TSTP Solution File: RNG124+1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : RNG124+1 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n013.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 17:42:04 EDT 2024
% Result : Theorem 0.35s 0.58s
% Output : Proof 0.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : RNG124+1 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.15 % Command : do_cvc5 %s %d
% 0.14/0.36 % Computer : n013.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat May 25 21:51:09 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.21/0.50 %----Proving TF0_NAR, FOF, or CNF
% 0.35/0.58 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.35/0.58 % SZS status Theorem for /export/starexec/sandbox2/tmp/tmp.B8v1mUFnAU/cvc5---1.0.5_18003.smt2
% 0.35/0.58 % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.B8v1mUFnAU/cvc5---1.0.5_18003.smt2
% 0.35/0.58 (assume a0 (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) true)))
% 0.35/0.58 (assume a1 (tptp.aElement0 tptp.sz00))
% 0.35/0.58 (assume a2 (tptp.aElement0 tptp.sz10))
% 0.35/0.58 (assume a3 (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (tptp.aElement0 (tptp.smndt0 W0)))))
% 0.35/0.58 (assume a4 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtpldt0 W0 W1)))))
% 0.35/0.58 (assume a5 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtasdt0 W0 W1)))))
% 0.35/0.58 (assume a6 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W1 W0)))))
% 0.35/0.58 (assume a7 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1) (tptp.aElement0 W2)) (= (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 W0 (tptp.sdtpldt0 W1 W2))))))
% 0.35/0.58 (assume a8 (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (and (= (tptp.sdtpldt0 W0 tptp.sz00) W0) (= W0 (tptp.sdtpldt0 tptp.sz00 W0))))))
% 0.35/0.58 (assume a9 (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (and (= (tptp.sdtpldt0 W0 (tptp.smndt0 W0)) tptp.sz00) (= tptp.sz00 (tptp.sdtpldt0 (tptp.smndt0 W0) W0))))))
% 0.35/0.58 (assume a10 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))
% 0.35/0.58 (assume a11 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1) (tptp.aElement0 W2)) (= (tptp.sdtasdt0 (tptp.sdtasdt0 W0 W1) W2) (tptp.sdtasdt0 W0 (tptp.sdtasdt0 W1 W2))))))
% 0.35/0.58 (assume a12 (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz10) W0) (= W0 (tptp.sdtasdt0 tptp.sz10 W0))))))
% 0.35/0.58 (assume a13 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1) (tptp.aElement0 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)))))))
% 0.35/0.58 (assume a14 (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (and (= (tptp.sdtasdt0 (tptp.smndt0 tptp.sz10) W0) (tptp.smndt0 W0)) (= (tptp.smndt0 W0) (tptp.sdtasdt0 W0 (tptp.smndt0 tptp.sz10)))))))
% 0.35/0.58 (assume a15 (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 W0))))))
% 0.35/0.58 (assume a16 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (=> (= (tptp.sdtasdt0 W0 W1) tptp.sz00) (or (= W0 tptp.sz00) (= W1 tptp.sz00))))))
% 0.35/0.58 (assume a17 (not (= tptp.sz10 tptp.sz00)))
% 0.35/0.58 (assume a18 (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) true)))
% 0.35/0.58 (assume a19 (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElement0 W1))))))
% 0.35/0.58 (assume a20 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.aSet0 W1)) (=> (and (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 W0) (tptp.aElementOf0 W2 W1))) (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 W1) (tptp.aElementOf0 W2 W0)))) (= W0 W1)))))
% 0.35/0.58 (assume a21 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.aSet0 W1)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtpldt1 W0 W1)) (and (tptp.aSet0 W2) (forall ((W3 $$unsorted)) (= (tptp.aElementOf0 W3 W2) (exists ((W4 $$unsorted) (W5 $$unsorted)) (and (tptp.aElementOf0 W4 W0) (tptp.aElementOf0 W5 W1) (= (tptp.sdtpldt0 W4 W5) W3)))))))))))
% 0.35/0.58 (assume a22 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.aSet0 W1)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtasasdt0 W0 W1)) (and (tptp.aSet0 W2) (forall ((W3 $$unsorted)) (= (tptp.aElementOf0 W3 W2) (and (tptp.aElementOf0 W3 W0) (tptp.aElementOf0 W3 W1))))))))))
% 0.35/0.58 (assume a23 (forall ((W0 $$unsorted)) (= (tptp.aIdeal0 W0) (and (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (and (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 W0) (tptp.aElementOf0 (tptp.sdtpldt0 W1 W2) W0))) (forall ((W2 $$unsorted)) (=> (tptp.aElement0 W2) (tptp.aElementOf0 (tptp.sdtasdt0 W2 W1) W0))))))))))
% 0.35/0.58 (assume a24 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aIdeal0 W0) (tptp.aIdeal0 W1)) (tptp.aIdeal0 (tptp.sdtpldt1 W0 W1)))))
% 0.35/0.58 (assume a25 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aIdeal0 W0) (tptp.aIdeal0 W1)) (tptp.aIdeal0 (tptp.sdtasasdt0 W0 W1)))))
% 0.35/0.58 (assume a26 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1) (tptp.aIdeal0 W2)) (= (tptp.sdteqdtlpzmzozddtrp0 W0 W1 W2) (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 W1)) W2)))))
% 0.35/0.58 (assume a27 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aIdeal0 W0) (tptp.aIdeal0 W1)) (=> (forall ((W2 $$unsorted)) (=> (tptp.aElement0 W2) (tptp.aElementOf0 W2 (tptp.sdtpldt1 W0 W1)))) (forall ((W2 $$unsorted) (W3 $$unsorted)) (=> (and (tptp.aElement0 W2) (tptp.aElement0 W3)) (exists ((W4 $$unsorted)) (and (tptp.aElement0 W4) (tptp.sdteqdtlpzmzozddtrp0 W4 W2 W0) (tptp.sdteqdtlpzmzozddtrp0 W4 W3 W1)))))))))
% 0.35/0.58 (assume a28 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) true)))
% 0.35/0.58 (assume a29 (forall ((W0 $$unsorted)) (=> (and (tptp.aElement0 W0) (not (= W0 tptp.sz00))) (tptp.aNaturalNumber0 (tptp.sbrdtbr0 W0)))))
% 0.35/0.58 (assume a30 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (tptp.iLess0 W0 W1) true))))
% 0.35/0.58 (assume a31 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1) (not (= W1 tptp.sz00))) (exists ((W2 $$unsorted) (W3 $$unsorted)) (and (tptp.aElement0 W2) (tptp.aElement0 W3) (= W0 (tptp.sdtpldt0 (tptp.sdtasdt0 W2 W1) W3)) (=> (not (= W3 tptp.sz00)) (tptp.iLess0 (tptp.sbrdtbr0 W3) (tptp.sbrdtbr0 W1))))))))
% 0.35/0.58 (assume a32 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (= (tptp.doDivides0 W0 W1) (exists ((W2 $$unsorted)) (and (tptp.aElement0 W2) (= (tptp.sdtasdt0 W0 W2) W1)))))))
% 0.35/0.58 (assume a33 (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (forall ((W1 $$unsorted)) (= (tptp.aDivisorOf0 W1 W0) (and (tptp.aElement0 W1) (tptp.doDivides0 W1 W0)))))))
% 0.35/0.58 (assume a34 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (forall ((W2 $$unsorted)) (= (tptp.aGcdOfAnd0 W2 W0 W1) (and (tptp.aDivisorOf0 W2 W0) (tptp.aDivisorOf0 W2 W1) (forall ((W3 $$unsorted)) (=> (and (tptp.aDivisorOf0 W3 W0) (tptp.aDivisorOf0 W3 W1)) (tptp.doDivides0 W3 W2)))))))))
% 0.35/0.58 (assume a35 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (= (tptp.misRelativelyPrime0 W0 W1) (tptp.aGcdOfAnd0 tptp.sz10 W0 W1)))))
% 0.35/0.58 (assume a36 (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (forall ((W1 $$unsorted)) (= (= W1 (tptp.slsdtgt0 W0)) (and (tptp.aSet0 W1) (forall ((W2 $$unsorted)) (= (tptp.aElementOf0 W2 W1) (exists ((W3 $$unsorted)) (and (tptp.aElement0 W3) (= (tptp.sdtasdt0 W0 W3) W2)))))))))))
% 0.35/0.58 (assume a37 (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (tptp.aIdeal0 (tptp.slsdtgt0 W0)))))
% 0.35/0.58 (assume a38 (and (tptp.aElement0 tptp.xa) (tptp.aElement0 tptp.xb)))
% 0.35/0.58 (assume a39 (or (not (= tptp.xa tptp.sz00)) (not (= tptp.xb tptp.sz00))))
% 0.35/0.58 (assume a40 (tptp.aGcdOfAnd0 tptp.xc tptp.xa tptp.xb))
% 0.35/0.58 (assume a41 (and (tptp.aIdeal0 tptp.xI) (= tptp.xI (tptp.sdtpldt1 (tptp.slsdtgt0 tptp.xa) (tptp.slsdtgt0 tptp.xb)))))
% 0.35/0.58 (assume a42 (and (tptp.aElementOf0 tptp.sz00 (tptp.slsdtgt0 tptp.xa)) (tptp.aElementOf0 tptp.xa (tptp.slsdtgt0 tptp.xa)) (tptp.aElementOf0 tptp.sz00 (tptp.slsdtgt0 tptp.xb)) (tptp.aElementOf0 tptp.xb (tptp.slsdtgt0 tptp.xb))))
% 0.35/0.58 (assume a43 (exists ((W0 $$unsorted)) (and (tptp.aElementOf0 W0 (tptp.sdtpldt1 (tptp.slsdtgt0 tptp.xa) (tptp.slsdtgt0 tptp.xb))) (not (= W0 tptp.sz00)))))
% 0.35/0.58 (assume a44 (and (tptp.aElementOf0 tptp.xu tptp.xI) (not (= tptp.xu tptp.sz00)) (forall ((W0 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.xI) (not (= W0 tptp.sz00))) (not (tptp.iLess0 (tptp.sbrdtbr0 W0) (tptp.sbrdtbr0 tptp.xu)))))))
% 0.35/0.58 (assume a45 (not (and (tptp.aDivisorOf0 tptp.xu tptp.xa) (tptp.aDivisorOf0 tptp.xu tptp.xb))))
% 0.35/0.58 (assume a46 (exists ((W0 $$unsorted) (W1 $$unsorted)) (and (tptp.aElement0 W0) (tptp.aElement0 W1) (= tptp.xu (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xa W0) (tptp.sdtasdt0 tptp.xb W1))))))
% 0.35/0.58 (assume a47 (not (not (tptp.doDivides0 tptp.xu tptp.xa))))
% 0.35/0.58 (assume a48 (not (tptp.doDivides0 tptp.xu tptp.xb)))
% 0.35/0.58 (assume a49 (and (tptp.aElement0 tptp.xq) (tptp.aElement0 tptp.xr) (= tptp.xb (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xq tptp.xu) tptp.xr)) (or (= tptp.xr tptp.sz00) (tptp.iLess0 (tptp.sbrdtbr0 tptp.xr) (tptp.sbrdtbr0 tptp.xu)))))
% 0.35/0.58 (assume a50 (not (= tptp.xr tptp.sz00)))
% 0.35/0.58 (assume a51 (tptp.aElementOf0 (tptp.smndt0 (tptp.sdtasdt0 tptp.xq tptp.xu)) tptp.xI))
% 0.35/0.58 (assume a52 (tptp.aElementOf0 tptp.xb tptp.xI))
% 0.35/0.58 (assume a53 (= tptp.xr (tptp.sdtpldt0 (tptp.smndt0 (tptp.sdtasdt0 tptp.xq tptp.xu)) tptp.xb)))
% 0.35/0.58 (assume a54 (tptp.aElementOf0 tptp.xr tptp.xI))
% 0.35/0.58 (assume a55 (not false))
% 0.35/0.58 (assume a56 true)
% 0.35/0.58 (step t1 (cl (=> (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xI)) (= tptp.sz00 W0) (not (tptp.iLess0 (tptp.sbrdtbr0 W0) (tptp.sbrdtbr0 tptp.xu))))) (or (not (tptp.aElementOf0 tptp.xr tptp.xI)) (= tptp.sz00 tptp.xr) (not (tptp.iLess0 (tptp.sbrdtbr0 tptp.xr) (tptp.sbrdtbr0 tptp.xu))))) (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xI)) (= tptp.sz00 W0) (not (tptp.iLess0 (tptp.sbrdtbr0 W0) (tptp.sbrdtbr0 tptp.xu)))))) :rule implies_neg1)
% 0.35/0.58 (anchor :step t2)
% 0.35/0.58 (assume t2.a0 (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xI)) (= tptp.sz00 W0) (not (tptp.iLess0 (tptp.sbrdtbr0 W0) (tptp.sbrdtbr0 tptp.xu))))))
% 0.35/0.58 (step t2.t1 (cl (or (not (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xI)) (= tptp.sz00 W0) (not (tptp.iLess0 (tptp.sbrdtbr0 W0) (tptp.sbrdtbr0 tptp.xu)))))) (or (not (tptp.aElementOf0 tptp.xr tptp.xI)) (= tptp.sz00 tptp.xr) (not (tptp.iLess0 (tptp.sbrdtbr0 tptp.xr) (tptp.sbrdtbr0 tptp.xu)))))) :rule forall_inst :args ((:= W0 tptp.xr)))
% 0.35/0.58 (step t2.t2 (cl (not (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xI)) (= tptp.sz00 W0) (not (tptp.iLess0 (tptp.sbrdtbr0 W0) (tptp.sbrdtbr0 tptp.xu)))))) (or (not (tptp.aElementOf0 tptp.xr tptp.xI)) (= tptp.sz00 tptp.xr) (not (tptp.iLess0 (tptp.sbrdtbr0 tptp.xr) (tptp.sbrdtbr0 tptp.xu))))) :rule or :premises (t2.t1))
% 0.35/0.58 (step t2.t3 (cl (or (not (tptp.aElementOf0 tptp.xr tptp.xI)) (= tptp.sz00 tptp.xr) (not (tptp.iLess0 (tptp.sbrdtbr0 tptp.xr) (tptp.sbrdtbr0 tptp.xu))))) :rule resolution :premises (t2.t2 t2.a0))
% 0.35/0.58 (step t2 (cl (not (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xI)) (= tptp.sz00 W0) (not (tptp.iLess0 (tptp.sbrdtbr0 W0) (tptp.sbrdtbr0 tptp.xu)))))) (or (not (tptp.aElementOf0 tptp.xr tptp.xI)) (= tptp.sz00 tptp.xr) (not (tptp.iLess0 (tptp.sbrdtbr0 tptp.xr) (tptp.sbrdtbr0 tptp.xu))))) :rule subproof :discharge (t2.a0))
% 0.35/0.58 (step t3 (cl (=> (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xI)) (= tptp.sz00 W0) (not (tptp.iLess0 (tptp.sbrdtbr0 W0) (tptp.sbrdtbr0 tptp.xu))))) (or (not (tptp.aElementOf0 tptp.xr tptp.xI)) (= tptp.sz00 tptp.xr) (not (tptp.iLess0 (tptp.sbrdtbr0 tptp.xr) (tptp.sbrdtbr0 tptp.xu))))) (or (not (tptp.aElementOf0 tptp.xr tptp.xI)) (= tptp.sz00 tptp.xr) (not (tptp.iLess0 (tptp.sbrdtbr0 tptp.xr) (tptp.sbrdtbr0 tptp.xu))))) :rule resolution :premises (t1 t2))
% 0.35/0.58 (step t4 (cl (=> (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xI)) (= tptp.sz00 W0) (not (tptp.iLess0 (tptp.sbrdtbr0 W0) (tptp.sbrdtbr0 tptp.xu))))) (or (not (tptp.aElementOf0 tptp.xr tptp.xI)) (= tptp.sz00 tptp.xr) (not (tptp.iLess0 (tptp.sbrdtbr0 tptp.xr) (tptp.sbrdtbr0 tptp.xu))))) (not (or (not (tptp.aElementOf0 tptp.xr tptp.xI)) (= tptp.sz00 tptp.xr) (not (tptp.iLess0 (tptp.sbrdtbr0 tptp.xr) (tptp.sbrdtbr0 tptp.xu)))))) :rule implies_neg2)
% 0.35/0.58 (step t5 (cl (=> (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xI)) (= tptp.sz00 W0) (not (tptp.iLess0 (tptp.sbrdtbr0 W0) (tptp.sbrdtbr0 tptp.xu))))) (or (not (tptp.aElementOf0 tptp.xr tptp.xI)) (= tptp.sz00 tptp.xr) (not (tptp.iLess0 (tptp.sbrdtbr0 tptp.xr) (tptp.sbrdtbr0 tptp.xu))))) (=> (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xI)) (= tptp.sz00 W0) (not (tptp.iLess0 (tptp.sbrdtbr0 W0) (tptp.sbrdtbr0 tptp.xu))))) (or (not (tptp.aElementOf0 tptp.xr tptp.xI)) (= tptp.sz00 tptp.xr) (not (tptp.iLess0 (tptp.sbrdtbr0 tptp.xr) (tptp.sbrdtbr0 tptp.xu)))))) :rule resolution :premises (t3 t4))
% 0.35/0.58 (step t6 (cl (=> (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xI)) (= tptp.sz00 W0) (not (tptp.iLess0 (tptp.sbrdtbr0 W0) (tptp.sbrdtbr0 tptp.xu))))) (or (not (tptp.aElementOf0 tptp.xr tptp.xI)) (= tptp.sz00 tptp.xr) (not (tptp.iLess0 (tptp.sbrdtbr0 tptp.xr) (tptp.sbrdtbr0 tptp.xu)))))) :rule contraction :premises (t5))
% 0.35/0.58 (step t7 (cl (not (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xI)) (= tptp.sz00 W0) (not (tptp.iLess0 (tptp.sbrdtbr0 W0) (tptp.sbrdtbr0 tptp.xu)))))) (or (not (tptp.aElementOf0 tptp.xr tptp.xI)) (= tptp.sz00 tptp.xr) (not (tptp.iLess0 (tptp.sbrdtbr0 tptp.xr) (tptp.sbrdtbr0 tptp.xu))))) :rule implies :premises (t6))
% 0.35/0.58 (step t8 (cl (not (or (not (tptp.aElementOf0 tptp.xr tptp.xI)) (= tptp.sz00 tptp.xr) (not (tptp.iLess0 (tptp.sbrdtbr0 tptp.xr) (tptp.sbrdtbr0 tptp.xu))))) (not (tptp.aElementOf0 tptp.xr tptp.xI)) (= tptp.sz00 tptp.xr) (not (tptp.iLess0 (tptp.sbrdtbr0 tptp.xr) (tptp.sbrdtbr0 tptp.xu)))) :rule or_pos)
% 0.35/0.58 (step t9 (cl (= tptp.sz00 tptp.xr) (not (tptp.iLess0 (tptp.sbrdtbr0 tptp.xr) (tptp.sbrdtbr0 tptp.xu))) (not (tptp.aElementOf0 tptp.xr tptp.xI)) (not (or (not (tptp.aElementOf0 tptp.xr tptp.xI)) (= tptp.sz00 tptp.xr) (not (tptp.iLess0 (tptp.sbrdtbr0 tptp.xr) (tptp.sbrdtbr0 tptp.xu)))))) :rule reordering :premises (t8))
% 0.35/0.58 (step t10 (cl (not (= tptp.sz00 tptp.xr))) :rule not_symm :premises (a50))
% 0.35/0.58 (step t11 (cl (not (= (and (tptp.aElement0 tptp.xq) (tptp.aElement0 tptp.xr) (= tptp.xb (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xq tptp.xu) tptp.xr)) (or (= tptp.xr tptp.sz00) (tptp.iLess0 (tptp.sbrdtbr0 tptp.xr) (tptp.sbrdtbr0 tptp.xu)))) (and (tptp.aElement0 tptp.xq) (tptp.aElement0 tptp.xr) (= tptp.xb (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xq tptp.xu) tptp.xr)) (or (= tptp.sz00 tptp.xr) (tptp.iLess0 (tptp.sbrdtbr0 tptp.xr) (tptp.sbrdtbr0 tptp.xu)))))) (not (and (tptp.aElement0 tptp.xq) (tptp.aElement0 tptp.xr) (= tptp.xb (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xq tptp.xu) tptp.xr)) (or (= tptp.xr tptp.sz00) (tptp.iLess0 (tptp.sbrdtbr0 tptp.xr) (tptp.sbrdtbr0 tptp.xu))))) (and (tptp.aElement0 tptp.xq) (tptp.aElement0 tptp.xr) (= tptp.xb (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xq tptp.xu) tptp.xr)) (or (= tptp.sz00 tptp.xr) (tptp.iLess0 (tptp.sbrdtbr0 tptp.xr) (tptp.sbrdtbr0 tptp.xu))))) :rule equiv_pos2)
% 0.35/0.58 (step t12 (cl (= (tptp.aElement0 tptp.xq) (tptp.aElement0 tptp.xq))) :rule refl)
% 0.35/0.58 (step t13 (cl (= (tptp.aElement0 tptp.xr) (tptp.aElement0 tptp.xr))) :rule refl)
% 0.35/0.58 (step t14 (cl (= (= tptp.xb (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xq tptp.xu) tptp.xr)) (= tptp.xb (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xq tptp.xu) tptp.xr)))) :rule refl)
% 0.35/0.58 (step t15 (cl (= (= tptp.xr tptp.sz00) (= tptp.sz00 tptp.xr))) :rule all_simplify)
% 0.35/0.58 (step t16 (cl (= (tptp.iLess0 (tptp.sbrdtbr0 tptp.xr) (tptp.sbrdtbr0 tptp.xu)) (tptp.iLess0 (tptp.sbrdtbr0 tptp.xr) (tptp.sbrdtbr0 tptp.xu)))) :rule refl)
% 0.35/0.58 (step t17 (cl (= (or (= tptp.xr tptp.sz00) (tptp.iLess0 (tptp.sbrdtbr0 tptp.xr) (tptp.sbrdtbr0 tptp.xu))) (or (= tptp.sz00 tptp.xr) (tptp.iLess0 (tptp.sbrdtbr0 tptp.xr) (tptp.sbrdtbr0 tptp.xu))))) :rule cong :premises (t15 t16))
% 0.35/0.58 (step t18 (cl (= (and (tptp.aElement0 tptp.xq) (tptp.aElement0 tptp.xr) (= tptp.xb (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xq tptp.xu) tptp.xr)) (or (= tptp.xr tptp.sz00) (tptp.iLess0 (tptp.sbrdtbr0 tptp.xr) (tptp.sbrdtbr0 tptp.xu)))) (and (tptp.aElement0 tptp.xq) (tptp.aElement0 tptp.xr) (= tptp.xb (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xq tptp.xu) tptp.xr)) (or (= tptp.sz00 tptp.xr) (tptp.iLess0 (tptp.sbrdtbr0 tptp.xr) (tptp.sbrdtbr0 tptp.xu)))))) :rule cong :premises (t12 t13 t14 t17))
% 0.35/0.58 (step t19 (cl (and (tptp.aElement0 tptp.xq) (tptp.aElement0 tptp.xr) (= tptp.xb (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xq tptp.xu) tptp.xr)) (or (= tptp.sz00 tptp.xr) (tptp.iLess0 (tptp.sbrdtbr0 tptp.xr) (tptp.sbrdtbr0 tptp.xu))))) :rule resolution :premises (t11 t18 a49))
% 0.35/0.58 (step t20 (cl (or (= tptp.sz00 tptp.xr) (tptp.iLess0 (tptp.sbrdtbr0 tptp.xr) (tptp.sbrdtbr0 tptp.xu)))) :rule and :premises (t19))
% 0.35/0.58 (step t21 (cl (= tptp.sz00 tptp.xr) (tptp.iLess0 (tptp.sbrdtbr0 tptp.xr) (tptp.sbrdtbr0 tptp.xu))) :rule or :premises (t20))
% 0.35/0.58 (step t22 (cl (tptp.iLess0 (tptp.sbrdtbr0 tptp.xr) (tptp.sbrdtbr0 tptp.xu)) (= tptp.sz00 tptp.xr)) :rule reordering :premises (t21))
% 0.35/0.58 (step t23 (cl (tptp.iLess0 (tptp.sbrdtbr0 tptp.xr) (tptp.sbrdtbr0 tptp.xu))) :rule resolution :premises (t22 t10))
% 0.35/0.58 (step t24 (cl (not (or (not (tptp.aElementOf0 tptp.xr tptp.xI)) (= tptp.sz00 tptp.xr) (not (tptp.iLess0 (tptp.sbrdtbr0 tptp.xr) (tptp.sbrdtbr0 tptp.xu)))))) :rule resolution :premises (t9 t10 t23 a54))
% 0.35/0.58 (step t25 (cl (not (= (and (tptp.aElementOf0 tptp.xu tptp.xI) (not (= tptp.xu tptp.sz00)) (forall ((W0 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.xI) (not (= W0 tptp.sz00))) (not (tptp.iLess0 (tptp.sbrdtbr0 W0) (tptp.sbrdtbr0 tptp.xu)))))) (and (tptp.aElementOf0 tptp.xu tptp.xI) (not (= tptp.sz00 tptp.xu)) (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xI)) (= tptp.sz00 W0) (not (tptp.iLess0 (tptp.sbrdtbr0 W0) (tptp.sbrdtbr0 tptp.xu)))))))) (not (and (tptp.aElementOf0 tptp.xu tptp.xI) (not (= tptp.xu tptp.sz00)) (forall ((W0 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.xI) (not (= W0 tptp.sz00))) (not (tptp.iLess0 (tptp.sbrdtbr0 W0) (tptp.sbrdtbr0 tptp.xu))))))) (and (tptp.aElementOf0 tptp.xu tptp.xI) (not (= tptp.sz00 tptp.xu)) (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xI)) (= tptp.sz00 W0) (not (tptp.iLess0 (tptp.sbrdtbr0 W0) (tptp.sbrdtbr0 tptp.xu))))))) :rule equiv_pos2)
% 0.35/0.58 (step t26 (cl (= (tptp.aElementOf0 tptp.xu tptp.xI) (tptp.aElementOf0 tptp.xu tptp.xI))) :rule refl)
% 0.35/0.58 (step t27 (cl (= (= tptp.xu tptp.sz00) (= tptp.sz00 tptp.xu))) :rule all_simplify)
% 0.35/0.58 (step t28 (cl (= (not (= tptp.xu tptp.sz00)) (not (= tptp.sz00 tptp.xu)))) :rule cong :premises (t27))
% 0.35/0.58 (anchor :step t29 :args ((W0 $$unsorted) (:= W0 W0)))
% 0.35/0.58 (step t29.t1 (cl (= W0 W0)) :rule refl)
% 0.35/0.58 (step t29.t2 (cl (= (tptp.aElementOf0 W0 tptp.xI) (tptp.aElementOf0 W0 tptp.xI))) :rule refl)
% 0.35/0.58 (step t29.t3 (cl (= (= W0 tptp.sz00) (= tptp.sz00 W0))) :rule all_simplify)
% 0.35/0.58 (step t29.t4 (cl (= (not (= W0 tptp.sz00)) (not (= tptp.sz00 W0)))) :rule cong :premises (t29.t3))
% 0.35/0.58 (step t29.t5 (cl (= (and (tptp.aElementOf0 W0 tptp.xI) (not (= W0 tptp.sz00))) (and (tptp.aElementOf0 W0 tptp.xI) (not (= tptp.sz00 W0))))) :rule cong :premises (t29.t2 t29.t4))
% 0.35/0.58 (step t29.t6 (cl (= (not (tptp.iLess0 (tptp.sbrdtbr0 W0) (tptp.sbrdtbr0 tptp.xu))) (not (tptp.iLess0 (tptp.sbrdtbr0 W0) (tptp.sbrdtbr0 tptp.xu))))) :rule refl)
% 0.35/0.58 (step t29.t7 (cl (= (=> (and (tptp.aElementOf0 W0 tptp.xI) (not (= W0 tptp.sz00))) (not (tptp.iLess0 (tptp.sbrdtbr0 W0) (tptp.sbrdtbr0 tptp.xu)))) (=> (and (tptp.aElementOf0 W0 tptp.xI) (not (= tptp.sz00 W0))) (not (tptp.iLess0 (tptp.sbrdtbr0 W0) (tptp.sbrdtbr0 tptp.xu)))))) :rule cong :premises (t29.t5 t29.t6))
% 0.35/0.58 (step t29 (cl (= (forall ((W0 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.xI) (not (= W0 tptp.sz00))) (not (tptp.iLess0 (tptp.sbrdtbr0 W0) (tptp.sbrdtbr0 tptp.xu))))) (forall ((W0 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.xI) (not (= tptp.sz00 W0))) (not (tptp.iLess0 (tptp.sbrdtbr0 W0) (tptp.sbrdtbr0 tptp.xu))))))) :rule bind)
% 0.35/0.58 (step t30 (cl (= (forall ((W0 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.xI) (not (= tptp.sz00 W0))) (not (tptp.iLess0 (tptp.sbrdtbr0 W0) (tptp.sbrdtbr0 tptp.xu))))) (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xI)) (= tptp.sz00 W0) (not (tptp.iLess0 (tptp.sbrdtbr0 W0) (tptp.sbrdtbr0 tptp.xu))))))) :rule all_simplify)
% 0.35/0.58 (step t31 (cl (= (forall ((W0 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.xI) (not (= W0 tptp.sz00))) (not (tptp.iLess0 (tptp.sbrdtbr0 W0) (tptp.sbrdtbr0 tptp.xu))))) (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xI)) (= tptp.sz00 W0) (not (tptp.iLess0 (tptp.sbrdtbr0 W0) (tptp.sbrdtbr0 tptp.xu))))))) :rule trans :premises (t29 t30))
% 0.35/0.59 (step t32 (cl (= (and (tptp.aElementOf0 tptp.xu tptp.xI) (not (= tptp.xu tptp.sz00)) (forall ((W0 $$unsorted)) (=> (and (tptp.aElementOf0 W0 tptp.xI) (not (= W0 tptp.sz00))) (not (tptp.iLess0 (tptp.sbrdtbr0 W0) (tptp.sbrdtbr0 tptp.xu)))))) (and (tptp.aElementOf0 tptp.xu tptp.xI) (not (= tptp.sz00 tptp.xu)) (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xI)) (= tptp.sz00 W0) (not (tptp.iLess0 (tptp.sbrdtbr0 W0) (tptp.sbrdtbr0 tptp.xu)))))))) :rule cong :premises (t26 t28 t31))
% 0.35/0.59 (step t33 (cl (and (tptp.aElementOf0 tptp.xu tptp.xI) (not (= tptp.sz00 tptp.xu)) (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xI)) (= tptp.sz00 W0) (not (tptp.iLess0 (tptp.sbrdtbr0 W0) (tptp.sbrdtbr0 tptp.xu))))))) :rule resolution :premises (t25 t32 a44))
% 0.35/0.59 (step t34 (cl (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xI)) (= tptp.sz00 W0) (not (tptp.iLess0 (tptp.sbrdtbr0 W0) (tptp.sbrdtbr0 tptp.xu)))))) :rule and :premises (t33))
% 0.35/0.59 (step t35 (cl) :rule resolution :premises (t7 t24 t34))
% 0.35/0.59
% 0.35/0.59 % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.B8v1mUFnAU/cvc5---1.0.5_18003.smt2
% 0.35/0.59 % cvc5---1.0.5 exiting
% 0.35/0.59 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------