TSTP Solution File: ARI619_2 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ARI619_2 : TPTP v8.2.0. Released v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n025.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 16:34:16 EDT 2024
% Result : Theorem 0.20s 0.54s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : ARI619_2 : TPTP v8.2.0. Released v5.1.0.
% 0.13/0.14 % Command : do_cvc5 %s %d
% 0.13/0.35 % Computer : n025.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon May 27 05:34:24 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.20/0.49 %----Proving TF0_ARI
% 0.20/0.54 --- Run --finite-model-find --decision=internal at 15...
% 0.20/0.54 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15...
% 0.20/0.54 % SZS status Theorem for /export/starexec/sandbox2/tmp/tmp.8XeJH3845u/cvc5---1.0.5_29066.smt2
% 0.20/0.54 % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.8XeJH3845u/cvc5---1.0.5_29066.smt2
% 0.20/0.54 (assume a0 (not (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (<= 2.0 X) (exists ((Y Real)) (and (= (* 2.0 Y) X) (tptp.pow2 Y))))))) (not (tptp.pow2 5.0)))))
% 0.20/0.54 (assume a1 true)
% 0.20/0.54 (step t1 (cl (not (= (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 (/ 5 4)) (or (= (/ 5 4) 1.0) (and (>= (/ 5 4) 2) (tptp.pow2 (* (/ 1 2) (/ 5 4))))))) (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (not (tptp.pow2 (/ 5 4)))))) (not (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 (/ 5 4)) (or (= (/ 5 4) 1.0) (and (>= (/ 5 4) 2) (tptp.pow2 (* (/ 1 2) (/ 5 4)))))))) (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (not (tptp.pow2 (/ 5 4))))) :rule equiv_pos2)
% 0.20/0.54 (step t2 (cl (= (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))))) :rule refl)
% 0.20/0.54 (step t3 (cl (= (tptp.pow2 (/ 5 4)) (tptp.pow2 (/ 5 4)))) :rule refl)
% 0.20/0.54 (step t4 (cl (= (= (/ 5 4) 1.0) false)) :rule all_simplify)
% 0.20/0.54 (step t5 (cl (= (>= (/ 5 4) 2) false)) :rule all_simplify)
% 0.20/0.54 (step t6 (cl (= (* (/ 1 2) (/ 5 4)) (/ 5 8))) :rule all_simplify)
% 0.20/0.54 (step t7 (cl (= (tptp.pow2 (* (/ 1 2) (/ 5 4))) (tptp.pow2 (/ 5 8)))) :rule cong :premises (t6))
% 0.20/0.54 (step t8 (cl (= (and (>= (/ 5 4) 2) (tptp.pow2 (* (/ 1 2) (/ 5 4)))) (and false (tptp.pow2 (/ 5 8))))) :rule cong :premises (t5 t7))
% 0.20/0.54 (step t9 (cl (= (and false (tptp.pow2 (/ 5 8))) false)) :rule all_simplify)
% 0.20/0.54 (step t10 (cl (= (and (>= (/ 5 4) 2) (tptp.pow2 (* (/ 1 2) (/ 5 4)))) false)) :rule trans :premises (t8 t9))
% 0.20/0.54 (step t11 (cl (= (or (= (/ 5 4) 1.0) (and (>= (/ 5 4) 2) (tptp.pow2 (* (/ 1 2) (/ 5 4))))) (or false false))) :rule cong :premises (t4 t10))
% 0.20/0.54 (step t12 (cl (= (or false false) false)) :rule all_simplify)
% 0.20/0.54 (step t13 (cl (= (or (= (/ 5 4) 1.0) (and (>= (/ 5 4) 2) (tptp.pow2 (* (/ 1 2) (/ 5 4))))) false)) :rule trans :premises (t11 t12))
% 0.20/0.54 (step t14 (cl (= (= (tptp.pow2 (/ 5 4)) (or (= (/ 5 4) 1.0) (and (>= (/ 5 4) 2) (tptp.pow2 (* (/ 1 2) (/ 5 4)))))) (= (tptp.pow2 (/ 5 4)) false))) :rule cong :premises (t3 t13))
% 0.20/0.54 (step t15 (cl (= (= (tptp.pow2 (/ 5 4)) false) (not (tptp.pow2 (/ 5 4))))) :rule all_simplify)
% 0.20/0.54 (step t16 (cl (= (= (tptp.pow2 (/ 5 4)) (or (= (/ 5 4) 1.0) (and (>= (/ 5 4) 2) (tptp.pow2 (* (/ 1 2) (/ 5 4)))))) (not (tptp.pow2 (/ 5 4))))) :rule trans :premises (t14 t15))
% 0.20/0.54 (step t17 (cl (= (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 (/ 5 4)) (or (= (/ 5 4) 1.0) (and (>= (/ 5 4) 2) (tptp.pow2 (* (/ 1 2) (/ 5 4))))))) (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (not (tptp.pow2 (/ 5 4)))))) :rule cong :premises (t2 t16))
% 0.20/0.54 (step t18 (cl (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 (/ 5 4)) (or (= (/ 5 4) 1.0) (and (>= (/ 5 4) 2) (tptp.pow2 (* (/ 1 2) (/ 5 4))))))) (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X))))))) :rule implies_neg1)
% 0.20/0.54 (anchor :step t19)
% 0.20/0.54 (assume t19.a0 (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))))
% 0.20/0.54 (step t19.t1 (cl (or (not (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X))))))) (= (tptp.pow2 (/ 5 4)) (or (= (/ 5 4) 1.0) (and (>= (/ 5 4) 2) (tptp.pow2 (* (/ 1 2) (/ 5 4)))))))) :rule forall_inst :args ((:= X (/ 5 4))))
% 0.20/0.54 (step t19.t2 (cl (not (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X))))))) (= (tptp.pow2 (/ 5 4)) (or (= (/ 5 4) 1.0) (and (>= (/ 5 4) 2) (tptp.pow2 (* (/ 1 2) (/ 5 4))))))) :rule or :premises (t19.t1))
% 0.20/0.54 (step t19.t3 (cl (= (tptp.pow2 (/ 5 4)) (or (= (/ 5 4) 1.0) (and (>= (/ 5 4) 2) (tptp.pow2 (* (/ 1 2) (/ 5 4))))))) :rule resolution :premises (t19.t2 t19.a0))
% 0.20/0.54 (step t19 (cl (not (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X))))))) (= (tptp.pow2 (/ 5 4)) (or (= (/ 5 4) 1.0) (and (>= (/ 5 4) 2) (tptp.pow2 (* (/ 1 2) (/ 5 4))))))) :rule subproof :discharge (t19.a0))
% 0.20/0.54 (step t20 (cl (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 (/ 5 4)) (or (= (/ 5 4) 1.0) (and (>= (/ 5 4) 2) (tptp.pow2 (* (/ 1 2) (/ 5 4))))))) (= (tptp.pow2 (/ 5 4)) (or (= (/ 5 4) 1.0) (and (>= (/ 5 4) 2) (tptp.pow2 (* (/ 1 2) (/ 5 4))))))) :rule resolution :premises (t18 t19))
% 0.20/0.54 (step t21 (cl (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 (/ 5 4)) (or (= (/ 5 4) 1.0) (and (>= (/ 5 4) 2) (tptp.pow2 (* (/ 1 2) (/ 5 4))))))) (not (= (tptp.pow2 (/ 5 4)) (or (= (/ 5 4) 1.0) (and (>= (/ 5 4) 2) (tptp.pow2 (* (/ 1 2) (/ 5 4)))))))) :rule implies_neg2)
% 0.20/0.54 (step t22 (cl (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 (/ 5 4)) (or (= (/ 5 4) 1.0) (and (>= (/ 5 4) 2) (tptp.pow2 (* (/ 1 2) (/ 5 4))))))) (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 (/ 5 4)) (or (= (/ 5 4) 1.0) (and (>= (/ 5 4) 2) (tptp.pow2 (* (/ 1 2) (/ 5 4)))))))) :rule resolution :premises (t20 t21))
% 0.20/0.54 (step t23 (cl (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 (/ 5 4)) (or (= (/ 5 4) 1.0) (and (>= (/ 5 4) 2) (tptp.pow2 (* (/ 1 2) (/ 5 4)))))))) :rule contraction :premises (t22))
% 0.20/0.54 (step t24 (cl (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (not (tptp.pow2 (/ 5 4))))) :rule resolution :premises (t1 t17 t23))
% 0.20/0.54 (step t25 (cl (not (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X))))))) (not (tptp.pow2 (/ 5 4)))) :rule implies :premises (t24))
% 0.20/0.54 (step t26 (cl (not (= (tptp.pow2 (/ 5 2)) (tptp.pow2 (/ 5 4)))) (not (tptp.pow2 (/ 5 2))) (tptp.pow2 (/ 5 4))) :rule equiv_pos2)
% 0.20/0.54 (step t27 (cl (not (tptp.pow2 (/ 5 2))) (tptp.pow2 (/ 5 4)) (not (= (tptp.pow2 (/ 5 2)) (tptp.pow2 (/ 5 4))))) :rule reordering :premises (t26))
% 0.20/0.54 (step t28 (cl (not (= (tptp.pow2 5.0) (tptp.pow2 (/ 5 2)))) (not (tptp.pow2 5.0)) (tptp.pow2 (/ 5 2))) :rule equiv_pos2)
% 0.20/0.54 (step t29 (cl (not (tptp.pow2 5.0)) (tptp.pow2 (/ 5 2)) (not (= (tptp.pow2 5.0) (tptp.pow2 (/ 5 2))))) :rule reordering :premises (t28))
% 0.20/0.54 (step t30 (cl (not (not (not (tptp.pow2 5.0)))) (tptp.pow2 5.0)) :rule not_not)
% 0.20/0.54 (step t31 (cl (not (= (not (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (<= 2.0 X) (exists ((Y Real)) (and (= (* 2.0 Y) X) (tptp.pow2 Y))))))) (not (tptp.pow2 5.0)))) (not (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (not (tptp.pow2 5.0)))))) (not (not (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (<= 2.0 X) (exists ((Y Real)) (and (= (* 2.0 Y) X) (tptp.pow2 Y))))))) (not (tptp.pow2 5.0))))) (not (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (not (tptp.pow2 5.0))))) :rule equiv_pos2)
% 0.20/0.54 (anchor :step t32 :args ((X Real) (:= X X)))
% 0.20/0.54 (step t32.t1 (cl (= X X)) :rule refl)
% 0.20/0.54 (step t32.t2 (cl (= (tptp.pow2 X) (tptp.pow2 X))) :rule refl)
% 0.20/0.54 (step t32.t3 (cl (= (= X 1.0) (= X 1.0))) :rule refl)
% 0.20/0.54 (step t32.t4 (cl (= (<= 2.0 X) (>= X 2))) :rule all_simplify)
% 0.20/0.54 (anchor :step t32.t5 :args ((Y Real) (:= Y Y)))
% 0.20/0.54 (step t32.t5.t1 (cl (= Y Y)) :rule refl)
% 0.20/0.54 (step t32.t5.t2 (cl (= (* 2.0 Y) (* 2 Y))) :rule all_simplify)
% 0.20/0.54 (step t32.t5.t3 (cl (= X X)) :rule refl)
% 0.20/0.54 (step t32.t5.t4 (cl (= (= (* 2.0 Y) X) (= (* 2 Y) X))) :rule cong :premises (t32.t5.t2 t32.t5.t3))
% 0.20/0.54 (step t32.t5.t5 (cl (= (= (* 2 Y) X) (= X (* 2 Y)))) :rule all_simplify)
% 0.20/0.54 (step t32.t5.t6 (cl (= (= (* 2.0 Y) X) (= X (* 2 Y)))) :rule trans :premises (t32.t5.t4 t32.t5.t5))
% 0.20/0.54 (step t32.t5.t7 (cl (= (tptp.pow2 Y) (tptp.pow2 Y))) :rule refl)
% 0.20/0.54 (step t32.t5.t8 (cl (= (and (= (* 2.0 Y) X) (tptp.pow2 Y)) (and (= X (* 2 Y)) (tptp.pow2 Y)))) :rule cong :premises (t32.t5.t6 t32.t5.t7))
% 0.20/0.54 (step t32.t5 (cl (= (exists ((Y Real)) (and (= (* 2.0 Y) X) (tptp.pow2 Y))) (exists ((Y Real)) (and (= X (* 2 Y)) (tptp.pow2 Y))))) :rule bind)
% 0.20/0.54 (step t32.t6 (cl (= (exists ((Y Real)) (and (= X (* 2 Y)) (tptp.pow2 Y))) (not (forall ((Y Real)) (not (and (= X (* 2 Y)) (tptp.pow2 Y))))))) :rule all_simplify)
% 0.20/0.54 (step t32.t7 (cl (= (forall ((Y Real)) (not (and (= X (* 2 Y)) (tptp.pow2 Y)))) (forall ((Y Real)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y)))))) :rule all_simplify)
% 0.20/0.54 (step t32.t8 (cl (= (forall ((Y Real)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y)))) (or (not (= X (* 2 (* X (/ 1 2))))) (not (tptp.pow2 (* X (/ 1 2))))))) :rule all_simplify)
% 0.20/0.54 (step t32.t9 (cl (= X X)) :rule refl)
% 0.20/0.54 (step t32.t10 (cl (= 2 2)) :rule refl)
% 0.20/0.54 (step t32.t11 (cl (= (* X (/ 1 2)) (* (/ 1 2) X))) :rule all_simplify)
% 0.20/0.54 (step t32.t12 (cl (= (* 2 (* X (/ 1 2))) (* 2 (* (/ 1 2) X)))) :rule cong :premises (t32.t10 t32.t11))
% 0.20/0.54 (step t32.t13 (cl (= (* 2 (* (/ 1 2) X)) X)) :rule all_simplify)
% 0.20/0.54 (step t32.t14 (cl (= (* 2 (* X (/ 1 2))) X)) :rule trans :premises (t32.t12 t32.t13))
% 0.20/0.54 (step t32.t15 (cl (= (= X (* 2 (* X (/ 1 2)))) (= X X))) :rule cong :premises (t32.t9 t32.t14))
% 0.20/0.54 (step t32.t16 (cl (= (= X X) true)) :rule all_simplify)
% 0.20/0.54 (step t32.t17 (cl (= (= X (* 2 (* X (/ 1 2)))) true)) :rule trans :premises (t32.t15 t32.t16))
% 0.20/0.54 (step t32.t18 (cl (= (not (= X (* 2 (* X (/ 1 2))))) (not true))) :rule cong :premises (t32.t17))
% 0.20/0.54 (step t32.t19 (cl (= (not true) false)) :rule all_simplify)
% 0.20/0.54 (step t32.t20 (cl (= (not (= X (* 2 (* X (/ 1 2))))) false)) :rule trans :premises (t32.t18 t32.t19))
% 0.20/0.54 (step t32.t21 (cl (= (tptp.pow2 (* X (/ 1 2))) (tptp.pow2 (* (/ 1 2) X)))) :rule cong :premises (t32.t11))
% 0.20/0.54 (step t32.t22 (cl (= (not (tptp.pow2 (* X (/ 1 2)))) (not (tptp.pow2 (* (/ 1 2) X))))) :rule cong :premises (t32.t21))
% 0.20/0.54 (step t32.t23 (cl (= (or (not (= X (* 2 (* X (/ 1 2))))) (not (tptp.pow2 (* X (/ 1 2))))) (or false (not (tptp.pow2 (* (/ 1 2) X)))))) :rule cong :premises (t32.t20 t32.t22))
% 0.20/0.54 (step t32.t24 (cl (= (or false (not (tptp.pow2 (* (/ 1 2) X)))) (not (tptp.pow2 (* (/ 1 2) X))))) :rule all_simplify)
% 0.20/0.54 (step t32.t25 (cl (= (or (not (= X (* 2 (* X (/ 1 2))))) (not (tptp.pow2 (* X (/ 1 2))))) (not (tptp.pow2 (* (/ 1 2) X))))) :rule trans :premises (t32.t23 t32.t24))
% 0.20/0.54 (step t32.t26 (cl (= (forall ((Y Real)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y)))) (not (tptp.pow2 (* (/ 1 2) X))))) :rule trans :premises (t32.t8 t32.t25))
% 0.20/0.54 (step t32.t27 (cl (= (forall ((Y Real)) (not (and (= X (* 2 Y)) (tptp.pow2 Y)))) (not (tptp.pow2 (* (/ 1 2) X))))) :rule trans :premises (t32.t7 t32.t26))
% 0.20/0.54 (step t32.t28 (cl (= (not (forall ((Y Real)) (not (and (= X (* 2 Y)) (tptp.pow2 Y))))) (not (not (tptp.pow2 (* (/ 1 2) X)))))) :rule cong :premises (t32.t27))
% 0.20/0.54 (step t32.t29 (cl (= (not (not (tptp.pow2 (* (/ 1 2) X)))) (tptp.pow2 (* (/ 1 2) X)))) :rule all_simplify)
% 0.20/0.54 (step t32.t30 (cl (= (not (forall ((Y Real)) (not (and (= X (* 2 Y)) (tptp.pow2 Y))))) (tptp.pow2 (* (/ 1 2) X)))) :rule trans :premises (t32.t28 t32.t29))
% 0.20/0.54 (step t32.t31 (cl (= (exists ((Y Real)) (and (= X (* 2 Y)) (tptp.pow2 Y))) (tptp.pow2 (* (/ 1 2) X)))) :rule trans :premises (t32.t6 t32.t30))
% 0.20/0.54 (step t32.t32 (cl (= (exists ((Y Real)) (and (= (* 2.0 Y) X) (tptp.pow2 Y))) (tptp.pow2 (* (/ 1 2) X)))) :rule trans :premises (t32.t5 t32.t31))
% 0.20/0.54 (step t32.t33 (cl (= (and (<= 2.0 X) (exists ((Y Real)) (and (= (* 2.0 Y) X) (tptp.pow2 Y)))) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X))))) :rule cong :premises (t32.t4 t32.t32))
% 0.20/0.54 (step t32.t34 (cl (= (or (= X 1.0) (and (<= 2.0 X) (exists ((Y Real)) (and (= (* 2.0 Y) X) (tptp.pow2 Y))))) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) :rule cong :premises (t32.t3 t32.t33))
% 0.20/0.54 (step t32.t35 (cl (= (= (tptp.pow2 X) (or (= X 1.0) (and (<= 2.0 X) (exists ((Y Real)) (and (= (* 2.0 Y) X) (tptp.pow2 Y)))))) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X))))))) :rule cong :premises (t32.t2 t32.t34))
% 0.20/0.54 (step t32 (cl (= (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (<= 2.0 X) (exists ((Y Real)) (and (= (* 2.0 Y) X) (tptp.pow2 Y))))))) (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))))) :rule bind)
% 0.20/0.54 (step t33 (cl (= (not (tptp.pow2 5.0)) (not (tptp.pow2 5.0)))) :rule refl)
% 0.20/0.54 (step t34 (cl (= (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (<= 2.0 X) (exists ((Y Real)) (and (= (* 2.0 Y) X) (tptp.pow2 Y))))))) (not (tptp.pow2 5.0))) (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (not (tptp.pow2 5.0))))) :rule cong :premises (t32 t33))
% 0.20/0.54 (step t35 (cl (= (not (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (<= 2.0 X) (exists ((Y Real)) (and (= (* 2.0 Y) X) (tptp.pow2 Y))))))) (not (tptp.pow2 5.0)))) (not (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (not (tptp.pow2 5.0)))))) :rule cong :premises (t34))
% 0.20/0.54 (step t36 (cl (not (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (not (tptp.pow2 5.0))))) :rule resolution :premises (t31 t35 a0))
% 0.20/0.54 (step t37 (cl (not (not (tptp.pow2 5.0)))) :rule not_implies2 :premises (t36))
% 0.20/0.54 (step t38 (cl (tptp.pow2 5.0)) :rule resolution :premises (t30 t37))
% 0.20/0.54 (step t39 (cl (not (= (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 5.0) (or (= 5.0 1.0) (and (>= 5.0 2) (tptp.pow2 (* (/ 1 2) 5.0)))))) (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 5.0) (tptp.pow2 (/ 5 2)))))) (not (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 5.0) (or (= 5.0 1.0) (and (>= 5.0 2) (tptp.pow2 (* (/ 1 2) 5.0))))))) (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 5.0) (tptp.pow2 (/ 5 2))))) :rule equiv_pos2)
% 0.20/0.54 (step t40 (cl (= (tptp.pow2 5.0) (tptp.pow2 5.0))) :rule refl)
% 0.20/0.54 (step t41 (cl (= (= 5.0 1.0) false)) :rule all_simplify)
% 0.20/0.54 (step t42 (cl (= (>= 5.0 2) true)) :rule all_simplify)
% 0.20/0.54 (step t43 (cl (= (* (/ 1 2) 5.0) (/ 5 2))) :rule all_simplify)
% 0.20/0.54 (step t44 (cl (= (tptp.pow2 (* (/ 1 2) 5.0)) (tptp.pow2 (/ 5 2)))) :rule cong :premises (t43))
% 0.20/0.54 (step t45 (cl (= (and (>= 5.0 2) (tptp.pow2 (* (/ 1 2) 5.0))) (and true (tptp.pow2 (/ 5 2))))) :rule cong :premises (t42 t44))
% 0.20/0.54 (step t46 (cl (= (and true (tptp.pow2 (/ 5 2))) (tptp.pow2 (/ 5 2)))) :rule all_simplify)
% 0.20/0.54 (step t47 (cl (= (and (>= 5.0 2) (tptp.pow2 (* (/ 1 2) 5.0))) (tptp.pow2 (/ 5 2)))) :rule trans :premises (t45 t46))
% 0.20/0.54 (step t48 (cl (= (or (= 5.0 1.0) (and (>= 5.0 2) (tptp.pow2 (* (/ 1 2) 5.0)))) (or false (tptp.pow2 (/ 5 2))))) :rule cong :premises (t41 t47))
% 0.20/0.54 (step t49 (cl (= (or false (tptp.pow2 (/ 5 2))) (tptp.pow2 (/ 5 2)))) :rule all_simplify)
% 0.20/0.54 (step t50 (cl (= (or (= 5.0 1.0) (and (>= 5.0 2) (tptp.pow2 (* (/ 1 2) 5.0)))) (tptp.pow2 (/ 5 2)))) :rule trans :premises (t48 t49))
% 0.20/0.54 (step t51 (cl (= (= (tptp.pow2 5.0) (or (= 5.0 1.0) (and (>= 5.0 2) (tptp.pow2 (* (/ 1 2) 5.0))))) (= (tptp.pow2 5.0) (tptp.pow2 (/ 5 2))))) :rule cong :premises (t40 t50))
% 0.20/0.54 (step t52 (cl (= (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 5.0) (or (= 5.0 1.0) (and (>= 5.0 2) (tptp.pow2 (* (/ 1 2) 5.0)))))) (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 5.0) (tptp.pow2 (/ 5 2)))))) :rule cong :premises (t2 t51))
% 0.20/0.54 (step t53 (cl (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 5.0) (or (= 5.0 1.0) (and (>= 5.0 2) (tptp.pow2 (* (/ 1 2) 5.0)))))) (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X))))))) :rule implies_neg1)
% 0.20/0.54 (anchor :step t54)
% 0.20/0.54 (assume t54.a0 (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))))
% 0.20/0.54 (step t54.t1 (cl (or (not (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X))))))) (= (tptp.pow2 5.0) (or (= 5.0 1.0) (and (>= 5.0 2) (tptp.pow2 (* (/ 1 2) 5.0))))))) :rule forall_inst :args ((:= X 5.0)))
% 0.20/0.54 (step t54.t2 (cl (not (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X))))))) (= (tptp.pow2 5.0) (or (= 5.0 1.0) (and (>= 5.0 2) (tptp.pow2 (* (/ 1 2) 5.0)))))) :rule or :premises (t54.t1))
% 0.20/0.54 (step t54.t3 (cl (= (tptp.pow2 5.0) (or (= 5.0 1.0) (and (>= 5.0 2) (tptp.pow2 (* (/ 1 2) 5.0)))))) :rule resolution :premises (t54.t2 t54.a0))
% 0.20/0.54 (step t54 (cl (not (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X))))))) (= (tptp.pow2 5.0) (or (= 5.0 1.0) (and (>= 5.0 2) (tptp.pow2 (* (/ 1 2) 5.0)))))) :rule subproof :discharge (t54.a0))
% 0.20/0.54 (step t55 (cl (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 5.0) (or (= 5.0 1.0) (and (>= 5.0 2) (tptp.pow2 (* (/ 1 2) 5.0)))))) (= (tptp.pow2 5.0) (or (= 5.0 1.0) (and (>= 5.0 2) (tptp.pow2 (* (/ 1 2) 5.0)))))) :rule resolution :premises (t53 t54))
% 0.20/0.54 (step t56 (cl (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 5.0) (or (= 5.0 1.0) (and (>= 5.0 2) (tptp.pow2 (* (/ 1 2) 5.0)))))) (not (= (tptp.pow2 5.0) (or (= 5.0 1.0) (and (>= 5.0 2) (tptp.pow2 (* (/ 1 2) 5.0))))))) :rule implies_neg2)
% 0.20/0.54 (step t57 (cl (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 5.0) (or (= 5.0 1.0) (and (>= 5.0 2) (tptp.pow2 (* (/ 1 2) 5.0)))))) (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 5.0) (or (= 5.0 1.0) (and (>= 5.0 2) (tptp.pow2 (* (/ 1 2) 5.0))))))) :rule resolution :premises (t55 t56))
% 0.20/0.54 (step t58 (cl (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 5.0) (or (= 5.0 1.0) (and (>= 5.0 2) (tptp.pow2 (* (/ 1 2) 5.0))))))) :rule contraction :premises (t57))
% 0.20/0.54 (step t59 (cl (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 5.0) (tptp.pow2 (/ 5 2))))) :rule resolution :premises (t39 t52 t58))
% 0.20/0.54 (step t60 (cl (not (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X))))))) (= (tptp.pow2 5.0) (tptp.pow2 (/ 5 2)))) :rule implies :premises (t59))
% 0.20/0.54 (step t61 (cl (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X))))))) :rule not_implies1 :premises (t36))
% 0.20/0.54 (step t62 (cl (= (tptp.pow2 5.0) (tptp.pow2 (/ 5 2)))) :rule resolution :premises (t60 t61))
% 0.20/0.54 (step t63 (cl (tptp.pow2 (/ 5 2))) :rule resolution :premises (t29 t38 t62))
% 0.20/0.54 (step t64 (cl (not (= (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 (/ 5 2)) (or (= (/ 5 2) 1.0) (and (>= (/ 5 2) 2) (tptp.pow2 (* (/ 1 2) (/ 5 2))))))) (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 (/ 5 2)) (tptp.pow2 (/ 5 4)))))) (not (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 (/ 5 2)) (or (= (/ 5 2) 1.0) (and (>= (/ 5 2) 2) (tptp.pow2 (* (/ 1 2) (/ 5 2)))))))) (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 (/ 5 2)) (tptp.pow2 (/ 5 4))))) :rule equiv_pos2)
% 0.20/0.54 (step t65 (cl (= (tptp.pow2 (/ 5 2)) (tptp.pow2 (/ 5 2)))) :rule refl)
% 0.20/0.54 (step t66 (cl (= (= (/ 5 2) 1.0) false)) :rule all_simplify)
% 0.20/0.54 (step t67 (cl (= (>= (/ 5 2) 2) true)) :rule all_simplify)
% 0.20/0.54 (step t68 (cl (= (* (/ 1 2) (/ 5 2)) (/ 5 4))) :rule all_simplify)
% 0.20/0.54 (step t69 (cl (= (tptp.pow2 (* (/ 1 2) (/ 5 2))) (tptp.pow2 (/ 5 4)))) :rule cong :premises (t68))
% 0.20/0.54 (step t70 (cl (= (and (>= (/ 5 2) 2) (tptp.pow2 (* (/ 1 2) (/ 5 2)))) (and true (tptp.pow2 (/ 5 4))))) :rule cong :premises (t67 t69))
% 0.20/0.54 (step t71 (cl (= (and true (tptp.pow2 (/ 5 4))) (tptp.pow2 (/ 5 4)))) :rule all_simplify)
% 0.20/0.54 (step t72 (cl (= (and (>= (/ 5 2) 2) (tptp.pow2 (* (/ 1 2) (/ 5 2)))) (tptp.pow2 (/ 5 4)))) :rule trans :premises (t70 t71))
% 0.20/0.54 (step t73 (cl (= (or (= (/ 5 2) 1.0) (and (>= (/ 5 2) 2) (tptp.pow2 (* (/ 1 2) (/ 5 2))))) (or false (tptp.pow2 (/ 5 4))))) :rule cong :premises (t66 t72))
% 0.20/0.54 (step t74 (cl (= (or false (tptp.pow2 (/ 5 4))) (tptp.pow2 (/ 5 4)))) :rule all_simplify)
% 0.20/0.54 (step t75 (cl (= (or (= (/ 5 2) 1.0) (and (>= (/ 5 2) 2) (tptp.pow2 (* (/ 1 2) (/ 5 2))))) (tptp.pow2 (/ 5 4)))) :rule trans :premises (t73 t74))
% 0.20/0.54 (step t76 (cl (= (= (tptp.pow2 (/ 5 2)) (or (= (/ 5 2) 1.0) (and (>= (/ 5 2) 2) (tptp.pow2 (* (/ 1 2) (/ 5 2)))))) (= (tptp.pow2 (/ 5 2)) (tptp.pow2 (/ 5 4))))) :rule cong :premises (t65 t75))
% 0.20/0.54 (step t77 (cl (= (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 (/ 5 2)) (or (= (/ 5 2) 1.0) (and (>= (/ 5 2) 2) (tptp.pow2 (* (/ 1 2) (/ 5 2))))))) (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 (/ 5 2)) (tptp.pow2 (/ 5 4)))))) :rule cong :premises (t2 t76))
% 0.20/0.54 (step t78 (cl (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 (/ 5 2)) (or (= (/ 5 2) 1.0) (and (>= (/ 5 2) 2) (tptp.pow2 (* (/ 1 2) (/ 5 2))))))) (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X))))))) :rule implies_neg1)
% 0.20/0.54 (anchor :step t79)
% 0.20/0.54 (assume t79.a0 (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))))
% 0.20/0.54 (step t79.t1 (cl (or (not (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X))))))) (= (tptp.pow2 (/ 5 2)) (or (= (/ 5 2) 1.0) (and (>= (/ 5 2) 2) (tptp.pow2 (* (/ 1 2) (/ 5 2)))))))) :rule forall_inst :args ((:= X (/ 5 2))))
% 0.20/0.54 (step t79.t2 (cl (not (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X))))))) (= (tptp.pow2 (/ 5 2)) (or (= (/ 5 2) 1.0) (and (>= (/ 5 2) 2) (tptp.pow2 (* (/ 1 2) (/ 5 2))))))) :rule or :premises (t79.t1))
% 0.20/0.54 (step t79.t3 (cl (= (tptp.pow2 (/ 5 2)) (or (= (/ 5 2) 1.0) (and (>= (/ 5 2) 2) (tptp.pow2 (* (/ 1 2) (/ 5 2))))))) :rule resolution :premises (t79.t2 t79.a0))
% 0.20/0.54 (step t79 (cl (not (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X))))))) (= (tptp.pow2 (/ 5 2)) (or (= (/ 5 2) 1.0) (and (>= (/ 5 2) 2) (tptp.pow2 (* (/ 1 2) (/ 5 2))))))) :rule subproof :discharge (t79.a0))
% 0.20/0.54 (step t80 (cl (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 (/ 5 2)) (or (= (/ 5 2) 1.0) (and (>= (/ 5 2) 2) (tptp.pow2 (* (/ 1 2) (/ 5 2))))))) (= (tptp.pow2 (/ 5 2)) (or (= (/ 5 2) 1.0) (and (>= (/ 5 2) 2) (tptp.pow2 (* (/ 1 2) (/ 5 2))))))) :rule resolution :premises (t78 t79))
% 0.20/0.54 (step t81 (cl (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 (/ 5 2)) (or (= (/ 5 2) 1.0) (and (>= (/ 5 2) 2) (tptp.pow2 (* (/ 1 2) (/ 5 2))))))) (not (= (tptp.pow2 (/ 5 2)) (or (= (/ 5 2) 1.0) (and (>= (/ 5 2) 2) (tptp.pow2 (* (/ 1 2) (/ 5 2)))))))) :rule implies_neg2)
% 0.20/0.54 (step t82 (cl (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 (/ 5 2)) (or (= (/ 5 2) 1.0) (and (>= (/ 5 2) 2) (tptp.pow2 (* (/ 1 2) (/ 5 2))))))) (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 (/ 5 2)) (or (= (/ 5 2) 1.0) (and (>= (/ 5 2) 2) (tptp.pow2 (* (/ 1 2) (/ 5 2)))))))) :rule resolution :premises (t80 t81))
% 0.20/0.54 (step t83 (cl (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 (/ 5 2)) (or (= (/ 5 2) 1.0) (and (>= (/ 5 2) 2) (tptp.pow2 (* (/ 1 2) (/ 5 2)))))))) :rule contraction :premises (t82))
% 0.20/0.54 (step t84 (cl (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 (/ 5 2)) (tptp.pow2 (/ 5 4))))) :rule resolution :premises (t64 t77 t83))
% 0.20/0.54 (step t85 (cl (not (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X))))))) (= (tptp.pow2 (/ 5 2)) (tptp.pow2 (/ 5 4)))) :rule implies :premises (t84))
% 0.20/0.54 (step t86 (cl (= (tptp.pow2 (/ 5 2)) (tptp.pow2 (/ 5 4)))) :rule resolution :premises (t85 t61))
% 0.20/0.54 (step t87 (cl (tptp.pow2 (/ 5 4))) :rule resolution :premises (t27 t63 t86))
% 0.20/0.54 (step t88 (cl) :rule resolution :premises (t25 t87 t61))
% 0.20/0.54
% 0.20/0.54 % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.8XeJH3845u/cvc5---1.0.5_29066.smt2
% 0.20/0.54 % cvc5---1.0.5 exiting
% 0.20/0.54 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------