TSTP Solution File: NUM489+3 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM489+3 : TPTP v8.2.0. Released v4.0.0.
% 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 17:33:42 EDT 2024
% Result : Theorem 0.35s 0.55s
% Output : Proof 0.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM489+3 : TPTP v8.2.0. Released v4.0.0.
% 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 : Tue May 28 03:19:39 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.20/0.51 %----Proving TF0_NAR, FOF, or CNF
% 0.35/0.55 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.35/0.55 % SZS status Theorem for /export/starexec/sandbox/tmp/tmp.YUrCaKtaOy/cvc5---1.0.5_14121.smt2
% 0.35/0.55 % SZS output start Proof for /export/starexec/sandbox/tmp/tmp.YUrCaKtaOy/cvc5---1.0.5_14121.smt2
% 0.35/0.55 (assume a0 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) true)))
% 0.35/0.55 (assume a1 (tptp.aNaturalNumber0 tptp.sz00))
% 0.35/0.55 (assume a2 (and (tptp.aNaturalNumber0 tptp.sz10) (not (= tptp.sz10 tptp.sz00))))
% 0.35/0.55 (assume a3 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))))
% 0.35/0.55 (assume a4 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))))
% 0.35/0.55 (assume a5 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W1 W0)))))
% 0.35/0.55 (assume a6 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (= (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 W0 (tptp.sdtpldt0 W1 W2))))))
% 0.35/0.55 (assume a7 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtpldt0 W0 tptp.sz00) W0) (= W0 (tptp.sdtpldt0 tptp.sz00 W0))))))
% 0.35/0.55 (assume a8 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))
% 0.35/0.55 (assume a9 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (= (tptp.sdtasdt0 (tptp.sdtasdt0 W0 W1) W2) (tptp.sdtasdt0 W0 (tptp.sdtasdt0 W1 W2))))))
% 0.35/0.55 (assume a10 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz10) W0) (= W0 (tptp.sdtasdt0 tptp.sz10 W0))))))
% 0.35/0.55 (assume a11 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 W0))))))
% 0.35/0.55 (assume a12 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (and (= (tptp.sdtasdt0 W0 (tptp.sdtpldt0 W1 W2)) (tptp.sdtpldt0 (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W0 W2))) (= (tptp.sdtasdt0 (tptp.sdtpldt0 W1 W2) W0) (tptp.sdtpldt0 (tptp.sdtasdt0 W1 W0) (tptp.sdtasdt0 W2 W0)))))))
% 0.35/0.55 (assume a13 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (or (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W0 W2)) (= (tptp.sdtpldt0 W1 W0) (tptp.sdtpldt0 W2 W0))) (= W1 W2)))))
% 0.35/0.55 (assume a14 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (=> (not (= W0 tptp.sz00)) (forall ((W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (or (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W0 W2)) (= (tptp.sdtasdt0 W1 W0) (tptp.sdtasdt0 W2 W0))) (= W1 W2))))))))
% 0.35/0.55 (assume a15 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (= (tptp.sdtpldt0 W0 W1) tptp.sz00) (and (= W0 tptp.sz00) (= W1 tptp.sz00))))))
% 0.35/0.55 (assume a16 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (= (tptp.sdtasdt0 W0 W1) tptp.sz00) (or (= W0 tptp.sz00) (= W1 tptp.sz00))))))
% 0.35/0.55 (assume a17 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtlseqdt0 W0 W1) (exists ((W2 $$unsorted)) (and (tptp.aNaturalNumber0 W2) (= (tptp.sdtpldt0 W0 W2) W1)))))))
% 0.35/0.55 (assume a18 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (tptp.sdtlseqdt0 W0 W1) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtmndt0 W1 W0)) (and (tptp.aNaturalNumber0 W2) (= (tptp.sdtpldt0 W0 W2) W1))))))))
% 0.35/0.55 (assume a19 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (tptp.sdtlseqdt0 W0 W0))))
% 0.35/0.55 (assume a20 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W0)) (= W0 W1)))))
% 0.35/0.55 (assume a21 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W2)) (tptp.sdtlseqdt0 W0 W2)))))
% 0.35/0.55 (assume a22 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (or (tptp.sdtlseqdt0 W0 W1) (and (not (= W1 W0)) (tptp.sdtlseqdt0 W1 W0))))))
% 0.35/0.55 (assume a23 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 W1)) (tptp.sdtlseqdt0 W0 W1)) (forall ((W2 $$unsorted)) (=> (tptp.aNaturalNumber0 W2) (and (not (= (tptp.sdtpldt0 W2 W0) (tptp.sdtpldt0 W2 W1))) (tptp.sdtlseqdt0 (tptp.sdtpldt0 W2 W0) (tptp.sdtpldt0 W2 W1)) (not (= (tptp.sdtpldt0 W0 W2) (tptp.sdtpldt0 W1 W2))) (tptp.sdtlseqdt0 (tptp.sdtpldt0 W0 W2) (tptp.sdtpldt0 W1 W2)))))))))
% 0.35/0.55 (assume a24 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (not (= W0 tptp.sz00)) (not (= W1 W2)) (tptp.sdtlseqdt0 W1 W2)) (and (not (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W0 W2))) (tptp.sdtlseqdt0 (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W0 W2)) (not (= (tptp.sdtasdt0 W1 W0) (tptp.sdtasdt0 W2 W0))) (tptp.sdtlseqdt0 (tptp.sdtasdt0 W1 W0) (tptp.sdtasdt0 W2 W0)))))))
% 0.35/0.55 (assume a25 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (or (= W0 tptp.sz00) (= W0 tptp.sz10) (and (not (= tptp.sz10 W0)) (tptp.sdtlseqdt0 tptp.sz10 W0))))))
% 0.35/0.55 (assume a26 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (not (= W0 tptp.sz00)) (tptp.sdtlseqdt0 W1 (tptp.sdtasdt0 W1 W0))))))
% 0.35/0.55 (assume a27 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (tptp.iLess0 W0 W1) true))))
% 0.35/0.55 (assume a28 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 W1)) (tptp.sdtlseqdt0 W0 W1)) (tptp.iLess0 W0 W1)))))
% 0.35/0.55 (assume a29 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.doDivides0 W0 W1) (exists ((W2 $$unsorted)) (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtasdt0 W0 W2))))))))
% 0.35/0.55 (assume a30 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 tptp.sz00)) (tptp.doDivides0 W0 W1)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtsldt0 W1 W0)) (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtasdt0 W0 W2)))))))))
% 0.35/0.55 (assume a31 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.doDivides0 W0 W1) (tptp.doDivides0 W1 W2)) (tptp.doDivides0 W0 W2)))))
% 0.35/0.55 (assume a32 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.doDivides0 W0 W1) (tptp.doDivides0 W0 W2)) (tptp.doDivides0 W0 (tptp.sdtpldt0 W1 W2))))))
% 0.35/0.55 (assume a33 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.doDivides0 W0 W1) (tptp.doDivides0 W0 (tptp.sdtpldt0 W1 W2))) (tptp.doDivides0 W0 W2)))))
% 0.35/0.55 (assume a34 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (tptp.doDivides0 W0 W1) (not (= W1 tptp.sz00))) (tptp.sdtlseqdt0 W0 W1)))))
% 0.35/0.55 (assume a35 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 tptp.sz00)) (tptp.doDivides0 W0 W1)) (forall ((W2 $$unsorted)) (=> (tptp.aNaturalNumber0 W2) (= (tptp.sdtasdt0 W2 (tptp.sdtsldt0 W1 W0)) (tptp.sdtsldt0 (tptp.sdtasdt0 W2 W1) W0))))))))
% 0.35/0.55 (assume a36 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (= (tptp.isPrime0 W0) (and (not (= W0 tptp.sz00)) (not (= W0 tptp.sz10)) (forall ((W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W1) (tptp.doDivides0 W1 W0)) (or (= W1 tptp.sz10) (= W1 W0)))))))))
% 0.35/0.55 (assume a37 (forall ((W0 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (not (= W0 tptp.sz00)) (not (= W0 tptp.sz10))) (exists ((W1 $$unsorted)) (and (tptp.aNaturalNumber0 W1) (tptp.doDivides0 W1 W0) (tptp.isPrime0 W1))))))
% 0.35/0.55 (assume a38 (and (tptp.aNaturalNumber0 tptp.xn) (tptp.aNaturalNumber0 tptp.xm) (tptp.aNaturalNumber0 tptp.xp)))
% 0.35/0.55 (assume a39 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (or (and (not (= W2 tptp.sz00)) (not (= W2 tptp.sz10)) (forall ((W3 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W3) (exists ((W4 $$unsorted)) (and (tptp.aNaturalNumber0 W4) (= W2 (tptp.sdtasdt0 W3 W4)))) (tptp.doDivides0 W3 W2)) (or (= W3 tptp.sz10) (= W3 W2))))) (tptp.isPrime0 W2)) (or (exists ((W3 $$unsorted)) (and (tptp.aNaturalNumber0 W3) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W2 W3)))) (tptp.doDivides0 W2 (tptp.sdtasdt0 W0 W1)))) (=> (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)) (or (and (exists ((W3 $$unsorted)) (and (tptp.aNaturalNumber0 W3) (= W0 (tptp.sdtasdt0 W2 W3)))) (tptp.doDivides0 W2 W0)) (and (exists ((W3 $$unsorted)) (and (tptp.aNaturalNumber0 W3) (= W1 (tptp.sdtasdt0 W2 W3)))) (tptp.doDivides0 W2 W1))))))))
% 0.35/0.55 (assume a40 (and (not (= tptp.xp tptp.sz00)) (not (= tptp.xp tptp.sz10)) (forall ((W0 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (or (exists ((W1 $$unsorted)) (and (tptp.aNaturalNumber0 W1) (= tptp.xp (tptp.sdtasdt0 W0 W1)))) (tptp.doDivides0 W0 tptp.xp))) (or (= W0 tptp.sz10) (= W0 tptp.xp)))) (tptp.isPrime0 tptp.xp) (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtasdt0 tptp.xn tptp.xm) (tptp.sdtasdt0 tptp.xp W0)))) (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xm))))
% 0.35/0.55 (assume a41 (and (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 tptp.xp W0) tptp.xn))) (tptp.sdtlseqdt0 tptp.xp tptp.xn)))
% 0.35/0.55 (assume a42 (and (tptp.aNaturalNumber0 tptp.xr) (= (tptp.sdtpldt0 tptp.xp tptp.xr) tptp.xn) (= tptp.xr (tptp.sdtmndt0 tptp.xn tptp.xp))))
% 0.35/0.55 (assume a43 (and (not (= tptp.xr tptp.xn)) (exists ((W0 $$unsorted)) (and (tptp.aNaturalNumber0 W0) (= (tptp.sdtpldt0 tptp.xr W0) tptp.xn))) (tptp.sdtlseqdt0 tptp.xr tptp.xn)))
% 0.35/0.55 (assume a44 (not (= tptp.xn (tptp.sdtpldt0 tptp.xp tptp.xr))))
% 0.35/0.55 (assume a45 true)
% 0.35/0.55 (step t1 (cl (not (= (and (tptp.aNaturalNumber0 tptp.xr) (= (tptp.sdtpldt0 tptp.xp tptp.xr) tptp.xn) (= tptp.xr (tptp.sdtmndt0 tptp.xn tptp.xp))) (and (tptp.aNaturalNumber0 tptp.xr) (= tptp.xn (tptp.sdtpldt0 tptp.xp tptp.xr)) (= tptp.xr (tptp.sdtmndt0 tptp.xn tptp.xp))))) (not (and (tptp.aNaturalNumber0 tptp.xr) (= (tptp.sdtpldt0 tptp.xp tptp.xr) tptp.xn) (= tptp.xr (tptp.sdtmndt0 tptp.xn tptp.xp)))) (and (tptp.aNaturalNumber0 tptp.xr) (= tptp.xn (tptp.sdtpldt0 tptp.xp tptp.xr)) (= tptp.xr (tptp.sdtmndt0 tptp.xn tptp.xp)))) :rule equiv_pos2)
% 0.35/0.55 (step t2 (cl (= (tptp.aNaturalNumber0 tptp.xr) (tptp.aNaturalNumber0 tptp.xr))) :rule refl)
% 0.35/0.55 (step t3 (cl (= (= (tptp.sdtpldt0 tptp.xp tptp.xr) tptp.xn) (= tptp.xn (tptp.sdtpldt0 tptp.xp tptp.xr)))) :rule all_simplify)
% 0.35/0.55 (step t4 (cl (= (= tptp.xr (tptp.sdtmndt0 tptp.xn tptp.xp)) (= tptp.xr (tptp.sdtmndt0 tptp.xn tptp.xp)))) :rule refl)
% 0.35/0.55 (step t5 (cl (= (and (tptp.aNaturalNumber0 tptp.xr) (= (tptp.sdtpldt0 tptp.xp tptp.xr) tptp.xn) (= tptp.xr (tptp.sdtmndt0 tptp.xn tptp.xp))) (and (tptp.aNaturalNumber0 tptp.xr) (= tptp.xn (tptp.sdtpldt0 tptp.xp tptp.xr)) (= tptp.xr (tptp.sdtmndt0 tptp.xn tptp.xp))))) :rule cong :premises (t2 t3 t4))
% 0.35/0.55 (step t6 (cl (and (tptp.aNaturalNumber0 tptp.xr) (= tptp.xn (tptp.sdtpldt0 tptp.xp tptp.xr)) (= tptp.xr (tptp.sdtmndt0 tptp.xn tptp.xp)))) :rule resolution :premises (t1 t5 a42))
% 0.35/0.55 (step t7 (cl (= tptp.xn (tptp.sdtpldt0 tptp.xp tptp.xr))) :rule and :premises (t6))
% 0.35/0.55 (step t8 (cl) :rule resolution :premises (a44 t7))
% 0.35/0.56
% 0.35/0.56 % SZS output end Proof for /export/starexec/sandbox/tmp/tmp.YUrCaKtaOy/cvc5---1.0.5_14121.smt2
% 0.35/0.56 % cvc5---1.0.5 exiting
% 0.35/0.56 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------