%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : HEN005-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n007.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 22.10s 22.29s
% Output : CNFRefutation 22.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 16
% Syntax : Number of clauses : 56 ( 25 unt; 0 nHn; 44 RR)
% Number of literals : 114 ( 22 equ; 59 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 67 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(quotient_less_equal,axiom,
( ~ less_equal(X,Y)
| quotient(X,Y,zero) ) ).
cnf(less_equal_quotient,axiom,
( ~ quotient(X,Y,zero)
| less_equal(X,Y) ) ).
cnf(quotient_property,axiom,
( ~ quotient(X,Y,V1)
| ~ quotient(Y,Z,V2)
| ~ quotient(X,Z,V3)
| ~ quotient(V3,V2,V4)
| ~ quotient(V1,Z,V5)
| less_equal(V4,V5) ) ).
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(closure,axiom,
quotient(X,Y,divide(X,Y)) ).
cnf(well_defined,axiom,
( ~ quotient(X,Y,Z)
| ~ quotient(X,Y,W)
| Z = W ) ).
cnf(zero_divide_anything_is_zero,axiom,
quotient(zero,X,zero) ).
cnf(x_divde_zero_is_x,axiom,
quotient(X,zero,X) ).
cnf(xLEy,hypothesis,
less_equal(x,y) ).
cnf(yLEz,hypothesis,
less_equal(y,z) ).
cnf(prove_transitivity_of_less_equal,negated_conjecture,
~ less_equal(x,z) ).
cnf(refute_0_0,plain,
( ~ quotient(x,z,zero)
| less_equal(x,z) ),
inference(subst,[],[less_equal_quotient:[bind(X,$fot(x)),bind(Y,$fot(z))]]) ).
cnf(refute_0_1,plain,
quotient(x,z,divide(x,z)),
inference(subst,[],[closure:[bind(X,$fot(x)),bind(Y,$fot(z))]]) ).
cnf(refute_0_2,plain,
less_equal(zero,X_21),
inference(subst,[],[zero_is_smallest:[bind(X,$fot(X_21))]]) ).
cnf(refute_0_3,plain,
( ~ less_equal(X_21,zero)
| ~ less_equal(zero,X_21)
| zero = X_21 ),
inference(subst,[],[less_equal_and_equal:[bind(X,$fot(zero)),bind(Y,$fot(X_21))]]) ).
cnf(refute_0_4,plain,
( ~ less_equal(X_21,zero)
| zero = X_21 ),
inference(resolve,[$cnf( less_equal(zero,X_21) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ less_equal(divide(x,z),zero)
| zero = divide(x,z) ),
inference(subst,[],[refute_0_4:[bind(X_21,$fot(divide(x,z)))]]) ).
cnf(refute_0_6,plain,
( ~ less_equal(x,y)
| quotient(x,y,zero) ),
inference(subst,[],[quotient_less_equal:[bind(X,$fot(x)),bind(Y,$fot(y))]]) ).
cnf(refute_0_7,plain,
quotient(x,y,zero),
inference(resolve,[$cnf( less_equal(x,y) )],[xLEy,refute_0_6]) ).
cnf(refute_0_8,plain,
quotient(divide(X_3996,z),zero,divide(divide(X_3996,z),zero)),
inference(subst,[],[closure:[bind(X,$fot(divide(X_3996,z))),bind(Y,$fot(zero))]]) ).
cnf(refute_0_9,plain,
quotient(X_3994,z,divide(X_3994,z)),
inference(subst,[],[closure:[bind(X,$fot(X_3994)),bind(Y,$fot(z))]]) ).
cnf(refute_0_10,plain,
quotient(zero,z,zero),
inference(subst,[],[zero_divide_anything_is_zero:[bind(X,$fot(z))]]) ).
cnf(refute_0_11,plain,
( ~ less_equal(y,z)
| quotient(y,z,zero) ),
inference(subst,[],[quotient_less_equal:[bind(X,$fot(y)),bind(Y,$fot(z))]]) ).
cnf(refute_0_12,plain,
quotient(y,z,zero),
inference(resolve,[$cnf( less_equal(y,z) )],[yLEz,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ quotient(X_2253,z,X_2257)
| ~ quotient(X_2255,zero,X_2256)
| ~ quotient(X_2258,y,X_2253)
| ~ quotient(X_2258,z,X_2255)
| ~ quotient(y,z,zero)
| less_equal(X_2256,X_2257) ),
inference(subst,[],[quotient_property:[bind(V1,$fot(X_2253)),bind(V2,$fot(zero)),bind(V3,$fot(X_2255)),bind(V4,$fot(X_2256)),bind(V5,$fot(X_2257)),bind(X,$fot(X_2258)),bind(Y,$fot(y)),bind(Z,$fot(z))]]) ).
cnf(refute_0_14,plain,
( ~ quotient(X_2253,z,X_2257)
| ~ quotient(X_2255,zero,X_2256)
| ~ quotient(X_2258,y,X_2253)
| ~ quotient(X_2258,z,X_2255)
| less_equal(X_2256,X_2257) ),
inference(resolve,[$cnf( quotient(y,z,zero) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ quotient(X_3965,zero,X_3966)
| ~ quotient(X_3968,y,zero)
| ~ quotient(X_3968,z,X_3965)
| ~ quotient(zero,z,zero)
| less_equal(X_3966,zero) ),
inference(subst,[],[refute_0_14:[bind(X_2253,$fot(zero)),bind(X_2255,$fot(X_3965)),bind(X_2256,$fot(X_3966)),bind(X_2257,$fot(zero)),bind(X_2258,$fot(X_3968))]]) ).
cnf(refute_0_16,plain,
( ~ quotient(X_3965,zero,X_3966)
| ~ quotient(X_3968,y,zero)
| ~ quotient(X_3968,z,X_3965)
| less_equal(X_3966,zero) ),
inference(resolve,[$cnf( quotient(zero,z,zero) )],[refute_0_10,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ quotient(X_3994,y,zero)
| ~ quotient(X_3994,z,divide(X_3994,z))
| ~ quotient(divide(X_3994,z),zero,X_3993)
| less_equal(X_3993,zero) ),
inference(subst,[],[refute_0_16:[bind(X_3965,$fot(divide(X_3994,z))),bind(X_3966,$fot(X_3993)),bind(X_3968,$fot(X_3994))]]) ).
cnf(refute_0_18,plain,
( ~ quotient(X_3994,y,zero)
| ~ quotient(divide(X_3994,z),zero,X_3993)
| less_equal(X_3993,zero) ),
inference(resolve,[$cnf( quotient(X_3994,z,divide(X_3994,z)) )],[refute_0_9,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ quotient(X_3996,y,zero)
| ~ quotient(divide(X_3996,z),zero,divide(divide(X_3996,z),zero))
| less_equal(divide(divide(X_3996,z),zero),zero) ),
inference(subst,[],[refute_0_18:[bind(X_3993,$fot(divide(divide(X_3996,z),zero))),bind(X_3994,$fot(X_3996))]]) ).
cnf(refute_0_20,plain,
( ~ quotient(X_3996,y,zero)
| less_equal(divide(divide(X_3996,z),zero),zero) ),
inference(resolve,[$cnf( quotient(divide(X_3996,z),zero,divide(divide(X_3996,z),zero)) )],[refute_0_8,refute_0_19]) ).
cnf(refute_0_21,plain,
quotient(X_45,zero,divide(X_45,zero)),
inference(subst,[],[closure:[bind(X,$fot(X_45)),bind(Y,$fot(zero))]]) ).
cnf(refute_0_22,plain,
quotient(X_31,zero,X_31),
inference(subst,[],[x_divde_zero_is_x:[bind(X,$fot(X_31))]]) ).
cnf(refute_0_23,plain,
( ~ quotient(X_31,zero,X_31)
| ~ quotient(X_31,zero,X_34)
| X_34 = X_31 ),
inference(subst,[],[well_defined:[bind(W,$fot(X_31)),bind(X,$fot(X_31)),bind(Y,$fot(zero)),bind(Z,$fot(X_34))]]) ).
cnf(refute_0_24,plain,
( ~ quotient(X_31,zero,X_34)
| X_34 = X_31 ),
inference(resolve,[$cnf( quotient(X_31,zero,X_31) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ quotient(X_45,zero,divide(X_45,zero))
| divide(X_45,zero) = X_45 ),
inference(subst,[],[refute_0_24:[bind(X_31,$fot(X_45)),bind(X_34,$fot(divide(X_45,zero)))]]) ).
cnf(refute_0_26,plain,
divide(X_45,zero) = X_45,
inference(resolve,[$cnf( quotient(X_45,zero,divide(X_45,zero)) )],[refute_0_21,refute_0_25]) ).
cnf(refute_0_27,plain,
divide(divide(X_3996,z),zero) = divide(X_3996,z),
inference(subst,[],[refute_0_26:[bind(X_45,$fot(divide(X_3996,z)))]]) ).
cnf(refute_0_28,plain,
( ~ less_equal(divide(divide(X_3996,z),zero),zero)
| divide(divide(X_3996,z),zero) != divide(X_3996,z)
| less_equal(divide(X_3996,z),zero) ),
introduced(tautology,[equality,[$cnf( less_equal(divide(divide(X_3996,z),zero),zero) ),[0],$fot(divide(X_3996,z))]]) ).
cnf(refute_0_29,plain,
( ~ less_equal(divide(divide(X_3996,z),zero),zero)
| less_equal(divide(X_3996,z),zero) ),
inference(resolve,[$cnf( $equal(divide(divide(X_3996,z),zero),divide(X_3996,z)) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
( ~ quotient(X_3996,y,zero)
| less_equal(divide(X_3996,z),zero) ),
inference(resolve,[$cnf( less_equal(divide(divide(X_3996,z),zero),zero) )],[refute_0_20,refute_0_29]) ).
cnf(refute_0_31,plain,
( ~ quotient(x,y,zero)
| less_equal(divide(x,z),zero) ),
inference(subst,[],[refute_0_30:[bind(X_3996,$fot(x))]]) ).
cnf(refute_0_32,plain,
less_equal(divide(x,z),zero),
inference(resolve,[$cnf( quotient(x,y,zero) )],[refute_0_7,refute_0_31]) ).
cnf(refute_0_33,plain,
zero = divide(x,z),
inference(resolve,[$cnf( less_equal(divide(x,z),zero) )],[refute_0_32,refute_0_5]) ).
cnf(refute_0_34,plain,
X0 = X0,
introduced(tautology,[refl,[$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( $equal(X0,X0) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
( zero != divide(x,z)
| divide(x,z) = zero ),
inference(subst,[],[refute_0_36:[bind(X0,$fot(zero)),bind(Y0,$fot(divide(x,z)))]]) ).
cnf(refute_0_38,plain,
divide(x,z) = zero,
inference(resolve,[$cnf( $equal(zero,divide(x,z)) )],[refute_0_33,refute_0_37]) ).
cnf(refute_0_39,plain,
( divide(x,z) != zero
| ~ quotient(x,z,divide(x,z))
| quotient(x,z,zero) ),
introduced(tautology,[equality,[$cnf( quotient(x,z,divide(x,z)) ),[2],$fot(zero)]]) ).
cnf(refute_0_40,plain,
( ~ quotient(x,z,divide(x,z))
| quotient(x,z,zero) ),
inference(resolve,[$cnf( $equal(divide(x,z),zero) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
quotient(x,z,zero),
inference(resolve,[$cnf( quotient(x,z,divide(x,z)) )],[refute_0_1,refute_0_40]) ).
cnf(refute_0_42,plain,
less_equal(x,z),
inference(resolve,[$cnf( quotient(x,z,zero) )],[refute_0_41,refute_0_0]) ).
cnf(refute_0_43,plain,
$false,
inference(resolve,[$cnf( less_equal(x,z) )],[refute_0_42,prove_transitivity_of_less_equal]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : HEN005-2 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n007.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 13:06:24 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 22.10/22.29 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.10/22.29
% 22.10/22.29 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 22.10/22.30
%------------------------------------------------------------------------------