%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : HEN008-5 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n003.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 0.77s 0.94s
% Output : CNFRefutation 0.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 15
% Syntax : Number of clauses : 38 ( 18 unt; 0 nHn; 23 RR)
% Number of literals : 68 ( 67 equ; 32 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 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 : 35 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
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(divide_and_equal,axiom,
( divide(X,Y) != zero
| divide(Y,X) != zero
| X = Y ) ).
cnf(a_divide_b_is_zero,hypothesis,
divide(a,b) = zero ).
cnf(prove_property_of_divide3,negated_conjecture,
divide(divide(a,c),divide(b,c)) != zero ).
cnf(refute_0_0,plain,
( divide(divide(divide(a,X_6),divide(b,X_6)),zero) != zero
| divide(zero,divide(divide(a,X_6),divide(b,X_6))) != zero
| zero = divide(divide(a,X_6),divide(b,X_6)) ),
inference(subst,[],[divide_and_equal:[bind(X,$fot(zero)),bind(Y,$fot(divide(divide(a,X_6),divide(b,X_6))))]]) ).
cnf(refute_0_1,plain,
divide(divide(divide(a,X_6),divide(b,X_6)),divide(divide(a,b),X_6)) = zero,
inference(subst,[],[quotient_property:[bind(X,$fot(a)),bind(Y,$fot(b)),bind(Z,$fot(X_6))]]) ).
cnf(refute_0_2,plain,
( divide(divide(divide(a,X_6),divide(b,X_6)),divide(divide(a,b),X_6)) != zero
| divide(a,b) != zero
| divide(divide(divide(a,X_6),divide(b,X_6)),divide(zero,X_6)) = zero ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(divide(a,X_6),divide(b,X_6)),divide(divide(a,b),X_6)),zero) ),[0,1,0],$fot(zero)]]) ).
cnf(refute_0_3,plain,
( divide(divide(divide(a,X_6),divide(b,X_6)),divide(divide(a,b),X_6)) != zero
| divide(divide(divide(a,X_6),divide(b,X_6)),divide(zero,X_6)) = zero ),
inference(resolve,[$cnf( $equal(divide(a,b),zero) )],[a_divide_b_is_zero,refute_0_2]) ).
cnf(refute_0_4,plain,
divide(divide(divide(a,X_6),divide(b,X_6)),divide(zero,X_6)) = zero,
inference(resolve,[$cnf( $equal(divide(divide(divide(a,X_6),divide(b,X_6)),divide(divide(a,b),X_6)),zero) )],[refute_0_1,refute_0_3]) ).
cnf(refute_0_5,plain,
divide(zero,X_6) = zero,
inference(subst,[],[zero_is_smallest:[bind(X,$fot(X_6))]]) ).
cnf(refute_0_6,plain,
divide(divide(divide(a,X_6),divide(b,X_6)),divide(zero,X_6)) = divide(divide(divide(a,X_6),divide(b,X_6)),divide(zero,X_6)),
introduced(tautology,[refl,[$fot(divide(divide(divide(a,X_6),divide(b,X_6)),divide(zero,X_6)))]]) ).
cnf(refute_0_7,plain,
( divide(divide(divide(a,X_6),divide(b,X_6)),divide(zero,X_6)) != divide(divide(divide(a,X_6),divide(b,X_6)),divide(zero,X_6))
| divide(zero,X_6) != zero
| divide(divide(divide(a,X_6),divide(b,X_6)),divide(zero,X_6)) = divide(divide(divide(a,X_6),divide(b,X_6)),zero) ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(divide(a,X_6),divide(b,X_6)),divide(zero,X_6)),divide(divide(divide(a,X_6),divide(b,X_6)),divide(zero,X_6))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_8,plain,
( divide(zero,X_6) != zero
| divide(divide(divide(a,X_6),divide(b,X_6)),divide(zero,X_6)) = divide(divide(divide(a,X_6),divide(b,X_6)),zero) ),
inference(resolve,[$cnf( $equal(divide(divide(divide(a,X_6),divide(b,X_6)),divide(zero,X_6)),divide(divide(divide(a,X_6),divide(b,X_6)),divide(zero,X_6))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
divide(divide(divide(a,X_6),divide(b,X_6)),divide(zero,X_6)) = divide(divide(divide(a,X_6),divide(b,X_6)),zero),
inference(resolve,[$cnf( $equal(divide(zero,X_6),zero) )],[refute_0_5,refute_0_8]) ).
cnf(refute_0_10,plain,
( divide(divide(divide(a,X_6),divide(b,X_6)),divide(zero,X_6)) != divide(divide(divide(a,X_6),divide(b,X_6)),zero)
| divide(divide(divide(a,X_6),divide(b,X_6)),divide(zero,X_6)) != zero
| divide(divide(divide(a,X_6),divide(b,X_6)),zero) = zero ),
introduced(tautology,[equality,[$cnf( $equal(divide(divide(divide(a,X_6),divide(b,X_6)),divide(zero,X_6)),zero) ),[0],$fot(divide(divide(divide(a,X_6),divide(b,X_6)),zero))]]) ).
cnf(refute_0_11,plain,
( divide(divide(divide(a,X_6),divide(b,X_6)),divide(zero,X_6)) != zero
| divide(divide(divide(a,X_6),divide(b,X_6)),zero) = zero ),
inference(resolve,[$cnf( $equal(divide(divide(divide(a,X_6),divide(b,X_6)),divide(zero,X_6)),divide(divide(divide(a,X_6),divide(b,X_6)),zero)) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
divide(divide(divide(a,X_6),divide(b,X_6)),zero) = zero,
inference(resolve,[$cnf( $equal(divide(divide(divide(a,X_6),divide(b,X_6)),divide(zero,X_6)),zero) )],[refute_0_4,refute_0_11]) ).
cnf(refute_0_13,plain,
( divide(divide(divide(a,X_6),divide(b,X_6)),zero) != zero
| zero != zero
| divide(divide(divide(a,X_6),divide(b,X_6)),zero) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(divide(divide(divide(a,X_6),divide(b,X_6)),zero),zero) ),[0],$fot(zero)]]) ).
cnf(refute_0_14,plain,
( zero != zero
| divide(divide(divide(a,X_6),divide(b,X_6)),zero) = zero ),
inference(resolve,[$cnf( $equal(divide(divide(divide(a,X_6),divide(b,X_6)),zero),zero) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
( divide(zero,divide(divide(a,X_6),divide(b,X_6))) != zero
| zero != zero
| zero = divide(divide(a,X_6),divide(b,X_6)) ),
inference(resolve,[$cnf( $equal(divide(divide(divide(a,X_6),divide(b,X_6)),zero),zero) )],[refute_0_14,refute_0_0]) ).
cnf(refute_0_16,plain,
zero = zero,
introduced(tautology,[refl,[$fot(zero)]]) ).
cnf(refute_0_17,plain,
( divide(zero,divide(divide(a,X_6),divide(b,X_6))) != zero
| zero = divide(divide(a,X_6),divide(b,X_6)) ),
inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_16,refute_0_15]) ).
cnf(refute_0_18,plain,
divide(zero,divide(divide(a,X_6),divide(b,X_6))) = zero,
inference(subst,[],[zero_is_smallest:[bind(X,$fot(divide(divide(a,X_6),divide(b,X_6))))]]) ).
cnf(refute_0_19,plain,
( divide(zero,divide(divide(a,X_6),divide(b,X_6))) != zero
| zero != zero
| divide(zero,divide(divide(a,X_6),divide(b,X_6))) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(divide(zero,divide(divide(a,X_6),divide(b,X_6))),zero) ),[0],$fot(zero)]]) ).
cnf(refute_0_20,plain,
( zero != zero
| divide(zero,divide(divide(a,X_6),divide(b,X_6))) = zero ),
inference(resolve,[$cnf( $equal(divide(zero,divide(divide(a,X_6),divide(b,X_6))),zero) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
( zero != zero
| zero = divide(divide(a,X_6),divide(b,X_6)) ),
inference(resolve,[$cnf( $equal(divide(zero,divide(divide(a,X_6),divide(b,X_6))),zero) )],[refute_0_20,refute_0_17]) ).
cnf(refute_0_22,plain,
zero = divide(divide(a,X_6),divide(b,X_6)),
inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_16,refute_0_21]) ).
cnf(refute_0_23,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_24,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_25,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
( zero != divide(divide(a,X_6),divide(b,X_6))
| divide(divide(a,X_6),divide(b,X_6)) = zero ),
inference(subst,[],[refute_0_25:[bind(X0,$fot(zero)),bind(Y0,$fot(divide(divide(a,X_6),divide(b,X_6))))]]) ).
cnf(refute_0_27,plain,
divide(divide(a,X_6),divide(b,X_6)) = zero,
inference(resolve,[$cnf( $equal(zero,divide(divide(a,X_6),divide(b,X_6))) )],[refute_0_22,refute_0_26]) ).
cnf(refute_0_28,plain,
divide(divide(a,c),divide(b,c)) = zero,
inference(subst,[],[refute_0_27:[bind(X_6,$fot(c))]]) ).
cnf(refute_0_29,plain,
( divide(divide(a,c),divide(b,c)) != zero
| zero != zero
| divide(divide(a,c),divide(b,c)) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(divide(divide(a,c),divide(b,c)),zero) ),[0],$fot(zero)]]) ).
cnf(refute_0_30,plain,
( zero != zero
| divide(divide(a,c),divide(b,c)) = zero ),
inference(resolve,[$cnf( $equal(divide(divide(a,c),divide(b,c)),zero) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
zero != zero,
inference(resolve,[$cnf( $equal(divide(divide(a,c),divide(b,c)),zero) )],[refute_0_30,prove_property_of_divide3]) ).
cnf(refute_0_32,plain,
$false,
inference(resolve,[$cnf( $equal(zero,zero) )],[refute_0_16,refute_0_31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : HEN008-5 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n003.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 14:42:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.77/0.94 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.77/0.94
% 0.77/0.94 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.77/0.94
%------------------------------------------------------------------------------