TSTP Solution File: ARI621_1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ARI621_1 : 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 0.21s 0.56s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : ARI621_1 : TPTP v8.2.0. Released v5.1.0.
% 0.08/0.14 % Command : do_cvc5 %s %d
% 0.14/0.36 % Computer : n025.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon May 27 05:42:09 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.21/0.51 %----Proving TF0_ARI
% 0.21/0.56 --- Run --finite-model-find --decision=internal at 15...
% 0.21/0.56 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15...
% 0.21/0.56 % SZS status Theorem for /export/starexec/sandbox2/tmp/tmp.4R9fOgFHFW/cvc5---1.0.5_16898.smt2
% 0.21/0.56 % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.4R9fOgFHFW/cvc5---1.0.5_16898.smt2
% 0.21/0.56 (assume a0 (not (=> (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (<= 2 X) (exists ((Y Int)) (and (= (* 2 Y) X) (tptp.pow2 Y))))))) (not (tptp.pow2 12)))))
% 0.21/0.56 (assume a1 true)
% 0.21/0.56 (step t1 (cl (not (= (=> (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))))) (= (tptp.pow2 3) (or (= 3 1) (and (>= 3 2) (not (forall ((Y Int)) (or (not (= 3 (* 2 Y))) (not (tptp.pow2 Y))))))))) (=> (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))))) (not (tptp.pow2 3))))) (not (=> (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))))) (= (tptp.pow2 3) (or (= 3 1) (and (>= 3 2) (not (forall ((Y Int)) (or (not (= 3 (* 2 Y))) (not (tptp.pow2 Y)))))))))) (=> (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))))) (not (tptp.pow2 3)))) :rule equiv_pos2)
% 0.21/0.56 (step t2 (cl (= (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))))) (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))))))) :rule refl)
% 0.21/0.56 (step t3 (cl (= (tptp.pow2 3) (tptp.pow2 3))) :rule refl)
% 0.21/0.56 (step t4 (cl (= (= 3 1) false)) :rule all_simplify)
% 0.21/0.56 (step t5 (cl (= (>= 3 2) true)) :rule all_simplify)
% 0.21/0.56 (anchor :step t6 :args ((Y Int) (:= Y Y)))
% 0.21/0.56 (step t6.t1 (cl (= Y Y)) :rule refl)
% 0.21/0.56 (step t6.t2 (cl (= (= 3 (* 2 Y)) false)) :rule all_simplify)
% 0.21/0.56 (step t6.t3 (cl (= (not (= 3 (* 2 Y))) (not false))) :rule cong :premises (t6.t2))
% 0.21/0.56 (step t6.t4 (cl (= (not false) true)) :rule all_simplify)
% 0.21/0.56 (step t6.t5 (cl (= (not (= 3 (* 2 Y))) true)) :rule trans :premises (t6.t3 t6.t4))
% 0.21/0.56 (step t6.t6 (cl (= (not (tptp.pow2 Y)) (not (tptp.pow2 Y)))) :rule refl)
% 0.21/0.56 (step t6.t7 (cl (= (or (not (= 3 (* 2 Y))) (not (tptp.pow2 Y))) (or true (not (tptp.pow2 Y))))) :rule cong :premises (t6.t5 t6.t6))
% 0.21/0.56 (step t6.t8 (cl (= (or true (not (tptp.pow2 Y))) true)) :rule all_simplify)
% 0.21/0.56 (step t6.t9 (cl (= (or (not (= 3 (* 2 Y))) (not (tptp.pow2 Y))) true)) :rule trans :premises (t6.t7 t6.t8))
% 0.21/0.56 (step t6 (cl (= (forall ((Y Int)) (or (not (= 3 (* 2 Y))) (not (tptp.pow2 Y)))) (forall ((Y Int)) true))) :rule bind)
% 0.21/0.56 (step t7 (cl (= (forall ((Y Int)) true) true)) :rule all_simplify)
% 0.21/0.56 (step t8 (cl (= (forall ((Y Int)) (or (not (= 3 (* 2 Y))) (not (tptp.pow2 Y)))) true)) :rule trans :premises (t6 t7))
% 0.21/0.56 (step t9 (cl (= (not (forall ((Y Int)) (or (not (= 3 (* 2 Y))) (not (tptp.pow2 Y))))) (not true))) :rule cong :premises (t8))
% 0.21/0.56 (step t10 (cl (= (not true) false)) :rule all_simplify)
% 0.21/0.56 (step t11 (cl (= (not (forall ((Y Int)) (or (not (= 3 (* 2 Y))) (not (tptp.pow2 Y))))) false)) :rule trans :premises (t9 t10))
% 0.21/0.56 (step t12 (cl (= (and (>= 3 2) (not (forall ((Y Int)) (or (not (= 3 (* 2 Y))) (not (tptp.pow2 Y)))))) (and true false))) :rule cong :premises (t5 t11))
% 0.21/0.56 (step t13 (cl (= (and true false) false)) :rule all_simplify)
% 0.21/0.56 (step t14 (cl (= (and (>= 3 2) (not (forall ((Y Int)) (or (not (= 3 (* 2 Y))) (not (tptp.pow2 Y)))))) false)) :rule trans :premises (t12 t13))
% 0.21/0.56 (step t15 (cl (= (or (= 3 1) (and (>= 3 2) (not (forall ((Y Int)) (or (not (= 3 (* 2 Y))) (not (tptp.pow2 Y))))))) (or false false))) :rule cong :premises (t4 t14))
% 0.21/0.56 (step t16 (cl (= (or false false) false)) :rule all_simplify)
% 0.21/0.56 (step t17 (cl (= (or (= 3 1) (and (>= 3 2) (not (forall ((Y Int)) (or (not (= 3 (* 2 Y))) (not (tptp.pow2 Y))))))) false)) :rule trans :premises (t15 t16))
% 0.21/0.56 (step t18 (cl (= (= (tptp.pow2 3) (or (= 3 1) (and (>= 3 2) (not (forall ((Y Int)) (or (not (= 3 (* 2 Y))) (not (tptp.pow2 Y)))))))) (= (tptp.pow2 3) false))) :rule cong :premises (t3 t17))
% 0.21/0.56 (step t19 (cl (= (= (tptp.pow2 3) false) (not (tptp.pow2 3)))) :rule all_simplify)
% 0.21/0.56 (step t20 (cl (= (= (tptp.pow2 3) (or (= 3 1) (and (>= 3 2) (not (forall ((Y Int)) (or (not (= 3 (* 2 Y))) (not (tptp.pow2 Y)))))))) (not (tptp.pow2 3)))) :rule trans :premises (t18 t19))
% 0.21/0.56 (step t21 (cl (= (=> (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))))) (= (tptp.pow2 3) (or (= 3 1) (and (>= 3 2) (not (forall ((Y Int)) (or (not (= 3 (* 2 Y))) (not (tptp.pow2 Y))))))))) (=> (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))))) (not (tptp.pow2 3))))) :rule cong :premises (t2 t20))
% 0.21/0.56 (step t22 (cl (=> (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))))) (= (tptp.pow2 3) (or (= 3 1) (and (>= 3 2) (not (forall ((Y Int)) (or (not (= 3 (* 2 Y))) (not (tptp.pow2 Y))))))))) (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y)))))))))) :rule implies_neg1)
% 0.21/0.56 (anchor :step t23)
% 0.21/0.56 (assume t23.a0 (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))))))
% 0.21/0.56 (step t23.t1 (cl (or (not (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y)))))))))) (= (tptp.pow2 3) (or (= 3 1) (and (>= 3 2) (not (forall ((Y Int)) (or (not (= 3 (* 2 Y))) (not (tptp.pow2 Y)))))))))) :rule forall_inst :args ((:= X 3)))
% 0.21/0.56 (step t23.t2 (cl (not (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y)))))))))) (= (tptp.pow2 3) (or (= 3 1) (and (>= 3 2) (not (forall ((Y Int)) (or (not (= 3 (* 2 Y))) (not (tptp.pow2 Y))))))))) :rule or :premises (t23.t1))
% 0.21/0.56 (step t23.t3 (cl (= (tptp.pow2 3) (or (= 3 1) (and (>= 3 2) (not (forall ((Y Int)) (or (not (= 3 (* 2 Y))) (not (tptp.pow2 Y))))))))) :rule resolution :premises (t23.t2 t23.a0))
% 0.21/0.56 (step t23 (cl (not (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y)))))))))) (= (tptp.pow2 3) (or (= 3 1) (and (>= 3 2) (not (forall ((Y Int)) (or (not (= 3 (* 2 Y))) (not (tptp.pow2 Y))))))))) :rule subproof :discharge (t23.a0))
% 0.21/0.56 (step t24 (cl (=> (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))))) (= (tptp.pow2 3) (or (= 3 1) (and (>= 3 2) (not (forall ((Y Int)) (or (not (= 3 (* 2 Y))) (not (tptp.pow2 Y))))))))) (= (tptp.pow2 3) (or (= 3 1) (and (>= 3 2) (not (forall ((Y Int)) (or (not (= 3 (* 2 Y))) (not (tptp.pow2 Y))))))))) :rule resolution :premises (t22 t23))
% 0.21/0.56 (step t25 (cl (=> (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))))) (= (tptp.pow2 3) (or (= 3 1) (and (>= 3 2) (not (forall ((Y Int)) (or (not (= 3 (* 2 Y))) (not (tptp.pow2 Y))))))))) (not (= (tptp.pow2 3) (or (= 3 1) (and (>= 3 2) (not (forall ((Y Int)) (or (not (= 3 (* 2 Y))) (not (tptp.pow2 Y)))))))))) :rule implies_neg2)
% 0.21/0.56 (step t26 (cl (=> (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))))) (= (tptp.pow2 3) (or (= 3 1) (and (>= 3 2) (not (forall ((Y Int)) (or (not (= 3 (* 2 Y))) (not (tptp.pow2 Y))))))))) (=> (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))))) (= (tptp.pow2 3) (or (= 3 1) (and (>= 3 2) (not (forall ((Y Int)) (or (not (= 3 (* 2 Y))) (not (tptp.pow2 Y)))))))))) :rule resolution :premises (t24 t25))
% 0.21/0.56 (step t27 (cl (=> (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))))) (= (tptp.pow2 3) (or (= 3 1) (and (>= 3 2) (not (forall ((Y Int)) (or (not (= 3 (* 2 Y))) (not (tptp.pow2 Y)))))))))) :rule contraction :premises (t26))
% 0.21/0.56 (step t28 (cl (=> (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))))) (not (tptp.pow2 3)))) :rule resolution :premises (t1 t21 t27))
% 0.21/0.56 (step t29 (cl (not (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y)))))))))) (not (tptp.pow2 3))) :rule implies :premises (t28))
% 0.21/0.56 (step t30 (cl (not (= (tptp.pow2 6) (tptp.pow2 3))) (not (tptp.pow2 6)) (tptp.pow2 3)) :rule equiv_pos2)
% 0.21/0.56 (step t31 (cl (not (tptp.pow2 6)) (tptp.pow2 3) (not (= (tptp.pow2 6) (tptp.pow2 3)))) :rule reordering :premises (t30))
% 0.21/0.56 (step t32 (cl (not (= (tptp.pow2 12) (tptp.pow2 6))) (not (tptp.pow2 12)) (tptp.pow2 6)) :rule equiv_pos2)
% 0.21/0.56 (step t33 (cl (not (tptp.pow2 12)) (tptp.pow2 6) (not (= (tptp.pow2 12) (tptp.pow2 6)))) :rule reordering :premises (t32))
% 0.21/0.56 (step t34 (cl (not (not (not (tptp.pow2 12)))) (tptp.pow2 12)) :rule not_not)
% 0.21/0.56 (step t35 (cl (not (= (not (=> (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (<= 2 X) (exists ((Y Int)) (and (= (* 2 Y) X) (tptp.pow2 Y))))))) (not (tptp.pow2 12)))) (not (=> (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))))) (not (tptp.pow2 12)))))) (not (not (=> (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (<= 2 X) (exists ((Y Int)) (and (= (* 2 Y) X) (tptp.pow2 Y))))))) (not (tptp.pow2 12))))) (not (=> (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))))) (not (tptp.pow2 12))))) :rule equiv_pos2)
% 0.21/0.56 (anchor :step t36 :args ((X Int) (:= X X)))
% 0.21/0.56 (step t36.t1 (cl (= X X)) :rule refl)
% 0.21/0.56 (step t36.t2 (cl (= (tptp.pow2 X) (tptp.pow2 X))) :rule refl)
% 0.21/0.56 (step t36.t3 (cl (= (= X 1) (= X 1))) :rule refl)
% 0.21/0.56 (step t36.t4 (cl (= (<= 2 X) (>= X 2))) :rule all_simplify)
% 0.21/0.56 (anchor :step t36.t5 :args ((Y Int) (:= Y Y)))
% 0.21/0.56 (step t36.t5.t1 (cl (= Y Y)) :rule refl)
% 0.21/0.56 (step t36.t5.t2 (cl (= (= (* 2 Y) X) (= X (* 2 Y)))) :rule all_simplify)
% 0.21/0.56 (step t36.t5.t3 (cl (= (tptp.pow2 Y) (tptp.pow2 Y))) :rule refl)
% 0.21/0.56 (step t36.t5.t4 (cl (= (and (= (* 2 Y) X) (tptp.pow2 Y)) (and (= X (* 2 Y)) (tptp.pow2 Y)))) :rule cong :premises (t36.t5.t2 t36.t5.t3))
% 0.21/0.56 (step t36.t5 (cl (= (exists ((Y Int)) (and (= (* 2 Y) X) (tptp.pow2 Y))) (exists ((Y Int)) (and (= X (* 2 Y)) (tptp.pow2 Y))))) :rule bind)
% 0.21/0.56 (step t36.t6 (cl (= (exists ((Y Int)) (and (= X (* 2 Y)) (tptp.pow2 Y))) (not (forall ((Y Int)) (not (and (= X (* 2 Y)) (tptp.pow2 Y))))))) :rule all_simplify)
% 0.21/0.56 (step t36.t7 (cl (= (forall ((Y Int)) (not (and (= X (* 2 Y)) (tptp.pow2 Y)))) (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y)))))) :rule all_simplify)
% 0.21/0.56 (step t36.t8 (cl (= (not (forall ((Y Int)) (not (and (= X (* 2 Y)) (tptp.pow2 Y))))) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))) :rule cong :premises (t36.t7))
% 0.21/0.56 (step t36.t9 (cl (= (exists ((Y Int)) (and (= X (* 2 Y)) (tptp.pow2 Y))) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))) :rule trans :premises (t36.t6 t36.t8))
% 0.21/0.56 (step t36.t10 (cl (= (exists ((Y Int)) (and (= (* 2 Y) X) (tptp.pow2 Y))) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))) :rule trans :premises (t36.t5 t36.t9))
% 0.21/0.56 (step t36.t11 (cl (= (and (<= 2 X) (exists ((Y Int)) (and (= (* 2 Y) X) (tptp.pow2 Y)))) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y)))))))) :rule cong :premises (t36.t4 t36.t10))
% 0.21/0.56 (step t36.t12 (cl (= (or (= X 1) (and (<= 2 X) (exists ((Y Int)) (and (= (* 2 Y) X) (tptp.pow2 Y))))) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))))) :rule cong :premises (t36.t3 t36.t11))
% 0.21/0.56 (step t36.t13 (cl (= (= (tptp.pow2 X) (or (= X 1) (and (<= 2 X) (exists ((Y Int)) (and (= (* 2 Y) X) (tptp.pow2 Y)))))) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y)))))))))) :rule cong :premises (t36.t2 t36.t12))
% 0.21/0.56 (step t36 (cl (= (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (<= 2 X) (exists ((Y Int)) (and (= (* 2 Y) X) (tptp.pow2 Y))))))) (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))))))) :rule bind)
% 0.21/0.56 (step t37 (cl (= (not (tptp.pow2 12)) (not (tptp.pow2 12)))) :rule refl)
% 0.21/0.56 (step t38 (cl (= (=> (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (<= 2 X) (exists ((Y Int)) (and (= (* 2 Y) X) (tptp.pow2 Y))))))) (not (tptp.pow2 12))) (=> (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))))) (not (tptp.pow2 12))))) :rule cong :premises (t36 t37))
% 0.21/0.56 (step t39 (cl (= (not (=> (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (<= 2 X) (exists ((Y Int)) (and (= (* 2 Y) X) (tptp.pow2 Y))))))) (not (tptp.pow2 12)))) (not (=> (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))))) (not (tptp.pow2 12)))))) :rule cong :premises (t38))
% 0.21/0.56 (step t40 (cl (not (=> (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))))) (not (tptp.pow2 12))))) :rule resolution :premises (t35 t39 a0))
% 0.21/0.56 (step t41 (cl (not (not (tptp.pow2 12)))) :rule not_implies2 :premises (t40))
% 0.21/0.56 (step t42 (cl (tptp.pow2 12)) :rule resolution :premises (t34 t41))
% 0.21/0.56 (step t43 (cl (not (= (=> (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))))) (= (tptp.pow2 12) (or (= 12 1) (and (>= 12 2) (not (forall ((Y Int)) (or (not (= 12 (* 2 Y))) (not (tptp.pow2 Y))))))))) (=> (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))))) (= (tptp.pow2 12) (tptp.pow2 6))))) (not (=> (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))))) (= (tptp.pow2 12) (or (= 12 1) (and (>= 12 2) (not (forall ((Y Int)) (or (not (= 12 (* 2 Y))) (not (tptp.pow2 Y)))))))))) (=> (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))))) (= (tptp.pow2 12) (tptp.pow2 6)))) :rule equiv_pos2)
% 0.21/0.56 (step t44 (cl (= (tptp.pow2 12) (tptp.pow2 12))) :rule refl)
% 0.21/0.56 (step t45 (cl (= (= 12 1) false)) :rule all_simplify)
% 0.21/0.56 (step t46 (cl (= (>= 12 2) true)) :rule all_simplify)
% 0.21/0.56 (anchor :step t47 :args ((Y Int) (:= Y Y)))
% 0.21/0.56 (step t47.t1 (cl (= Y Y)) :rule refl)
% 0.21/0.56 (step t47.t2 (cl (= (= 12 (* 2 Y)) (= Y 6))) :rule all_simplify)
% 0.21/0.56 (step t47.t3 (cl (= (not (= 12 (* 2 Y))) (not (= Y 6)))) :rule cong :premises (t47.t2))
% 0.21/0.56 (step t47.t4 (cl (= (not (tptp.pow2 Y)) (not (tptp.pow2 Y)))) :rule refl)
% 0.21/0.56 (step t47.t5 (cl (= (or (not (= 12 (* 2 Y))) (not (tptp.pow2 Y))) (or (not (= Y 6)) (not (tptp.pow2 Y))))) :rule cong :premises (t47.t3 t47.t4))
% 0.21/0.56 (step t47 (cl (= (forall ((Y Int)) (or (not (= 12 (* 2 Y))) (not (tptp.pow2 Y)))) (forall ((Y Int)) (or (not (= Y 6)) (not (tptp.pow2 Y)))))) :rule bind)
% 0.21/0.56 (step t48 (cl (= (forall ((Y Int)) (or (not (= Y 6)) (not (tptp.pow2 Y)))) (or (not (= 6 6)) (not (tptp.pow2 6))))) :rule all_simplify)
% 0.21/0.56 (step t49 (cl (= (= 6 6) true)) :rule all_simplify)
% 0.21/0.56 (step t50 (cl (= (not (= 6 6)) (not true))) :rule cong :premises (t49))
% 0.21/0.56 (step t51 (cl (= (not (= 6 6)) false)) :rule trans :premises (t50 t10))
% 0.21/0.56 (step t52 (cl (= (not (tptp.pow2 6)) (not (tptp.pow2 6)))) :rule refl)
% 0.21/0.56 (step t53 (cl (= (or (not (= 6 6)) (not (tptp.pow2 6))) (or false (not (tptp.pow2 6))))) :rule cong :premises (t51 t52))
% 0.21/0.56 (step t54 (cl (= (or false (not (tptp.pow2 6))) (not (tptp.pow2 6)))) :rule all_simplify)
% 0.21/0.56 (step t55 (cl (= (or (not (= 6 6)) (not (tptp.pow2 6))) (not (tptp.pow2 6)))) :rule trans :premises (t53 t54))
% 0.21/0.56 (step t56 (cl (= (forall ((Y Int)) (or (not (= Y 6)) (not (tptp.pow2 Y)))) (not (tptp.pow2 6)))) :rule trans :premises (t48 t55))
% 0.21/0.56 (step t57 (cl (= (forall ((Y Int)) (or (not (= 12 (* 2 Y))) (not (tptp.pow2 Y)))) (not (tptp.pow2 6)))) :rule trans :premises (t47 t56))
% 0.21/0.56 (step t58 (cl (= (not (forall ((Y Int)) (or (not (= 12 (* 2 Y))) (not (tptp.pow2 Y))))) (not (not (tptp.pow2 6))))) :rule cong :premises (t57))
% 0.21/0.56 (step t59 (cl (= (not (not (tptp.pow2 6))) (tptp.pow2 6))) :rule all_simplify)
% 0.21/0.56 (step t60 (cl (= (not (forall ((Y Int)) (or (not (= 12 (* 2 Y))) (not (tptp.pow2 Y))))) (tptp.pow2 6))) :rule trans :premises (t58 t59))
% 0.21/0.56 (step t61 (cl (= (and (>= 12 2) (not (forall ((Y Int)) (or (not (= 12 (* 2 Y))) (not (tptp.pow2 Y)))))) (and true (tptp.pow2 6)))) :rule cong :premises (t46 t60))
% 0.21/0.56 (step t62 (cl (= (and true (tptp.pow2 6)) (tptp.pow2 6))) :rule all_simplify)
% 0.21/0.56 (step t63 (cl (= (and (>= 12 2) (not (forall ((Y Int)) (or (not (= 12 (* 2 Y))) (not (tptp.pow2 Y)))))) (tptp.pow2 6))) :rule trans :premises (t61 t62))
% 0.21/0.56 (step t64 (cl (= (or (= 12 1) (and (>= 12 2) (not (forall ((Y Int)) (or (not (= 12 (* 2 Y))) (not (tptp.pow2 Y))))))) (or false (tptp.pow2 6)))) :rule cong :premises (t45 t63))
% 0.21/0.56 (step t65 (cl (= (or false (tptp.pow2 6)) (tptp.pow2 6))) :rule all_simplify)
% 0.21/0.56 (step t66 (cl (= (or (= 12 1) (and (>= 12 2) (not (forall ((Y Int)) (or (not (= 12 (* 2 Y))) (not (tptp.pow2 Y))))))) (tptp.pow2 6))) :rule trans :premises (t64 t65))
% 0.21/0.56 (step t67 (cl (= (= (tptp.pow2 12) (or (= 12 1) (and (>= 12 2) (not (forall ((Y Int)) (or (not (= 12 (* 2 Y))) (not (tptp.pow2 Y)))))))) (= (tptp.pow2 12) (tptp.pow2 6)))) :rule cong :premises (t44 t66))
% 0.21/0.56 (step t68 (cl (= (=> (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))))) (= (tptp.pow2 12) (or (= 12 1) (and (>= 12 2) (not (forall ((Y Int)) (or (not (= 12 (* 2 Y))) (not (tptp.pow2 Y))))))))) (=> (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))))) (= (tptp.pow2 12) (tptp.pow2 6))))) :rule cong :premises (t2 t67))
% 0.21/0.56 (step t69 (cl (=> (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))))) (= (tptp.pow2 12) (or (= 12 1) (and (>= 12 2) (not (forall ((Y Int)) (or (not (= 12 (* 2 Y))) (not (tptp.pow2 Y))))))))) (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y)))))))))) :rule implies_neg1)
% 0.21/0.56 (anchor :step t70)
% 0.21/0.56 (assume t70.a0 (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))))))
% 0.21/0.56 (step t70.t1 (cl (or (not (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y)))))))))) (= (tptp.pow2 12) (or (= 12 1) (and (>= 12 2) (not (forall ((Y Int)) (or (not (= 12 (* 2 Y))) (not (tptp.pow2 Y)))))))))) :rule forall_inst :args ((:= X 12)))
% 0.21/0.56 (step t70.t2 (cl (not (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y)))))))))) (= (tptp.pow2 12) (or (= 12 1) (and (>= 12 2) (not (forall ((Y Int)) (or (not (= 12 (* 2 Y))) (not (tptp.pow2 Y))))))))) :rule or :premises (t70.t1))
% 0.21/0.56 (step t70.t3 (cl (= (tptp.pow2 12) (or (= 12 1) (and (>= 12 2) (not (forall ((Y Int)) (or (not (= 12 (* 2 Y))) (not (tptp.pow2 Y))))))))) :rule resolution :premises (t70.t2 t70.a0))
% 0.21/0.56 (step t70 (cl (not (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y)))))))))) (= (tptp.pow2 12) (or (= 12 1) (and (>= 12 2) (not (forall ((Y Int)) (or (not (= 12 (* 2 Y))) (not (tptp.pow2 Y))))))))) :rule subproof :discharge (t70.a0))
% 0.21/0.56 (step t71 (cl (=> (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))))) (= (tptp.pow2 12) (or (= 12 1) (and (>= 12 2) (not (forall ((Y Int)) (or (not (= 12 (* 2 Y))) (not (tptp.pow2 Y))))))))) (= (tptp.pow2 12) (or (= 12 1) (and (>= 12 2) (not (forall ((Y Int)) (or (not (= 12 (* 2 Y))) (not (tptp.pow2 Y))))))))) :rule resolution :premises (t69 t70))
% 0.21/0.56 (step t72 (cl (=> (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))))) (= (tptp.pow2 12) (or (= 12 1) (and (>= 12 2) (not (forall ((Y Int)) (or (not (= 12 (* 2 Y))) (not (tptp.pow2 Y))))))))) (not (= (tptp.pow2 12) (or (= 12 1) (and (>= 12 2) (not (forall ((Y Int)) (or (not (= 12 (* 2 Y))) (not (tptp.pow2 Y)))))))))) :rule implies_neg2)
% 0.21/0.56 (step t73 (cl (=> (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))))) (= (tptp.pow2 12) (or (= 12 1) (and (>= 12 2) (not (forall ((Y Int)) (or (not (= 12 (* 2 Y))) (not (tptp.pow2 Y))))))))) (=> (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))))) (= (tptp.pow2 12) (or (= 12 1) (and (>= 12 2) (not (forall ((Y Int)) (or (not (= 12 (* 2 Y))) (not (tptp.pow2 Y)))))))))) :rule resolution :premises (t71 t72))
% 0.21/0.56 (step t74 (cl (=> (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))))) (= (tptp.pow2 12) (or (= 12 1) (and (>= 12 2) (not (forall ((Y Int)) (or (not (= 12 (* 2 Y))) (not (tptp.pow2 Y)))))))))) :rule contraction :premises (t73))
% 0.21/0.56 (step t75 (cl (=> (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))))) (= (tptp.pow2 12) (tptp.pow2 6)))) :rule resolution :premises (t43 t68 t74))
% 0.21/0.56 (step t76 (cl (not (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y)))))))))) (= (tptp.pow2 12) (tptp.pow2 6))) :rule implies :premises (t75))
% 0.21/0.56 (step t77 (cl (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y)))))))))) :rule not_implies1 :premises (t40))
% 0.21/0.56 (step t78 (cl (= (tptp.pow2 12) (tptp.pow2 6))) :rule resolution :premises (t76 t77))
% 0.21/0.56 (step t79 (cl (tptp.pow2 6)) :rule resolution :premises (t33 t42 t78))
% 0.21/0.56 (step t80 (cl (not (= (=> (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))))) (= (tptp.pow2 6) (or (= 6 1) (and (>= 6 2) (not (forall ((Y Int)) (or (not (= 6 (* 2 Y))) (not (tptp.pow2 Y))))))))) (=> (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))))) (= (tptp.pow2 6) (tptp.pow2 3))))) (not (=> (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))))) (= (tptp.pow2 6) (or (= 6 1) (and (>= 6 2) (not (forall ((Y Int)) (or (not (= 6 (* 2 Y))) (not (tptp.pow2 Y)))))))))) (=> (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))))) (= (tptp.pow2 6) (tptp.pow2 3)))) :rule equiv_pos2)
% 0.21/0.56 (step t81 (cl (= (tptp.pow2 6) (tptp.pow2 6))) :rule refl)
% 0.21/0.56 (step t82 (cl (= (= 6 1) false)) :rule all_simplify)
% 0.21/0.56 (step t83 (cl (= (>= 6 2) true)) :rule all_simplify)
% 0.21/0.56 (anchor :step t84 :args ((Y Int) (:= Y Y)))
% 0.21/0.56 (step t84.t1 (cl (= Y Y)) :rule refl)
% 0.21/0.56 (step t84.t2 (cl (= (= 6 (* 2 Y)) (= Y 3))) :rule all_simplify)
% 0.21/0.56 (step t84.t3 (cl (= (not (= 6 (* 2 Y))) (not (= Y 3)))) :rule cong :premises (t84.t2))
% 0.21/0.56 (step t84.t4 (cl (= (not (tptp.pow2 Y)) (not (tptp.pow2 Y)))) :rule refl)
% 0.21/0.56 (step t84.t5 (cl (= (or (not (= 6 (* 2 Y))) (not (tptp.pow2 Y))) (or (not (= Y 3)) (not (tptp.pow2 Y))))) :rule cong :premises (t84.t3 t84.t4))
% 0.21/0.56 (step t84 (cl (= (forall ((Y Int)) (or (not (= 6 (* 2 Y))) (not (tptp.pow2 Y)))) (forall ((Y Int)) (or (not (= Y 3)) (not (tptp.pow2 Y)))))) :rule bind)
% 0.21/0.56 (step t85 (cl (= (forall ((Y Int)) (or (not (= Y 3)) (not (tptp.pow2 Y)))) (or (not (= 3 3)) (not (tptp.pow2 3))))) :rule all_simplify)
% 0.21/0.56 (step t86 (cl (= (= 3 3) true)) :rule all_simplify)
% 0.21/0.56 (step t87 (cl (= (not (= 3 3)) (not true))) :rule cong :premises (t86))
% 0.21/0.56 (step t88 (cl (= (not (= 3 3)) false)) :rule trans :premises (t87 t10))
% 0.21/0.56 (step t89 (cl (= (not (tptp.pow2 3)) (not (tptp.pow2 3)))) :rule refl)
% 0.21/0.56 (step t90 (cl (= (or (not (= 3 3)) (not (tptp.pow2 3))) (or false (not (tptp.pow2 3))))) :rule cong :premises (t88 t89))
% 0.21/0.56 (step t91 (cl (= (or false (not (tptp.pow2 3))) (not (tptp.pow2 3)))) :rule all_simplify)
% 0.21/0.56 (step t92 (cl (= (or (not (= 3 3)) (not (tptp.pow2 3))) (not (tptp.pow2 3)))) :rule trans :premises (t90 t91))
% 0.21/0.56 (step t93 (cl (= (forall ((Y Int)) (or (not (= Y 3)) (not (tptp.pow2 Y)))) (not (tptp.pow2 3)))) :rule trans :premises (t85 t92))
% 0.21/0.56 (step t94 (cl (= (forall ((Y Int)) (or (not (= 6 (* 2 Y))) (not (tptp.pow2 Y)))) (not (tptp.pow2 3)))) :rule trans :premises (t84 t93))
% 0.21/0.56 (step t95 (cl (= (not (forall ((Y Int)) (or (not (= 6 (* 2 Y))) (not (tptp.pow2 Y))))) (not (not (tptp.pow2 3))))) :rule cong :premises (t94))
% 0.21/0.56 (step t96 (cl (= (not (not (tptp.pow2 3))) (tptp.pow2 3))) :rule all_simplify)
% 0.21/0.56 (step t97 (cl (= (not (forall ((Y Int)) (or (not (= 6 (* 2 Y))) (not (tptp.pow2 Y))))) (tptp.pow2 3))) :rule trans :premises (t95 t96))
% 0.21/0.56 (step t98 (cl (= (and (>= 6 2) (not (forall ((Y Int)) (or (not (= 6 (* 2 Y))) (not (tptp.pow2 Y)))))) (and true (tptp.pow2 3)))) :rule cong :premises (t83 t97))
% 0.21/0.56 (step t99 (cl (= (and true (tptp.pow2 3)) (tptp.pow2 3))) :rule all_simplify)
% 0.21/0.56 (step t100 (cl (= (and (>= 6 2) (not (forall ((Y Int)) (or (not (= 6 (* 2 Y))) (not (tptp.pow2 Y)))))) (tptp.pow2 3))) :rule trans :premises (t98 t99))
% 0.21/0.56 (step t101 (cl (= (or (= 6 1) (and (>= 6 2) (not (forall ((Y Int)) (or (not (= 6 (* 2 Y))) (not (tptp.pow2 Y))))))) (or false (tptp.pow2 3)))) :rule cong :premises (t82 t100))
% 0.21/0.56 (step t102 (cl (= (or false (tptp.pow2 3)) (tptp.pow2 3))) :rule all_simplify)
% 0.21/0.56 (step t103 (cl (= (or (= 6 1) (and (>= 6 2) (not (forall ((Y Int)) (or (not (= 6 (* 2 Y))) (not (tptp.pow2 Y))))))) (tptp.pow2 3))) :rule trans :premises (t101 t102))
% 0.21/0.56 (step t104 (cl (= (= (tptp.pow2 6) (or (= 6 1) (and (>= 6 2) (not (forall ((Y Int)) (or (not (= 6 (* 2 Y))) (not (tptp.pow2 Y)))))))) (= (tptp.pow2 6) (tptp.pow2 3)))) :rule cong :premises (t81 t103))
% 0.21/0.56 (step t105 (cl (= (=> (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))))) (= (tptp.pow2 6) (or (= 6 1) (and (>= 6 2) (not (forall ((Y Int)) (or (not (= 6 (* 2 Y))) (not (tptp.pow2 Y))))))))) (=> (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))))) (= (tptp.pow2 6) (tptp.pow2 3))))) :rule cong :premises (t2 t104))
% 0.21/0.56 (step t106 (cl (=> (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))))) (= (tptp.pow2 6) (or (= 6 1) (and (>= 6 2) (not (forall ((Y Int)) (or (not (= 6 (* 2 Y))) (not (tptp.pow2 Y))))))))) (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y)))))))))) :rule implies_neg1)
% 0.21/0.56 (anchor :step t107)
% 0.21/0.56 (assume t107.a0 (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))))))
% 0.21/0.56 (step t107.t1 (cl (or (not (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y)))))))))) (= (tptp.pow2 6) (or (= 6 1) (and (>= 6 2) (not (forall ((Y Int)) (or (not (= 6 (* 2 Y))) (not (tptp.pow2 Y)))))))))) :rule forall_inst :args ((:= X 6)))
% 0.21/0.56 (step t107.t2 (cl (not (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y)))))))))) (= (tptp.pow2 6) (or (= 6 1) (and (>= 6 2) (not (forall ((Y Int)) (or (not (= 6 (* 2 Y))) (not (tptp.pow2 Y))))))))) :rule or :premises (t107.t1))
% 0.21/0.56 (step t107.t3 (cl (= (tptp.pow2 6) (or (= 6 1) (and (>= 6 2) (not (forall ((Y Int)) (or (not (= 6 (* 2 Y))) (not (tptp.pow2 Y))))))))) :rule resolution :premises (t107.t2 t107.a0))
% 0.21/0.56 (step t107 (cl (not (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y)))))))))) (= (tptp.pow2 6) (or (= 6 1) (and (>= 6 2) (not (forall ((Y Int)) (or (not (= 6 (* 2 Y))) (not (tptp.pow2 Y))))))))) :rule subproof :discharge (t107.a0))
% 0.21/0.56 (step t108 (cl (=> (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))))) (= (tptp.pow2 6) (or (= 6 1) (and (>= 6 2) (not (forall ((Y Int)) (or (not (= 6 (* 2 Y))) (not (tptp.pow2 Y))))))))) (= (tptp.pow2 6) (or (= 6 1) (and (>= 6 2) (not (forall ((Y Int)) (or (not (= 6 (* 2 Y))) (not (tptp.pow2 Y))))))))) :rule resolution :premises (t106 t107))
% 0.21/0.56 (step t109 (cl (=> (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))))) (= (tptp.pow2 6) (or (= 6 1) (and (>= 6 2) (not (forall ((Y Int)) (or (not (= 6 (* 2 Y))) (not (tptp.pow2 Y))))))))) (not (= (tptp.pow2 6) (or (= 6 1) (and (>= 6 2) (not (forall ((Y Int)) (or (not (= 6 (* 2 Y))) (not (tptp.pow2 Y)))))))))) :rule implies_neg2)
% 0.21/0.56 (step t110 (cl (=> (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))))) (= (tptp.pow2 6) (or (= 6 1) (and (>= 6 2) (not (forall ((Y Int)) (or (not (= 6 (* 2 Y))) (not (tptp.pow2 Y))))))))) (=> (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))))) (= (tptp.pow2 6) (or (= 6 1) (and (>= 6 2) (not (forall ((Y Int)) (or (not (= 6 (* 2 Y))) (not (tptp.pow2 Y)))))))))) :rule resolution :premises (t108 t109))
% 0.21/0.56 (step t111 (cl (=> (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))))) (= (tptp.pow2 6) (or (= 6 1) (and (>= 6 2) (not (forall ((Y Int)) (or (not (= 6 (* 2 Y))) (not (tptp.pow2 Y)))))))))) :rule contraction :premises (t110))
% 0.21/0.56 (step t112 (cl (=> (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y))))))))) (= (tptp.pow2 6) (tptp.pow2 3)))) :rule resolution :premises (t80 t105 t111))
% 0.21/0.56 (step t113 (cl (not (forall ((X Int)) (= (tptp.pow2 X) (or (= X 1) (and (>= X 2) (not (forall ((Y Int)) (or (not (= X (* 2 Y))) (not (tptp.pow2 Y)))))))))) (= (tptp.pow2 6) (tptp.pow2 3))) :rule implies :premises (t112))
% 0.21/0.56 (step t114 (cl (= (tptp.pow2 6) (tptp.pow2 3))) :rule resolution :premises (t113 t77))
% 0.21/0.56 (step t115 (cl (tptp.pow2 3)) :rule resolution :premises (t31 t79 t114))
% 0.21/0.56 (step t116 (cl) :rule resolution :premises (t29 t115 t77))
% 0.21/0.56
% 0.21/0.56 % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.4R9fOgFHFW/cvc5---1.0.5_16898.smt2
% 0.21/0.56 % cvc5---1.0.5 exiting
% 0.21/0.56 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------