TSTP Solution File: ARI676_1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ARI676_1 : TPTP v8.2.0. Released v6.3.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n032.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 16:34:28 EDT 2024
% Result : Theorem 0.15s 0.44s
% Output : Proof 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : ARI676_1 : TPTP v8.2.0. Released v6.3.0.
% 0.05/0.10 % Command : do_cvc5 %s %d
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Mon May 27 05:21:23 EDT 2024
% 0.09/0.29 % CPUTime :
% 0.15/0.41 %----Proving TF0_ARI
% 0.15/0.44 --- Run --finite-model-find --decision=internal at 15...
% 0.15/0.44 % SZS status Theorem for /export/starexec/sandbox/tmp/tmp.E79om7cxQf/cvc5---1.0.5_26348.smt2
% 0.15/0.44 % SZS output start Proof for /export/starexec/sandbox/tmp/tmp.E79om7cxQf/cvc5---1.0.5_26348.smt2
% 0.15/0.44 (assume a0 (not (<= 0 (+ (* tptp.a tptp.a) 10))))
% 0.15/0.44 (assume a1 true)
% 0.15/0.44 (step t1 (cl (not (= (or (not (not (>= (* tptp.a tptp.a) (- 10)))) (not (= (* tptp.a tptp.a) 0))) (or (>= (* tptp.a tptp.a) (- 10)) (not (= (* tptp.a tptp.a) 0))))) (not (or (not (not (>= (* tptp.a tptp.a) (- 10)))) (not (= (* tptp.a tptp.a) 0)))) (or (>= (* tptp.a tptp.a) (- 10)) (not (= (* tptp.a tptp.a) 0)))) :rule equiv_pos2)
% 0.15/0.44 (step t2 (cl (= (= (= (not (not (>= (* tptp.a tptp.a) (- 10)))) (>= (* tptp.a tptp.a) (- 10))) true) (= (not (not (>= (* tptp.a tptp.a) (- 10)))) (>= (* tptp.a tptp.a) (- 10))))) :rule equiv_simplify)
% 0.15/0.44 (step t3 (cl (not (= (= (not (not (>= (* tptp.a tptp.a) (- 10)))) (>= (* tptp.a tptp.a) (- 10))) true)) (= (not (not (>= (* tptp.a tptp.a) (- 10)))) (>= (* tptp.a tptp.a) (- 10)))) :rule equiv1 :premises (t2))
% 0.15/0.44 (step t4 (cl (= (= (not (not (>= (* tptp.a tptp.a) (- 10)))) (>= (* tptp.a tptp.a) (- 10))) (= (>= (* tptp.a tptp.a) (- 10)) (not (not (>= (* tptp.a tptp.a) (- 10))))))) :rule all_simplify)
% 0.15/0.44 (step t5 (cl (= (>= (* tptp.a tptp.a) (- 10)) (>= (* tptp.a tptp.a) (- 10)))) :rule refl)
% 0.15/0.44 (step t6 (cl (= (not (not (>= (* tptp.a tptp.a) (- 10)))) (>= (* tptp.a tptp.a) (- 10)))) :rule all_simplify)
% 0.15/0.44 (step t7 (cl (= (= (>= (* tptp.a tptp.a) (- 10)) (not (not (>= (* tptp.a tptp.a) (- 10))))) (= (>= (* tptp.a tptp.a) (- 10)) (>= (* tptp.a tptp.a) (- 10))))) :rule cong :premises (t5 t6))
% 0.15/0.44 (step t8 (cl (= (= (>= (* tptp.a tptp.a) (- 10)) (>= (* tptp.a tptp.a) (- 10))) true)) :rule all_simplify)
% 0.15/0.44 (step t9 (cl (= (= (>= (* tptp.a tptp.a) (- 10)) (not (not (>= (* tptp.a tptp.a) (- 10))))) true)) :rule trans :premises (t7 t8))
% 0.15/0.44 (step t10 (cl (= (= (not (not (>= (* tptp.a tptp.a) (- 10)))) (>= (* tptp.a tptp.a) (- 10))) true)) :rule trans :premises (t4 t9))
% 0.15/0.44 (step t11 (cl (= (not (not (>= (* tptp.a tptp.a) (- 10)))) (>= (* tptp.a tptp.a) (- 10)))) :rule resolution :premises (t3 t10))
% 0.15/0.44 (step t12 (cl (= (not (= (* tptp.a tptp.a) 0)) (not (= (* tptp.a tptp.a) 0)))) :rule refl)
% 0.15/0.44 (step t13 (cl (= (or (not (not (>= (* tptp.a tptp.a) (- 10)))) (not (= (* tptp.a tptp.a) 0))) (or (>= (* tptp.a tptp.a) (- 10)) (not (= (* tptp.a tptp.a) 0))))) :rule cong :premises (t11 t12))
% 0.15/0.44 (step t14 (cl (not (= (=> (and (not (>= (* tptp.a tptp.a) (- 10))) (= (* tptp.a tptp.a) 0)) (and (= (* tptp.a tptp.a) 0) (not (>= (* tptp.a tptp.a) (- 10))))) (not (and (not (>= (* tptp.a tptp.a) (- 10))) (= (* tptp.a tptp.a) 0))))) (not (=> (and (not (>= (* tptp.a tptp.a) (- 10))) (= (* tptp.a tptp.a) 0)) (and (= (* tptp.a tptp.a) 0) (not (>= (* tptp.a tptp.a) (- 10)))))) (not (and (not (>= (* tptp.a tptp.a) (- 10))) (= (* tptp.a tptp.a) 0)))) :rule equiv_pos2)
% 0.15/0.44 (step t15 (cl (= (and (not (>= (* tptp.a tptp.a) (- 10))) (= (* tptp.a tptp.a) 0)) (and (not (>= (* tptp.a tptp.a) (- 10))) (= (* tptp.a tptp.a) 0)))) :rule refl)
% 0.15/0.44 (step t16 (cl (= (= (and (= (* tptp.a tptp.a) 0) (not (>= (* tptp.a tptp.a) (- 10)))) false) (not (and (= (* tptp.a tptp.a) 0) (not (>= (* tptp.a tptp.a) (- 10))))))) :rule equiv_simplify)
% 0.15/0.44 (step t17 (cl (= (and (= (* tptp.a tptp.a) 0) (not (>= (* tptp.a tptp.a) (- 10)))) false) (not (not (and (= (* tptp.a tptp.a) 0) (not (>= (* tptp.a tptp.a) (- 10))))))) :rule equiv2 :premises (t16))
% 0.15/0.44 (step t18 (cl (not (not (not (and (= (* tptp.a tptp.a) 0) (not (>= (* tptp.a tptp.a) (- 10))))))) (and (= (* tptp.a tptp.a) 0) (not (>= (* tptp.a tptp.a) (- 10))))) :rule not_not)
% 0.15/0.44 (step t19 (cl (= (and (= (* tptp.a tptp.a) 0) (not (>= (* tptp.a tptp.a) (- 10)))) false) (and (= (* tptp.a tptp.a) 0) (not (>= (* tptp.a tptp.a) (- 10))))) :rule resolution :premises (t17 t18))
% 0.15/0.44 (step t20 (cl (=> (and (= (* tptp.a tptp.a) 0) (not (>= (* tptp.a tptp.a) (- 10)))) false) (and (= (* tptp.a tptp.a) 0) (not (>= (* tptp.a tptp.a) (- 10))))) :rule implies_neg1)
% 0.15/0.44 (anchor :step t21)
% 0.15/0.44 (assume t21.a0 (= (* tptp.a tptp.a) 0))
% 0.15/0.44 (assume t21.a1 (not (>= (* tptp.a tptp.a) (- 10))))
% 0.15/0.44 (step t21.t1 (cl (=> (= (* tptp.a tptp.a) 0) false) (= (* tptp.a tptp.a) 0)) :rule implies_neg1)
% 0.15/0.44 (anchor :step t21.t2)
% 0.15/0.44 (assume t21.t2.a0 (= (* tptp.a tptp.a) 0))
% 0.15/0.44 (step t21.t2.t1 (cl (not (= (<= (+ (* (- 1.0) (* tptp.a tptp.a)) (* 1.0 (* tptp.a tptp.a))) (+ (* (- 1.0) 0) (* 1.0 (- 11)))) false)) (not (<= (+ (* (- 1.0) (* tptp.a tptp.a)) (* 1.0 (* tptp.a tptp.a))) (+ (* (- 1.0) 0) (* 1.0 (- 11))))) false) :rule equiv_pos2)
% 0.15/0.44 (step t21.t2.t2 (cl (= (* (- 1.0) (* tptp.a tptp.a)) (to_real (* (- 1) (* tptp.a tptp.a))))) :rule all_simplify)
% 0.15/0.44 (step t21.t2.t3 (cl (= (* 1.0 (* tptp.a tptp.a)) (to_real (* tptp.a tptp.a)))) :rule all_simplify)
% 0.15/0.44 (step t21.t2.t4 (cl (= (+ (* (- 1.0) (* tptp.a tptp.a)) (* 1.0 (* tptp.a tptp.a))) (+ (to_real (* (- 1) (* tptp.a tptp.a))) (to_real (* tptp.a tptp.a))))) :rule cong :premises (t21.t2.t2 t21.t2.t3))
% 0.15/0.44 (step t21.t2.t5 (cl (= (+ (to_real (* (- 1) (* tptp.a tptp.a))) (to_real (* tptp.a tptp.a))) 0.0)) :rule all_simplify)
% 0.15/0.44 (step t21.t2.t6 (cl (= (+ (* (- 1.0) (* tptp.a tptp.a)) (* 1.0 (* tptp.a tptp.a))) 0.0)) :rule trans :premises (t21.t2.t4 t21.t2.t5))
% 0.15/0.44 (step t21.t2.t7 (cl (= (* (- 1.0) 0) 0.0)) :rule all_simplify)
% 0.15/0.44 (step t21.t2.t8 (cl (= (* 1.0 (- 11)) (- 11.0))) :rule all_simplify)
% 0.15/0.44 (step t21.t2.t9 (cl (= (+ (* (- 1.0) 0) (* 1.0 (- 11))) (+ 0.0 (- 11.0)))) :rule cong :premises (t21.t2.t7 t21.t2.t8))
% 0.15/0.44 (step t21.t2.t10 (cl (= (+ 0.0 (- 11.0)) (- 11.0))) :rule all_simplify)
% 0.15/0.44 (step t21.t2.t11 (cl (= (+ (* (- 1.0) 0) (* 1.0 (- 11))) (- 11.0))) :rule trans :premises (t21.t2.t9 t21.t2.t10))
% 0.15/0.44 (step t21.t2.t12 (cl (= (<= (+ (* (- 1.0) (* tptp.a tptp.a)) (* 1.0 (* tptp.a tptp.a))) (+ (* (- 1.0) 0) (* 1.0 (- 11)))) (<= 0.0 (- 11.0)))) :rule cong :premises (t21.t2.t6 t21.t2.t11))
% 0.15/0.44 (step t21.t2.t13 (cl (= (<= 0.0 (- 11.0)) false)) :rule all_simplify)
% 0.15/0.44 (step t21.t2.t14 (cl (= (<= (+ (* (- 1.0) (* tptp.a tptp.a)) (* 1.0 (* tptp.a tptp.a))) (+ (* (- 1.0) 0) (* 1.0 (- 11)))) false)) :rule trans :premises (t21.t2.t12 t21.t2.t13))
% 0.15/0.44 (step t21.t2.t15 (cl (not (= (* (- 1.0) (* tptp.a tptp.a)) (* (- 1.0) 0))) (not (<= (* 1.0 (* tptp.a tptp.a)) (* 1.0 (- 11)))) (<= (+ (* (- 1.0) (* tptp.a tptp.a)) (* 1.0 (* tptp.a tptp.a))) (+ (* (- 1.0) 0) (* 1.0 (- 11))))) :rule la_generic :args ((- 1) 1 1))
% 0.15/0.44 (step t21.t2.t16 (cl (=> (and (< (- 1.0) 0) (= (* tptp.a tptp.a) 0)) (= (* (- 1.0) (* tptp.a tptp.a)) (* (- 1.0) 0)))) :rule la_mult_neg)
% 0.15/0.44 (step t21.t2.t17 (cl (not (and (< (- 1.0) 0) (= (* tptp.a tptp.a) 0))) (= (* (- 1.0) (* tptp.a tptp.a)) (* (- 1.0) 0))) :rule implies :premises (t21.t2.t16))
% 0.15/0.44 (step t21.t2.t18 (cl (and (< (- 1.0) 0) (= (* tptp.a tptp.a) 0)) (not (< (- 1.0) 0)) (not (= (* tptp.a tptp.a) 0))) :rule and_neg)
% 0.15/0.44 (step t21.t2.t19 (cl (= (= (< (- 1.0) 0) true) (< (- 1.0) 0))) :rule equiv_simplify)
% 0.15/0.44 (step t21.t2.t20 (cl (not (= (< (- 1.0) 0) true)) (< (- 1.0) 0)) :rule equiv1 :premises (t21.t2.t19))
% 0.15/0.44 (step t21.t2.t21 (cl (= (< (- 1.0) 0) true)) :rule hole :args ((< (- 1.0) 0)))
% 0.15/0.44 (step t21.t2.t22 (cl (< (- 1.0) 0)) :rule resolution :premises (t21.t2.t20 t21.t2.t21))
% 0.15/0.44 (step t21.t2.t23 (cl (and (< (- 1.0) 0) (= (* tptp.a tptp.a) 0))) :rule resolution :premises (t21.t2.t18 t21.t2.t22 t21.t2.a0))
% 0.15/0.44 (step t21.t2.t24 (cl (= (* (- 1.0) (* tptp.a tptp.a)) (* (- 1.0) 0))) :rule resolution :premises (t21.t2.t17 t21.t2.t23))
% 0.15/0.44 (step t21.t2.t25 (cl (=> (and (> 1.0 0) (<= (* tptp.a tptp.a) (- 11))) (<= (* 1.0 (* tptp.a tptp.a)) (* 1.0 (- 11))))) :rule la_mult_pos)
% 0.15/0.44 (step t21.t2.t26 (cl (not (and (> 1.0 0) (<= (* tptp.a tptp.a) (- 11)))) (<= (* 1.0 (* tptp.a tptp.a)) (* 1.0 (- 11)))) :rule implies :premises (t21.t2.t25))
% 0.15/0.44 (step t21.t2.t27 (cl (and (> 1.0 0) (<= (* tptp.a tptp.a) (- 11))) (not (> 1.0 0)) (not (<= (* tptp.a tptp.a) (- 11)))) :rule and_neg)
% 0.15/0.44 (step t21.t2.t28 (cl (= (= (> 1.0 0) true) (> 1.0 0))) :rule equiv_simplify)
% 0.15/0.44 (step t21.t2.t29 (cl (not (= (> 1.0 0) true)) (> 1.0 0)) :rule equiv1 :premises (t21.t2.t28))
% 0.15/0.44 (step t21.t2.t30 (cl (= (> 1.0 0) true)) :rule hole :args ((> 1.0 0)))
% 0.15/0.44 (step t21.t2.t31 (cl (> 1.0 0)) :rule resolution :premises (t21.t2.t29 t21.t2.t30))
% 0.15/0.44 (step t21.t2.t32 (cl (not (< (* tptp.a tptp.a) (- 10))) (<= (* tptp.a tptp.a) (- 11))) :rule la_generic :args (1 1))
% 0.15/0.44 (step t21.t2.t33 (cl (not (= (not (>= (* tptp.a tptp.a) (- 10))) (< (* tptp.a tptp.a) (- 10)))) (not (not (>= (* tptp.a tptp.a) (- 10)))) (< (* tptp.a tptp.a) (- 10))) :rule equiv_pos2)
% 0.15/0.44 (step t21.t2.t34 (cl (= (< (* tptp.a tptp.a) (- 10)) (not (>= (* tptp.a tptp.a) (- 10))))) :rule all_simplify)
% 0.15/0.44 (step t21.t2.t35 (cl (= (not (>= (* tptp.a tptp.a) (- 10))) (< (* tptp.a tptp.a) (- 10)))) :rule symm :premises (t21.t2.t34))
% 0.15/0.44 (step t21.t2.t36 (cl (< (* tptp.a tptp.a) (- 10))) :rule resolution :premises (t21.t2.t33 t21.t2.t35 t21.a1))
% 0.15/0.44 (step t21.t2.t37 (cl (<= (* tptp.a tptp.a) (- 11))) :rule resolution :premises (t21.t2.t32 t21.t2.t36))
% 0.15/0.44 (step t21.t2.t38 (cl (and (> 1.0 0) (<= (* tptp.a tptp.a) (- 11)))) :rule resolution :premises (t21.t2.t27 t21.t2.t31 t21.t2.t37))
% 0.15/0.44 (step t21.t2.t39 (cl (<= (* 1.0 (* tptp.a tptp.a)) (* 1.0 (- 11)))) :rule resolution :premises (t21.t2.t26 t21.t2.t38))
% 0.15/0.44 (step t21.t2.t40 (cl (<= (+ (* (- 1.0) (* tptp.a tptp.a)) (* 1.0 (* tptp.a tptp.a))) (+ (* (- 1.0) 0) (* 1.0 (- 11))))) :rule resolution :premises (t21.t2.t15 t21.t2.t24 t21.t2.t39))
% 0.15/0.44 (step t21.t2.t41 (cl false) :rule resolution :premises (t21.t2.t1 t21.t2.t14 t21.t2.t40))
% 0.15/0.44 (step t21.t2 (cl (not (= (* tptp.a tptp.a) 0)) false) :rule subproof :discharge (t21.t2.a0))
% 0.15/0.44 (step t21.t3 (cl (=> (= (* tptp.a tptp.a) 0) false) false) :rule resolution :premises (t21.t1 t21.t2))
% 0.15/0.44 (step t21.t4 (cl (=> (= (* tptp.a tptp.a) 0) false) (not false)) :rule implies_neg2)
% 0.15/0.44 (step t21.t5 (cl (=> (= (* tptp.a tptp.a) 0) false) (=> (= (* tptp.a tptp.a) 0) false)) :rule resolution :premises (t21.t3 t21.t4))
% 0.15/0.44 (step t21.t6 (cl (=> (= (* tptp.a tptp.a) 0) false)) :rule contraction :premises (t21.t5))
% 0.15/0.44 (step t21.t7 (cl (= (=> (= (* tptp.a tptp.a) 0) false) (not (= (* tptp.a tptp.a) 0)))) :rule implies_simplify)
% 0.15/0.44 (step t21.t8 (cl (not (=> (= (* tptp.a tptp.a) 0) false)) (not (= (* tptp.a tptp.a) 0))) :rule equiv1 :premises (t21.t7))
% 0.15/0.44 (step t21.t9 (cl (not (= (* tptp.a tptp.a) 0))) :rule resolution :premises (t21.t6 t21.t8))
% 0.15/0.44 (step t21.t10 (cl) :rule resolution :premises (t21.a0 t21.t9))
% 0.15/0.44 (step t21 (cl (not (= (* tptp.a tptp.a) 0)) (not (not (>= (* tptp.a tptp.a) (- 10)))) false) :rule subproof :discharge (t21.a0 t21.a1))
% 0.15/0.44 (step t22 (cl (not (and (= (* tptp.a tptp.a) 0) (not (>= (* tptp.a tptp.a) (- 10))))) (= (* tptp.a tptp.a) 0)) :rule and_pos)
% 0.15/0.44 (step t23 (cl (not (and (= (* tptp.a tptp.a) 0) (not (>= (* tptp.a tptp.a) (- 10))))) (not (>= (* tptp.a tptp.a) (- 10)))) :rule and_pos)
% 0.15/0.44 (step t24 (cl false (not (and (= (* tptp.a tptp.a) 0) (not (>= (* tptp.a tptp.a) (- 10))))) (not (and (= (* tptp.a tptp.a) 0) (not (>= (* tptp.a tptp.a) (- 10)))))) :rule resolution :premises (t21 t22 t23))
% 0.15/0.44 (step t25 (cl (not (and (= (* tptp.a tptp.a) 0) (not (>= (* tptp.a tptp.a) (- 10))))) (not (and (= (* tptp.a tptp.a) 0) (not (>= (* tptp.a tptp.a) (- 10))))) false) :rule reordering :premises (t24))
% 0.15/0.44 (step t26 (cl (not (and (= (* tptp.a tptp.a) 0) (not (>= (* tptp.a tptp.a) (- 10))))) false) :rule contraction :premises (t25))
% 0.15/0.44 (step t27 (cl (=> (and (= (* tptp.a tptp.a) 0) (not (>= (* tptp.a tptp.a) (- 10)))) false) false) :rule resolution :premises (t20 t26))
% 0.15/0.44 (step t28 (cl (=> (and (= (* tptp.a tptp.a) 0) (not (>= (* tptp.a tptp.a) (- 10)))) false) (not false)) :rule implies_neg2)
% 0.15/0.44 (step t29 (cl (=> (and (= (* tptp.a tptp.a) 0) (not (>= (* tptp.a tptp.a) (- 10)))) false) (=> (and (= (* tptp.a tptp.a) 0) (not (>= (* tptp.a tptp.a) (- 10)))) false)) :rule resolution :premises (t27 t28))
% 0.15/0.44 (step t30 (cl (=> (and (= (* tptp.a tptp.a) 0) (not (>= (* tptp.a tptp.a) (- 10)))) false)) :rule contraction :premises (t29))
% 0.15/0.44 (step t31 (cl (= (=> (and (= (* tptp.a tptp.a) 0) (not (>= (* tptp.a tptp.a) (- 10)))) false) (not (and (= (* tptp.a tptp.a) 0) (not (>= (* tptp.a tptp.a) (- 10))))))) :rule implies_simplify)
% 0.15/0.44 (step t32 (cl (not (=> (and (= (* tptp.a tptp.a) 0) (not (>= (* tptp.a tptp.a) (- 10)))) false)) (not (and (= (* tptp.a tptp.a) 0) (not (>= (* tptp.a tptp.a) (- 10)))))) :rule equiv1 :premises (t31))
% 0.15/0.44 (step t33 (cl (not (and (= (* tptp.a tptp.a) 0) (not (>= (* tptp.a tptp.a) (- 10)))))) :rule resolution :premises (t30 t32))
% 0.15/0.44 (step t34 (cl (= (and (= (* tptp.a tptp.a) 0) (not (>= (* tptp.a tptp.a) (- 10)))) false)) :rule resolution :premises (t19 t33))
% 0.15/0.44 (step t35 (cl (= (=> (and (not (>= (* tptp.a tptp.a) (- 10))) (= (* tptp.a tptp.a) 0)) (and (= (* tptp.a tptp.a) 0) (not (>= (* tptp.a tptp.a) (- 10))))) (=> (and (not (>= (* tptp.a tptp.a) (- 10))) (= (* tptp.a tptp.a) 0)) false))) :rule cong :premises (t15 t34))
% 0.15/0.44 (step t36 (cl (= (=> (and (not (>= (* tptp.a tptp.a) (- 10))) (= (* tptp.a tptp.a) 0)) false) (not (and (not (>= (* tptp.a tptp.a) (- 10))) (= (* tptp.a tptp.a) 0))))) :rule all_simplify)
% 0.15/0.44 (step t37 (cl (= (=> (and (not (>= (* tptp.a tptp.a) (- 10))) (= (* tptp.a tptp.a) 0)) (and (= (* tptp.a tptp.a) 0) (not (>= (* tptp.a tptp.a) (- 10))))) (not (and (not (>= (* tptp.a tptp.a) (- 10))) (= (* tptp.a tptp.a) 0))))) :rule trans :premises (t35 t36))
% 0.15/0.44 (step t38 (cl (=> (and (not (>= (* tptp.a tptp.a) (- 10))) (= (* tptp.a tptp.a) 0)) (and (= (* tptp.a tptp.a) 0) (not (>= (* tptp.a tptp.a) (- 10))))) (and (not (>= (* tptp.a tptp.a) (- 10))) (= (* tptp.a tptp.a) 0))) :rule implies_neg1)
% 0.15/0.44 (anchor :step t39)
% 0.15/0.44 (assume t39.a0 (not (>= (* tptp.a tptp.a) (- 10))))
% 0.15/0.44 (assume t39.a1 (= (* tptp.a tptp.a) 0))
% 0.15/0.44 (step t39.t1 (cl (and (= (* tptp.a tptp.a) 0) (not (>= (* tptp.a tptp.a) (- 10)))) (not (= (* tptp.a tptp.a) 0)) (not (not (>= (* tptp.a tptp.a) (- 10))))) :rule and_neg)
% 0.15/0.44 (step t39.t2 (cl (and (= (* tptp.a tptp.a) 0) (not (>= (* tptp.a tptp.a) (- 10))))) :rule resolution :premises (t39.t1 t39.a1 t39.a0))
% 0.15/0.44 (step t39 (cl (not (not (>= (* tptp.a tptp.a) (- 10)))) (not (= (* tptp.a tptp.a) 0)) (and (= (* tptp.a tptp.a) 0) (not (>= (* tptp.a tptp.a) (- 10))))) :rule subproof :discharge (t39.a0 t39.a1))
% 0.15/0.44 (step t40 (cl (not (and (not (>= (* tptp.a tptp.a) (- 10))) (= (* tptp.a tptp.a) 0))) (not (>= (* tptp.a tptp.a) (- 10)))) :rule and_pos)
% 0.15/0.44 (step t41 (cl (not (and (not (>= (* tptp.a tptp.a) (- 10))) (= (* tptp.a tptp.a) 0))) (= (* tptp.a tptp.a) 0)) :rule and_pos)
% 0.15/0.44 (step t42 (cl (and (= (* tptp.a tptp.a) 0) (not (>= (* tptp.a tptp.a) (- 10)))) (not (and (not (>= (* tptp.a tptp.a) (- 10))) (= (* tptp.a tptp.a) 0))) (not (and (not (>= (* tptp.a tptp.a) (- 10))) (= (* tptp.a tptp.a) 0)))) :rule resolution :premises (t39 t40 t41))
% 0.15/0.44 (step t43 (cl (not (and (not (>= (* tptp.a tptp.a) (- 10))) (= (* tptp.a tptp.a) 0))) (not (and (not (>= (* tptp.a tptp.a) (- 10))) (= (* tptp.a tptp.a) 0))) (and (= (* tptp.a tptp.a) 0) (not (>= (* tptp.a tptp.a) (- 10))))) :rule reordering :premises (t42))
% 0.15/0.44 (step t44 (cl (not (and (not (>= (* tptp.a tptp.a) (- 10))) (= (* tptp.a tptp.a) 0))) (and (= (* tptp.a tptp.a) 0) (not (>= (* tptp.a tptp.a) (- 10))))) :rule contraction :premises (t43))
% 0.15/0.44 (step t45 (cl (=> (and (not (>= (* tptp.a tptp.a) (- 10))) (= (* tptp.a tptp.a) 0)) (and (= (* tptp.a tptp.a) 0) (not (>= (* tptp.a tptp.a) (- 10))))) (and (= (* tptp.a tptp.a) 0) (not (>= (* tptp.a tptp.a) (- 10))))) :rule resolution :premises (t38 t44))
% 0.15/0.44 (step t46 (cl (=> (and (not (>= (* tptp.a tptp.a) (- 10))) (= (* tptp.a tptp.a) 0)) (and (= (* tptp.a tptp.a) 0) (not (>= (* tptp.a tptp.a) (- 10))))) (not (and (= (* tptp.a tptp.a) 0) (not (>= (* tptp.a tptp.a) (- 10)))))) :rule implies_neg2)
% 0.15/0.44 (step t47 (cl (=> (and (not (>= (* tptp.a tptp.a) (- 10))) (= (* tptp.a tptp.a) 0)) (and (= (* tptp.a tptp.a) 0) (not (>= (* tptp.a tptp.a) (- 10))))) (=> (and (not (>= (* tptp.a tptp.a) (- 10))) (= (* tptp.a tptp.a) 0)) (and (= (* tptp.a tptp.a) 0) (not (>= (* tptp.a tptp.a) (- 10)))))) :rule resolution :premises (t45 t46))
% 0.15/0.44 (step t48 (cl (=> (and (not (>= (* tptp.a tptp.a) (- 10))) (= (* tptp.a tptp.a) 0)) (and (= (* tptp.a tptp.a) 0) (not (>= (* tptp.a tptp.a) (- 10)))))) :rule contraction :premises (t47))
% 0.15/0.44 (step t49 (cl (not (and (not (>= (* tptp.a tptp.a) (- 10))) (= (* tptp.a tptp.a) 0)))) :rule resolution :premises (t14 t37 t48))
% 0.15/0.44 (step t50 (cl (not (not (>= (* tptp.a tptp.a) (- 10)))) (not (= (* tptp.a tptp.a) 0))) :rule not_and :premises (t49))
% 0.15/0.44 (step t51 (cl (or (not (not (>= (* tptp.a tptp.a) (- 10)))) (not (= (* tptp.a tptp.a) 0))) (not (not (not (>= (* tptp.a tptp.a) (- 10)))))) :rule or_neg)
% 0.15/0.44 (step t52 (cl (or (not (not (>= (* tptp.a tptp.a) (- 10)))) (not (= (* tptp.a tptp.a) 0))) (not (not (= (* tptp.a tptp.a) 0)))) :rule or_neg)
% 0.15/0.44 (step t53 (cl (or (not (not (>= (* tptp.a tptp.a) (- 10)))) (not (= (* tptp.a tptp.a) 0))) (or (not (not (>= (* tptp.a tptp.a) (- 10)))) (not (= (* tptp.a tptp.a) 0)))) :rule resolution :premises (t50 t51 t52))
% 0.15/0.44 (step t54 (cl (or (not (not (>= (* tptp.a tptp.a) (- 10)))) (not (= (* tptp.a tptp.a) 0)))) :rule contraction :premises (t53))
% 0.15/0.44 (step t55 (cl (or (>= (* tptp.a tptp.a) (- 10)) (not (= (* tptp.a tptp.a) 0)))) :rule resolution :premises (t1 t13 t54))
% 0.15/0.44 (step t56 (cl (>= (* tptp.a tptp.a) (- 10)) (not (= (* tptp.a tptp.a) 0))) :rule or :premises (t55))
% 0.15/0.44 (step t57 (cl (=> (= tptp.a 0) (= (* tptp.a tptp.a) 0)) (= tptp.a 0)) :rule implies_neg1)
% 0.15/0.44 (anchor :step t58)
% 0.15/0.44 (assume t58.a0 (= tptp.a 0))
% 0.15/0.44 (step t58.t1 (cl (= (= (= (* tptp.a tptp.a) 0) true) (= (* tptp.a tptp.a) 0))) :rule equiv_simplify)
% 0.15/0.44 (step t58.t2 (cl (not (= (= (* tptp.a tptp.a) 0) true)) (= (* tptp.a tptp.a) 0)) :rule equiv1 :premises (t58.t1))
% 0.15/0.44 (step t58.t3 (cl (= (* tptp.a tptp.a) (* 0 0))) :rule cong :premises (t58.a0 t58.a0))
% 0.15/0.44 (step t58.t4 (cl (= 0 0)) :rule refl)
% 0.15/0.44 (step t58.t5 (cl (= (= (* tptp.a tptp.a) 0) (= (* 0 0) 0))) :rule cong :premises (t58.t3 t58.t4))
% 0.15/0.44 (step t58.t6 (cl (= (* 0 0) 0)) :rule all_simplify)
% 0.15/0.44 (step t58.t7 (cl (= 0 0)) :rule refl)
% 0.15/0.44 (step t58.t8 (cl (= (= (* 0 0) 0) (= 0 0))) :rule cong :premises (t58.t6 t58.t7))
% 0.15/0.44 (step t58.t9 (cl (= (= 0 0) true)) :rule all_simplify)
% 0.15/0.44 (step t58.t10 (cl (= (= (* 0 0) 0) true)) :rule trans :premises (t58.t8 t58.t9))
% 0.15/0.44 (step t58.t11 (cl (= (= (* tptp.a tptp.a) 0) true)) :rule trans :premises (t58.t5 t58.t10))
% 0.15/0.44 (step t58.t12 (cl (= (* tptp.a tptp.a) 0)) :rule resolution :premises (t58.t2 t58.t11))
% 0.15/0.44 (step t58 (cl (not (= tptp.a 0)) (= (* tptp.a tptp.a) 0)) :rule subproof :discharge (t58.a0))
% 0.15/0.44 (step t59 (cl (=> (= tptp.a 0) (= (* tptp.a tptp.a) 0)) (= (* tptp.a tptp.a) 0)) :rule resolution :premises (t57 t58))
% 0.15/0.44 (step t60 (cl (=> (= tptp.a 0) (= (* tptp.a tptp.a) 0)) (not (= (* tptp.a tptp.a) 0))) :rule implies_neg2)
% 0.15/0.44 (step t61 (cl (=> (= tptp.a 0) (= (* tptp.a tptp.a) 0)) (=> (= tptp.a 0) (= (* tptp.a tptp.a) 0))) :rule resolution :premises (t59 t60))
% 0.15/0.44 (step t62 (cl (=> (= tptp.a 0) (= (* tptp.a tptp.a) 0))) :rule contraction :premises (t61))
% 0.15/0.44 (step t63 (cl (not (= tptp.a 0)) (= (* tptp.a tptp.a) 0)) :rule implies :premises (t62))
% 0.15/0.44 (step t64 (cl (= (* tptp.a tptp.a) 0) (not (= tptp.a 0))) :rule reordering :premises (t63))
% 0.15/0.44 (step t65 (cl (not (= (or (not (not (= tptp.a 0))) (>= (* tptp.a tptp.a) 1)) (or (= tptp.a 0) (>= (* tptp.a tptp.a) 1)))) (not (or (not (not (= tptp.a 0))) (>= (* tptp.a tptp.a) 1))) (or (= tptp.a 0) (>= (* tptp.a tptp.a) 1))) :rule equiv_pos2)
% 0.15/0.44 (step t66 (cl (= (= (= (not (not (= tptp.a 0))) (= tptp.a 0)) true) (= (not (not (= tptp.a 0))) (= tptp.a 0)))) :rule equiv_simplify)
% 0.15/0.44 (step t67 (cl (not (= (= (not (not (= tptp.a 0))) (= tptp.a 0)) true)) (= (not (not (= tptp.a 0))) (= tptp.a 0))) :rule equiv1 :premises (t66))
% 0.15/0.44 (step t68 (cl (= (= (not (not (= tptp.a 0))) (= tptp.a 0)) (= (= tptp.a 0) (not (not (= tptp.a 0)))))) :rule all_simplify)
% 0.15/0.44 (step t69 (cl (= (= tptp.a 0) (= tptp.a 0))) :rule refl)
% 0.15/0.44 (step t70 (cl (= (not (not (= tptp.a 0))) (= tptp.a 0))) :rule all_simplify)
% 0.15/0.44 (step t71 (cl (= (= (= tptp.a 0) (not (not (= tptp.a 0)))) (= (= tptp.a 0) (= tptp.a 0)))) :rule cong :premises (t69 t70))
% 0.15/0.44 (step t72 (cl (= (= (= tptp.a 0) (= tptp.a 0)) true)) :rule all_simplify)
% 0.15/0.44 (step t73 (cl (= (= (= tptp.a 0) (not (not (= tptp.a 0)))) true)) :rule trans :premises (t71 t72))
% 0.15/0.44 (step t74 (cl (= (= (not (not (= tptp.a 0))) (= tptp.a 0)) true)) :rule trans :premises (t68 t73))
% 0.15/0.44 (step t75 (cl (= (not (not (= tptp.a 0))) (= tptp.a 0))) :rule resolution :premises (t67 t74))
% 0.15/0.44 (step t76 (cl (= (>= (* tptp.a tptp.a) 1) (>= (* tptp.a tptp.a) 1))) :rule refl)
% 0.15/0.44 (step t77 (cl (= (or (not (not (= tptp.a 0))) (>= (* tptp.a tptp.a) 1)) (or (= tptp.a 0) (>= (* tptp.a tptp.a) 1)))) :rule cong :premises (t75 t76))
% 0.15/0.44 (step t78 (cl (not (= (=> (not (= tptp.a 0)) (> (* tptp.a tptp.a) 0)) (=> (not (= tptp.a 0)) (>= (* tptp.a tptp.a) 1)))) (not (=> (not (= tptp.a 0)) (> (* tptp.a tptp.a) 0))) (=> (not (= tptp.a 0)) (>= (* tptp.a tptp.a) 1))) :rule equiv_pos2)
% 0.15/0.44 (step t79 (cl (= (not (= tptp.a 0)) (not (= tptp.a 0)))) :rule refl)
% 0.15/0.44 (step t80 (cl (= (> (* tptp.a tptp.a) 0) (not (<= (* tptp.a tptp.a) 0)))) :rule all_simplify)
% 0.15/0.44 (step t81 (cl (= (<= (* tptp.a tptp.a) 0) (not (>= (* tptp.a tptp.a) 1)))) :rule all_simplify)
% 0.15/0.44 (step t82 (cl (= (not (<= (* tptp.a tptp.a) 0)) (not (not (>= (* tptp.a tptp.a) 1))))) :rule cong :premises (t81))
% 0.15/0.44 (step t83 (cl (= (not (not (>= (* tptp.a tptp.a) 1))) (>= (* tptp.a tptp.a) 1))) :rule all_simplify)
% 0.15/0.44 (step t84 (cl (= (not (<= (* tptp.a tptp.a) 0)) (>= (* tptp.a tptp.a) 1))) :rule trans :premises (t82 t83))
% 0.15/0.44 (step t85 (cl (= (> (* tptp.a tptp.a) 0) (>= (* tptp.a tptp.a) 1))) :rule trans :premises (t80 t84))
% 0.15/0.44 (step t86 (cl (= (=> (not (= tptp.a 0)) (> (* tptp.a tptp.a) 0)) (=> (not (= tptp.a 0)) (>= (* tptp.a tptp.a) 1)))) :rule cong :premises (t79 t85))
% 0.15/0.44 (step t87 (cl (=> (not (= tptp.a 0)) (> (* tptp.a tptp.a) 0))) :rule hole :args ((not (= tptp.a 0)) (* tptp.a tptp.a)))
% 0.15/0.44 (step t88 (cl (=> (not (= tptp.a 0)) (>= (* tptp.a tptp.a) 1))) :rule resolution :premises (t78 t86 t87))
% 0.15/0.44 (step t89 (cl (not (not (= tptp.a 0))) (>= (* tptp.a tptp.a) 1)) :rule implies :premises (t88))
% 0.15/0.44 (step t90 (cl (or (not (not (= tptp.a 0))) (>= (* tptp.a tptp.a) 1)) (not (not (not (= tptp.a 0))))) :rule or_neg)
% 0.15/0.44 (step t91 (cl (or (not (not (= tptp.a 0))) (>= (* tptp.a tptp.a) 1)) (not (>= (* tptp.a tptp.a) 1))) :rule or_neg)
% 0.15/0.44 (step t92 (cl (or (not (not (= tptp.a 0))) (>= (* tptp.a tptp.a) 1)) (or (not (not (= tptp.a 0))) (>= (* tptp.a tptp.a) 1))) :rule resolution :premises (t89 t90 t91))
% 0.15/0.44 (step t93 (cl (or (not (not (= tptp.a 0))) (>= (* tptp.a tptp.a) 1))) :rule contraction :premises (t92))
% 0.15/0.44 (step t94 (cl (or (= tptp.a 0) (>= (* tptp.a tptp.a) 1))) :rule resolution :premises (t65 t77 t93))
% 0.15/0.44 (step t95 (cl (= tptp.a 0) (>= (* tptp.a tptp.a) 1)) :rule or :premises (t94))
% 0.15/0.44 (step t96 (cl (not (= (or (not (not (>= (* tptp.a tptp.a) (- 10)))) (not (>= (* tptp.a tptp.a) 1))) (or (>= (* tptp.a tptp.a) (- 10)) (not (>= (* tptp.a tptp.a) 1))))) (not (or (not (not (>= (* tptp.a tptp.a) (- 10)))) (not (>= (* tptp.a tptp.a) 1)))) (or (>= (* tptp.a tptp.a) (- 10)) (not (>= (* tptp.a tptp.a) 1)))) :rule equiv_pos2)
% 0.15/0.44 (step t97 (cl (= (not (>= (* tptp.a tptp.a) 1)) (not (>= (* tptp.a tptp.a) 1)))) :rule refl)
% 0.15/0.44 (step t98 (cl (= (or (not (not (>= (* tptp.a tptp.a) (- 10)))) (not (>= (* tptp.a tptp.a) 1))) (or (>= (* tptp.a tptp.a) (- 10)) (not (>= (* tptp.a tptp.a) 1))))) :rule cong :premises (t11 t97))
% 0.15/0.44 (step t99 (cl (not (= (=> (and (not (>= (* tptp.a tptp.a) (- 10))) (>= (* tptp.a tptp.a) 1)) (and (>= (* tptp.a tptp.a) 1) (not (>= (* tptp.a tptp.a) (- 10))))) (not (and (not (>= (* tptp.a tptp.a) (- 10))) (>= (* tptp.a tptp.a) 1))))) (not (=> (and (not (>= (* tptp.a tptp.a) (- 10))) (>= (* tptp.a tptp.a) 1)) (and (>= (* tptp.a tptp.a) 1) (not (>= (* tptp.a tptp.a) (- 10)))))) (not (and (not (>= (* tptp.a tptp.a) (- 10))) (>= (* tptp.a tptp.a) 1)))) :rule equiv_pos2)
% 0.15/0.44 (step t100 (cl (= (and (not (>= (* tptp.a tptp.a) (- 10))) (>= (* tptp.a tptp.a) 1)) (and (not (>= (* tptp.a tptp.a) (- 10))) (>= (* tptp.a tptp.a) 1)))) :rule refl)
% 0.15/0.44 (step t101 (cl (= (= (and (>= (* tptp.a tptp.a) 1) (not (>= (* tptp.a tptp.a) (- 10)))) false) (not (and (>= (* tptp.a tptp.a) 1) (not (>= (* tptp.a tptp.a) (- 10))))))) :rule equiv_simplify)
% 0.15/0.44 (step t102 (cl (= (and (>= (* tptp.a tptp.a) 1) (not (>= (* tptp.a tptp.a) (- 10)))) false) (not (not (and (>= (* tptp.a tptp.a) 1) (not (>= (* tptp.a tptp.a) (- 10))))))) :rule equiv2 :premises (t101))
% 0.15/0.44 (step t103 (cl (not (not (not (and (>= (* tptp.a tptp.a) 1) (not (>= (* tptp.a tptp.a) (- 10))))))) (and (>= (* tptp.a tptp.a) 1) (not (>= (* tptp.a tptp.a) (- 10))))) :rule not_not)
% 0.15/0.44 (step t104 (cl (= (and (>= (* tptp.a tptp.a) 1) (not (>= (* tptp.a tptp.a) (- 10)))) false) (and (>= (* tptp.a tptp.a) 1) (not (>= (* tptp.a tptp.a) (- 10))))) :rule resolution :premises (t102 t103))
% 0.15/0.44 (step t105 (cl (=> (and (>= (* tptp.a tptp.a) 1) (not (>= (* tptp.a tptp.a) (- 10)))) false) (and (>= (* tptp.a tptp.a) 1) (not (>= (* tptp.a tptp.a) (- 10))))) :rule implies_neg1)
% 0.15/0.44 (anchor :step t106)
% 0.15/0.44 (assume t106.a0 (>= (* tptp.a tptp.a) 1))
% 0.15/0.44 (assume t106.a1 (not (>= (* tptp.a tptp.a) (- 10))))
% 0.15/0.44 (step t106.t1 (cl (not (= (not (>= (* tptp.a tptp.a) 1)) (< (* tptp.a tptp.a) 1))) (not (not (>= (* tptp.a tptp.a) 1))) (< (* tptp.a tptp.a) 1)) :rule equiv_pos2)
% 0.15/0.44 (step t106.t2 (cl (= (< (* tptp.a tptp.a) 1) (not (>= (* tptp.a tptp.a) 1)))) :rule all_simplify)
% 0.15/0.44 (step t106.t3 (cl (= (not (>= (* tptp.a tptp.a) 1)) (< (* tptp.a tptp.a) 1))) :rule symm :premises (t106.t2))
% 0.15/0.44 (step t106.t4 (cl (=> (>= (* tptp.a tptp.a) 1) false) (>= (* tptp.a tptp.a) 1)) :rule implies_neg1)
% 0.15/0.44 (anchor :step t106.t5)
% 0.15/0.44 (assume t106.t5.a0 (>= (* tptp.a tptp.a) 1))
% 0.15/0.44 (step t106.t5.t1 (cl (not (= (<= (+ (* (- 1.0) (* tptp.a tptp.a)) (* 1.0 (* tptp.a tptp.a))) (+ (* (- 1.0) 1) (* 1.0 (- 11)))) false)) (not (<= (+ (* (- 1.0) (* tptp.a tptp.a)) (* 1.0 (* tptp.a tptp.a))) (+ (* (- 1.0) 1) (* 1.0 (- 11))))) false) :rule equiv_pos2)
% 0.15/0.44 (step t106.t5.t2 (cl (= (* (- 1.0) (* tptp.a tptp.a)) (to_real (* (- 1) (* tptp.a tptp.a))))) :rule all_simplify)
% 0.15/0.44 (step t106.t5.t3 (cl (= (* 1.0 (* tptp.a tptp.a)) (to_real (* tptp.a tptp.a)))) :rule all_simplify)
% 0.15/0.44 (step t106.t5.t4 (cl (= (+ (* (- 1.0) (* tptp.a tptp.a)) (* 1.0 (* tptp.a tptp.a))) (+ (to_real (* (- 1) (* tptp.a tptp.a))) (to_real (* tptp.a tptp.a))))) :rule cong :premises (t106.t5.t2 t106.t5.t3))
% 0.15/0.44 (step t106.t5.t5 (cl (= (+ (to_real (* (- 1) (* tptp.a tptp.a))) (to_real (* tptp.a tptp.a))) 0.0)) :rule all_simplify)
% 0.15/0.44 (step t106.t5.t6 (cl (= (+ (* (- 1.0) (* tptp.a tptp.a)) (* 1.0 (* tptp.a tptp.a))) 0.0)) :rule trans :premises (t106.t5.t4 t106.t5.t5))
% 0.15/0.44 (step t106.t5.t7 (cl (= (* (- 1.0) 1) (- 1.0))) :rule all_simplify)
% 0.15/0.44 (step t106.t5.t8 (cl (= (* 1.0 (- 11)) (- 11.0))) :rule all_simplify)
% 0.15/0.44 (step t106.t5.t9 (cl (= (+ (* (- 1.0) 1) (* 1.0 (- 11))) (+ (- 1.0) (- 11.0)))) :rule cong :premises (t106.t5.t7 t106.t5.t8))
% 0.15/0.44 (step t106.t5.t10 (cl (= (+ (- 1.0) (- 11.0)) (- 12.0))) :rule all_simplify)
% 0.15/0.44 (step t106.t5.t11 (cl (= (+ (* (- 1.0) 1) (* 1.0 (- 11))) (- 12.0))) :rule trans :premises (t106.t5.t9 t106.t5.t10))
% 0.15/0.44 (step t106.t5.t12 (cl (= (<= (+ (* (- 1.0) (* tptp.a tptp.a)) (* 1.0 (* tptp.a tptp.a))) (+ (* (- 1.0) 1) (* 1.0 (- 11)))) (<= 0.0 (- 12.0)))) :rule cong :premises (t106.t5.t6 t106.t5.t11))
% 0.15/0.44 (step t106.t5.t13 (cl (= (<= 0.0 (- 12.0)) false)) :rule all_simplify)
% 0.15/0.44 (step t106.t5.t14 (cl (= (<= (+ (* (- 1.0) (* tptp.a tptp.a)) (* 1.0 (* tptp.a tptp.a))) (+ (* (- 1.0) 1) (* 1.0 (- 11)))) false)) :rule trans :premises (t106.t5.t12 t106.t5.t13))
% 0.15/0.44 (step t106.t5.t15 (cl (not (<= (* (- 1.0) (* tptp.a tptp.a)) (* (- 1.0) 1))) (not (<= (* 1.0 (* tptp.a tptp.a)) (* 1.0 (- 11)))) (<= (+ (* (- 1.0) (* tptp.a tptp.a)) (* 1.0 (* tptp.a tptp.a))) (+ (* (- 1.0) 1) (* 1.0 (- 11))))) :rule la_generic :args (1 1 1))
% 0.15/0.44 (step t106.t5.t16 (cl (=> (and (< (- 1.0) 0) (>= (* tptp.a tptp.a) 1)) (<= (* (- 1.0) (* tptp.a tptp.a)) (* (- 1.0) 1)))) :rule la_mult_neg)
% 0.15/0.44 (step t106.t5.t17 (cl (not (and (< (- 1.0) 0) (>= (* tptp.a tptp.a) 1))) (<= (* (- 1.0) (* tptp.a tptp.a)) (* (- 1.0) 1))) :rule implies :premises (t106.t5.t16))
% 0.15/0.44 (step t106.t5.t18 (cl (and (< (- 1.0) 0) (>= (* tptp.a tptp.a) 1)) (not (< (- 1.0) 0)) (not (>= (* tptp.a tptp.a) 1))) :rule and_neg)
% 0.15/0.44 (step t106.t5.t19 (cl (= (= (< (- 1.0) 0) true) (< (- 1.0) 0))) :rule equiv_simplify)
% 0.15/0.44 (step t106.t5.t20 (cl (not (= (< (- 1.0) 0) true)) (< (- 1.0) 0)) :rule equiv1 :premises (t106.t5.t19))
% 0.15/0.44 (step t106.t5.t21 (cl (= (< (- 1.0) 0) true)) :rule hole :args ((< (- 1.0) 0)))
% 0.15/0.44 (step t106.t5.t22 (cl (< (- 1.0) 0)) :rule resolution :premises (t106.t5.t20 t106.t5.t21))
% 0.15/0.44 (step t106.t5.t23 (cl (and (< (- 1.0) 0) (>= (* tptp.a tptp.a) 1))) :rule resolution :premises (t106.t5.t18 t106.t5.t22 t106.t5.a0))
% 0.15/0.44 (step t106.t5.t24 (cl (<= (* (- 1.0) (* tptp.a tptp.a)) (* (- 1.0) 1))) :rule resolution :premises (t106.t5.t17 t106.t5.t23))
% 0.15/0.44 (step t106.t5.t25 (cl (=> (and (> 1.0 0) (<= (* tptp.a tptp.a) (- 11))) (<= (* 1.0 (* tptp.a tptp.a)) (* 1.0 (- 11))))) :rule la_mult_pos)
% 0.15/0.44 (step t106.t5.t26 (cl (not (and (> 1.0 0) (<= (* tptp.a tptp.a) (- 11)))) (<= (* 1.0 (* tptp.a tptp.a)) (* 1.0 (- 11)))) :rule implies :premises (t106.t5.t25))
% 0.15/0.44 (step t106.t5.t27 (cl (and (> 1.0 0) (<= (* tptp.a tptp.a) (- 11))) (not (> 1.0 0)) (not (<= (* tptp.a tptp.a) (- 11)))) :rule and_neg)
% 0.15/0.44 (step t106.t5.t28 (cl (= (= (> 1.0 0) true) (> 1.0 0))) :rule equiv_simplify)
% 0.15/0.44 (step t106.t5.t29 (cl (not (= (> 1.0 0) true)) (> 1.0 0)) :rule equiv1 :premises (t106.t5.t28))
% 0.15/0.44 (step t106.t5.t30 (cl (= (> 1.0 0) true)) :rule hole :args ((> 1.0 0)))
% 0.15/0.44 (step t106.t5.t31 (cl (> 1.0 0)) :rule resolution :premises (t106.t5.t29 t106.t5.t30))
% 0.15/0.44 (step t106.t5.t32 (cl (not (< (* tptp.a tptp.a) (- 10))) (<= (* tptp.a tptp.a) (- 11))) :rule la_generic :args (1 1))
% 0.15/0.44 (step t106.t5.t33 (cl (not (= (not (>= (* tptp.a tptp.a) (- 10))) (< (* tptp.a tptp.a) (- 10)))) (not (not (>= (* tptp.a tptp.a) (- 10)))) (< (* tptp.a tptp.a) (- 10))) :rule equiv_pos2)
% 0.15/0.44 (step t106.t5.t34 (cl (= (< (* tptp.a tptp.a) (- 10)) (not (>= (* tptp.a tptp.a) (- 10))))) :rule all_simplify)
% 0.15/0.44 (step t106.t5.t35 (cl (= (not (>= (* tptp.a tptp.a) (- 10))) (< (* tptp.a tptp.a) (- 10)))) :rule symm :premises (t106.t5.t34))
% 0.15/0.44 (step t106.t5.t36 (cl (< (* tptp.a tptp.a) (- 10))) :rule resolution :premises (t106.t5.t33 t106.t5.t35 t106.a1))
% 0.15/0.44 (step t106.t5.t37 (cl (<= (* tptp.a tptp.a) (- 11))) :rule resolution :premises (t106.t5.t32 t106.t5.t36))
% 0.15/0.44 (step t106.t5.t38 (cl (and (> 1.0 0) (<= (* tptp.a tptp.a) (- 11)))) :rule resolution :premises (t106.t5.t27 t106.t5.t31 t106.t5.t37))
% 0.15/0.44 (step t106.t5.t39 (cl (<= (* 1.0 (* tptp.a tptp.a)) (* 1.0 (- 11)))) :rule resolution :premises (t106.t5.t26 t106.t5.t38))
% 0.15/0.44 (step t106.t5.t40 (cl (<= (+ (* (- 1.0) (* tptp.a tptp.a)) (* 1.0 (* tptp.a tptp.a))) (+ (* (- 1.0) 1) (* 1.0 (- 11))))) :rule resolution :premises (t106.t5.t15 t106.t5.t24 t106.t5.t39))
% 0.15/0.44 (step t106.t5.t41 (cl false) :rule resolution :premises (t106.t5.t1 t106.t5.t14 t106.t5.t40))
% 0.15/0.44 (step t106.t5 (cl (not (>= (* tptp.a tptp.a) 1)) false) :rule subproof :discharge (t106.t5.a0))
% 0.15/0.44 (step t106.t6 (cl (=> (>= (* tptp.a tptp.a) 1) false) false) :rule resolution :premises (t106.t4 t106.t5))
% 0.15/0.44 (step t106.t7 (cl (=> (>= (* tptp.a tptp.a) 1) false) (not false)) :rule implies_neg2)
% 0.15/0.44 (step t106.t8 (cl (=> (>= (* tptp.a tptp.a) 1) false) (=> (>= (* tptp.a tptp.a) 1) false)) :rule resolution :premises (t106.t6 t106.t7))
% 0.15/0.44 (step t106.t9 (cl (=> (>= (* tptp.a tptp.a) 1) false)) :rule contraction :premises (t106.t8))
% 0.15/0.44 (step t106.t10 (cl (= (=> (>= (* tptp.a tptp.a) 1) false) (not (>= (* tptp.a tptp.a) 1)))) :rule implies_simplify)
% 0.15/0.44 (step t106.t11 (cl (not (=> (>= (* tptp.a tptp.a) 1) false)) (not (>= (* tptp.a tptp.a) 1))) :rule equiv1 :premises (t106.t10))
% 0.15/0.44 (step t106.t12 (cl (not (>= (* tptp.a tptp.a) 1))) :rule resolution :premises (t106.t9 t106.t11))
% 0.15/0.44 (step t106.t13 (cl (< (* tptp.a tptp.a) 1)) :rule resolution :premises (t106.t1 t106.t3 t106.t12))
% 0.15/0.44 (step t106.t14 (cl (not (= (>= (* tptp.a tptp.a) 1) (not (< (* tptp.a tptp.a) 1)))) (not (>= (* tptp.a tptp.a) 1)) (not (< (* tptp.a tptp.a) 1))) :rule equiv_pos2)
% 0.15/0.44 (step t106.t15 (cl (= (not (< (* tptp.a tptp.a) 1)) (not (not (>= (* tptp.a tptp.a) 1))))) :rule cong :premises (t106.t2))
% 0.15/0.44 (step t106.t16 (cl (= (not (< (* tptp.a tptp.a) 1)) (>= (* tptp.a tptp.a) 1))) :rule trans :premises (t106.t15 t83))
% 0.15/0.44 (step t106.t17 (cl (= (>= (* tptp.a tptp.a) 1) (not (< (* tptp.a tptp.a) 1)))) :rule symm :premises (t106.t16))
% 0.15/0.44 (step t106.t18 (cl (not (< (* tptp.a tptp.a) 1))) :rule resolution :premises (t106.t14 t106.t17 t106.a0))
% 0.15/0.44 (step t106.t19 (cl) :rule resolution :premises (t106.t13 t106.t18))
% 0.15/0.44 (step t106 (cl (not (>= (* tptp.a tptp.a) 1)) (not (not (>= (* tptp.a tptp.a) (- 10)))) false) :rule subproof :discharge (t106.a0 t106.a1))
% 0.15/0.44 (step t107 (cl (not (and (>= (* tptp.a tptp.a) 1) (not (>= (* tptp.a tptp.a) (- 10))))) (>= (* tptp.a tptp.a) 1)) :rule and_pos)
% 0.15/0.44 (step t108 (cl (not (and (>= (* tptp.a tptp.a) 1) (not (>= (* tptp.a tptp.a) (- 10))))) (not (>= (* tptp.a tptp.a) (- 10)))) :rule and_pos)
% 0.15/0.44 (step t109 (cl false (not (and (>= (* tptp.a tptp.a) 1) (not (>= (* tptp.a tptp.a) (- 10))))) (not (and (>= (* tptp.a tptp.a) 1) (not (>= (* tptp.a tptp.a) (- 10)))))) :rule resolution :premises (t106 t107 t108))
% 0.15/0.44 (step t110 (cl (not (and (>= (* tptp.a tptp.a) 1) (not (>= (* tptp.a tptp.a) (- 10))))) (not (and (>= (* tptp.a tptp.a) 1) (not (>= (* tptp.a tptp.a) (- 10))))) false) :rule reordering :premises (t109))
% 0.15/0.44 (step t111 (cl (not (and (>= (* tptp.a tptp.a) 1) (not (>= (* tptp.a tptp.a) (- 10))))) false) :rule contraction :premises (t110))
% 0.15/0.44 (step t112 (cl (=> (and (>= (* tptp.a tptp.a) 1) (not (>= (* tptp.a tptp.a) (- 10)))) false) false) :rule resolution :premises (t105 t111))
% 0.15/0.44 (step t113 (cl (=> (and (>= (* tptp.a tptp.a) 1) (not (>= (* tptp.a tptp.a) (- 10)))) false) (not false)) :rule implies_neg2)
% 0.15/0.44 (step t114 (cl (=> (and (>= (* tptp.a tptp.a) 1) (not (>= (* tptp.a tptp.a) (- 10)))) false) (=> (and (>= (* tptp.a tptp.a) 1) (not (>= (* tptp.a tptp.a) (- 10)))) false)) :rule resolution :premises (t112 t113))
% 0.15/0.44 (step t115 (cl (=> (and (>= (* tptp.a tptp.a) 1) (not (>= (* tptp.a tptp.a) (- 10)))) false)) :rule contraction :premises (t114))
% 0.15/0.44 (step t116 (cl (= (=> (and (>= (* tptp.a tptp.a) 1) (not (>= (* tptp.a tptp.a) (- 10)))) false) (not (and (>= (* tptp.a tptp.a) 1) (not (>= (* tptp.a tptp.a) (- 10))))))) :rule implies_simplify)
% 0.15/0.44 (step t117 (cl (not (=> (and (>= (* tptp.a tptp.a) 1) (not (>= (* tptp.a tptp.a) (- 10)))) false)) (not (and (>= (* tptp.a tptp.a) 1) (not (>= (* tptp.a tptp.a) (- 10)))))) :rule equiv1 :premises (t116))
% 0.15/0.44 (step t118 (cl (not (and (>= (* tptp.a tptp.a) 1) (not (>= (* tptp.a tptp.a) (- 10)))))) :rule resolution :premises (t115 t117))
% 0.15/0.44 (step t119 (cl (= (and (>= (* tptp.a tptp.a) 1) (not (>= (* tptp.a tptp.a) (- 10)))) false)) :rule resolution :premises (t104 t118))
% 0.15/0.44 (step t120 (cl (= (=> (and (not (>= (* tptp.a tptp.a) (- 10))) (>= (* tptp.a tptp.a) 1)) (and (>= (* tptp.a tptp.a) 1) (not (>= (* tptp.a tptp.a) (- 10))))) (=> (and (not (>= (* tptp.a tptp.a) (- 10))) (>= (* tptp.a tptp.a) 1)) false))) :rule cong :premises (t100 t119))
% 0.15/0.44 (step t121 (cl (= (=> (and (not (>= (* tptp.a tptp.a) (- 10))) (>= (* tptp.a tptp.a) 1)) false) (not (and (not (>= (* tptp.a tptp.a) (- 10))) (>= (* tptp.a tptp.a) 1))))) :rule all_simplify)
% 0.15/0.44 (step t122 (cl (= (=> (and (not (>= (* tptp.a tptp.a) (- 10))) (>= (* tptp.a tptp.a) 1)) (and (>= (* tptp.a tptp.a) 1) (not (>= (* tptp.a tptp.a) (- 10))))) (not (and (not (>= (* tptp.a tptp.a) (- 10))) (>= (* tptp.a tptp.a) 1))))) :rule trans :premises (t120 t121))
% 0.15/0.44 (step t123 (cl (=> (and (not (>= (* tptp.a tptp.a) (- 10))) (>= (* tptp.a tptp.a) 1)) (and (>= (* tptp.a tptp.a) 1) (not (>= (* tptp.a tptp.a) (- 10))))) (and (not (>= (* tptp.a tptp.a) (- 10))) (>= (* tptp.a tptp.a) 1))) :rule implies_neg1)
% 0.15/0.44 (anchor :step t124)
% 0.15/0.44 (assume t124.a0 (not (>= (* tptp.a tptp.a) (- 10))))
% 0.15/0.44 (assume t124.a1 (>= (* tptp.a tptp.a) 1))
% 0.15/0.44 (step t124.t1 (cl (and (>= (* tptp.a tptp.a) 1) (not (>= (* tptp.a tptp.a) (- 10)))) (not (>= (* tptp.a tptp.a) 1)) (not (not (>= (* tptp.a tptp.a) (- 10))))) :rule and_neg)
% 0.15/0.44 (step t124.t2 (cl (and (>= (* tptp.a tptp.a) 1) (not (>= (* tptp.a tptp.a) (- 10))))) :rule resolution :premises (t124.t1 t124.a1 t124.a0))
% 0.15/0.44 (step t124 (cl (not (not (>= (* tptp.a tptp.a) (- 10)))) (not (>= (* tptp.a tptp.a) 1)) (and (>= (* tptp.a tptp.a) 1) (not (>= (* tptp.a tptp.a) (- 10))))) :rule subproof :discharge (t124.a0 t124.a1))
% 0.15/0.44 (step t125 (cl (not (and (not (>= (* tptp.a tptp.a) (- 10))) (>= (* tptp.a tptp.a) 1))) (not (>= (* tptp.a tptp.a) (- 10)))) :rule and_pos)
% 0.15/0.44 (step t126 (cl (not (and (not (>= (* tptp.a tptp.a) (- 10))) (>= (* tptp.a tptp.a) 1))) (>= (* tptp.a tptp.a) 1)) :rule and_pos)
% 0.15/0.44 (step t127 (cl (and (>= (* tptp.a tptp.a) 1) (not (>= (* tptp.a tptp.a) (- 10)))) (not (and (not (>= (* tptp.a tptp.a) (- 10))) (>= (* tptp.a tptp.a) 1))) (not (and (not (>= (* tptp.a tptp.a) (- 10))) (>= (* tptp.a tptp.a) 1)))) :rule resolution :premises (t124 t125 t126))
% 0.15/0.44 (step t128 (cl (not (and (not (>= (* tptp.a tptp.a) (- 10))) (>= (* tptp.a tptp.a) 1))) (not (and (not (>= (* tptp.a tptp.a) (- 10))) (>= (* tptp.a tptp.a) 1))) (and (>= (* tptp.a tptp.a) 1) (not (>= (* tptp.a tptp.a) (- 10))))) :rule reordering :premises (t127))
% 0.15/0.44 (step t129 (cl (not (and (not (>= (* tptp.a tptp.a) (- 10))) (>= (* tptp.a tptp.a) 1))) (and (>= (* tptp.a tptp.a) 1) (not (>= (* tptp.a tptp.a) (- 10))))) :rule contraction :premises (t128))
% 0.15/0.44 (step t130 (cl (=> (and (not (>= (* tptp.a tptp.a) (- 10))) (>= (* tptp.a tptp.a) 1)) (and (>= (* tptp.a tptp.a) 1) (not (>= (* tptp.a tptp.a) (- 10))))) (and (>= (* tptp.a tptp.a) 1) (not (>= (* tptp.a tptp.a) (- 10))))) :rule resolution :premises (t123 t129))
% 0.15/0.44 (step t131 (cl (=> (and (not (>= (* tptp.a tptp.a) (- 10))) (>= (* tptp.a tptp.a) 1)) (and (>= (* tptp.a tptp.a) 1) (not (>= (* tptp.a tptp.a) (- 10))))) (not (and (>= (* tptp.a tptp.a) 1) (not (>= (* tptp.a tptp.a) (- 10)))))) :rule implies_neg2)
% 0.15/0.44 (step t132 (cl (=> (and (not (>= (* tptp.a tptp.a) (- 10))) (>= (* tptp.a tptp.a) 1)) (and (>= (* tptp.a tptp.a) 1) (not (>= (* tptp.a tptp.a) (- 10))))) (=> (and (not (>= (* tptp.a tptp.a) (- 10))) (>= (* tptp.a tptp.a) 1)) (and (>= (* tptp.a tptp.a) 1) (not (>= (* tptp.a tptp.a) (- 10)))))) :rule resolution :premises (t130 t131))
% 0.15/0.44 (step t133 (cl (=> (and (not (>= (* tptp.a tptp.a) (- 10))) (>= (* tptp.a tptp.a) 1)) (and (>= (* tptp.a tptp.a) 1) (not (>= (* tptp.a tptp.a) (- 10)))))) :rule contraction :premises (t132))
% 0.15/0.44 (step t134 (cl (not (and (not (>= (* tptp.a tptp.a) (- 10))) (>= (* tptp.a tptp.a) 1)))) :rule resolution :premises (t99 t122 t133))
% 0.15/0.44 (step t135 (cl (not (not (>= (* tptp.a tptp.a) (- 10)))) (not (>= (* tptp.a tptp.a) 1))) :rule not_and :premises (t134))
% 0.15/0.44 (step t136 (cl (or (not (not (>= (* tptp.a tptp.a) (- 10)))) (not (>= (* tptp.a tptp.a) 1))) (not (not (not (>= (* tptp.a tptp.a) (- 10)))))) :rule or_neg)
% 0.15/0.44 (step t137 (cl (or (not (not (>= (* tptp.a tptp.a) (- 10)))) (not (>= (* tptp.a tptp.a) 1))) (not (not (>= (* tptp.a tptp.a) 1)))) :rule or_neg)
% 0.15/0.44 (step t138 (cl (or (not (not (>= (* tptp.a tptp.a) (- 10)))) (not (>= (* tptp.a tptp.a) 1))) (or (not (not (>= (* tptp.a tptp.a) (- 10)))) (not (>= (* tptp.a tptp.a) 1)))) :rule resolution :premises (t135 t136 t137))
% 0.15/0.44 (step t139 (cl (or (not (not (>= (* tptp.a tptp.a) (- 10)))) (not (>= (* tptp.a tptp.a) 1)))) :rule contraction :premises (t138))
% 0.15/0.44 (step t140 (cl (or (>= (* tptp.a tptp.a) (- 10)) (not (>= (* tptp.a tptp.a) 1)))) :rule resolution :premises (t96 t98 t139))
% 0.15/0.44 (step t141 (cl (>= (* tptp.a tptp.a) (- 10)) (not (>= (* tptp.a tptp.a) 1))) :rule or :premises (t140))
% 0.15/0.44 (step t142 (cl (not (= (not (<= 0 (+ (* tptp.a tptp.a) 10))) (not (>= (* tptp.a tptp.a) (- 10))))) (not (not (<= 0 (+ (* tptp.a tptp.a) 10)))) (not (>= (* tptp.a tptp.a) (- 10)))) :rule equiv_pos2)
% 0.15/0.44 (step t143 (cl (= 0 0)) :rule refl)
% 0.15/0.44 (step t144 (cl (= (* tptp.a tptp.a) (* tptp.a tptp.a))) :rule all_simplify)
% 0.15/0.44 (step t145 (cl (= 10 10)) :rule refl)
% 0.15/0.44 (step t146 (cl (= (+ (* tptp.a tptp.a) 10) (+ (* tptp.a tptp.a) 10))) :rule cong :premises (t144 t145))
% 0.15/0.44 (step t147 (cl (= (+ (* tptp.a tptp.a) 10) (+ 10 (* tptp.a tptp.a)))) :rule all_simplify)
% 0.15/0.44 (step t148 (cl (= (+ (* tptp.a tptp.a) 10) (+ 10 (* tptp.a tptp.a)))) :rule trans :premises (t146 t147))
% 0.15/0.44 (step t149 (cl (= (<= 0 (+ (* tptp.a tptp.a) 10)) (<= 0 (+ 10 (* tptp.a tptp.a))))) :rule cong :premises (t143 t148))
% 0.15/0.44 (step t150 (cl (= (<= 0 (+ 10 (* tptp.a tptp.a))) (>= (* tptp.a tptp.a) (- 10)))) :rule all_simplify)
% 0.15/0.44 (step t151 (cl (= (<= 0 (+ (* tptp.a tptp.a) 10)) (>= (* tptp.a tptp.a) (- 10)))) :rule trans :premises (t149 t150))
% 0.15/0.44 (step t152 (cl (= (not (<= 0 (+ (* tptp.a tptp.a) 10))) (not (>= (* tptp.a tptp.a) (- 10))))) :rule cong :premises (t151))
% 0.15/0.44 (step t153 (cl (not (>= (* tptp.a tptp.a) (- 10)))) :rule resolution :premises (t142 t152 a0))
% 0.15/0.44 (step t154 (cl (not (>= (* tptp.a tptp.a) 1))) :rule resolution :premises (t141 t153))
% 0.15/0.44 (step t155 (cl (= tptp.a 0)) :rule resolution :premises (t95 t154))
% 0.15/0.44 (step t156 (cl (= (* tptp.a tptp.a) 0)) :rule resolution :premises (t64 t155))
% 0.15/0.44 (step t157 (cl) :rule resolution :premises (t56 t156 t153))
% 0.15/0.44
% 0.15/0.44 % SZS output end Proof for /export/starexec/sandbox/tmp/tmp.E79om7cxQf/cvc5---1.0.5_26348.smt2
% 0.15/0.44 % cvc5---1.0.5 exiting
% 0.15/0.44 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------