TSTP Solution File: ARI601_1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ARI601_1 : TPTP v8.2.0. Released v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n016.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 16:34:13 EDT 2024
% Result : Theorem 0.23s 0.57s
% Output : Proof 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : ARI601_1 : TPTP v8.2.0. Released v5.1.0.
% 0.07/0.15 % Command : do_cvc5 %s %d
% 0.16/0.37 % Computer : n016.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Mon May 27 05:43:39 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.23/0.52 %----Proving TF0_ARI
% 0.23/0.57 --- Run --finite-model-find --decision=internal at 15...
% 0.23/0.57 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 15...
% 0.23/0.57 % SZS status Theorem for /export/starexec/sandbox/tmp/tmp.Kx0h5Awj9g/cvc5---1.0.5_10901.smt2
% 0.23/0.57 % SZS output start Proof for /export/starexec/sandbox/tmp/tmp.Kx0h5Awj9g/cvc5---1.0.5_10901.smt2
% 0.23/0.57 (assume a0 (not (=> (forall ((X Int)) (> (tptp.f X) X)) (=> (< 3 tptp.a) (< 4 (tptp.f (+ tptp.a 1)))))))
% 0.23/0.57 (assume a1 true)
% 0.23/0.57 (step t1 (cl (not (= (or (not (>= tptp.a 4)) (not (not (>= (tptp.f (+ 1 tptp.a)) 5))) (not (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))))) (or (not (>= tptp.a 4)) (>= (tptp.f (+ 1 tptp.a)) 5) (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))))) (not (or (not (>= tptp.a 4)) (not (not (>= (tptp.f (+ 1 tptp.a)) 5))) (not (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)))))) (or (not (>= tptp.a 4)) (>= (tptp.f (+ 1 tptp.a)) 5) (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)))) :rule equiv_pos2)
% 0.23/0.57 (step t2 (cl (= (not (>= tptp.a 4)) (not (>= tptp.a 4)))) :rule refl)
% 0.23/0.57 (step t3 (cl (= (not (not (>= (tptp.f (+ 1 tptp.a)) 5))) (>= (tptp.f (+ 1 tptp.a)) 5))) :rule all_simplify)
% 0.23/0.57 (step t4 (cl (= (= (= (not (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)))) (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) true) (= (not (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)))) (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))))) :rule equiv_simplify)
% 0.23/0.57 (step t5 (cl (not (= (= (not (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)))) (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) true)) (= (not (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)))) (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)))) :rule equiv1 :premises (t4))
% 0.23/0.57 (step t6 (cl (= (= (not (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)))) (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (= (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)) (not (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))))))) :rule all_simplify)
% 0.23/0.57 (step t7 (cl (= (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)) (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)))) :rule refl)
% 0.23/0.57 (step t8 (cl (= (not (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)))) (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)))) :rule all_simplify)
% 0.23/0.57 (step t9 (cl (= (= (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)) (not (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))))) (= (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)) (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))))) :rule cong :premises (t7 t8))
% 0.23/0.57 (step t10 (cl (= (= (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)) (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) true)) :rule all_simplify)
% 0.23/0.57 (step t11 (cl (= (= (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)) (not (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))))) true)) :rule trans :premises (t9 t10))
% 0.23/0.57 (step t12 (cl (= (= (not (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)))) (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) true)) :rule trans :premises (t6 t11))
% 0.23/0.57 (step t13 (cl (= (not (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)))) (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)))) :rule resolution :premises (t5 t12))
% 0.23/0.57 (step t14 (cl (= (or (not (>= tptp.a 4)) (not (not (>= (tptp.f (+ 1 tptp.a)) 5))) (not (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))))) (or (not (>= tptp.a 4)) (>= (tptp.f (+ 1 tptp.a)) 5) (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))))) :rule cong :premises (t2 t3 t13))
% 0.23/0.57 (step t15 (cl (not (= (=> (and (>= tptp.a 4) (not (>= (tptp.f (+ 1 tptp.a)) 5)) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)))) (and (>= tptp.a 4) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (not (>= (tptp.f (+ 1 tptp.a)) 5)))) (not (and (>= tptp.a 4) (not (>= (tptp.f (+ 1 tptp.a)) 5)) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))))))) (not (=> (and (>= tptp.a 4) (not (>= (tptp.f (+ 1 tptp.a)) 5)) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)))) (and (>= tptp.a 4) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (not (>= (tptp.f (+ 1 tptp.a)) 5))))) (not (and (>= tptp.a 4) (not (>= (tptp.f (+ 1 tptp.a)) 5)) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)))))) :rule equiv_pos2)
% 0.23/0.57 (step t16 (cl (= (and (>= tptp.a 4) (not (>= (tptp.f (+ 1 tptp.a)) 5)) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)))) (and (>= tptp.a 4) (not (>= (tptp.f (+ 1 tptp.a)) 5)) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)))))) :rule refl)
% 0.23/0.57 (step t17 (cl (= (= (and (>= tptp.a 4) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (not (>= (tptp.f (+ 1 tptp.a)) 5))) false) (not (and (>= tptp.a 4) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (not (>= (tptp.f (+ 1 tptp.a)) 5)))))) :rule equiv_simplify)
% 0.23/0.57 (step t18 (cl (= (and (>= tptp.a 4) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (not (>= (tptp.f (+ 1 tptp.a)) 5))) false) (not (not (and (>= tptp.a 4) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (not (>= (tptp.f (+ 1 tptp.a)) 5)))))) :rule equiv2 :premises (t17))
% 0.23/0.57 (step t19 (cl (not (not (not (and (>= tptp.a 4) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (not (>= (tptp.f (+ 1 tptp.a)) 5)))))) (and (>= tptp.a 4) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (not (>= (tptp.f (+ 1 tptp.a)) 5)))) :rule not_not)
% 0.23/0.57 (step t20 (cl (= (and (>= tptp.a 4) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (not (>= (tptp.f (+ 1 tptp.a)) 5))) false) (and (>= tptp.a 4) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (not (>= (tptp.f (+ 1 tptp.a)) 5)))) :rule resolution :premises (t18 t19))
% 0.23/0.57 (step t21 (cl (=> (and (>= tptp.a 4) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (not (>= (tptp.f (+ 1 tptp.a)) 5))) false) (and (>= tptp.a 4) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (not (>= (tptp.f (+ 1 tptp.a)) 5)))) :rule implies_neg1)
% 0.23/0.57 (anchor :step t22)
% 0.23/0.57 (assume t22.a0 (>= tptp.a 4))
% 0.23/0.57 (assume t22.a1 (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))))
% 0.23/0.57 (assume t22.a2 (not (>= (tptp.f (+ 1 tptp.a)) 5)))
% 0.23/0.57 (step t22.t1 (cl (not (= (not (>= (tptp.f (+ 1 tptp.a)) 5)) (< (tptp.f (+ 1 tptp.a)) 5))) (not (not (>= (tptp.f (+ 1 tptp.a)) 5))) (< (tptp.f (+ 1 tptp.a)) 5)) :rule equiv_pos2)
% 0.23/0.57 (step t22.t2 (cl (= (< (tptp.f (+ 1 tptp.a)) 5) (not (>= (tptp.f (+ 1 tptp.a)) 5)))) :rule all_simplify)
% 0.23/0.57 (step t22.t3 (cl (= (not (>= (tptp.f (+ 1 tptp.a)) 5)) (< (tptp.f (+ 1 tptp.a)) 5))) :rule symm :premises (t22.t2))
% 0.23/0.57 (step t22.t4 (cl (< (tptp.f (+ 1 tptp.a)) 5)) :rule resolution :premises (t22.t1 t22.t3 t22.a2))
% 0.23/0.57 (step t22.t5 (cl (not (= (>= (tptp.f (+ 1 tptp.a)) 5) (not (< (tptp.f (+ 1 tptp.a)) 5)))) (not (>= (tptp.f (+ 1 tptp.a)) 5)) (not (< (tptp.f (+ 1 tptp.a)) 5))) :rule equiv_pos2)
% 0.23/0.57 (step t22.t6 (cl (= (not (< (tptp.f (+ 1 tptp.a)) 5)) (not (not (>= (tptp.f (+ 1 tptp.a)) 5))))) :rule cong :premises (t22.t2))
% 0.23/0.57 (step t22.t7 (cl (= (not (not (>= (tptp.f (+ 1 tptp.a)) 5))) (>= (tptp.f (+ 1 tptp.a)) 5))) :rule all_simplify)
% 0.23/0.57 (step t22.t8 (cl (= (not (< (tptp.f (+ 1 tptp.a)) 5)) (>= (tptp.f (+ 1 tptp.a)) 5))) :rule trans :premises (t22.t6 t22.t7))
% 0.23/0.57 (step t22.t9 (cl (= (>= (tptp.f (+ 1 tptp.a)) 5) (not (< (tptp.f (+ 1 tptp.a)) 5)))) :rule symm :premises (t22.t8))
% 0.23/0.57 (step t22.t10 (cl (not (= (not (< (tptp.f (+ 1 tptp.a)) 5)) (>= (tptp.f (+ 1 tptp.a)) 5))) (not (not (< (tptp.f (+ 1 tptp.a)) 5))) (>= (tptp.f (+ 1 tptp.a)) 5)) :rule equiv_pos2)
% 0.23/0.57 (step t22.t11 (cl (=> (< (tptp.f (+ 1 tptp.a)) 5) false) (< (tptp.f (+ 1 tptp.a)) 5)) :rule implies_neg1)
% 0.23/0.57 (anchor :step t22.t12)
% 0.23/0.57 (assume t22.t12.a0 (< (tptp.f (+ 1 tptp.a)) 5))
% 0.23/0.57 (step t22.t12.t1 (cl (not (= (< (+ (* 1.0 (tptp.f (+ 1 tptp.a))) (* 1.0 (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a))))) (* (- 1.0) tptp.a)) (+ (* 1.0 5) (* 1.0 (- 1)) (* (- 1.0) 4))) false)) (not (< (+ (* 1.0 (tptp.f (+ 1 tptp.a))) (* 1.0 (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a))))) (* (- 1.0) tptp.a)) (+ (* 1.0 5) (* 1.0 (- 1)) (* (- 1.0) 4)))) false) :rule equiv_pos2)
% 0.23/0.57 (step t22.t12.t2 (cl (= (< (+ (* 1.0 (tptp.f (+ 1 tptp.a))) (* 1.0 (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a))))) (* (- 1.0) tptp.a)) (+ (* 1.0 5) (* 1.0 (- 1)) (* (- 1.0) 4))) (not (>= (+ (* 1.0 (tptp.f (+ 1 tptp.a))) (* 1.0 (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a))))) (* (- 1.0) tptp.a)) (+ (* 1.0 5) (* 1.0 (- 1)) (* (- 1.0) 4)))))) :rule all_simplify)
% 0.23/0.57 (step t22.t12.t3 (cl (= (* 1.0 (tptp.f (+ 1 tptp.a))) (to_real (tptp.f (+ 1 tptp.a))))) :rule all_simplify)
% 0.23/0.57 (step t22.t12.t4 (cl (= (* 1.0 (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a))))) (to_real (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a))))))) :rule all_simplify)
% 0.23/0.57 (step t22.t12.t5 (cl (= (* (- 1.0) tptp.a) (to_real (* (- 1) tptp.a)))) :rule all_simplify)
% 0.23/0.57 (step t22.t12.t6 (cl (= (+ (* 1.0 (tptp.f (+ 1 tptp.a))) (* 1.0 (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a))))) (* (- 1.0) tptp.a)) (+ (to_real (tptp.f (+ 1 tptp.a))) (to_real (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a))))) (to_real (* (- 1) tptp.a))))) :rule cong :premises (t22.t12.t3 t22.t12.t4 t22.t12.t5))
% 0.23/0.57 (step t22.t12.t7 (cl (= (+ (to_real (tptp.f (+ 1 tptp.a))) (to_real (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a))))) (to_real (* (- 1) tptp.a))) 0.0)) :rule all_simplify)
% 0.23/0.57 (step t22.t12.t8 (cl (= (+ (* 1.0 (tptp.f (+ 1 tptp.a))) (* 1.0 (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a))))) (* (- 1.0) tptp.a)) 0.0)) :rule trans :premises (t22.t12.t6 t22.t12.t7))
% 0.23/0.57 (step t22.t12.t9 (cl (= (* 1.0 5) 5.0)) :rule all_simplify)
% 0.23/0.57 (step t22.t12.t10 (cl (= (* 1.0 (- 1)) (- 1.0))) :rule all_simplify)
% 0.23/0.57 (step t22.t12.t11 (cl (= (* (- 1.0) 4) (- 4.0))) :rule all_simplify)
% 0.23/0.57 (step t22.t12.t12 (cl (= (+ (* 1.0 5) (* 1.0 (- 1)) (* (- 1.0) 4)) (+ 5.0 (- 1.0) (- 4.0)))) :rule cong :premises (t22.t12.t9 t22.t12.t10 t22.t12.t11))
% 0.23/0.57 (step t22.t12.t13 (cl (= (+ 5.0 (- 1.0) (- 4.0)) 0.0)) :rule all_simplify)
% 0.23/0.57 (step t22.t12.t14 (cl (= (+ (* 1.0 5) (* 1.0 (- 1)) (* (- 1.0) 4)) 0.0)) :rule trans :premises (t22.t12.t12 t22.t12.t13))
% 0.23/0.57 (step t22.t12.t15 (cl (= (>= (+ (* 1.0 (tptp.f (+ 1 tptp.a))) (* 1.0 (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a))))) (* (- 1.0) tptp.a)) (+ (* 1.0 5) (* 1.0 (- 1)) (* (- 1.0) 4))) (>= 0.0 0.0))) :rule cong :premises (t22.t12.t8 t22.t12.t14))
% 0.23/0.57 (step t22.t12.t16 (cl (= (>= 0.0 0.0) true)) :rule all_simplify)
% 0.23/0.57 (step t22.t12.t17 (cl (= (>= (+ (* 1.0 (tptp.f (+ 1 tptp.a))) (* 1.0 (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a))))) (* (- 1.0) tptp.a)) (+ (* 1.0 5) (* 1.0 (- 1)) (* (- 1.0) 4))) true)) :rule trans :premises (t22.t12.t15 t22.t12.t16))
% 0.23/0.57 (step t22.t12.t18 (cl (= (not (>= (+ (* 1.0 (tptp.f (+ 1 tptp.a))) (* 1.0 (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a))))) (* (- 1.0) tptp.a)) (+ (* 1.0 5) (* 1.0 (- 1)) (* (- 1.0) 4)))) (not true))) :rule cong :premises (t22.t12.t17))
% 0.23/0.57 (step t22.t12.t19 (cl (= (not true) false)) :rule all_simplify)
% 0.23/0.57 (step t22.t12.t20 (cl (= (not (>= (+ (* 1.0 (tptp.f (+ 1 tptp.a))) (* 1.0 (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a))))) (* (- 1.0) tptp.a)) (+ (* 1.0 5) (* 1.0 (- 1)) (* (- 1.0) 4)))) false)) :rule trans :premises (t22.t12.t18 t22.t12.t19))
% 0.23/0.57 (step t22.t12.t21 (cl (= (< (+ (* 1.0 (tptp.f (+ 1 tptp.a))) (* 1.0 (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a))))) (* (- 1.0) tptp.a)) (+ (* 1.0 5) (* 1.0 (- 1)) (* (- 1.0) 4))) false)) :rule trans :premises (t22.t12.t2 t22.t12.t20))
% 0.23/0.57 (step t22.t12.t22 (cl (not (< (* 1.0 (tptp.f (+ 1 tptp.a))) (* 1.0 5))) (not (< (* 1.0 (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a))))) (* 1.0 (- 1)))) (not (<= (* (- 1.0) tptp.a) (* (- 1.0) 4))) (< (+ (* 1.0 (tptp.f (+ 1 tptp.a))) (* 1.0 (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a))))) (* (- 1.0) tptp.a)) (+ (* 1.0 5) (* 1.0 (- 1)) (* (- 1.0) 4)))) :rule la_generic :args (1 1 1 1))
% 0.23/0.57 (step t22.t12.t23 (cl (=> (and (> 1.0 0) (< (tptp.f (+ 1 tptp.a)) 5)) (< (* 1.0 (tptp.f (+ 1 tptp.a))) (* 1.0 5)))) :rule la_mult_pos)
% 0.23/0.57 (step t22.t12.t24 (cl (not (and (> 1.0 0) (< (tptp.f (+ 1 tptp.a)) 5))) (< (* 1.0 (tptp.f (+ 1 tptp.a))) (* 1.0 5))) :rule implies :premises (t22.t12.t23))
% 0.23/0.57 (step t22.t12.t25 (cl (and (> 1.0 0) (< (tptp.f (+ 1 tptp.a)) 5)) (not (> 1.0 0)) (not (< (tptp.f (+ 1 tptp.a)) 5))) :rule and_neg)
% 0.23/0.57 (step t22.t12.t26 (cl (= (= (> 1.0 0) true) (> 1.0 0))) :rule equiv_simplify)
% 0.23/0.57 (step t22.t12.t27 (cl (not (= (> 1.0 0) true)) (> 1.0 0)) :rule equiv1 :premises (t22.t12.t26))
% 0.23/0.57 (step t22.t12.t28 (cl (= (> 1.0 0) true)) :rule hole :args ((> 1.0 0)))
% 0.23/0.57 (step t22.t12.t29 (cl (> 1.0 0)) :rule resolution :premises (t22.t12.t27 t22.t12.t28))
% 0.23/0.57 (step t22.t12.t30 (cl (and (> 1.0 0) (< (tptp.f (+ 1 tptp.a)) 5))) :rule resolution :premises (t22.t12.t25 t22.t12.t29 t22.t12.a0))
% 0.23/0.57 (step t22.t12.t31 (cl (< (* 1.0 (tptp.f (+ 1 tptp.a))) (* 1.0 5))) :rule resolution :premises (t22.t12.t24 t22.t12.t30))
% 0.23/0.57 (step t22.t12.t32 (cl (=> (and (> 1.0 0) (< (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (< (* 1.0 (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a))))) (* 1.0 (- 1))))) :rule la_mult_pos)
% 0.23/0.57 (step t22.t12.t33 (cl (not (and (> 1.0 0) (< (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)))) (< (* 1.0 (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a))))) (* 1.0 (- 1)))) :rule implies :premises (t22.t12.t32))
% 0.23/0.57 (step t22.t12.t34 (cl (and (> 1.0 0) (< (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (not (> 1.0 0)) (not (< (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)))) :rule and_neg)
% 0.23/0.57 (step t22.t12.t35 (cl (not (= (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (< (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)))) (not (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)))) (< (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) :rule equiv_pos2)
% 0.23/0.57 (step t22.t12.t36 (cl (= (< (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))))) :rule all_simplify)
% 0.23/0.57 (step t22.t12.t37 (cl (= (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (< (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)))) :rule symm :premises (t22.t12.t36))
% 0.23/0.57 (step t22.t12.t38 (cl (< (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) :rule resolution :premises (t22.t12.t35 t22.t12.t37 t22.a1))
% 0.23/0.57 (step t22.t12.t39 (cl (and (> 1.0 0) (< (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)))) :rule resolution :premises (t22.t12.t34 t22.t12.t29 t22.t12.t38))
% 0.23/0.57 (step t22.t12.t40 (cl (< (* 1.0 (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a))))) (* 1.0 (- 1)))) :rule resolution :premises (t22.t12.t33 t22.t12.t39))
% 0.23/0.57 (step t22.t12.t41 (cl (=> (and (< (- 1.0) 0) (>= tptp.a 4)) (<= (* (- 1.0) tptp.a) (* (- 1.0) 4)))) :rule la_mult_neg)
% 0.23/0.57 (step t22.t12.t42 (cl (not (and (< (- 1.0) 0) (>= tptp.a 4))) (<= (* (- 1.0) tptp.a) (* (- 1.0) 4))) :rule implies :premises (t22.t12.t41))
% 0.23/0.57 (step t22.t12.t43 (cl (and (< (- 1.0) 0) (>= tptp.a 4)) (not (< (- 1.0) 0)) (not (>= tptp.a 4))) :rule and_neg)
% 0.23/0.57 (step t22.t12.t44 (cl (= (= (< (- 1.0) 0) true) (< (- 1.0) 0))) :rule equiv_simplify)
% 0.23/0.57 (step t22.t12.t45 (cl (not (= (< (- 1.0) 0) true)) (< (- 1.0) 0)) :rule equiv1 :premises (t22.t12.t44))
% 0.23/0.57 (step t22.t12.t46 (cl (= (< (- 1.0) 0) true)) :rule hole :args ((< (- 1.0) 0)))
% 0.23/0.57 (step t22.t12.t47 (cl (< (- 1.0) 0)) :rule resolution :premises (t22.t12.t45 t22.t12.t46))
% 0.23/0.57 (step t22.t12.t48 (cl (and (< (- 1.0) 0) (>= tptp.a 4))) :rule resolution :premises (t22.t12.t43 t22.t12.t47 t22.a0))
% 0.23/0.57 (step t22.t12.t49 (cl (<= (* (- 1.0) tptp.a) (* (- 1.0) 4))) :rule resolution :premises (t22.t12.t42 t22.t12.t48))
% 0.23/0.57 (step t22.t12.t50 (cl (< (+ (* 1.0 (tptp.f (+ 1 tptp.a))) (* 1.0 (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a))))) (* (- 1.0) tptp.a)) (+ (* 1.0 5) (* 1.0 (- 1)) (* (- 1.0) 4)))) :rule resolution :premises (t22.t12.t22 t22.t12.t31 t22.t12.t40 t22.t12.t49))
% 0.23/0.57 (step t22.t12.t51 (cl false) :rule resolution :premises (t22.t12.t1 t22.t12.t21 t22.t12.t50))
% 0.23/0.57 (step t22.t12 (cl (not (< (tptp.f (+ 1 tptp.a)) 5)) false) :rule subproof :discharge (t22.t12.a0))
% 0.23/0.57 (step t22.t13 (cl (=> (< (tptp.f (+ 1 tptp.a)) 5) false) false) :rule resolution :premises (t22.t11 t22.t12))
% 0.23/0.57 (step t22.t14 (cl (=> (< (tptp.f (+ 1 tptp.a)) 5) false) (not false)) :rule implies_neg2)
% 0.23/0.57 (step t22.t15 (cl (=> (< (tptp.f (+ 1 tptp.a)) 5) false) (=> (< (tptp.f (+ 1 tptp.a)) 5) false)) :rule resolution :premises (t22.t13 t22.t14))
% 0.23/0.57 (step t22.t16 (cl (=> (< (tptp.f (+ 1 tptp.a)) 5) false)) :rule contraction :premises (t22.t15))
% 0.23/0.57 (step t22.t17 (cl (= (=> (< (tptp.f (+ 1 tptp.a)) 5) false) (not (< (tptp.f (+ 1 tptp.a)) 5)))) :rule implies_simplify)
% 0.23/0.57 (step t22.t18 (cl (not (=> (< (tptp.f (+ 1 tptp.a)) 5) false)) (not (< (tptp.f (+ 1 tptp.a)) 5))) :rule equiv1 :premises (t22.t17))
% 0.23/0.57 (step t22.t19 (cl (not (< (tptp.f (+ 1 tptp.a)) 5))) :rule resolution :premises (t22.t16 t22.t18))
% 0.23/0.57 (step t22.t20 (cl (>= (tptp.f (+ 1 tptp.a)) 5)) :rule resolution :premises (t22.t10 t22.t8 t22.t19))
% 0.23/0.57 (step t22.t21 (cl (not (< (tptp.f (+ 1 tptp.a)) 5))) :rule resolution :premises (t22.t5 t22.t9 t22.t20))
% 0.23/0.57 (step t22.t22 (cl) :rule resolution :premises (t22.t4 t22.t21))
% 0.23/0.57 (step t22 (cl (not (>= tptp.a 4)) (not (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)))) (not (not (>= (tptp.f (+ 1 tptp.a)) 5))) false) :rule subproof :discharge (t22.a0 t22.a1 t22.a2))
% 0.23/0.57 (step t23 (cl (not (and (>= tptp.a 4) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (not (>= (tptp.f (+ 1 tptp.a)) 5)))) (>= tptp.a 4)) :rule and_pos)
% 0.23/0.57 (step t24 (cl (not (and (>= tptp.a 4) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (not (>= (tptp.f (+ 1 tptp.a)) 5)))) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)))) :rule and_pos)
% 0.23/0.57 (step t25 (cl (not (and (>= tptp.a 4) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (not (>= (tptp.f (+ 1 tptp.a)) 5)))) (not (>= (tptp.f (+ 1 tptp.a)) 5))) :rule and_pos)
% 0.23/0.57 (step t26 (cl false (not (and (>= tptp.a 4) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (not (>= (tptp.f (+ 1 tptp.a)) 5)))) (not (and (>= tptp.a 4) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (not (>= (tptp.f (+ 1 tptp.a)) 5)))) (not (and (>= tptp.a 4) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (not (>= (tptp.f (+ 1 tptp.a)) 5))))) :rule resolution :premises (t22 t23 t24 t25))
% 0.23/0.57 (step t27 (cl (not (and (>= tptp.a 4) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (not (>= (tptp.f (+ 1 tptp.a)) 5)))) (not (and (>= tptp.a 4) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (not (>= (tptp.f (+ 1 tptp.a)) 5)))) (not (and (>= tptp.a 4) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (not (>= (tptp.f (+ 1 tptp.a)) 5)))) false) :rule reordering :premises (t26))
% 0.23/0.57 (step t28 (cl (not (and (>= tptp.a 4) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (not (>= (tptp.f (+ 1 tptp.a)) 5)))) false) :rule contraction :premises (t27))
% 0.23/0.57 (step t29 (cl (=> (and (>= tptp.a 4) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (not (>= (tptp.f (+ 1 tptp.a)) 5))) false) false) :rule resolution :premises (t21 t28))
% 0.23/0.57 (step t30 (cl (=> (and (>= tptp.a 4) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (not (>= (tptp.f (+ 1 tptp.a)) 5))) false) (not false)) :rule implies_neg2)
% 0.23/0.57 (step t31 (cl (=> (and (>= tptp.a 4) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (not (>= (tptp.f (+ 1 tptp.a)) 5))) false) (=> (and (>= tptp.a 4) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (not (>= (tptp.f (+ 1 tptp.a)) 5))) false)) :rule resolution :premises (t29 t30))
% 0.23/0.57 (step t32 (cl (=> (and (>= tptp.a 4) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (not (>= (tptp.f (+ 1 tptp.a)) 5))) false)) :rule contraction :premises (t31))
% 0.23/0.57 (step t33 (cl (= (=> (and (>= tptp.a 4) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (not (>= (tptp.f (+ 1 tptp.a)) 5))) false) (not (and (>= tptp.a 4) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (not (>= (tptp.f (+ 1 tptp.a)) 5)))))) :rule implies_simplify)
% 0.23/0.57 (step t34 (cl (not (=> (and (>= tptp.a 4) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (not (>= (tptp.f (+ 1 tptp.a)) 5))) false)) (not (and (>= tptp.a 4) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (not (>= (tptp.f (+ 1 tptp.a)) 5))))) :rule equiv1 :premises (t33))
% 0.23/0.57 (step t35 (cl (not (and (>= tptp.a 4) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (not (>= (tptp.f (+ 1 tptp.a)) 5))))) :rule resolution :premises (t32 t34))
% 0.23/0.57 (step t36 (cl (= (and (>= tptp.a 4) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (not (>= (tptp.f (+ 1 tptp.a)) 5))) false)) :rule resolution :premises (t20 t35))
% 0.23/0.57 (step t37 (cl (= (=> (and (>= tptp.a 4) (not (>= (tptp.f (+ 1 tptp.a)) 5)) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)))) (and (>= tptp.a 4) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (not (>= (tptp.f (+ 1 tptp.a)) 5)))) (=> (and (>= tptp.a 4) (not (>= (tptp.f (+ 1 tptp.a)) 5)) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)))) false))) :rule cong :premises (t16 t36))
% 0.23/0.57 (step t38 (cl (= (=> (and (>= tptp.a 4) (not (>= (tptp.f (+ 1 tptp.a)) 5)) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)))) false) (not (and (>= tptp.a 4) (not (>= (tptp.f (+ 1 tptp.a)) 5)) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))))))) :rule all_simplify)
% 0.23/0.57 (step t39 (cl (= (=> (and (>= tptp.a 4) (not (>= (tptp.f (+ 1 tptp.a)) 5)) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)))) (and (>= tptp.a 4) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (not (>= (tptp.f (+ 1 tptp.a)) 5)))) (not (and (>= tptp.a 4) (not (>= (tptp.f (+ 1 tptp.a)) 5)) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))))))) :rule trans :premises (t37 t38))
% 0.23/0.57 (step t40 (cl (=> (and (>= tptp.a 4) (not (>= (tptp.f (+ 1 tptp.a)) 5)) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)))) (and (>= tptp.a 4) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (not (>= (tptp.f (+ 1 tptp.a)) 5)))) (and (>= tptp.a 4) (not (>= (tptp.f (+ 1 tptp.a)) 5)) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))))) :rule implies_neg1)
% 0.23/0.57 (anchor :step t41)
% 0.23/0.57 (assume t41.a0 (>= tptp.a 4))
% 0.23/0.57 (assume t41.a1 (not (>= (tptp.f (+ 1 tptp.a)) 5)))
% 0.23/0.57 (assume t41.a2 (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))))
% 0.23/0.57 (step t41.t1 (cl (and (>= tptp.a 4) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (not (>= (tptp.f (+ 1 tptp.a)) 5))) (not (>= tptp.a 4)) (not (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)))) (not (not (>= (tptp.f (+ 1 tptp.a)) 5)))) :rule and_neg)
% 0.23/0.57 (step t41.t2 (cl (and (>= tptp.a 4) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (not (>= (tptp.f (+ 1 tptp.a)) 5)))) :rule resolution :premises (t41.t1 t41.a0 t41.a2 t41.a1))
% 0.23/0.57 (step t41 (cl (not (>= tptp.a 4)) (not (not (>= (tptp.f (+ 1 tptp.a)) 5))) (not (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)))) (and (>= tptp.a 4) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (not (>= (tptp.f (+ 1 tptp.a)) 5)))) :rule subproof :discharge (t41.a0 t41.a1 t41.a2))
% 0.23/0.57 (step t42 (cl (not (and (>= tptp.a 4) (not (>= (tptp.f (+ 1 tptp.a)) 5)) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))))) (>= tptp.a 4)) :rule and_pos)
% 0.23/0.57 (step t43 (cl (not (and (>= tptp.a 4) (not (>= (tptp.f (+ 1 tptp.a)) 5)) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))))) (not (>= (tptp.f (+ 1 tptp.a)) 5))) :rule and_pos)
% 0.23/0.57 (step t44 (cl (not (and (>= tptp.a 4) (not (>= (tptp.f (+ 1 tptp.a)) 5)) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))))) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)))) :rule and_pos)
% 0.23/0.57 (step t45 (cl (and (>= tptp.a 4) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (not (>= (tptp.f (+ 1 tptp.a)) 5))) (not (and (>= tptp.a 4) (not (>= (tptp.f (+ 1 tptp.a)) 5)) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))))) (not (and (>= tptp.a 4) (not (>= (tptp.f (+ 1 tptp.a)) 5)) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))))) (not (and (>= tptp.a 4) (not (>= (tptp.f (+ 1 tptp.a)) 5)) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)))))) :rule resolution :premises (t41 t42 t43 t44))
% 0.23/0.57 (step t46 (cl (not (and (>= tptp.a 4) (not (>= (tptp.f (+ 1 tptp.a)) 5)) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))))) (not (and (>= tptp.a 4) (not (>= (tptp.f (+ 1 tptp.a)) 5)) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))))) (not (and (>= tptp.a 4) (not (>= (tptp.f (+ 1 tptp.a)) 5)) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))))) (and (>= tptp.a 4) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (not (>= (tptp.f (+ 1 tptp.a)) 5)))) :rule reordering :premises (t45))
% 0.23/0.57 (step t47 (cl (not (and (>= tptp.a 4) (not (>= (tptp.f (+ 1 tptp.a)) 5)) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))))) (and (>= tptp.a 4) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (not (>= (tptp.f (+ 1 tptp.a)) 5)))) :rule contraction :premises (t46))
% 0.23/0.57 (step t48 (cl (=> (and (>= tptp.a 4) (not (>= (tptp.f (+ 1 tptp.a)) 5)) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)))) (and (>= tptp.a 4) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (not (>= (tptp.f (+ 1 tptp.a)) 5)))) (and (>= tptp.a 4) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (not (>= (tptp.f (+ 1 tptp.a)) 5)))) :rule resolution :premises (t40 t47))
% 0.23/0.57 (step t49 (cl (=> (and (>= tptp.a 4) (not (>= (tptp.f (+ 1 tptp.a)) 5)) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)))) (and (>= tptp.a 4) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (not (>= (tptp.f (+ 1 tptp.a)) 5)))) (not (and (>= tptp.a 4) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (not (>= (tptp.f (+ 1 tptp.a)) 5))))) :rule implies_neg2)
% 0.23/0.57 (step t50 (cl (=> (and (>= tptp.a 4) (not (>= (tptp.f (+ 1 tptp.a)) 5)) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)))) (and (>= tptp.a 4) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (not (>= (tptp.f (+ 1 tptp.a)) 5)))) (=> (and (>= tptp.a 4) (not (>= (tptp.f (+ 1 tptp.a)) 5)) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)))) (and (>= tptp.a 4) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (not (>= (tptp.f (+ 1 tptp.a)) 5))))) :rule resolution :premises (t48 t49))
% 0.23/0.57 (step t51 (cl (=> (and (>= tptp.a 4) (not (>= (tptp.f (+ 1 tptp.a)) 5)) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)))) (and (>= tptp.a 4) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) (not (>= (tptp.f (+ 1 tptp.a)) 5))))) :rule contraction :premises (t50))
% 0.23/0.57 (step t52 (cl (not (and (>= tptp.a 4) (not (>= (tptp.f (+ 1 tptp.a)) 5)) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)))))) :rule resolution :premises (t15 t39 t51))
% 0.23/0.57 (step t53 (cl (not (>= tptp.a 4)) (not (not (>= (tptp.f (+ 1 tptp.a)) 5))) (not (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))))) :rule not_and :premises (t52))
% 0.23/0.57 (step t54 (cl (or (not (>= tptp.a 4)) (not (not (>= (tptp.f (+ 1 tptp.a)) 5))) (not (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))))) (not (not (>= tptp.a 4)))) :rule or_neg)
% 0.23/0.57 (step t55 (cl (or (not (>= tptp.a 4)) (not (not (>= (tptp.f (+ 1 tptp.a)) 5))) (not (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))))) (not (not (not (>= (tptp.f (+ 1 tptp.a)) 5))))) :rule or_neg)
% 0.23/0.57 (step t56 (cl (or (not (>= tptp.a 4)) (not (not (>= (tptp.f (+ 1 tptp.a)) 5))) (not (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))))) (not (not (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)))))) :rule or_neg)
% 0.23/0.57 (step t57 (cl (or (not (>= tptp.a 4)) (not (not (>= (tptp.f (+ 1 tptp.a)) 5))) (not (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))))) (or (not (>= tptp.a 4)) (not (not (>= (tptp.f (+ 1 tptp.a)) 5))) (not (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))))) (or (not (>= tptp.a 4)) (not (not (>= (tptp.f (+ 1 tptp.a)) 5))) (not (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)))))) :rule resolution :premises (t53 t54 t55 t56))
% 0.23/0.57 (step t58 (cl (or (not (>= tptp.a 4)) (not (not (>= (tptp.f (+ 1 tptp.a)) 5))) (not (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)))))) :rule contraction :premises (t57))
% 0.23/0.57 (step t59 (cl (or (not (>= tptp.a 4)) (>= (tptp.f (+ 1 tptp.a)) 5) (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)))) :rule resolution :premises (t1 t14 t58))
% 0.23/0.57 (step t60 (cl (not (>= tptp.a 4)) (>= (tptp.f (+ 1 tptp.a)) 5) (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))) :rule or :premises (t59))
% 0.23/0.57 (step t61 (cl (not (= (=> (forall ((X Int)) (not (>= (+ X (* (- 1) (tptp.f X))) 0))) (not (>= (+ (+ 1 tptp.a) (* (- 1) (tptp.f (+ 1 tptp.a)))) 0))) (=> (forall ((X Int)) (not (>= (+ X (* (- 1) (tptp.f X))) 0))) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)))))) (not (=> (forall ((X Int)) (not (>= (+ X (* (- 1) (tptp.f X))) 0))) (not (>= (+ (+ 1 tptp.a) (* (- 1) (tptp.f (+ 1 tptp.a)))) 0)))) (=> (forall ((X Int)) (not (>= (+ X (* (- 1) (tptp.f X))) 0))) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))))) :rule equiv_pos2)
% 0.23/0.57 (step t62 (cl (= (forall ((X Int)) (not (>= (+ X (* (- 1) (tptp.f X))) 0))) (forall ((X Int)) (not (>= (+ X (* (- 1) (tptp.f X))) 0))))) :rule refl)
% 0.23/0.57 (step t63 (cl (= (+ (+ 1 tptp.a) (* (- 1) (tptp.f (+ 1 tptp.a)))) (+ 1 tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))))) :rule all_simplify)
% 0.23/0.57 (step t64 (cl (= 0 0)) :rule refl)
% 0.23/0.57 (step t65 (cl (= (>= (+ (+ 1 tptp.a) (* (- 1) (tptp.f (+ 1 tptp.a)))) 0) (>= (+ 1 tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) 0))) :rule cong :premises (t63 t64))
% 0.23/0.57 (step t66 (cl (= (>= (+ 1 tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) 0) (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)))) :rule all_simplify)
% 0.23/0.57 (step t67 (cl (= (>= (+ (+ 1 tptp.a) (* (- 1) (tptp.f (+ 1 tptp.a)))) 0) (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)))) :rule trans :premises (t65 t66))
% 0.23/0.57 (step t68 (cl (= (not (>= (+ (+ 1 tptp.a) (* (- 1) (tptp.f (+ 1 tptp.a)))) 0)) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))))) :rule cong :premises (t67))
% 0.23/0.57 (step t69 (cl (= (=> (forall ((X Int)) (not (>= (+ X (* (- 1) (tptp.f X))) 0))) (not (>= (+ (+ 1 tptp.a) (* (- 1) (tptp.f (+ 1 tptp.a)))) 0))) (=> (forall ((X Int)) (not (>= (+ X (* (- 1) (tptp.f X))) 0))) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)))))) :rule cong :premises (t62 t68))
% 0.23/0.57 (step t70 (cl (=> (forall ((X Int)) (not (>= (+ X (* (- 1) (tptp.f X))) 0))) (not (>= (+ (+ 1 tptp.a) (* (- 1) (tptp.f (+ 1 tptp.a)))) 0))) (forall ((X Int)) (not (>= (+ X (* (- 1) (tptp.f X))) 0)))) :rule implies_neg1)
% 0.23/0.57 (anchor :step t71)
% 0.23/0.57 (assume t71.a0 (forall ((X Int)) (not (>= (+ X (* (- 1) (tptp.f X))) 0))))
% 0.23/0.57 (step t71.t1 (cl (or (not (forall ((X Int)) (not (>= (+ X (* (- 1) (tptp.f X))) 0)))) (not (>= (+ (+ 1 tptp.a) (* (- 1) (tptp.f (+ 1 tptp.a)))) 0)))) :rule forall_inst :args ((:= X (+ 1 tptp.a))))
% 0.23/0.57 (step t71.t2 (cl (not (forall ((X Int)) (not (>= (+ X (* (- 1) (tptp.f X))) 0)))) (not (>= (+ (+ 1 tptp.a) (* (- 1) (tptp.f (+ 1 tptp.a)))) 0))) :rule or :premises (t71.t1))
% 0.23/0.57 (step t71.t3 (cl (not (>= (+ (+ 1 tptp.a) (* (- 1) (tptp.f (+ 1 tptp.a)))) 0))) :rule resolution :premises (t71.t2 t71.a0))
% 0.23/0.57 (step t71 (cl (not (forall ((X Int)) (not (>= (+ X (* (- 1) (tptp.f X))) 0)))) (not (>= (+ (+ 1 tptp.a) (* (- 1) (tptp.f (+ 1 tptp.a)))) 0))) :rule subproof :discharge (t71.a0))
% 0.23/0.57 (step t72 (cl (=> (forall ((X Int)) (not (>= (+ X (* (- 1) (tptp.f X))) 0))) (not (>= (+ (+ 1 tptp.a) (* (- 1) (tptp.f (+ 1 tptp.a)))) 0))) (not (>= (+ (+ 1 tptp.a) (* (- 1) (tptp.f (+ 1 tptp.a)))) 0))) :rule resolution :premises (t70 t71))
% 0.23/0.57 (step t73 (cl (=> (forall ((X Int)) (not (>= (+ X (* (- 1) (tptp.f X))) 0))) (not (>= (+ (+ 1 tptp.a) (* (- 1) (tptp.f (+ 1 tptp.a)))) 0))) (not (not (>= (+ (+ 1 tptp.a) (* (- 1) (tptp.f (+ 1 tptp.a)))) 0)))) :rule implies_neg2)
% 0.23/0.57 (step t74 (cl (=> (forall ((X Int)) (not (>= (+ X (* (- 1) (tptp.f X))) 0))) (not (>= (+ (+ 1 tptp.a) (* (- 1) (tptp.f (+ 1 tptp.a)))) 0))) (=> (forall ((X Int)) (not (>= (+ X (* (- 1) (tptp.f X))) 0))) (not (>= (+ (+ 1 tptp.a) (* (- 1) (tptp.f (+ 1 tptp.a)))) 0)))) :rule resolution :premises (t72 t73))
% 0.23/0.57 (step t75 (cl (=> (forall ((X Int)) (not (>= (+ X (* (- 1) (tptp.f X))) 0))) (not (>= (+ (+ 1 tptp.a) (* (- 1) (tptp.f (+ 1 tptp.a)))) 0)))) :rule contraction :premises (t74))
% 0.23/0.57 (step t76 (cl (=> (forall ((X Int)) (not (>= (+ X (* (- 1) (tptp.f X))) 0))) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1))))) :rule resolution :premises (t61 t69 t75))
% 0.23/0.57 (step t77 (cl (not (forall ((X Int)) (not (>= (+ X (* (- 1) (tptp.f X))) 0)))) (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)))) :rule implies :premises (t76))
% 0.23/0.57 (step t78 (cl (not (= (not (=> (forall ((X Int)) (> (tptp.f X) X)) (=> (< 3 tptp.a) (< 4 (tptp.f (+ tptp.a 1)))))) (not (=> (forall ((X Int)) (not (>= (+ X (* (- 1) (tptp.f X))) 0))) (=> (>= tptp.a 4) (>= (tptp.f (+ 1 tptp.a)) 5)))))) (not (not (=> (forall ((X Int)) (> (tptp.f X) X)) (=> (< 3 tptp.a) (< 4 (tptp.f (+ tptp.a 1))))))) (not (=> (forall ((X Int)) (not (>= (+ X (* (- 1) (tptp.f X))) 0))) (=> (>= tptp.a 4) (>= (tptp.f (+ 1 tptp.a)) 5))))) :rule equiv_pos2)
% 0.23/0.57 (anchor :step t79 :args ((X Int) (:= X X)))
% 0.23/0.57 (step t79.t1 (cl (= X X)) :rule refl)
% 0.23/0.57 (step t79.t2 (cl (= (> (tptp.f X) X) (not (<= (tptp.f X) X)))) :rule all_simplify)
% 0.23/0.57 (step t79.t3 (cl (= (<= (tptp.f X) X) (>= (+ X (* (- 1) (tptp.f X))) 0))) :rule all_simplify)
% 0.23/0.57 (step t79.t4 (cl (= (not (<= (tptp.f X) X)) (not (>= (+ X (* (- 1) (tptp.f X))) 0)))) :rule cong :premises (t79.t3))
% 0.23/0.57 (step t79.t5 (cl (= (> (tptp.f X) X) (not (>= (+ X (* (- 1) (tptp.f X))) 0)))) :rule trans :premises (t79.t2 t79.t4))
% 0.23/0.57 (step t79 (cl (= (forall ((X Int)) (> (tptp.f X) X)) (forall ((X Int)) (not (>= (+ X (* (- 1) (tptp.f X))) 0))))) :rule bind)
% 0.23/0.57 (step t80 (cl (= (< 3 tptp.a) (not (>= 3 tptp.a)))) :rule all_simplify)
% 0.23/0.57 (step t81 (cl (= (>= 3 tptp.a) (not (>= tptp.a 4)))) :rule all_simplify)
% 0.23/0.57 (step t82 (cl (= (not (>= 3 tptp.a)) (not (not (>= tptp.a 4))))) :rule cong :premises (t81))
% 0.23/0.57 (step t83 (cl (= (not (not (>= tptp.a 4))) (>= tptp.a 4))) :rule all_simplify)
% 0.23/0.57 (step t84 (cl (= (not (>= 3 tptp.a)) (>= tptp.a 4))) :rule trans :premises (t82 t83))
% 0.23/0.57 (step t85 (cl (= (< 3 tptp.a) (>= tptp.a 4))) :rule trans :premises (t80 t84))
% 0.23/0.57 (step t86 (cl (= (< 4 (tptp.f (+ tptp.a 1))) (not (>= 4 (tptp.f (+ tptp.a 1)))))) :rule all_simplify)
% 0.23/0.57 (step t87 (cl (= 4 4)) :rule refl)
% 0.23/0.57 (step t88 (cl (= (+ tptp.a 1) (+ 1 tptp.a))) :rule all_simplify)
% 0.23/0.57 (step t89 (cl (= (tptp.f (+ tptp.a 1)) (tptp.f (+ 1 tptp.a)))) :rule cong :premises (t88))
% 0.23/0.57 (step t90 (cl (= (>= 4 (tptp.f (+ tptp.a 1))) (>= 4 (tptp.f (+ 1 tptp.a))))) :rule cong :premises (t87 t89))
% 0.23/0.57 (step t91 (cl (= (>= 4 (tptp.f (+ 1 tptp.a))) (not (>= (tptp.f (+ 1 tptp.a)) 5)))) :rule all_simplify)
% 0.23/0.57 (step t92 (cl (= (>= 4 (tptp.f (+ tptp.a 1))) (not (>= (tptp.f (+ 1 tptp.a)) 5)))) :rule trans :premises (t90 t91))
% 0.23/0.57 (step t93 (cl (= (not (>= 4 (tptp.f (+ tptp.a 1)))) (not (not (>= (tptp.f (+ 1 tptp.a)) 5))))) :rule cong :premises (t92))
% 0.23/0.57 (step t94 (cl (= (not (not (>= (tptp.f (+ 1 tptp.a)) 5))) (>= (tptp.f (+ 1 tptp.a)) 5))) :rule all_simplify)
% 0.23/0.57 (step t95 (cl (= (not (>= 4 (tptp.f (+ tptp.a 1)))) (>= (tptp.f (+ 1 tptp.a)) 5))) :rule trans :premises (t93 t94))
% 0.23/0.57 (step t96 (cl (= (< 4 (tptp.f (+ tptp.a 1))) (>= (tptp.f (+ 1 tptp.a)) 5))) :rule trans :premises (t86 t95))
% 0.23/0.57 (step t97 (cl (= (=> (< 3 tptp.a) (< 4 (tptp.f (+ tptp.a 1)))) (=> (>= tptp.a 4) (>= (tptp.f (+ 1 tptp.a)) 5)))) :rule cong :premises (t85 t96))
% 0.23/0.57 (step t98 (cl (= (=> (forall ((X Int)) (> (tptp.f X) X)) (=> (< 3 tptp.a) (< 4 (tptp.f (+ tptp.a 1))))) (=> (forall ((X Int)) (not (>= (+ X (* (- 1) (tptp.f X))) 0))) (=> (>= tptp.a 4) (>= (tptp.f (+ 1 tptp.a)) 5))))) :rule cong :premises (t79 t97))
% 0.23/0.57 (step t99 (cl (= (not (=> (forall ((X Int)) (> (tptp.f X) X)) (=> (< 3 tptp.a) (< 4 (tptp.f (+ tptp.a 1)))))) (not (=> (forall ((X Int)) (not (>= (+ X (* (- 1) (tptp.f X))) 0))) (=> (>= tptp.a 4) (>= (tptp.f (+ 1 tptp.a)) 5)))))) :rule cong :premises (t98))
% 0.23/0.57 (step t100 (cl (not (=> (forall ((X Int)) (not (>= (+ X (* (- 1) (tptp.f X))) 0))) (=> (>= tptp.a 4) (>= (tptp.f (+ 1 tptp.a)) 5))))) :rule resolution :premises (t78 t99 a0))
% 0.23/0.57 (step t101 (cl (forall ((X Int)) (not (>= (+ X (* (- 1) (tptp.f X))) 0)))) :rule not_implies1 :premises (t100))
% 0.23/0.57 (step t102 (cl (not (>= (+ tptp.a (* (- 1) (tptp.f (+ 1 tptp.a)))) (- 1)))) :rule resolution :premises (t77 t101))
% 0.23/0.57 (step t103 (cl (not (=> (>= tptp.a 4) (>= (tptp.f (+ 1 tptp.a)) 5)))) :rule not_implies2 :premises (t100))
% 0.23/0.57 (step t104 (cl (not (>= (tptp.f (+ 1 tptp.a)) 5))) :rule not_implies2 :premises (t103))
% 0.23/0.57 (step t105 (cl (>= tptp.a 4)) :rule not_implies1 :premises (t103))
% 0.23/0.57 (step t106 (cl) :rule resolution :premises (t60 t102 t104 t105))
% 0.23/0.57
% 0.23/0.57 % SZS output end Proof for /export/starexec/sandbox/tmp/tmp.Kx0h5Awj9g/cvc5---1.0.5_10901.smt2
% 0.23/0.57 % cvc5---1.0.5 exiting
% 0.23/0.58 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------