TSTP Solution File: ARI577_1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ARI577_1 : TPTP v8.2.0. Released v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n027.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 16:34:10 EDT 2024
% Result : Theorem 0.18s 0.48s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : ARI577_1 : TPTP v8.2.0. Released v5.1.0.
% 0.11/0.12 % Command : do_cvc5 %s %d
% 0.12/0.32 % Computer : n027.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon May 27 05:28:09 EDT 2024
% 0.18/0.33 % CPUTime :
% 0.18/0.45 %----Proving TF0_ARI
% 0.18/0.48 --- Run --finite-model-find --decision=internal at 15...
% 0.18/0.48 % SZS status Theorem for /export/starexec/sandbox2/tmp/tmp.G3yajnQtsa/cvc5---1.0.5_27351.smt2
% 0.18/0.48 % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.G3yajnQtsa/cvc5---1.0.5_27351.smt2
% 0.18/0.48 (assume a0 (not (exists ((X Int) (Y Int)) (and (<= 4 Y) (<= (+ Y 1) X) (<= (+ X Y) 10)))))
% 0.18/0.48 (assume a1 true)
% 0.18/0.48 (step t1 (cl (not (= (=> (forall ((X Int) (Y Int)) (or (not (>= Y 4)) (not (>= (+ X (* (- 1) Y)) 1)) (>= (+ X Y) 11))) (or (not (>= 4 4)) (not (>= (+ 6 (* (- 1) 4)) 1)) (>= (+ 6 4) 11))) (not (forall ((X Int) (Y Int)) (or (not (>= Y 4)) (not (>= (+ X (* (- 1) Y)) 1)) (>= (+ X Y) 11)))))) (not (=> (forall ((X Int) (Y Int)) (or (not (>= Y 4)) (not (>= (+ X (* (- 1) Y)) 1)) (>= (+ X Y) 11))) (or (not (>= 4 4)) (not (>= (+ 6 (* (- 1) 4)) 1)) (>= (+ 6 4) 11)))) (not (forall ((X Int) (Y Int)) (or (not (>= Y 4)) (not (>= (+ X (* (- 1) Y)) 1)) (>= (+ X Y) 11))))) :rule equiv_pos2)
% 0.18/0.48 (step t2 (cl (= (forall ((X Int) (Y Int)) (or (not (>= Y 4)) (not (>= (+ X (* (- 1) Y)) 1)) (>= (+ X Y) 11))) (forall ((X Int) (Y Int)) (or (not (>= Y 4)) (not (>= (+ X (* (- 1) Y)) 1)) (>= (+ X Y) 11))))) :rule refl)
% 0.18/0.48 (step t3 (cl (= (>= 4 4) true)) :rule all_simplify)
% 0.18/0.48 (step t4 (cl (= (not (>= 4 4)) (not true))) :rule cong :premises (t3))
% 0.18/0.48 (step t5 (cl (= (not true) false)) :rule all_simplify)
% 0.18/0.48 (step t6 (cl (= (not (>= 4 4)) false)) :rule trans :premises (t4 t5))
% 0.18/0.48 (step t7 (cl (= 6 6)) :rule refl)
% 0.18/0.48 (step t8 (cl (= (* (- 1) 4) (- 4))) :rule all_simplify)
% 0.18/0.48 (step t9 (cl (= (+ 6 (* (- 1) 4)) (+ 6 (- 4)))) :rule cong :premises (t7 t8))
% 0.18/0.48 (step t10 (cl (= (+ 6 (- 4)) 2)) :rule all_simplify)
% 0.18/0.48 (step t11 (cl (= (+ 6 (* (- 1) 4)) 2)) :rule trans :premises (t9 t10))
% 0.18/0.48 (step t12 (cl (= 1 1)) :rule refl)
% 0.18/0.48 (step t13 (cl (= (>= (+ 6 (* (- 1) 4)) 1) (>= 2 1))) :rule cong :premises (t11 t12))
% 0.18/0.48 (step t14 (cl (= (>= 2 1) true)) :rule all_simplify)
% 0.18/0.48 (step t15 (cl (= (>= (+ 6 (* (- 1) 4)) 1) true)) :rule trans :premises (t13 t14))
% 0.18/0.48 (step t16 (cl (= (not (>= (+ 6 (* (- 1) 4)) 1)) (not true))) :rule cong :premises (t15))
% 0.18/0.48 (step t17 (cl (= (not (>= (+ 6 (* (- 1) 4)) 1)) false)) :rule trans :premises (t16 t5))
% 0.18/0.48 (step t18 (cl (= (+ 6 4) 10)) :rule all_simplify)
% 0.18/0.48 (step t19 (cl (= 11 11)) :rule refl)
% 0.18/0.48 (step t20 (cl (= (>= (+ 6 4) 11) (>= 10 11))) :rule cong :premises (t18 t19))
% 0.18/0.48 (step t21 (cl (= (>= 10 11) false)) :rule all_simplify)
% 0.18/0.48 (step t22 (cl (= (>= (+ 6 4) 11) false)) :rule trans :premises (t20 t21))
% 0.18/0.48 (step t23 (cl (= (or (not (>= 4 4)) (not (>= (+ 6 (* (- 1) 4)) 1)) (>= (+ 6 4) 11)) (or false false false))) :rule cong :premises (t6 t17 t22))
% 0.18/0.48 (step t24 (cl (= (or false false false) false)) :rule all_simplify)
% 0.18/0.48 (step t25 (cl (= (or (not (>= 4 4)) (not (>= (+ 6 (* (- 1) 4)) 1)) (>= (+ 6 4) 11)) false)) :rule trans :premises (t23 t24))
% 0.18/0.48 (step t26 (cl (= (=> (forall ((X Int) (Y Int)) (or (not (>= Y 4)) (not (>= (+ X (* (- 1) Y)) 1)) (>= (+ X Y) 11))) (or (not (>= 4 4)) (not (>= (+ 6 (* (- 1) 4)) 1)) (>= (+ 6 4) 11))) (=> (forall ((X Int) (Y Int)) (or (not (>= Y 4)) (not (>= (+ X (* (- 1) Y)) 1)) (>= (+ X Y) 11))) false))) :rule cong :premises (t2 t25))
% 0.18/0.48 (step t27 (cl (= (=> (forall ((X Int) (Y Int)) (or (not (>= Y 4)) (not (>= (+ X (* (- 1) Y)) 1)) (>= (+ X Y) 11))) false) (not (forall ((X Int) (Y Int)) (or (not (>= Y 4)) (not (>= (+ X (* (- 1) Y)) 1)) (>= (+ X Y) 11)))))) :rule all_simplify)
% 0.18/0.48 (step t28 (cl (= (=> (forall ((X Int) (Y Int)) (or (not (>= Y 4)) (not (>= (+ X (* (- 1) Y)) 1)) (>= (+ X Y) 11))) (or (not (>= 4 4)) (not (>= (+ 6 (* (- 1) 4)) 1)) (>= (+ 6 4) 11))) (not (forall ((X Int) (Y Int)) (or (not (>= Y 4)) (not (>= (+ X (* (- 1) Y)) 1)) (>= (+ X Y) 11)))))) :rule trans :premises (t26 t27))
% 0.18/0.48 (step t29 (cl (=> (forall ((X Int) (Y Int)) (or (not (>= Y 4)) (not (>= (+ X (* (- 1) Y)) 1)) (>= (+ X Y) 11))) (or (not (>= 4 4)) (not (>= (+ 6 (* (- 1) 4)) 1)) (>= (+ 6 4) 11))) (forall ((X Int) (Y Int)) (or (not (>= Y 4)) (not (>= (+ X (* (- 1) Y)) 1)) (>= (+ X Y) 11)))) :rule implies_neg1)
% 0.18/0.48 (anchor :step t30)
% 0.18/0.48 (assume t30.a0 (forall ((X Int) (Y Int)) (or (not (>= Y 4)) (not (>= (+ X (* (- 1) Y)) 1)) (>= (+ X Y) 11))))
% 0.18/0.48 (step t30.t1 (cl (or (not (forall ((X Int) (Y Int)) (or (not (>= Y 4)) (not (>= (+ X (* (- 1) Y)) 1)) (>= (+ X Y) 11)))) (or (not (>= 4 4)) (not (>= (+ 6 (* (- 1) 4)) 1)) (>= (+ 6 4) 11)))) :rule forall_inst :args ((:= X 6) (:= Y 4)))
% 0.18/0.48 (step t30.t2 (cl (not (forall ((X Int) (Y Int)) (or (not (>= Y 4)) (not (>= (+ X (* (- 1) Y)) 1)) (>= (+ X Y) 11)))) (or (not (>= 4 4)) (not (>= (+ 6 (* (- 1) 4)) 1)) (>= (+ 6 4) 11))) :rule or :premises (t30.t1))
% 0.18/0.48 (step t30.t3 (cl (or (not (>= 4 4)) (not (>= (+ 6 (* (- 1) 4)) 1)) (>= (+ 6 4) 11))) :rule resolution :premises (t30.t2 t30.a0))
% 0.18/0.48 (step t30 (cl (not (forall ((X Int) (Y Int)) (or (not (>= Y 4)) (not (>= (+ X (* (- 1) Y)) 1)) (>= (+ X Y) 11)))) (or (not (>= 4 4)) (not (>= (+ 6 (* (- 1) 4)) 1)) (>= (+ 6 4) 11))) :rule subproof :discharge (t30.a0))
% 0.18/0.48 (step t31 (cl (=> (forall ((X Int) (Y Int)) (or (not (>= Y 4)) (not (>= (+ X (* (- 1) Y)) 1)) (>= (+ X Y) 11))) (or (not (>= 4 4)) (not (>= (+ 6 (* (- 1) 4)) 1)) (>= (+ 6 4) 11))) (or (not (>= 4 4)) (not (>= (+ 6 (* (- 1) 4)) 1)) (>= (+ 6 4) 11))) :rule resolution :premises (t29 t30))
% 0.18/0.48 (step t32 (cl (=> (forall ((X Int) (Y Int)) (or (not (>= Y 4)) (not (>= (+ X (* (- 1) Y)) 1)) (>= (+ X Y) 11))) (or (not (>= 4 4)) (not (>= (+ 6 (* (- 1) 4)) 1)) (>= (+ 6 4) 11))) (not (or (not (>= 4 4)) (not (>= (+ 6 (* (- 1) 4)) 1)) (>= (+ 6 4) 11)))) :rule implies_neg2)
% 0.18/0.48 (step t33 (cl (=> (forall ((X Int) (Y Int)) (or (not (>= Y 4)) (not (>= (+ X (* (- 1) Y)) 1)) (>= (+ X Y) 11))) (or (not (>= 4 4)) (not (>= (+ 6 (* (- 1) 4)) 1)) (>= (+ 6 4) 11))) (=> (forall ((X Int) (Y Int)) (or (not (>= Y 4)) (not (>= (+ X (* (- 1) Y)) 1)) (>= (+ X Y) 11))) (or (not (>= 4 4)) (not (>= (+ 6 (* (- 1) 4)) 1)) (>= (+ 6 4) 11)))) :rule resolution :premises (t31 t32))
% 0.18/0.48 (step t34 (cl (=> (forall ((X Int) (Y Int)) (or (not (>= Y 4)) (not (>= (+ X (* (- 1) Y)) 1)) (>= (+ X Y) 11))) (or (not (>= 4 4)) (not (>= (+ 6 (* (- 1) 4)) 1)) (>= (+ 6 4) 11)))) :rule contraction :premises (t33))
% 0.18/0.48 (step t35 (cl (not (forall ((X Int) (Y Int)) (or (not (>= Y 4)) (not (>= (+ X (* (- 1) Y)) 1)) (>= (+ X Y) 11))))) :rule resolution :premises (t1 t28 t34))
% 0.18/0.48 (step t36 (cl (not (= (not (exists ((X Int) (Y Int)) (and (<= 4 Y) (<= (+ Y 1) X) (<= (+ X Y) 10)))) (forall ((X Int) (Y Int)) (or (not (>= Y 4)) (not (>= (+ X (* (- 1) Y)) 1)) (>= (+ X Y) 11))))) (not (not (exists ((X Int) (Y Int)) (and (<= 4 Y) (<= (+ Y 1) X) (<= (+ X Y) 10))))) (forall ((X Int) (Y Int)) (or (not (>= Y 4)) (not (>= (+ X (* (- 1) Y)) 1)) (>= (+ X Y) 11)))) :rule equiv_pos2)
% 0.18/0.48 (anchor :step t37 :args ((X Int) (:= X X) (Y Int) (:= Y Y)))
% 0.18/0.48 (step t37.t1 (cl (= X X)) :rule refl)
% 0.18/0.48 (step t37.t2 (cl (= Y Y)) :rule refl)
% 0.18/0.48 (step t37.t3 (cl (= (<= 4 Y) (>= Y 4))) :rule all_simplify)
% 0.18/0.48 (step t37.t4 (cl (= (+ Y 1) (+ 1 Y))) :rule all_simplify)
% 0.18/0.48 (step t37.t5 (cl (= X X)) :rule refl)
% 0.18/0.48 (step t37.t6 (cl (= (<= (+ Y 1) X) (<= (+ 1 Y) X))) :rule cong :premises (t37.t4 t37.t5))
% 0.18/0.48 (step t37.t7 (cl (= (<= (+ 1 Y) X) (>= (+ X (* (- 1) Y)) 1))) :rule all_simplify)
% 0.18/0.48 (step t37.t8 (cl (= (<= (+ Y 1) X) (>= (+ X (* (- 1) Y)) 1))) :rule trans :premises (t37.t6 t37.t7))
% 0.18/0.48 (step t37.t9 (cl (= (<= (+ X Y) 10) (not (>= (+ X Y) 11)))) :rule all_simplify)
% 0.18/0.48 (step t37.t10 (cl (= (and (<= 4 Y) (<= (+ Y 1) X) (<= (+ X Y) 10)) (and (>= Y 4) (>= (+ X (* (- 1) Y)) 1) (not (>= (+ X Y) 11))))) :rule cong :premises (t37.t3 t37.t8 t37.t9))
% 0.18/0.48 (step t37 (cl (= (exists ((X Int) (Y Int)) (and (<= 4 Y) (<= (+ Y 1) X) (<= (+ X Y) 10))) (exists ((X Int) (Y Int)) (and (>= Y 4) (>= (+ X (* (- 1) Y)) 1) (not (>= (+ X Y) 11)))))) :rule bind)
% 0.18/0.48 (step t38 (cl (= (exists ((X Int) (Y Int)) (and (>= Y 4) (>= (+ X (* (- 1) Y)) 1) (not (>= (+ X Y) 11)))) (not (forall ((X Int) (Y Int)) (not (and (>= Y 4) (>= (+ X (* (- 1) Y)) 1) (not (>= (+ X Y) 11)))))))) :rule all_simplify)
% 0.18/0.48 (step t39 (cl (= (forall ((X Int) (Y Int)) (not (and (>= Y 4) (>= (+ X (* (- 1) Y)) 1) (not (>= (+ X Y) 11))))) (forall ((X Int) (Y Int)) (or (not (>= Y 4)) (not (>= (+ X (* (- 1) Y)) 1)) (>= (+ X Y) 11))))) :rule all_simplify)
% 0.18/0.48 (step t40 (cl (= (not (forall ((X Int) (Y Int)) (not (and (>= Y 4) (>= (+ X (* (- 1) Y)) 1) (not (>= (+ X Y) 11)))))) (not (forall ((X Int) (Y Int)) (or (not (>= Y 4)) (not (>= (+ X (* (- 1) Y)) 1)) (>= (+ X Y) 11)))))) :rule cong :premises (t39))
% 0.18/0.48 (step t41 (cl (= (exists ((X Int) (Y Int)) (and (>= Y 4) (>= (+ X (* (- 1) Y)) 1) (not (>= (+ X Y) 11)))) (not (forall ((X Int) (Y Int)) (or (not (>= Y 4)) (not (>= (+ X (* (- 1) Y)) 1)) (>= (+ X Y) 11)))))) :rule trans :premises (t38 t40))
% 0.18/0.48 (step t42 (cl (= (exists ((X Int) (Y Int)) (and (<= 4 Y) (<= (+ Y 1) X) (<= (+ X Y) 10))) (not (forall ((X Int) (Y Int)) (or (not (>= Y 4)) (not (>= (+ X (* (- 1) Y)) 1)) (>= (+ X Y) 11)))))) :rule trans :premises (t37 t41))
% 0.18/0.48 (step t43 (cl (= (not (exists ((X Int) (Y Int)) (and (<= 4 Y) (<= (+ Y 1) X) (<= (+ X Y) 10)))) (not (not (forall ((X Int) (Y Int)) (or (not (>= Y 4)) (not (>= (+ X (* (- 1) Y)) 1)) (>= (+ X Y) 11))))))) :rule cong :premises (t42))
% 0.18/0.48 (step t44 (cl (= (not (not (forall ((X Int) (Y Int)) (or (not (>= Y 4)) (not (>= (+ X (* (- 1) Y)) 1)) (>= (+ X Y) 11))))) (forall ((X Int) (Y Int)) (or (not (>= Y 4)) (not (>= (+ X (* (- 1) Y)) 1)) (>= (+ X Y) 11))))) :rule all_simplify)
% 0.18/0.48 (step t45 (cl (= (not (exists ((X Int) (Y Int)) (and (<= 4 Y) (<= (+ Y 1) X) (<= (+ X Y) 10)))) (forall ((X Int) (Y Int)) (or (not (>= Y 4)) (not (>= (+ X (* (- 1) Y)) 1)) (>= (+ X Y) 11))))) :rule trans :premises (t43 t44))
% 0.18/0.48 (step t46 (cl (forall ((X Int) (Y Int)) (or (not (>= Y 4)) (not (>= (+ X (* (- 1) Y)) 1)) (>= (+ X Y) 11)))) :rule resolution :premises (t36 t45 a0))
% 0.18/0.48 (step t47 (cl) :rule resolution :premises (t35 t46))
% 0.18/0.48
% 0.18/0.48 % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.G3yajnQtsa/cvc5---1.0.5_27351.smt2
% 0.18/0.48 % cvc5---1.0.5 exiting
% 0.18/0.48 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------