207)) != zero
| less_equal(divide(a,X_207),divide(b,X_207)) ),
inference(subst,[],[quotient_less_equal2:[bind(X,$fot(divide(a,X_207))),bind(Y,$fot(divide(b,X_207)))]]) ).
cnf(refute_0_1,plain,
less_equal(divide(divide(a,X_16),divide(b,X_16)),divide(divide(a,b),X_16)),
inference(subst,[],[quotient_property:[bind(X,$fot(a)),bind(Y,$fot(b)),bind(Z,$fot(X_16))]]) ).
cnf(refute_0_2,plain,
( ~ less_equal(a,b)
| divide(a,b) = zero ),
inference(subst,[],[quotient_less_equal1:[bind(X,$fot(a)),bind(Y,$fot(b))]]) ).
cnf(refute_0_3,plain,
divide(a,b) = zero,
inference(resolve,[$cnf( less_equal(a,b) )],[a_LE_b,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ less_equal(divide(divide(a,X_16),divide(b,X_16)),divide(divide(a,b),X_16))
| divide(a,b) != zero
| less_equal(divide(divide(a,X_16),divide(b,X_16)),divide(zero,X_16)) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(divide(a,X_16),divide(b,X_16)),divide(divide(a,b),X_16)) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_5,plain,
( ~ less_equal(divide(divide(a,X_16),divide(b,X_16)),divide(divide(a,b),X_16))
| less_equal(divide(divide(a,X_16),divide(b,X_16)),divide(zero,X_16)) ),
inference(resolve,[$cnf( $equal(divide(a,b),zero) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
less_equal(divide(divide(a,X_16),divide(b,X_16)),divide(zero,X_16)),
inference(resolve,[$cnf( less_equal(divide(divide(a,X_16),divide(b,X_16)),divide(divide(a,b),X_16)) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
divide(zero,X_16) = zero,
inference(subst,[],[zero_divide_anything_is_zero:[bind(X,$fot(X_16))]]) ).
cnf(refute_0_8,plain,
( ~ less_equal(divide(divide(a,X_16),divide(b,X_16)),divide(zero,X_16))
| divide(zero,X_16) != zero
| less_equal(divide(divide(a,X_16),divide(b,X_16)),zero) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(divide(a,X_16),divide(b,X_16)),divide(zero,X_16)) ),[1],$fot(zero)]]) ).
cnf(refute_0_9,plain,
( ~ less_equal(divide(divide(a,X_16),divide(b,X_16)),divide(zero,X_16))
| less_equal(divide(divide(a,X_16),divide(b,X_16)),zero) ),
inference(resolve,[$cnf( $equal(divide(zero,X_16),zero) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
less_equal(divide(divide(a,X_16),divide(b,X_16)),zero),
inference(resolve,[$cnf( less_equal(divide(divide(a,X_16),divide(b,X_16)),divide(zero,X_16)) )],[refute_0_6,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ less_equal(divide(divide(a,X_16),divide(b,X_16)),zero)
| ~ less_equal(zero,divide(divide(a,X_16),divide(b,X_16)))
| divide(divide(a,X_16),divide(b,X_16)) = zero ),
inference(subst,[],[less_equal_and_equal:[bind(X,$fot(divide(divide(a,X_16),divide(b,X_16)))),bind(Y,$fot(zero))]]) ).
cnf(refute_0_12,plain,
( ~ less_equal(zero,divide(divide(a,X_16),divide(b,X_16)))
| divide(divide(a,X_16),divide(b,X_16)) = zero ),
inference(resolve,[$cnf( less_equal(divide(divide(a,X_16),divide(b,X_16)),zero) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
less_equal(zero,divide(divide(a,X_16),divide(b,X_16))),
inference(subst,[],[zero_is_smallest:[bind(X,$fot(divide(divide(a,X_16),divide(b,X_16))))]]) ).
cnf(refute_0_14,plain,
divide(divide(a,X_16),divide(b,X_16)) = zero,
inference(resolve,[$cnf( less_equal(zero,divide(divide(a,X_16),divide(b,X_16))) )],[refute_0_13,refute_0_12]) ).
cnf(refute_0_15,plain,
divide(divide(a,X_207),divide(b,X_207)) = zero,
inference(subst,[],[refute_0_14:[bind(X_16,$fot(X_207))]]) ).
cnf(refute_0_16,plain,
( divide(divide(a,X_207),divide(b,X_207)) != zero
| zero != zero
| divide(divide(a,X_207),divide(b,X_207)) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(divide(divide(a,X_207),divide(b,X_207)),zero) ),[0],$fot(zero)]]) ).
cnf(refute_0_17,plain,
( zero != zero
| divide(divide(a,X_207),divide(b,X_207)) = zero ),
inference(resolve,[$cnf( $equal(divide(divide(a,X_207),divide(b,X_207)),zero) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
( zero != zero
| less_equal(divide(a,X_207),divide(b,X_207)) ),
inference(resolve,[$cnf( $equal(divide(divide(a,X_207),divide(b,X_207)),zero) )],[refute_0_17,refute_0_0]) ).
cnf(refute_0_19,plain,
zero = zero,
introduced(tautology,[refl,[$fot(zero)]]) ).
cnf(refute_0_20,plain,
less_equal(divide(a,X_207),divide(b,X_207)),
inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_19,refute_0_18]) ).
cnf(refute_0_21,plain,
less_equal(divide(a,c),divide(b,c)),
inference(subst,[],[refute_0_20:[bind(X_207,$fot(c))]]) ).
cnf(refute_0_22,plain,
$false,
inference(resolve,[$cnf( less_equal(divide(a,c),divide(b,c)) )],[refute_0_21,prove_a_divide_c_LE_b_divide_c]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.09 % Problem : HEN008-4 : TPTP v8.1.0. Released v1.0.0.
% 0.09/0.10 % Command : metis --show proof --show saturation %s
% 0.09/0.30 % Computer : n029.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 600
% 0.09/0.30 % DateTime : Fri Jul 1 13:30:09 EDT 2022
% 0.09/0.30 % CPUTime :
% 0.09/0.30 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.61/0.79 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.61/0.79
% 0.61/0.79 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.61/0.80
%------------------------------------------------------------------------------