TSTP Solution File: ARI578_1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ARI578_1 : TPTP v8.2.0. Released v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n009.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 0.19s 0.51s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : ARI578_1 : TPTP v8.2.0. Released v5.1.0.
% 0.14/0.14 % Command : do_cvc5 %s %d
% 0.14/0.34 % Computer : n009.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon May 27 05:08:08 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.19/0.49 %----Proving TF0_ARI
% 0.19/0.51 --- Run --finite-model-find --decision=internal at 15...
% 0.19/0.51 % SZS status Theorem for /export/starexec/sandbox/tmp/tmp.RFLoPDnYWC/cvc5---1.0.5_819.smt2
% 0.19/0.51 % SZS output start Proof for /export/starexec/sandbox/tmp/tmp.RFLoPDnYWC/cvc5---1.0.5_819.smt2
% 0.19/0.51 (assume a0 (not (exists ((X Int) (Y Int)) (and (<= 2 X) (<= 2 Y) (<= (+ X Y) 9) (<= 12 (+ (* 2 X) Y))))))
% 0.19/0.51 (assume a1 true)
% 0.19/0.51 (step t1 (cl (not (= (=> (forall ((X Int) (Y Int)) (or (not (>= X 2)) (not (>= Y 2)) (>= (+ X Y) 10) (not (>= (+ (* 2 X) Y) 12)))) (or (not (>= 7 2)) (not (>= 2 2)) (>= (+ 7 2) 10) (not (>= (+ (* 2 7) 2) 12)))) (not (forall ((X Int) (Y Int)) (or (not (>= X 2)) (not (>= Y 2)) (>= (+ X Y) 10) (not (>= (+ (* 2 X) Y) 12))))))) (not (=> (forall ((X Int) (Y Int)) (or (not (>= X 2)) (not (>= Y 2)) (>= (+ X Y) 10) (not (>= (+ (* 2 X) Y) 12)))) (or (not (>= 7 2)) (not (>= 2 2)) (>= (+ 7 2) 10) (not (>= (+ (* 2 7) 2) 12))))) (not (forall ((X Int) (Y Int)) (or (not (>= X 2)) (not (>= Y 2)) (>= (+ X Y) 10) (not (>= (+ (* 2 X) Y) 12)))))) :rule equiv_pos2)
% 0.19/0.51 (step t2 (cl (= (forall ((X Int) (Y Int)) (or (not (>= X 2)) (not (>= Y 2)) (>= (+ X Y) 10) (not (>= (+ (* 2 X) Y) 12)))) (forall ((X Int) (Y Int)) (or (not (>= X 2)) (not (>= Y 2)) (>= (+ X Y) 10) (not (>= (+ (* 2 X) Y) 12)))))) :rule refl)
% 0.19/0.51 (step t3 (cl (= (>= 7 2) true)) :rule all_simplify)
% 0.19/0.51 (step t4 (cl (= (not (>= 7 2)) (not true))) :rule cong :premises (t3))
% 0.19/0.51 (step t5 (cl (= (not true) false)) :rule all_simplify)
% 0.19/0.51 (step t6 (cl (= (not (>= 7 2)) false)) :rule trans :premises (t4 t5))
% 0.19/0.51 (step t7 (cl (= (>= 2 2) true)) :rule all_simplify)
% 0.19/0.51 (step t8 (cl (= (not (>= 2 2)) (not true))) :rule cong :premises (t7))
% 0.19/0.51 (step t9 (cl (= (not (>= 2 2)) false)) :rule trans :premises (t8 t5))
% 0.19/0.51 (step t10 (cl (= (+ 7 2) 9)) :rule all_simplify)
% 0.19/0.51 (step t11 (cl (= 10 10)) :rule refl)
% 0.19/0.51 (step t12 (cl (= (>= (+ 7 2) 10) (>= 9 10))) :rule cong :premises (t10 t11))
% 0.19/0.51 (step t13 (cl (= (>= 9 10) false)) :rule all_simplify)
% 0.19/0.51 (step t14 (cl (= (>= (+ 7 2) 10) false)) :rule trans :premises (t12 t13))
% 0.19/0.51 (step t15 (cl (= (* 2 7) 14)) :rule all_simplify)
% 0.19/0.51 (step t16 (cl (= 2 2)) :rule refl)
% 0.19/0.51 (step t17 (cl (= (+ (* 2 7) 2) (+ 14 2))) :rule cong :premises (t15 t16))
% 0.19/0.51 (step t18 (cl (= (+ 14 2) 16)) :rule all_simplify)
% 0.19/0.51 (step t19 (cl (= (+ (* 2 7) 2) 16)) :rule trans :premises (t17 t18))
% 0.19/0.51 (step t20 (cl (= 12 12)) :rule refl)
% 0.19/0.51 (step t21 (cl (= (>= (+ (* 2 7) 2) 12) (>= 16 12))) :rule cong :premises (t19 t20))
% 0.19/0.51 (step t22 (cl (= (>= 16 12) true)) :rule all_simplify)
% 0.19/0.51 (step t23 (cl (= (>= (+ (* 2 7) 2) 12) true)) :rule trans :premises (t21 t22))
% 0.19/0.51 (step t24 (cl (= (not (>= (+ (* 2 7) 2) 12)) (not true))) :rule cong :premises (t23))
% 0.19/0.51 (step t25 (cl (= (not (>= (+ (* 2 7) 2) 12)) false)) :rule trans :premises (t24 t5))
% 0.19/0.51 (step t26 (cl (= (or (not (>= 7 2)) (not (>= 2 2)) (>= (+ 7 2) 10) (not (>= (+ (* 2 7) 2) 12))) (or false false false false))) :rule cong :premises (t6 t9 t14 t25))
% 0.19/0.51 (step t27 (cl (= (or false false false false) false)) :rule all_simplify)
% 0.19/0.51 (step t28 (cl (= (or (not (>= 7 2)) (not (>= 2 2)) (>= (+ 7 2) 10) (not (>= (+ (* 2 7) 2) 12))) false)) :rule trans :premises (t26 t27))
% 0.19/0.51 (step t29 (cl (= (=> (forall ((X Int) (Y Int)) (or (not (>= X 2)) (not (>= Y 2)) (>= (+ X Y) 10) (not (>= (+ (* 2 X) Y) 12)))) (or (not (>= 7 2)) (not (>= 2 2)) (>= (+ 7 2) 10) (not (>= (+ (* 2 7) 2) 12)))) (=> (forall ((X Int) (Y Int)) (or (not (>= X 2)) (not (>= Y 2)) (>= (+ X Y) 10) (not (>= (+ (* 2 X) Y) 12)))) false))) :rule cong :premises (t2 t28))
% 0.19/0.51 (step t30 (cl (= (=> (forall ((X Int) (Y Int)) (or (not (>= X 2)) (not (>= Y 2)) (>= (+ X Y) 10) (not (>= (+ (* 2 X) Y) 12)))) false) (not (forall ((X Int) (Y Int)) (or (not (>= X 2)) (not (>= Y 2)) (>= (+ X Y) 10) (not (>= (+ (* 2 X) Y) 12))))))) :rule all_simplify)
% 0.19/0.51 (step t31 (cl (= (=> (forall ((X Int) (Y Int)) (or (not (>= X 2)) (not (>= Y 2)) (>= (+ X Y) 10) (not (>= (+ (* 2 X) Y) 12)))) (or (not (>= 7 2)) (not (>= 2 2)) (>= (+ 7 2) 10) (not (>= (+ (* 2 7) 2) 12)))) (not (forall ((X Int) (Y Int)) (or (not (>= X 2)) (not (>= Y 2)) (>= (+ X Y) 10) (not (>= (+ (* 2 X) Y) 12))))))) :rule trans :premises (t29 t30))
% 0.19/0.51 (step t32 (cl (=> (forall ((X Int) (Y Int)) (or (not (>= X 2)) (not (>= Y 2)) (>= (+ X Y) 10) (not (>= (+ (* 2 X) Y) 12)))) (or (not (>= 7 2)) (not (>= 2 2)) (>= (+ 7 2) 10) (not (>= (+ (* 2 7) 2) 12)))) (forall ((X Int) (Y Int)) (or (not (>= X 2)) (not (>= Y 2)) (>= (+ X Y) 10) (not (>= (+ (* 2 X) Y) 12))))) :rule implies_neg1)
% 0.19/0.51 (anchor :step t33)
% 0.19/0.51 (assume t33.a0 (forall ((X Int) (Y Int)) (or (not (>= X 2)) (not (>= Y 2)) (>= (+ X Y) 10) (not (>= (+ (* 2 X) Y) 12)))))
% 0.19/0.51 (step t33.t1 (cl (or (not (forall ((X Int) (Y Int)) (or (not (>= X 2)) (not (>= Y 2)) (>= (+ X Y) 10) (not (>= (+ (* 2 X) Y) 12))))) (or (not (>= 7 2)) (not (>= 2 2)) (>= (+ 7 2) 10) (not (>= (+ (* 2 7) 2) 12))))) :rule forall_inst :args ((:= X 7) (:= Y 2)))
% 0.19/0.51 (step t33.t2 (cl (not (forall ((X Int) (Y Int)) (or (not (>= X 2)) (not (>= Y 2)) (>= (+ X Y) 10) (not (>= (+ (* 2 X) Y) 12))))) (or (not (>= 7 2)) (not (>= 2 2)) (>= (+ 7 2) 10) (not (>= (+ (* 2 7) 2) 12)))) :rule or :premises (t33.t1))
% 0.19/0.51 (step t33.t3 (cl (or (not (>= 7 2)) (not (>= 2 2)) (>= (+ 7 2) 10) (not (>= (+ (* 2 7) 2) 12)))) :rule resolution :premises (t33.t2 t33.a0))
% 0.19/0.51 (step t33 (cl (not (forall ((X Int) (Y Int)) (or (not (>= X 2)) (not (>= Y 2)) (>= (+ X Y) 10) (not (>= (+ (* 2 X) Y) 12))))) (or (not (>= 7 2)) (not (>= 2 2)) (>= (+ 7 2) 10) (not (>= (+ (* 2 7) 2) 12)))) :rule subproof :discharge (t33.a0))
% 0.19/0.51 (step t34 (cl (=> (forall ((X Int) (Y Int)) (or (not (>= X 2)) (not (>= Y 2)) (>= (+ X Y) 10) (not (>= (+ (* 2 X) Y) 12)))) (or (not (>= 7 2)) (not (>= 2 2)) (>= (+ 7 2) 10) (not (>= (+ (* 2 7) 2) 12)))) (or (not (>= 7 2)) (not (>= 2 2)) (>= (+ 7 2) 10) (not (>= (+ (* 2 7) 2) 12)))) :rule resolution :premises (t32 t33))
% 0.19/0.51 (step t35 (cl (=> (forall ((X Int) (Y Int)) (or (not (>= X 2)) (not (>= Y 2)) (>= (+ X Y) 10) (not (>= (+ (* 2 X) Y) 12)))) (or (not (>= 7 2)) (not (>= 2 2)) (>= (+ 7 2) 10) (not (>= (+ (* 2 7) 2) 12)))) (not (or (not (>= 7 2)) (not (>= 2 2)) (>= (+ 7 2) 10) (not (>= (+ (* 2 7) 2) 12))))) :rule implies_neg2)
% 0.19/0.51 (step t36 (cl (=> (forall ((X Int) (Y Int)) (or (not (>= X 2)) (not (>= Y 2)) (>= (+ X Y) 10) (not (>= (+ (* 2 X) Y) 12)))) (or (not (>= 7 2)) (not (>= 2 2)) (>= (+ 7 2) 10) (not (>= (+ (* 2 7) 2) 12)))) (=> (forall ((X Int) (Y Int)) (or (not (>= X 2)) (not (>= Y 2)) (>= (+ X Y) 10) (not (>= (+ (* 2 X) Y) 12)))) (or (not (>= 7 2)) (not (>= 2 2)) (>= (+ 7 2) 10) (not (>= (+ (* 2 7) 2) 12))))) :rule resolution :premises (t34 t35))
% 0.19/0.51 (step t37 (cl (=> (forall ((X Int) (Y Int)) (or (not (>= X 2)) (not (>= Y 2)) (>= (+ X Y) 10) (not (>= (+ (* 2 X) Y) 12)))) (or (not (>= 7 2)) (not (>= 2 2)) (>= (+ 7 2) 10) (not (>= (+ (* 2 7) 2) 12))))) :rule contraction :premises (t36))
% 0.19/0.51 (step t38 (cl (not (forall ((X Int) (Y Int)) (or (not (>= X 2)) (not (>= Y 2)) (>= (+ X Y) 10) (not (>= (+ (* 2 X) Y) 12)))))) :rule resolution :premises (t1 t31 t37))
% 0.19/0.51 (step t39 (cl (not (= (not (exists ((X Int) (Y Int)) (and (<= 2 X) (<= 2 Y) (<= (+ X Y) 9) (<= 12 (+ (* 2 X) Y))))) (forall ((X Int) (Y Int)) (or (not (>= X 2)) (not (>= Y 2)) (>= (+ X Y) 10) (not (>= (+ (* 2 X) Y) 12)))))) (not (not (exists ((X Int) (Y Int)) (and (<= 2 X) (<= 2 Y) (<= (+ X Y) 9) (<= 12 (+ (* 2 X) Y)))))) (forall ((X Int) (Y Int)) (or (not (>= X 2)) (not (>= Y 2)) (>= (+ X Y) 10) (not (>= (+ (* 2 X) Y) 12))))) :rule equiv_pos2)
% 0.19/0.51 (anchor :step t40 :args ((X Int) (:= X X) (Y Int) (:= Y Y)))
% 0.19/0.51 (step t40.t1 (cl (= X X)) :rule refl)
% 0.19/0.51 (step t40.t2 (cl (= Y Y)) :rule refl)
% 0.19/0.51 (step t40.t3 (cl (= (<= 2 X) (>= X 2))) :rule all_simplify)
% 0.19/0.51 (step t40.t4 (cl (= (<= 2 Y) (>= Y 2))) :rule all_simplify)
% 0.19/0.51 (step t40.t5 (cl (= (<= (+ X Y) 9) (not (>= (+ X Y) 10)))) :rule all_simplify)
% 0.19/0.51 (step t40.t6 (cl (= (<= 12 (+ (* 2 X) Y)) (>= (+ (* 2 X) Y) 12))) :rule all_simplify)
% 0.19/0.51 (step t40.t7 (cl (= (and (<= 2 X) (<= 2 Y) (<= (+ X Y) 9) (<= 12 (+ (* 2 X) Y))) (and (>= X 2) (>= Y 2) (not (>= (+ X Y) 10)) (>= (+ (* 2 X) Y) 12)))) :rule cong :premises (t40.t3 t40.t4 t40.t5 t40.t6))
% 0.19/0.51 (step t40 (cl (= (exists ((X Int) (Y Int)) (and (<= 2 X) (<= 2 Y) (<= (+ X Y) 9) (<= 12 (+ (* 2 X) Y)))) (exists ((X Int) (Y Int)) (and (>= X 2) (>= Y 2) (not (>= (+ X Y) 10)) (>= (+ (* 2 X) Y) 12))))) :rule bind)
% 0.19/0.51 (step t41 (cl (= (exists ((X Int) (Y Int)) (and (>= X 2) (>= Y 2) (not (>= (+ X Y) 10)) (>= (+ (* 2 X) Y) 12))) (not (forall ((X Int) (Y Int)) (not (and (>= X 2) (>= Y 2) (not (>= (+ X Y) 10)) (>= (+ (* 2 X) Y) 12))))))) :rule all_simplify)
% 0.19/0.52 (step t42 (cl (= (forall ((X Int) (Y Int)) (not (and (>= X 2) (>= Y 2) (not (>= (+ X Y) 10)) (>= (+ (* 2 X) Y) 12)))) (forall ((X Int) (Y Int)) (or (not (>= X 2)) (not (>= Y 2)) (>= (+ X Y) 10) (not (>= (+ (* 2 X) Y) 12)))))) :rule all_simplify)
% 0.19/0.52 (step t43 (cl (= (not (forall ((X Int) (Y Int)) (not (and (>= X 2) (>= Y 2) (not (>= (+ X Y) 10)) (>= (+ (* 2 X) Y) 12))))) (not (forall ((X Int) (Y Int)) (or (not (>= X 2)) (not (>= Y 2)) (>= (+ X Y) 10) (not (>= (+ (* 2 X) Y) 12))))))) :rule cong :premises (t42))
% 0.19/0.52 (step t44 (cl (= (exists ((X Int) (Y Int)) (and (>= X 2) (>= Y 2) (not (>= (+ X Y) 10)) (>= (+ (* 2 X) Y) 12))) (not (forall ((X Int) (Y Int)) (or (not (>= X 2)) (not (>= Y 2)) (>= (+ X Y) 10) (not (>= (+ (* 2 X) Y) 12))))))) :rule trans :premises (t41 t43))
% 0.19/0.52 (step t45 (cl (= (exists ((X Int) (Y Int)) (and (<= 2 X) (<= 2 Y) (<= (+ X Y) 9) (<= 12 (+ (* 2 X) Y)))) (not (forall ((X Int) (Y Int)) (or (not (>= X 2)) (not (>= Y 2)) (>= (+ X Y) 10) (not (>= (+ (* 2 X) Y) 12))))))) :rule trans :premises (t40 t44))
% 0.19/0.52 (step t46 (cl (= (not (exists ((X Int) (Y Int)) (and (<= 2 X) (<= 2 Y) (<= (+ X Y) 9) (<= 12 (+ (* 2 X) Y))))) (not (not (forall ((X Int) (Y Int)) (or (not (>= X 2)) (not (>= Y 2)) (>= (+ X Y) 10) (not (>= (+ (* 2 X) Y) 12)))))))) :rule cong :premises (t45))
% 0.19/0.52 (step t47 (cl (= (not (not (forall ((X Int) (Y Int)) (or (not (>= X 2)) (not (>= Y 2)) (>= (+ X Y) 10) (not (>= (+ (* 2 X) Y) 12)))))) (forall ((X Int) (Y Int)) (or (not (>= X 2)) (not (>= Y 2)) (>= (+ X Y) 10) (not (>= (+ (* 2 X) Y) 12)))))) :rule all_simplify)
% 0.19/0.52 (step t48 (cl (= (not (exists ((X Int) (Y Int)) (and (<= 2 X) (<= 2 Y) (<= (+ X Y) 9) (<= 12 (+ (* 2 X) Y))))) (forall ((X Int) (Y Int)) (or (not (>= X 2)) (not (>= Y 2)) (>= (+ X Y) 10) (not (>= (+ (* 2 X) Y) 12)))))) :rule trans :premises (t46 t47))
% 0.19/0.52 (step t49 (cl (forall ((X Int) (Y Int)) (or (not (>= X 2)) (not (>= Y 2)) (>= (+ X Y) 10) (not (>= (+ (* 2 X) Y) 12))))) :rule resolution :premises (t39 t48 a0))
% 0.19/0.52 (step t50 (cl) :rule resolution :premises (t38 t49))
% 0.19/0.52
% 0.19/0.52 % SZS output end Proof for /export/starexec/sandbox/tmp/tmp.RFLoPDnYWC/cvc5---1.0.5_819.smt2
% 0.19/0.52 % cvc5---1.0.5 exiting
% 0.19/0.52 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------