%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : HEN006-5 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n010.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 12:58:37 EDT 2022
% Result : Unsatisfiable 0.19s 0.37s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 17
% Syntax : Number of clauses : 45 ( 25 unt; 0 nHn; 32 RR)
% Number of literals : 76 ( 75 equ; 32 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 34 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(quotient_smaller_than_numerator,axiom,
divide(divide(X,Y),X) = zero ).
cnf(quotient_property,axiom,
divide(divide(divide(X,Z),divide(Y,Z)),divide(divide(X,Y),Z)) = zero ).
cnf(zero_is_smallest,axiom,
divide(zero,X) = zero ).
cnf(x_divide_zero_is_x,axiom,
divide(X,zero) = X ).
cnf(a_divide_b_divide_d_is_zero,hypothesis,
divide(divide(a,b),d) = zero ).
cnf(prove_property_of_divide1,negated_conjecture,
divide(divide(a,d),b) != zero ).
cnf(refute_0_0,plain,
divide(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),divide(divide(divide(a,d),divide(b,d)),Z)) = zero,
inference(subst,[],[quotient_property:[bind(X,$fot(divide(a,d))),bind(Y,$fot(divide(b,d)))]]) ).
cnf(refute_0_1,plain,
divide(divide(divide(a,d),divide(b,d)),divide(divide(a,b),d)) = zero,
inference(subst,[],[quotient_property:[bind(X,$fot(a)),bind(Y,$fot(b)),bind(Z,$fot(d))]]) ).
cnf(refute_0_2,plain,
( divide(divide(divide(a,d),divide(b,d)),divide(divide(a,b),d)) != zero
| divide(divide(a,b),d) != zero
| divide(divide(divide(a,d),divide(b,d)),zero) = zero ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(divide(a,d),divide(b,d)),divide(divide(a,b),d)),zero) ),[0,1],$fot(zero)]]) ).
cnf(refute_0_3,plain,
( divide(divide(divide(a,d),divide(b,d)),divide(divide(a,b),d)) != zero
| divide(divide(divide(a,d),divide(b,d)),zero) = zero ),
inference(resolve,[$cnf( $equal(divide(divide(a,b),d),zero) )],[a_divide_b_divide_d_is_zero,refute_0_2]) ).
cnf(refute_0_4,plain,
divide(divide(divide(a,d),divide(b,d)),zero) = zero,
inference(resolve,[$cnf( $equal(divide(divide(divide(a,d),divide(b,d)),divide(divide(a,b),d)),zero) )],[refute_0_1,refute_0_3]) ).
cnf(refute_0_5,plain,
divide(divide(divide(a,d),divide(b,d)),zero) = divide(divide(a,d),divide(b,d)),
inference(subst,[],[x_divide_zero_is_x:[bind(X,$fot(divide(divide(a,d),divide(b,d))))]]) ).
cnf(refute_0_6,plain,
( divide(divide(divide(a,d),divide(b,d)),zero) != divide(divide(a,d),divide(b,d))
| divide(divide(divide(a,d),divide(b,d)),zero) != zero
| divide(divide(a,d),divide(b,d)) = zero ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(divide(a,d),divide(b,d)),zero),zero) ),[0],$fot(divide(divide(a,d),divide(b,d)))]]) ).
cnf(refute_0_7,plain,
( divide(divide(divide(a,d),divide(b,d)),zero) != zero
| divide(divide(a,d),divide(b,d)) = zero ),
inference(resolve,[$cnf( $equal(divide(divide(divide(a,d),divide(b,d)),zero),divide(divide(a,d),divide(b,d))) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
divide(divide(a,d),divide(b,d)) = zero,
inference(resolve,[$cnf( $equal(divide(divide(divide(a,d),divide(b,d)),zero),zero) )],[refute_0_4,refute_0_7]) ).
cnf(refute_0_9,plain,
( divide(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),divide(divide(divide(a,d),divide(b,d)),Z)) != zero
| divide(divide(a,d),divide(b,d)) != zero
| divide(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),divide(zero,Z)) = zero ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),divide(divide(divide(a,d),divide(b,d)),Z)),zero) ),[0,1,0],$fot(zero)]]) ).
cnf(refute_0_10,plain,
( divide(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),divide(divide(divide(a,d),divide(b,d)),Z)) != zero
| divide(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),divide(zero,Z)) = zero ),
inference(resolve,[$cnf( $equal(divide(divide(a,d),divide(b,d)),zero) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
divide(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),divide(zero,Z)) = zero,
inference(resolve,[$cnf( $equal(divide(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),divide(divide(divide(a,d),divide(b,d)),Z)),zero) )],[refute_0_0,refute_0_10]) ).
cnf(refute_0_12,plain,
divide(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),zero) = divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),
inference(subst,[],[x_divide_zero_is_x:[bind(X,$fot(divide(divide(divide(a,d),Z),divide(divide(b,d),Z))))]]) ).
cnf(refute_0_13,plain,
divide(zero,Z) = zero,
inference(subst,[],[zero_is_smallest:[bind(X,$fot(Z))]]) ).
cnf(refute_0_14,plain,
divide(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),divide(zero,Z)) = divide(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),divide(zero,Z)),
introduced(tautology,[refl,[$fot(divide(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),divide(zero,Z)))]]) ).
cnf(refute_0_15,plain,
( divide(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),divide(zero,Z)) != divide(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),divide(zero,Z))
| divide(zero,Z) != zero
| divide(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),divide(zero,Z)) = divide(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),zero) ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),divide(zero,Z)),divide(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),divide(zero,Z))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_16,plain,
( divide(zero,Z) != zero
| divide(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),divide(zero,Z)) = divide(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),zero) ),
inference(resolve,[$cnf( $equal(divide(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),divide(zero,Z)),divide(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),divide(zero,Z))) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
divide(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),divide(zero,Z)) = divide(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),zero),
inference(resolve,[$cnf( $equal(divide(zero,Z),zero) )],[refute_0_13,refute_0_16]) ).
cnf(refute_0_18,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_19,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_20,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_22,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
( divide(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),divide(zero,Z)) != divide(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),zero)
| divide(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),zero) != divide(divide(divide(a,d),Z),divide(divide(b,d),Z))
| divide(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),divide(zero,Z)) = divide(divide(divide(a,d),Z),divide(divide(b,d),Z)) ),
inference(subst,[],[refute_0_22:[bind(X0,$fot(divide(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),divide(zero,Z)))),bind(Y0,$fot(divide(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),zero))),bind(Z0,$fot(divide(divide(divide(a,d),Z),divide(divide(b,d),Z))))]]) ).
cnf(refute_0_24,plain,
( divide(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),zero) != divide(divide(divide(a,d),Z),divide(divide(b,d),Z))
| divide(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),divide(zero,Z)) = divide(divide(divide(a,d),Z),divide(divide(b,d),Z)) ),
inference(resolve,[$cnf( $equal(divide(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),divide(zero,Z)),divide(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),zero)) )],[refute_0_17,refute_0_23]) ).
cnf(refute_0_25,plain,
divide(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),divide(zero,Z)) = divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),
inference(resolve,[$cnf( $equal(divide(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),zero),divide(divide(divide(a,d),Z),divide(divide(b,d),Z))) )],[refute_0_12,refute_0_24]) ).
cnf(refute_0_26,plain,
( divide(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),divide(zero,Z)) != divide(divide(divide(a,d),Z),divide(divide(b,d),Z))
| divide(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),divide(zero,Z)) != zero
| divide(divide(divide(a,d),Z),divide(divide(b,d),Z)) = zero ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),divide(zero,Z)),zero) ),[0],$fot(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)))]]) ).
cnf(refute_0_27,plain,
( divide(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),divide(zero,Z)) != zero
| divide(divide(divide(a,d),Z),divide(divide(b,d),Z)) = zero ),
inference(resolve,[$cnf( $equal(divide(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),divide(zero,Z)),divide(divide(divide(a,d),Z),divide(divide(b,d),Z))) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
divide(divide(divide(a,d),Z),divide(divide(b,d),Z)) = zero,
inference(resolve,[$cnf( $equal(divide(divide(divide(divide(a,d),Z),divide(divide(b,d),Z)),divide(zero,Z)),zero) )],[refute_0_11,refute_0_27]) ).
cnf(refute_0_29,plain,
divide(divide(divide(a,d),b),divide(divide(b,d),b)) = zero,
inference(subst,[],[refute_0_28:[bind(Z,$fot(b))]]) ).
cnf(refute_0_30,plain,
divide(divide(b,d),b) = zero,
inference(subst,[],[quotient_smaller_than_numerator:[bind(X,$fot(b)),bind(Y,$fot(d))]]) ).
cnf(refute_0_31,plain,
( divide(divide(divide(a,d),b),divide(divide(b,d),b)) != zero
| divide(divide(b,d),b) != zero
| divide(divide(divide(a,d),b),zero) = zero ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(divide(a,d),b),divide(divide(b,d),b)),zero) ),[0,1],$fot(zero)]]) ).
cnf(refute_0_32,plain,
( divide(divide(divide(a,d),b),divide(divide(b,d),b)) != zero
| divide(divide(divide(a,d),b),zero) = zero ),
inference(resolve,[$cnf( $equal(divide(divide(b,d),b),zero) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
divide(divide(divide(a,d),b),zero) = zero,
inference(resolve,[$cnf( $equal(divide(divide(divide(a,d),b),divide(divide(b,d),b)),zero) )],[refute_0_29,refute_0_32]) ).
cnf(refute_0_34,plain,
divide(divide(divide(a,d),b),zero) = divide(divide(a,d),b),
inference(subst,[],[x_divide_zero_is_x:[bind(X,$fot(divide(divide(a,d),b)))]]) ).
cnf(refute_0_35,plain,
( divide(divide(divide(a,d),b),zero) != divide(divide(a,d),b)
| divide(divide(divide(a,d),b),zero) != zero
| divide(divide(a,d),b) = zero ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(divide(a,d),b),zero),zero) ),[0],$fot(divide(divide(a,d),b))]]) ).
cnf(refute_0_36,plain,
( divide(divide(divide(a,d),b),zero) != zero
| divide(divide(a,d),b) = zero ),
inference(resolve,[$cnf( $equal(divide(divide(divide(a,d),b),zero),divide(divide(a,d),b)) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
divide(divide(a,d),b) = zero,
inference(resolve,[$cnf( $equal(divide(divide(divide(a,d),b),zero),zero) )],[refute_0_33,refute_0_36]) ).
cnf(refute_0_38,plain,
$false,
inference(resolve,[$cnf( $equal(divide(divide(a,d),b),zero) )],[refute_0_37,prove_property_of_divide1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : HEN006-5 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n010.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 14:34:33 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.37 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.37
% 0.19/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.38
%------------------------------------------------------------------------------