%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : GEG021_1 : TPTP v8.2.0. Bugfixed v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : do_cvc5 %s %d

% Computer : n017.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  : 300s
% DateTime : Wed May 29 16:44:39 EDT 2024

% Result   : Theorem 0.22s 0.55s
% Output   : Proof 0.22s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14  % Problem    : GEG021_1 : TPTP v8.2.0. Bugfixed v5.2.0.
% 0.12/0.15  % Command    : do_cvc5 %s %d
% 0.16/0.36  % Computer : n017.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37  % CPULimit   : 300
% 0.16/0.37  % WCLimit    : 300
% 0.16/0.37  % DateTime   : Sun May 26 08:19:09 EDT 2024
% 0.16/0.37  % CPUTime    : 
% 0.22/0.50  %----Proving TF0_ARI
% 0.22/0.55  --- Run --finite-model-find --decision=internal at 15...
% 0.22/0.55  % SZS status Theorem for /export/starexec/sandbox/tmp/tmp.W6c4Uga70l/cvc5---1.0.5_2273.smt2
% 0.22/0.55  % SZS output start Proof for /export/starexec/sandbox/tmp/tmp.W6c4Uga70l/cvc5---1.0.5_2273.smt2
% 0.22/0.55  (assume a0 (not (=> (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (<= (tptp.d X Z) (+ (tptp.d X Y) (tptp.d Y Z)))) (forall ((X tptp.city)) (= (tptp.d X X) 0)) (= (tptp.d tptp.berlin tptp.munich) 510) (= (tptp.d tptp.berlin tptp.cologne) 480) (= (tptp.d tptp.berlin tptp.frankfurt) 420) (= (tptp.d tptp.saarbruecken tptp.frankfurt) 160) (= (tptp.d tptp.saarbruecken tptp.cologne) 190) (= (tptp.d tptp.hamburg tptp.cologne) 360) (= (tptp.d tptp.hamburg tptp.frankfurt) 390) (= (tptp.d tptp.cologne tptp.frankfurt) 150) (= (tptp.d tptp.hamburg tptp.kiel) 90) (= (tptp.d tptp.hamburg tptp.berlin) 250) (= (tptp.d tptp.munich tptp.frankfurt) 300) (= (tptp.d tptp.munich tptp.saarbruecken) 360)) (<= (tptp.d tptp.cologne tptp.berlin) 500))))
% 0.22/0.55  (assume a1 true)
% 0.22/0.55  (step t1 (cl (not (= (=> (and (= (tptp.d tptp.berlin tptp.cologne) 480) (>= (tptp.d tptp.cologne tptp.berlin) 501) (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin))) (and (= 480 (tptp.d tptp.cologne tptp.berlin)) (>= (tptp.d tptp.cologne tptp.berlin) 501))) (not (and (= (tptp.d tptp.berlin tptp.cologne) 480) (>= (tptp.d tptp.cologne tptp.berlin) 501) (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin)))))) (not (=> (and (= (tptp.d tptp.berlin tptp.cologne) 480) (>= (tptp.d tptp.cologne tptp.berlin) 501) (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin))) (and (= 480 (tptp.d tptp.cologne tptp.berlin)) (>= (tptp.d tptp.cologne tptp.berlin) 501)))) (not (and (= (tptp.d tptp.berlin tptp.cologne) 480) (>= (tptp.d tptp.cologne tptp.berlin) 501) (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin))))) :rule equiv_pos2)
% 0.22/0.55  (step t2 (cl (= (and (= (tptp.d tptp.berlin tptp.cologne) 480) (>= (tptp.d tptp.cologne tptp.berlin) 501) (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin))) (and (= (tptp.d tptp.berlin tptp.cologne) 480) (>= (tptp.d tptp.cologne tptp.berlin) 501) (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin))))) :rule refl)
% 0.22/0.55  (step t3 (cl (= (= (and (= 480 (tptp.d tptp.cologne tptp.berlin)) (>= (tptp.d tptp.cologne tptp.berlin) 501)) false) (not (and (= 480 (tptp.d tptp.cologne tptp.berlin)) (>= (tptp.d tptp.cologne tptp.berlin) 501))))) :rule equiv_simplify)
% 0.22/0.55  (step t4 (cl (= (and (= 480 (tptp.d tptp.cologne tptp.berlin)) (>= (tptp.d tptp.cologne tptp.berlin) 501)) false) (not (not (and (= 480 (tptp.d tptp.cologne tptp.berlin)) (>= (tptp.d tptp.cologne tptp.berlin) 501))))) :rule equiv2 :premises (t3))
% 0.22/0.55  (step t5 (cl (not (not (not (and (= 480 (tptp.d tptp.cologne tptp.berlin)) (>= (tptp.d tptp.cologne tptp.berlin) 501))))) (and (= 480 (tptp.d tptp.cologne tptp.berlin)) (>= (tptp.d tptp.cologne tptp.berlin) 501))) :rule not_not)
% 0.22/0.55  (step t6 (cl (= (and (= 480 (tptp.d tptp.cologne tptp.berlin)) (>= (tptp.d tptp.cologne tptp.berlin) 501)) false) (and (= 480 (tptp.d tptp.cologne tptp.berlin)) (>= (tptp.d tptp.cologne tptp.berlin) 501))) :rule resolution :premises (t4 t5))
% 0.22/0.55  (step t7 (cl (=> (and (= 480 (tptp.d tptp.cologne tptp.berlin)) (>= (tptp.d tptp.cologne tptp.berlin) 501)) false) (and (= 480 (tptp.d tptp.cologne tptp.berlin)) (>= (tptp.d tptp.cologne tptp.berlin) 501))) :rule implies_neg1)
% 0.22/0.55  (anchor :step t8)
% 0.22/0.55  (assume t8.a0 (= 480 (tptp.d tptp.cologne tptp.berlin)))
% 0.22/0.55  (assume t8.a1 (>= (tptp.d tptp.cologne tptp.berlin) 501))
% 0.22/0.55  (step t8.t1 (cl (= (tptp.d tptp.cologne tptp.berlin) 480)) :rule symm :premises (t8.a0))
% 0.22/0.55  (step t8.t2 (cl (=> (= (tptp.d tptp.cologne tptp.berlin) 480) false) (= (tptp.d tptp.cologne tptp.berlin) 480)) :rule implies_neg1)
% 0.22/0.55  (anchor :step t8.t3)
% 0.22/0.55  (assume t8.t3.a0 (= (tptp.d tptp.cologne tptp.berlin) 480))
% 0.22/0.55  (step t8.t3.t1 (cl (not (= (<= (+ (* 1.0 (tptp.d tptp.cologne tptp.berlin)) (* (- 1.0) (tptp.d tptp.cologne tptp.berlin))) (+ (* 1.0 480) (* (- 1.0) 501))) false)) (not (<= (+ (* 1.0 (tptp.d tptp.cologne tptp.berlin)) (* (- 1.0) (tptp.d tptp.cologne tptp.berlin))) (+ (* 1.0 480) (* (- 1.0) 501)))) false) :rule equiv_pos2)
% 0.22/0.55  (step t8.t3.t2 (cl (= (* 1.0 (tptp.d tptp.cologne tptp.berlin)) (to_real (tptp.d tptp.cologne tptp.berlin)))) :rule all_simplify)
% 0.22/0.55  (step t8.t3.t3 (cl (= (* (- 1.0) (tptp.d tptp.cologne tptp.berlin)) (to_real (* (- 1) (tptp.d tptp.cologne tptp.berlin))))) :rule all_simplify)
% 0.22/0.55  (step t8.t3.t4 (cl (= (+ (* 1.0 (tptp.d tptp.cologne tptp.berlin)) (* (- 1.0) (tptp.d tptp.cologne tptp.berlin))) (+ (to_real (tptp.d tptp.cologne tptp.berlin)) (to_real (* (- 1) (tptp.d tptp.cologne tptp.berlin)))))) :rule cong :premises (t8.t3.t2 t8.t3.t3))
% 0.22/0.55  (step t8.t3.t5 (cl (= (+ (to_real (tptp.d tptp.cologne tptp.berlin)) (to_real (* (- 1) (tptp.d tptp.cologne tptp.berlin)))) 0.0)) :rule all_simplify)
% 0.22/0.55  (step t8.t3.t6 (cl (= (+ (* 1.0 (tptp.d tptp.cologne tptp.berlin)) (* (- 1.0) (tptp.d tptp.cologne tptp.berlin))) 0.0)) :rule trans :premises (t8.t3.t4 t8.t3.t5))
% 0.22/0.55  (step t8.t3.t7 (cl (= (* 1.0 480) 480.0)) :rule all_simplify)
% 0.22/0.55  (step t8.t3.t8 (cl (= (* (- 1.0) 501) (- 501.0))) :rule all_simplify)
% 0.22/0.55  (step t8.t3.t9 (cl (= (+ (* 1.0 480) (* (- 1.0) 501)) (+ 480.0 (- 501.0)))) :rule cong :premises (t8.t3.t7 t8.t3.t8))
% 0.22/0.55  (step t8.t3.t10 (cl (= (+ 480.0 (- 501.0)) (- 21.0))) :rule all_simplify)
% 0.22/0.55  (step t8.t3.t11 (cl (= (+ (* 1.0 480) (* (- 1.0) 501)) (- 21.0))) :rule trans :premises (t8.t3.t9 t8.t3.t10))
% 0.22/0.55  (step t8.t3.t12 (cl (= (<= (+ (* 1.0 (tptp.d tptp.cologne tptp.berlin)) (* (- 1.0) (tptp.d tptp.cologne tptp.berlin))) (+ (* 1.0 480) (* (- 1.0) 501))) (<= 0.0 (- 21.0)))) :rule cong :premises (t8.t3.t6 t8.t3.t11))
% 0.22/0.55  (step t8.t3.t13 (cl (= (<= 0.0 (- 21.0)) false)) :rule all_simplify)
% 0.22/0.55  (step t8.t3.t14 (cl (= (<= (+ (* 1.0 (tptp.d tptp.cologne tptp.berlin)) (* (- 1.0) (tptp.d tptp.cologne tptp.berlin))) (+ (* 1.0 480) (* (- 1.0) 501))) false)) :rule trans :premises (t8.t3.t12 t8.t3.t13))
% 0.22/0.55  (step t8.t3.t15 (cl (not (= (* 1.0 (tptp.d tptp.cologne tptp.berlin)) (* 1.0 480))) (not (<= (* (- 1.0) (tptp.d tptp.cologne tptp.berlin)) (* (- 1.0) 501))) (<= (+ (* 1.0 (tptp.d tptp.cologne tptp.berlin)) (* (- 1.0) (tptp.d tptp.cologne tptp.berlin))) (+ (* 1.0 480) (* (- 1.0) 501)))) :rule la_generic :args ((- 1) 1 1))
% 0.22/0.55  (step t8.t3.t16 (cl (=> (and (> 1.0 0) (= (tptp.d tptp.cologne tptp.berlin) 480)) (= (* 1.0 (tptp.d tptp.cologne tptp.berlin)) (* 1.0 480)))) :rule la_mult_pos)
% 0.22/0.55  (step t8.t3.t17 (cl (not (and (> 1.0 0) (= (tptp.d tptp.cologne tptp.berlin) 480))) (= (* 1.0 (tptp.d tptp.cologne tptp.berlin)) (* 1.0 480))) :rule implies :premises (t8.t3.t16))
% 0.22/0.55  (step t8.t3.t18 (cl (and (> 1.0 0) (= (tptp.d tptp.cologne tptp.berlin) 480)) (not (> 1.0 0)) (not (= (tptp.d tptp.cologne tptp.berlin) 480))) :rule and_neg)
% 0.22/0.55  (step t8.t3.t19 (cl (= (= (> 1.0 0) true) (> 1.0 0))) :rule equiv_simplify)
% 0.22/0.55  (step t8.t3.t20 (cl (not (= (> 1.0 0) true)) (> 1.0 0)) :rule equiv1 :premises (t8.t3.t19))
% 0.22/0.55  (step t8.t3.t21 (cl (= (> 1.0 0) true)) :rule hole :args ((> 1.0 0)))
% 0.22/0.55  (step t8.t3.t22 (cl (> 1.0 0)) :rule resolution :premises (t8.t3.t20 t8.t3.t21))
% 0.22/0.55  (step t8.t3.t23 (cl (and (> 1.0 0) (= (tptp.d tptp.cologne tptp.berlin) 480))) :rule resolution :premises (t8.t3.t18 t8.t3.t22 t8.t3.a0))
% 0.22/0.55  (step t8.t3.t24 (cl (= (* 1.0 (tptp.d tptp.cologne tptp.berlin)) (* 1.0 480))) :rule resolution :premises (t8.t3.t17 t8.t3.t23))
% 0.22/0.55  (step t8.t3.t25 (cl (=> (and (< (- 1.0) 0) (>= (tptp.d tptp.cologne tptp.berlin) 501)) (<= (* (- 1.0) (tptp.d tptp.cologne tptp.berlin)) (* (- 1.0) 501)))) :rule la_mult_neg)
% 0.22/0.55  (step t8.t3.t26 (cl (not (and (< (- 1.0) 0) (>= (tptp.d tptp.cologne tptp.berlin) 501))) (<= (* (- 1.0) (tptp.d tptp.cologne tptp.berlin)) (* (- 1.0) 501))) :rule implies :premises (t8.t3.t25))
% 0.22/0.55  (step t8.t3.t27 (cl (and (< (- 1.0) 0) (>= (tptp.d tptp.cologne tptp.berlin) 501)) (not (< (- 1.0) 0)) (not (>= (tptp.d tptp.cologne tptp.berlin) 501))) :rule and_neg)
% 0.22/0.55  (step t8.t3.t28 (cl (= (= (< (- 1.0) 0) true) (< (- 1.0) 0))) :rule equiv_simplify)
% 0.22/0.55  (step t8.t3.t29 (cl (not (= (< (- 1.0) 0) true)) (< (- 1.0) 0)) :rule equiv1 :premises (t8.t3.t28))
% 0.22/0.55  (step t8.t3.t30 (cl (= (< (- 1.0) 0) true)) :rule hole :args ((< (- 1.0) 0)))
% 0.22/0.55  (step t8.t3.t31 (cl (< (- 1.0) 0)) :rule resolution :premises (t8.t3.t29 t8.t3.t30))
% 0.22/0.55  (step t8.t3.t32 (cl (and (< (- 1.0) 0) (>= (tptp.d tptp.cologne tptp.berlin) 501))) :rule resolution :premises (t8.t3.t27 t8.t3.t31 t8.a1))
% 0.22/0.55  (step t8.t3.t33 (cl (<= (* (- 1.0) (tptp.d tptp.cologne tptp.berlin)) (* (- 1.0) 501))) :rule resolution :premises (t8.t3.t26 t8.t3.t32))
% 0.22/0.55  (step t8.t3.t34 (cl (<= (+ (* 1.0 (tptp.d tptp.cologne tptp.berlin)) (* (- 1.0) (tptp.d tptp.cologne tptp.berlin))) (+ (* 1.0 480) (* (- 1.0) 501)))) :rule resolution :premises (t8.t3.t15 t8.t3.t24 t8.t3.t33))
% 0.22/0.55  (step t8.t3.t35 (cl false) :rule resolution :premises (t8.t3.t1 t8.t3.t14 t8.t3.t34))
% 0.22/0.55  (step t8.t3 (cl (not (= (tptp.d tptp.cologne tptp.berlin) 480)) false) :rule subproof :discharge (t8.t3.a0))
% 0.22/0.55  (step t8.t4 (cl (=> (= (tptp.d tptp.cologne tptp.berlin) 480) false) false) :rule resolution :premises (t8.t2 t8.t3))
% 0.22/0.55  (step t8.t5 (cl (=> (= (tptp.d tptp.cologne tptp.berlin) 480) false) (not false)) :rule implies_neg2)
% 0.22/0.55  (step t8.t6 (cl (=> (= (tptp.d tptp.cologne tptp.berlin) 480) false) (=> (= (tptp.d tptp.cologne tptp.berlin) 480) false)) :rule resolution :premises (t8.t4 t8.t5))
% 0.22/0.55  (step t8.t7 (cl (=> (= (tptp.d tptp.cologne tptp.berlin) 480) false)) :rule contraction :premises (t8.t6))
% 0.22/0.55  (step t8.t8 (cl (= (=> (= (tptp.d tptp.cologne tptp.berlin) 480) false) (not (= (tptp.d tptp.cologne tptp.berlin) 480)))) :rule implies_simplify)
% 0.22/0.55  (step t8.t9 (cl (not (=> (= (tptp.d tptp.cologne tptp.berlin) 480) false)) (not (= (tptp.d tptp.cologne tptp.berlin) 480))) :rule equiv1 :premises (t8.t8))
% 0.22/0.55  (step t8.t10 (cl (not (= (tptp.d tptp.cologne tptp.berlin) 480))) :rule resolution :premises (t8.t7 t8.t9))
% 0.22/0.55  (step t8.t11 (cl) :rule resolution :premises (t8.t1 t8.t10))
% 0.22/0.55  (step t8 (cl (not (= 480 (tptp.d tptp.cologne tptp.berlin))) (not (>= (tptp.d tptp.cologne tptp.berlin) 501)) false) :rule subproof :discharge (t8.a0 t8.a1))
% 0.22/0.55  (step t9 (cl (not (and (= 480 (tptp.d tptp.cologne tptp.berlin)) (>= (tptp.d tptp.cologne tptp.berlin) 501))) (= 480 (tptp.d tptp.cologne tptp.berlin))) :rule and_pos)
% 0.22/0.55  (step t10 (cl (not (and (= 480 (tptp.d tptp.cologne tptp.berlin)) (>= (tptp.d tptp.cologne tptp.berlin) 501))) (>= (tptp.d tptp.cologne tptp.berlin) 501)) :rule and_pos)
% 0.22/0.55  (step t11 (cl false (not (and (= 480 (tptp.d tptp.cologne tptp.berlin)) (>= (tptp.d tptp.cologne tptp.berlin) 501))) (not (and (= 480 (tptp.d tptp.cologne tptp.berlin)) (>= (tptp.d tptp.cologne tptp.berlin) 501)))) :rule resolution :premises (t8 t9 t10))
% 0.22/0.55  (step t12 (cl (not (and (= 480 (tptp.d tptp.cologne tptp.berlin)) (>= (tptp.d tptp.cologne tptp.berlin) 501))) (not (and (= 480 (tptp.d tptp.cologne tptp.berlin)) (>= (tptp.d tptp.cologne tptp.berlin) 501))) false) :rule reordering :premises (t11))
% 0.22/0.55  (step t13 (cl (not (and (= 480 (tptp.d tptp.cologne tptp.berlin)) (>= (tptp.d tptp.cologne tptp.berlin) 501))) false) :rule contraction :premises (t12))
% 0.22/0.55  (step t14 (cl (=> (and (= 480 (tptp.d tptp.cologne tptp.berlin)) (>= (tptp.d tptp.cologne tptp.berlin) 501)) false) false) :rule resolution :premises (t7 t13))
% 0.22/0.55  (step t15 (cl (=> (and (= 480 (tptp.d tptp.cologne tptp.berlin)) (>= (tptp.d tptp.cologne tptp.berlin) 501)) false) (not false)) :rule implies_neg2)
% 0.22/0.55  (step t16 (cl (=> (and (= 480 (tptp.d tptp.cologne tptp.berlin)) (>= (tptp.d tptp.cologne tptp.berlin) 501)) false) (=> (and (= 480 (tptp.d tptp.cologne tptp.berlin)) (>= (tptp.d tptp.cologne tptp.berlin) 501)) false)) :rule resolution :premises (t14 t15))
% 0.22/0.55  (step t17 (cl (=> (and (= 480 (tptp.d tptp.cologne tptp.berlin)) (>= (tptp.d tptp.cologne tptp.berlin) 501)) false)) :rule contraction :premises (t16))
% 0.22/0.55  (step t18 (cl (= (=> (and (= 480 (tptp.d tptp.cologne tptp.berlin)) (>= (tptp.d tptp.cologne tptp.berlin) 501)) false) (not (and (= 480 (tptp.d tptp.cologne tptp.berlin)) (>= (tptp.d tptp.cologne tptp.berlin) 501))))) :rule implies_simplify)
% 0.22/0.55  (step t19 (cl (not (=> (and (= 480 (tptp.d tptp.cologne tptp.berlin)) (>= (tptp.d tptp.cologne tptp.berlin) 501)) false)) (not (and (= 480 (tptp.d tptp.cologne tptp.berlin)) (>= (tptp.d tptp.cologne tptp.berlin) 501)))) :rule equiv1 :premises (t18))
% 0.22/0.55  (step t20 (cl (not (and (= 480 (tptp.d tptp.cologne tptp.berlin)) (>= (tptp.d tptp.cologne tptp.berlin) 501)))) :rule resolution :premises (t17 t19))
% 0.22/0.55  (step t21 (cl (= (and (= 480 (tptp.d tptp.cologne tptp.berlin)) (>= (tptp.d tptp.cologne tptp.berlin) 501)) false)) :rule resolution :premises (t6 t20))
% 0.22/0.55  (step t22 (cl (= (=> (and (= (tptp.d tptp.berlin tptp.cologne) 480) (>= (tptp.d tptp.cologne tptp.berlin) 501) (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin))) (and (= 480 (tptp.d tptp.cologne tptp.berlin)) (>= (tptp.d tptp.cologne tptp.berlin) 501))) (=> (and (= (tptp.d tptp.berlin tptp.cologne) 480) (>= (tptp.d tptp.cologne tptp.berlin) 501) (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin))) false))) :rule cong :premises (t2 t21))
% 0.22/0.55  (step t23 (cl (= (=> (and (= (tptp.d tptp.berlin tptp.cologne) 480) (>= (tptp.d tptp.cologne tptp.berlin) 501) (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin))) false) (not (and (= (tptp.d tptp.berlin tptp.cologne) 480) (>= (tptp.d tptp.cologne tptp.berlin) 501) (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin)))))) :rule all_simplify)
% 0.22/0.55  (step t24 (cl (= (=> (and (= (tptp.d tptp.berlin tptp.cologne) 480) (>= (tptp.d tptp.cologne tptp.berlin) 501) (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin))) (and (= 480 (tptp.d tptp.cologne tptp.berlin)) (>= (tptp.d tptp.cologne tptp.berlin) 501))) (not (and (= (tptp.d tptp.berlin tptp.cologne) 480) (>= (tptp.d tptp.cologne tptp.berlin) 501) (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin)))))) :rule trans :premises (t22 t23))
% 0.22/0.55  (step t25 (cl (=> (and (= (tptp.d tptp.berlin tptp.cologne) 480) (>= (tptp.d tptp.cologne tptp.berlin) 501) (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin))) (and (= 480 (tptp.d tptp.cologne tptp.berlin)) (>= (tptp.d tptp.cologne tptp.berlin) 501))) (and (= (tptp.d tptp.berlin tptp.cologne) 480) (>= (tptp.d tptp.cologne tptp.berlin) 501) (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin)))) :rule implies_neg1)
% 0.22/0.55  (anchor :step t26)
% 0.22/0.55  (assume t26.a0 (= (tptp.d tptp.berlin tptp.cologne) 480))
% 0.22/0.55  (assume t26.a1 (>= (tptp.d tptp.cologne tptp.berlin) 501))
% 0.22/0.55  (assume t26.a2 (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin)))
% 0.22/0.55  (step t26.t1 (cl (and (= 480 (tptp.d tptp.cologne tptp.berlin)) (>= (tptp.d tptp.cologne tptp.berlin) 501)) (not (= 480 (tptp.d tptp.cologne tptp.berlin))) (not (>= (tptp.d tptp.cologne tptp.berlin) 501))) :rule and_neg)
% 0.22/0.55  (step t26.t2 (cl (=> (and (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin)) (= (tptp.d tptp.berlin tptp.cologne) 480)) (= 480 (tptp.d tptp.cologne tptp.berlin))) (and (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin)) (= (tptp.d tptp.berlin tptp.cologne) 480))) :rule implies_neg1)
% 0.22/0.55  (anchor :step t26.t3)
% 0.22/0.55  (assume t26.t3.a0 (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin)))
% 0.22/0.55  (assume t26.t3.a1 (= (tptp.d tptp.berlin tptp.cologne) 480))
% 0.22/0.55  (step t26.t3.t1 (cl (= 480 (tptp.d tptp.berlin tptp.cologne))) :rule symm :premises (t26.t3.a1))
% 0.22/0.55  (step t26.t3.t2 (cl (= (tptp.d tptp.cologne tptp.berlin) (tptp.d tptp.berlin tptp.cologne))) :rule symm :premises (t26.t3.a0))
% 0.22/0.55  (step t26.t3.t3 (cl (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin))) :rule symm :premises (t26.t3.t2))
% 0.22/0.55  (step t26.t3.t4 (cl (= 480 (tptp.d tptp.cologne tptp.berlin))) :rule trans :premises (t26.t3.t1 t26.t3.t3))
% 0.22/0.55  (step t26.t3 (cl (not (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin))) (not (= (tptp.d tptp.berlin tptp.cologne) 480)) (= 480 (tptp.d tptp.cologne tptp.berlin))) :rule subproof :discharge (t26.t3.a0 t26.t3.a1))
% 0.22/0.55  (step t26.t4 (cl (not (and (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin)) (= (tptp.d tptp.berlin tptp.cologne) 480))) (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin))) :rule and_pos)
% 0.22/0.55  (step t26.t5 (cl (not (and (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin)) (= (tptp.d tptp.berlin tptp.cologne) 480))) (= (tptp.d tptp.berlin tptp.cologne) 480)) :rule and_pos)
% 0.22/0.55  (step t26.t6 (cl (= 480 (tptp.d tptp.cologne tptp.berlin)) (not (and (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin)) (= (tptp.d tptp.berlin tptp.cologne) 480))) (not (and (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin)) (= (tptp.d tptp.berlin tptp.cologne) 480)))) :rule resolution :premises (t26.t3 t26.t4 t26.t5))
% 0.22/0.55  (step t26.t7 (cl (not (and (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin)) (= (tptp.d tptp.berlin tptp.cologne) 480))) (not (and (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin)) (= (tptp.d tptp.berlin tptp.cologne) 480))) (= 480 (tptp.d tptp.cologne tptp.berlin))) :rule reordering :premises (t26.t6))
% 0.22/0.55  (step t26.t8 (cl (not (and (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin)) (= (tptp.d tptp.berlin tptp.cologne) 480))) (= 480 (tptp.d tptp.cologne tptp.berlin))) :rule contraction :premises (t26.t7))
% 0.22/0.55  (step t26.t9 (cl (=> (and (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin)) (= (tptp.d tptp.berlin tptp.cologne) 480)) (= 480 (tptp.d tptp.cologne tptp.berlin))) (= 480 (tptp.d tptp.cologne tptp.berlin))) :rule resolution :premises (t26.t2 t26.t8))
% 0.22/0.55  (step t26.t10 (cl (=> (and (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin)) (= (tptp.d tptp.berlin tptp.cologne) 480)) (= 480 (tptp.d tptp.cologne tptp.berlin))) (not (= 480 (tptp.d tptp.cologne tptp.berlin)))) :rule implies_neg2)
% 0.22/0.55  (step t26.t11 (cl (=> (and (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin)) (= (tptp.d tptp.berlin tptp.cologne) 480)) (= 480 (tptp.d tptp.cologne tptp.berlin))) (=> (and (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin)) (= (tptp.d tptp.berlin tptp.cologne) 480)) (= 480 (tptp.d tptp.cologne tptp.berlin)))) :rule resolution :premises (t26.t9 t26.t10))
% 0.22/0.55  (step t26.t12 (cl (=> (and (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin)) (= (tptp.d tptp.berlin tptp.cologne) 480)) (= 480 (tptp.d tptp.cologne tptp.berlin)))) :rule contraction :premises (t26.t11))
% 0.22/0.55  (step t26.t13 (cl (not (and (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin)) (= (tptp.d tptp.berlin tptp.cologne) 480))) (= 480 (tptp.d tptp.cologne tptp.berlin))) :rule implies :premises (t26.t12))
% 0.22/0.55  (step t26.t14 (cl (and (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin)) (= (tptp.d tptp.berlin tptp.cologne) 480)) (not (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin))) (not (= (tptp.d tptp.berlin tptp.cologne) 480))) :rule and_neg)
% 0.22/0.55  (step t26.t15 (cl (and (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin)) (= (tptp.d tptp.berlin tptp.cologne) 480))) :rule resolution :premises (t26.t14 t26.a2 t26.a0))
% 0.22/0.55  (step t26.t16 (cl (= 480 (tptp.d tptp.cologne tptp.berlin))) :rule resolution :premises (t26.t13 t26.t15))
% 0.22/0.55  (step t26.t17 (cl (and (= 480 (tptp.d tptp.cologne tptp.berlin)) (>= (tptp.d tptp.cologne tptp.berlin) 501))) :rule resolution :premises (t26.t1 t26.t16 t26.a1))
% 0.22/0.55  (step t26 (cl (not (= (tptp.d tptp.berlin tptp.cologne) 480)) (not (>= (tptp.d tptp.cologne tptp.berlin) 501)) (not (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin))) (and (= 480 (tptp.d tptp.cologne tptp.berlin)) (>= (tptp.d tptp.cologne tptp.berlin) 501))) :rule subproof :discharge (t26.a0 t26.a1 t26.a2))
% 0.22/0.55  (step t27 (cl (not (and (= (tptp.d tptp.berlin tptp.cologne) 480) (>= (tptp.d tptp.cologne tptp.berlin) 501) (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin)))) (= (tptp.d tptp.berlin tptp.cologne) 480)) :rule and_pos)
% 0.22/0.55  (step t28 (cl (not (and (= (tptp.d tptp.berlin tptp.cologne) 480) (>= (tptp.d tptp.cologne tptp.berlin) 501) (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin)))) (>= (tptp.d tptp.cologne tptp.berlin) 501)) :rule and_pos)
% 0.22/0.55  (step t29 (cl (not (and (= (tptp.d tptp.berlin tptp.cologne) 480) (>= (tptp.d tptp.cologne tptp.berlin) 501) (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin)))) (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin))) :rule and_pos)
% 0.22/0.55  (step t30 (cl (and (= 480 (tptp.d tptp.cologne tptp.berlin)) (>= (tptp.d tptp.cologne tptp.berlin) 501)) (not (and (= (tptp.d tptp.berlin tptp.cologne) 480) (>= (tptp.d tptp.cologne tptp.berlin) 501) (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin)))) (not (and (= (tptp.d tptp.berlin tptp.cologne) 480) (>= (tptp.d tptp.cologne tptp.berlin) 501) (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin)))) (not (and (= (tptp.d tptp.berlin tptp.cologne) 480) (>= (tptp.d tptp.cologne tptp.berlin) 501) (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin))))) :rule resolution :premises (t26 t27 t28 t29))
% 0.22/0.55  (step t31 (cl (not (and (= (tptp.d tptp.berlin tptp.cologne) 480) (>= (tptp.d tptp.cologne tptp.berlin) 501) (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin)))) (not (and (= (tptp.d tptp.berlin tptp.cologne) 480) (>= (tptp.d tptp.cologne tptp.berlin) 501) (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin)))) (not (and (= (tptp.d tptp.berlin tptp.cologne) 480) (>= (tptp.d tptp.cologne tptp.berlin) 501) (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin)))) (and (= 480 (tptp.d tptp.cologne tptp.berlin)) (>= (tptp.d tptp.cologne tptp.berlin) 501))) :rule reordering :premises (t30))
% 0.22/0.55  (step t32 (cl (not (and (= (tptp.d tptp.berlin tptp.cologne) 480) (>= (tptp.d tptp.cologne tptp.berlin) 501) (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin)))) (and (= 480 (tptp.d tptp.cologne tptp.berlin)) (>= (tptp.d tptp.cologne tptp.berlin) 501))) :rule contraction :premises (t31))
% 0.22/0.55  (step t33 (cl (=> (and (= (tptp.d tptp.berlin tptp.cologne) 480) (>= (tptp.d tptp.cologne tptp.berlin) 501) (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin))) (and (= 480 (tptp.d tptp.cologne tptp.berlin)) (>= (tptp.d tptp.cologne tptp.berlin) 501))) (and (= 480 (tptp.d tptp.cologne tptp.berlin)) (>= (tptp.d tptp.cologne tptp.berlin) 501))) :rule resolution :premises (t25 t32))
% 0.22/0.55  (step t34 (cl (=> (and (= (tptp.d tptp.berlin tptp.cologne) 480) (>= (tptp.d tptp.cologne tptp.berlin) 501) (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin))) (and (= 480 (tptp.d tptp.cologne tptp.berlin)) (>= (tptp.d tptp.cologne tptp.berlin) 501))) (not (and (= 480 (tptp.d tptp.cologne tptp.berlin)) (>= (tptp.d tptp.cologne tptp.berlin) 501)))) :rule implies_neg2)
% 0.22/0.55  (step t35 (cl (=> (and (= (tptp.d tptp.berlin tptp.cologne) 480) (>= (tptp.d tptp.cologne tptp.berlin) 501) (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin))) (and (= 480 (tptp.d tptp.cologne tptp.berlin)) (>= (tptp.d tptp.cologne tptp.berlin) 501))) (=> (and (= (tptp.d tptp.berlin tptp.cologne) 480) (>= (tptp.d tptp.cologne tptp.berlin) 501) (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin))) (and (= 480 (tptp.d tptp.cologne tptp.berlin)) (>= (tptp.d tptp.cologne tptp.berlin) 501)))) :rule resolution :premises (t33 t34))
% 0.22/0.55  (step t36 (cl (=> (and (= (tptp.d tptp.berlin tptp.cologne) 480) (>= (tptp.d tptp.cologne tptp.berlin) 501) (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin))) (and (= 480 (tptp.d tptp.cologne tptp.berlin)) (>= (tptp.d tptp.cologne tptp.berlin) 501)))) :rule contraction :premises (t35))
% 0.22/0.55  (step t37 (cl (not (and (= (tptp.d tptp.berlin tptp.cologne) 480) (>= (tptp.d tptp.cologne tptp.berlin) 501) (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin))))) :rule resolution :premises (t1 t24 t36))
% 0.22/0.55  (step t38 (cl (not (= (tptp.d tptp.berlin tptp.cologne) 480)) (not (>= (tptp.d tptp.cologne tptp.berlin) 501)) (not (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin)))) :rule not_and :premises (t37))
% 0.22/0.55  (step t39 (cl (not (>= (tptp.d tptp.cologne tptp.berlin) 501)) (not (= (tptp.d tptp.berlin tptp.cologne) 480)) (not (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin)))) :rule reordering :premises (t38))
% 0.22/0.55  (step t40 (cl (=> (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin))) (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X)))) :rule implies_neg1)
% 0.22/0.55  (anchor :step t41)
% 0.22/0.55  (assume t41.a0 (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))))
% 0.22/0.55  (step t41.t1 (cl (or (not (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X)))) (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin)))) :rule forall_inst :args ((:= X tptp.berlin) (:= Y tptp.cologne)))
% 0.22/0.55  (step t41.t2 (cl (not (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X)))) (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin))) :rule or :premises (t41.t1))
% 0.22/0.55  (step t41.t3 (cl (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin))) :rule resolution :premises (t41.t2 t41.a0))
% 0.22/0.55  (step t41 (cl (not (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X)))) (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin))) :rule subproof :discharge (t41.a0))
% 0.22/0.55  (step t42 (cl (=> (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin))) (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin))) :rule resolution :premises (t40 t41))
% 0.22/0.55  (step t43 (cl (=> (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin))) (not (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin)))) :rule implies_neg2)
% 0.22/0.55  (step t44 (cl (=> (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin))) (=> (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin)))) :rule resolution :premises (t42 t43))
% 0.22/0.55  (step t45 (cl (=> (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin)))) :rule contraction :premises (t44))
% 0.22/0.55  (step t46 (cl (not (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X)))) (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin))) :rule implies :premises (t45))
% 0.22/0.55  (step t47 (cl (not (= (not (=> (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (<= (tptp.d X Z) (+ (tptp.d X Y) (tptp.d Y Z)))) (forall ((X tptp.city)) (= (tptp.d X X) 0)) (= (tptp.d tptp.berlin tptp.munich) 510) (= (tptp.d tptp.berlin tptp.cologne) 480) (= (tptp.d tptp.berlin tptp.frankfurt) 420) (= (tptp.d tptp.saarbruecken tptp.frankfurt) 160) (= (tptp.d tptp.saarbruecken tptp.cologne) 190) (= (tptp.d tptp.hamburg tptp.cologne) 360) (= (tptp.d tptp.hamburg tptp.frankfurt) 390) (= (tptp.d tptp.cologne tptp.frankfurt) 150) (= (tptp.d tptp.hamburg tptp.kiel) 90) (= (tptp.d tptp.hamburg tptp.berlin) 250) (= (tptp.d tptp.munich tptp.frankfurt) 300) (= (tptp.d tptp.munich tptp.saarbruecken) 360)) (<= (tptp.d tptp.cologne tptp.berlin) 500))) (not (=> (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))) (forall ((X tptp.city)) (= (tptp.d X X) 0))) (not (>= (tptp.d tptp.cologne tptp.berlin) 501)))))) (not (not (=> (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (<= (tptp.d X Z) (+ (tptp.d X Y) (tptp.d Y Z)))) (forall ((X tptp.city)) (= (tptp.d X X) 0)) (= (tptp.d tptp.berlin tptp.munich) 510) (= (tptp.d tptp.berlin tptp.cologne) 480) (= (tptp.d tptp.berlin tptp.frankfurt) 420) (= (tptp.d tptp.saarbruecken tptp.frankfurt) 160) (= (tptp.d tptp.saarbruecken tptp.cologne) 190) (= (tptp.d tptp.hamburg tptp.cologne) 360) (= (tptp.d tptp.hamburg tptp.frankfurt) 390) (= (tptp.d tptp.cologne tptp.frankfurt) 150) (= (tptp.d tptp.hamburg tptp.kiel) 90) (= (tptp.d tptp.hamburg tptp.berlin) 250) (= (tptp.d tptp.munich tptp.frankfurt) 300) (= (tptp.d tptp.munich tptp.saarbruecken) 360)) (<= (tptp.d tptp.cologne tptp.berlin) 500)))) (not (=> (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))) (forall ((X tptp.city)) (= (tptp.d X X) 0))) (not (>= (tptp.d tptp.cologne tptp.berlin) 501))))) :rule equiv_pos2)
% 0.22/0.55  (step t48 (cl (= (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))))) :rule refl)
% 0.22/0.55  (anchor :step t49 :args ((X tptp.city) (:= X X) (Y tptp.city) (:= Y Y) (Z tptp.city) (:= Z Z)))
% 0.22/0.55  (step t49.t1 (cl (= X X)) :rule refl)
% 0.22/0.55  (step t49.t2 (cl (= Y Y)) :rule refl)
% 0.22/0.55  (step t49.t3 (cl (= Z Z)) :rule refl)
% 0.22/0.55  (step t49.t4 (cl (= (<= (tptp.d X Z) (+ (tptp.d X Y) (tptp.d Y Z))) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1)))) :rule all_simplify)
% 0.22/0.55  (step t49 (cl (= (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (<= (tptp.d X Z) (+ (tptp.d X Y) (tptp.d Y Z)))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))))) :rule bind)
% 0.22/0.55  (step t50 (cl (= (forall ((X tptp.city)) (= (tptp.d X X) 0)) (forall ((X tptp.city)) (= (tptp.d X X) 0)))) :rule refl)
% 0.22/0.55  (step t51 (cl (= (= (tptp.d tptp.berlin tptp.munich) 510) (= (tptp.d tptp.berlin tptp.munich) 510))) :rule refl)
% 0.22/0.55  (step t52 (cl (= (= (tptp.d tptp.berlin tptp.cologne) 480) (= (tptp.d tptp.berlin tptp.cologne) 480))) :rule refl)
% 0.22/0.55  (step t53 (cl (= (= (tptp.d tptp.berlin tptp.frankfurt) 420) (= (tptp.d tptp.berlin tptp.frankfurt) 420))) :rule refl)
% 0.22/0.55  (step t54 (cl (= (= (tptp.d tptp.saarbruecken tptp.frankfurt) 160) (= (tptp.d tptp.saarbruecken tptp.frankfurt) 160))) :rule refl)
% 0.22/0.55  (step t55 (cl (= (= (tptp.d tptp.saarbruecken tptp.cologne) 190) (= (tptp.d tptp.saarbruecken tptp.cologne) 190))) :rule refl)
% 0.22/0.55  (step t56 (cl (= (= (tptp.d tptp.hamburg tptp.cologne) 360) (= (tptp.d tptp.hamburg tptp.cologne) 360))) :rule refl)
% 0.22/0.55  (step t57 (cl (= (= (tptp.d tptp.hamburg tptp.frankfurt) 390) (= (tptp.d tptp.hamburg tptp.frankfurt) 390))) :rule refl)
% 0.22/0.55  (step t58 (cl (= (= (tptp.d tptp.cologne tptp.frankfurt) 150) (= (tptp.d tptp.cologne tptp.frankfurt) 150))) :rule refl)
% 0.22/0.55  (step t59 (cl (= (= (tptp.d tptp.hamburg tptp.kiel) 90) (= (tptp.d tptp.hamburg tptp.kiel) 90))) :rule refl)
% 0.22/0.55  (step t60 (cl (= (= (tptp.d tptp.hamburg tptp.berlin) 250) (= (tptp.d tptp.hamburg tptp.berlin) 250))) :rule refl)
% 0.22/0.55  (step t61 (cl (= (= (tptp.d tptp.munich tptp.frankfurt) 300) (= (tptp.d tptp.munich tptp.frankfurt) 300))) :rule refl)
% 0.22/0.55  (step t62 (cl (= (= (tptp.d tptp.munich tptp.saarbruecken) 360) (= (tptp.d tptp.munich tptp.saarbruecken) 360))) :rule refl)
% 0.22/0.55  (step t63 (cl (= (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (<= (tptp.d X Z) (+ (tptp.d X Y) (tptp.d Y Z)))) (forall ((X tptp.city)) (= (tptp.d X X) 0)) (= (tptp.d tptp.berlin tptp.munich) 510) (= (tptp.d tptp.berlin tptp.cologne) 480) (= (tptp.d tptp.berlin tptp.frankfurt) 420) (= (tptp.d tptp.saarbruecken tptp.frankfurt) 160) (= (tptp.d tptp.saarbruecken tptp.cologne) 190) (= (tptp.d tptp.hamburg tptp.cologne) 360) (= (tptp.d tptp.hamburg tptp.frankfurt) 390) (= (tptp.d tptp.cologne tptp.frankfurt) 150) (= (tptp.d tptp.hamburg tptp.kiel) 90) (= (tptp.d tptp.hamburg tptp.berlin) 250) (= (tptp.d tptp.munich tptp.frankfurt) 300) (= (tptp.d tptp.munich tptp.saarbruecken) 360)) (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))) (forall ((X tptp.city)) (= (tptp.d X X) 0)) (= (tptp.d tptp.berlin tptp.munich) 510) (= (tptp.d tptp.berlin tptp.cologne) 480) (= (tptp.d tptp.berlin tptp.frankfurt) 420) (= (tptp.d tptp.saarbruecken tptp.frankfurt) 160) (= (tptp.d tptp.saarbruecken tptp.cologne) 190) (= (tptp.d tptp.hamburg tptp.cologne) 360) (= (tptp.d tptp.hamburg tptp.frankfurt) 390) (= (tptp.d tptp.cologne tptp.frankfurt) 150) (= (tptp.d tptp.hamburg tptp.kiel) 90) (= (tptp.d tptp.hamburg tptp.berlin) 250) (= (tptp.d tptp.munich tptp.frankfurt) 300) (= (tptp.d tptp.munich tptp.saarbruecken) 360)))) :rule cong :premises (t48 t49 t50 t51 t52 t53 t54 t55 t56 t57 t58 t59 t60 t61 t62))
% 0.22/0.55  (step t64 (cl (= (<= (tptp.d tptp.cologne tptp.berlin) 500) (not (>= (tptp.d tptp.cologne tptp.berlin) 501)))) :rule all_simplify)
% 0.22/0.55  (step t65 (cl (= (=> (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (<= (tptp.d X Z) (+ (tptp.d X Y) (tptp.d Y Z)))) (forall ((X tptp.city)) (= (tptp.d X X) 0)) (= (tptp.d tptp.berlin tptp.munich) 510) (= (tptp.d tptp.berlin tptp.cologne) 480) (= (tptp.d tptp.berlin tptp.frankfurt) 420) (= (tptp.d tptp.saarbruecken tptp.frankfurt) 160) (= (tptp.d tptp.saarbruecken tptp.cologne) 190) (= (tptp.d tptp.hamburg tptp.cologne) 360) (= (tptp.d tptp.hamburg tptp.frankfurt) 390) (= (tptp.d tptp.cologne tptp.frankfurt) 150) (= (tptp.d tptp.hamburg tptp.kiel) 90) (= (tptp.d tptp.hamburg tptp.berlin) 250) (= (tptp.d tptp.munich tptp.frankfurt) 300) (= (tptp.d tptp.munich tptp.saarbruecken) 360)) (<= (tptp.d tptp.cologne tptp.berlin) 500)) (=> (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))) (forall ((X tptp.city)) (= (tptp.d X X) 0)) (= (tptp.d tptp.berlin tptp.munich) 510) (= (tptp.d tptp.berlin tptp.cologne) 480) (= (tptp.d tptp.berlin tptp.frankfurt) 420) (= (tptp.d tptp.saarbruecken tptp.frankfurt) 160) (= (tptp.d tptp.saarbruecken tptp.cologne) 190) (= (tptp.d tptp.hamburg tptp.cologne) 360) (= (tptp.d tptp.hamburg tptp.frankfurt) 390) (= (tptp.d tptp.cologne tptp.frankfurt) 150) (= (tptp.d tptp.hamburg tptp.kiel) 90) (= (tptp.d tptp.hamburg tptp.berlin) 250) (= (tptp.d tptp.munich tptp.frankfurt) 300) (= (tptp.d tptp.munich tptp.saarbruecken) 360)) (not (>= (tptp.d tptp.cologne tptp.berlin) 501))))) :rule cong :premises (t63 t64))
% 0.22/0.55  (step t66 (cl (= (not (=> (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (<= (tptp.d X Z) (+ (tptp.d X Y) (tptp.d Y Z)))) (forall ((X tptp.city)) (= (tptp.d X X) 0)) (= (tptp.d tptp.berlin tptp.munich) 510) (= (tptp.d tptp.berlin tptp.cologne) 480) (= (tptp.d tptp.berlin tptp.frankfurt) 420) (= (tptp.d tptp.saarbruecken tptp.frankfurt) 160) (= (tptp.d tptp.saarbruecken tptp.cologne) 190) (= (tptp.d tptp.hamburg tptp.cologne) 360) (= (tptp.d tptp.hamburg tptp.frankfurt) 390) (= (tptp.d tptp.cologne tptp.frankfurt) 150) (= (tptp.d tptp.hamburg tptp.kiel) 90) (= (tptp.d tptp.hamburg tptp.berlin) 250) (= (tptp.d tptp.munich tptp.frankfurt) 300) (= (tptp.d tptp.munich tptp.saarbruecken) 360)) (<= (tptp.d tptp.cologne tptp.berlin) 500))) (not (=> (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))) (forall ((X tptp.city)) (= (tptp.d X X) 0)) (= (tptp.d tptp.berlin tptp.munich) 510) (= (tptp.d tptp.berlin tptp.cologne) 480) (= (tptp.d tptp.berlin tptp.frankfurt) 420) (= (tptp.d tptp.saarbruecken tptp.frankfurt) 160) (= (tptp.d tptp.saarbruecken tptp.cologne) 190) (= (tptp.d tptp.hamburg tptp.cologne) 360) (= (tptp.d tptp.hamburg tptp.frankfurt) 390) (= (tptp.d tptp.cologne tptp.frankfurt) 150) (= (tptp.d tptp.hamburg tptp.kiel) 90) (= (tptp.d tptp.hamburg tptp.berlin) 250) (= (tptp.d tptp.munich tptp.frankfurt) 300) (= (tptp.d tptp.munich tptp.saarbruecken) 360)) (not (>= (tptp.d tptp.cologne tptp.berlin) 501)))))) :rule cong :premises (t65))
% 0.22/0.55  (step t67 (cl (= (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))))) :rule refl)
% 0.22/0.55  (step t68 (cl (= (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))))) :rule refl)
% 0.22/0.55  (step t69 (cl (= (forall ((X tptp.city)) (= (tptp.d X X) 0)) (forall ((X tptp.city)) (= (tptp.d X X) 0)))) :rule refl)
% 0.22/0.55  (step t70 (cl (and (= (tptp.d tptp.munich tptp.saarbruecken) 360) (= (tptp.d tptp.munich tptp.frankfurt) 300) (= (tptp.d tptp.hamburg tptp.berlin) 250) (= (tptp.d tptp.hamburg tptp.kiel) 90) (= (tptp.d tptp.cologne tptp.frankfurt) 150) (= (tptp.d tptp.hamburg tptp.frankfurt) 390) (= (tptp.d tptp.hamburg tptp.cologne) 360) (= (tptp.d tptp.saarbruecken tptp.cologne) 190) (= (tptp.d tptp.saarbruecken tptp.frankfurt) 160) (= (tptp.d tptp.berlin tptp.frankfurt) 420) (= (tptp.d tptp.berlin tptp.cologne) 480) (= (tptp.d tptp.berlin tptp.munich) 510)) (not (= (tptp.d tptp.munich tptp.saarbruecken) 360)) (not (= (tptp.d tptp.munich tptp.frankfurt) 300)) (not (= (tptp.d tptp.hamburg tptp.berlin) 250)) (not (= (tptp.d tptp.hamburg tptp.kiel) 90)) (not (= (tptp.d tptp.cologne tptp.frankfurt) 150)) (not (= (tptp.d tptp.hamburg tptp.frankfurt) 390)) (not (= (tptp.d tptp.hamburg tptp.cologne) 360)) (not (= (tptp.d tptp.saarbruecken tptp.cologne) 190)) (not (= (tptp.d tptp.saarbruecken tptp.frankfurt) 160)) (not (= (tptp.d tptp.berlin tptp.frankfurt) 420)) (not (= (tptp.d tptp.berlin tptp.cologne) 480)) (not (= (tptp.d tptp.berlin tptp.munich) 510))) :rule and_neg)
% 0.22/0.55  (step t71 (cl (not (= (not (=> (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (<= (tptp.d X Z) (+ (tptp.d X Y) (tptp.d Y Z)))) (forall ((X tptp.city)) (= (tptp.d X X) 0)) (= (tptp.d tptp.berlin tptp.munich) 510) (= (tptp.d tptp.berlin tptp.cologne) 480) (= (tptp.d tptp.berlin tptp.frankfurt) 420) (= (tptp.d tptp.saarbruecken tptp.frankfurt) 160) (= (tptp.d tptp.saarbruecken tptp.cologne) 190) (= (tptp.d tptp.hamburg tptp.cologne) 360) (= (tptp.d tptp.hamburg tptp.frankfurt) 390) (= (tptp.d tptp.cologne tptp.frankfurt) 150) (= (tptp.d tptp.hamburg tptp.kiel) 90) (= (tptp.d tptp.hamburg tptp.berlin) 250) (= (tptp.d tptp.munich tptp.frankfurt) 300) (= (tptp.d tptp.munich tptp.saarbruecken) 360)) (<= (tptp.d tptp.cologne tptp.berlin) 500))) (not (=> (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))) (forall ((X tptp.city)) (= (tptp.d X X) 0)) (= (tptp.d tptp.berlin tptp.munich) 510) (= (tptp.d tptp.berlin tptp.cologne) 480) (= (tptp.d tptp.berlin tptp.frankfurt) 420) (= (tptp.d tptp.saarbruecken tptp.frankfurt) 160) (= (tptp.d tptp.saarbruecken tptp.cologne) 190) (= (tptp.d tptp.hamburg tptp.cologne) 360) (= (tptp.d tptp.hamburg tptp.frankfurt) 390) (= (tptp.d tptp.cologne tptp.frankfurt) 150) (= (tptp.d tptp.hamburg tptp.kiel) 90) (= (tptp.d tptp.hamburg tptp.berlin) 250) (= (tptp.d tptp.munich tptp.frankfurt) 300) (= (tptp.d tptp.munich tptp.saarbruecken) 360)) (not (>= (tptp.d tptp.cologne tptp.berlin) 501)))))) (not (not (=> (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (<= (tptp.d X Z) (+ (tptp.d X Y) (tptp.d Y Z)))) (forall ((X tptp.city)) (= (tptp.d X X) 0)) (= (tptp.d tptp.berlin tptp.munich) 510) (= (tptp.d tptp.berlin tptp.cologne) 480) (= (tptp.d tptp.berlin tptp.frankfurt) 420) (= (tptp.d tptp.saarbruecken tptp.frankfurt) 160) (= (tptp.d tptp.saarbruecken tptp.cologne) 190) (= (tptp.d tptp.hamburg tptp.cologne) 360) (= (tptp.d tptp.hamburg tptp.frankfurt) 390) (= (tptp.d tptp.cologne tptp.frankfurt) 150) (= (tptp.d tptp.hamburg tptp.kiel) 90) (= (tptp.d tptp.hamburg tptp.berlin) 250) (= (tptp.d tptp.munich tptp.frankfurt) 300) (= (tptp.d tptp.munich tptp.saarbruecken) 360)) (<= (tptp.d tptp.cologne tptp.berlin) 500)))) (not (=> (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))) (forall ((X tptp.city)) (= (tptp.d X X) 0)) (= (tptp.d tptp.berlin tptp.munich) 510) (= (tptp.d tptp.berlin tptp.cologne) 480) (= (tptp.d tptp.berlin tptp.frankfurt) 420) (= (tptp.d tptp.saarbruecken tptp.frankfurt) 160) (= (tptp.d tptp.saarbruecken tptp.cologne) 190) (= (tptp.d tptp.hamburg tptp.cologne) 360) (= (tptp.d tptp.hamburg tptp.frankfurt) 390) (= (tptp.d tptp.cologne tptp.frankfurt) 150) (= (tptp.d tptp.hamburg tptp.kiel) 90) (= (tptp.d tptp.hamburg tptp.berlin) 250) (= (tptp.d tptp.munich tptp.frankfurt) 300) (= (tptp.d tptp.munich tptp.saarbruecken) 360)) (not (>= (tptp.d tptp.cologne tptp.berlin) 501))))) :rule equiv_pos2)
% 0.22/0.55  (step t72 (cl (not (=> (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))) (forall ((X tptp.city)) (= (tptp.d X X) 0)) (= (tptp.d tptp.berlin tptp.munich) 510) (= (tptp.d tptp.berlin tptp.cologne) 480) (= (tptp.d tptp.berlin tptp.frankfurt) 420) (= (tptp.d tptp.saarbruecken tptp.frankfurt) 160) (= (tptp.d tptp.saarbruecken tptp.cologne) 190) (= (tptp.d tptp.hamburg tptp.cologne) 360) (= (tptp.d tptp.hamburg tptp.frankfurt) 390) (= (tptp.d tptp.cologne tptp.frankfurt) 150) (= (tptp.d tptp.hamburg tptp.kiel) 90) (= (tptp.d tptp.hamburg tptp.berlin) 250) (= (tptp.d tptp.munich tptp.frankfurt) 300) (= (tptp.d tptp.munich tptp.saarbruecken) 360)) (not (>= (tptp.d tptp.cologne tptp.berlin) 501))))) :rule resolution :premises (t71 t66 a0))
% 0.22/0.55  (step t73 (cl (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))) (forall ((X tptp.city)) (= (tptp.d X X) 0)) (= (tptp.d tptp.berlin tptp.munich) 510) (= (tptp.d tptp.berlin tptp.cologne) 480) (= (tptp.d tptp.berlin tptp.frankfurt) 420) (= (tptp.d tptp.saarbruecken tptp.frankfurt) 160) (= (tptp.d tptp.saarbruecken tptp.cologne) 190) (= (tptp.d tptp.hamburg tptp.cologne) 360) (= (tptp.d tptp.hamburg tptp.frankfurt) 390) (= (tptp.d tptp.cologne tptp.frankfurt) 150) (= (tptp.d tptp.hamburg tptp.kiel) 90) (= (tptp.d tptp.hamburg tptp.berlin) 250) (= (tptp.d tptp.munich tptp.frankfurt) 300) (= (tptp.d tptp.munich tptp.saarbruecken) 360))) :rule not_implies1 :premises (t72))
% 0.22/0.55  (step t74 (cl (= (tptp.d tptp.munich tptp.saarbruecken) 360)) :rule and :premises (t73))
% 0.22/0.55  (step t75 (cl (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))) (forall ((X tptp.city)) (= (tptp.d X X) 0)) (= (tptp.d tptp.berlin tptp.munich) 510) (= (tptp.d tptp.berlin tptp.cologne) 480) (= (tptp.d tptp.berlin tptp.frankfurt) 420) (= (tptp.d tptp.saarbruecken tptp.frankfurt) 160) (= (tptp.d tptp.saarbruecken tptp.cologne) 190) (= (tptp.d tptp.hamburg tptp.cologne) 360) (= (tptp.d tptp.hamburg tptp.frankfurt) 390) (= (tptp.d tptp.cologne tptp.frankfurt) 150) (= (tptp.d tptp.hamburg tptp.kiel) 90) (= (tptp.d tptp.hamburg tptp.berlin) 250) (= (tptp.d tptp.munich tptp.frankfurt) 300) (= (tptp.d tptp.munich tptp.saarbruecken) 360))) :rule not_implies1 :premises (t72))
% 0.22/0.55  (step t76 (cl (= (tptp.d tptp.munich tptp.frankfurt) 300)) :rule and :premises (t75))
% 0.22/0.55  (step t77 (cl (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))) (forall ((X tptp.city)) (= (tptp.d X X) 0)) (= (tptp.d tptp.berlin tptp.munich) 510) (= (tptp.d tptp.berlin tptp.cologne) 480) (= (tptp.d tptp.berlin tptp.frankfurt) 420) (= (tptp.d tptp.saarbruecken tptp.frankfurt) 160) (= (tptp.d tptp.saarbruecken tptp.cologne) 190) (= (tptp.d tptp.hamburg tptp.cologne) 360) (= (tptp.d tptp.hamburg tptp.frankfurt) 390) (= (tptp.d tptp.cologne tptp.frankfurt) 150) (= (tptp.d tptp.hamburg tptp.kiel) 90) (= (tptp.d tptp.hamburg tptp.berlin) 250) (= (tptp.d tptp.munich tptp.frankfurt) 300) (= (tptp.d tptp.munich tptp.saarbruecken) 360))) :rule not_implies1 :premises (t72))
% 0.22/0.55  (step t78 (cl (= (tptp.d tptp.hamburg tptp.berlin) 250)) :rule and :premises (t77))
% 0.22/0.55  (step t79 (cl (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))) (forall ((X tptp.city)) (= (tptp.d X X) 0)) (= (tptp.d tptp.berlin tptp.munich) 510) (= (tptp.d tptp.berlin tptp.cologne) 480) (= (tptp.d tptp.berlin tptp.frankfurt) 420) (= (tptp.d tptp.saarbruecken tptp.frankfurt) 160) (= (tptp.d tptp.saarbruecken tptp.cologne) 190) (= (tptp.d tptp.hamburg tptp.cologne) 360) (= (tptp.d tptp.hamburg tptp.frankfurt) 390) (= (tptp.d tptp.cologne tptp.frankfurt) 150) (= (tptp.d tptp.hamburg tptp.kiel) 90) (= (tptp.d tptp.hamburg tptp.berlin) 250) (= (tptp.d tptp.munich tptp.frankfurt) 300) (= (tptp.d tptp.munich tptp.saarbruecken) 360))) :rule not_implies1 :premises (t72))
% 0.22/0.55  (step t80 (cl (= (tptp.d tptp.hamburg tptp.kiel) 90)) :rule and :premises (t79))
% 0.22/0.55  (step t81 (cl (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))) (forall ((X tptp.city)) (= (tptp.d X X) 0)) (= (tptp.d tptp.berlin tptp.munich) 510) (= (tptp.d tptp.berlin tptp.cologne) 480) (= (tptp.d tptp.berlin tptp.frankfurt) 420) (= (tptp.d tptp.saarbruecken tptp.frankfurt) 160) (= (tptp.d tptp.saarbruecken tptp.cologne) 190) (= (tptp.d tptp.hamburg tptp.cologne) 360) (= (tptp.d tptp.hamburg tptp.frankfurt) 390) (= (tptp.d tptp.cologne tptp.frankfurt) 150) (= (tptp.d tptp.hamburg tptp.kiel) 90) (= (tptp.d tptp.hamburg tptp.berlin) 250) (= (tptp.d tptp.munich tptp.frankfurt) 300) (= (tptp.d tptp.munich tptp.saarbruecken) 360))) :rule not_implies1 :premises (t72))
% 0.22/0.55  (step t82 (cl (= (tptp.d tptp.cologne tptp.frankfurt) 150)) :rule and :premises (t81))
% 0.22/0.55  (step t83 (cl (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))) (forall ((X tptp.city)) (= (tptp.d X X) 0)) (= (tptp.d tptp.berlin tptp.munich) 510) (= (tptp.d tptp.berlin tptp.cologne) 480) (= (tptp.d tptp.berlin tptp.frankfurt) 420) (= (tptp.d tptp.saarbruecken tptp.frankfurt) 160) (= (tptp.d tptp.saarbruecken tptp.cologne) 190) (= (tptp.d tptp.hamburg tptp.cologne) 360) (= (tptp.d tptp.hamburg tptp.frankfurt) 390) (= (tptp.d tptp.cologne tptp.frankfurt) 150) (= (tptp.d tptp.hamburg tptp.kiel) 90) (= (tptp.d tptp.hamburg tptp.berlin) 250) (= (tptp.d tptp.munich tptp.frankfurt) 300) (= (tptp.d tptp.munich tptp.saarbruecken) 360))) :rule not_implies1 :premises (t72))
% 0.22/0.55  (step t84 (cl (= (tptp.d tptp.hamburg tptp.frankfurt) 390)) :rule and :premises (t83))
% 0.22/0.55  (step t85 (cl (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))) (forall ((X tptp.city)) (= (tptp.d X X) 0)) (= (tptp.d tptp.berlin tptp.munich) 510) (= (tptp.d tptp.berlin tptp.cologne) 480) (= (tptp.d tptp.berlin tptp.frankfurt) 420) (= (tptp.d tptp.saarbruecken tptp.frankfurt) 160) (= (tptp.d tptp.saarbruecken tptp.cologne) 190) (= (tptp.d tptp.hamburg tptp.cologne) 360) (= (tptp.d tptp.hamburg tptp.frankfurt) 390) (= (tptp.d tptp.cologne tptp.frankfurt) 150) (= (tptp.d tptp.hamburg tptp.kiel) 90) (= (tptp.d tptp.hamburg tptp.berlin) 250) (= (tptp.d tptp.munich tptp.frankfurt) 300) (= (tptp.d tptp.munich tptp.saarbruecken) 360))) :rule not_implies1 :premises (t72))
% 0.22/0.55  (step t86 (cl (= (tptp.d tptp.hamburg tptp.cologne) 360)) :rule and :premises (t85))
% 0.22/0.55  (step t87 (cl (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))) (forall ((X tptp.city)) (= (tptp.d X X) 0)) (= (tptp.d tptp.berlin tptp.munich) 510) (= (tptp.d tptp.berlin tptp.cologne) 480) (= (tptp.d tptp.berlin tptp.frankfurt) 420) (= (tptp.d tptp.saarbruecken tptp.frankfurt) 160) (= (tptp.d tptp.saarbruecken tptp.cologne) 190) (= (tptp.d tptp.hamburg tptp.cologne) 360) (= (tptp.d tptp.hamburg tptp.frankfurt) 390) (= (tptp.d tptp.cologne tptp.frankfurt) 150) (= (tptp.d tptp.hamburg tptp.kiel) 90) (= (tptp.d tptp.hamburg tptp.berlin) 250) (= (tptp.d tptp.munich tptp.frankfurt) 300) (= (tptp.d tptp.munich tptp.saarbruecken) 360))) :rule not_implies1 :premises (t72))
% 0.22/0.55  (step t88 (cl (= (tptp.d tptp.saarbruecken tptp.cologne) 190)) :rule and :premises (t87))
% 0.22/0.55  (step t89 (cl (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))) (forall ((X tptp.city)) (= (tptp.d X X) 0)) (= (tptp.d tptp.berlin tptp.munich) 510) (= (tptp.d tptp.berlin tptp.cologne) 480) (= (tptp.d tptp.berlin tptp.frankfurt) 420) (= (tptp.d tptp.saarbruecken tptp.frankfurt) 160) (= (tptp.d tptp.saarbruecken tptp.cologne) 190) (= (tptp.d tptp.hamburg tptp.cologne) 360) (= (tptp.d tptp.hamburg tptp.frankfurt) 390) (= (tptp.d tptp.cologne tptp.frankfurt) 150) (= (tptp.d tptp.hamburg tptp.kiel) 90) (= (tptp.d tptp.hamburg tptp.berlin) 250) (= (tptp.d tptp.munich tptp.frankfurt) 300) (= (tptp.d tptp.munich tptp.saarbruecken) 360))) :rule not_implies1 :premises (t72))
% 0.22/0.55  (step t90 (cl (= (tptp.d tptp.saarbruecken tptp.frankfurt) 160)) :rule and :premises (t89))
% 0.22/0.55  (step t91 (cl (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))) (forall ((X tptp.city)) (= (tptp.d X X) 0)) (= (tptp.d tptp.berlin tptp.munich) 510) (= (tptp.d tptp.berlin tptp.cologne) 480) (= (tptp.d tptp.berlin tptp.frankfurt) 420) (= (tptp.d tptp.saarbruecken tptp.frankfurt) 160) (= (tptp.d tptp.saarbruecken tptp.cologne) 190) (= (tptp.d tptp.hamburg tptp.cologne) 360) (= (tptp.d tptp.hamburg tptp.frankfurt) 390) (= (tptp.d tptp.cologne tptp.frankfurt) 150) (= (tptp.d tptp.hamburg tptp.kiel) 90) (= (tptp.d tptp.hamburg tptp.berlin) 250) (= (tptp.d tptp.munich tptp.frankfurt) 300) (= (tptp.d tptp.munich tptp.saarbruecken) 360))) :rule not_implies1 :premises (t72))
% 0.22/0.55  (step t92 (cl (= (tptp.d tptp.berlin tptp.frankfurt) 420)) :rule and :premises (t91))
% 0.22/0.55  (step t93 (cl (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))) (forall ((X tptp.city)) (= (tptp.d X X) 0)) (= (tptp.d tptp.berlin tptp.munich) 510) (= (tptp.d tptp.berlin tptp.cologne) 480) (= (tptp.d tptp.berlin tptp.frankfurt) 420) (= (tptp.d tptp.saarbruecken tptp.frankfurt) 160) (= (tptp.d tptp.saarbruecken tptp.cologne) 190) (= (tptp.d tptp.hamburg tptp.cologne) 360) (= (tptp.d tptp.hamburg tptp.frankfurt) 390) (= (tptp.d tptp.cologne tptp.frankfurt) 150) (= (tptp.d tptp.hamburg tptp.kiel) 90) (= (tptp.d tptp.hamburg tptp.berlin) 250) (= (tptp.d tptp.munich tptp.frankfurt) 300) (= (tptp.d tptp.munich tptp.saarbruecken) 360))) :rule not_implies1 :premises (t72))
% 0.22/0.55  (step t94 (cl (= (tptp.d tptp.berlin tptp.cologne) 480)) :rule and :premises (t93))
% 0.22/0.55  (step t95 (cl (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))) (forall ((X tptp.city)) (= (tptp.d X X) 0)) (= (tptp.d tptp.berlin tptp.munich) 510) (= (tptp.d tptp.berlin tptp.cologne) 480) (= (tptp.d tptp.berlin tptp.frankfurt) 420) (= (tptp.d tptp.saarbruecken tptp.frankfurt) 160) (= (tptp.d tptp.saarbruecken tptp.cologne) 190) (= (tptp.d tptp.hamburg tptp.cologne) 360) (= (tptp.d tptp.hamburg tptp.frankfurt) 390) (= (tptp.d tptp.cologne tptp.frankfurt) 150) (= (tptp.d tptp.hamburg tptp.kiel) 90) (= (tptp.d tptp.hamburg tptp.berlin) 250) (= (tptp.d tptp.munich tptp.frankfurt) 300) (= (tptp.d tptp.munich tptp.saarbruecken) 360))) :rule not_implies1 :premises (t72))
% 0.22/0.55  (step t96 (cl (= (tptp.d tptp.berlin tptp.munich) 510)) :rule and :premises (t95))
% 0.22/0.55  (step t97 (cl (and (= (tptp.d tptp.munich tptp.saarbruecken) 360) (= (tptp.d tptp.munich tptp.frankfurt) 300) (= (tptp.d tptp.hamburg tptp.berlin) 250) (= (tptp.d tptp.hamburg tptp.kiel) 90) (= (tptp.d tptp.cologne tptp.frankfurt) 150) (= (tptp.d tptp.hamburg tptp.frankfurt) 390) (= (tptp.d tptp.hamburg tptp.cologne) 360) (= (tptp.d tptp.saarbruecken tptp.cologne) 190) (= (tptp.d tptp.saarbruecken tptp.frankfurt) 160) (= (tptp.d tptp.berlin tptp.frankfurt) 420) (= (tptp.d tptp.berlin tptp.cologne) 480) (= (tptp.d tptp.berlin tptp.munich) 510))) :rule resolution :premises (t70 t74 t76 t78 t80 t82 t84 t86 t88 t90 t92 t94 t96))
% 0.22/0.55  (step t98 (cl (= (tptp.d tptp.berlin tptp.munich) 510)) :rule and :premises (t97))
% 0.22/0.55  (step t99 (cl (= 510 510)) :rule refl)
% 0.22/0.55  (step t100 (cl (= (= (tptp.d tptp.berlin tptp.munich) 510) (= 510 510))) :rule cong :premises (t98 t99))
% 0.22/0.55  (step t101 (cl (= (tptp.d tptp.berlin tptp.cologne) 480)) :rule and :premises (t97))
% 0.22/0.55  (step t102 (cl (= 480 480)) :rule refl)
% 0.22/0.55  (step t103 (cl (= (= (tptp.d tptp.berlin tptp.cologne) 480) (= 480 480))) :rule cong :premises (t101 t102))
% 0.22/0.55  (step t104 (cl (= (tptp.d tptp.berlin tptp.frankfurt) 420)) :rule and :premises (t97))
% 0.22/0.55  (step t105 (cl (= 420 420)) :rule refl)
% 0.22/0.55  (step t106 (cl (= (= (tptp.d tptp.berlin tptp.frankfurt) 420) (= 420 420))) :rule cong :premises (t104 t105))
% 0.22/0.55  (step t107 (cl (= (tptp.d tptp.saarbruecken tptp.frankfurt) 160)) :rule and :premises (t97))
% 0.22/0.55  (step t108 (cl (= 160 160)) :rule refl)
% 0.22/0.55  (step t109 (cl (= (= (tptp.d tptp.saarbruecken tptp.frankfurt) 160) (= 160 160))) :rule cong :premises (t107 t108))
% 0.22/0.55  (step t110 (cl (= (tptp.d tptp.saarbruecken tptp.cologne) 190)) :rule and :premises (t97))
% 0.22/0.55  (step t111 (cl (= 190 190)) :rule refl)
% 0.22/0.55  (step t112 (cl (= (= (tptp.d tptp.saarbruecken tptp.cologne) 190) (= 190 190))) :rule cong :premises (t110 t111))
% 0.22/0.55  (step t113 (cl (= (tptp.d tptp.hamburg tptp.cologne) 360)) :rule and :premises (t97))
% 0.22/0.55  (step t114 (cl (= 360 360)) :rule refl)
% 0.22/0.55  (step t115 (cl (= (= (tptp.d tptp.hamburg tptp.cologne) 360) (= 360 360))) :rule cong :premises (t113 t114))
% 0.22/0.55  (step t116 (cl (= (tptp.d tptp.hamburg tptp.frankfurt) 390)) :rule and :premises (t97))
% 0.22/0.55  (step t117 (cl (= 390 390)) :rule refl)
% 0.22/0.55  (step t118 (cl (= (= (tptp.d tptp.hamburg tptp.frankfurt) 390) (= 390 390))) :rule cong :premises (t116 t117))
% 0.22/0.55  (step t119 (cl (= (tptp.d tptp.cologne tptp.frankfurt) 150)) :rule and :premises (t97))
% 0.22/0.55  (step t120 (cl (= 150 150)) :rule refl)
% 0.22/0.55  (step t121 (cl (= (= (tptp.d tptp.cologne tptp.frankfurt) 150) (= 150 150))) :rule cong :premises (t119 t120))
% 0.22/0.55  (step t122 (cl (= (tptp.d tptp.hamburg tptp.kiel) 90)) :rule and :premises (t97))
% 0.22/0.55  (step t123 (cl (= 90 90)) :rule refl)
% 0.22/0.55  (step t124 (cl (= (= (tptp.d tptp.hamburg tptp.kiel) 90) (= 90 90))) :rule cong :premises (t122 t123))
% 0.22/0.55  (step t125 (cl (= (tptp.d tptp.hamburg tptp.berlin) 250)) :rule and :premises (t97))
% 0.22/0.55  (step t126 (cl (= 250 250)) :rule refl)
% 0.22/0.55  (step t127 (cl (= (= (tptp.d tptp.hamburg tptp.berlin) 250) (= 250 250))) :rule cong :premises (t125 t126))
% 0.22/0.55  (step t128 (cl (= (tptp.d tptp.munich tptp.frankfurt) 300)) :rule and :premises (t97))
% 0.22/0.55  (step t129 (cl (= 300 300)) :rule refl)
% 0.22/0.55  (step t130 (cl (= (= (tptp.d tptp.munich tptp.frankfurt) 300) (= 300 300))) :rule cong :premises (t128 t129))
% 0.22/0.55  (step t131 (cl (= (tptp.d tptp.munich tptp.saarbruecken) 360)) :rule and :premises (t97))
% 0.22/0.55  (step t132 (cl (= (= (tptp.d tptp.munich tptp.saarbruecken) 360) (= 360 360))) :rule cong :premises (t131 t114))
% 0.22/0.55  (step t133 (cl (= (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))) (forall ((X tptp.city)) (= (tptp.d X X) 0)) (= (tptp.d tptp.berlin tptp.munich) 510) (= (tptp.d tptp.berlin tptp.cologne) 480) (= (tptp.d tptp.berlin tptp.frankfurt) 420) (= (tptp.d tptp.saarbruecken tptp.frankfurt) 160) (= (tptp.d tptp.saarbruecken tptp.cologne) 190) (= (tptp.d tptp.hamburg tptp.cologne) 360) (= (tptp.d tptp.hamburg tptp.frankfurt) 390) (= (tptp.d tptp.cologne tptp.frankfurt) 150) (= (tptp.d tptp.hamburg tptp.kiel) 90) (= (tptp.d tptp.hamburg tptp.berlin) 250) (= (tptp.d tptp.munich tptp.frankfurt) 300) (= (tptp.d tptp.munich tptp.saarbruecken) 360)) (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))) (forall ((X tptp.city)) (= (tptp.d X X) 0)) (= 510 510) (= 480 480) (= 420 420) (= 160 160) (= 190 190) (= 360 360) (= 390 390) (= 150 150) (= 90 90) (= 250 250) (= 300 300) (= 360 360)))) :rule cong :premises (t67 t68 t69 t100 t103 t106 t109 t112 t115 t118 t121 t124 t127 t130 t132))
% 0.22/0.55  (step t134 (cl (= (not (>= (tptp.d tptp.cologne tptp.berlin) 501)) (not (>= (tptp.d tptp.cologne tptp.berlin) 501)))) :rule refl)
% 0.22/0.55  (step t135 (cl (= (=> (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))) (forall ((X tptp.city)) (= (tptp.d X X) 0)) (= (tptp.d tptp.berlin tptp.munich) 510) (= (tptp.d tptp.berlin tptp.cologne) 480) (= (tptp.d tptp.berlin tptp.frankfurt) 420) (= (tptp.d tptp.saarbruecken tptp.frankfurt) 160) (= (tptp.d tptp.saarbruecken tptp.cologne) 190) (= (tptp.d tptp.hamburg tptp.cologne) 360) (= (tptp.d tptp.hamburg tptp.frankfurt) 390) (= (tptp.d tptp.cologne tptp.frankfurt) 150) (= (tptp.d tptp.hamburg tptp.kiel) 90) (= (tptp.d tptp.hamburg tptp.berlin) 250) (= (tptp.d tptp.munich tptp.frankfurt) 300) (= (tptp.d tptp.munich tptp.saarbruecken) 360)) (not (>= (tptp.d tptp.cologne tptp.berlin) 501))) (=> (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))) (forall ((X tptp.city)) (= (tptp.d X X) 0)) (= 510 510) (= 480 480) (= 420 420) (= 160 160) (= 190 190) (= 360 360) (= 390 390) (= 150 150) (= 90 90) (= 250 250) (= 300 300) (= 360 360)) (not (>= (tptp.d tptp.cologne tptp.berlin) 501))))) :rule cong :premises (t133 t134))
% 0.22/0.55  (step t136 (cl (= (not (=> (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))) (forall ((X tptp.city)) (= (tptp.d X X) 0)) (= (tptp.d tptp.berlin tptp.munich) 510) (= (tptp.d tptp.berlin tptp.cologne) 480) (= (tptp.d tptp.berlin tptp.frankfurt) 420) (= (tptp.d tptp.saarbruecken tptp.frankfurt) 160) (= (tptp.d tptp.saarbruecken tptp.cologne) 190) (= (tptp.d tptp.hamburg tptp.cologne) 360) (= (tptp.d tptp.hamburg tptp.frankfurt) 390) (= (tptp.d tptp.cologne tptp.frankfurt) 150) (= (tptp.d tptp.hamburg tptp.kiel) 90) (= (tptp.d tptp.hamburg tptp.berlin) 250) (= (tptp.d tptp.munich tptp.frankfurt) 300) (= (tptp.d tptp.munich tptp.saarbruecken) 360)) (not (>= (tptp.d tptp.cologne tptp.berlin) 501)))) (not (=> (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))) (forall ((X tptp.city)) (= (tptp.d X X) 0)) (= 510 510) (= 480 480) (= 420 420) (= 160 160) (= 190 190) (= 360 360) (= 390 390) (= 150 150) (= 90 90) (= 250 250) (= 300 300) (= 360 360)) (not (>= (tptp.d tptp.cologne tptp.berlin) 501)))))) :rule cong :premises (t135))
% 0.22/0.55  (step t137 (cl (= (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))))) :rule refl)
% 0.22/0.55  (step t138 (cl (= (= 510 510) true)) :rule all_simplify)
% 0.22/0.55  (step t139 (cl (= (= 480 480) true)) :rule all_simplify)
% 0.22/0.55  (step t140 (cl (= (= 420 420) true)) :rule all_simplify)
% 0.22/0.55  (step t141 (cl (= (= 160 160) true)) :rule all_simplify)
% 0.22/0.55  (step t142 (cl (= (= 190 190) true)) :rule all_simplify)
% 0.22/0.55  (step t143 (cl (= (= 360 360) true)) :rule all_simplify)
% 0.22/0.55  (step t144 (cl (= (= 390 390) true)) :rule all_simplify)
% 0.22/0.55  (step t145 (cl (= (= 150 150) true)) :rule all_simplify)
% 0.22/0.55  (step t146 (cl (= (= 90 90) true)) :rule all_simplify)
% 0.22/0.55  (step t147 (cl (= (= 250 250) true)) :rule all_simplify)
% 0.22/0.55  (step t148 (cl (= (= 300 300) true)) :rule all_simplify)
% 0.22/0.55  (step t149 (cl (= (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))) (forall ((X tptp.city)) (= (tptp.d X X) 0)) (= 510 510) (= 480 480) (= 420 420) (= 160 160) (= 190 190) (= 360 360) (= 390 390) (= 150 150) (= 90 90) (= 250 250) (= 300 300) (= 360 360)) (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))) (forall ((X tptp.city)) (= (tptp.d X X) 0)) true true true true true true true true true true true true))) :rule cong :premises (t48 t137 t50 t138 t139 t140 t141 t142 t143 t144 t145 t146 t147 t148 t143))
% 0.22/0.55  (step t150 (cl (= (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))) (forall ((X tptp.city)) (= (tptp.d X X) 0)) true true true true true true true true true true true true) (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))) (forall ((X tptp.city)) (= (tptp.d X X) 0))))) :rule all_simplify)
% 0.22/0.55  (step t151 (cl (= (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))) (forall ((X tptp.city)) (= (tptp.d X X) 0)) (= 510 510) (= 480 480) (= 420 420) (= 160 160) (= 190 190) (= 360 360) (= 390 390) (= 150 150) (= 90 90) (= 250 250) (= 300 300) (= 360 360)) (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))) (forall ((X tptp.city)) (= (tptp.d X X) 0))))) :rule trans :premises (t149 t150))
% 0.22/0.55  (step t152 (cl (= (not (>= (tptp.d tptp.cologne tptp.berlin) 501)) (not (>= (tptp.d tptp.cologne tptp.berlin) 501)))) :rule refl)
% 0.22/0.55  (step t153 (cl (= (=> (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))) (forall ((X tptp.city)) (= (tptp.d X X) 0)) (= 510 510) (= 480 480) (= 420 420) (= 160 160) (= 190 190) (= 360 360) (= 390 390) (= 150 150) (= 90 90) (= 250 250) (= 300 300) (= 360 360)) (not (>= (tptp.d tptp.cologne tptp.berlin) 501))) (=> (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))) (forall ((X tptp.city)) (= (tptp.d X X) 0))) (not (>= (tptp.d tptp.cologne tptp.berlin) 501))))) :rule cong :premises (t151 t152))
% 0.22/0.55  (step t154 (cl (= (not (=> (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))) (forall ((X tptp.city)) (= (tptp.d X X) 0)) (= 510 510) (= 480 480) (= 420 420) (= 160 160) (= 190 190) (= 360 360) (= 390 390) (= 150 150) (= 90 90) (= 250 250) (= 300 300) (= 360 360)) (not (>= (tptp.d tptp.cologne tptp.berlin) 501)))) (not (=> (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))) (forall ((X tptp.city)) (= (tptp.d X X) 0))) (not (>= (tptp.d tptp.cologne tptp.berlin) 501)))))) :rule cong :premises (t153))
% 0.22/0.55  (step t155 (cl (= (not (=> (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))) (forall ((X tptp.city)) (= (tptp.d X X) 0)) (= (tptp.d tptp.berlin tptp.munich) 510) (= (tptp.d tptp.berlin tptp.cologne) 480) (= (tptp.d tptp.berlin tptp.frankfurt) 420) (= (tptp.d tptp.saarbruecken tptp.frankfurt) 160) (= (tptp.d tptp.saarbruecken tptp.cologne) 190) (= (tptp.d tptp.hamburg tptp.cologne) 360) (= (tptp.d tptp.hamburg tptp.frankfurt) 390) (= (tptp.d tptp.cologne tptp.frankfurt) 150) (= (tptp.d tptp.hamburg tptp.kiel) 90) (= (tptp.d tptp.hamburg tptp.berlin) 250) (= (tptp.d tptp.munich tptp.frankfurt) 300) (= (tptp.d tptp.munich tptp.saarbruecken) 360)) (not (>= (tptp.d tptp.cologne tptp.berlin) 501)))) (not (=> (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))) (forall ((X tptp.city)) (= (tptp.d X X) 0))) (not (>= (tptp.d tptp.cologne tptp.berlin) 501)))))) :rule trans :premises (t136 t154))
% 0.22/0.55  (step t156 (cl (= (not (=> (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (<= (tptp.d X Z) (+ (tptp.d X Y) (tptp.d Y Z)))) (forall ((X tptp.city)) (= (tptp.d X X) 0)) (= (tptp.d tptp.berlin tptp.munich) 510) (= (tptp.d tptp.berlin tptp.cologne) 480) (= (tptp.d tptp.berlin tptp.frankfurt) 420) (= (tptp.d tptp.saarbruecken tptp.frankfurt) 160) (= (tptp.d tptp.saarbruecken tptp.cologne) 190) (= (tptp.d tptp.hamburg tptp.cologne) 360) (= (tptp.d tptp.hamburg tptp.frankfurt) 390) (= (tptp.d tptp.cologne tptp.frankfurt) 150) (= (tptp.d tptp.hamburg tptp.kiel) 90) (= (tptp.d tptp.hamburg tptp.berlin) 250) (= (tptp.d tptp.munich tptp.frankfurt) 300) (= (tptp.d tptp.munich tptp.saarbruecken) 360)) (<= (tptp.d tptp.cologne tptp.berlin) 500))) (not (=> (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))) (forall ((X tptp.city)) (= (tptp.d X X) 0))) (not (>= (tptp.d tptp.cologne tptp.berlin) 501)))))) :rule trans :premises (t66 t155))
% 0.22/0.55  (step t157 (cl (not (=> (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))) (forall ((X tptp.city)) (= (tptp.d X X) 0))) (not (>= (tptp.d tptp.cologne tptp.berlin) 501))))) :rule resolution :premises (t47 t156 a0))
% 0.22/0.55  (step t158 (cl (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))) (forall ((X tptp.city)) (= (tptp.d X X) 0)))) :rule not_implies1 :premises (t157))
% 0.22/0.55  (step t159 (cl (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X)))) :rule and :premises (t158))
% 0.22/0.55  (step t160 (cl (= (tptp.d tptp.berlin tptp.cologne) (tptp.d tptp.cologne tptp.berlin))) :rule resolution :premises (t46 t159))
% 0.22/0.55  (step t161 (cl (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))) (forall ((X tptp.city)) (= (tptp.d X X) 0)) (>= (tptp.d tptp.cologne tptp.berlin) 501) (= (tptp.d tptp.berlin tptp.munich) 510) (= (tptp.d tptp.berlin tptp.cologne) 480) (= (tptp.d tptp.berlin tptp.frankfurt) 420) (= (tptp.d tptp.saarbruecken tptp.frankfurt) 160) (= (tptp.d tptp.saarbruecken tptp.cologne) 190) (= (tptp.d tptp.hamburg tptp.cologne) 360) (= (tptp.d tptp.hamburg tptp.frankfurt) 390) (= (tptp.d tptp.cologne tptp.frankfurt) 150) (= (tptp.d tptp.hamburg tptp.kiel) 90) (= (tptp.d tptp.hamburg tptp.berlin) 250) (= (tptp.d tptp.munich tptp.frankfurt) 300) (= (tptp.d tptp.munich tptp.saarbruecken) 360)) (not (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X)))) (not (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1)))) (not (forall ((X tptp.city)) (= (tptp.d X X) 0))) (not (>= (tptp.d tptp.cologne tptp.berlin) 501)) (not (= (tptp.d tptp.berlin tptp.munich) 510)) (not (= (tptp.d tptp.berlin tptp.cologne) 480)) (not (= (tptp.d tptp.berlin tptp.frankfurt) 420)) (not (= (tptp.d tptp.saarbruecken tptp.frankfurt) 160)) (not (= (tptp.d tptp.saarbruecken tptp.cologne) 190)) (not (= (tptp.d tptp.hamburg tptp.cologne) 360)) (not (= (tptp.d tptp.hamburg tptp.frankfurt) 390)) (not (= (tptp.d tptp.cologne tptp.frankfurt) 150)) (not (= (tptp.d tptp.hamburg tptp.kiel) 90)) (not (= (tptp.d tptp.hamburg tptp.berlin) 250)) (not (= (tptp.d tptp.munich tptp.frankfurt) 300)) (not (= (tptp.d tptp.munich tptp.saarbruecken) 360))) :rule and_neg)
% 0.22/0.55  (step t162 (cl (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))) (forall ((X tptp.city)) (= (tptp.d X X) 0)) (= (tptp.d tptp.berlin tptp.munich) 510) (= (tptp.d tptp.berlin tptp.cologne) 480) (= (tptp.d tptp.berlin tptp.frankfurt) 420) (= (tptp.d tptp.saarbruecken tptp.frankfurt) 160) (= (tptp.d tptp.saarbruecken tptp.cologne) 190) (= (tptp.d tptp.hamburg tptp.cologne) 360) (= (tptp.d tptp.hamburg tptp.frankfurt) 390) (= (tptp.d tptp.cologne tptp.frankfurt) 150) (= (tptp.d tptp.hamburg tptp.kiel) 90) (= (tptp.d tptp.hamburg tptp.berlin) 250) (= (tptp.d tptp.munich tptp.frankfurt) 300) (= (tptp.d tptp.munich tptp.saarbruecken) 360))) :rule not_implies1 :premises (t72))
% 0.22/0.55  (step t163 (cl (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X)))) :rule and :premises (t162))
% 0.22/0.55  (step t164 (cl (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))) (forall ((X tptp.city)) (= (tptp.d X X) 0)) (= (tptp.d tptp.berlin tptp.munich) 510) (= (tptp.d tptp.berlin tptp.cologne) 480) (= (tptp.d tptp.berlin tptp.frankfurt) 420) (= (tptp.d tptp.saarbruecken tptp.frankfurt) 160) (= (tptp.d tptp.saarbruecken tptp.cologne) 190) (= (tptp.d tptp.hamburg tptp.cologne) 360) (= (tptp.d tptp.hamburg tptp.frankfurt) 390) (= (tptp.d tptp.cologne tptp.frankfurt) 150) (= (tptp.d tptp.hamburg tptp.kiel) 90) (= (tptp.d tptp.hamburg tptp.berlin) 250) (= (tptp.d tptp.munich tptp.frankfurt) 300) (= (tptp.d tptp.munich tptp.saarbruecken) 360))) :rule not_implies1 :premises (t72))
% 0.22/0.55  (step t165 (cl (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1)))) :rule and :premises (t164))
% 0.22/0.55  (step t166 (cl (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))) (forall ((X tptp.city)) (= (tptp.d X X) 0)) (= (tptp.d tptp.berlin tptp.munich) 510) (= (tptp.d tptp.berlin tptp.cologne) 480) (= (tptp.d tptp.berlin tptp.frankfurt) 420) (= (tptp.d tptp.saarbruecken tptp.frankfurt) 160) (= (tptp.d tptp.saarbruecken tptp.cologne) 190) (= (tptp.d tptp.hamburg tptp.cologne) 360) (= (tptp.d tptp.hamburg tptp.frankfurt) 390) (= (tptp.d tptp.cologne tptp.frankfurt) 150) (= (tptp.d tptp.hamburg tptp.kiel) 90) (= (tptp.d tptp.hamburg tptp.berlin) 250) (= (tptp.d tptp.munich tptp.frankfurt) 300) (= (tptp.d tptp.munich tptp.saarbruecken) 360))) :rule not_implies1 :premises (t72))
% 0.22/0.55  (step t167 (cl (forall ((X tptp.city)) (= (tptp.d X X) 0))) :rule and :premises (t166))
% 0.22/0.55  (step t168 (cl (not (not (not (>= (tptp.d tptp.cologne tptp.berlin) 501)))) (>= (tptp.d tptp.cologne tptp.berlin) 501)) :rule not_not)
% 0.22/0.55  (step t169 (cl (not (= (not (=> (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (<= (tptp.d X Z) (+ (tptp.d X Y) (tptp.d Y Z)))) (forall ((X tptp.city)) (= (tptp.d X X) 0)) (= (tptp.d tptp.berlin tptp.munich) 510) (= (tptp.d tptp.berlin tptp.cologne) 480) (= (tptp.d tptp.berlin tptp.frankfurt) 420) (= (tptp.d tptp.saarbruecken tptp.frankfurt) 160) (= (tptp.d tptp.saarbruecken tptp.cologne) 190) (= (tptp.d tptp.hamburg tptp.cologne) 360) (= (tptp.d tptp.hamburg tptp.frankfurt) 390) (= (tptp.d tptp.cologne tptp.frankfurt) 150) (= (tptp.d tptp.hamburg tptp.kiel) 90) (= (tptp.d tptp.hamburg tptp.berlin) 250) (= (tptp.d tptp.munich tptp.frankfurt) 300) (= (tptp.d tptp.munich tptp.saarbruecken) 360)) (<= (tptp.d tptp.cologne tptp.berlin) 500))) (not (=> (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))) (forall ((X tptp.city)) (= (tptp.d X X) 0)) (= (tptp.d tptp.berlin tptp.munich) 510) (= (tptp.d tptp.berlin tptp.cologne) 480) (= (tptp.d tptp.berlin tptp.frankfurt) 420) (= (tptp.d tptp.saarbruecken tptp.frankfurt) 160) (= (tptp.d tptp.saarbruecken tptp.cologne) 190) (= (tptp.d tptp.hamburg tptp.cologne) 360) (= (tptp.d tptp.hamburg tptp.frankfurt) 390) (= (tptp.d tptp.cologne tptp.frankfurt) 150) (= (tptp.d tptp.hamburg tptp.kiel) 90) (= (tptp.d tptp.hamburg tptp.berlin) 250) (= (tptp.d tptp.munich tptp.frankfurt) 300) (= (tptp.d tptp.munich tptp.saarbruecken) 360)) (not (>= (tptp.d tptp.cologne tptp.berlin) 501)))))) (not (not (=> (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (<= (tptp.d X Z) (+ (tptp.d X Y) (tptp.d Y Z)))) (forall ((X tptp.city)) (= (tptp.d X X) 0)) (= (tptp.d tptp.berlin tptp.munich) 510) (= (tptp.d tptp.berlin tptp.cologne) 480) (= (tptp.d tptp.berlin tptp.frankfurt) 420) (= (tptp.d tptp.saarbruecken tptp.frankfurt) 160) (= (tptp.d tptp.saarbruecken tptp.cologne) 190) (= (tptp.d tptp.hamburg tptp.cologne) 360) (= (tptp.d tptp.hamburg tptp.frankfurt) 390) (= (tptp.d tptp.cologne tptp.frankfurt) 150) (= (tptp.d tptp.hamburg tptp.kiel) 90) (= (tptp.d tptp.hamburg tptp.berlin) 250) (= (tptp.d tptp.munich tptp.frankfurt) 300) (= (tptp.d tptp.munich tptp.saarbruecken) 360)) (<= (tptp.d tptp.cologne tptp.berlin) 500)))) (not (=> (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))) (forall ((X tptp.city)) (= (tptp.d X X) 0)) (= (tptp.d tptp.berlin tptp.munich) 510) (= (tptp.d tptp.berlin tptp.cologne) 480) (= (tptp.d tptp.berlin tptp.frankfurt) 420) (= (tptp.d tptp.saarbruecken tptp.frankfurt) 160) (= (tptp.d tptp.saarbruecken tptp.cologne) 190) (= (tptp.d tptp.hamburg tptp.cologne) 360) (= (tptp.d tptp.hamburg tptp.frankfurt) 390) (= (tptp.d tptp.cologne tptp.frankfurt) 150) (= (tptp.d tptp.hamburg tptp.kiel) 90) (= (tptp.d tptp.hamburg tptp.berlin) 250) (= (tptp.d tptp.munich tptp.frankfurt) 300) (= (tptp.d tptp.munich tptp.saarbruecken) 360)) (not (>= (tptp.d tptp.cologne tptp.berlin) 501))))) :rule equiv_pos2)
% 0.22/0.55  (step t170 (cl (not (=> (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))) (forall ((X tptp.city)) (= (tptp.d X X) 0)) (= (tptp.d tptp.berlin tptp.munich) 510) (= (tptp.d tptp.berlin tptp.cologne) 480) (= (tptp.d tptp.berlin tptp.frankfurt) 420) (= (tptp.d tptp.saarbruecken tptp.frankfurt) 160) (= (tptp.d tptp.saarbruecken tptp.cologne) 190) (= (tptp.d tptp.hamburg tptp.cologne) 360) (= (tptp.d tptp.hamburg tptp.frankfurt) 390) (= (tptp.d tptp.cologne tptp.frankfurt) 150) (= (tptp.d tptp.hamburg tptp.kiel) 90) (= (tptp.d tptp.hamburg tptp.berlin) 250) (= (tptp.d tptp.munich tptp.frankfurt) 300) (= (tptp.d tptp.munich tptp.saarbruecken) 360)) (not (>= (tptp.d tptp.cologne tptp.berlin) 501))))) :rule resolution :premises (t169 t66 a0))
% 0.22/0.55  (step t171 (cl (not (not (>= (tptp.d tptp.cologne tptp.berlin) 501)))) :rule not_implies2 :premises (t170))
% 0.22/0.55  (step t172 (cl (>= (tptp.d tptp.cologne tptp.berlin) 501)) :rule resolution :premises (t168 t171))
% 0.22/0.55  (step t173 (cl (= (tptp.d tptp.berlin tptp.munich) 510)) :rule and :premises (t95))
% 0.22/0.55  (step t174 (cl (= (tptp.d tptp.berlin tptp.cologne) 480)) :rule and :premises (t93))
% 0.22/0.55  (step t175 (cl (= (tptp.d tptp.berlin tptp.frankfurt) 420)) :rule and :premises (t91))
% 0.22/0.55  (step t176 (cl (= (tptp.d tptp.saarbruecken tptp.frankfurt) 160)) :rule and :premises (t89))
% 0.22/0.55  (step t177 (cl (= (tptp.d tptp.saarbruecken tptp.cologne) 190)) :rule and :premises (t87))
% 0.22/0.55  (step t178 (cl (= (tptp.d tptp.hamburg tptp.cologne) 360)) :rule and :premises (t85))
% 0.22/0.55  (step t179 (cl (= (tptp.d tptp.hamburg tptp.frankfurt) 390)) :rule and :premises (t83))
% 0.22/0.55  (step t180 (cl (= (tptp.d tptp.cologne tptp.frankfurt) 150)) :rule and :premises (t81))
% 0.22/0.55  (step t181 (cl (= (tptp.d tptp.hamburg tptp.kiel) 90)) :rule and :premises (t79))
% 0.22/0.55  (step t182 (cl (= (tptp.d tptp.hamburg tptp.berlin) 250)) :rule and :premises (t77))
% 0.22/0.55  (step t183 (cl (= (tptp.d tptp.munich tptp.frankfurt) 300)) :rule and :premises (t75))
% 0.22/0.55  (step t184 (cl (= (tptp.d tptp.munich tptp.saarbruecken) 360)) :rule and :premises (t73))
% 0.22/0.55  (step t185 (cl (and (forall ((X tptp.city) (Y tptp.city)) (= (tptp.d X Y) (tptp.d Y X))) (forall ((X tptp.city) (Y tptp.city) (Z tptp.city)) (not (>= (+ (tptp.d X Z) (* (- 1) (tptp.d X Y)) (* (- 1) (tptp.d Y Z))) 1))) (forall ((X tptp.city)) (= (tptp.d X X) 0)) (>= (tptp.d tptp.cologne tptp.berlin) 501) (= (tptp.d tptp.berlin tptp.munich) 510) (= (tptp.d tptp.berlin tptp.cologne) 480) (= (tptp.d tptp.berlin tptp.frankfurt) 420) (= (tptp.d tptp.saarbruecken tptp.frankfurt) 160) (= (tptp.d tptp.saarbruecken tptp.cologne) 190) (= (tptp.d tptp.hamburg tptp.cologne) 360) (= (tptp.d tptp.hamburg tptp.frankfurt) 390) (= (tptp.d tptp.cologne tptp.frankfurt) 150) (= (tptp.d tptp.hamburg tptp.kiel) 90) (= (tptp.d tptp.hamburg tptp.berlin) 250) (= (tptp.d tptp.munich tptp.frankfurt) 300) (= (tptp.d tptp.munich tptp.saarbruecken) 360))) :rule resolution :premises (t161 t163 t165 t167 t172 t173 t174 t175 t176 t177 t178 t179 t180 t181 t182 t183 t184))
% 0.22/0.55  (step t186 (cl (= (tptp.d tptp.berlin tptp.cologne) 480)) :rule and :premises (t185))
% 0.22/0.55  (step t187 (cl (not (not (not (>= (tptp.d tptp.cologne tptp.berlin) 501)))) (>= (tptp.d tptp.cologne tptp.berlin) 501)) :rule not_not)
% 0.22/0.55  (step t188 (cl (not (not (>= (tptp.d tptp.cologne tptp.berlin) 501)))) :rule not_implies2 :premises (t157))
% 0.22/0.55  (step t189 (cl (>= (tptp.d tptp.cologne tptp.berlin) 501)) :rule resolution :premises (t187 t188))
% 0.22/0.55  (step t190 (cl) :rule resolution :premises (t39 t160 t186 t189))
% 0.22/0.55  
% 0.22/0.55  % SZS output end Proof for /export/starexec/sandbox/tmp/tmp.W6c4Uga70l/cvc5---1.0.5_2273.smt2
% 0.22/0.55  % cvc5---1.0.5 exiting
% 0.22/0.56  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------