TSTP Solution File: HEN005-3 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : HEN005-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n028.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 12:58:34 EDT 2022
% Result : Unsatisfiable 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 16
% Syntax : Number of clauses : 52 ( 25 unt; 0 nHn; 43 RR)
% Number of literals : 88 ( 43 equ; 37 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 : 26 ( 4 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(a_LE_b,hypothesis,
less_equal(a,b) ).
cnf(b_LE_c,hypothesis,
less_equal(b,c) ).
cnf(prove_a_LE_c,negated_conjecture,
~ less_equal(a,c) ).
cnf(refute_0_0,plain,
( divide(a,c) != zero
| less_equal(a,c) ),
inference(subst,[],[quotient_less_equal2:[bind(X,$fot(a)),bind(Y,$fot(c))]]) ).
cnf(refute_0_1,plain,
( ~ less_equal(divide(a,c),zero)
| ~ less_equal(zero,divide(a,c))
| zero = divide(a,c) ),
inference(subst,[],[less_equal_and_equal:[bind(X,$fot(zero)),bind(Y,$fot(divide(a,c)))]]) ).
cnf(refute_0_2,plain,
( divide(divide(a,c),zero) != zero
| less_equal(divide(a,c),zero) ),
inference(subst,[],[quotient_less_equal2:[bind(X,$fot(divide(a,c))),bind(Y,$fot(zero))]]) ).
cnf(refute_0_3,plain,
less_equal(divide(divide(a,X_14),divide(b,X_14)),divide(divide(a,b),X_14)),
inference(subst,[],[quotient_property:[bind(X,$fot(a)),bind(Y,$fot(b)),bind(Z,$fot(X_14))]]) ).
cnf(refute_0_4,plain,
( ~ less_equal(a,b)
| divide(a,b) = zero ),
inference(subst,[],[quotient_less_equal1:[bind(X,$fot(a)),bind(Y,$fot(b))]]) ).
cnf(refute_0_5,plain,
divide(a,b) = zero,
inference(resolve,[$cnf( less_equal(a,b) )],[a_LE_b,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ less_equal(divide(divide(a,X_14),divide(b,X_14)),divide(divide(a,b),X_14))
| divide(a,b) != zero
| less_equal(divide(divide(a,X_14),divide(b,X_14)),divide(zero,X_14)) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(divide(a,X_14),divide(b,X_14)),divide(divide(a,b),X_14)) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_7,plain,
( ~ less_equal(divide(divide(a,X_14),divide(b,X_14)),divide(divide(a,b),X_14))
| less_equal(divide(divide(a,X_14),divide(b,X_14)),divide(zero,X_14)) ),
inference(resolve,[$cnf( $equal(divide(a,b),zero) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
less_equal(divide(divide(a,X_14),divide(b,X_14)),divide(zero,X_14)),
inference(resolve,[$cnf( less_equal(divide(divide(a,X_14),divide(b,X_14)),divide(divide(a,b),X_14)) )],[refute_0_3,refute_0_7]) ).
cnf(refute_0_9,plain,
less_equal(zero,X_5),
inference(subst,[],[zero_is_smallest:[bind(X,$fot(X_5))]]) ).
cnf(refute_0_10,plain,
( ~ less_equal(zero,X_5)
| divide(zero,X_5) = zero ),
inference(subst,[],[quotient_less_equal1:[bind(X,$fot(zero)),bind(Y,$fot(X_5))]]) ).
cnf(refute_0_11,plain,
divide(zero,X_5) = zero,
inference(resolve,[$cnf( less_equal(zero,X_5) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
divide(zero,X_14) = zero,
inference(subst,[],[refute_0_11:[bind(X_5,$fot(X_14))]]) ).
cnf(refute_0_13,plain,
( ~ less_equal(divide(divide(a,X_14),divide(b,X_14)),divide(zero,X_14))
| divide(zero,X_14) != zero
| less_equal(divide(divide(a,X_14),divide(b,X_14)),zero) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(divide(a,X_14),divide(b,X_14)),divide(zero,X_14)) ),[1],$fot(zero)]]) ).
cnf(refute_0_14,plain,
( ~ less_equal(divide(divide(a,X_14),divide(b,X_14)),divide(zero,X_14))
| less_equal(divide(divide(a,X_14),divide(b,X_14)),zero) ),
inference(resolve,[$cnf( $equal(divide(zero,X_14),zero) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
less_equal(divide(divide(a,X_14),divide(b,X_14)),zero),
inference(resolve,[$cnf( less_equal(divide(divide(a,X_14),divide(b,X_14)),divide(zero,X_14)) )],[refute_0_8,refute_0_14]) ).
cnf(refute_0_16,plain,
less_equal(divide(divide(a,c),divide(b,c)),zero),
inference(subst,[],[refute_0_15:[bind(X_14,$fot(c))]]) ).
cnf(refute_0_17,plain,
( ~ less_equal(b,c)
| divide(b,c) = zero ),
inference(subst,[],[quotient_less_equal1:[bind(X,$fot(b)),bind(Y,$fot(c))]]) ).
cnf(refute_0_18,plain,
divide(b,c) = zero,
inference(resolve,[$cnf( less_equal(b,c) )],[b_LE_c,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ less_equal(divide(divide(a,c),divide(b,c)),zero)
| divide(b,c) != zero
| less_equal(divide(divide(a,c),zero),zero) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(divide(a,c),divide(b,c)),zero) ),[0,1],$fot(zero)]]) ).
cnf(refute_0_20,plain,
( ~ less_equal(divide(divide(a,c),divide(b,c)),zero)
| less_equal(divide(divide(a,c),zero),zero) ),
inference(resolve,[$cnf( $equal(divide(b,c),zero) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
less_equal(divide(divide(a,c),zero),zero),
inference(resolve,[$cnf( less_equal(divide(divide(a,c),divide(b,c)),zero) )],[refute_0_16,refute_0_20]) ).
cnf(refute_0_22,plain,
( ~ less_equal(divide(divide(a,c),zero),zero)
| ~ less_equal(zero,divide(divide(a,c),zero))
| divide(divide(a,c),zero) = zero ),
inference(subst,[],[less_equal_and_equal:[bind(X,$fot(divide(divide(a,c),zero))),bind(Y,$fot(zero))]]) ).
cnf(refute_0_23,plain,
( ~ less_equal(zero,divide(divide(a,c),zero))
| divide(divide(a,c),zero) = zero ),
inference(resolve,[$cnf( less_equal(divide(divide(a,c),zero),zero) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
less_equal(zero,divide(divide(a,c),zero)),
inference(subst,[],[zero_is_smallest:[bind(X,$fot(divide(divide(a,c),zero)))]]) ).
cnf(refute_0_25,plain,
divide(divide(a,c),zero) = zero,
inference(resolve,[$cnf( less_equal(zero,divide(divide(a,c),zero)) )],[refute_0_24,refute_0_23]) ).
cnf(refute_0_26,plain,
( divide(divide(a,c),zero) != zero
| zero != zero
| divide(divide(a,c),zero) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(divide(divide(a,c),zero),zero) ),[0],$fot(zero)]]) ).
cnf(refute_0_27,plain,
( zero != zero
| divide(divide(a,c),zero) = zero ),
inference(resolve,[$cnf( $equal(divide(divide(a,c),zero),zero) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
( zero != zero
| less_equal(divide(a,c),zero) ),
inference(resolve,[$cnf( $equal(divide(divide(a,c),zero),zero) )],[refute_0_27,refute_0_2]) ).
cnf(refute_0_29,plain,
zero = zero,
introduced(tautology,[refl,[$fot(zero)]]) ).
cnf(refute_0_30,plain,
less_equal(divide(a,c),zero),
inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_29,refute_0_28]) ).
cnf(refute_0_31,plain,
( ~ less_equal(zero,divide(a,c))
| zero = divide(a,c) ),
inference(resolve,[$cnf( less_equal(divide(a,c),zero) )],[refute_0_30,refute_0_1]) ).
cnf(refute_0_32,plain,
less_equal(zero,divide(a,c)),
inference(subst,[],[zero_is_smallest:[bind(X,$fot(divide(a,c)))]]) ).
cnf(refute_0_33,plain,
zero = divide(a,c),
inference(resolve,[$cnf( less_equal(zero,divide(a,c)) )],[refute_0_32,refute_0_31]) ).
cnf(refute_0_34,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_35,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_36,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
( zero != divide(a,c)
| divide(a,c) = zero ),
inference(subst,[],[refute_0_36:[bind(X0,$fot(zero)),bind(Y0,$fot(divide(a,c)))]]) ).
cnf(refute_0_38,plain,
divide(a,c) = zero,
inference(resolve,[$cnf( $equal(zero,divide(a,c)) )],[refute_0_33,refute_0_37]) ).
cnf(refute_0_39,plain,
( divide(a,c) != zero
| zero != zero
| divide(a,c) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(divide(a,c),zero) ),[0],$fot(zero)]]) ).
cnf(refute_0_40,plain,
( zero != zero
| divide(a,c) = zero ),
inference(resolve,[$cnf( $equal(divide(a,c),zero) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
( zero != zero
| less_equal(a,c) ),
inference(resolve,[$cnf( $equal(divide(a,c),zero) )],[refute_0_40,refute_0_0]) ).
cnf(refute_0_42,plain,
less_equal(a,c),
inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_29,refute_0_41]) ).
cnf(refute_0_43,plain,
$false,
inference(resolve,[$cnf( less_equal(a,c) )],[refute_0_42,prove_a_LE_c]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : HEN005-3 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n028.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Fri Jul 1 13:59:16 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.39 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.39
% 0.13/0.39 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.40
%------------------------------------------------------------------------------