TSTP Solution File: HEN009-2 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : HEN009-2 : 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 12:58:42 EDT 2022
% Result : Unsatisfiable 0.42s 0.57s
% Output : CNFRefutation 0.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of clauses : 53 ( 22 unt; 0 nHn; 46 RR)
% Number of literals : 107 ( 13 equ; 57 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(less_equal_quotient,axiom,
( ~ quotient(X,Y,zero)
| less_equal(X,Y) ) ).
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(x_divide_x_is_zero,axiom,
quotient(X,X,zero) ).
cnf(transitivity_of_less_equal,axiom,
( ~ less_equal(X,Y)
| ~ less_equal(Y,Z)
| less_equal(X,Z) ) ).
cnf(xQyLEz_implies_xQzLEy,axiom,
( ~ quotient(X,Y,W1)
| ~ less_equal(W1,Z)
| ~ quotient(X,Z,W2)
| less_equal(W2,Y) ) ).
cnf(identity_divide_a,hypothesis,
quotient(identity,a,idQa) ).
cnf(identity_divide_idQa,hypothesis,
quotient(identity,idQa,idQ_idQa) ).
cnf(identity_divide_idQ_idQa,hypothesis,
quotient(identity,idQ_idQa,idQ__idQ_idQa) ).
cnf(prove_one_inversion_equals_three,negated_conjecture,
idQa != idQ__idQ_idQa ).
cnf(refute_0_0,plain,
( ~ less_equal(idQ_idQa,X_281)
| ~ quotient(identity,X_281,X_278)
| ~ quotient(identity,idQa,idQ_idQa)
| less_equal(X_278,idQa) ),
inference(subst,[],[xQyLEz_implies_xQzLEy:[bind(W1,$fot(idQ_idQa)),bind(W2,$fot(X_278)),bind(X,$fot(identity)),bind(Y,$fot(idQa)),bind(Z,$fot(X_281))]]) ).
cnf(refute_0_1,plain,
( ~ less_equal(idQ_idQa,X_281)
| ~ quotient(identity,X_281,X_278)
| less_equal(X_278,idQa) ),
inference(resolve,[$cnf( quotient(identity,idQa,idQ_idQa) )],[identity_divide_idQa,refute_0_0]) ).
cnf(refute_0_2,plain,
( ~ less_equal(idQ_idQa,idQ_idQa)
| ~ quotient(identity,idQ_idQa,idQ__idQ_idQa)
| less_equal(idQ__idQ_idQa,idQa) ),
inference(subst,[],[refute_0_1:[bind(X_278,$fot(idQ__idQ_idQa)),bind(X_281,$fot(idQ_idQa))]]) ).
cnf(refute_0_3,plain,
( ~ less_equal(idQ_idQa,idQ_idQa)
| less_equal(idQ__idQ_idQa,idQa) ),
inference(resolve,[$cnf( quotient(identity,idQ_idQa,idQ__idQ_idQa) )],[identity_divide_idQ_idQa,refute_0_2]) ).
cnf(refute_0_4,plain,
quotient(X_11,X_11,zero),
inference(subst,[],[x_divide_x_is_zero:[bind(X,$fot(X_11))]]) ).
cnf(refute_0_5,plain,
( ~ quotient(X_11,X_11,zero)
| less_equal(X_11,X_11) ),
inference(subst,[],[less_equal_quotient:[bind(X,$fot(X_11)),bind(Y,$fot(X_11))]]) ).
cnf(refute_0_6,plain,
less_equal(X_11,X_11),
inference(resolve,[$cnf( quotient(X_11,X_11,zero) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
less_equal(idQ_idQa,idQ_idQa),
inference(subst,[],[refute_0_6:[bind(X_11,$fot(idQ_idQa))]]) ).
cnf(refute_0_8,plain,
less_equal(idQ__idQ_idQa,idQa),
inference(resolve,[$cnf( less_equal(idQ_idQa,idQ_idQa) )],[refute_0_7,refute_0_3]) ).
cnf(refute_0_9,plain,
( ~ less_equal(idQ__idQ_idQa,idQa)
| ~ less_equal(idQa,idQ__idQ_idQa)
| idQ__idQ_idQa = idQa ),
inference(subst,[],[less_equal_and_equal:[bind(X,$fot(idQ__idQ_idQa)),bind(Y,$fot(idQa))]]) ).
cnf(refute_0_10,plain,
quotient(identity,X_306,divide(identity,X_306)),
inference(subst,[],[closure:[bind(X,$fot(identity)),bind(Y,$fot(X_306))]]) ).
cnf(refute_0_11,plain,
( ~ less_equal(X_277,a)
| ~ quotient(identity,X_280,X_277)
| ~ quotient(identity,a,idQa)
| less_equal(idQa,X_280) ),
inference(subst,[],[xQyLEz_implies_xQzLEy:[bind(W1,$fot(X_277)),bind(W2,$fot(idQa)),bind(X,$fot(identity)),bind(Y,$fot(X_280)),bind(Z,$fot(a))]]) ).
cnf(refute_0_12,plain,
( ~ less_equal(X_277,a)
| ~ quotient(identity,X_280,X_277)
| less_equal(idQa,X_280) ),
inference(resolve,[$cnf( quotient(identity,a,idQa) )],[identity_divide_a,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ less_equal(divide(identity,X_306),a)
| ~ quotient(identity,X_306,divide(identity,X_306))
| less_equal(idQa,X_306) ),
inference(subst,[],[refute_0_12:[bind(X_277,$fot(divide(identity,X_306))),bind(X_280,$fot(X_306))]]) ).
cnf(refute_0_14,plain,
( ~ less_equal(divide(identity,X_306),a)
| less_equal(idQa,X_306) ),
inference(resolve,[$cnf( quotient(identity,X_306,divide(identity,X_306)) )],[refute_0_10,refute_0_13]) ).
cnf(refute_0_15,plain,
( ~ less_equal(divide(identity,idQ__idQ_idQa),a)
| less_equal(idQa,idQ__idQ_idQa) ),
inference(subst,[],[refute_0_14:[bind(X_306,$fot(idQ__idQ_idQa))]]) ).
cnf(refute_0_16,plain,
( ~ less_equal(divide(identity,idQ__idQ_idQa),idQ_idQa)
| ~ less_equal(idQ_idQa,Z)
| less_equal(divide(identity,idQ__idQ_idQa),Z) ),
inference(subst,[],[transitivity_of_less_equal:[bind(X,$fot(divide(identity,idQ__idQ_idQa))),bind(Y,$fot(idQ_idQa))]]) ).
cnf(refute_0_17,plain,
less_equal(idQ__idQ_idQa,idQ__idQ_idQa),
inference(subst,[],[refute_0_6:[bind(X_11,$fot(idQ__idQ_idQa))]]) ).
cnf(refute_0_18,plain,
quotient(identity,X_283,divide(identity,X_283)),
inference(subst,[],[closure:[bind(X,$fot(identity)),bind(Y,$fot(X_283))]]) ).
cnf(refute_0_19,plain,
( ~ less_equal(idQ__idQ_idQa,X_281)
| ~ quotient(identity,X_281,X_278)
| ~ quotient(identity,idQ_idQa,idQ__idQ_idQa)
| less_equal(X_278,idQ_idQa) ),
inference(subst,[],[xQyLEz_implies_xQzLEy:[bind(W1,$fot(idQ__idQ_idQa)),bind(W2,$fot(X_278)),bind(X,$fot(identity)),bind(Y,$fot(idQ_idQa)),bind(Z,$fot(X_281))]]) ).
cnf(refute_0_20,plain,
( ~ less_equal(idQ__idQ_idQa,X_281)
| ~ quotient(identity,X_281,X_278)
| less_equal(X_278,idQ_idQa) ),
inference(resolve,[$cnf( quotient(identity,idQ_idQa,idQ__idQ_idQa) )],[identity_divide_idQ_idQa,refute_0_19]) ).
cnf(refute_0_21,plain,
( ~ less_equal(idQ__idQ_idQa,X_283)
| ~ quotient(identity,X_283,divide(identity,X_283))
| less_equal(divide(identity,X_283),idQ_idQa) ),
inference(subst,[],[refute_0_20:[bind(X_278,$fot(divide(identity,X_283))),bind(X_281,$fot(X_283))]]) ).
cnf(refute_0_22,plain,
( ~ less_equal(idQ__idQ_idQa,X_283)
| less_equal(divide(identity,X_283),idQ_idQa) ),
inference(resolve,[$cnf( quotient(identity,X_283,divide(identity,X_283)) )],[refute_0_18,refute_0_21]) ).
cnf(refute_0_23,plain,
( ~ less_equal(idQ__idQ_idQa,idQ__idQ_idQa)
| less_equal(divide(identity,idQ__idQ_idQa),idQ_idQa) ),
inference(subst,[],[refute_0_22:[bind(X_283,$fot(idQ__idQ_idQa))]]) ).
cnf(refute_0_24,plain,
less_equal(divide(identity,idQ__idQ_idQa),idQ_idQa),
inference(resolve,[$cnf( less_equal(idQ__idQ_idQa,idQ__idQ_idQa) )],[refute_0_17,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ less_equal(idQ_idQa,Z)
| less_equal(divide(identity,idQ__idQ_idQa),Z) ),
inference(resolve,[$cnf( less_equal(divide(identity,idQ__idQ_idQa),idQ_idQa) )],[refute_0_24,refute_0_16]) ).
cnf(refute_0_26,plain,
( ~ less_equal(idQ_idQa,a)
| less_equal(divide(identity,idQ__idQ_idQa),a) ),
inference(subst,[],[refute_0_25:[bind(Z,$fot(a))]]) ).
cnf(refute_0_27,plain,
( ~ less_equal(idQa,X_281)
| ~ quotient(identity,X_281,X_278)
| ~ quotient(identity,a,idQa)
| less_equal(X_278,a) ),
inference(subst,[],[xQyLEz_implies_xQzLEy:[bind(W1,$fot(idQa)),bind(W2,$fot(X_278)),bind(X,$fot(identity)),bind(Y,$fot(a)),bind(Z,$fot(X_281))]]) ).
cnf(refute_0_28,plain,
( ~ less_equal(idQa,X_281)
| ~ quotient(identity,X_281,X_278)
| less_equal(X_278,a) ),
inference(resolve,[$cnf( quotient(identity,a,idQa) )],[identity_divide_a,refute_0_27]) ).
cnf(refute_0_29,plain,
( ~ less_equal(idQa,idQa)
| ~ quotient(identity,idQa,idQ_idQa)
| less_equal(idQ_idQa,a) ),
inference(subst,[],[refute_0_28:[bind(X_278,$fot(idQ_idQa)),bind(X_281,$fot(idQa))]]) ).
cnf(refute_0_30,plain,
( ~ less_equal(idQa,idQa)
| less_equal(idQ_idQa,a) ),
inference(resolve,[$cnf( quotient(identity,idQa,idQ_idQa) )],[identity_divide_idQa,refute_0_29]) ).
cnf(refute_0_31,plain,
less_equal(idQa,idQa),
inference(subst,[],[refute_0_6:[bind(X_11,$fot(idQa))]]) ).
cnf(refute_0_32,plain,
less_equal(idQ_idQa,a),
inference(resolve,[$cnf( less_equal(idQa,idQa) )],[refute_0_31,refute_0_30]) ).
cnf(refute_0_33,plain,
less_equal(divide(identity,idQ__idQ_idQa),a),
inference(resolve,[$cnf( less_equal(idQ_idQa,a) )],[refute_0_32,refute_0_26]) ).
cnf(refute_0_34,plain,
less_equal(idQa,idQ__idQ_idQa),
inference(resolve,[$cnf( less_equal(divide(identity,idQ__idQ_idQa),a) )],[refute_0_33,refute_0_15]) ).
cnf(refute_0_35,plain,
( ~ less_equal(idQ__idQ_idQa,idQa)
| idQ__idQ_idQa = idQa ),
inference(resolve,[$cnf( less_equal(idQa,idQ__idQ_idQa) )],[refute_0_34,refute_0_9]) ).
cnf(refute_0_36,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_37,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_38,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
( idQ__idQ_idQa != idQa
| idQa = idQ__idQ_idQa ),
inference(subst,[],[refute_0_38:[bind(X0,$fot(idQ__idQ_idQa)),bind(Y0,$fot(idQa))]]) ).
cnf(refute_0_40,plain,
idQ__idQ_idQa != idQa,
inference(resolve,[$cnf( $equal(idQa,idQ__idQ_idQa) )],[refute_0_39,prove_one_inversion_equals_three]) ).
cnf(refute_0_41,plain,
~ less_equal(idQ__idQ_idQa,idQa),
inference(resolve,[$cnf( $equal(idQ__idQ_idQa,idQa) )],[refute_0_35,refute_0_40]) ).
cnf(refute_0_42,plain,
$false,
inference(resolve,[$cnf( less_equal(idQ__idQ_idQa,idQa) )],[refute_0_8,refute_0_41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : HEN009-2 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % 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 14:18:03 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.42/0.57 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.42/0.57
% 0.42/0.57 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.42/0.57
%------------------------------------------------------------------------------