TSTP Solution File: ARI621_2 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ARI621_2 : TPTP v8.2.0. Released v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n026.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 16:34:17 EDT 2024
% Result : Theorem 0.18s 0.51s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : ARI621_2 : TPTP v8.2.0. Released v5.1.0.
% 0.09/0.12 % Command : do_cvc5 %s %d
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon May 27 05:13:09 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.18/0.46 %----Proving TF0_ARI
% 0.18/0.51 --- Run --finite-model-find --decision=internal at 15...
% 0.18/0.51 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15...
% 0.18/0.51 % SZS status Theorem for /export/starexec/sandbox2/tmp/tmp.gnOUDY82hh/cvc5---1.0.5_8926.smt2
% 0.18/0.51 % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.gnOUDY82hh/cvc5---1.0.5_8926.smt2
% 0.18/0.51 (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 12.0)))))
% 0.18/0.51 (assume a1 true)
% 0.18/0.51 (step t1 (cl (not (= (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 (/ 3 2)) (or (= (/ 3 2) 1.0) (and (>= (/ 3 2) 2) (tptp.pow2 (* (/ 1 2) (/ 3 2))))))) (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (not (tptp.pow2 (/ 3 2)))))) (not (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 (/ 3 2)) (or (= (/ 3 2) 1.0) (and (>= (/ 3 2) 2) (tptp.pow2 (* (/ 1 2) (/ 3 2)))))))) (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (not (tptp.pow2 (/ 3 2))))) :rule equiv_pos2)
% 0.18/0.51 (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)
% 0.18/0.51 (step t3 (cl (= (tptp.pow2 (/ 3 2)) (tptp.pow2 (/ 3 2)))) :rule refl)
% 0.18/0.51 (step t4 (cl (= (= (/ 3 2) 1.0) false)) :rule all_simplify)
% 0.18/0.51 (step t5 (cl (= (>= (/ 3 2) 2) false)) :rule all_simplify)
% 0.18/0.51 (step t6 (cl (= (* (/ 1 2) (/ 3 2)) (/ 3 4))) :rule all_simplify)
% 0.18/0.51 (step t7 (cl (= (tptp.pow2 (* (/ 1 2) (/ 3 2))) (tptp.pow2 (/ 3 4)))) :rule cong :premises (t6))
% 0.18/0.51 (step t8 (cl (= (and (>= (/ 3 2) 2) (tptp.pow2 (* (/ 1 2) (/ 3 2)))) (and false (tptp.pow2 (/ 3 4))))) :rule cong :premises (t5 t7))
% 0.18/0.51 (step t9 (cl (= (and false (tptp.pow2 (/ 3 4))) false)) :rule all_simplify)
% 0.18/0.51 (step t10 (cl (= (and (>= (/ 3 2) 2) (tptp.pow2 (* (/ 1 2) (/ 3 2)))) false)) :rule trans :premises (t8 t9))
% 0.18/0.51 (step t11 (cl (= (or (= (/ 3 2) 1.0) (and (>= (/ 3 2) 2) (tptp.pow2 (* (/ 1 2) (/ 3 2))))) (or false false))) :rule cong :premises (t4 t10))
% 0.18/0.51 (step t12 (cl (= (or false false) false)) :rule all_simplify)
% 0.18/0.51 (step t13 (cl (= (or (= (/ 3 2) 1.0) (and (>= (/ 3 2) 2) (tptp.pow2 (* (/ 1 2) (/ 3 2))))) false)) :rule trans :premises (t11 t12))
% 0.18/0.51 (step t14 (cl (= (= (tptp.pow2 (/ 3 2)) (or (= (/ 3 2) 1.0) (and (>= (/ 3 2) 2) (tptp.pow2 (* (/ 1 2) (/ 3 2)))))) (= (tptp.pow2 (/ 3 2)) false))) :rule cong :premises (t3 t13))
% 0.18/0.51 (step t15 (cl (= (= (tptp.pow2 (/ 3 2)) false) (not (tptp.pow2 (/ 3 2))))) :rule all_simplify)
% 0.18/0.51 (step t16 (cl (= (= (tptp.pow2 (/ 3 2)) (or (= (/ 3 2) 1.0) (and (>= (/ 3 2) 2) (tptp.pow2 (* (/ 1 2) (/ 3 2)))))) (not (tptp.pow2 (/ 3 2))))) :rule trans :premises (t14 t15))
% 0.18/0.51 (step t17 (cl (= (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 (/ 3 2)) (or (= (/ 3 2) 1.0) (and (>= (/ 3 2) 2) (tptp.pow2 (* (/ 1 2) (/ 3 2))))))) (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (not (tptp.pow2 (/ 3 2)))))) :rule cong :premises (t2 t16))
% 0.18/0.51 (step t18 (cl (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 (/ 3 2)) (or (= (/ 3 2) 1.0) (and (>= (/ 3 2) 2) (tptp.pow2 (* (/ 1 2) (/ 3 2))))))) (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X))))))) :rule implies_neg1)
% 0.18/0.51 (anchor :step t19)
% 0.18/0.51 (assume t19.a0 (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))))
% 0.18/0.51 (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 (/ 3 2)) (or (= (/ 3 2) 1.0) (and (>= (/ 3 2) 2) (tptp.pow2 (* (/ 1 2) (/ 3 2)))))))) :rule forall_inst :args ((:= X (/ 3 2))))
% 0.18/0.51 (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 (/ 3 2)) (or (= (/ 3 2) 1.0) (and (>= (/ 3 2) 2) (tptp.pow2 (* (/ 1 2) (/ 3 2))))))) :rule or :premises (t19.t1))
% 0.18/0.51 (step t19.t3 (cl (= (tptp.pow2 (/ 3 2)) (or (= (/ 3 2) 1.0) (and (>= (/ 3 2) 2) (tptp.pow2 (* (/ 1 2) (/ 3 2))))))) :rule resolution :premises (t19.t2 t19.a0))
% 0.18/0.51 (step t19 (cl (not (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X))))))) (= (tptp.pow2 (/ 3 2)) (or (= (/ 3 2) 1.0) (and (>= (/ 3 2) 2) (tptp.pow2 (* (/ 1 2) (/ 3 2))))))) :rule subproof :discharge (t19.a0))
% 0.18/0.51 (step t20 (cl (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 (/ 3 2)) (or (= (/ 3 2) 1.0) (and (>= (/ 3 2) 2) (tptp.pow2 (* (/ 1 2) (/ 3 2))))))) (= (tptp.pow2 (/ 3 2)) (or (= (/ 3 2) 1.0) (and (>= (/ 3 2) 2) (tptp.pow2 (* (/ 1 2) (/ 3 2))))))) :rule resolution :premises (t18 t19))
% 0.18/0.51 (step t21 (cl (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 (/ 3 2)) (or (= (/ 3 2) 1.0) (and (>= (/ 3 2) 2) (tptp.pow2 (* (/ 1 2) (/ 3 2))))))) (not (= (tptp.pow2 (/ 3 2)) (or (= (/ 3 2) 1.0) (and (>= (/ 3 2) 2) (tptp.pow2 (* (/ 1 2) (/ 3 2)))))))) :rule implies_neg2)
% 0.18/0.51 (step t22 (cl (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 (/ 3 2)) (or (= (/ 3 2) 1.0) (and (>= (/ 3 2) 2) (tptp.pow2 (* (/ 1 2) (/ 3 2))))))) (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 (/ 3 2)) (or (= (/ 3 2) 1.0) (and (>= (/ 3 2) 2) (tptp.pow2 (* (/ 1 2) (/ 3 2)))))))) :rule resolution :premises (t20 t21))
% 0.18/0.51 (step t23 (cl (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 (/ 3 2)) (or (= (/ 3 2) 1.0) (and (>= (/ 3 2) 2) (tptp.pow2 (* (/ 1 2) (/ 3 2)))))))) :rule contraction :premises (t22))
% 0.18/0.51 (step t24 (cl (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (not (tptp.pow2 (/ 3 2))))) :rule resolution :premises (t1 t17 t23))
% 0.18/0.51 (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 (/ 3 2)))) :rule implies :premises (t24))
% 0.18/0.51 (step t26 (cl (not (= (tptp.pow2 3.0) (tptp.pow2 (/ 3 2)))) (not (tptp.pow2 3.0)) (tptp.pow2 (/ 3 2))) :rule equiv_pos2)
% 0.18/0.51 (step t27 (cl (not (tptp.pow2 3.0)) (tptp.pow2 (/ 3 2)) (not (= (tptp.pow2 3.0) (tptp.pow2 (/ 3 2))))) :rule reordering :premises (t26))
% 0.18/0.51 (step t28 (cl (not (= (tptp.pow2 6.0) (tptp.pow2 3.0))) (not (tptp.pow2 6.0)) (tptp.pow2 3.0)) :rule equiv_pos2)
% 0.18/0.51 (step t29 (cl (not (tptp.pow2 6.0)) (tptp.pow2 3.0) (not (= (tptp.pow2 6.0) (tptp.pow2 3.0)))) :rule reordering :premises (t28))
% 0.18/0.51 (step t30 (cl (not (= (tptp.pow2 12.0) (tptp.pow2 6.0))) (not (tptp.pow2 12.0)) (tptp.pow2 6.0)) :rule equiv_pos2)
% 0.18/0.51 (step t31 (cl (not (tptp.pow2 12.0)) (tptp.pow2 6.0) (not (= (tptp.pow2 12.0) (tptp.pow2 6.0)))) :rule reordering :premises (t30))
% 0.18/0.51 (step t32 (cl (not (not (not (tptp.pow2 12.0)))) (tptp.pow2 12.0)) :rule not_not)
% 0.18/0.51 (step t33 (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 12.0)))) (not (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (not (tptp.pow2 12.0)))))) (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 12.0))))) (not (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (not (tptp.pow2 12.0))))) :rule equiv_pos2)
% 0.18/0.51 (anchor :step t34 :args ((X Real) (:= X X)))
% 0.18/0.51 (step t34.t1 (cl (= X X)) :rule refl)
% 0.18/0.51 (step t34.t2 (cl (= (tptp.pow2 X) (tptp.pow2 X))) :rule refl)
% 0.18/0.51 (step t34.t3 (cl (= (= X 1.0) (= X 1.0))) :rule refl)
% 0.18/0.51 (step t34.t4 (cl (= (<= 2.0 X) (>= X 2))) :rule all_simplify)
% 0.18/0.51 (anchor :step t34.t5 :args ((Y Real) (:= Y Y)))
% 0.18/0.51 (step t34.t5.t1 (cl (= Y Y)) :rule refl)
% 0.18/0.51 (step t34.t5.t2 (cl (= (* 2.0 Y) (* 2 Y))) :rule all_simplify)
% 0.18/0.51 (step t34.t5.t3 (cl (= X X)) :rule refl)
% 0.18/0.51 (step t34.t5.t4 (cl (= (= (* 2.0 Y) X) (= (* 2 Y) X))) :rule cong :premises (t34.t5.t2 t34.t5.t3))
% 0.18/0.51 (step t34.t5.t5 (cl (= (= (* 2 Y) X) (= X (* 2 Y)))) :rule all_simplify)
% 0.18/0.51 (step t34.t5.t6 (cl (= (= (* 2.0 Y) X) (= X (* 2 Y)))) :rule trans :premises (t34.t5.t4 t34.t5.t5))
% 0.18/0.51 (step t34.t5.t7 (cl (= (tptp.pow2 Y) (tptp.pow2 Y))) :rule refl)
% 0.18/0.51 (step t34.t5.t8 (cl (= (and (= (* 2.0 Y) X) (tptp.pow2 Y)) (and (= X (* 2 Y)) (tptp.pow2 Y)))) :rule cong :premises (t34.t5.t6 t34.t5.t7))
% 0.18/0.51 (step t34.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)
% 0.18/0.51 (step t34.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)
% 0.18/0.51 (step t34.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)
% 0.18/0.51 (step t34.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)
% 0.18/0.51 (step t34.t9 (cl (= X X)) :rule refl)
% 0.18/0.51 (step t34.t10 (cl (= 2 2)) :rule refl)
% 0.18/0.51 (step t34.t11 (cl (= (* X (/ 1 2)) (* (/ 1 2) X))) :rule all_simplify)
% 0.18/0.51 (step t34.t12 (cl (= (* 2 (* X (/ 1 2))) (* 2 (* (/ 1 2) X)))) :rule cong :premises (t34.t10 t34.t11))
% 0.18/0.51 (step t34.t13 (cl (= (* 2 (* (/ 1 2) X)) X)) :rule all_simplify)
% 0.18/0.51 (step t34.t14 (cl (= (* 2 (* X (/ 1 2))) X)) :rule trans :premises (t34.t12 t34.t13))
% 0.18/0.51 (step t34.t15 (cl (= (= X (* 2 (* X (/ 1 2)))) (= X X))) :rule cong :premises (t34.t9 t34.t14))
% 0.18/0.51 (step t34.t16 (cl (= (= X X) true)) :rule all_simplify)
% 0.18/0.51 (step t34.t17 (cl (= (= X (* 2 (* X (/ 1 2)))) true)) :rule trans :premises (t34.t15 t34.t16))
% 0.18/0.51 (step t34.t18 (cl (= (not (= X (* 2 (* X (/ 1 2))))) (not true))) :rule cong :premises (t34.t17))
% 0.18/0.51 (step t34.t19 (cl (= (not true) false)) :rule all_simplify)
% 0.18/0.51 (step t34.t20 (cl (= (not (= X (* 2 (* X (/ 1 2))))) false)) :rule trans :premises (t34.t18 t34.t19))
% 0.18/0.51 (step t34.t21 (cl (= (tptp.pow2 (* X (/ 1 2))) (tptp.pow2 (* (/ 1 2) X)))) :rule cong :premises (t34.t11))
% 0.18/0.51 (step t34.t22 (cl (= (not (tptp.pow2 (* X (/ 1 2)))) (not (tptp.pow2 (* (/ 1 2) X))))) :rule cong :premises (t34.t21))
% 0.18/0.51 (step t34.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 (t34.t20 t34.t22))
% 0.18/0.51 (step t34.t24 (cl (= (or false (not (tptp.pow2 (* (/ 1 2) X)))) (not (tptp.pow2 (* (/ 1 2) X))))) :rule all_simplify)
% 0.18/0.51 (step t34.t25 (cl (= (or (not (= X (* 2 (* X (/ 1 2))))) (not (tptp.pow2 (* X (/ 1 2))))) (not (tptp.pow2 (* (/ 1 2) X))))) :rule trans :premises (t34.t23 t34.t24))
% 0.18/0.51 (step t34.t26 (cl (= (forall ((Y Real)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y)))) (not (tptp.pow2 (* (/ 1 2) X))))) :rule trans :premises (t34.t8 t34.t25))
% 0.18/0.51 (step t34.t27 (cl (= (forall ((Y Real)) (not (and (= X (* 2 Y)) (tptp.pow2 Y)))) (not (tptp.pow2 (* (/ 1 2) X))))) :rule trans :premises (t34.t7 t34.t26))
% 0.18/0.51 (step t34.t28 (cl (= (not (forall ((Y Real)) (not (and (= X (* 2 Y)) (tptp.pow2 Y))))) (not (not (tptp.pow2 (* (/ 1 2) X)))))) :rule cong :premises (t34.t27))
% 0.18/0.51 (step t34.t29 (cl (= (not (not (tptp.pow2 (* (/ 1 2) X)))) (tptp.pow2 (* (/ 1 2) X)))) :rule all_simplify)
% 0.18/0.51 (step t34.t30 (cl (= (not (forall ((Y Real)) (not (and (= X (* 2 Y)) (tptp.pow2 Y))))) (tptp.pow2 (* (/ 1 2) X)))) :rule trans :premises (t34.t28 t34.t29))
% 0.18/0.51 (step t34.t31 (cl (= (exists ((Y Real)) (and (= X (* 2 Y)) (tptp.pow2 Y))) (tptp.pow2 (* (/ 1 2) X)))) :rule trans :premises (t34.t6 t34.t30))
% 0.18/0.51 (step t34.t32 (cl (= (exists ((Y Real)) (and (= (* 2.0 Y) X) (tptp.pow2 Y))) (tptp.pow2 (* (/ 1 2) X)))) :rule trans :premises (t34.t5 t34.t31))
% 0.18/0.51 (step t34.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 (t34.t4 t34.t32))
% 0.18/0.51 (step t34.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 (t34.t3 t34.t33))
% 0.18/0.51 (step t34.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 (t34.t2 t34.t34))
% 0.18/0.51 (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))))))) (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))))) :rule bind)
% 0.18/0.51 (step t35 (cl (= (not (tptp.pow2 12.0)) (not (tptp.pow2 12.0)))) :rule refl)
% 0.18/0.51 (step t36 (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 12.0))) (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (not (tptp.pow2 12.0))))) :rule cong :premises (t34 t35))
% 0.18/0.51 (step t37 (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 12.0)))) (not (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (not (tptp.pow2 12.0)))))) :rule cong :premises (t36))
% 0.18/0.51 (step t38 (cl (not (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (not (tptp.pow2 12.0))))) :rule resolution :premises (t33 t37 a0))
% 0.18/0.51 (step t39 (cl (not (not (tptp.pow2 12.0)))) :rule not_implies2 :premises (t38))
% 0.18/0.51 (step t40 (cl (tptp.pow2 12.0)) :rule resolution :premises (t32 t39))
% 0.18/0.51 (step t41 (cl (not (= (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 12.0) (or (= 12.0 1.0) (and (>= 12.0 2) (tptp.pow2 (* (/ 1 2) 12.0)))))) (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 12.0) (tptp.pow2 6.0))))) (not (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 12.0) (or (= 12.0 1.0) (and (>= 12.0 2) (tptp.pow2 (* (/ 1 2) 12.0))))))) (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 12.0) (tptp.pow2 6.0)))) :rule equiv_pos2)
% 0.18/0.51 (step t42 (cl (= (tptp.pow2 12.0) (tptp.pow2 12.0))) :rule refl)
% 0.18/0.51 (step t43 (cl (= (= 12.0 1.0) false)) :rule all_simplify)
% 0.18/0.51 (step t44 (cl (= (>= 12.0 2) true)) :rule all_simplify)
% 0.18/0.51 (step t45 (cl (= (* (/ 1 2) 12.0) 6.0)) :rule all_simplify)
% 0.18/0.51 (step t46 (cl (= (tptp.pow2 (* (/ 1 2) 12.0)) (tptp.pow2 6.0))) :rule cong :premises (t45))
% 0.18/0.51 (step t47 (cl (= (and (>= 12.0 2) (tptp.pow2 (* (/ 1 2) 12.0))) (and true (tptp.pow2 6.0)))) :rule cong :premises (t44 t46))
% 0.18/0.51 (step t48 (cl (= (and true (tptp.pow2 6.0)) (tptp.pow2 6.0))) :rule all_simplify)
% 0.18/0.51 (step t49 (cl (= (and (>= 12.0 2) (tptp.pow2 (* (/ 1 2) 12.0))) (tptp.pow2 6.0))) :rule trans :premises (t47 t48))
% 0.18/0.51 (step t50 (cl (= (or (= 12.0 1.0) (and (>= 12.0 2) (tptp.pow2 (* (/ 1 2) 12.0)))) (or false (tptp.pow2 6.0)))) :rule cong :premises (t43 t49))
% 0.18/0.51 (step t51 (cl (= (or false (tptp.pow2 6.0)) (tptp.pow2 6.0))) :rule all_simplify)
% 0.18/0.51 (step t52 (cl (= (or (= 12.0 1.0) (and (>= 12.0 2) (tptp.pow2 (* (/ 1 2) 12.0)))) (tptp.pow2 6.0))) :rule trans :premises (t50 t51))
% 0.18/0.51 (step t53 (cl (= (= (tptp.pow2 12.0) (or (= 12.0 1.0) (and (>= 12.0 2) (tptp.pow2 (* (/ 1 2) 12.0))))) (= (tptp.pow2 12.0) (tptp.pow2 6.0)))) :rule cong :premises (t42 t52))
% 0.18/0.51 (step t54 (cl (= (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 12.0) (or (= 12.0 1.0) (and (>= 12.0 2) (tptp.pow2 (* (/ 1 2) 12.0)))))) (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 12.0) (tptp.pow2 6.0))))) :rule cong :premises (t2 t53))
% 0.18/0.51 (step t55 (cl (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 12.0) (or (= 12.0 1.0) (and (>= 12.0 2) (tptp.pow2 (* (/ 1 2) 12.0)))))) (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X))))))) :rule implies_neg1)
% 0.18/0.51 (anchor :step t56)
% 0.18/0.51 (assume t56.a0 (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))))
% 0.18/0.51 (step t56.t1 (cl (or (not (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X))))))) (= (tptp.pow2 12.0) (or (= 12.0 1.0) (and (>= 12.0 2) (tptp.pow2 (* (/ 1 2) 12.0))))))) :rule forall_inst :args ((:= X 12.0)))
% 0.18/0.51 (step t56.t2 (cl (not (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X))))))) (= (tptp.pow2 12.0) (or (= 12.0 1.0) (and (>= 12.0 2) (tptp.pow2 (* (/ 1 2) 12.0)))))) :rule or :premises (t56.t1))
% 0.18/0.51 (step t56.t3 (cl (= (tptp.pow2 12.0) (or (= 12.0 1.0) (and (>= 12.0 2) (tptp.pow2 (* (/ 1 2) 12.0)))))) :rule resolution :premises (t56.t2 t56.a0))
% 0.18/0.51 (step t56 (cl (not (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X))))))) (= (tptp.pow2 12.0) (or (= 12.0 1.0) (and (>= 12.0 2) (tptp.pow2 (* (/ 1 2) 12.0)))))) :rule subproof :discharge (t56.a0))
% 0.18/0.51 (step t57 (cl (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 12.0) (or (= 12.0 1.0) (and (>= 12.0 2) (tptp.pow2 (* (/ 1 2) 12.0)))))) (= (tptp.pow2 12.0) (or (= 12.0 1.0) (and (>= 12.0 2) (tptp.pow2 (* (/ 1 2) 12.0)))))) :rule resolution :premises (t55 t56))
% 0.18/0.51 (step t58 (cl (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 12.0) (or (= 12.0 1.0) (and (>= 12.0 2) (tptp.pow2 (* (/ 1 2) 12.0)))))) (not (= (tptp.pow2 12.0) (or (= 12.0 1.0) (and (>= 12.0 2) (tptp.pow2 (* (/ 1 2) 12.0))))))) :rule implies_neg2)
% 0.18/0.51 (step t59 (cl (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 12.0) (or (= 12.0 1.0) (and (>= 12.0 2) (tptp.pow2 (* (/ 1 2) 12.0)))))) (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 12.0) (or (= 12.0 1.0) (and (>= 12.0 2) (tptp.pow2 (* (/ 1 2) 12.0))))))) :rule resolution :premises (t57 t58))
% 0.18/0.51 (step t60 (cl (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 12.0) (or (= 12.0 1.0) (and (>= 12.0 2) (tptp.pow2 (* (/ 1 2) 12.0))))))) :rule contraction :premises (t59))
% 0.18/0.51 (step t61 (cl (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 12.0) (tptp.pow2 6.0)))) :rule resolution :premises (t41 t54 t60))
% 0.18/0.51 (step t62 (cl (not (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X))))))) (= (tptp.pow2 12.0) (tptp.pow2 6.0))) :rule implies :premises (t61))
% 0.18/0.51 (step t63 (cl (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X))))))) :rule not_implies1 :premises (t38))
% 0.18/0.51 (step t64 (cl (= (tptp.pow2 12.0) (tptp.pow2 6.0))) :rule resolution :premises (t62 t63))
% 0.18/0.51 (step t65 (cl (tptp.pow2 6.0)) :rule resolution :premises (t31 t40 t64))
% 0.18/0.51 (step t66 (cl (not (= (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 6.0) (or (= 6.0 1.0) (and (>= 6.0 2) (tptp.pow2 (* (/ 1 2) 6.0)))))) (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 6.0) (tptp.pow2 3.0))))) (not (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 6.0) (or (= 6.0 1.0) (and (>= 6.0 2) (tptp.pow2 (* (/ 1 2) 6.0))))))) (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 6.0) (tptp.pow2 3.0)))) :rule equiv_pos2)
% 0.18/0.51 (step t67 (cl (= (tptp.pow2 6.0) (tptp.pow2 6.0))) :rule refl)
% 0.18/0.51 (step t68 (cl (= (= 6.0 1.0) false)) :rule all_simplify)
% 0.18/0.51 (step t69 (cl (= (>= 6.0 2) true)) :rule all_simplify)
% 0.18/0.51 (step t70 (cl (= (* (/ 1 2) 6.0) 3.0)) :rule all_simplify)
% 0.18/0.51 (step t71 (cl (= (tptp.pow2 (* (/ 1 2) 6.0)) (tptp.pow2 3.0))) :rule cong :premises (t70))
% 0.18/0.51 (step t72 (cl (= (and (>= 6.0 2) (tptp.pow2 (* (/ 1 2) 6.0))) (and true (tptp.pow2 3.0)))) :rule cong :premises (t69 t71))
% 0.18/0.51 (step t73 (cl (= (and true (tptp.pow2 3.0)) (tptp.pow2 3.0))) :rule all_simplify)
% 0.18/0.51 (step t74 (cl (= (and (>= 6.0 2) (tptp.pow2 (* (/ 1 2) 6.0))) (tptp.pow2 3.0))) :rule trans :premises (t72 t73))
% 0.18/0.51 (step t75 (cl (= (or (= 6.0 1.0) (and (>= 6.0 2) (tptp.pow2 (* (/ 1 2) 6.0)))) (or false (tptp.pow2 3.0)))) :rule cong :premises (t68 t74))
% 0.18/0.51 (step t76 (cl (= (or false (tptp.pow2 3.0)) (tptp.pow2 3.0))) :rule all_simplify)
% 0.18/0.51 (step t77 (cl (= (or (= 6.0 1.0) (and (>= 6.0 2) (tptp.pow2 (* (/ 1 2) 6.0)))) (tptp.pow2 3.0))) :rule trans :premises (t75 t76))
% 0.18/0.51 (step t78 (cl (= (= (tptp.pow2 6.0) (or (= 6.0 1.0) (and (>= 6.0 2) (tptp.pow2 (* (/ 1 2) 6.0))))) (= (tptp.pow2 6.0) (tptp.pow2 3.0)))) :rule cong :premises (t67 t77))
% 0.18/0.51 (step t79 (cl (= (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 6.0) (or (= 6.0 1.0) (and (>= 6.0 2) (tptp.pow2 (* (/ 1 2) 6.0)))))) (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 6.0) (tptp.pow2 3.0))))) :rule cong :premises (t2 t78))
% 0.18/0.51 (step t80 (cl (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 6.0) (or (= 6.0 1.0) (and (>= 6.0 2) (tptp.pow2 (* (/ 1 2) 6.0)))))) (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X))))))) :rule implies_neg1)
% 0.18/0.51 (anchor :step t81)
% 0.18/0.51 (assume t81.a0 (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))))
% 0.18/0.51 (step t81.t1 (cl (or (not (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X))))))) (= (tptp.pow2 6.0) (or (= 6.0 1.0) (and (>= 6.0 2) (tptp.pow2 (* (/ 1 2) 6.0))))))) :rule forall_inst :args ((:= X 6.0)))
% 0.18/0.51 (step t81.t2 (cl (not (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X))))))) (= (tptp.pow2 6.0) (or (= 6.0 1.0) (and (>= 6.0 2) (tptp.pow2 (* (/ 1 2) 6.0)))))) :rule or :premises (t81.t1))
% 0.18/0.51 (step t81.t3 (cl (= (tptp.pow2 6.0) (or (= 6.0 1.0) (and (>= 6.0 2) (tptp.pow2 (* (/ 1 2) 6.0)))))) :rule resolution :premises (t81.t2 t81.a0))
% 0.18/0.51 (step t81 (cl (not (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X))))))) (= (tptp.pow2 6.0) (or (= 6.0 1.0) (and (>= 6.0 2) (tptp.pow2 (* (/ 1 2) 6.0)))))) :rule subproof :discharge (t81.a0))
% 0.18/0.51 (step t82 (cl (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 6.0) (or (= 6.0 1.0) (and (>= 6.0 2) (tptp.pow2 (* (/ 1 2) 6.0)))))) (= (tptp.pow2 6.0) (or (= 6.0 1.0) (and (>= 6.0 2) (tptp.pow2 (* (/ 1 2) 6.0)))))) :rule resolution :premises (t80 t81))
% 0.18/0.51 (step t83 (cl (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 6.0) (or (= 6.0 1.0) (and (>= 6.0 2) (tptp.pow2 (* (/ 1 2) 6.0)))))) (not (= (tptp.pow2 6.0) (or (= 6.0 1.0) (and (>= 6.0 2) (tptp.pow2 (* (/ 1 2) 6.0))))))) :rule implies_neg2)
% 0.18/0.51 (step t84 (cl (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 6.0) (or (= 6.0 1.0) (and (>= 6.0 2) (tptp.pow2 (* (/ 1 2) 6.0)))))) (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 6.0) (or (= 6.0 1.0) (and (>= 6.0 2) (tptp.pow2 (* (/ 1 2) 6.0))))))) :rule resolution :premises (t82 t83))
% 0.18/0.51 (step t85 (cl (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 6.0) (or (= 6.0 1.0) (and (>= 6.0 2) (tptp.pow2 (* (/ 1 2) 6.0))))))) :rule contraction :premises (t84))
% 0.18/0.51 (step t86 (cl (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 6.0) (tptp.pow2 3.0)))) :rule resolution :premises (t66 t79 t85))
% 0.18/0.51 (step t87 (cl (not (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X))))))) (= (tptp.pow2 6.0) (tptp.pow2 3.0))) :rule implies :premises (t86))
% 0.18/0.51 (step t88 (cl (= (tptp.pow2 6.0) (tptp.pow2 3.0))) :rule resolution :premises (t87 t63))
% 0.18/0.51 (step t89 (cl (tptp.pow2 3.0)) :rule resolution :premises (t29 t65 t88))
% 0.18/0.51 (step t90 (cl (not (= (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 3.0) (or (= 3.0 1.0) (and (>= 3.0 2) (tptp.pow2 (* (/ 1 2) 3.0)))))) (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 3.0) (tptp.pow2 (/ 3 2)))))) (not (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 3.0) (or (= 3.0 1.0) (and (>= 3.0 2) (tptp.pow2 (* (/ 1 2) 3.0))))))) (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 3.0) (tptp.pow2 (/ 3 2))))) :rule equiv_pos2)
% 0.18/0.51 (step t91 (cl (= (tptp.pow2 3.0) (tptp.pow2 3.0))) :rule refl)
% 0.18/0.51 (step t92 (cl (= (= 3.0 1.0) false)) :rule all_simplify)
% 0.18/0.51 (step t93 (cl (= (>= 3.0 2) true)) :rule all_simplify)
% 0.18/0.51 (step t94 (cl (= (* (/ 1 2) 3.0) (/ 3 2))) :rule all_simplify)
% 0.18/0.51 (step t95 (cl (= (tptp.pow2 (* (/ 1 2) 3.0)) (tptp.pow2 (/ 3 2)))) :rule cong :premises (t94))
% 0.18/0.51 (step t96 (cl (= (and (>= 3.0 2) (tptp.pow2 (* (/ 1 2) 3.0))) (and true (tptp.pow2 (/ 3 2))))) :rule cong :premises (t93 t95))
% 0.18/0.51 (step t97 (cl (= (and true (tptp.pow2 (/ 3 2))) (tptp.pow2 (/ 3 2)))) :rule all_simplify)
% 0.18/0.51 (step t98 (cl (= (and (>= 3.0 2) (tptp.pow2 (* (/ 1 2) 3.0))) (tptp.pow2 (/ 3 2)))) :rule trans :premises (t96 t97))
% 0.18/0.51 (step t99 (cl (= (or (= 3.0 1.0) (and (>= 3.0 2) (tptp.pow2 (* (/ 1 2) 3.0)))) (or false (tptp.pow2 (/ 3 2))))) :rule cong :premises (t92 t98))
% 0.18/0.51 (step t100 (cl (= (or false (tptp.pow2 (/ 3 2))) (tptp.pow2 (/ 3 2)))) :rule all_simplify)
% 0.18/0.51 (step t101 (cl (= (or (= 3.0 1.0) (and (>= 3.0 2) (tptp.pow2 (* (/ 1 2) 3.0)))) (tptp.pow2 (/ 3 2)))) :rule trans :premises (t99 t100))
% 0.18/0.51 (step t102 (cl (= (= (tptp.pow2 3.0) (or (= 3.0 1.0) (and (>= 3.0 2) (tptp.pow2 (* (/ 1 2) 3.0))))) (= (tptp.pow2 3.0) (tptp.pow2 (/ 3 2))))) :rule cong :premises (t91 t101))
% 0.18/0.51 (step t103 (cl (= (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 3.0) (or (= 3.0 1.0) (and (>= 3.0 2) (tptp.pow2 (* (/ 1 2) 3.0)))))) (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 3.0) (tptp.pow2 (/ 3 2)))))) :rule cong :premises (t2 t102))
% 0.18/0.51 (step t104 (cl (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 3.0) (or (= 3.0 1.0) (and (>= 3.0 2) (tptp.pow2 (* (/ 1 2) 3.0)))))) (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X))))))) :rule implies_neg1)
% 0.18/0.51 (anchor :step t105)
% 0.18/0.51 (assume t105.a0 (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))))
% 0.18/0.51 (step t105.t1 (cl (or (not (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X))))))) (= (tptp.pow2 3.0) (or (= 3.0 1.0) (and (>= 3.0 2) (tptp.pow2 (* (/ 1 2) 3.0))))))) :rule forall_inst :args ((:= X 3.0)))
% 0.18/0.51 (step t105.t2 (cl (not (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X))))))) (= (tptp.pow2 3.0) (or (= 3.0 1.0) (and (>= 3.0 2) (tptp.pow2 (* (/ 1 2) 3.0)))))) :rule or :premises (t105.t1))
% 0.18/0.51 (step t105.t3 (cl (= (tptp.pow2 3.0) (or (= 3.0 1.0) (and (>= 3.0 2) (tptp.pow2 (* (/ 1 2) 3.0)))))) :rule resolution :premises (t105.t2 t105.a0))
% 0.18/0.51 (step t105 (cl (not (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X))))))) (= (tptp.pow2 3.0) (or (= 3.0 1.0) (and (>= 3.0 2) (tptp.pow2 (* (/ 1 2) 3.0)))))) :rule subproof :discharge (t105.a0))
% 0.18/0.51 (step t106 (cl (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 3.0) (or (= 3.0 1.0) (and (>= 3.0 2) (tptp.pow2 (* (/ 1 2) 3.0)))))) (= (tptp.pow2 3.0) (or (= 3.0 1.0) (and (>= 3.0 2) (tptp.pow2 (* (/ 1 2) 3.0)))))) :rule resolution :premises (t104 t105))
% 0.18/0.51 (step t107 (cl (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 3.0) (or (= 3.0 1.0) (and (>= 3.0 2) (tptp.pow2 (* (/ 1 2) 3.0)))))) (not (= (tptp.pow2 3.0) (or (= 3.0 1.0) (and (>= 3.0 2) (tptp.pow2 (* (/ 1 2) 3.0))))))) :rule implies_neg2)
% 0.18/0.51 (step t108 (cl (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 3.0) (or (= 3.0 1.0) (and (>= 3.0 2) (tptp.pow2 (* (/ 1 2) 3.0)))))) (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 3.0) (or (= 3.0 1.0) (and (>= 3.0 2) (tptp.pow2 (* (/ 1 2) 3.0))))))) :rule resolution :premises (t106 t107))
% 0.18/0.51 (step t109 (cl (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 3.0) (or (= 3.0 1.0) (and (>= 3.0 2) (tptp.pow2 (* (/ 1 2) 3.0))))))) :rule contraction :premises (t108))
% 0.18/0.51 (step t110 (cl (=> (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X)))))) (= (tptp.pow2 3.0) (tptp.pow2 (/ 3 2))))) :rule resolution :premises (t90 t103 t109))
% 0.18/0.51 (step t111 (cl (not (forall ((X Real)) (= (tptp.pow2 X) (or (= X 1.0) (and (>= X 2) (tptp.pow2 (* (/ 1 2) X))))))) (= (tptp.pow2 3.0) (tptp.pow2 (/ 3 2)))) :rule implies :premises (t110))
% 0.18/0.51 (step t112 (cl (= (tptp.pow2 3.0) (tptp.pow2 (/ 3 2)))) :rule resolution :premises (t111 t63))
% 0.18/0.51 (step t113 (cl (tptp.pow2 (/ 3 2))) :rule resolution :premises (t27 t89 t112))
% 0.18/0.51 (step t114 (cl) :rule resolution :premises (t25 t113 t63))
% 0.18/0.51
% 0.18/0.51 % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.gnOUDY82hh/cvc5---1.0.5_8926.smt2
% 0.18/0.51 % cvc5---1.0.5 exiting
% 0.18/0.51 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------