TSTP Solution File: ARI742_1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ARI742_1 : TPTP v8.2.0. Released v7.0.0.
% 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 16:34:38 EDT 2024
% Result : Theorem 0.36s 0.54s
% Output : Proof 0.36s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ARI742_1 : TPTP v8.2.0. Released v7.0.0.
% 0.07/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n025.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon May 27 05:23:54 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.21/0.51 %----Proving TF0_ARI
% 0.36/0.54 --- Run --finite-model-find --decision=internal at 15...
% 0.36/0.54 % SZS status Theorem for /export/starexec/sandbox/tmp/tmp.uylLitBpxZ/cvc5---1.0.5_12135.smt2
% 0.36/0.54 % SZS output start Proof for /export/starexec/sandbox/tmp/tmp.uylLitBpxZ/cvc5---1.0.5_12135.smt2
% 0.36/0.54 (assume a0 (forall ((X Real)) (= (tptp.sqr X) (* X X))))
% 0.36/0.54 (assume a1 (forall ((X Real)) (=> (<= 0.0 X) (<= 0.0 (tptp.sqrt X)))))
% 0.36/0.54 (assume a2 (forall ((X Real)) (=> (<= 0.0 X) (= (tptp.sqr (tptp.sqrt X)) X))))
% 0.36/0.54 (assume a3 (forall ((X Real)) (=> (<= 0.0 X) (= (tptp.sqrt (* X X)) X))))
% 0.36/0.54 (assume a4 (forall ((X Real) (Y Real)) (=> (and (<= 0.0 X) (<= 0.0 Y)) (= (tptp.sqrt (* X Y)) (* (tptp.sqrt X) (tptp.sqrt Y))))))
% 0.36/0.54 (assume a5 (forall ((X Real) (Y Real)) (=> (and (<= 0.0 X) (<= X Y)) (<= (tptp.sqrt X) (tptp.sqrt Y)))))
% 0.36/0.54 (assume a6 (not (= (tptp.sqrt 0.0) 0.0)))
% 0.36/0.54 (assume a7 true)
% 0.36/0.54 (step t1 (cl (not (= (=> (forall ((X Real)) (or (not (>= X 0)) (= X (tptp.sqrt (* X X))))) (or (not (>= 0.0 0)) (= 0.0 (tptp.sqrt (* 0.0 0.0))))) (=> (forall ((X Real)) (or (not (>= X 0)) (= X (tptp.sqrt (* X X))))) (= (tptp.sqrt 0.0) 0.0)))) (not (=> (forall ((X Real)) (or (not (>= X 0)) (= X (tptp.sqrt (* X X))))) (or (not (>= 0.0 0)) (= 0.0 (tptp.sqrt (* 0.0 0.0)))))) (=> (forall ((X Real)) (or (not (>= X 0)) (= X (tptp.sqrt (* X X))))) (= (tptp.sqrt 0.0) 0.0))) :rule equiv_pos2)
% 0.36/0.54 (step t2 (cl (= (forall ((X Real)) (or (not (>= X 0)) (= X (tptp.sqrt (* X X))))) (forall ((X Real)) (or (not (>= X 0)) (= X (tptp.sqrt (* X X))))))) :rule refl)
% 0.36/0.54 (step t3 (cl (= (>= 0.0 0) true)) :rule all_simplify)
% 0.36/0.54 (step t4 (cl (= (not (>= 0.0 0)) (not true))) :rule cong :premises (t3))
% 0.36/0.54 (step t5 (cl (= (not true) false)) :rule all_simplify)
% 0.36/0.54 (step t6 (cl (= (not (>= 0.0 0)) false)) :rule trans :premises (t4 t5))
% 0.36/0.54 (step t7 (cl (= 0.0 0.0)) :rule refl)
% 0.36/0.54 (step t8 (cl (= (* 0.0 0.0) 0.0)) :rule all_simplify)
% 0.36/0.54 (step t9 (cl (= (tptp.sqrt (* 0.0 0.0)) (tptp.sqrt 0.0))) :rule cong :premises (t8))
% 0.36/0.54 (step t10 (cl (= (= 0.0 (tptp.sqrt (* 0.0 0.0))) (= 0.0 (tptp.sqrt 0.0)))) :rule cong :premises (t7 t9))
% 0.36/0.54 (step t11 (cl (= (= 0.0 (tptp.sqrt 0.0)) (= (tptp.sqrt 0.0) 0.0))) :rule all_simplify)
% 0.36/0.54 (step t12 (cl (= (= 0.0 (tptp.sqrt (* 0.0 0.0))) (= (tptp.sqrt 0.0) 0.0))) :rule trans :premises (t10 t11))
% 0.36/0.54 (step t13 (cl (= (or (not (>= 0.0 0)) (= 0.0 (tptp.sqrt (* 0.0 0.0)))) (or false (= (tptp.sqrt 0.0) 0.0)))) :rule cong :premises (t6 t12))
% 0.36/0.54 (step t14 (cl (= (or false (= (tptp.sqrt 0.0) 0.0)) (= (tptp.sqrt 0.0) 0.0))) :rule all_simplify)
% 0.36/0.54 (step t15 (cl (= (or (not (>= 0.0 0)) (= 0.0 (tptp.sqrt (* 0.0 0.0)))) (= (tptp.sqrt 0.0) 0.0))) :rule trans :premises (t13 t14))
% 0.36/0.54 (step t16 (cl (= (=> (forall ((X Real)) (or (not (>= X 0)) (= X (tptp.sqrt (* X X))))) (or (not (>= 0.0 0)) (= 0.0 (tptp.sqrt (* 0.0 0.0))))) (=> (forall ((X Real)) (or (not (>= X 0)) (= X (tptp.sqrt (* X X))))) (= (tptp.sqrt 0.0) 0.0)))) :rule cong :premises (t2 t15))
% 0.36/0.54 (step t17 (cl (=> (forall ((X Real)) (or (not (>= X 0)) (= X (tptp.sqrt (* X X))))) (or (not (>= 0.0 0)) (= 0.0 (tptp.sqrt (* 0.0 0.0))))) (forall ((X Real)) (or (not (>= X 0)) (= X (tptp.sqrt (* X X)))))) :rule implies_neg1)
% 0.36/0.54 (anchor :step t18)
% 0.36/0.54 (assume t18.a0 (forall ((X Real)) (or (not (>= X 0)) (= X (tptp.sqrt (* X X))))))
% 0.36/0.54 (step t18.t1 (cl (or (not (forall ((X Real)) (or (not (>= X 0)) (= X (tptp.sqrt (* X X)))))) (or (not (>= 0.0 0)) (= 0.0 (tptp.sqrt (* 0.0 0.0)))))) :rule forall_inst :args ((:= X 0.0)))
% 0.36/0.54 (step t18.t2 (cl (not (forall ((X Real)) (or (not (>= X 0)) (= X (tptp.sqrt (* X X)))))) (or (not (>= 0.0 0)) (= 0.0 (tptp.sqrt (* 0.0 0.0))))) :rule or :premises (t18.t1))
% 0.36/0.54 (step t18.t3 (cl (or (not (>= 0.0 0)) (= 0.0 (tptp.sqrt (* 0.0 0.0))))) :rule resolution :premises (t18.t2 t18.a0))
% 0.36/0.54 (step t18 (cl (not (forall ((X Real)) (or (not (>= X 0)) (= X (tptp.sqrt (* X X)))))) (or (not (>= 0.0 0)) (= 0.0 (tptp.sqrt (* 0.0 0.0))))) :rule subproof :discharge (t18.a0))
% 0.36/0.54 (step t19 (cl (=> (forall ((X Real)) (or (not (>= X 0)) (= X (tptp.sqrt (* X X))))) (or (not (>= 0.0 0)) (= 0.0 (tptp.sqrt (* 0.0 0.0))))) (or (not (>= 0.0 0)) (= 0.0 (tptp.sqrt (* 0.0 0.0))))) :rule resolution :premises (t17 t18))
% 0.36/0.54 (step t20 (cl (=> (forall ((X Real)) (or (not (>= X 0)) (= X (tptp.sqrt (* X X))))) (or (not (>= 0.0 0)) (= 0.0 (tptp.sqrt (* 0.0 0.0))))) (not (or (not (>= 0.0 0)) (= 0.0 (tptp.sqrt (* 0.0 0.0)))))) :rule implies_neg2)
% 0.36/0.54 (step t21 (cl (=> (forall ((X Real)) (or (not (>= X 0)) (= X (tptp.sqrt (* X X))))) (or (not (>= 0.0 0)) (= 0.0 (tptp.sqrt (* 0.0 0.0))))) (=> (forall ((X Real)) (or (not (>= X 0)) (= X (tptp.sqrt (* X X))))) (or (not (>= 0.0 0)) (= 0.0 (tptp.sqrt (* 0.0 0.0)))))) :rule resolution :premises (t19 t20))
% 0.36/0.54 (step t22 (cl (=> (forall ((X Real)) (or (not (>= X 0)) (= X (tptp.sqrt (* X X))))) (or (not (>= 0.0 0)) (= 0.0 (tptp.sqrt (* 0.0 0.0)))))) :rule contraction :premises (t21))
% 0.36/0.54 (step t23 (cl (=> (forall ((X Real)) (or (not (>= X 0)) (= X (tptp.sqrt (* X X))))) (= (tptp.sqrt 0.0) 0.0))) :rule resolution :premises (t1 t16 t22))
% 0.36/0.54 (step t24 (cl (not (forall ((X Real)) (or (not (>= X 0)) (= X (tptp.sqrt (* X X)))))) (= (tptp.sqrt 0.0) 0.0)) :rule implies :premises (t23))
% 0.36/0.54 (step t25 (cl (= (tptp.sqrt 0.0) 0.0) (not (forall ((X Real)) (or (not (>= X 0)) (= X (tptp.sqrt (* X X))))))) :rule reordering :premises (t24))
% 0.36/0.54 (step t26 (cl (not (= (forall ((X Real)) (=> (<= 0.0 X) (= (tptp.sqrt (* X X)) X))) (forall ((X Real)) (or (not (>= X 0)) (= X (tptp.sqrt (* X X))))))) (not (forall ((X Real)) (=> (<= 0.0 X) (= (tptp.sqrt (* X X)) X)))) (forall ((X Real)) (or (not (>= X 0)) (= X (tptp.sqrt (* X X)))))) :rule equiv_pos2)
% 0.36/0.54 (anchor :step t27 :args ((X Real) (:= X X)))
% 0.36/0.54 (step t27.t1 (cl (= X X)) :rule refl)
% 0.36/0.54 (step t27.t2 (cl (= (<= 0.0 X) (>= X 0))) :rule all_simplify)
% 0.36/0.54 (step t27.t3 (cl (= (* X X) (* X X))) :rule all_simplify)
% 0.36/0.54 (step t27.t4 (cl (= (tptp.sqrt (* X X)) (tptp.sqrt (* X X)))) :rule cong :premises (t27.t3))
% 0.36/0.54 (step t27.t5 (cl (= X X)) :rule refl)
% 0.36/0.54 (step t27.t6 (cl (= (= (tptp.sqrt (* X X)) X) (= (tptp.sqrt (* X X)) X))) :rule cong :premises (t27.t4 t27.t5))
% 0.36/0.54 (step t27.t7 (cl (= (= (tptp.sqrt (* X X)) X) (= X (tptp.sqrt (* X X))))) :rule all_simplify)
% 0.36/0.54 (step t27.t8 (cl (= (= (tptp.sqrt (* X X)) X) (= X (tptp.sqrt (* X X))))) :rule trans :premises (t27.t6 t27.t7))
% 0.36/0.54 (step t27.t9 (cl (= (=> (<= 0.0 X) (= (tptp.sqrt (* X X)) X)) (=> (>= X 0) (= X (tptp.sqrt (* X X)))))) :rule cong :premises (t27.t2 t27.t8))
% 0.36/0.54 (step t27 (cl (= (forall ((X Real)) (=> (<= 0.0 X) (= (tptp.sqrt (* X X)) X))) (forall ((X Real)) (=> (>= X 0) (= X (tptp.sqrt (* X X))))))) :rule bind)
% 0.36/0.54 (step t28 (cl (= (forall ((X Real)) (=> (>= X 0) (= X (tptp.sqrt (* X X))))) (forall ((X Real)) (or (not (>= X 0)) (= X (tptp.sqrt (* X X))))))) :rule all_simplify)
% 0.36/0.54 (step t29 (cl (= (forall ((X Real)) (=> (<= 0.0 X) (= (tptp.sqrt (* X X)) X))) (forall ((X Real)) (or (not (>= X 0)) (= X (tptp.sqrt (* X X))))))) :rule trans :premises (t27 t28))
% 0.36/0.54 (step t30 (cl (forall ((X Real)) (or (not (>= X 0)) (= X (tptp.sqrt (* X X)))))) :rule resolution :premises (t26 t29 a3))
% 0.36/0.54 (step t31 (cl) :rule resolution :premises (t25 a6 t30))
% 0.36/0.54
% 0.36/0.54 % SZS output end Proof for /export/starexec/sandbox/tmp/tmp.uylLitBpxZ/cvc5---1.0.5_12135.smt2
% 0.36/0.54 % cvc5---1.0.5 exiting
% 0.36/0.54 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------