TSTP Solution File: NUM523+1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM523+1 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n017.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 17:33:51 EDT 2024
% Result : Theorem 5.24s 5.49s
% Output : Proof 5.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : NUM523+1 : TPTP v8.2.0. Released v4.0.0.
% 0.13/0.14 % Command : do_cvc5 %s %d
% 0.13/0.35 % Computer : n017.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue May 28 01:46:39 EDT 2024
% 0.20/0.35 % CPUTime :
% 0.20/0.51 %----Proving TF0_NAR, FOF, or CNF
% 5.24/5.49 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 5.24/5.49 % SZS status Theorem for /export/starexec/sandbox2/tmp/tmp.wMIrP9bN8W/cvc5---1.0.5_6644.smt2
% 5.24/5.49 % SZS output start Proof for /export/starexec/sandbox2/tmp/tmp.wMIrP9bN8W/cvc5---1.0.5_6644.smt2
% 5.24/5.49 (assume a0 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) true)))
% 5.24/5.49 (assume a1 (tptp.aNaturalNumber0 tptp.sz00))
% 5.24/5.49 (assume a2 (and (tptp.aNaturalNumber0 tptp.sz10) (not (= tptp.sz10 tptp.sz00))))
% 5.24/5.49 (assume a3 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))))
% 5.24/5.49 (assume a4 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))))
% 5.24/5.49 (assume a5 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W1 W0)))))
% 5.24/5.49 (assume a6 (forall ((W0 $$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))))))
% 5.24/5.49 (assume a7 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtpldt0 W0 tptp.sz00) W0) (= W0 (tptp.sdtpldt0 tptp.sz00 W0))))))
% 5.24/5.49 (assume a8 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))
% 5.24/5.49 (assume a9 (forall ((W0 $$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))))))
% 5.24/5.49 (assume a10 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz10) W0) (= W0 (tptp.sdtasdt0 tptp.sz10 W0))))))
% 5.24/5.49 (assume a11 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 W0))))))
% 5.24/5.49 (assume a12 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (and (= (tptp.sdtasdt0 W0 (tptp.sdtpldt0 W1 W2)) (tptp.sdtpldt0 (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W0 W2))) (= (tptp.sdtasdt0 (tptp.sdtpldt0 W1 W2) W0) (tptp.sdtpldt0 (tptp.sdtasdt0 W1 W0) (tptp.sdtasdt0 W2 W0)))))))
% 5.24/5.49 (assume a13 (forall ((W0 $$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)))))
% 5.24/5.49 (assume a14 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (=> (not (= W0 tptp.sz00)) (forall ((W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (or (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W0 W2)) (= (tptp.sdtasdt0 W1 W0) (tptp.sdtasdt0 W2 W0))) (= W1 W2))))))))
% 5.24/5.49 (assume a15 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (= (tptp.sdtpldt0 W0 W1) tptp.sz00) (and (= W0 tptp.sz00) (= W1 tptp.sz00))))))
% 5.24/5.49 (assume a16 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (= (tptp.sdtasdt0 W0 W1) tptp.sz00) (or (= W0 tptp.sz00) (= W1 tptp.sz00))))))
% 5.24/5.49 (assume a17 (forall ((W0 $$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)))))))
% 5.24/5.49 (assume a18 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (tptp.sdtlseqdt0 W0 W1) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtmndt0 W1 W0)) (and (tptp.aNaturalNumber0 W2) (= (tptp.sdtpldt0 W0 W2) W1))))))))
% 5.24/5.49 (assume a19 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (tptp.sdtlseqdt0 W0 W0))))
% 5.24/5.49 (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)))))
% 5.24/5.49 (assume a21 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W2)) (tptp.sdtlseqdt0 W0 W2)))))
% 5.24/5.49 (assume a22 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (or (tptp.sdtlseqdt0 W0 W1) (and (not (= W1 W0)) (tptp.sdtlseqdt0 W1 W0))))))
% 5.24/5.49 (assume a23 (forall ((W0 $$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)))))))))
% 5.24/5.49 (assume a24 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (not (= W0 tptp.sz00)) (not (= W1 W2)) (tptp.sdtlseqdt0 W1 W2)) (and (not (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W0 W2))) (tptp.sdtlseqdt0 (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W0 W2)) (not (= (tptp.sdtasdt0 W1 W0) (tptp.sdtasdt0 W2 W0))) (tptp.sdtlseqdt0 (tptp.sdtasdt0 W1 W0) (tptp.sdtasdt0 W2 W0)))))))
% 5.24/5.49 (assume a25 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (or (= W0 tptp.sz00) (= W0 tptp.sz10) (and (not (= tptp.sz10 W0)) (tptp.sdtlseqdt0 tptp.sz10 W0))))))
% 5.24/5.49 (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))))))
% 5.24/5.49 (assume a27 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (tptp.iLess0 W0 W1) true))))
% 5.24/5.49 (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)))))
% 5.24/5.49 (assume a29 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.doDivides0 W0 W1) (exists ((W2 $$unsorted)) (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtasdt0 W0 W2))))))))
% 5.24/5.49 (assume a30 (forall ((W0 $$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)))))))))
% 5.24/5.49 (assume a31 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.doDivides0 W0 W1) (tptp.doDivides0 W1 W2)) (tptp.doDivides0 W0 W2)))))
% 5.24/5.49 (assume a32 (forall ((W0 $$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))))))
% 5.24/5.49 (assume a33 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.doDivides0 W0 W1) (tptp.doDivides0 W0 (tptp.sdtpldt0 W1 W2))) (tptp.doDivides0 W0 W2)))))
% 5.24/5.49 (assume a34 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (tptp.doDivides0 W0 W1) (not (= W1 tptp.sz00))) (tptp.sdtlseqdt0 W0 W1)))))
% 5.24/5.49 (assume a35 (forall ((W0 $$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))))))))
% 5.24/5.49 (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)))))))))
% 5.24/5.49 (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))))))
% 5.24/5.49 (assume a38 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.isPrime0 W2) (tptp.doDivides0 W2 (tptp.sdtasdt0 W0 W1))) (or (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1))))))
% 5.24/5.49 (assume a39 (and (tptp.aNaturalNumber0 tptp.xn) (tptp.aNaturalNumber0 tptp.xm) (tptp.aNaturalNumber0 tptp.xp) (not (= tptp.xn tptp.sz00)) (not (= tptp.xm tptp.sz00)) (not (= tptp.xp tptp.sz00))))
% 5.24/5.49 (assume a40 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2) (not (= W0 tptp.sz00)) (not (= W1 tptp.sz00)) (not (= W2 tptp.sz00))) (=> (= (tptp.sdtasdt0 W2 (tptp.sdtasdt0 W1 W1)) (tptp.sdtasdt0 W0 W0)) (=> (tptp.iLess0 W0 tptp.xn) (not (tptp.isPrime0 W2)))))))
% 5.24/5.49 (assume a41 (= (tptp.sdtasdt0 tptp.xp (tptp.sdtasdt0 tptp.xm tptp.xm)) (tptp.sdtasdt0 tptp.xn tptp.xn)))
% 5.24/5.49 (assume a42 (tptp.isPrime0 tptp.xp))
% 5.24/5.49 (assume a43 (not (and (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (tptp.doDivides0 tptp.xp tptp.xn))))
% 5.24/5.49 (assume a44 true)
% 5.24/5.49 (step t1 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W2)) (not (tptp.isPrime0 W2)) (not (tptp.doDivides0 W2 (tptp.sdtasdt0 W0 W1))) (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1))) (or (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.isPrime0 tptp.xp)) (not (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn))) (tptp.doDivides0 tptp.xp tptp.xn) (tptp.doDivides0 tptp.xp tptp.xn))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W2)) (not (tptp.isPrime0 W2)) (not (tptp.doDivides0 W2 (tptp.sdtasdt0 W0 W1))) (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1)))) :rule implies_neg1)
% 5.24/5.49 (anchor :step t2)
% 5.24/5.49 (assume t2.a0 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W2)) (not (tptp.isPrime0 W2)) (not (tptp.doDivides0 W2 (tptp.sdtasdt0 W0 W1))) (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1))))
% 5.24/5.49 (step t2.t1 (cl (or (not (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W2)) (not (tptp.isPrime0 W2)) (not (tptp.doDivides0 W2 (tptp.sdtasdt0 W0 W1))) (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1)))) (or (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.isPrime0 tptp.xp)) (not (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn))) (tptp.doDivides0 tptp.xp tptp.xn) (tptp.doDivides0 tptp.xp tptp.xn)))) :rule forall_inst :args ((:= W0 tptp.xn) (:= W1 tptp.xn) (:= W2 tptp.xp)))
% 5.24/5.49 (step t2.t2 (cl (not (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W2)) (not (tptp.isPrime0 W2)) (not (tptp.doDivides0 W2 (tptp.sdtasdt0 W0 W1))) (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1)))) (or (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.isPrime0 tptp.xp)) (not (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn))) (tptp.doDivides0 tptp.xp tptp.xn) (tptp.doDivides0 tptp.xp tptp.xn))) :rule or :premises (t2.t1))
% 5.24/5.49 (step t2.t3 (cl (or (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.isPrime0 tptp.xp)) (not (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn))) (tptp.doDivides0 tptp.xp tptp.xn) (tptp.doDivides0 tptp.xp tptp.xn))) :rule resolution :premises (t2.t2 t2.a0))
% 5.24/5.49 (step t2 (cl (not (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W2)) (not (tptp.isPrime0 W2)) (not (tptp.doDivides0 W2 (tptp.sdtasdt0 W0 W1))) (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1)))) (or (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.isPrime0 tptp.xp)) (not (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn))) (tptp.doDivides0 tptp.xp tptp.xn) (tptp.doDivides0 tptp.xp tptp.xn))) :rule subproof :discharge (t2.a0))
% 5.24/5.49 (step t3 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W2)) (not (tptp.isPrime0 W2)) (not (tptp.doDivides0 W2 (tptp.sdtasdt0 W0 W1))) (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1))) (or (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.isPrime0 tptp.xp)) (not (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn))) (tptp.doDivides0 tptp.xp tptp.xn) (tptp.doDivides0 tptp.xp tptp.xn))) (or (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.isPrime0 tptp.xp)) (not (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn))) (tptp.doDivides0 tptp.xp tptp.xn) (tptp.doDivides0 tptp.xp tptp.xn))) :rule resolution :premises (t1 t2))
% 5.24/5.49 (step t4 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W2)) (not (tptp.isPrime0 W2)) (not (tptp.doDivides0 W2 (tptp.sdtasdt0 W0 W1))) (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1))) (or (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.isPrime0 tptp.xp)) (not (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn))) (tptp.doDivides0 tptp.xp tptp.xn) (tptp.doDivides0 tptp.xp tptp.xn))) (not (or (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.isPrime0 tptp.xp)) (not (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn))) (tptp.doDivides0 tptp.xp tptp.xn) (tptp.doDivides0 tptp.xp tptp.xn)))) :rule implies_neg2)
% 5.24/5.49 (step t5 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W2)) (not (tptp.isPrime0 W2)) (not (tptp.doDivides0 W2 (tptp.sdtasdt0 W0 W1))) (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1))) (or (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.isPrime0 tptp.xp)) (not (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn))) (tptp.doDivides0 tptp.xp tptp.xn) (tptp.doDivides0 tptp.xp tptp.xn))) (=> (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W2)) (not (tptp.isPrime0 W2)) (not (tptp.doDivides0 W2 (tptp.sdtasdt0 W0 W1))) (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1))) (or (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.isPrime0 tptp.xp)) (not (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn))) (tptp.doDivides0 tptp.xp tptp.xn) (tptp.doDivides0 tptp.xp tptp.xn)))) :rule resolution :premises (t3 t4))
% 5.24/5.49 (step t6 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W2)) (not (tptp.isPrime0 W2)) (not (tptp.doDivides0 W2 (tptp.sdtasdt0 W0 W1))) (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1))) (or (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.isPrime0 tptp.xp)) (not (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn))) (tptp.doDivides0 tptp.xp tptp.xn) (tptp.doDivides0 tptp.xp tptp.xn)))) :rule contraction :premises (t5))
% 5.24/5.49 (step t7 (cl (not (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W2)) (not (tptp.isPrime0 W2)) (not (tptp.doDivides0 W2 (tptp.sdtasdt0 W0 W1))) (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1)))) (or (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.isPrime0 tptp.xp)) (not (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn))) (tptp.doDivides0 tptp.xp tptp.xn) (tptp.doDivides0 tptp.xp tptp.xn))) :rule implies :premises (t6))
% 5.24/5.49 (step t8 (cl (not (or (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.isPrime0 tptp.xp)) (not (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn))) (tptp.doDivides0 tptp.xp tptp.xn) (tptp.doDivides0 tptp.xp tptp.xn))) (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.isPrime0 tptp.xp)) (not (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn))) (tptp.doDivides0 tptp.xp tptp.xn) (tptp.doDivides0 tptp.xp tptp.xn)) :rule or_pos)
% 5.24/5.49 (step t9 (cl (not (or (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.isPrime0 tptp.xp)) (not (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn))) (tptp.doDivides0 tptp.xp tptp.xn) (tptp.doDivides0 tptp.xp tptp.xn))) (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.isPrime0 tptp.xp)) (not (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn))) (tptp.doDivides0 tptp.xp tptp.xn)) :rule contraction :premises (t8))
% 5.24/5.49 (step t10 (cl (tptp.doDivides0 tptp.xp tptp.xn) (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.isPrime0 tptp.xp)) (not (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn))) (not (or (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.isPrime0 tptp.xp)) (not (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn))) (tptp.doDivides0 tptp.xp tptp.xn) (tptp.doDivides0 tptp.xp tptp.xn)))) :rule reordering :premises (t9))
% 5.24/5.49 (step t11 (cl (not (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn))) (not (tptp.doDivides0 tptp.xp tptp.xn))) :rule not_and :premises (a43))
% 5.24/5.49 (step t12 (cl (not (= (or (not (= (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2)))))))) (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (not (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2)))))))) (or (not (= (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2)))))))) (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2)))))))) (not (or (not (= (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2)))))))) (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (not (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2))))))))) (or (not (= (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2)))))))) (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2))))))) :rule equiv_pos2)
% 5.24/5.49 (step t13 (cl (= (not (= (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2)))))))) (not (= (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2)))))))))) :rule refl)
% 5.24/5.49 (step t14 (cl (= (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)))) :rule refl)
% 5.24/5.49 (step t15 (cl (= (= (= (not (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2))))))) (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2)))))) true) (= (not (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2))))))) (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2)))))))) :rule equiv_simplify)
% 5.24/5.49 (step t16 (cl (not (= (= (not (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2))))))) (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2)))))) true)) (= (not (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2))))))) (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2))))))) :rule equiv1 :premises (t15))
% 5.24/5.49 (step t17 (cl (= (= (not (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2))))))) (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2)))))) (= (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2))))) (not (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2)))))))))) :rule all_simplify)
% 5.24/5.49 (step t18 (cl (= (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2))))) (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2))))))) :rule refl)
% 5.24/5.49 (step t19 (cl (= (not (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2))))))) (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2))))))) :rule all_simplify)
% 5.24/5.49 (step t20 (cl (= (= (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2))))) (not (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2)))))))) (= (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2))))) (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2)))))))) :rule cong :premises (t18 t19))
% 5.24/5.49 (step t21 (cl (= (= (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2))))) (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2)))))) true)) :rule all_simplify)
% 5.24/5.49 (step t22 (cl (= (= (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2))))) (not (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2)))))))) true)) :rule trans :premises (t20 t21))
% 5.24/5.49 (step t23 (cl (= (= (not (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2))))))) (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2)))))) true)) :rule trans :premises (t17 t22))
% 5.24/5.49 (step t24 (cl (= (not (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2))))))) (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2))))))) :rule resolution :premises (t16 t23))
% 5.24/5.49 (step t25 (cl (= (or (not (= (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2)))))))) (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (not (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2)))))))) (or (not (= (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2)))))))) (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2)))))))) :rule cong :premises (t13 t14 t24))
% 5.24/5.49 (step t26 (cl (not (= (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2)))))))) (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (not (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2)))))))) :rule equiv_pos1)
% 5.24/5.49 (step t27 (cl (or (not (= (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2)))))))) (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (not (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2)))))))) (not (not (= (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2)))))))))) :rule or_neg)
% 5.24/5.49 (step t28 (cl (or (not (= (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2)))))))) (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (not (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2)))))))) (not (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)))) :rule or_neg)
% 5.24/5.49 (step t29 (cl (or (not (= (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2)))))))) (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (not (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2)))))))) (not (not (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2))))))))) :rule or_neg)
% 5.24/5.49 (step t30 (cl (or (not (= (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2)))))))) (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (not (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2)))))))) (or (not (= (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2)))))))) (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (not (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2)))))))) (or (not (= (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2)))))))) (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (not (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2))))))))) :rule resolution :premises (t26 t27 t28 t29))
% 5.24/5.49 (step t31 (cl (or (not (= (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2)))))))) (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (not (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2))))))))) :rule contraction :premises (t30))
% 5.24/5.49 (step t32 (cl (or (not (= (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2)))))))) (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2))))))) :rule resolution :premises (t12 t25 t31))
% 5.24/5.49 (step t33 (cl (not (= (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2)))))))) (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2)))))) :rule or :premises (t32))
% 5.24/5.49 (step t34 (cl (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2))))) (not (= (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2))))))))) :rule reordering :premises (t33))
% 5.24/5.49 (step t35 (cl (not (= (=> (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2))))) (or (not (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xm tptp.xm))) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp (tptp.sdtasdt0 tptp.xm tptp.xm)))))) (=> (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2))))) (or (not (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xm tptp.xm))) (not (= (tptp.sdtasdt0 tptp.xp (tptp.sdtasdt0 tptp.xm tptp.xm)) (tptp.sdtasdt0 tptp.xn tptp.xn))))))) (not (=> (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2))))) (or (not (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xm tptp.xm))) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp (tptp.sdtasdt0 tptp.xm tptp.xm))))))) (=> (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2))))) (or (not (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xm tptp.xm))) (not (= (tptp.sdtasdt0 tptp.xp (tptp.sdtasdt0 tptp.xm tptp.xm)) (tptp.sdtasdt0 tptp.xn tptp.xn)))))) :rule equiv_pos2)
% 5.24/5.49 (step t36 (cl (= (not (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xm tptp.xm))) (not (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xm tptp.xm))))) :rule refl)
% 5.24/5.49 (step t37 (cl (= (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp (tptp.sdtasdt0 tptp.xm tptp.xm))) (= (tptp.sdtasdt0 tptp.xp (tptp.sdtasdt0 tptp.xm tptp.xm)) (tptp.sdtasdt0 tptp.xn tptp.xn)))) :rule all_simplify)
% 5.24/5.49 (step t38 (cl (= (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp (tptp.sdtasdt0 tptp.xm tptp.xm)))) (not (= (tptp.sdtasdt0 tptp.xp (tptp.sdtasdt0 tptp.xm tptp.xm)) (tptp.sdtasdt0 tptp.xn tptp.xn))))) :rule cong :premises (t37))
% 5.24/5.49 (step t39 (cl (= (or (not (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xm tptp.xm))) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp (tptp.sdtasdt0 tptp.xm tptp.xm))))) (or (not (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xm tptp.xm))) (not (= (tptp.sdtasdt0 tptp.xp (tptp.sdtasdt0 tptp.xm tptp.xm)) (tptp.sdtasdt0 tptp.xn tptp.xn)))))) :rule cong :premises (t36 t38))
% 5.24/5.49 (step t40 (cl (= (=> (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2))))) (or (not (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xm tptp.xm))) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp (tptp.sdtasdt0 tptp.xm tptp.xm)))))) (=> (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2))))) (or (not (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xm tptp.xm))) (not (= (tptp.sdtasdt0 tptp.xp (tptp.sdtasdt0 tptp.xm tptp.xm)) (tptp.sdtasdt0 tptp.xn tptp.xn))))))) :rule cong :premises (t18 t39))
% 5.24/5.49 (step t41 (cl (=> (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2))))) (or (not (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xm tptp.xm))) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp (tptp.sdtasdt0 tptp.xm tptp.xm)))))) (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2)))))) :rule implies_neg1)
% 5.24/5.49 (anchor :step t42)
% 5.24/5.49 (assume t42.a0 (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2))))))
% 5.24/5.49 (step t42.t1 (cl (or (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2)))))) (or (not (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xm tptp.xm))) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp (tptp.sdtasdt0 tptp.xm tptp.xm))))))) :rule forall_inst :args ((:= W2 (tptp.sdtasdt0 tptp.xm tptp.xm))))
% 5.24/5.49 (step t42.t2 (cl (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2)))))) (or (not (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xm tptp.xm))) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp (tptp.sdtasdt0 tptp.xm tptp.xm)))))) :rule or :premises (t42.t1))
% 5.24/5.49 (step t42.t3 (cl (or (not (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xm tptp.xm))) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp (tptp.sdtasdt0 tptp.xm tptp.xm)))))) :rule resolution :premises (t42.t2 t42.a0))
% 5.24/5.49 (step t42 (cl (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2)))))) (or (not (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xm tptp.xm))) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp (tptp.sdtasdt0 tptp.xm tptp.xm)))))) :rule subproof :discharge (t42.a0))
% 5.24/5.49 (step t43 (cl (=> (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2))))) (or (not (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xm tptp.xm))) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp (tptp.sdtasdt0 tptp.xm tptp.xm)))))) (or (not (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xm tptp.xm))) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp (tptp.sdtasdt0 tptp.xm tptp.xm)))))) :rule resolution :premises (t41 t42))
% 5.24/5.49 (step t44 (cl (=> (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2))))) (or (not (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xm tptp.xm))) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp (tptp.sdtasdt0 tptp.xm tptp.xm)))))) (not (or (not (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xm tptp.xm))) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp (tptp.sdtasdt0 tptp.xm tptp.xm))))))) :rule implies_neg2)
% 5.24/5.49 (step t45 (cl (=> (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2))))) (or (not (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xm tptp.xm))) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp (tptp.sdtasdt0 tptp.xm tptp.xm)))))) (=> (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2))))) (or (not (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xm tptp.xm))) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp (tptp.sdtasdt0 tptp.xm tptp.xm))))))) :rule resolution :premises (t43 t44))
% 5.24/5.49 (step t46 (cl (=> (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2))))) (or (not (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xm tptp.xm))) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp (tptp.sdtasdt0 tptp.xm tptp.xm))))))) :rule contraction :premises (t45))
% 5.24/5.49 (step t47 (cl (=> (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2))))) (or (not (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xm tptp.xm))) (not (= (tptp.sdtasdt0 tptp.xp (tptp.sdtasdt0 tptp.xm tptp.xm)) (tptp.sdtasdt0 tptp.xn tptp.xn)))))) :rule resolution :premises (t35 t40 t46))
% 5.24/5.49 (step t48 (cl (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2)))))) (or (not (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xm tptp.xm))) (not (= (tptp.sdtasdt0 tptp.xp (tptp.sdtasdt0 tptp.xm tptp.xm)) (tptp.sdtasdt0 tptp.xn tptp.xn))))) :rule implies :premises (t47))
% 5.24/5.49 (step t49 (cl (not (or (not (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xm tptp.xm))) (not (= (tptp.sdtasdt0 tptp.xp (tptp.sdtasdt0 tptp.xm tptp.xm)) (tptp.sdtasdt0 tptp.xn tptp.xn))))) (not (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xm tptp.xm))) (not (= (tptp.sdtasdt0 tptp.xp (tptp.sdtasdt0 tptp.xm tptp.xm)) (tptp.sdtasdt0 tptp.xn tptp.xn)))) :rule or_pos)
% 5.24/5.49 (step t50 (cl (not (= (tptp.sdtasdt0 tptp.xp (tptp.sdtasdt0 tptp.xm tptp.xm)) (tptp.sdtasdt0 tptp.xn tptp.xn))) (not (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xm tptp.xm))) (not (or (not (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xm tptp.xm))) (not (= (tptp.sdtasdt0 tptp.xp (tptp.sdtasdt0 tptp.xm tptp.xm)) (tptp.sdtasdt0 tptp.xn tptp.xn)))))) :rule reordering :premises (t49))
% 5.24/5.49 (step t51 (cl (not (or (not (tptp.aNaturalNumber0 tptp.xm)) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xm tptp.xm)))) (not (tptp.aNaturalNumber0 tptp.xm)) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xm tptp.xm))) :rule or_pos)
% 5.24/5.49 (step t52 (cl (not (or (not (tptp.aNaturalNumber0 tptp.xm)) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xm tptp.xm)))) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xm tptp.xm))) :rule contraction :premises (t51))
% 5.24/5.49 (step t53 (cl (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xm tptp.xm)) (not (or (not (tptp.aNaturalNumber0 tptp.xm)) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xm tptp.xm))))) :rule reordering :premises (t52))
% 5.24/5.49 (step t54 (cl (not (= (and (tptp.aNaturalNumber0 tptp.xn) (tptp.aNaturalNumber0 tptp.xm) (tptp.aNaturalNumber0 tptp.xp) (not (= tptp.xn tptp.sz00)) (not (= tptp.xm tptp.sz00)) (not (= tptp.xp tptp.sz00))) (and (tptp.aNaturalNumber0 tptp.xn) (tptp.aNaturalNumber0 tptp.xm) (tptp.aNaturalNumber0 tptp.xp) (not (= tptp.sz00 tptp.xn)) (not (= tptp.sz00 tptp.xm)) (not (= tptp.sz00 tptp.xp))))) (not (and (tptp.aNaturalNumber0 tptp.xn) (tptp.aNaturalNumber0 tptp.xm) (tptp.aNaturalNumber0 tptp.xp) (not (= tptp.xn tptp.sz00)) (not (= tptp.xm tptp.sz00)) (not (= tptp.xp tptp.sz00)))) (and (tptp.aNaturalNumber0 tptp.xn) (tptp.aNaturalNumber0 tptp.xm) (tptp.aNaturalNumber0 tptp.xp) (not (= tptp.sz00 tptp.xn)) (not (= tptp.sz00 tptp.xm)) (not (= tptp.sz00 tptp.xp)))) :rule equiv_pos2)
% 5.24/5.49 (step t55 (cl (= (tptp.aNaturalNumber0 tptp.xn) (tptp.aNaturalNumber0 tptp.xn))) :rule refl)
% 5.24/5.49 (step t56 (cl (= (tptp.aNaturalNumber0 tptp.xm) (tptp.aNaturalNumber0 tptp.xm))) :rule refl)
% 5.24/5.49 (step t57 (cl (= (tptp.aNaturalNumber0 tptp.xp) (tptp.aNaturalNumber0 tptp.xp))) :rule refl)
% 5.24/5.49 (step t58 (cl (= (= tptp.xn tptp.sz00) (= tptp.sz00 tptp.xn))) :rule all_simplify)
% 5.24/5.49 (step t59 (cl (= (not (= tptp.xn tptp.sz00)) (not (= tptp.sz00 tptp.xn)))) :rule cong :premises (t58))
% 5.24/5.49 (step t60 (cl (= (= tptp.xm tptp.sz00) (= tptp.sz00 tptp.xm))) :rule all_simplify)
% 5.24/5.49 (step t61 (cl (= (not (= tptp.xm tptp.sz00)) (not (= tptp.sz00 tptp.xm)))) :rule cong :premises (t60))
% 5.24/5.49 (step t62 (cl (= (= tptp.xp tptp.sz00) (= tptp.sz00 tptp.xp))) :rule all_simplify)
% 5.24/5.49 (step t63 (cl (= (not (= tptp.xp tptp.sz00)) (not (= tptp.sz00 tptp.xp)))) :rule cong :premises (t62))
% 5.24/5.49 (step t64 (cl (= (and (tptp.aNaturalNumber0 tptp.xn) (tptp.aNaturalNumber0 tptp.xm) (tptp.aNaturalNumber0 tptp.xp) (not (= tptp.xn tptp.sz00)) (not (= tptp.xm tptp.sz00)) (not (= tptp.xp tptp.sz00))) (and (tptp.aNaturalNumber0 tptp.xn) (tptp.aNaturalNumber0 tptp.xm) (tptp.aNaturalNumber0 tptp.xp) (not (= tptp.sz00 tptp.xn)) (not (= tptp.sz00 tptp.xm)) (not (= tptp.sz00 tptp.xp))))) :rule cong :premises (t55 t56 t57 t59 t61 t63))
% 5.24/5.49 (step t65 (cl (and (tptp.aNaturalNumber0 tptp.xn) (tptp.aNaturalNumber0 tptp.xm) (tptp.aNaturalNumber0 tptp.xp) (not (= tptp.sz00 tptp.xn)) (not (= tptp.sz00 tptp.xm)) (not (= tptp.sz00 tptp.xp)))) :rule resolution :premises (t54 t64 a39))
% 5.24/5.49 (step t66 (cl (tptp.aNaturalNumber0 tptp.xm)) :rule and :premises (t65))
% 5.24/5.49 (step t67 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))) (or (not (tptp.aNaturalNumber0 tptp.xm)) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xm tptp.xm)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1))))) :rule implies_neg1)
% 5.24/5.49 (anchor :step t68)
% 5.24/5.49 (assume t68.a0 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))))
% 5.24/5.49 (step t68.t1 (cl (or (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1))))) (or (not (tptp.aNaturalNumber0 tptp.xm)) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xm tptp.xm))))) :rule forall_inst :args ((:= W0 tptp.xm) (:= W1 tptp.xm)))
% 5.24/5.49 (step t68.t2 (cl (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1))))) (or (not (tptp.aNaturalNumber0 tptp.xm)) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xm tptp.xm)))) :rule or :premises (t68.t1))
% 5.24/5.49 (step t68.t3 (cl (or (not (tptp.aNaturalNumber0 tptp.xm)) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xm tptp.xm)))) :rule resolution :premises (t68.t2 t68.a0))
% 5.24/5.49 (step t68 (cl (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1))))) (or (not (tptp.aNaturalNumber0 tptp.xm)) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xm tptp.xm)))) :rule subproof :discharge (t68.a0))
% 5.24/5.49 (step t69 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))) (or (not (tptp.aNaturalNumber0 tptp.xm)) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xm tptp.xm)))) (or (not (tptp.aNaturalNumber0 tptp.xm)) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xm tptp.xm)))) :rule resolution :premises (t67 t68))
% 5.24/5.49 (step t70 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))) (or (not (tptp.aNaturalNumber0 tptp.xm)) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xm tptp.xm)))) (not (or (not (tptp.aNaturalNumber0 tptp.xm)) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xm tptp.xm))))) :rule implies_neg2)
% 5.24/5.49 (step t71 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))) (or (not (tptp.aNaturalNumber0 tptp.xm)) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xm tptp.xm)))) (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))) (or (not (tptp.aNaturalNumber0 tptp.xm)) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xm tptp.xm))))) :rule resolution :premises (t69 t70))
% 5.24/5.49 (step t72 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))) (or (not (tptp.aNaturalNumber0 tptp.xm)) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xm tptp.xm))))) :rule contraction :premises (t71))
% 5.24/5.49 (step t73 (cl (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1))))) (or (not (tptp.aNaturalNumber0 tptp.xm)) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xm tptp.xm)))) :rule implies :premises (t72))
% 5.24/5.49 (step t74 (cl (not (= (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))))) (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1))))) :rule equiv_pos2)
% 5.24/5.49 (step t75 (cl (= (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))))) :rule all_simplify)
% 5.24/5.49 (step t76 (cl (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1))))) :rule resolution :premises (t74 t75 a4))
% 5.24/5.49 (step t77 (cl (or (not (tptp.aNaturalNumber0 tptp.xm)) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xm tptp.xm)))) :rule resolution :premises (t73 t76))
% 5.24/5.49 (step t78 (cl (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xm tptp.xm))) :rule resolution :premises (t53 t66 t77))
% 5.24/5.49 (step t79 (cl (not (or (not (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xm tptp.xm))) (not (= (tptp.sdtasdt0 tptp.xp (tptp.sdtasdt0 tptp.xm tptp.xm)) (tptp.sdtasdt0 tptp.xn tptp.xn)))))) :rule resolution :premises (t50 a41 t78))
% 5.24/5.49 (step t80 (cl (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2))))))) :rule resolution :premises (t48 t79))
% 5.24/5.49 (step t81 (cl (not (or (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xn tptp.xn))) (= (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2))))))))) (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xn tptp.xn))) (= (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2)))))))) :rule or_pos)
% 5.24/5.49 (step t82 (cl (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xn tptp.xn))) (= (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2))))))) (not (or (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xn tptp.xn))) (= (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2)))))))))) :rule reordering :premises (t81))
% 5.24/5.49 (step t83 (cl (tptp.aNaturalNumber0 tptp.xp)) :rule and :premises (t65))
% 5.24/5.49 (step t84 (cl (not (or (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xn)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xn tptp.xn)))) (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xn)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xn tptp.xn))) :rule or_pos)
% 5.24/5.49 (step t85 (cl (not (or (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xn)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xn tptp.xn)))) (not (tptp.aNaturalNumber0 tptp.xn)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xn tptp.xn))) :rule contraction :premises (t84))
% 5.24/5.49 (step t86 (cl (not (tptp.aNaturalNumber0 tptp.xn)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xn tptp.xn)) (not (or (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xn)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xn tptp.xn))))) :rule reordering :premises (t85))
% 5.24/5.49 (step t87 (cl (tptp.aNaturalNumber0 tptp.xn)) :rule and :premises (t65))
% 5.24/5.49 (step t88 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))) (or (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xn)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xn tptp.xn)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1))))) :rule implies_neg1)
% 5.24/5.49 (anchor :step t89)
% 5.24/5.49 (assume t89.a0 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))))
% 5.24/5.49 (step t89.t1 (cl (or (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1))))) (or (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xn)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xn tptp.xn))))) :rule forall_inst :args ((:= W0 tptp.xn) (:= W1 tptp.xn)))
% 5.24/5.49 (step t89.t2 (cl (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1))))) (or (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xn)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xn tptp.xn)))) :rule or :premises (t89.t1))
% 5.24/5.49 (step t89.t3 (cl (or (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xn)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xn tptp.xn)))) :rule resolution :premises (t89.t2 t89.a0))
% 5.24/5.49 (step t89 (cl (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1))))) (or (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xn)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xn tptp.xn)))) :rule subproof :discharge (t89.a0))
% 5.24/5.49 (step t90 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))) (or (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xn)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xn tptp.xn)))) (or (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xn)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xn tptp.xn)))) :rule resolution :premises (t88 t89))
% 5.24/5.49 (step t91 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))) (or (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xn)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xn tptp.xn)))) (not (or (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xn)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xn tptp.xn))))) :rule implies_neg2)
% 5.24/5.49 (step t92 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))) (or (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xn)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xn tptp.xn)))) (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))) (or (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xn)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xn tptp.xn))))) :rule resolution :premises (t90 t91))
% 5.24/5.49 (step t93 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))) (or (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xn)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xn tptp.xn))))) :rule contraction :premises (t92))
% 5.24/5.49 (step t94 (cl (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1))))) (or (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xn)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xn tptp.xn)))) :rule implies :premises (t93))
% 5.24/5.49 (step t95 (cl (or (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xn)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xn tptp.xn)))) :rule resolution :premises (t94 t76))
% 5.24/5.49 (step t96 (cl (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xn tptp.xn))) :rule resolution :premises (t86 t87 t95))
% 5.24/5.49 (step t97 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= (tptp.doDivides0 W0 W1) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= W1 (tptp.sdtasdt0 W0 W2))))))))) (or (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xn tptp.xn))) (= (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2))))))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= (tptp.doDivides0 W0 W1) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= W1 (tptp.sdtasdt0 W0 W2)))))))))) :rule implies_neg1)
% 5.24/5.49 (anchor :step t98)
% 5.24/5.49 (assume t98.a0 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= (tptp.doDivides0 W0 W1) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= W1 (tptp.sdtasdt0 W0 W2))))))))))
% 5.24/5.49 (step t98.t1 (cl (or (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= (tptp.doDivides0 W0 W1) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= W1 (tptp.sdtasdt0 W0 W2)))))))))) (or (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xn tptp.xn))) (= (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2)))))))))) :rule forall_inst :args ((:= W0 tptp.xp) (:= W1 (tptp.sdtasdt0 tptp.xn tptp.xn))))
% 5.24/5.49 (step t98.t2 (cl (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= (tptp.doDivides0 W0 W1) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= W1 (tptp.sdtasdt0 W0 W2)))))))))) (or (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xn tptp.xn))) (= (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2))))))))) :rule or :premises (t98.t1))
% 5.24/5.49 (step t98.t3 (cl (or (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xn tptp.xn))) (= (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2))))))))) :rule resolution :premises (t98.t2 t98.a0))
% 5.24/5.49 (step t98 (cl (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= (tptp.doDivides0 W0 W1) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= W1 (tptp.sdtasdt0 W0 W2)))))))))) (or (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xn tptp.xn))) (= (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2))))))))) :rule subproof :discharge (t98.a0))
% 5.24/5.49 (step t99 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= (tptp.doDivides0 W0 W1) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= W1 (tptp.sdtasdt0 W0 W2))))))))) (or (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xn tptp.xn))) (= (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2))))))))) (or (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xn tptp.xn))) (= (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2))))))))) :rule resolution :premises (t97 t98))
% 5.24/5.49 (step t100 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= (tptp.doDivides0 W0 W1) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= W1 (tptp.sdtasdt0 W0 W2))))))))) (or (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xn tptp.xn))) (= (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2))))))))) (not (or (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xn tptp.xn))) (= (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2)))))))))) :rule implies_neg2)
% 5.24/5.49 (step t101 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= (tptp.doDivides0 W0 W1) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= W1 (tptp.sdtasdt0 W0 W2))))))))) (or (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xn tptp.xn))) (= (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2))))))))) (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= (tptp.doDivides0 W0 W1) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= W1 (tptp.sdtasdt0 W0 W2))))))))) (or (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xn tptp.xn))) (= (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2)))))))))) :rule resolution :premises (t99 t100))
% 5.24/5.49 (step t102 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= (tptp.doDivides0 W0 W1) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= W1 (tptp.sdtasdt0 W0 W2))))))))) (or (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xn tptp.xn))) (= (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2)))))))))) :rule contraction :premises (t101))
% 5.24/5.49 (step t103 (cl (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= (tptp.doDivides0 W0 W1) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= W1 (tptp.sdtasdt0 W0 W2)))))))))) (or (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xn tptp.xn))) (= (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2))))))))) :rule implies :premises (t102))
% 5.24/5.49 (step t104 (cl (not (= (forall ((W0 $$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))))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= (tptp.doDivides0 W0 W1) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= W1 (tptp.sdtasdt0 W0 W2))))))))))) (not (forall ((W0 $$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)))))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= (tptp.doDivides0 W0 W1) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= W1 (tptp.sdtasdt0 W0 W2)))))))))) :rule equiv_pos2)
% 5.24/5.49 (anchor :step t105 :args ((W0 $$unsorted) (:= W0 W0) (W1 $$unsorted) (:= W1 W1)))
% 5.24/5.49 (step t105.t1 (cl (= W0 W0)) :rule refl)
% 5.24/5.49 (step t105.t2 (cl (= W1 W1)) :rule refl)
% 5.24/5.49 (step t105.t3 (cl (= (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)))) :rule refl)
% 5.24/5.49 (step t105.t4 (cl (= (tptp.doDivides0 W0 W1) (tptp.doDivides0 W0 W1))) :rule refl)
% 5.24/5.49 (step t105.t5 (cl (= (exists ((W2 $$unsorted)) (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtasdt0 W0 W2)))) (not (forall ((W2 $$unsorted)) (not (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtasdt0 W0 W2)))))))) :rule all_simplify)
% 5.24/5.49 (step t105.t6 (cl (= (forall ((W2 $$unsorted)) (not (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtasdt0 W0 W2))))) (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= W1 (tptp.sdtasdt0 W0 W2))))))) :rule all_simplify)
% 5.24/5.49 (step t105.t7 (cl (= (not (forall ((W2 $$unsorted)) (not (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtasdt0 W0 W2)))))) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= W1 (tptp.sdtasdt0 W0 W2)))))))) :rule cong :premises (t105.t6))
% 5.24/5.49 (step t105.t8 (cl (= (exists ((W2 $$unsorted)) (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtasdt0 W0 W2)))) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= W1 (tptp.sdtasdt0 W0 W2)))))))) :rule trans :premises (t105.t5 t105.t7))
% 5.24/5.49 (step t105.t9 (cl (= (= (tptp.doDivides0 W0 W1) (exists ((W2 $$unsorted)) (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtasdt0 W0 W2))))) (= (tptp.doDivides0 W0 W1) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= W1 (tptp.sdtasdt0 W0 W2))))))))) :rule cong :premises (t105.t4 t105.t8))
% 5.24/5.49 (step t105.t10 (cl (= (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.doDivides0 W0 W1) (exists ((W2 $$unsorted)) (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtasdt0 W0 W2)))))) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.doDivides0 W0 W1) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= W1 (tptp.sdtasdt0 W0 W2)))))))))) :rule cong :premises (t105.t3 t105.t9))
% 5.24/5.49 (step t105 (cl (= (forall ((W0 $$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))))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.doDivides0 W0 W1) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= W1 (tptp.sdtasdt0 W0 W2))))))))))) :rule bind)
% 5.24/5.49 (step t106 (cl (= (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.doDivides0 W0 W1) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= W1 (tptp.sdtasdt0 W0 W2))))))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= (tptp.doDivides0 W0 W1) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= W1 (tptp.sdtasdt0 W0 W2))))))))))) :rule all_simplify)
% 5.24/5.49 (step t107 (cl (= (forall ((W0 $$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))))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= (tptp.doDivides0 W0 W1) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= W1 (tptp.sdtasdt0 W0 W2))))))))))) :rule trans :premises (t105 t106))
% 5.24/5.49 (step t108 (cl (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= (tptp.doDivides0 W0 W1) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= W1 (tptp.sdtasdt0 W0 W2)))))))))) :rule resolution :premises (t104 t107 a29))
% 5.24/5.49 (step t109 (cl (or (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.aNaturalNumber0 (tptp.sdtasdt0 tptp.xn tptp.xn))) (= (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2))))))))) :rule resolution :premises (t103 t108))
% 5.24/5.49 (step t110 (cl (= (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn)) (not (forall ((W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W2)) (not (= (tptp.sdtasdt0 tptp.xn tptp.xn) (tptp.sdtasdt0 tptp.xp W2)))))))) :rule resolution :premises (t82 t83 t96 t109))
% 5.34/5.52 (step t111 (cl (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn))) :rule resolution :premises (t34 t80 t110))
% 5.34/5.52 (step t112 (cl (not (tptp.doDivides0 tptp.xp tptp.xn))) :rule resolution :premises (t11 t111))
% 5.34/5.52 (step t113 (cl (not (or (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.isPrime0 tptp.xp)) (not (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xn))) (tptp.doDivides0 tptp.xp tptp.xn) (tptp.doDivides0 tptp.xp tptp.xn)))) :rule resolution :premises (t10 t112 t87 t83 a42 t111))
% 5.34/5.52 (step t114 (cl (not (= (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.isPrime0 W2) (tptp.doDivides0 W2 (tptp.sdtasdt0 W0 W1))) (or (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W2)) (not (tptp.isPrime0 W2)) (not (tptp.doDivides0 W2 (tptp.sdtasdt0 W0 W1))) (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1))))) (not (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.isPrime0 W2) (tptp.doDivides0 W2 (tptp.sdtasdt0 W0 W1))) (or (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1)))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W2)) (not (tptp.isPrime0 W2)) (not (tptp.doDivides0 W2 (tptp.sdtasdt0 W0 W1))) (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1)))) :rule equiv_pos2)
% 5.34/5.52 (step t115 (cl (= (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.isPrime0 W2) (tptp.doDivides0 W2 (tptp.sdtasdt0 W0 W1))) (or (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W2)) (not (tptp.isPrime0 W2)) (not (tptp.doDivides0 W2 (tptp.sdtasdt0 W0 W1))) (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1))))) :rule all_simplify)
% 5.34/5.52 (step t116 (cl (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W2)) (not (tptp.isPrime0 W2)) (not (tptp.doDivides0 W2 (tptp.sdtasdt0 W0 W1))) (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1)))) :rule resolution :premises (t114 t115 a38))
% 5.34/5.52 (step t117 (cl) :rule resolution :premises (t7 t113 t116))
% 5.34/5.52
% 5.34/5.52 % SZS output end Proof for /export/starexec/sandbox2/tmp/tmp.wMIrP9bN8W/cvc5---1.0.5_6644.smt2
% 5.34/5.52 % cvc5---1.0.5 exiting
% 5.34/5.52 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------