%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : NUM495+1 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : do_cvc5 %s %d

% Computer : n023.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 17:33:43 EDT 2024

% Result   : Theorem 25.61s 26.09s
% Output   : Proof 25.61s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13  % Problem    : NUM495+1 : TPTP v8.2.0. Released v4.0.0.
% 0.10/0.14  % Command    : do_cvc5 %s %d
% 0.13/0.35  % Computer : n023.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   : Mon May 27 23:38:39 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.19/0.51  %----Proving TF0_NAR, FOF, or CNF
% 25.61/26.09  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 25.61/26.09  --- Run --no-e-matching --full-saturate-quant at 5...
% 25.61/26.09  --- Run --no-e-matching --enum-inst-sum --full-saturate-quant at 5...
% 25.61/26.09  --- Run --finite-model-find --uf-ss=no-minimal at 5...
% 25.61/26.09  --- Run --multi-trigger-when-single --full-saturate-quant at 5...
% 25.61/26.09  % SZS status Theorem for /export/starexec/sandbox/tmp/tmp.sHAYK2mJce/cvc5---1.0.5_28636.smt2
% 25.61/26.09  % SZS output start Proof for /export/starexec/sandbox/tmp/tmp.sHAYK2mJce/cvc5---1.0.5_28636.smt2
% 25.61/26.09  (assume a0 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) true)))
% 25.61/26.09  (assume a1 (tptp.aNaturalNumber0 tptp.sz00))
% 25.61/26.09  (assume a2 (and (tptp.aNaturalNumber0 tptp.sz10) (not (= tptp.sz10 tptp.sz00))))
% 25.61/26.09  (assume a3 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))))
% 25.61/26.09  (assume a4 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtasdt0 W0 W1)))))
% 25.61/26.09  (assume a5 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W1 W0)))))
% 25.61/26.09  (assume a6 (forall ((W0 $$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))))))
% 25.61/26.09  (assume a7 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtpldt0 W0 tptp.sz00) W0) (= W0 (tptp.sdtpldt0 tptp.sz00 W0))))))
% 25.61/26.09  (assume a8 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))
% 25.61/26.09  (assume a9 (forall ((W0 $$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))))))
% 25.61/26.09  (assume a10 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz10) W0) (= W0 (tptp.sdtasdt0 tptp.sz10 W0))))))
% 25.61/26.09  (assume a11 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 W0))))))
% 25.61/26.09  (assume a12 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (and (= (tptp.sdtasdt0 W0 (tptp.sdtpldt0 W1 W2)) (tptp.sdtpldt0 (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W0 W2))) (= (tptp.sdtasdt0 (tptp.sdtpldt0 W1 W2) W0) (tptp.sdtpldt0 (tptp.sdtasdt0 W1 W0) (tptp.sdtasdt0 W2 W0)))))))
% 25.61/26.09  (assume a13 (forall ((W0 $$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)))))
% 25.61/26.09  (assume a14 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (=> (not (= W0 tptp.sz00)) (forall ((W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (or (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W0 W2)) (= (tptp.sdtasdt0 W1 W0) (tptp.sdtasdt0 W2 W0))) (= W1 W2))))))))
% 25.61/26.09  (assume a15 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (= (tptp.sdtpldt0 W0 W1) tptp.sz00) (and (= W0 tptp.sz00) (= W1 tptp.sz00))))))
% 25.61/26.09  (assume a16 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (= (tptp.sdtasdt0 W0 W1) tptp.sz00) (or (= W0 tptp.sz00) (= W1 tptp.sz00))))))
% 25.61/26.09  (assume a17 (forall ((W0 $$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)))))))
% 25.61/26.09  (assume a18 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (tptp.sdtlseqdt0 W0 W1) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtmndt0 W1 W0)) (and (tptp.aNaturalNumber0 W2) (= (tptp.sdtpldt0 W0 W2) W1))))))))
% 25.61/26.09  (assume a19 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (tptp.sdtlseqdt0 W0 W0))))
% 25.61/26.09  (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)))))
% 25.61/26.09  (assume a21 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W2)) (tptp.sdtlseqdt0 W0 W2)))))
% 25.61/26.09  (assume a22 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (or (tptp.sdtlseqdt0 W0 W1) (and (not (= W1 W0)) (tptp.sdtlseqdt0 W1 W0))))))
% 25.61/26.09  (assume a23 (forall ((W0 $$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)))))))))
% 25.61/26.09  (assume a24 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (not (= W0 tptp.sz00)) (not (= W1 W2)) (tptp.sdtlseqdt0 W1 W2)) (and (not (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W0 W2))) (tptp.sdtlseqdt0 (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W0 W2)) (not (= (tptp.sdtasdt0 W1 W0) (tptp.sdtasdt0 W2 W0))) (tptp.sdtlseqdt0 (tptp.sdtasdt0 W1 W0) (tptp.sdtasdt0 W2 W0)))))))
% 25.61/26.09  (assume a25 (forall ((W0 $$unsorted)) (=> (tptp.aNaturalNumber0 W0) (or (= W0 tptp.sz00) (= W0 tptp.sz10) (and (not (= tptp.sz10 W0)) (tptp.sdtlseqdt0 tptp.sz10 W0))))))
% 25.61/26.09  (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))))))
% 25.61/26.09  (assume a27 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (tptp.iLess0 W0 W1) true))))
% 25.61/26.09  (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)))))
% 25.61/26.09  (assume a29 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (= (tptp.doDivides0 W0 W1) (exists ((W2 $$unsorted)) (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtasdt0 W0 W2))))))))
% 25.61/26.09  (assume a30 (forall ((W0 $$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)))))))))
% 25.61/26.09  (assume a31 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.doDivides0 W0 W1) (tptp.doDivides0 W1 W2)) (tptp.doDivides0 W0 W2)))))
% 25.61/26.09  (assume a32 (forall ((W0 $$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))))))
% 25.61/26.09  (assume a33 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1) (tptp.aNaturalNumber0 W2)) (=> (and (tptp.doDivides0 W0 W1) (tptp.doDivides0 W0 (tptp.sdtpldt0 W1 W2))) (tptp.doDivides0 W0 W2)))))
% 25.61/26.09  (assume a34 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (tptp.doDivides0 W0 W1) (not (= W1 tptp.sz00))) (tptp.sdtlseqdt0 W0 W1)))))
% 25.61/26.09  (assume a35 (forall ((W0 $$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))))))))
% 25.61/26.09  (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)))))))))
% 25.61/26.09  (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))))))
% 25.61/26.09  (assume a38 (and (tptp.aNaturalNumber0 tptp.xn) (tptp.aNaturalNumber0 tptp.xm) (tptp.aNaturalNumber0 tptp.xp)))
% 25.61/26.09  (assume a39 (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))) (=> (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)) (or (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1)))))))
% 25.61/26.09  (assume a40 (and (tptp.isPrime0 tptp.xp) (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xn tptp.xm))))
% 25.61/26.09  (assume a41 (tptp.sdtlseqdt0 tptp.xp tptp.xn))
% 25.61/26.09  (assume a42 (= tptp.xr (tptp.sdtmndt0 tptp.xn tptp.xp)))
% 25.61/26.09  (assume a43 (and (not (= tptp.xr tptp.xn)) (tptp.sdtlseqdt0 tptp.xr tptp.xn)))
% 25.61/26.09  (assume a44 (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xr tptp.xm)))
% 25.61/26.09  (assume a45 (and (not (= (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xr tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.sdtlseqdt0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xr tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))))
% 25.61/26.09  (assume a46 (not (or (tptp.doDivides0 tptp.xp tptp.xr) (tptp.doDivides0 tptp.xp tptp.xm))))
% 25.61/26.09  (assume a47 true)
% 25.61/26.09  (step t1 (cl (not (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp))) (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (= (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp)) (not (tptp.sdtlseqdt0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)))) (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp))) (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (= (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp)) (not (tptp.sdtlseqdt0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) :rule or_pos)
% 25.61/26.09  (step t2 (cl (= (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp)) (not (tptp.sdtlseqdt0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp))) (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)) (not (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp))) (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (= (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp)) (not (tptp.sdtlseqdt0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))))) :rule reordering :premises (t1))
% 25.61/26.09  (step t3 (cl (not (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm))) (not (tptp.aNaturalNumber0 tptp.xp)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp)))) (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm))) (not (tptp.aNaturalNumber0 tptp.xp)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp))) :rule or_pos)
% 25.61/26.09  (step t4 (cl (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm))) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp)) (not (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm))) (not (tptp.aNaturalNumber0 tptp.xp)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp))))) :rule reordering :premises (t3))
% 25.61/26.09  (step t5 (cl (tptp.aNaturalNumber0 tptp.xp)) :rule and :premises (a38))
% 25.61/26.09  (step t6 (cl (not (or (not (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp))) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm)))) (not (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp))) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm))) :rule or_pos)
% 25.61/26.09  (step t7 (cl (not (tptp.aNaturalNumber0 tptp.xm)) (not (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp))) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm)) (not (or (not (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp))) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm))))) :rule reordering :premises (t6))
% 25.61/26.09  (step t8 (cl (tptp.aNaturalNumber0 tptp.xm)) :rule and :premises (a38))
% 25.61/26.09  (step t9 (cl (not (and (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp)) (= tptp.xn (tptp.sdtpldt0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp))))) (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp))) :rule and_pos)
% 25.61/26.09  (step t10 (cl (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp)) (not (and (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp)) (= tptp.xn (tptp.sdtpldt0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)))))) :rule reordering :premises (t9))
% 25.61/26.09  (step t11 (cl (not (or (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.sdtlseqdt0 tptp.xp tptp.xn)) (and (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp)) (= tptp.xn (tptp.sdtpldt0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)))))) (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.sdtlseqdt0 tptp.xp tptp.xn)) (and (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp)) (= tptp.xn (tptp.sdtpldt0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp))))) :rule or_pos)
% 25.61/26.09  (step t12 (cl (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.sdtlseqdt0 tptp.xp tptp.xn)) (and (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp)) (= tptp.xn (tptp.sdtpldt0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)))) (not (or (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.sdtlseqdt0 tptp.xp tptp.xn)) (and (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp)) (= tptp.xn (tptp.sdtpldt0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp))))))) :rule reordering :premises (t11))
% 25.61/26.09  (step t13 (cl (tptp.aNaturalNumber0 tptp.xn)) :rule and :premises (a38))
% 25.61/26.09  (step t14 (cl (not (= (=> (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1410 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (= (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1410) (= W1 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1410))) (= (tptp.sdtmndt0 W1 W0) BOUND_VARIABLE_1410)))) (or (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.sdtlseqdt0 tptp.xp tptp.xn)) (= (and (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp)) (= tptp.xn (tptp.sdtpldt0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)))) (= (tptp.sdtmndt0 tptp.xn tptp.xp) (tptp.sdtmndt0 tptp.xn tptp.xp))))) (=> (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1410 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (= (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1410) (= W1 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1410))) (= (tptp.sdtmndt0 W1 W0) BOUND_VARIABLE_1410)))) (or (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.sdtlseqdt0 tptp.xp tptp.xn)) (and (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp)) (= tptp.xn (tptp.sdtpldt0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)))))))) (not (=> (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1410 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (= (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1410) (= W1 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1410))) (= (tptp.sdtmndt0 W1 W0) BOUND_VARIABLE_1410)))) (or (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.sdtlseqdt0 tptp.xp tptp.xn)) (= (and (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp)) (= tptp.xn (tptp.sdtpldt0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)))) (= (tptp.sdtmndt0 tptp.xn tptp.xp) (tptp.sdtmndt0 tptp.xn tptp.xp)))))) (=> (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1410 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (= (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1410) (= W1 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1410))) (= (tptp.sdtmndt0 W1 W0) BOUND_VARIABLE_1410)))) (or (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.sdtlseqdt0 tptp.xp tptp.xn)) (and (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp)) (= tptp.xn (tptp.sdtpldt0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp))))))) :rule equiv_pos2)
% 25.61/26.09  (step t15 (cl (= (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1410 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (= (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1410) (= W1 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1410))) (= (tptp.sdtmndt0 W1 W0) BOUND_VARIABLE_1410)))) (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1410 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (= (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1410) (= W1 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1410))) (= (tptp.sdtmndt0 W1 W0) BOUND_VARIABLE_1410)))))) :rule refl)
% 25.61/26.09  (step t16 (cl (= (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.aNaturalNumber0 tptp.xp)))) :rule refl)
% 25.61/26.09  (step t17 (cl (= (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xn)))) :rule refl)
% 25.61/26.09  (step t18 (cl (= (not (tptp.sdtlseqdt0 tptp.xp tptp.xn)) (not (tptp.sdtlseqdt0 tptp.xp tptp.xn)))) :rule refl)
% 25.61/26.09  (step t19 (cl (= (= (and (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp)) (= tptp.xn (tptp.sdtpldt0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)))) (= (tptp.sdtmndt0 tptp.xn tptp.xp) (tptp.sdtmndt0 tptp.xn tptp.xp))) (= (= (tptp.sdtmndt0 tptp.xn tptp.xp) (tptp.sdtmndt0 tptp.xn tptp.xp)) (and (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp)) (= tptp.xn (tptp.sdtpldt0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp))))))) :rule all_simplify)
% 25.61/26.09  (step t20 (cl (= (= (tptp.sdtmndt0 tptp.xn tptp.xp) (tptp.sdtmndt0 tptp.xn tptp.xp)) true)) :rule all_simplify)
% 25.61/26.09  (step t21 (cl (= (and (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp)) (= tptp.xn (tptp.sdtpldt0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)))) (and (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp)) (= tptp.xn (tptp.sdtpldt0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)))))) :rule refl)
% 25.61/26.09  (step t22 (cl (= (= (= (tptp.sdtmndt0 tptp.xn tptp.xp) (tptp.sdtmndt0 tptp.xn tptp.xp)) (and (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp)) (= tptp.xn (tptp.sdtpldt0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp))))) (= true (and (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp)) (= tptp.xn (tptp.sdtpldt0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp))))))) :rule cong :premises (t20 t21))
% 25.61/26.09  (step t23 (cl (= (= true (and (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp)) (= tptp.xn (tptp.sdtpldt0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp))))) (and (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp)) (= tptp.xn (tptp.sdtpldt0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)))))) :rule all_simplify)
% 25.61/26.09  (step t24 (cl (= (= (= (tptp.sdtmndt0 tptp.xn tptp.xp) (tptp.sdtmndt0 tptp.xn tptp.xp)) (and (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp)) (= tptp.xn (tptp.sdtpldt0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp))))) (and (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp)) (= tptp.xn (tptp.sdtpldt0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)))))) :rule trans :premises (t22 t23))
% 25.61/26.09  (step t25 (cl (= (= (and (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp)) (= tptp.xn (tptp.sdtpldt0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)))) (= (tptp.sdtmndt0 tptp.xn tptp.xp) (tptp.sdtmndt0 tptp.xn tptp.xp))) (and (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp)) (= tptp.xn (tptp.sdtpldt0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)))))) :rule trans :premises (t19 t24))
% 25.61/26.09  (step t26 (cl (= (or (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.sdtlseqdt0 tptp.xp tptp.xn)) (= (and (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp)) (= tptp.xn (tptp.sdtpldt0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)))) (= (tptp.sdtmndt0 tptp.xn tptp.xp) (tptp.sdtmndt0 tptp.xn tptp.xp)))) (or (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.sdtlseqdt0 tptp.xp tptp.xn)) (and (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp)) (= tptp.xn (tptp.sdtpldt0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp))))))) :rule cong :premises (t16 t17 t18 t25))
% 25.61/26.09  (step t27 (cl (= (=> (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1410 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (= (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1410) (= W1 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1410))) (= (tptp.sdtmndt0 W1 W0) BOUND_VARIABLE_1410)))) (or (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.sdtlseqdt0 tptp.xp tptp.xn)) (= (and (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp)) (= tptp.xn (tptp.sdtpldt0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)))) (= (tptp.sdtmndt0 tptp.xn tptp.xp) (tptp.sdtmndt0 tptp.xn tptp.xp))))) (=> (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1410 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (= (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1410) (= W1 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1410))) (= (tptp.sdtmndt0 W1 W0) BOUND_VARIABLE_1410)))) (or (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.sdtlseqdt0 tptp.xp tptp.xn)) (and (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp)) (= tptp.xn (tptp.sdtpldt0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)))))))) :rule cong :premises (t15 t26))
% 25.61/26.09  (step t28 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1410 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (= (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1410) (= W1 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1410))) (= (tptp.sdtmndt0 W1 W0) BOUND_VARIABLE_1410)))) (or (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.sdtlseqdt0 tptp.xp tptp.xn)) (= (and (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp)) (= tptp.xn (tptp.sdtpldt0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)))) (= (tptp.sdtmndt0 tptp.xn tptp.xp) (tptp.sdtmndt0 tptp.xn tptp.xp))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1410 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (= (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1410) (= W1 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1410))) (= (tptp.sdtmndt0 W1 W0) BOUND_VARIABLE_1410))))) :rule implies_neg1)
% 25.61/26.09  (anchor :step t29)
% 25.61/26.09  (assume t29.a0 (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1410 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (= (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1410) (= W1 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1410))) (= (tptp.sdtmndt0 W1 W0) BOUND_VARIABLE_1410)))))
% 25.61/26.09  (step t29.t1 (cl (or (not (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1410 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (= (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1410) (= W1 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1410))) (= (tptp.sdtmndt0 W1 W0) BOUND_VARIABLE_1410))))) (or (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.sdtlseqdt0 tptp.xp tptp.xn)) (= (and (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp)) (= tptp.xn (tptp.sdtpldt0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)))) (= (tptp.sdtmndt0 tptp.xn tptp.xp) (tptp.sdtmndt0 tptp.xn tptp.xp)))))) :rule forall_inst :args ((:= W0 tptp.xp) (:= W1 tptp.xn) (:= BOUND_VARIABLE_1410 (tptp.sdtmndt0 tptp.xn tptp.xp))))
% 25.61/26.09  (step t29.t2 (cl (not (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1410 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (= (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1410) (= W1 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1410))) (= (tptp.sdtmndt0 W1 W0) BOUND_VARIABLE_1410))))) (or (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.sdtlseqdt0 tptp.xp tptp.xn)) (= (and (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp)) (= tptp.xn (tptp.sdtpldt0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)))) (= (tptp.sdtmndt0 tptp.xn tptp.xp) (tptp.sdtmndt0 tptp.xn tptp.xp))))) :rule or :premises (t29.t1))
% 25.61/26.09  (step t29.t3 (cl (or (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.sdtlseqdt0 tptp.xp tptp.xn)) (= (and (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp)) (= tptp.xn (tptp.sdtpldt0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)))) (= (tptp.sdtmndt0 tptp.xn tptp.xp) (tptp.sdtmndt0 tptp.xn tptp.xp))))) :rule resolution :premises (t29.t2 t29.a0))
% 25.61/26.09  (step t29 (cl (not (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1410 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (= (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1410) (= W1 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1410))) (= (tptp.sdtmndt0 W1 W0) BOUND_VARIABLE_1410))))) (or (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.sdtlseqdt0 tptp.xp tptp.xn)) (= (and (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp)) (= tptp.xn (tptp.sdtpldt0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)))) (= (tptp.sdtmndt0 tptp.xn tptp.xp) (tptp.sdtmndt0 tptp.xn tptp.xp))))) :rule subproof :discharge (t29.a0))
% 25.61/26.09  (step t30 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1410 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (= (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1410) (= W1 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1410))) (= (tptp.sdtmndt0 W1 W0) BOUND_VARIABLE_1410)))) (or (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.sdtlseqdt0 tptp.xp tptp.xn)) (= (and (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp)) (= tptp.xn (tptp.sdtpldt0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)))) (= (tptp.sdtmndt0 tptp.xn tptp.xp) (tptp.sdtmndt0 tptp.xn tptp.xp))))) (or (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.sdtlseqdt0 tptp.xp tptp.xn)) (= (and (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp)) (= tptp.xn (tptp.sdtpldt0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)))) (= (tptp.sdtmndt0 tptp.xn tptp.xp) (tptp.sdtmndt0 tptp.xn tptp.xp))))) :rule resolution :premises (t28 t29))
% 25.61/26.09  (step t31 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1410 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (= (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1410) (= W1 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1410))) (= (tptp.sdtmndt0 W1 W0) BOUND_VARIABLE_1410)))) (or (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.sdtlseqdt0 tptp.xp tptp.xn)) (= (and (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp)) (= tptp.xn (tptp.sdtpldt0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)))) (= (tptp.sdtmndt0 tptp.xn tptp.xp) (tptp.sdtmndt0 tptp.xn tptp.xp))))) (not (or (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.sdtlseqdt0 tptp.xp tptp.xn)) (= (and (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp)) (= tptp.xn (tptp.sdtpldt0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)))) (= (tptp.sdtmndt0 tptp.xn tptp.xp) (tptp.sdtmndt0 tptp.xn tptp.xp)))))) :rule implies_neg2)
% 25.61/26.09  (step t32 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1410 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (= (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1410) (= W1 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1410))) (= (tptp.sdtmndt0 W1 W0) BOUND_VARIABLE_1410)))) (or (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.sdtlseqdt0 tptp.xp tptp.xn)) (= (and (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp)) (= tptp.xn (tptp.sdtpldt0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)))) (= (tptp.sdtmndt0 tptp.xn tptp.xp) (tptp.sdtmndt0 tptp.xn tptp.xp))))) (=> (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1410 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (= (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1410) (= W1 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1410))) (= (tptp.sdtmndt0 W1 W0) BOUND_VARIABLE_1410)))) (or (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.sdtlseqdt0 tptp.xp tptp.xn)) (= (and (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp)) (= tptp.xn (tptp.sdtpldt0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)))) (= (tptp.sdtmndt0 tptp.xn tptp.xp) (tptp.sdtmndt0 tptp.xn tptp.xp)))))) :rule resolution :premises (t30 t31))
% 25.61/26.09  (step t33 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1410 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (= (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1410) (= W1 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1410))) (= (tptp.sdtmndt0 W1 W0) BOUND_VARIABLE_1410)))) (or (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.sdtlseqdt0 tptp.xp tptp.xn)) (= (and (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp)) (= tptp.xn (tptp.sdtpldt0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)))) (= (tptp.sdtmndt0 tptp.xn tptp.xp) (tptp.sdtmndt0 tptp.xn tptp.xp)))))) :rule contraction :premises (t32))
% 25.61/26.09  (step t34 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1410 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (= (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1410) (= W1 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1410))) (= (tptp.sdtmndt0 W1 W0) BOUND_VARIABLE_1410)))) (or (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.sdtlseqdt0 tptp.xp tptp.xn)) (and (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp)) (= tptp.xn (tptp.sdtpldt0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp))))))) :rule resolution :premises (t14 t27 t33))
% 25.61/26.09  (step t35 (cl (not (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1410 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (= (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1410) (= W1 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1410))) (= (tptp.sdtmndt0 W1 W0) BOUND_VARIABLE_1410))))) (or (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.sdtlseqdt0 tptp.xp tptp.xn)) (and (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp)) (= tptp.xn (tptp.sdtpldt0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)))))) :rule implies :premises (t34))
% 25.61/26.09  (step t36 (cl (not (= (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (tptp.sdtlseqdt0 W0 W1) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtmndt0 W1 W0)) (and (tptp.aNaturalNumber0 W2) (= (tptp.sdtpldt0 W0 W2) W1))))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1410 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (= (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1410) (= W1 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1410))) (= (tptp.sdtmndt0 W1 W0) BOUND_VARIABLE_1410)))))) (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (tptp.sdtlseqdt0 W0 W1) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtmndt0 W1 W0)) (and (tptp.aNaturalNumber0 W2) (= (tptp.sdtpldt0 W0 W2) W1)))))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1410 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (= (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1410) (= W1 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1410))) (= (tptp.sdtmndt0 W1 W0) BOUND_VARIABLE_1410))))) :rule equiv_pos2)
% 25.61/26.09  (anchor :step t37 :args ((W0 $$unsorted) (:= W0 W0) (W1 $$unsorted) (:= W1 W1)))
% 25.61/26.09  (step t37.t1 (cl (= W0 W0)) :rule refl)
% 25.61/26.09  (step t37.t2 (cl (= W1 W1)) :rule refl)
% 25.61/26.09  (step t37.t3 (cl (= (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)))) :rule refl)
% 25.61/26.09  (step t37.t4 (cl (= (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W0 W1))) :rule refl)
% 25.61/26.09  (anchor :step t37.t5 :args ((W2 $$unsorted) (:= W2 W2)))
% 25.61/26.09  (step t37.t5.t1 (cl (= W2 W2)) :rule refl)
% 25.61/26.09  (step t37.t5.t2 (cl (= (= W2 (tptp.sdtmndt0 W1 W0)) (= W2 (tptp.sdtmndt0 W1 W0)))) :rule refl)
% 25.61/26.09  (step t37.t5.t3 (cl (= (tptp.aNaturalNumber0 W2) (tptp.aNaturalNumber0 W2))) :rule refl)
% 25.61/26.09  (step t37.t5.t4 (cl (= (= (tptp.sdtpldt0 W0 W2) W1) (= W1 (tptp.sdtpldt0 W0 W2)))) :rule all_simplify)
% 25.61/26.09  (step t37.t5.t5 (cl (= (and (tptp.aNaturalNumber0 W2) (= (tptp.sdtpldt0 W0 W2) W1)) (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtpldt0 W0 W2))))) :rule cong :premises (t37.t5.t3 t37.t5.t4))
% 25.61/26.09  (step t37.t5.t6 (cl (= (= (= W2 (tptp.sdtmndt0 W1 W0)) (and (tptp.aNaturalNumber0 W2) (= (tptp.sdtpldt0 W0 W2) W1))) (= (= W2 (tptp.sdtmndt0 W1 W0)) (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtpldt0 W0 W2)))))) :rule cong :premises (t37.t5.t2 t37.t5.t5))
% 25.61/26.09  (step t37.t5 (cl (= (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtmndt0 W1 W0)) (and (tptp.aNaturalNumber0 W2) (= (tptp.sdtpldt0 W0 W2) W1)))) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtmndt0 W1 W0)) (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtpldt0 W0 W2))))))) :rule bind)
% 25.61/26.09  (step t37.t6 (cl (= (=> (tptp.sdtlseqdt0 W0 W1) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtmndt0 W1 W0)) (and (tptp.aNaturalNumber0 W2) (= (tptp.sdtpldt0 W0 W2) W1))))) (=> (tptp.sdtlseqdt0 W0 W1) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtmndt0 W1 W0)) (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtpldt0 W0 W2)))))))) :rule cong :premises (t37.t4 t37.t5))
% 25.61/26.09  (step t37.t7 (cl (= (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (tptp.sdtlseqdt0 W0 W1) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtmndt0 W1 W0)) (and (tptp.aNaturalNumber0 W2) (= (tptp.sdtpldt0 W0 W2) W1)))))) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (tptp.sdtlseqdt0 W0 W1) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtmndt0 W1 W0)) (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtpldt0 W0 W2))))))))) :rule cong :premises (t37.t3 t37.t6))
% 25.61/26.09  (step t37 (cl (= (forall ((W0 $$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))))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (tptp.sdtlseqdt0 W0 W1) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtmndt0 W1 W0)) (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtpldt0 W0 W2)))))))))) :rule bind)
% 25.61/26.09  (step t38 (cl (= (forall ((W0 $$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) (= W1 (tptp.sdtpldt0 W0 W2)))))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtmndt0 W1 W0)) (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtpldt0 W0 W2))))))))) :rule all_simplify)
% 25.61/26.09  (step t39 (cl (= (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtmndt0 W1 W0)) (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtpldt0 W0 W2))))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1410 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (= (= BOUND_VARIABLE_1410 (tptp.sdtmndt0 W1 W0)) (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1410) (= W1 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1410)))))))) :rule all_simplify)
% 25.61/26.09  (anchor :step t40 :args ((W0 $$unsorted) (:= W0 W0) (W1 $$unsorted) (:= W1 W1) (BOUND_VARIABLE_1410 $$unsorted) (:= BOUND_VARIABLE_1410 BOUND_VARIABLE_1410)))
% 25.61/26.09  (step t40.t1 (cl (= W0 W0)) :rule refl)
% 25.61/26.09  (step t40.t2 (cl (= W1 W1)) :rule refl)
% 25.61/26.09  (step t40.t3 (cl (= BOUND_VARIABLE_1410 BOUND_VARIABLE_1410)) :rule refl)
% 25.61/26.09  (step t40.t4 (cl (= (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W0)))) :rule refl)
% 25.61/26.09  (step t40.t5 (cl (= (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W1)))) :rule refl)
% 25.61/26.09  (step t40.t6 (cl (= (not (tptp.sdtlseqdt0 W0 W1)) (not (tptp.sdtlseqdt0 W0 W1)))) :rule refl)
% 25.61/26.09  (step t40.t7 (cl (= (= BOUND_VARIABLE_1410 (tptp.sdtmndt0 W1 W0)) (= (tptp.sdtmndt0 W1 W0) BOUND_VARIABLE_1410))) :rule all_simplify)
% 25.61/26.09  (step t40.t8 (cl (= (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1410) (= W1 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1410))) (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1410) (= W1 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1410))))) :rule refl)
% 25.61/26.09  (step t40.t9 (cl (= (= (= BOUND_VARIABLE_1410 (tptp.sdtmndt0 W1 W0)) (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1410) (= W1 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1410)))) (= (= (tptp.sdtmndt0 W1 W0) BOUND_VARIABLE_1410) (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1410) (= W1 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1410)))))) :rule cong :premises (t40.t7 t40.t8))
% 25.61/26.09  (step t40.t10 (cl (= (= (= (tptp.sdtmndt0 W1 W0) BOUND_VARIABLE_1410) (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1410) (= W1 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1410)))) (= (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1410) (= W1 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1410))) (= (tptp.sdtmndt0 W1 W0) BOUND_VARIABLE_1410)))) :rule all_simplify)
% 25.61/26.09  (step t40.t11 (cl (= (= (= BOUND_VARIABLE_1410 (tptp.sdtmndt0 W1 W0)) (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1410) (= W1 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1410)))) (= (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1410) (= W1 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1410))) (= (tptp.sdtmndt0 W1 W0) BOUND_VARIABLE_1410)))) :rule trans :premises (t40.t9 t40.t10))
% 25.61/26.09  (step t40.t12 (cl (= (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (= (= BOUND_VARIABLE_1410 (tptp.sdtmndt0 W1 W0)) (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1410) (= W1 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1410))))) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (= (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1410) (= W1 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1410))) (= (tptp.sdtmndt0 W1 W0) BOUND_VARIABLE_1410))))) :rule cong :premises (t40.t4 t40.t5 t40.t6 t40.t11))
% 25.61/26.09  (step t40 (cl (= (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1410 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (= (= BOUND_VARIABLE_1410 (tptp.sdtmndt0 W1 W0)) (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1410) (= W1 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1410)))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1410 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (= (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1410) (= W1 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1410))) (= (tptp.sdtmndt0 W1 W0) BOUND_VARIABLE_1410)))))) :rule bind)
% 25.61/26.09  (step t41 (cl (= (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtmndt0 W1 W0)) (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtpldt0 W0 W2))))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1410 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (= (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1410) (= W1 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1410))) (= (tptp.sdtmndt0 W1 W0) BOUND_VARIABLE_1410)))))) :rule trans :premises (t39 t40))
% 25.61/26.09  (step t42 (cl (= (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (tptp.sdtlseqdt0 W0 W1) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtmndt0 W1 W0)) (and (tptp.aNaturalNumber0 W2) (= W1 (tptp.sdtpldt0 W0 W2)))))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1410 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (= (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1410) (= W1 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1410))) (= (tptp.sdtmndt0 W1 W0) BOUND_VARIABLE_1410)))))) :rule trans :premises (t38 t41))
% 25.61/26.09  (step t43 (cl (= (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (tptp.sdtlseqdt0 W0 W1) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtmndt0 W1 W0)) (and (tptp.aNaturalNumber0 W2) (= (tptp.sdtpldt0 W0 W2) W1))))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1410 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (= (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1410) (= W1 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1410))) (= (tptp.sdtmndt0 W1 W0) BOUND_VARIABLE_1410)))))) :rule trans :premises (t37 t42))
% 25.61/26.09  (step t44 (cl (forall ((W0 $$unsorted) (W1 $$unsorted) (BOUND_VARIABLE_1410 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (= (and (tptp.aNaturalNumber0 BOUND_VARIABLE_1410) (= W1 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1410))) (= (tptp.sdtmndt0 W1 W0) BOUND_VARIABLE_1410))))) :rule resolution :premises (t36 t43 a18))
% 25.61/26.09  (step t45 (cl (or (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.sdtlseqdt0 tptp.xp tptp.xn)) (and (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp)) (= tptp.xn (tptp.sdtpldt0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)))))) :rule resolution :premises (t35 t44))
% 25.61/26.09  (step t46 (cl (and (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp)) (= tptp.xn (tptp.sdtpldt0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp))))) :rule resolution :premises (t12 t13 t5 a41 t45))
% 25.61/26.09  (step t47 (cl (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp))) :rule resolution :premises (t10 t46))
% 25.61/26.09  (step t48 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))) (or (not (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp))) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1))))) :rule implies_neg1)
% 25.61/26.09  (anchor :step t49)
% 25.61/26.09  (assume t49.a0 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))))
% 25.61/26.09  (step t49.t1 (cl (or (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1))))) (or (not (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp))) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm))))) :rule forall_inst :args ((:= W0 (tptp.sdtmndt0 tptp.xn tptp.xp)) (:= W1 tptp.xm)))
% 25.61/26.09  (step t49.t2 (cl (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1))))) (or (not (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp))) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm)))) :rule or :premises (t49.t1))
% 25.61/26.09  (step t49.t3 (cl (or (not (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp))) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm)))) :rule resolution :premises (t49.t2 t49.a0))
% 25.61/26.09  (step t49 (cl (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1))))) (or (not (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp))) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm)))) :rule subproof :discharge (t49.a0))
% 25.61/26.09  (step t50 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))) (or (not (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp))) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm)))) (or (not (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp))) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm)))) :rule resolution :premises (t48 t49))
% 25.61/26.09  (step t51 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))) (or (not (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp))) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm)))) (not (or (not (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp))) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm))))) :rule implies_neg2)
% 25.61/26.09  (step t52 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))) (or (not (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp))) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm)))) (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))) (or (not (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp))) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm))))) :rule resolution :premises (t50 t51))
% 25.61/26.09  (step t53 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))) (or (not (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp))) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm))))) :rule contraction :premises (t52))
% 25.61/26.09  (step t54 (cl (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1))))) (or (not (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp))) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm)))) :rule implies :premises (t53))
% 25.61/26.09  (step t55 (cl (not (= (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))))) (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1))))) :rule equiv_pos2)
% 25.61/26.09  (step t56 (cl (= (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))))) :rule all_simplify)
% 25.61/26.09  (step t57 (cl (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1))))) :rule resolution :premises (t55 t56 a3))
% 25.61/26.09  (step t58 (cl (or (not (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp))) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm)))) :rule resolution :premises (t54 t57))
% 25.61/26.09  (step t59 (cl (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm))) :rule resolution :premises (t7 t8 t47 t58))
% 25.61/26.09  (step t60 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))) (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm))) (not (tptp.aNaturalNumber0 tptp.xp)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1))))) :rule implies_neg1)
% 25.61/26.09  (anchor :step t61)
% 25.61/26.09  (assume t61.a0 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))))
% 25.61/26.09  (step t61.t1 (cl (or (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1))))) (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm))) (not (tptp.aNaturalNumber0 tptp.xp)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp))))) :rule forall_inst :args ((:= W0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm)) (:= W1 tptp.xp)))
% 25.61/26.09  (step t61.t2 (cl (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1))))) (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm))) (not (tptp.aNaturalNumber0 tptp.xp)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp)))) :rule or :premises (t61.t1))
% 25.61/26.09  (step t61.t3 (cl (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm))) (not (tptp.aNaturalNumber0 tptp.xp)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp)))) :rule resolution :premises (t61.t2 t61.a0))
% 25.61/26.09  (step t61 (cl (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1))))) (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm))) (not (tptp.aNaturalNumber0 tptp.xp)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp)))) :rule subproof :discharge (t61.a0))
% 25.61/26.09  (step t62 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))) (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm))) (not (tptp.aNaturalNumber0 tptp.xp)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp)))) (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm))) (not (tptp.aNaturalNumber0 tptp.xp)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp)))) :rule resolution :premises (t60 t61))
% 25.61/26.09  (step t63 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))) (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm))) (not (tptp.aNaturalNumber0 tptp.xp)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp)))) (not (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm))) (not (tptp.aNaturalNumber0 tptp.xp)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp))))) :rule implies_neg2)
% 25.61/26.09  (step t64 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))) (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm))) (not (tptp.aNaturalNumber0 tptp.xp)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp)))) (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))) (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm))) (not (tptp.aNaturalNumber0 tptp.xp)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp))))) :rule resolution :premises (t62 t63))
% 25.61/26.09  (step t65 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))) (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm))) (not (tptp.aNaturalNumber0 tptp.xp)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp))))) :rule contraction :premises (t64))
% 25.61/26.09  (step t66 (cl (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1))))) (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm))) (not (tptp.aNaturalNumber0 tptp.xp)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp)))) :rule implies :premises (t65))
% 25.61/26.09  (step t67 (cl (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm))) (not (tptp.aNaturalNumber0 tptp.xp)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp)))) :rule resolution :premises (t66 t57))
% 25.61/26.09  (step t68 (cl (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp))) :rule resolution :premises (t4 t5 t59 t67))
% 25.61/26.09  (step t69 (cl (not (or (not (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp))) (not (tptp.aNaturalNumber0 tptp.xm)) (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.isPrime0 tptp.xp)) (not (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm))) (not (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.doDivides0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)) (tptp.doDivides0 tptp.xp tptp.xm))) (not (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp))) (not (tptp.aNaturalNumber0 tptp.xm)) (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.isPrime0 tptp.xp)) (not (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm))) (not (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.doDivides0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)) (tptp.doDivides0 tptp.xp tptp.xm)) :rule or_pos)
% 25.61/26.09  (step t70 (cl (tptp.doDivides0 tptp.xp tptp.xm) (tptp.doDivides0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)) (not (tptp.aNaturalNumber0 tptp.xm)) (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.isPrime0 tptp.xp)) (not (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm))) (not (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp))) (not (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (not (or (not (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp))) (not (tptp.aNaturalNumber0 tptp.xm)) (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.isPrime0 tptp.xp)) (not (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm))) (not (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.doDivides0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)) (tptp.doDivides0 tptp.xp tptp.xm)))) :rule reordering :premises (t69))
% 25.61/26.09  (step t71 (cl (not (= (not (or (tptp.doDivides0 tptp.xp tptp.xr) (tptp.doDivides0 tptp.xp tptp.xm))) (not (or (tptp.doDivides0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)) (tptp.doDivides0 tptp.xp tptp.xm))))) (not (not (or (tptp.doDivides0 tptp.xp tptp.xr) (tptp.doDivides0 tptp.xp tptp.xm)))) (not (or (tptp.doDivides0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)) (tptp.doDivides0 tptp.xp tptp.xm)))) :rule equiv_pos2)
% 25.61/26.09  (step t72 (cl (= tptp.xp tptp.xp)) :rule refl)
% 25.61/26.09  (step t73 (cl (= (tptp.doDivides0 tptp.xp tptp.xr) (tptp.doDivides0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)))) :rule cong :premises (t72 a42))
% 25.61/26.09  (step t74 (cl (= (tptp.doDivides0 tptp.xp tptp.xm) (tptp.doDivides0 tptp.xp tptp.xm))) :rule refl)
% 25.61/26.09  (step t75 (cl (= (or (tptp.doDivides0 tptp.xp tptp.xr) (tptp.doDivides0 tptp.xp tptp.xm)) (or (tptp.doDivides0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)) (tptp.doDivides0 tptp.xp tptp.xm)))) :rule cong :premises (t73 t74))
% 25.61/26.09  (step t76 (cl (= (not (or (tptp.doDivides0 tptp.xp tptp.xr) (tptp.doDivides0 tptp.xp tptp.xm))) (not (or (tptp.doDivides0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)) (tptp.doDivides0 tptp.xp tptp.xm))))) :rule cong :premises (t75))
% 25.61/26.09  (step t77 (cl (not (or (tptp.doDivides0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)) (tptp.doDivides0 tptp.xp tptp.xm)))) :rule resolution :premises (t71 t76 a46))
% 25.61/26.09  (step t78 (cl (not (tptp.doDivides0 tptp.xp tptp.xm))) :rule not_or :premises (t77))
% 25.61/26.09  (step t79 (cl (not (tptp.doDivides0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)))) :rule not_or :premises (t77))
% 25.61/26.09  (step t80 (cl (tptp.isPrime0 tptp.xp)) :rule and :premises (a40))
% 25.61/26.09  (step t81 (cl (not (= (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xr tptp.xm)) (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm)))) (not (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xr tptp.xm))) (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm))) :rule equiv_pos2)
% 25.61/26.09  (step t82 (cl (= tptp.xp tptp.xp)) :rule refl)
% 25.61/26.09  (step t83 (cl (= tptp.xm tptp.xm)) :rule refl)
% 25.61/26.09  (step t84 (cl (= (tptp.sdtasdt0 tptp.xr tptp.xm) (tptp.sdtasdt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm))) :rule cong :premises (a42 t83))
% 25.61/26.09  (step t85 (cl (= (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 tptp.xr tptp.xm)) (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm)))) :rule cong :premises (t82 t84))
% 25.61/26.09  (step t86 (cl (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm))) :rule resolution :premises (t81 t85 a44))
% 25.61/26.09  (step t87 (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))) (not (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1))) (or (not (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp))) (not (tptp.aNaturalNumber0 tptp.xm)) (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.isPrime0 tptp.xp)) (not (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm))) (not (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.doDivides0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)) (tptp.doDivides0 tptp.xp tptp.xm))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W2)) (not (tptp.isPrime0 W2)) (not (tptp.doDivides0 W2 (tptp.sdtasdt0 W0 W1))) (not (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1)))) :rule implies_neg1)
% 25.61/26.09  (anchor :step t88)
% 25.61/26.09  (assume t88.a0 (forall ((W0 $$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))) (not (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1))))
% 25.61/26.09  (step t88.t1 (cl (or (not (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W2)) (not (tptp.isPrime0 W2)) (not (tptp.doDivides0 W2 (tptp.sdtasdt0 W0 W1))) (not (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1)))) (or (not (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp))) (not (tptp.aNaturalNumber0 tptp.xm)) (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.isPrime0 tptp.xp)) (not (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm))) (not (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.doDivides0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)) (tptp.doDivides0 tptp.xp tptp.xm)))) :rule forall_inst :args ((:= W0 (tptp.sdtmndt0 tptp.xn tptp.xp)) (:= W1 tptp.xm) (:= W2 tptp.xp)))
% 25.61/26.09  (step t88.t2 (cl (not (forall ((W0 $$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))) (not (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1)))) (or (not (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp))) (not (tptp.aNaturalNumber0 tptp.xm)) (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.isPrime0 tptp.xp)) (not (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm))) (not (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.doDivides0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)) (tptp.doDivides0 tptp.xp tptp.xm))) :rule or :premises (t88.t1))
% 25.61/26.09  (step t88.t3 (cl (or (not (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp))) (not (tptp.aNaturalNumber0 tptp.xm)) (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.isPrime0 tptp.xp)) (not (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm))) (not (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.doDivides0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)) (tptp.doDivides0 tptp.xp tptp.xm))) :rule resolution :premises (t88.t2 t88.a0))
% 25.61/26.09  (step t88 (cl (not (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W2)) (not (tptp.isPrime0 W2)) (not (tptp.doDivides0 W2 (tptp.sdtasdt0 W0 W1))) (not (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1)))) (or (not (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp))) (not (tptp.aNaturalNumber0 tptp.xm)) (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.isPrime0 tptp.xp)) (not (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm))) (not (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.doDivides0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)) (tptp.doDivides0 tptp.xp tptp.xm))) :rule subproof :discharge (t88.a0))
% 25.61/26.09  (step t89 (cl (=> (forall ((W0 $$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))) (not (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1))) (or (not (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp))) (not (tptp.aNaturalNumber0 tptp.xm)) (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.isPrime0 tptp.xp)) (not (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm))) (not (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.doDivides0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)) (tptp.doDivides0 tptp.xp tptp.xm))) (or (not (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp))) (not (tptp.aNaturalNumber0 tptp.xm)) (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.isPrime0 tptp.xp)) (not (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm))) (not (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.doDivides0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)) (tptp.doDivides0 tptp.xp tptp.xm))) :rule resolution :premises (t87 t88))
% 25.61/26.09  (step t90 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W2)) (not (tptp.isPrime0 W2)) (not (tptp.doDivides0 W2 (tptp.sdtasdt0 W0 W1))) (not (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1))) (or (not (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp))) (not (tptp.aNaturalNumber0 tptp.xm)) (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.isPrime0 tptp.xp)) (not (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm))) (not (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.doDivides0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)) (tptp.doDivides0 tptp.xp tptp.xm))) (not (or (not (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp))) (not (tptp.aNaturalNumber0 tptp.xm)) (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.isPrime0 tptp.xp)) (not (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm))) (not (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.doDivides0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)) (tptp.doDivides0 tptp.xp tptp.xm)))) :rule implies_neg2)
% 25.61/26.09  (step t91 (cl (=> (forall ((W0 $$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))) (not (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1))) (or (not (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp))) (not (tptp.aNaturalNumber0 tptp.xm)) (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.isPrime0 tptp.xp)) (not (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm))) (not (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.doDivides0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)) (tptp.doDivides0 tptp.xp tptp.xm))) (=> (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W2)) (not (tptp.isPrime0 W2)) (not (tptp.doDivides0 W2 (tptp.sdtasdt0 W0 W1))) (not (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1))) (or (not (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp))) (not (tptp.aNaturalNumber0 tptp.xm)) (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.isPrime0 tptp.xp)) (not (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm))) (not (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.doDivides0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)) (tptp.doDivides0 tptp.xp tptp.xm)))) :rule resolution :premises (t89 t90))
% 25.61/26.09  (step t92 (cl (=> (forall ((W0 $$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))) (not (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1))) (or (not (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp))) (not (tptp.aNaturalNumber0 tptp.xm)) (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.isPrime0 tptp.xp)) (not (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm))) (not (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.doDivides0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)) (tptp.doDivides0 tptp.xp tptp.xm)))) :rule contraction :premises (t91))
% 25.61/26.09  (step t93 (cl (not (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W2)) (not (tptp.isPrime0 W2)) (not (tptp.doDivides0 W2 (tptp.sdtasdt0 W0 W1))) (not (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1)))) (or (not (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp))) (not (tptp.aNaturalNumber0 tptp.xm)) (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.isPrime0 tptp.xp)) (not (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm))) (not (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.doDivides0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)) (tptp.doDivides0 tptp.xp tptp.xm))) :rule implies :premises (t92))
% 25.61/26.09  (step t94 (cl (not (= (forall ((W0 $$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))) (=> (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)) (or (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1)))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W2)) (not (tptp.isPrime0 W2)) (not (tptp.doDivides0 W2 (tptp.sdtasdt0 W0 W1))) (not (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1))))) (not (forall ((W0 $$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))) (=> (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)) (or (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1))))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W2)) (not (tptp.isPrime0 W2)) (not (tptp.doDivides0 W2 (tptp.sdtasdt0 W0 W1))) (not (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1)))) :rule equiv_pos2)
% 25.61/26.09  (step t95 (cl (= (forall ((W0 $$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))) (=> (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)) (or (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1)))))) (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (not (tptp.aNaturalNumber0 W2)) (not (tptp.isPrime0 W2)) (not (tptp.doDivides0 W2 (tptp.sdtasdt0 W0 W1))) (not (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1))))) :rule all_simplify)
% 25.61/26.09  (step t96 (cl (forall ((W0 $$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))) (not (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.doDivides0 W2 W0) (tptp.doDivides0 W2 W1)))) :rule resolution :premises (t94 t95 a39))
% 25.61/26.09  (step t97 (cl (or (not (tptp.aNaturalNumber0 (tptp.sdtmndt0 tptp.xn tptp.xp))) (not (tptp.aNaturalNumber0 tptp.xm)) (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.isPrime0 tptp.xp)) (not (tptp.doDivides0 tptp.xp (tptp.sdtasdt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm))) (not (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.doDivides0 tptp.xp (tptp.sdtmndt0 tptp.xn tptp.xp)) (tptp.doDivides0 tptp.xp tptp.xm))) :rule resolution :premises (t93 t96))
% 25.61/26.09  (step t98 (cl (not (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)))) :rule resolution :premises (t70 t78 t79 t8 t5 t80 t86 t47 t97))
% 25.61/26.09  (step t99 (cl (not (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 tptp.xn tptp.xm))) (not (tptp.aNaturalNumber0 tptp.xp)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)))) (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 tptp.xn tptp.xm))) (not (tptp.aNaturalNumber0 tptp.xp)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) :rule or_pos)
% 25.61/26.09  (step t100 (cl (not (tptp.aNaturalNumber0 tptp.xp)) (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 tptp.xn tptp.xm))) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)) (not (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 tptp.xn tptp.xm))) (not (tptp.aNaturalNumber0 tptp.xp)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))))) :rule reordering :premises (t99))
% 25.61/26.09  (step t101 (cl (not (or (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 tptp.xn tptp.xm)))) (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 tptp.xn tptp.xm))) :rule or_pos)
% 25.61/26.09  (step t102 (cl (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 tptp.xn tptp.xm)) (not (or (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 tptp.xn tptp.xm))))) :rule reordering :premises (t101))
% 25.61/26.09  (step t103 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))) (or (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 tptp.xn tptp.xm)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1))))) :rule implies_neg1)
% 25.61/26.09  (anchor :step t104)
% 25.61/26.09  (assume t104.a0 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))))
% 25.61/26.09  (step t104.t1 (cl (or (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1))))) (or (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 tptp.xn tptp.xm))))) :rule forall_inst :args ((:= W0 tptp.xn) (:= W1 tptp.xm)))
% 25.61/26.09  (step t104.t2 (cl (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1))))) (or (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 tptp.xn tptp.xm)))) :rule or :premises (t104.t1))
% 25.61/26.09  (step t104.t3 (cl (or (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 tptp.xn tptp.xm)))) :rule resolution :premises (t104.t2 t104.a0))
% 25.61/26.09  (step t104 (cl (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1))))) (or (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 tptp.xn tptp.xm)))) :rule subproof :discharge (t104.a0))
% 25.61/26.09  (step t105 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))) (or (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 tptp.xn tptp.xm)))) (or (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 tptp.xn tptp.xm)))) :rule resolution :premises (t103 t104))
% 25.61/26.09  (step t106 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))) (or (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 tptp.xn tptp.xm)))) (not (or (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 tptp.xn tptp.xm))))) :rule implies_neg2)
% 25.61/26.09  (step t107 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))) (or (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 tptp.xn tptp.xm)))) (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))) (or (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 tptp.xn tptp.xm))))) :rule resolution :premises (t105 t106))
% 25.61/26.09  (step t108 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))) (or (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 tptp.xn tptp.xm))))) :rule contraction :premises (t107))
% 25.61/26.09  (step t109 (cl (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1))))) (or (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 tptp.xn tptp.xm)))) :rule implies :premises (t108))
% 25.61/26.09  (step t110 (cl (or (not (tptp.aNaturalNumber0 tptp.xn)) (not (tptp.aNaturalNumber0 tptp.xm)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 tptp.xn tptp.xm)))) :rule resolution :premises (t109 t57))
% 25.61/26.09  (step t111 (cl (tptp.aNaturalNumber0 (tptp.sdtpldt0 tptp.xn tptp.xm))) :rule resolution :premises (t102 t13 t8 t110))
% 25.61/26.09  (step t112 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))) (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 tptp.xn tptp.xm))) (not (tptp.aNaturalNumber0 tptp.xp)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1))))) :rule implies_neg1)
% 25.61/26.09  (anchor :step t113)
% 25.61/26.09  (assume t113.a0 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))))
% 25.61/26.09  (step t113.t1 (cl (or (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1))))) (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 tptp.xn tptp.xm))) (not (tptp.aNaturalNumber0 tptp.xp)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))))) :rule forall_inst :args ((:= W0 (tptp.sdtpldt0 tptp.xn tptp.xm)) (:= W1 tptp.xp)))
% 25.61/26.09  (step t113.t2 (cl (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1))))) (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 tptp.xn tptp.xm))) (not (tptp.aNaturalNumber0 tptp.xp)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)))) :rule or :premises (t113.t1))
% 25.61/26.09  (step t113.t3 (cl (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 tptp.xn tptp.xm))) (not (tptp.aNaturalNumber0 tptp.xp)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)))) :rule resolution :premises (t113.t2 t113.a0))
% 25.61/26.09  (step t113 (cl (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1))))) (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 tptp.xn tptp.xm))) (not (tptp.aNaturalNumber0 tptp.xp)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)))) :rule subproof :discharge (t113.a0))
% 25.61/26.09  (step t114 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))) (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 tptp.xn tptp.xm))) (not (tptp.aNaturalNumber0 tptp.xp)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)))) (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 tptp.xn tptp.xm))) (not (tptp.aNaturalNumber0 tptp.xp)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)))) :rule resolution :premises (t112 t113))
% 25.61/26.09  (step t115 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))) (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 tptp.xn tptp.xm))) (not (tptp.aNaturalNumber0 tptp.xp)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)))) (not (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 tptp.xn tptp.xm))) (not (tptp.aNaturalNumber0 tptp.xp)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))))) :rule implies_neg2)
% 25.61/26.09  (step t116 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))) (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 tptp.xn tptp.xm))) (not (tptp.aNaturalNumber0 tptp.xp)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)))) (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))) (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 tptp.xn tptp.xm))) (not (tptp.aNaturalNumber0 tptp.xp)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))))) :rule resolution :premises (t114 t115))
% 25.61/26.09  (step t117 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1)))) (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 tptp.xn tptp.xm))) (not (tptp.aNaturalNumber0 tptp.xp)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))))) :rule contraction :premises (t116))
% 25.61/26.09  (step t118 (cl (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 W0 W1))))) (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 tptp.xn tptp.xm))) (not (tptp.aNaturalNumber0 tptp.xp)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)))) :rule implies :premises (t117))
% 25.61/26.09  (step t119 (cl (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 tptp.xn tptp.xm))) (not (tptp.aNaturalNumber0 tptp.xp)) (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)))) :rule resolution :premises (t118 t57))
% 25.61/26.09  (step t120 (cl (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) :rule resolution :premises (t100 t5 t111 t119))
% 25.61/26.09  (step t121 (cl (not (= (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= W0 W1) (not (tptp.sdtlseqdt0 W0 W1)) (tptp.iLess0 W0 W1))) (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp))) (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (= (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)) (not (tptp.sdtlseqdt0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)))) (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= W0 W1) (not (tptp.sdtlseqdt0 W0 W1)) (tptp.iLess0 W0 W1))) (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp))) (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (= (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp)) (not (tptp.sdtlseqdt0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)))))) (not (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= W0 W1) (not (tptp.sdtlseqdt0 W0 W1)) (tptp.iLess0 W0 W1))) (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp))) (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (= (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)) (not (tptp.sdtlseqdt0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))))) (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= W0 W1) (not (tptp.sdtlseqdt0 W0 W1)) (tptp.iLess0 W0 W1))) (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp))) (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (= (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp)) (not (tptp.sdtlseqdt0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))))) :rule equiv_pos2)
% 25.61/26.09  (step t122 (cl (= (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= W0 W1) (not (tptp.sdtlseqdt0 W0 W1)) (tptp.iLess0 W0 W1))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= W0 W1) (not (tptp.sdtlseqdt0 W0 W1)) (tptp.iLess0 W0 W1))))) :rule refl)
% 25.61/26.09  (step t123 (cl (= (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp))) (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp))))) :rule refl)
% 25.61/26.09  (step t124 (cl (= (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))))) :rule refl)
% 25.61/26.09  (step t125 (cl (= (= (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)) (= (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp)))) :rule all_simplify)
% 25.61/26.09  (step t126 (cl (= (not (tptp.sdtlseqdt0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (not (tptp.sdtlseqdt0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))))) :rule refl)
% 25.61/26.09  (step t127 (cl (= (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)) (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)))) :rule refl)
% 25.61/26.09  (step t128 (cl (= (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp))) (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (= (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)) (not (tptp.sdtlseqdt0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp))) (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (= (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp)) (not (tptp.sdtlseqdt0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))))) :rule cong :premises (t123 t124 t125 t126 t127))
% 25.61/26.09  (step t129 (cl (= (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= W0 W1) (not (tptp.sdtlseqdt0 W0 W1)) (tptp.iLess0 W0 W1))) (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp))) (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (= (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)) (not (tptp.sdtlseqdt0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)))) (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= W0 W1) (not (tptp.sdtlseqdt0 W0 W1)) (tptp.iLess0 W0 W1))) (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp))) (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (= (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp)) (not (tptp.sdtlseqdt0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)))))) :rule cong :premises (t122 t128))
% 25.61/26.09  (step t130 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= W0 W1) (not (tptp.sdtlseqdt0 W0 W1)) (tptp.iLess0 W0 W1))) (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp))) (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (= (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)) (not (tptp.sdtlseqdt0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= W0 W1) (not (tptp.sdtlseqdt0 W0 W1)) (tptp.iLess0 W0 W1)))) :rule implies_neg1)
% 25.61/26.09  (anchor :step t131)
% 25.61/26.09  (assume t131.a0 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= W0 W1) (not (tptp.sdtlseqdt0 W0 W1)) (tptp.iLess0 W0 W1))))
% 25.61/26.09  (step t131.t1 (cl (or (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= W0 W1) (not (tptp.sdtlseqdt0 W0 W1)) (tptp.iLess0 W0 W1)))) (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp))) (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (= (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)) (not (tptp.sdtlseqdt0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))))) :rule forall_inst :args ((:= W0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp)) (:= W1 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))))
% 25.61/26.09  (step t131.t2 (cl (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= W0 W1) (not (tptp.sdtlseqdt0 W0 W1)) (tptp.iLess0 W0 W1)))) (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp))) (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (= (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)) (not (tptp.sdtlseqdt0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)))) :rule or :premises (t131.t1))
% 25.61/26.09  (step t131.t3 (cl (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp))) (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (= (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)) (not (tptp.sdtlseqdt0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)))) :rule resolution :premises (t131.t2 t131.a0))
% 25.61/26.09  (step t131 (cl (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= W0 W1) (not (tptp.sdtlseqdt0 W0 W1)) (tptp.iLess0 W0 W1)))) (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp))) (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (= (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)) (not (tptp.sdtlseqdt0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)))) :rule subproof :discharge (t131.a0))
% 25.61/26.09  (step t132 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= W0 W1) (not (tptp.sdtlseqdt0 W0 W1)) (tptp.iLess0 W0 W1))) (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp))) (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (= (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)) (not (tptp.sdtlseqdt0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)))) (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp))) (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (= (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)) (not (tptp.sdtlseqdt0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)))) :rule resolution :premises (t130 t131))
% 25.61/26.09  (step t133 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= W0 W1) (not (tptp.sdtlseqdt0 W0 W1)) (tptp.iLess0 W0 W1))) (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp))) (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (= (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)) (not (tptp.sdtlseqdt0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)))) (not (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp))) (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (= (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)) (not (tptp.sdtlseqdt0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))))) :rule implies_neg2)
% 25.61/26.09  (step t134 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= W0 W1) (not (tptp.sdtlseqdt0 W0 W1)) (tptp.iLess0 W0 W1))) (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp))) (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (= (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)) (not (tptp.sdtlseqdt0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)))) (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= W0 W1) (not (tptp.sdtlseqdt0 W0 W1)) (tptp.iLess0 W0 W1))) (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp))) (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (= (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)) (not (tptp.sdtlseqdt0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))))) :rule resolution :premises (t132 t133))
% 25.61/26.09  (step t135 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= W0 W1) (not (tptp.sdtlseqdt0 W0 W1)) (tptp.iLess0 W0 W1))) (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp))) (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (= (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)) (not (tptp.sdtlseqdt0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))))) :rule contraction :premises (t134))
% 25.61/26.09  (step t136 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= W0 W1) (not (tptp.sdtlseqdt0 W0 W1)) (tptp.iLess0 W0 W1))) (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp))) (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (= (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp)) (not (tptp.sdtlseqdt0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))))) :rule resolution :premises (t121 t129 t135))
% 25.61/26.09  (step t137 (cl (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= W0 W1) (not (tptp.sdtlseqdt0 W0 W1)) (tptp.iLess0 W0 W1)))) (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp))) (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (= (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp)) (not (tptp.sdtlseqdt0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)))) :rule implies :premises (t136))
% 25.61/26.09  (step t138 (cl (not (= (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 W1)) (tptp.sdtlseqdt0 W0 W1)) (tptp.iLess0 W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= W0 W1) (not (tptp.sdtlseqdt0 W0 W1)) (tptp.iLess0 W0 W1))))) (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 W1)) (tptp.sdtlseqdt0 W0 W1)) (tptp.iLess0 W0 W1))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= W0 W1) (not (tptp.sdtlseqdt0 W0 W1)) (tptp.iLess0 W0 W1)))) :rule equiv_pos2)
% 25.61/26.09  (step t139 (cl (= (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aNaturalNumber0 W0) (tptp.aNaturalNumber0 W1)) (=> (and (not (= W0 W1)) (tptp.sdtlseqdt0 W0 W1)) (tptp.iLess0 W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= W0 W1) (not (tptp.sdtlseqdt0 W0 W1)) (tptp.iLess0 W0 W1))))) :rule all_simplify)
% 25.61/26.09  (step t140 (cl (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aNaturalNumber0 W0)) (not (tptp.aNaturalNumber0 W1)) (= W0 W1) (not (tptp.sdtlseqdt0 W0 W1)) (tptp.iLess0 W0 W1)))) :rule resolution :premises (t138 t139 a28))
% 25.61/26.09  (step t141 (cl (or (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp))) (not (tptp.aNaturalNumber0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (= (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp)) (not (tptp.sdtlseqdt0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.iLess0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)))) :rule resolution :premises (t137 t140))
% 25.61/26.09  (step t142 (cl (not (= (and (not (= (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xr tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.sdtlseqdt0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xr tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (and (not (= (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp))) (tptp.sdtlseqdt0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))))) (not (and (not (= (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xr tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.sdtlseqdt0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xr tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)))) (and (not (= (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp))) (tptp.sdtlseqdt0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)))) :rule equiv_pos2)
% 25.61/26.09  (step t143 (cl (= (= (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xr tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)) (= (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xr tptp.xm) tptp.xp)))) :rule all_simplify)
% 25.61/26.09  (step t144 (cl (= (not (= (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xr tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (not (= (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xr tptp.xm) tptp.xp))))) :rule cong :premises (t143))
% 25.61/26.09  (step t145 (cl (= (tptp.sdtlseqdt0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xr tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)) (tptp.sdtlseqdt0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xr tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)))) :rule refl)
% 25.61/26.09  (step t146 (cl (= (and (not (= (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xr tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.sdtlseqdt0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xr tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (and (not (= (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xr tptp.xm) tptp.xp))) (tptp.sdtlseqdt0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xr tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))))) :rule cong :premises (t144 t145))
% 25.61/26.09  (step t147 (cl (= (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) :rule refl)
% 25.61/26.09  (step t148 (cl (= tptp.xm tptp.xm)) :rule refl)
% 25.61/26.09  (step t149 (cl (= (tptp.sdtpldt0 tptp.xr tptp.xm) (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm))) :rule cong :premises (a42 t148))
% 25.61/26.09  (step t150 (cl (= tptp.xp tptp.xp)) :rule refl)
% 25.61/26.09  (step t151 (cl (= (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xr tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp))) :rule cong :premises (t149 t150))
% 25.61/26.09  (step t152 (cl (= (= (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xr tptp.xm) tptp.xp)) (= (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp)))) :rule cong :premises (t147 t151))
% 25.61/26.09  (step t153 (cl (= (not (= (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xr tptp.xm) tptp.xp))) (not (= (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp))))) :rule cong :premises (t152))
% 25.61/26.09  (step t154 (cl (= (tptp.sdtlseqdt0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xr tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)) (tptp.sdtlseqdt0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)))) :rule cong :premises (t151 t147))
% 25.61/26.09  (step t155 (cl (= (and (not (= (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xr tptp.xm) tptp.xp))) (tptp.sdtlseqdt0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xr tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (and (not (= (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp))) (tptp.sdtlseqdt0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))))) :rule cong :premises (t153 t154))
% 25.61/26.09  (step t156 (cl (= (and (not (= (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xr tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (tptp.sdtlseqdt0 (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xr tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) (and (not (= (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp))) (tptp.sdtlseqdt0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))))) :rule trans :premises (t146 t155))
% 25.61/26.09  (step t157 (cl (and (not (= (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp))) (tptp.sdtlseqdt0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp)))) :rule resolution :premises (t142 t156 a45))
% 25.61/26.09  (step t158 (cl (tptp.sdtlseqdt0 (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp))) :rule and :premises (t157))
% 25.61/26.09  (step t159 (cl (not (= (tptp.sdtpldt0 (tptp.sdtpldt0 tptp.xn tptp.xm) tptp.xp) (tptp.sdtpldt0 (tptp.sdtpldt0 (tptp.sdtmndt0 tptp.xn tptp.xp) tptp.xm) tptp.xp)))) :rule and :premises (t157))
% 25.61/26.09  (step t160 (cl) :rule resolution :premises (t2 t68 t98 t120 t141 t158 t159))
% 25.61/26.09  
% 25.61/26.09  % SZS output end Proof for /export/starexec/sandbox/tmp/tmp.sHAYK2mJce/cvc5---1.0.5_28636.smt2
% 25.61/26.09  % cvc5---1.0.5 exiting
% 25.61/26.10  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------