%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : RNG099+2 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : do_cvc5 %s %d

% Computer : n021.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 17:41:54 EDT 2024

% Result   : Theorem 0.38s 0.56s
% Output   : Proof 0.38s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : RNG099+2 : TPTP v8.2.0. Released v4.0.0.
% 0.03/0.14  % Command    : do_cvc5 %s %d
% 0.14/0.35  % Computer : n021.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Sat May 25 21:42:54 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.20/0.51  %----Proving TF0_NAR, FOF, or CNF
% 0.38/0.56  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.38/0.56  % SZS status Theorem for /export/starexec/sandbox/tmp/tmp.R4TOeFgMh0/cvc5---1.0.5_17353.smt2
% 0.38/0.56  % SZS output start Proof for /export/starexec/sandbox/tmp/tmp.R4TOeFgMh0/cvc5---1.0.5_17353.smt2
% 0.38/0.56  (assume a0 (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) true)))
% 0.38/0.56  (assume a1 (tptp.aElement0 tptp.sz00))
% 0.38/0.56  (assume a2 (tptp.aElement0 tptp.sz10))
% 0.38/0.56  (assume a3 (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (tptp.aElement0 (tptp.smndt0 W0)))))
% 0.38/0.56  (assume a4 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtpldt0 W0 W1)))))
% 0.38/0.56  (assume a5 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtasdt0 W0 W1)))))
% 0.38/0.56  (assume a6 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (= (tptp.sdtpldt0 W0 W1) (tptp.sdtpldt0 W1 W0)))))
% 0.38/0.56  (assume a7 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1) (tptp.aElement0 W2)) (= (tptp.sdtpldt0 (tptp.sdtpldt0 W0 W1) W2) (tptp.sdtpldt0 W0 (tptp.sdtpldt0 W1 W2))))))
% 0.38/0.56  (assume a8 (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (and (= (tptp.sdtpldt0 W0 tptp.sz00) W0) (= W0 (tptp.sdtpldt0 tptp.sz00 W0))))))
% 0.38/0.56  (assume a9 (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (and (= (tptp.sdtpldt0 W0 (tptp.smndt0 W0)) tptp.sz00) (= tptp.sz00 (tptp.sdtpldt0 (tptp.smndt0 W0) W0))))))
% 0.38/0.56  (assume a10 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (= (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W1 W0)))))
% 0.38/0.56  (assume a11 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1) (tptp.aElement0 W2)) (= (tptp.sdtasdt0 (tptp.sdtasdt0 W0 W1) W2) (tptp.sdtasdt0 W0 (tptp.sdtasdt0 W1 W2))))))
% 0.38/0.56  (assume a12 (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz10) W0) (= W0 (tptp.sdtasdt0 tptp.sz10 W0))))))
% 0.38/0.56  (assume a13 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1) (tptp.aElement0 W2)) (and (= (tptp.sdtasdt0 W0 (tptp.sdtpldt0 W1 W2)) (tptp.sdtpldt0 (tptp.sdtasdt0 W0 W1) (tptp.sdtasdt0 W0 W2))) (= (tptp.sdtasdt0 (tptp.sdtpldt0 W1 W2) W0) (tptp.sdtpldt0 (tptp.sdtasdt0 W1 W0) (tptp.sdtasdt0 W2 W0)))))))
% 0.38/0.56  (assume a14 (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (and (= (tptp.sdtasdt0 (tptp.smndt0 tptp.sz10) W0) (tptp.smndt0 W0)) (= (tptp.smndt0 W0) (tptp.sdtasdt0 W0 (tptp.smndt0 tptp.sz10)))))))
% 0.38/0.56  (assume a15 (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (and (= (tptp.sdtasdt0 W0 tptp.sz00) tptp.sz00) (= tptp.sz00 (tptp.sdtasdt0 tptp.sz00 W0))))))
% 0.38/0.56  (assume a16 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (=> (= (tptp.sdtasdt0 W0 W1) tptp.sz00) (or (= W0 tptp.sz00) (= W1 tptp.sz00))))))
% 0.38/0.56  (assume a17 (not (= tptp.sz10 tptp.sz00)))
% 0.38/0.56  (assume a18 (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) true)))
% 0.38/0.56  (assume a19 (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElement0 W1))))))
% 0.38/0.56  (assume a20 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.aSet0 W1)) (=> (and (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 W0) (tptp.aElementOf0 W2 W1))) (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 W1) (tptp.aElementOf0 W2 W0)))) (= W0 W1)))))
% 0.38/0.56  (assume a21 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.aSet0 W1)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtpldt1 W0 W1)) (and (tptp.aSet0 W2) (forall ((W3 $$unsorted)) (= (tptp.aElementOf0 W3 W2) (exists ((W4 $$unsorted) (W5 $$unsorted)) (and (tptp.aElementOf0 W4 W0) (tptp.aElementOf0 W5 W1) (= (tptp.sdtpldt0 W4 W5) W3)))))))))))
% 0.38/0.56  (assume a22 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aSet0 W0) (tptp.aSet0 W1)) (forall ((W2 $$unsorted)) (= (= W2 (tptp.sdtasasdt0 W0 W1)) (and (tptp.aSet0 W2) (forall ((W3 $$unsorted)) (= (tptp.aElementOf0 W3 W2) (and (tptp.aElementOf0 W3 W0) (tptp.aElementOf0 W3 W1))))))))))
% 0.38/0.56  (assume a23 (forall ((W0 $$unsorted)) (= (tptp.aIdeal0 W0) (and (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (and (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 W0) (tptp.aElementOf0 (tptp.sdtpldt0 W1 W2) W0))) (forall ((W2 $$unsorted)) (=> (tptp.aElement0 W2) (tptp.aElementOf0 (tptp.sdtasdt0 W2 W1) W0))))))))))
% 0.38/0.56  (assume a24 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aIdeal0 W0) (tptp.aIdeal0 W1)) (tptp.aIdeal0 (tptp.sdtpldt1 W0 W1)))))
% 0.38/0.56  (assume a25 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aIdeal0 W0) (tptp.aIdeal0 W1)) (tptp.aIdeal0 (tptp.sdtasasdt0 W0 W1)))))
% 0.38/0.56  (assume a26 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1) (tptp.aIdeal0 W2)) (= (tptp.sdteqdtlpzmzozddtrp0 W0 W1 W2) (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 W1)) W2)))))
% 0.38/0.56  (assume a27 (and (tptp.aSet0 tptp.xI) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xI) (and (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 tptp.xI) (tptp.aElementOf0 (tptp.sdtpldt0 W0 W1) tptp.xI))) (forall ((W1 $$unsorted)) (=> (tptp.aElement0 W1) (tptp.aElementOf0 (tptp.sdtasdt0 W1 W0) tptp.xI)))))) (tptp.aIdeal0 tptp.xI) (tptp.aSet0 tptp.xJ) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xJ) (and (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 tptp.xJ) (tptp.aElementOf0 (tptp.sdtpldt0 W0 W1) tptp.xJ))) (forall ((W1 $$unsorted)) (=> (tptp.aElement0 W1) (tptp.aElementOf0 (tptp.sdtasdt0 W1 W0) tptp.xJ)))))) (tptp.aIdeal0 tptp.xJ)))
% 0.38/0.56  (assume a28 (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (and (exists ((W1 $$unsorted) (W2 $$unsorted)) (and (tptp.aElementOf0 W1 tptp.xI) (tptp.aElementOf0 W2 tptp.xJ) (= (tptp.sdtpldt0 W1 W2) W0))) (tptp.aElementOf0 W0 (tptp.sdtpldt1 tptp.xI tptp.xJ))))))
% 0.38/0.56  (assume a29 (and (tptp.aElement0 tptp.xx) (tptp.aElement0 tptp.xy)))
% 0.38/0.56  (assume a30 (and (tptp.aElementOf0 tptp.xa tptp.xI) (tptp.aElementOf0 tptp.xb tptp.xJ) (= (tptp.sdtpldt0 tptp.xa tptp.xb) tptp.sz10)))
% 0.38/0.56  (assume a31 (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))
% 0.38/0.56  (assume a32 (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xw (tptp.smndt0 tptp.xx)) tptp.xI))
% 0.38/0.56  (assume a33 (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xw (tptp.smndt0 tptp.xy)) tptp.xJ))
% 0.38/0.56  (assume a34 (not (exists ((W0 $$unsorted)) (and (tptp.aElement0 W0) (or (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xx)) tptp.xI) (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xx tptp.xI)) (or (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xy)) tptp.xJ) (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xy tptp.xJ))))))
% 0.38/0.56  (assume a35 true)
% 0.38/0.56  (step t1 (cl (not (= (or (not (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))) (not (not (tptp.aElement0 tptp.xw))) (not (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))) (or (not (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))) (tptp.aElement0 tptp.xw) (not (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))))) (not (or (not (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))) (not (not (tptp.aElement0 tptp.xw))) (not (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))))) (or (not (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))) (tptp.aElement0 tptp.xw) (not (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))))) :rule equiv_pos2)
% 0.38/0.56  (step t2 (cl (= (not (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))) (not (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))))) :rule refl)
% 0.38/0.56  (step t3 (cl (= (= (= (not (not (tptp.aElement0 tptp.xw))) (tptp.aElement0 tptp.xw)) true) (= (not (not (tptp.aElement0 tptp.xw))) (tptp.aElement0 tptp.xw)))) :rule equiv_simplify)
% 0.38/0.56  (step t4 (cl (not (= (= (not (not (tptp.aElement0 tptp.xw))) (tptp.aElement0 tptp.xw)) true)) (= (not (not (tptp.aElement0 tptp.xw))) (tptp.aElement0 tptp.xw))) :rule equiv1 :premises (t3))
% 0.38/0.56  (step t5 (cl (= (= (not (not (tptp.aElement0 tptp.xw))) (tptp.aElement0 tptp.xw)) (= (tptp.aElement0 tptp.xw) (not (not (tptp.aElement0 tptp.xw)))))) :rule all_simplify)
% 0.38/0.56  (step t6 (cl (= (tptp.aElement0 tptp.xw) (tptp.aElement0 tptp.xw))) :rule refl)
% 0.38/0.56  (step t7 (cl (= (not (not (tptp.aElement0 tptp.xw))) (tptp.aElement0 tptp.xw))) :rule all_simplify)
% 0.38/0.56  (step t8 (cl (= (= (tptp.aElement0 tptp.xw) (not (not (tptp.aElement0 tptp.xw)))) (= (tptp.aElement0 tptp.xw) (tptp.aElement0 tptp.xw)))) :rule cong :premises (t6 t7))
% 0.38/0.56  (step t9 (cl (= (= (tptp.aElement0 tptp.xw) (tptp.aElement0 tptp.xw)) true)) :rule all_simplify)
% 0.38/0.56  (step t10 (cl (= (= (tptp.aElement0 tptp.xw) (not (not (tptp.aElement0 tptp.xw)))) true)) :rule trans :premises (t8 t9))
% 0.38/0.56  (step t11 (cl (= (= (not (not (tptp.aElement0 tptp.xw))) (tptp.aElement0 tptp.xw)) true)) :rule trans :premises (t5 t10))
% 0.38/0.56  (step t12 (cl (= (not (not (tptp.aElement0 tptp.xw))) (tptp.aElement0 tptp.xw))) :rule resolution :premises (t4 t11))
% 0.38/0.56  (step t13 (cl (= (not (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))) (not (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))))) :rule refl)
% 0.38/0.56  (step t14 (cl (= (or (not (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))) (not (not (tptp.aElement0 tptp.xw))) (not (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))) (or (not (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))) (tptp.aElement0 tptp.xw) (not (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))))) :rule cong :premises (t2 t12 t13))
% 0.38/0.56  (step t15 (cl (and (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))) (not (tptp.aElement0 tptp.xw))) (not (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))) (not (not (tptp.aElement0 tptp.xw)))) :rule and_neg)
% 0.38/0.56  (step t16 (cl (=> (and (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))) (not (tptp.aElement0 tptp.xw))) (not (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))) (and (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))) (not (tptp.aElement0 tptp.xw)))) :rule implies_neg1)
% 0.38/0.56  (anchor :step t17)
% 0.38/0.56  (assume t17.a0 (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))
% 0.38/0.56  (assume t17.a1 (not (tptp.aElement0 tptp.xw)))
% 0.38/0.56  (step t17.t1 (cl (=> (and (not (tptp.aElement0 tptp.xw)) (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))) (not (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))) (and (not (tptp.aElement0 tptp.xw)) (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))) :rule implies_neg1)
% 0.38/0.56  (anchor :step t17.t2)
% 0.38/0.56  (assume t17.t2.a0 (not (tptp.aElement0 tptp.xw)))
% 0.38/0.56  (assume t17.t2.a1 (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))
% 0.38/0.56  (step t17.t2.t1 (cl (= (= (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))) false) (not (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))))) :rule equiv_simplify)
% 0.38/0.56  (step t17.t2.t2 (cl (not (= (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))) false)) (not (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))) :rule equiv1 :premises (t17.t2.t1))
% 0.38/0.56  (step t17.t2.t3 (cl (= (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)) tptp.xw)) :rule symm :premises (t17.t2.a1))
% 0.38/0.56  (step t17.t2.t4 (cl (= (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))) (tptp.aElement0 tptp.xw))) :rule cong :premises (t17.t2.t3))
% 0.38/0.56  (step t17.t2.t5 (cl (= (= (tptp.aElement0 tptp.xw) false) (not (tptp.aElement0 tptp.xw)))) :rule equiv_simplify)
% 0.38/0.56  (step t17.t2.t6 (cl (= (tptp.aElement0 tptp.xw) false) (not (not (tptp.aElement0 tptp.xw)))) :rule equiv2 :premises (t17.t2.t5))
% 0.38/0.56  (step t17.t2.t7 (cl (not (not (not (tptp.aElement0 tptp.xw)))) (tptp.aElement0 tptp.xw)) :rule not_not)
% 0.38/0.56  (step t17.t2.t8 (cl (= (tptp.aElement0 tptp.xw) false) (tptp.aElement0 tptp.xw)) :rule resolution :premises (t17.t2.t6 t17.t2.t7))
% 0.38/0.56  (step t17.t2.t9 (cl (= (tptp.aElement0 tptp.xw) false)) :rule resolution :premises (t17.t2.t8 t17.t2.a0))
% 0.38/0.56  (step t17.t2.t10 (cl (= (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))) false)) :rule trans :premises (t17.t2.t4 t17.t2.t9))
% 0.38/0.56  (step t17.t2.t11 (cl (not (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))) :rule resolution :premises (t17.t2.t2 t17.t2.t10))
% 0.38/0.56  (step t17.t2 (cl (not (not (tptp.aElement0 tptp.xw))) (not (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))) (not (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))) :rule subproof :discharge (t17.t2.a0 t17.t2.a1))
% 0.38/0.56  (step t17.t3 (cl (not (and (not (tptp.aElement0 tptp.xw)) (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))) (not (tptp.aElement0 tptp.xw))) :rule and_pos)
% 0.38/0.56  (step t17.t4 (cl (not (and (not (tptp.aElement0 tptp.xw)) (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))) (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))) :rule and_pos)
% 0.38/0.56  (step t17.t5 (cl (not (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))) (not (and (not (tptp.aElement0 tptp.xw)) (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))) (not (and (not (tptp.aElement0 tptp.xw)) (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))))) :rule resolution :premises (t17.t2 t17.t3 t17.t4))
% 0.38/0.56  (step t17.t6 (cl (not (and (not (tptp.aElement0 tptp.xw)) (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))) (not (and (not (tptp.aElement0 tptp.xw)) (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))) (not (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))) :rule reordering :premises (t17.t5))
% 0.38/0.56  (step t17.t7 (cl (not (and (not (tptp.aElement0 tptp.xw)) (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))) (not (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))) :rule contraction :premises (t17.t6))
% 0.38/0.56  (step t17.t8 (cl (=> (and (not (tptp.aElement0 tptp.xw)) (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))) (not (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))) (not (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))) :rule resolution :premises (t17.t1 t17.t7))
% 0.38/0.56  (step t17.t9 (cl (=> (and (not (tptp.aElement0 tptp.xw)) (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))) (not (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))) (not (not (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))))) :rule implies_neg2)
% 0.38/0.56  (step t17.t10 (cl (=> (and (not (tptp.aElement0 tptp.xw)) (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))) (not (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))) (=> (and (not (tptp.aElement0 tptp.xw)) (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))) (not (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))))) :rule resolution :premises (t17.t8 t17.t9))
% 0.38/0.56  (step t17.t11 (cl (=> (and (not (tptp.aElement0 tptp.xw)) (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))) (not (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))))) :rule contraction :premises (t17.t10))
% 0.38/0.56  (step t17.t12 (cl (not (and (not (tptp.aElement0 tptp.xw)) (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))) (not (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))) :rule implies :premises (t17.t11))
% 0.38/0.56  (step t17.t13 (cl (and (not (tptp.aElement0 tptp.xw)) (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))) (not (not (tptp.aElement0 tptp.xw))) (not (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))) :rule and_neg)
% 0.38/0.56  (step t17.t14 (cl (and (not (tptp.aElement0 tptp.xw)) (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))) :rule resolution :premises (t17.t13 t17.a1 t17.a0))
% 0.38/0.56  (step t17.t15 (cl (not (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))) :rule resolution :premises (t17.t12 t17.t14))
% 0.38/0.56  (step t17 (cl (not (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))) (not (not (tptp.aElement0 tptp.xw))) (not (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))) :rule subproof :discharge (t17.a0 t17.a1))
% 0.38/0.56  (step t18 (cl (not (and (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))) (not (tptp.aElement0 tptp.xw)))) (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))) :rule and_pos)
% 0.38/0.56  (step t19 (cl (not (and (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))) (not (tptp.aElement0 tptp.xw)))) (not (tptp.aElement0 tptp.xw))) :rule and_pos)
% 0.38/0.56  (step t20 (cl (not (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))) (not (and (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))) (not (tptp.aElement0 tptp.xw)))) (not (and (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))) (not (tptp.aElement0 tptp.xw))))) :rule resolution :premises (t17 t18 t19))
% 0.38/0.56  (step t21 (cl (not (and (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))) (not (tptp.aElement0 tptp.xw)))) (not (and (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))) (not (tptp.aElement0 tptp.xw)))) (not (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))) :rule reordering :premises (t20))
% 0.38/0.56  (step t22 (cl (not (and (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))) (not (tptp.aElement0 tptp.xw)))) (not (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))) :rule contraction :premises (t21))
% 0.38/0.56  (step t23 (cl (=> (and (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))) (not (tptp.aElement0 tptp.xw))) (not (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))) (not (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))) :rule resolution :premises (t16 t22))
% 0.38/0.56  (step t24 (cl (=> (and (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))) (not (tptp.aElement0 tptp.xw))) (not (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))) (not (not (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))))) :rule implies_neg2)
% 0.38/0.56  (step t25 (cl (=> (and (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))) (not (tptp.aElement0 tptp.xw))) (not (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))) (=> (and (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))) (not (tptp.aElement0 tptp.xw))) (not (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))))) :rule resolution :premises (t23 t24))
% 0.38/0.56  (step t26 (cl (=> (and (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))) (not (tptp.aElement0 tptp.xw))) (not (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))))) :rule contraction :premises (t25))
% 0.38/0.56  (step t27 (cl (not (and (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))) (not (tptp.aElement0 tptp.xw)))) (not (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))) :rule implies :premises (t26))
% 0.38/0.56  (step t28 (cl (not (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))) (not (not (tptp.aElement0 tptp.xw))) (not (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))) :rule resolution :premises (t15 t27))
% 0.38/0.56  (step t29 (cl (or (not (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))) (not (not (tptp.aElement0 tptp.xw))) (not (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))) (not (not (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))))) :rule or_neg)
% 0.38/0.56  (step t30 (cl (or (not (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))) (not (not (tptp.aElement0 tptp.xw))) (not (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))) (not (not (not (tptp.aElement0 tptp.xw))))) :rule or_neg)
% 0.38/0.56  (step t31 (cl (or (not (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))) (not (not (tptp.aElement0 tptp.xw))) (not (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))) (not (not (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))))) :rule or_neg)
% 0.38/0.56  (step t32 (cl (or (not (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))) (not (not (tptp.aElement0 tptp.xw))) (not (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))) (or (not (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))) (not (not (tptp.aElement0 tptp.xw))) (not (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))) (or (not (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))) (not (not (tptp.aElement0 tptp.xw))) (not (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))))) :rule resolution :premises (t28 t29 t30 t31))
% 0.38/0.56  (step t33 (cl (or (not (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))) (not (not (tptp.aElement0 tptp.xw))) (not (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))))) :rule contraction :premises (t32))
% 0.38/0.56  (step t34 (cl (or (not (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))) (tptp.aElement0 tptp.xw) (not (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))))) :rule resolution :premises (t1 t14 t33))
% 0.38/0.56  (step t35 (cl (not (= tptp.xw (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))) (tptp.aElement0 tptp.xw) (not (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))) :rule or :premises (t34))
% 0.38/0.56  (step t36 (cl (not (or (not (tptp.aElement0 (tptp.sdtasdt0 tptp.xy tptp.xa))) (not (tptp.aElement0 (tptp.sdtasdt0 tptp.xx tptp.xb))) (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))) (not (tptp.aElement0 (tptp.sdtasdt0 tptp.xy tptp.xa))) (not (tptp.aElement0 (tptp.sdtasdt0 tptp.xx tptp.xb))) (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))) :rule or_pos)
% 0.38/0.56  (step t37 (cl (not (tptp.aElement0 (tptp.sdtasdt0 tptp.xy tptp.xa))) (not (tptp.aElement0 (tptp.sdtasdt0 tptp.xx tptp.xb))) (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))) (not (or (not (tptp.aElement0 (tptp.sdtasdt0 tptp.xy tptp.xa))) (not (tptp.aElement0 (tptp.sdtasdt0 tptp.xx tptp.xb))) (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))))) :rule reordering :premises (t36))
% 0.38/0.56  (step t38 (cl (not (or (not (tptp.aElement0 tptp.xy)) (not (tptp.aElement0 tptp.xa)) (tptp.aElement0 (tptp.sdtasdt0 tptp.xy tptp.xa)))) (not (tptp.aElement0 tptp.xy)) (not (tptp.aElement0 tptp.xa)) (tptp.aElement0 (tptp.sdtasdt0 tptp.xy tptp.xa))) :rule or_pos)
% 0.38/0.56  (step t39 (cl (not (tptp.aElement0 tptp.xy)) (tptp.aElement0 (tptp.sdtasdt0 tptp.xy tptp.xa)) (not (tptp.aElement0 tptp.xa)) (not (or (not (tptp.aElement0 tptp.xy)) (not (tptp.aElement0 tptp.xa)) (tptp.aElement0 (tptp.sdtasdt0 tptp.xy tptp.xa))))) :rule reordering :premises (t38))
% 0.38/0.56  (step t40 (cl (tptp.aElement0 tptp.xy)) :rule and :premises (a29))
% 0.38/0.56  (step t41 (cl (not (or (not (tptp.aSet0 tptp.xI)) (not (tptp.aElementOf0 tptp.xa tptp.xI)) (tptp.aElement0 tptp.xa))) (not (tptp.aSet0 tptp.xI)) (not (tptp.aElementOf0 tptp.xa tptp.xI)) (tptp.aElement0 tptp.xa)) :rule or_pos)
% 0.38/0.56  (step t42 (cl (not (tptp.aSet0 tptp.xI)) (not (tptp.aElementOf0 tptp.xa tptp.xI)) (tptp.aElement0 tptp.xa) (not (or (not (tptp.aSet0 tptp.xI)) (not (tptp.aElementOf0 tptp.xa tptp.xI)) (tptp.aElement0 tptp.xa)))) :rule reordering :premises (t41))
% 0.38/0.56  (step t43 (cl (not (= (and (tptp.aSet0 tptp.xI) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xI) (and (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 tptp.xI) (tptp.aElementOf0 (tptp.sdtpldt0 W0 W1) tptp.xI))) (forall ((W1 $$unsorted)) (=> (tptp.aElement0 W1) (tptp.aElementOf0 (tptp.sdtasdt0 W1 W0) tptp.xI)))))) (tptp.aIdeal0 tptp.xI) (tptp.aSet0 tptp.xJ) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xJ) (and (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 tptp.xJ) (tptp.aElementOf0 (tptp.sdtpldt0 W0 W1) tptp.xJ))) (forall ((W1 $$unsorted)) (=> (tptp.aElement0 W1) (tptp.aElementOf0 (tptp.sdtasdt0 W1 W0) tptp.xJ)))))) (tptp.aIdeal0 tptp.xJ)) (and (tptp.aSet0 tptp.xI) (forall ((W0 $$unsorted) (BOUND_VARIABLE_1330 $$unsorted) (BOUND_VARIABLE_1323 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xI)) (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_1323 tptp.xI)) (tptp.aElementOf0 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1323) tptp.xI)) (or (not (tptp.aElement0 BOUND_VARIABLE_1330)) (tptp.aElementOf0 (tptp.sdtasdt0 BOUND_VARIABLE_1330 W0) tptp.xI))))) (tptp.aIdeal0 tptp.xI) (tptp.aSet0 tptp.xJ) (forall ((W0 $$unsorted) (BOUND_VARIABLE_1360 $$unsorted) (BOUND_VARIABLE_1353 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xJ)) (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_1353 tptp.xJ)) (tptp.aElementOf0 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1353) tptp.xJ)) (or (not (tptp.aElement0 BOUND_VARIABLE_1360)) (tptp.aElementOf0 (tptp.sdtasdt0 BOUND_VARIABLE_1360 W0) tptp.xJ))))) (tptp.aIdeal0 tptp.xJ)))) (not (and (tptp.aSet0 tptp.xI) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xI) (and (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 tptp.xI) (tptp.aElementOf0 (tptp.sdtpldt0 W0 W1) tptp.xI))) (forall ((W1 $$unsorted)) (=> (tptp.aElement0 W1) (tptp.aElementOf0 (tptp.sdtasdt0 W1 W0) tptp.xI)))))) (tptp.aIdeal0 tptp.xI) (tptp.aSet0 tptp.xJ) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xJ) (and (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 tptp.xJ) (tptp.aElementOf0 (tptp.sdtpldt0 W0 W1) tptp.xJ))) (forall ((W1 $$unsorted)) (=> (tptp.aElement0 W1) (tptp.aElementOf0 (tptp.sdtasdt0 W1 W0) tptp.xJ)))))) (tptp.aIdeal0 tptp.xJ))) (and (tptp.aSet0 tptp.xI) (forall ((W0 $$unsorted) (BOUND_VARIABLE_1330 $$unsorted) (BOUND_VARIABLE_1323 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xI)) (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_1323 tptp.xI)) (tptp.aElementOf0 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1323) tptp.xI)) (or (not (tptp.aElement0 BOUND_VARIABLE_1330)) (tptp.aElementOf0 (tptp.sdtasdt0 BOUND_VARIABLE_1330 W0) tptp.xI))))) (tptp.aIdeal0 tptp.xI) (tptp.aSet0 tptp.xJ) (forall ((W0 $$unsorted) (BOUND_VARIABLE_1360 $$unsorted) (BOUND_VARIABLE_1353 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xJ)) (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_1353 tptp.xJ)) (tptp.aElementOf0 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1353) tptp.xJ)) (or (not (tptp.aElement0 BOUND_VARIABLE_1360)) (tptp.aElementOf0 (tptp.sdtasdt0 BOUND_VARIABLE_1360 W0) tptp.xJ))))) (tptp.aIdeal0 tptp.xJ))) :rule equiv_pos2)
% 0.38/0.56  (step t44 (cl (= (tptp.aSet0 tptp.xI) (tptp.aSet0 tptp.xI))) :rule refl)
% 0.38/0.56  (anchor :step t45 :args ((W0 $$unsorted) (:= W0 W0)))
% 0.38/0.56  (step t45.t1 (cl (= W0 W0)) :rule refl)
% 0.38/0.56  (step t45.t2 (cl (= (tptp.aElementOf0 W0 tptp.xI) (tptp.aElementOf0 W0 tptp.xI))) :rule refl)
% 0.38/0.56  (step t45.t3 (cl (= (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 tptp.xI) (tptp.aElementOf0 (tptp.sdtpldt0 W0 W1) tptp.xI))) (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.xI)) (tptp.aElementOf0 (tptp.sdtpldt0 W0 W1) tptp.xI))))) :rule all_simplify)
% 0.38/0.56  (step t45.t4 (cl (= (forall ((W1 $$unsorted)) (=> (tptp.aElement0 W1) (tptp.aElementOf0 (tptp.sdtasdt0 W1 W0) tptp.xI))) (forall ((W1 $$unsorted)) (or (not (tptp.aElement0 W1)) (tptp.aElementOf0 (tptp.sdtasdt0 W1 W0) tptp.xI))))) :rule all_simplify)
% 0.38/0.56  (step t45.t5 (cl (= (and (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 tptp.xI) (tptp.aElementOf0 (tptp.sdtpldt0 W0 W1) tptp.xI))) (forall ((W1 $$unsorted)) (=> (tptp.aElement0 W1) (tptp.aElementOf0 (tptp.sdtasdt0 W1 W0) tptp.xI)))) (and (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.xI)) (tptp.aElementOf0 (tptp.sdtpldt0 W0 W1) tptp.xI))) (forall ((W1 $$unsorted)) (or (not (tptp.aElement0 W1)) (tptp.aElementOf0 (tptp.sdtasdt0 W1 W0) tptp.xI)))))) :rule cong :premises (t45.t3 t45.t4))
% 0.38/0.56  (step t45.t6 (cl (= (=> (tptp.aElementOf0 W0 tptp.xI) (and (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 tptp.xI) (tptp.aElementOf0 (tptp.sdtpldt0 W0 W1) tptp.xI))) (forall ((W1 $$unsorted)) (=> (tptp.aElement0 W1) (tptp.aElementOf0 (tptp.sdtasdt0 W1 W0) tptp.xI))))) (=> (tptp.aElementOf0 W0 tptp.xI) (and (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.xI)) (tptp.aElementOf0 (tptp.sdtpldt0 W0 W1) tptp.xI))) (forall ((W1 $$unsorted)) (or (not (tptp.aElement0 W1)) (tptp.aElementOf0 (tptp.sdtasdt0 W1 W0) tptp.xI))))))) :rule cong :premises (t45.t2 t45.t5))
% 0.38/0.56  (step t45 (cl (= (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xI) (and (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 tptp.xI) (tptp.aElementOf0 (tptp.sdtpldt0 W0 W1) tptp.xI))) (forall ((W1 $$unsorted)) (=> (tptp.aElement0 W1) (tptp.aElementOf0 (tptp.sdtasdt0 W1 W0) tptp.xI)))))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xI) (and (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.xI)) (tptp.aElementOf0 (tptp.sdtpldt0 W0 W1) tptp.xI))) (forall ((W1 $$unsorted)) (or (not (tptp.aElement0 W1)) (tptp.aElementOf0 (tptp.sdtasdt0 W1 W0) tptp.xI)))))))) :rule bind)
% 0.38/0.56  (step t46 (cl (= (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xI) (and (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.xI)) (tptp.aElementOf0 (tptp.sdtpldt0 W0 W1) tptp.xI))) (forall ((W1 $$unsorted)) (or (not (tptp.aElement0 W1)) (tptp.aElementOf0 (tptp.sdtasdt0 W1 W0) tptp.xI)))))) (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xI)) (and (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.xI)) (tptp.aElementOf0 (tptp.sdtpldt0 W0 W1) tptp.xI))) (forall ((W1 $$unsorted)) (or (not (tptp.aElement0 W1)) (tptp.aElementOf0 (tptp.sdtasdt0 W1 W0) tptp.xI)))))))) :rule all_simplify)
% 0.38/0.56  (step t47 (cl (= (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xI)) (and (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.xI)) (tptp.aElementOf0 (tptp.sdtpldt0 W0 W1) tptp.xI))) (forall ((W1 $$unsorted)) (or (not (tptp.aElement0 W1)) (tptp.aElementOf0 (tptp.sdtasdt0 W1 W0) tptp.xI)))))) (forall ((W0 $$unsorted) (BOUND_VARIABLE_1330 $$unsorted) (BOUND_VARIABLE_1323 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xI)) (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_1323 tptp.xI)) (tptp.aElementOf0 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1323) tptp.xI)) (or (not (tptp.aElement0 BOUND_VARIABLE_1330)) (tptp.aElementOf0 (tptp.sdtasdt0 BOUND_VARIABLE_1330 W0) tptp.xI))))))) :rule all_simplify)
% 0.38/0.56  (step t48 (cl (= (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xI) (and (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.xI)) (tptp.aElementOf0 (tptp.sdtpldt0 W0 W1) tptp.xI))) (forall ((W1 $$unsorted)) (or (not (tptp.aElement0 W1)) (tptp.aElementOf0 (tptp.sdtasdt0 W1 W0) tptp.xI)))))) (forall ((W0 $$unsorted) (BOUND_VARIABLE_1330 $$unsorted) (BOUND_VARIABLE_1323 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xI)) (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_1323 tptp.xI)) (tptp.aElementOf0 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1323) tptp.xI)) (or (not (tptp.aElement0 BOUND_VARIABLE_1330)) (tptp.aElementOf0 (tptp.sdtasdt0 BOUND_VARIABLE_1330 W0) tptp.xI))))))) :rule trans :premises (t46 t47))
% 0.38/0.56  (step t49 (cl (= (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xI) (and (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 tptp.xI) (tptp.aElementOf0 (tptp.sdtpldt0 W0 W1) tptp.xI))) (forall ((W1 $$unsorted)) (=> (tptp.aElement0 W1) (tptp.aElementOf0 (tptp.sdtasdt0 W1 W0) tptp.xI)))))) (forall ((W0 $$unsorted) (BOUND_VARIABLE_1330 $$unsorted) (BOUND_VARIABLE_1323 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xI)) (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_1323 tptp.xI)) (tptp.aElementOf0 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1323) tptp.xI)) (or (not (tptp.aElement0 BOUND_VARIABLE_1330)) (tptp.aElementOf0 (tptp.sdtasdt0 BOUND_VARIABLE_1330 W0) tptp.xI))))))) :rule trans :premises (t45 t48))
% 0.38/0.56  (step t50 (cl (= (tptp.aIdeal0 tptp.xI) (tptp.aIdeal0 tptp.xI))) :rule refl)
% 0.38/0.56  (step t51 (cl (= (tptp.aSet0 tptp.xJ) (tptp.aSet0 tptp.xJ))) :rule refl)
% 0.38/0.56  (anchor :step t52 :args ((W0 $$unsorted) (:= W0 W0)))
% 0.38/0.56  (step t52.t1 (cl (= W0 W0)) :rule refl)
% 0.38/0.56  (step t52.t2 (cl (= (tptp.aElementOf0 W0 tptp.xJ) (tptp.aElementOf0 W0 tptp.xJ))) :rule refl)
% 0.38/0.56  (step t52.t3 (cl (= (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 tptp.xJ) (tptp.aElementOf0 (tptp.sdtpldt0 W0 W1) tptp.xJ))) (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.xJ)) (tptp.aElementOf0 (tptp.sdtpldt0 W0 W1) tptp.xJ))))) :rule all_simplify)
% 0.38/0.56  (step t52.t4 (cl (= (forall ((W1 $$unsorted)) (=> (tptp.aElement0 W1) (tptp.aElementOf0 (tptp.sdtasdt0 W1 W0) tptp.xJ))) (forall ((W1 $$unsorted)) (or (not (tptp.aElement0 W1)) (tptp.aElementOf0 (tptp.sdtasdt0 W1 W0) tptp.xJ))))) :rule all_simplify)
% 0.38/0.56  (step t52.t5 (cl (= (and (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 tptp.xJ) (tptp.aElementOf0 (tptp.sdtpldt0 W0 W1) tptp.xJ))) (forall ((W1 $$unsorted)) (=> (tptp.aElement0 W1) (tptp.aElementOf0 (tptp.sdtasdt0 W1 W0) tptp.xJ)))) (and (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.xJ)) (tptp.aElementOf0 (tptp.sdtpldt0 W0 W1) tptp.xJ))) (forall ((W1 $$unsorted)) (or (not (tptp.aElement0 W1)) (tptp.aElementOf0 (tptp.sdtasdt0 W1 W0) tptp.xJ)))))) :rule cong :premises (t52.t3 t52.t4))
% 0.38/0.56  (step t52.t6 (cl (= (=> (tptp.aElementOf0 W0 tptp.xJ) (and (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 tptp.xJ) (tptp.aElementOf0 (tptp.sdtpldt0 W0 W1) tptp.xJ))) (forall ((W1 $$unsorted)) (=> (tptp.aElement0 W1) (tptp.aElementOf0 (tptp.sdtasdt0 W1 W0) tptp.xJ))))) (=> (tptp.aElementOf0 W0 tptp.xJ) (and (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.xJ)) (tptp.aElementOf0 (tptp.sdtpldt0 W0 W1) tptp.xJ))) (forall ((W1 $$unsorted)) (or (not (tptp.aElement0 W1)) (tptp.aElementOf0 (tptp.sdtasdt0 W1 W0) tptp.xJ))))))) :rule cong :premises (t52.t2 t52.t5))
% 0.38/0.56  (step t52 (cl (= (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xJ) (and (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 tptp.xJ) (tptp.aElementOf0 (tptp.sdtpldt0 W0 W1) tptp.xJ))) (forall ((W1 $$unsorted)) (=> (tptp.aElement0 W1) (tptp.aElementOf0 (tptp.sdtasdt0 W1 W0) tptp.xJ)))))) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xJ) (and (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.xJ)) (tptp.aElementOf0 (tptp.sdtpldt0 W0 W1) tptp.xJ))) (forall ((W1 $$unsorted)) (or (not (tptp.aElement0 W1)) (tptp.aElementOf0 (tptp.sdtasdt0 W1 W0) tptp.xJ)))))))) :rule bind)
% 0.38/0.56  (step t53 (cl (= (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xJ) (and (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.xJ)) (tptp.aElementOf0 (tptp.sdtpldt0 W0 W1) tptp.xJ))) (forall ((W1 $$unsorted)) (or (not (tptp.aElement0 W1)) (tptp.aElementOf0 (tptp.sdtasdt0 W1 W0) tptp.xJ)))))) (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xJ)) (and (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.xJ)) (tptp.aElementOf0 (tptp.sdtpldt0 W0 W1) tptp.xJ))) (forall ((W1 $$unsorted)) (or (not (tptp.aElement0 W1)) (tptp.aElementOf0 (tptp.sdtasdt0 W1 W0) tptp.xJ)))))))) :rule all_simplify)
% 0.38/0.56  (step t54 (cl (= (forall ((W0 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xJ)) (and (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.xJ)) (tptp.aElementOf0 (tptp.sdtpldt0 W0 W1) tptp.xJ))) (forall ((W1 $$unsorted)) (or (not (tptp.aElement0 W1)) (tptp.aElementOf0 (tptp.sdtasdt0 W1 W0) tptp.xJ)))))) (forall ((W0 $$unsorted) (BOUND_VARIABLE_1360 $$unsorted) (BOUND_VARIABLE_1353 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xJ)) (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_1353 tptp.xJ)) (tptp.aElementOf0 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1353) tptp.xJ)) (or (not (tptp.aElement0 BOUND_VARIABLE_1360)) (tptp.aElementOf0 (tptp.sdtasdt0 BOUND_VARIABLE_1360 W0) tptp.xJ))))))) :rule all_simplify)
% 0.38/0.56  (step t55 (cl (= (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xJ) (and (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 tptp.xJ)) (tptp.aElementOf0 (tptp.sdtpldt0 W0 W1) tptp.xJ))) (forall ((W1 $$unsorted)) (or (not (tptp.aElement0 W1)) (tptp.aElementOf0 (tptp.sdtasdt0 W1 W0) tptp.xJ)))))) (forall ((W0 $$unsorted) (BOUND_VARIABLE_1360 $$unsorted) (BOUND_VARIABLE_1353 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xJ)) (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_1353 tptp.xJ)) (tptp.aElementOf0 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1353) tptp.xJ)) (or (not (tptp.aElement0 BOUND_VARIABLE_1360)) (tptp.aElementOf0 (tptp.sdtasdt0 BOUND_VARIABLE_1360 W0) tptp.xJ))))))) :rule trans :premises (t53 t54))
% 0.38/0.56  (step t56 (cl (= (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xJ) (and (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 tptp.xJ) (tptp.aElementOf0 (tptp.sdtpldt0 W0 W1) tptp.xJ))) (forall ((W1 $$unsorted)) (=> (tptp.aElement0 W1) (tptp.aElementOf0 (tptp.sdtasdt0 W1 W0) tptp.xJ)))))) (forall ((W0 $$unsorted) (BOUND_VARIABLE_1360 $$unsorted) (BOUND_VARIABLE_1353 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xJ)) (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_1353 tptp.xJ)) (tptp.aElementOf0 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1353) tptp.xJ)) (or (not (tptp.aElement0 BOUND_VARIABLE_1360)) (tptp.aElementOf0 (tptp.sdtasdt0 BOUND_VARIABLE_1360 W0) tptp.xJ))))))) :rule trans :premises (t52 t55))
% 0.38/0.56  (step t57 (cl (= (tptp.aIdeal0 tptp.xJ) (tptp.aIdeal0 tptp.xJ))) :rule refl)
% 0.38/0.56  (step t58 (cl (= (and (tptp.aSet0 tptp.xI) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xI) (and (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 tptp.xI) (tptp.aElementOf0 (tptp.sdtpldt0 W0 W1) tptp.xI))) (forall ((W1 $$unsorted)) (=> (tptp.aElement0 W1) (tptp.aElementOf0 (tptp.sdtasdt0 W1 W0) tptp.xI)))))) (tptp.aIdeal0 tptp.xI) (tptp.aSet0 tptp.xJ) (forall ((W0 $$unsorted)) (=> (tptp.aElementOf0 W0 tptp.xJ) (and (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 tptp.xJ) (tptp.aElementOf0 (tptp.sdtpldt0 W0 W1) tptp.xJ))) (forall ((W1 $$unsorted)) (=> (tptp.aElement0 W1) (tptp.aElementOf0 (tptp.sdtasdt0 W1 W0) tptp.xJ)))))) (tptp.aIdeal0 tptp.xJ)) (and (tptp.aSet0 tptp.xI) (forall ((W0 $$unsorted) (BOUND_VARIABLE_1330 $$unsorted) (BOUND_VARIABLE_1323 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xI)) (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_1323 tptp.xI)) (tptp.aElementOf0 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1323) tptp.xI)) (or (not (tptp.aElement0 BOUND_VARIABLE_1330)) (tptp.aElementOf0 (tptp.sdtasdt0 BOUND_VARIABLE_1330 W0) tptp.xI))))) (tptp.aIdeal0 tptp.xI) (tptp.aSet0 tptp.xJ) (forall ((W0 $$unsorted) (BOUND_VARIABLE_1360 $$unsorted) (BOUND_VARIABLE_1353 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xJ)) (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_1353 tptp.xJ)) (tptp.aElementOf0 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1353) tptp.xJ)) (or (not (tptp.aElement0 BOUND_VARIABLE_1360)) (tptp.aElementOf0 (tptp.sdtasdt0 BOUND_VARIABLE_1360 W0) tptp.xJ))))) (tptp.aIdeal0 tptp.xJ)))) :rule cong :premises (t44 t49 t50 t51 t56 t57))
% 0.38/0.56  (step t59 (cl (and (tptp.aSet0 tptp.xI) (forall ((W0 $$unsorted) (BOUND_VARIABLE_1330 $$unsorted) (BOUND_VARIABLE_1323 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xI)) (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_1323 tptp.xI)) (tptp.aElementOf0 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1323) tptp.xI)) (or (not (tptp.aElement0 BOUND_VARIABLE_1330)) (tptp.aElementOf0 (tptp.sdtasdt0 BOUND_VARIABLE_1330 W0) tptp.xI))))) (tptp.aIdeal0 tptp.xI) (tptp.aSet0 tptp.xJ) (forall ((W0 $$unsorted) (BOUND_VARIABLE_1360 $$unsorted) (BOUND_VARIABLE_1353 $$unsorted)) (or (not (tptp.aElementOf0 W0 tptp.xJ)) (and (or (not (tptp.aElementOf0 BOUND_VARIABLE_1353 tptp.xJ)) (tptp.aElementOf0 (tptp.sdtpldt0 W0 BOUND_VARIABLE_1353) tptp.xJ)) (or (not (tptp.aElement0 BOUND_VARIABLE_1360)) (tptp.aElementOf0 (tptp.sdtasdt0 BOUND_VARIABLE_1360 W0) tptp.xJ))))) (tptp.aIdeal0 tptp.xJ))) :rule resolution :premises (t43 t58 a27))
% 0.38/0.56  (step t60 (cl (tptp.aSet0 tptp.xI)) :rule and :premises (t59))
% 0.38/0.56  (step t61 (cl (not (= (and (tptp.aElementOf0 tptp.xa tptp.xI) (tptp.aElementOf0 tptp.xb tptp.xJ) (= (tptp.sdtpldt0 tptp.xa tptp.xb) tptp.sz10)) (and (tptp.aElementOf0 tptp.xa tptp.xI) (tptp.aElementOf0 tptp.xb tptp.xJ) (= tptp.sz10 (tptp.sdtpldt0 tptp.xa tptp.xb))))) (not (and (tptp.aElementOf0 tptp.xa tptp.xI) (tptp.aElementOf0 tptp.xb tptp.xJ) (= (tptp.sdtpldt0 tptp.xa tptp.xb) tptp.sz10))) (and (tptp.aElementOf0 tptp.xa tptp.xI) (tptp.aElementOf0 tptp.xb tptp.xJ) (= tptp.sz10 (tptp.sdtpldt0 tptp.xa tptp.xb)))) :rule equiv_pos2)
% 0.38/0.56  (step t62 (cl (= (tptp.aElementOf0 tptp.xa tptp.xI) (tptp.aElementOf0 tptp.xa tptp.xI))) :rule refl)
% 0.38/0.56  (step t63 (cl (= (tptp.aElementOf0 tptp.xb tptp.xJ) (tptp.aElementOf0 tptp.xb tptp.xJ))) :rule refl)
% 0.38/0.56  (step t64 (cl (= (= (tptp.sdtpldt0 tptp.xa tptp.xb) tptp.sz10) (= tptp.sz10 (tptp.sdtpldt0 tptp.xa tptp.xb)))) :rule all_simplify)
% 0.38/0.56  (step t65 (cl (= (and (tptp.aElementOf0 tptp.xa tptp.xI) (tptp.aElementOf0 tptp.xb tptp.xJ) (= (tptp.sdtpldt0 tptp.xa tptp.xb) tptp.sz10)) (and (tptp.aElementOf0 tptp.xa tptp.xI) (tptp.aElementOf0 tptp.xb tptp.xJ) (= tptp.sz10 (tptp.sdtpldt0 tptp.xa tptp.xb))))) :rule cong :premises (t62 t63 t64))
% 0.38/0.56  (step t66 (cl (and (tptp.aElementOf0 tptp.xa tptp.xI) (tptp.aElementOf0 tptp.xb tptp.xJ) (= tptp.sz10 (tptp.sdtpldt0 tptp.xa tptp.xb)))) :rule resolution :premises (t61 t65 a30))
% 0.38/0.56  (step t67 (cl (tptp.aElementOf0 tptp.xa tptp.xI)) :rule and :premises (t66))
% 0.38/0.56  (step t68 (cl (=> (forall ((W0 $$unsorted) (BOUND_VARIABLE_1150 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_1150 W0)) (tptp.aElement0 BOUND_VARIABLE_1150))) (or (not (tptp.aSet0 tptp.xI)) (not (tptp.aElementOf0 tptp.xa tptp.xI)) (tptp.aElement0 tptp.xa))) (forall ((W0 $$unsorted) (BOUND_VARIABLE_1150 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_1150 W0)) (tptp.aElement0 BOUND_VARIABLE_1150)))) :rule implies_neg1)
% 0.38/0.56  (anchor :step t69)
% 0.38/0.56  (assume t69.a0 (forall ((W0 $$unsorted) (BOUND_VARIABLE_1150 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_1150 W0)) (tptp.aElement0 BOUND_VARIABLE_1150))))
% 0.38/0.56  (step t69.t1 (cl (or (not (forall ((W0 $$unsorted) (BOUND_VARIABLE_1150 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_1150 W0)) (tptp.aElement0 BOUND_VARIABLE_1150)))) (or (not (tptp.aSet0 tptp.xI)) (not (tptp.aElementOf0 tptp.xa tptp.xI)) (tptp.aElement0 tptp.xa)))) :rule forall_inst :args ((:= W0 tptp.xI) (:= BOUND_VARIABLE_1150 tptp.xa)))
% 0.38/0.56  (step t69.t2 (cl (not (forall ((W0 $$unsorted) (BOUND_VARIABLE_1150 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_1150 W0)) (tptp.aElement0 BOUND_VARIABLE_1150)))) (or (not (tptp.aSet0 tptp.xI)) (not (tptp.aElementOf0 tptp.xa tptp.xI)) (tptp.aElement0 tptp.xa))) :rule or :premises (t69.t1))
% 0.38/0.56  (step t69.t3 (cl (or (not (tptp.aSet0 tptp.xI)) (not (tptp.aElementOf0 tptp.xa tptp.xI)) (tptp.aElement0 tptp.xa))) :rule resolution :premises (t69.t2 t69.a0))
% 0.38/0.56  (step t69 (cl (not (forall ((W0 $$unsorted) (BOUND_VARIABLE_1150 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_1150 W0)) (tptp.aElement0 BOUND_VARIABLE_1150)))) (or (not (tptp.aSet0 tptp.xI)) (not (tptp.aElementOf0 tptp.xa tptp.xI)) (tptp.aElement0 tptp.xa))) :rule subproof :discharge (t69.a0))
% 0.38/0.56  (step t70 (cl (=> (forall ((W0 $$unsorted) (BOUND_VARIABLE_1150 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_1150 W0)) (tptp.aElement0 BOUND_VARIABLE_1150))) (or (not (tptp.aSet0 tptp.xI)) (not (tptp.aElementOf0 tptp.xa tptp.xI)) (tptp.aElement0 tptp.xa))) (or (not (tptp.aSet0 tptp.xI)) (not (tptp.aElementOf0 tptp.xa tptp.xI)) (tptp.aElement0 tptp.xa))) :rule resolution :premises (t68 t69))
% 0.38/0.56  (step t71 (cl (=> (forall ((W0 $$unsorted) (BOUND_VARIABLE_1150 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_1150 W0)) (tptp.aElement0 BOUND_VARIABLE_1150))) (or (not (tptp.aSet0 tptp.xI)) (not (tptp.aElementOf0 tptp.xa tptp.xI)) (tptp.aElement0 tptp.xa))) (not (or (not (tptp.aSet0 tptp.xI)) (not (tptp.aElementOf0 tptp.xa tptp.xI)) (tptp.aElement0 tptp.xa)))) :rule implies_neg2)
% 0.38/0.56  (step t72 (cl (=> (forall ((W0 $$unsorted) (BOUND_VARIABLE_1150 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_1150 W0)) (tptp.aElement0 BOUND_VARIABLE_1150))) (or (not (tptp.aSet0 tptp.xI)) (not (tptp.aElementOf0 tptp.xa tptp.xI)) (tptp.aElement0 tptp.xa))) (=> (forall ((W0 $$unsorted) (BOUND_VARIABLE_1150 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_1150 W0)) (tptp.aElement0 BOUND_VARIABLE_1150))) (or (not (tptp.aSet0 tptp.xI)) (not (tptp.aElementOf0 tptp.xa tptp.xI)) (tptp.aElement0 tptp.xa)))) :rule resolution :premises (t70 t71))
% 0.38/0.56  (step t73 (cl (=> (forall ((W0 $$unsorted) (BOUND_VARIABLE_1150 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_1150 W0)) (tptp.aElement0 BOUND_VARIABLE_1150))) (or (not (tptp.aSet0 tptp.xI)) (not (tptp.aElementOf0 tptp.xa tptp.xI)) (tptp.aElement0 tptp.xa)))) :rule contraction :premises (t72))
% 0.38/0.56  (step t74 (cl (not (forall ((W0 $$unsorted) (BOUND_VARIABLE_1150 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_1150 W0)) (tptp.aElement0 BOUND_VARIABLE_1150)))) (or (not (tptp.aSet0 tptp.xI)) (not (tptp.aElementOf0 tptp.xa tptp.xI)) (tptp.aElement0 tptp.xa))) :rule implies :premises (t73))
% 0.38/0.56  (step t75 (cl (not (= (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElement0 W1))))) (forall ((W0 $$unsorted) (BOUND_VARIABLE_1150 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_1150 W0)) (tptp.aElement0 BOUND_VARIABLE_1150))))) (not (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElement0 W1)))))) (forall ((W0 $$unsorted) (BOUND_VARIABLE_1150 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_1150 W0)) (tptp.aElement0 BOUND_VARIABLE_1150)))) :rule equiv_pos2)
% 0.38/0.56  (anchor :step t76 :args ((W0 $$unsorted) (:= W0 W0)))
% 0.38/0.56  (step t76.t1 (cl (= W0 W0)) :rule refl)
% 0.38/0.56  (step t76.t2 (cl (= (tptp.aSet0 W0) (tptp.aSet0 W0))) :rule refl)
% 0.38/0.56  (step t76.t3 (cl (= (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElement0 W1))) (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 W0)) (tptp.aElement0 W1))))) :rule all_simplify)
% 0.38/0.56  (step t76.t4 (cl (= (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElement0 W1)))) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 W0)) (tptp.aElement0 W1)))))) :rule cong :premises (t76.t2 t76.t3))
% 0.38/0.56  (step t76 (cl (= (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElement0 W1))))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 W0)) (tptp.aElement0 W1))))))) :rule bind)
% 0.38/0.56  (step t77 (cl (= (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 W0)) (tptp.aElement0 W1))))) (forall ((W0 $$unsorted)) (or (not (tptp.aSet0 W0)) (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 W0)) (tptp.aElement0 W1))))))) :rule all_simplify)
% 0.38/0.56  (step t78 (cl (= (forall ((W0 $$unsorted)) (or (not (tptp.aSet0 W0)) (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 W0)) (tptp.aElement0 W1))))) (forall ((W0 $$unsorted) (BOUND_VARIABLE_1150 $$unsorted)) (or (not (tptp.aSet0 W0)) (or (not (tptp.aElementOf0 BOUND_VARIABLE_1150 W0)) (tptp.aElement0 BOUND_VARIABLE_1150)))))) :rule all_simplify)
% 0.38/0.56  (anchor :step t79 :args ((W0 $$unsorted) (:= W0 W0) (BOUND_VARIABLE_1150 $$unsorted) (:= BOUND_VARIABLE_1150 BOUND_VARIABLE_1150)))
% 0.38/0.56  (step t79.t1 (cl (= W0 W0)) :rule refl)
% 0.38/0.56  (step t79.t2 (cl (= BOUND_VARIABLE_1150 BOUND_VARIABLE_1150)) :rule refl)
% 0.38/0.56  (step t79.t3 (cl (= (or (not (tptp.aSet0 W0)) (or (not (tptp.aElementOf0 BOUND_VARIABLE_1150 W0)) (tptp.aElement0 BOUND_VARIABLE_1150))) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_1150 W0)) (tptp.aElement0 BOUND_VARIABLE_1150)))) :rule all_simplify)
% 0.38/0.56  (step t79 (cl (= (forall ((W0 $$unsorted) (BOUND_VARIABLE_1150 $$unsorted)) (or (not (tptp.aSet0 W0)) (or (not (tptp.aElementOf0 BOUND_VARIABLE_1150 W0)) (tptp.aElement0 BOUND_VARIABLE_1150)))) (forall ((W0 $$unsorted) (BOUND_VARIABLE_1150 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_1150 W0)) (tptp.aElement0 BOUND_VARIABLE_1150))))) :rule bind)
% 0.38/0.56  (step t80 (cl (= (forall ((W0 $$unsorted)) (or (not (tptp.aSet0 W0)) (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 W0)) (tptp.aElement0 W1))))) (forall ((W0 $$unsorted) (BOUND_VARIABLE_1150 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_1150 W0)) (tptp.aElement0 BOUND_VARIABLE_1150))))) :rule trans :premises (t78 t79))
% 0.38/0.56  (step t81 (cl (= (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 W0)) (tptp.aElement0 W1))))) (forall ((W0 $$unsorted) (BOUND_VARIABLE_1150 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_1150 W0)) (tptp.aElement0 BOUND_VARIABLE_1150))))) :rule trans :premises (t77 t80))
% 0.38/0.56  (step t82 (cl (= (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElement0 W1))))) (forall ((W0 $$unsorted) (BOUND_VARIABLE_1150 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_1150 W0)) (tptp.aElement0 BOUND_VARIABLE_1150))))) :rule trans :premises (t76 t81))
% 0.38/0.56  (step t83 (cl (forall ((W0 $$unsorted) (BOUND_VARIABLE_1150 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_1150 W0)) (tptp.aElement0 BOUND_VARIABLE_1150)))) :rule resolution :premises (t75 t82 a19))
% 0.38/0.56  (step t84 (cl (or (not (tptp.aSet0 tptp.xI)) (not (tptp.aElementOf0 tptp.xa tptp.xI)) (tptp.aElement0 tptp.xa))) :rule resolution :premises (t74 t83))
% 0.38/0.56  (step t85 (cl (tptp.aElement0 tptp.xa)) :rule resolution :premises (t42 t60 t67 t84))
% 0.38/0.56  (step t86 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtasdt0 W0 W1)))) (or (not (tptp.aElement0 tptp.xy)) (not (tptp.aElement0 tptp.xa)) (tptp.aElement0 (tptp.sdtasdt0 tptp.xy tptp.xa)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtasdt0 W0 W1))))) :rule implies_neg1)
% 0.38/0.56  (anchor :step t87)
% 0.38/0.56  (assume t87.a0 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtasdt0 W0 W1)))))
% 0.38/0.56  (step t87.t1 (cl (or (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtasdt0 W0 W1))))) (or (not (tptp.aElement0 tptp.xy)) (not (tptp.aElement0 tptp.xa)) (tptp.aElement0 (tptp.sdtasdt0 tptp.xy tptp.xa))))) :rule forall_inst :args ((:= W0 tptp.xy) (:= W1 tptp.xa)))
% 0.38/0.56  (step t87.t2 (cl (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtasdt0 W0 W1))))) (or (not (tptp.aElement0 tptp.xy)) (not (tptp.aElement0 tptp.xa)) (tptp.aElement0 (tptp.sdtasdt0 tptp.xy tptp.xa)))) :rule or :premises (t87.t1))
% 0.38/0.56  (step t87.t3 (cl (or (not (tptp.aElement0 tptp.xy)) (not (tptp.aElement0 tptp.xa)) (tptp.aElement0 (tptp.sdtasdt0 tptp.xy tptp.xa)))) :rule resolution :premises (t87.t2 t87.a0))
% 0.38/0.56  (step t87 (cl (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtasdt0 W0 W1))))) (or (not (tptp.aElement0 tptp.xy)) (not (tptp.aElement0 tptp.xa)) (tptp.aElement0 (tptp.sdtasdt0 tptp.xy tptp.xa)))) :rule subproof :discharge (t87.a0))
% 0.38/0.56  (step t88 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtasdt0 W0 W1)))) (or (not (tptp.aElement0 tptp.xy)) (not (tptp.aElement0 tptp.xa)) (tptp.aElement0 (tptp.sdtasdt0 tptp.xy tptp.xa)))) (or (not (tptp.aElement0 tptp.xy)) (not (tptp.aElement0 tptp.xa)) (tptp.aElement0 (tptp.sdtasdt0 tptp.xy tptp.xa)))) :rule resolution :premises (t86 t87))
% 0.38/0.56  (step t89 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtasdt0 W0 W1)))) (or (not (tptp.aElement0 tptp.xy)) (not (tptp.aElement0 tptp.xa)) (tptp.aElement0 (tptp.sdtasdt0 tptp.xy tptp.xa)))) (not (or (not (tptp.aElement0 tptp.xy)) (not (tptp.aElement0 tptp.xa)) (tptp.aElement0 (tptp.sdtasdt0 tptp.xy tptp.xa))))) :rule implies_neg2)
% 0.38/0.56  (step t90 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtasdt0 W0 W1)))) (or (not (tptp.aElement0 tptp.xy)) (not (tptp.aElement0 tptp.xa)) (tptp.aElement0 (tptp.sdtasdt0 tptp.xy tptp.xa)))) (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtasdt0 W0 W1)))) (or (not (tptp.aElement0 tptp.xy)) (not (tptp.aElement0 tptp.xa)) (tptp.aElement0 (tptp.sdtasdt0 tptp.xy tptp.xa))))) :rule resolution :premises (t88 t89))
% 0.38/0.56  (step t91 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtasdt0 W0 W1)))) (or (not (tptp.aElement0 tptp.xy)) (not (tptp.aElement0 tptp.xa)) (tptp.aElement0 (tptp.sdtasdt0 tptp.xy tptp.xa))))) :rule contraction :premises (t90))
% 0.38/0.56  (step t92 (cl (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtasdt0 W0 W1))))) (or (not (tptp.aElement0 tptp.xy)) (not (tptp.aElement0 tptp.xa)) (tptp.aElement0 (tptp.sdtasdt0 tptp.xy tptp.xa)))) :rule implies :premises (t91))
% 0.38/0.56  (step t93 (cl (not (= (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtasdt0 W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtasdt0 W0 W1)))))) (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtasdt0 W0 W1))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtasdt0 W0 W1))))) :rule equiv_pos2)
% 0.38/0.56  (step t94 (cl (= (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtasdt0 W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtasdt0 W0 W1)))))) :rule all_simplify)
% 0.38/0.56  (step t95 (cl (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtasdt0 W0 W1))))) :rule resolution :premises (t93 t94 a5))
% 0.38/0.56  (step t96 (cl (or (not (tptp.aElement0 tptp.xy)) (not (tptp.aElement0 tptp.xa)) (tptp.aElement0 (tptp.sdtasdt0 tptp.xy tptp.xa)))) :rule resolution :premises (t92 t95))
% 0.38/0.56  (step t97 (cl (tptp.aElement0 (tptp.sdtasdt0 tptp.xy tptp.xa))) :rule resolution :premises (t39 t40 t85 t96))
% 0.38/0.56  (step t98 (cl (not (or (not (tptp.aElement0 tptp.xx)) (not (tptp.aElement0 tptp.xb)) (tptp.aElement0 (tptp.sdtasdt0 tptp.xx tptp.xb)))) (not (tptp.aElement0 tptp.xx)) (not (tptp.aElement0 tptp.xb)) (tptp.aElement0 (tptp.sdtasdt0 tptp.xx tptp.xb))) :rule or_pos)
% 0.38/0.56  (step t99 (cl (not (tptp.aElement0 tptp.xx)) (tptp.aElement0 (tptp.sdtasdt0 tptp.xx tptp.xb)) (not (tptp.aElement0 tptp.xb)) (not (or (not (tptp.aElement0 tptp.xx)) (not (tptp.aElement0 tptp.xb)) (tptp.aElement0 (tptp.sdtasdt0 tptp.xx tptp.xb))))) :rule reordering :premises (t98))
% 0.38/0.56  (step t100 (cl (tptp.aElement0 tptp.xx)) :rule and :premises (a29))
% 0.38/0.56  (step t101 (cl (not (or (not (tptp.aSet0 tptp.xJ)) (not (tptp.aElementOf0 tptp.xb tptp.xJ)) (tptp.aElement0 tptp.xb))) (not (tptp.aSet0 tptp.xJ)) (not (tptp.aElementOf0 tptp.xb tptp.xJ)) (tptp.aElement0 tptp.xb)) :rule or_pos)
% 0.38/0.56  (step t102 (cl (not (tptp.aSet0 tptp.xJ)) (not (tptp.aElementOf0 tptp.xb tptp.xJ)) (tptp.aElement0 tptp.xb) (not (or (not (tptp.aSet0 tptp.xJ)) (not (tptp.aElementOf0 tptp.xb tptp.xJ)) (tptp.aElement0 tptp.xb)))) :rule reordering :premises (t101))
% 0.38/0.56  (step t103 (cl (tptp.aSet0 tptp.xJ)) :rule and :premises (t59))
% 0.38/0.56  (step t104 (cl (tptp.aElementOf0 tptp.xb tptp.xJ)) :rule and :premises (t66))
% 0.38/0.56  (step t105 (cl (=> (forall ((W0 $$unsorted) (BOUND_VARIABLE_1150 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_1150 W0)) (tptp.aElement0 BOUND_VARIABLE_1150))) (or (not (tptp.aSet0 tptp.xJ)) (not (tptp.aElementOf0 tptp.xb tptp.xJ)) (tptp.aElement0 tptp.xb))) (forall ((W0 $$unsorted) (BOUND_VARIABLE_1150 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_1150 W0)) (tptp.aElement0 BOUND_VARIABLE_1150)))) :rule implies_neg1)
% 0.38/0.56  (anchor :step t106)
% 0.38/0.56  (assume t106.a0 (forall ((W0 $$unsorted) (BOUND_VARIABLE_1150 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_1150 W0)) (tptp.aElement0 BOUND_VARIABLE_1150))))
% 0.38/0.56  (step t106.t1 (cl (or (not (forall ((W0 $$unsorted) (BOUND_VARIABLE_1150 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_1150 W0)) (tptp.aElement0 BOUND_VARIABLE_1150)))) (or (not (tptp.aSet0 tptp.xJ)) (not (tptp.aElementOf0 tptp.xb tptp.xJ)) (tptp.aElement0 tptp.xb)))) :rule forall_inst :args ((:= W0 tptp.xJ) (:= BOUND_VARIABLE_1150 tptp.xb)))
% 0.38/0.56  (step t106.t2 (cl (not (forall ((W0 $$unsorted) (BOUND_VARIABLE_1150 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_1150 W0)) (tptp.aElement0 BOUND_VARIABLE_1150)))) (or (not (tptp.aSet0 tptp.xJ)) (not (tptp.aElementOf0 tptp.xb tptp.xJ)) (tptp.aElement0 tptp.xb))) :rule or :premises (t106.t1))
% 0.38/0.56  (step t106.t3 (cl (or (not (tptp.aSet0 tptp.xJ)) (not (tptp.aElementOf0 tptp.xb tptp.xJ)) (tptp.aElement0 tptp.xb))) :rule resolution :premises (t106.t2 t106.a0))
% 0.38/0.56  (step t106 (cl (not (forall ((W0 $$unsorted) (BOUND_VARIABLE_1150 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_1150 W0)) (tptp.aElement0 BOUND_VARIABLE_1150)))) (or (not (tptp.aSet0 tptp.xJ)) (not (tptp.aElementOf0 tptp.xb tptp.xJ)) (tptp.aElement0 tptp.xb))) :rule subproof :discharge (t106.a0))
% 0.38/0.56  (step t107 (cl (=> (forall ((W0 $$unsorted) (BOUND_VARIABLE_1150 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_1150 W0)) (tptp.aElement0 BOUND_VARIABLE_1150))) (or (not (tptp.aSet0 tptp.xJ)) (not (tptp.aElementOf0 tptp.xb tptp.xJ)) (tptp.aElement0 tptp.xb))) (or (not (tptp.aSet0 tptp.xJ)) (not (tptp.aElementOf0 tptp.xb tptp.xJ)) (tptp.aElement0 tptp.xb))) :rule resolution :premises (t105 t106))
% 0.38/0.56  (step t108 (cl (=> (forall ((W0 $$unsorted) (BOUND_VARIABLE_1150 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_1150 W0)) (tptp.aElement0 BOUND_VARIABLE_1150))) (or (not (tptp.aSet0 tptp.xJ)) (not (tptp.aElementOf0 tptp.xb tptp.xJ)) (tptp.aElement0 tptp.xb))) (not (or (not (tptp.aSet0 tptp.xJ)) (not (tptp.aElementOf0 tptp.xb tptp.xJ)) (tptp.aElement0 tptp.xb)))) :rule implies_neg2)
% 0.38/0.56  (step t109 (cl (=> (forall ((W0 $$unsorted) (BOUND_VARIABLE_1150 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_1150 W0)) (tptp.aElement0 BOUND_VARIABLE_1150))) (or (not (tptp.aSet0 tptp.xJ)) (not (tptp.aElementOf0 tptp.xb tptp.xJ)) (tptp.aElement0 tptp.xb))) (=> (forall ((W0 $$unsorted) (BOUND_VARIABLE_1150 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_1150 W0)) (tptp.aElement0 BOUND_VARIABLE_1150))) (or (not (tptp.aSet0 tptp.xJ)) (not (tptp.aElementOf0 tptp.xb tptp.xJ)) (tptp.aElement0 tptp.xb)))) :rule resolution :premises (t107 t108))
% 0.38/0.56  (step t110 (cl (=> (forall ((W0 $$unsorted) (BOUND_VARIABLE_1150 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_1150 W0)) (tptp.aElement0 BOUND_VARIABLE_1150))) (or (not (tptp.aSet0 tptp.xJ)) (not (tptp.aElementOf0 tptp.xb tptp.xJ)) (tptp.aElement0 tptp.xb)))) :rule contraction :premises (t109))
% 0.38/0.56  (step t111 (cl (not (forall ((W0 $$unsorted) (BOUND_VARIABLE_1150 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_1150 W0)) (tptp.aElement0 BOUND_VARIABLE_1150)))) (or (not (tptp.aSet0 tptp.xJ)) (not (tptp.aElementOf0 tptp.xb tptp.xJ)) (tptp.aElement0 tptp.xb))) :rule implies :premises (t110))
% 0.38/0.56  (step t112 (cl (or (not (tptp.aSet0 tptp.xJ)) (not (tptp.aElementOf0 tptp.xb tptp.xJ)) (tptp.aElement0 tptp.xb))) :rule resolution :premises (t111 t83))
% 0.38/0.56  (step t113 (cl (tptp.aElement0 tptp.xb)) :rule resolution :premises (t102 t103 t104 t112))
% 0.38/0.56  (step t114 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtasdt0 W0 W1)))) (or (not (tptp.aElement0 tptp.xx)) (not (tptp.aElement0 tptp.xb)) (tptp.aElement0 (tptp.sdtasdt0 tptp.xx tptp.xb)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtasdt0 W0 W1))))) :rule implies_neg1)
% 0.38/0.56  (anchor :step t115)
% 0.38/0.56  (assume t115.a0 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtasdt0 W0 W1)))))
% 0.38/0.56  (step t115.t1 (cl (or (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtasdt0 W0 W1))))) (or (not (tptp.aElement0 tptp.xx)) (not (tptp.aElement0 tptp.xb)) (tptp.aElement0 (tptp.sdtasdt0 tptp.xx tptp.xb))))) :rule forall_inst :args ((:= W0 tptp.xx) (:= W1 tptp.xb)))
% 0.38/0.56  (step t115.t2 (cl (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtasdt0 W0 W1))))) (or (not (tptp.aElement0 tptp.xx)) (not (tptp.aElement0 tptp.xb)) (tptp.aElement0 (tptp.sdtasdt0 tptp.xx tptp.xb)))) :rule or :premises (t115.t1))
% 0.38/0.56  (step t115.t3 (cl (or (not (tptp.aElement0 tptp.xx)) (not (tptp.aElement0 tptp.xb)) (tptp.aElement0 (tptp.sdtasdt0 tptp.xx tptp.xb)))) :rule resolution :premises (t115.t2 t115.a0))
% 0.38/0.56  (step t115 (cl (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtasdt0 W0 W1))))) (or (not (tptp.aElement0 tptp.xx)) (not (tptp.aElement0 tptp.xb)) (tptp.aElement0 (tptp.sdtasdt0 tptp.xx tptp.xb)))) :rule subproof :discharge (t115.a0))
% 0.38/0.56  (step t116 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtasdt0 W0 W1)))) (or (not (tptp.aElement0 tptp.xx)) (not (tptp.aElement0 tptp.xb)) (tptp.aElement0 (tptp.sdtasdt0 tptp.xx tptp.xb)))) (or (not (tptp.aElement0 tptp.xx)) (not (tptp.aElement0 tptp.xb)) (tptp.aElement0 (tptp.sdtasdt0 tptp.xx tptp.xb)))) :rule resolution :premises (t114 t115))
% 0.38/0.56  (step t117 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtasdt0 W0 W1)))) (or (not (tptp.aElement0 tptp.xx)) (not (tptp.aElement0 tptp.xb)) (tptp.aElement0 (tptp.sdtasdt0 tptp.xx tptp.xb)))) (not (or (not (tptp.aElement0 tptp.xx)) (not (tptp.aElement0 tptp.xb)) (tptp.aElement0 (tptp.sdtasdt0 tptp.xx tptp.xb))))) :rule implies_neg2)
% 0.38/0.56  (step t118 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtasdt0 W0 W1)))) (or (not (tptp.aElement0 tptp.xx)) (not (tptp.aElement0 tptp.xb)) (tptp.aElement0 (tptp.sdtasdt0 tptp.xx tptp.xb)))) (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtasdt0 W0 W1)))) (or (not (tptp.aElement0 tptp.xx)) (not (tptp.aElement0 tptp.xb)) (tptp.aElement0 (tptp.sdtasdt0 tptp.xx tptp.xb))))) :rule resolution :premises (t116 t117))
% 0.38/0.56  (step t119 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtasdt0 W0 W1)))) (or (not (tptp.aElement0 tptp.xx)) (not (tptp.aElement0 tptp.xb)) (tptp.aElement0 (tptp.sdtasdt0 tptp.xx tptp.xb))))) :rule contraction :premises (t118))
% 0.38/0.56  (step t120 (cl (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtasdt0 W0 W1))))) (or (not (tptp.aElement0 tptp.xx)) (not (tptp.aElement0 tptp.xb)) (tptp.aElement0 (tptp.sdtasdt0 tptp.xx tptp.xb)))) :rule implies :premises (t119))
% 0.38/0.56  (step t121 (cl (or (not (tptp.aElement0 tptp.xx)) (not (tptp.aElement0 tptp.xb)) (tptp.aElement0 (tptp.sdtasdt0 tptp.xx tptp.xb)))) :rule resolution :premises (t120 t95))
% 0.38/0.56  (step t122 (cl (tptp.aElement0 (tptp.sdtasdt0 tptp.xx tptp.xb))) :rule resolution :premises (t99 t100 t113 t121))
% 0.38/0.56  (step t123 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtpldt0 W0 W1)))) (or (not (tptp.aElement0 (tptp.sdtasdt0 tptp.xy tptp.xa))) (not (tptp.aElement0 (tptp.sdtasdt0 tptp.xx tptp.xb))) (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtpldt0 W0 W1))))) :rule implies_neg1)
% 0.38/0.56  (anchor :step t124)
% 0.38/0.56  (assume t124.a0 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtpldt0 W0 W1)))))
% 0.38/0.56  (step t124.t1 (cl (or (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtpldt0 W0 W1))))) (or (not (tptp.aElement0 (tptp.sdtasdt0 tptp.xy tptp.xa))) (not (tptp.aElement0 (tptp.sdtasdt0 tptp.xx tptp.xb))) (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))))) :rule forall_inst :args ((:= W0 (tptp.sdtasdt0 tptp.xy tptp.xa)) (:= W1 (tptp.sdtasdt0 tptp.xx tptp.xb))))
% 0.38/0.56  (step t124.t2 (cl (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtpldt0 W0 W1))))) (or (not (tptp.aElement0 (tptp.sdtasdt0 tptp.xy tptp.xa))) (not (tptp.aElement0 (tptp.sdtasdt0 tptp.xx tptp.xb))) (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))) :rule or :premises (t124.t1))
% 0.38/0.56  (step t124.t3 (cl (or (not (tptp.aElement0 (tptp.sdtasdt0 tptp.xy tptp.xa))) (not (tptp.aElement0 (tptp.sdtasdt0 tptp.xx tptp.xb))) (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))) :rule resolution :premises (t124.t2 t124.a0))
% 0.38/0.56  (step t124 (cl (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtpldt0 W0 W1))))) (or (not (tptp.aElement0 (tptp.sdtasdt0 tptp.xy tptp.xa))) (not (tptp.aElement0 (tptp.sdtasdt0 tptp.xx tptp.xb))) (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))) :rule subproof :discharge (t124.a0))
% 0.38/0.56  (step t125 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtpldt0 W0 W1)))) (or (not (tptp.aElement0 (tptp.sdtasdt0 tptp.xy tptp.xa))) (not (tptp.aElement0 (tptp.sdtasdt0 tptp.xx tptp.xb))) (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))) (or (not (tptp.aElement0 (tptp.sdtasdt0 tptp.xy tptp.xa))) (not (tptp.aElement0 (tptp.sdtasdt0 tptp.xx tptp.xb))) (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))) :rule resolution :premises (t123 t124))
% 0.38/0.56  (step t126 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtpldt0 W0 W1)))) (or (not (tptp.aElement0 (tptp.sdtasdt0 tptp.xy tptp.xa))) (not (tptp.aElement0 (tptp.sdtasdt0 tptp.xx tptp.xb))) (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))) (not (or (not (tptp.aElement0 (tptp.sdtasdt0 tptp.xy tptp.xa))) (not (tptp.aElement0 (tptp.sdtasdt0 tptp.xx tptp.xb))) (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))))) :rule implies_neg2)
% 0.38/0.56  (step t127 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtpldt0 W0 W1)))) (or (not (tptp.aElement0 (tptp.sdtasdt0 tptp.xy tptp.xa))) (not (tptp.aElement0 (tptp.sdtasdt0 tptp.xx tptp.xb))) (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))) (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtpldt0 W0 W1)))) (or (not (tptp.aElement0 (tptp.sdtasdt0 tptp.xy tptp.xa))) (not (tptp.aElement0 (tptp.sdtasdt0 tptp.xx tptp.xb))) (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))))) :rule resolution :premises (t125 t126))
% 0.38/0.56  (step t128 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtpldt0 W0 W1)))) (or (not (tptp.aElement0 (tptp.sdtasdt0 tptp.xy tptp.xa))) (not (tptp.aElement0 (tptp.sdtasdt0 tptp.xx tptp.xb))) (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))))) :rule contraction :premises (t127))
% 0.38/0.56  (step t129 (cl (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtpldt0 W0 W1))))) (or (not (tptp.aElement0 (tptp.sdtasdt0 tptp.xy tptp.xa))) (not (tptp.aElement0 (tptp.sdtasdt0 tptp.xx tptp.xb))) (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))) :rule implies :premises (t128))
% 0.38/0.56  (step t130 (cl (not (= (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtpldt0 W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtpldt0 W0 W1)))))) (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtpldt0 W0 W1))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtpldt0 W0 W1))))) :rule equiv_pos2)
% 0.38/0.56  (step t131 (cl (= (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtpldt0 W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtpldt0 W0 W1)))))) :rule all_simplify)
% 0.38/0.56  (step t132 (cl (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (tptp.aElement0 (tptp.sdtpldt0 W0 W1))))) :rule resolution :premises (t130 t131 a4))
% 0.38/0.56  (step t133 (cl (or (not (tptp.aElement0 (tptp.sdtasdt0 tptp.xy tptp.xa))) (not (tptp.aElement0 (tptp.sdtasdt0 tptp.xx tptp.xb))) (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb))))) :rule resolution :premises (t129 t132))
% 0.38/0.56  (step t134 (cl (tptp.aElement0 (tptp.sdtpldt0 (tptp.sdtasdt0 tptp.xy tptp.xa) (tptp.sdtasdt0 tptp.xx tptp.xb)))) :rule resolution :premises (t37 t97 t122 t133))
% 0.38/0.56  (step t135 (cl (not (or (not (tptp.aElement0 tptp.xw)) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xw (tptp.smndt0 tptp.xx)) tptp.xI)) (not (tptp.sdteqdtlpzmzozddtrp0 tptp.xw tptp.xx tptp.xI))) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xw (tptp.smndt0 tptp.xy)) tptp.xJ)) (not (tptp.sdteqdtlpzmzozddtrp0 tptp.xw tptp.xy tptp.xJ))))) (not (tptp.aElement0 tptp.xw)) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xw (tptp.smndt0 tptp.xx)) tptp.xI)) (not (tptp.sdteqdtlpzmzozddtrp0 tptp.xw tptp.xx tptp.xI))) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xw (tptp.smndt0 tptp.xy)) tptp.xJ)) (not (tptp.sdteqdtlpzmzozddtrp0 tptp.xw tptp.xy tptp.xJ)))) :rule or_pos)
% 0.38/0.56  (step t136 (cl (not (tptp.aElement0 tptp.xw)) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xw (tptp.smndt0 tptp.xx)) tptp.xI)) (not (tptp.sdteqdtlpzmzozddtrp0 tptp.xw tptp.xx tptp.xI))) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xw (tptp.smndt0 tptp.xy)) tptp.xJ)) (not (tptp.sdteqdtlpzmzozddtrp0 tptp.xw tptp.xy tptp.xJ))) (not (or (not (tptp.aElement0 tptp.xw)) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xw (tptp.smndt0 tptp.xx)) tptp.xI)) (not (tptp.sdteqdtlpzmzozddtrp0 tptp.xw tptp.xx tptp.xI))) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xw (tptp.smndt0 tptp.xy)) tptp.xJ)) (not (tptp.sdteqdtlpzmzozddtrp0 tptp.xw tptp.xy tptp.xJ)))))) :rule reordering :premises (t135))
% 0.38/0.56  (step t137 (cl (not (and (not (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xw (tptp.smndt0 tptp.xx)) tptp.xI)) (not (tptp.sdteqdtlpzmzozddtrp0 tptp.xw tptp.xx tptp.xI)))) (not (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xw (tptp.smndt0 tptp.xx)) tptp.xI))) :rule and_pos)
% 0.38/0.56  (step t138 (cl (not (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xw (tptp.smndt0 tptp.xx)) tptp.xI)) (not (and (not (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xw (tptp.smndt0 tptp.xx)) tptp.xI)) (not (tptp.sdteqdtlpzmzozddtrp0 tptp.xw tptp.xx tptp.xI))))) :rule reordering :premises (t137))
% 0.38/0.56  (step t139 (cl (not (and (not (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xw (tptp.smndt0 tptp.xx)) tptp.xI)) (not (tptp.sdteqdtlpzmzozddtrp0 tptp.xw tptp.xx tptp.xI))))) :rule resolution :premises (t138 a32))
% 0.38/0.56  (step t140 (cl (not (and (not (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xw (tptp.smndt0 tptp.xy)) tptp.xJ)) (not (tptp.sdteqdtlpzmzozddtrp0 tptp.xw tptp.xy tptp.xJ)))) (not (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xw (tptp.smndt0 tptp.xy)) tptp.xJ))) :rule and_pos)
% 0.38/0.56  (step t141 (cl (not (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xw (tptp.smndt0 tptp.xy)) tptp.xJ)) (not (and (not (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xw (tptp.smndt0 tptp.xy)) tptp.xJ)) (not (tptp.sdteqdtlpzmzozddtrp0 tptp.xw tptp.xy tptp.xJ))))) :rule reordering :premises (t140))
% 0.38/0.56  (step t142 (cl (not (and (not (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xw (tptp.smndt0 tptp.xy)) tptp.xJ)) (not (tptp.sdteqdtlpzmzozddtrp0 tptp.xw tptp.xy tptp.xJ))))) :rule resolution :premises (t141 a33))
% 0.38/0.56  (step t143 (cl (=> (forall ((W0 $$unsorted)) (or (not (tptp.aElement0 W0)) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xx)) tptp.xI)) (not (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xx tptp.xI))) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xy)) tptp.xJ)) (not (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xy tptp.xJ))))) (or (not (tptp.aElement0 tptp.xw)) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xw (tptp.smndt0 tptp.xx)) tptp.xI)) (not (tptp.sdteqdtlpzmzozddtrp0 tptp.xw tptp.xx tptp.xI))) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xw (tptp.smndt0 tptp.xy)) tptp.xJ)) (not (tptp.sdteqdtlpzmzozddtrp0 tptp.xw tptp.xy tptp.xJ))))) (forall ((W0 $$unsorted)) (or (not (tptp.aElement0 W0)) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xx)) tptp.xI)) (not (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xx tptp.xI))) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xy)) tptp.xJ)) (not (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xy tptp.xJ)))))) :rule implies_neg1)
% 0.38/0.56  (anchor :step t144)
% 0.38/0.56  (assume t144.a0 (forall ((W0 $$unsorted)) (or (not (tptp.aElement0 W0)) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xx)) tptp.xI)) (not (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xx tptp.xI))) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xy)) tptp.xJ)) (not (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xy tptp.xJ))))))
% 0.38/0.56  (step t144.t1 (cl (or (not (forall ((W0 $$unsorted)) (or (not (tptp.aElement0 W0)) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xx)) tptp.xI)) (not (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xx tptp.xI))) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xy)) tptp.xJ)) (not (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xy tptp.xJ)))))) (or (not (tptp.aElement0 tptp.xw)) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xw (tptp.smndt0 tptp.xx)) tptp.xI)) (not (tptp.sdteqdtlpzmzozddtrp0 tptp.xw tptp.xx tptp.xI))) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xw (tptp.smndt0 tptp.xy)) tptp.xJ)) (not (tptp.sdteqdtlpzmzozddtrp0 tptp.xw tptp.xy tptp.xJ)))))) :rule forall_inst :args ((:= W0 tptp.xw)))
% 0.38/0.56  (step t144.t2 (cl (not (forall ((W0 $$unsorted)) (or (not (tptp.aElement0 W0)) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xx)) tptp.xI)) (not (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xx tptp.xI))) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xy)) tptp.xJ)) (not (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xy tptp.xJ)))))) (or (not (tptp.aElement0 tptp.xw)) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xw (tptp.smndt0 tptp.xx)) tptp.xI)) (not (tptp.sdteqdtlpzmzozddtrp0 tptp.xw tptp.xx tptp.xI))) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xw (tptp.smndt0 tptp.xy)) tptp.xJ)) (not (tptp.sdteqdtlpzmzozddtrp0 tptp.xw tptp.xy tptp.xJ))))) :rule or :premises (t144.t1))
% 0.38/0.56  (step t144.t3 (cl (or (not (tptp.aElement0 tptp.xw)) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xw (tptp.smndt0 tptp.xx)) tptp.xI)) (not (tptp.sdteqdtlpzmzozddtrp0 tptp.xw tptp.xx tptp.xI))) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xw (tptp.smndt0 tptp.xy)) tptp.xJ)) (not (tptp.sdteqdtlpzmzozddtrp0 tptp.xw tptp.xy tptp.xJ))))) :rule resolution :premises (t144.t2 t144.a0))
% 0.38/0.56  (step t144 (cl (not (forall ((W0 $$unsorted)) (or (not (tptp.aElement0 W0)) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xx)) tptp.xI)) (not (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xx tptp.xI))) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xy)) tptp.xJ)) (not (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xy tptp.xJ)))))) (or (not (tptp.aElement0 tptp.xw)) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xw (tptp.smndt0 tptp.xx)) tptp.xI)) (not (tptp.sdteqdtlpzmzozddtrp0 tptp.xw tptp.xx tptp.xI))) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xw (tptp.smndt0 tptp.xy)) tptp.xJ)) (not (tptp.sdteqdtlpzmzozddtrp0 tptp.xw tptp.xy tptp.xJ))))) :rule subproof :discharge (t144.a0))
% 0.38/0.56  (step t145 (cl (=> (forall ((W0 $$unsorted)) (or (not (tptp.aElement0 W0)) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xx)) tptp.xI)) (not (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xx tptp.xI))) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xy)) tptp.xJ)) (not (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xy tptp.xJ))))) (or (not (tptp.aElement0 tptp.xw)) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xw (tptp.smndt0 tptp.xx)) tptp.xI)) (not (tptp.sdteqdtlpzmzozddtrp0 tptp.xw tptp.xx tptp.xI))) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xw (tptp.smndt0 tptp.xy)) tptp.xJ)) (not (tptp.sdteqdtlpzmzozddtrp0 tptp.xw tptp.xy tptp.xJ))))) (or (not (tptp.aElement0 tptp.xw)) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xw (tptp.smndt0 tptp.xx)) tptp.xI)) (not (tptp.sdteqdtlpzmzozddtrp0 tptp.xw tptp.xx tptp.xI))) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xw (tptp.smndt0 tptp.xy)) tptp.xJ)) (not (tptp.sdteqdtlpzmzozddtrp0 tptp.xw tptp.xy tptp.xJ))))) :rule resolution :premises (t143 t144))
% 0.38/0.56  (step t146 (cl (=> (forall ((W0 $$unsorted)) (or (not (tptp.aElement0 W0)) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xx)) tptp.xI)) (not (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xx tptp.xI))) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xy)) tptp.xJ)) (not (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xy tptp.xJ))))) (or (not (tptp.aElement0 tptp.xw)) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xw (tptp.smndt0 tptp.xx)) tptp.xI)) (not (tptp.sdteqdtlpzmzozddtrp0 tptp.xw tptp.xx tptp.xI))) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xw (tptp.smndt0 tptp.xy)) tptp.xJ)) (not (tptp.sdteqdtlpzmzozddtrp0 tptp.xw tptp.xy tptp.xJ))))) (not (or (not (tptp.aElement0 tptp.xw)) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xw (tptp.smndt0 tptp.xx)) tptp.xI)) (not (tptp.sdteqdtlpzmzozddtrp0 tptp.xw tptp.xx tptp.xI))) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xw (tptp.smndt0 tptp.xy)) tptp.xJ)) (not (tptp.sdteqdtlpzmzozddtrp0 tptp.xw tptp.xy tptp.xJ)))))) :rule implies_neg2)
% 0.38/0.56  (step t147 (cl (=> (forall ((W0 $$unsorted)) (or (not (tptp.aElement0 W0)) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xx)) tptp.xI)) (not (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xx tptp.xI))) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xy)) tptp.xJ)) (not (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xy tptp.xJ))))) (or (not (tptp.aElement0 tptp.xw)) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xw (tptp.smndt0 tptp.xx)) tptp.xI)) (not (tptp.sdteqdtlpzmzozddtrp0 tptp.xw tptp.xx tptp.xI))) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xw (tptp.smndt0 tptp.xy)) tptp.xJ)) (not (tptp.sdteqdtlpzmzozddtrp0 tptp.xw tptp.xy tptp.xJ))))) (=> (forall ((W0 $$unsorted)) (or (not (tptp.aElement0 W0)) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xx)) tptp.xI)) (not (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xx tptp.xI))) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xy)) tptp.xJ)) (not (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xy tptp.xJ))))) (or (not (tptp.aElement0 tptp.xw)) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xw (tptp.smndt0 tptp.xx)) tptp.xI)) (not (tptp.sdteqdtlpzmzozddtrp0 tptp.xw tptp.xx tptp.xI))) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xw (tptp.smndt0 tptp.xy)) tptp.xJ)) (not (tptp.sdteqdtlpzmzozddtrp0 tptp.xw tptp.xy tptp.xJ)))))) :rule resolution :premises (t145 t146))
% 0.38/0.56  (step t148 (cl (=> (forall ((W0 $$unsorted)) (or (not (tptp.aElement0 W0)) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xx)) tptp.xI)) (not (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xx tptp.xI))) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xy)) tptp.xJ)) (not (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xy tptp.xJ))))) (or (not (tptp.aElement0 tptp.xw)) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xw (tptp.smndt0 tptp.xx)) tptp.xI)) (not (tptp.sdteqdtlpzmzozddtrp0 tptp.xw tptp.xx tptp.xI))) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xw (tptp.smndt0 tptp.xy)) tptp.xJ)) (not (tptp.sdteqdtlpzmzozddtrp0 tptp.xw tptp.xy tptp.xJ)))))) :rule contraction :premises (t147))
% 0.38/0.56  (step t149 (cl (not (forall ((W0 $$unsorted)) (or (not (tptp.aElement0 W0)) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xx)) tptp.xI)) (not (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xx tptp.xI))) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xy)) tptp.xJ)) (not (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xy tptp.xJ)))))) (or (not (tptp.aElement0 tptp.xw)) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xw (tptp.smndt0 tptp.xx)) tptp.xI)) (not (tptp.sdteqdtlpzmzozddtrp0 tptp.xw tptp.xx tptp.xI))) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xw (tptp.smndt0 tptp.xy)) tptp.xJ)) (not (tptp.sdteqdtlpzmzozddtrp0 tptp.xw tptp.xy tptp.xJ))))) :rule implies :premises (t148))
% 0.38/0.56  (step t150 (cl (not (= (not (exists ((W0 $$unsorted)) (and (tptp.aElement0 W0) (or (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xx)) tptp.xI) (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xx tptp.xI)) (or (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xy)) tptp.xJ) (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xy tptp.xJ))))) (forall ((W0 $$unsorted)) (or (not (tptp.aElement0 W0)) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xx)) tptp.xI)) (not (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xx tptp.xI))) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xy)) tptp.xJ)) (not (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xy tptp.xJ))))))) (not (not (exists ((W0 $$unsorted)) (and (tptp.aElement0 W0) (or (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xx)) tptp.xI) (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xx tptp.xI)) (or (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xy)) tptp.xJ) (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xy tptp.xJ)))))) (forall ((W0 $$unsorted)) (or (not (tptp.aElement0 W0)) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xx)) tptp.xI)) (not (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xx tptp.xI))) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xy)) tptp.xJ)) (not (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xy tptp.xJ)))))) :rule equiv_pos2)
% 0.38/0.56  (step t151 (cl (= (exists ((W0 $$unsorted)) (and (tptp.aElement0 W0) (or (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xx)) tptp.xI) (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xx tptp.xI)) (or (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xy)) tptp.xJ) (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xy tptp.xJ)))) (not (forall ((W0 $$unsorted)) (not (and (tptp.aElement0 W0) (or (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xx)) tptp.xI) (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xx tptp.xI)) (or (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xy)) tptp.xJ) (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xy tptp.xJ)))))))) :rule all_simplify)
% 0.38/0.56  (step t152 (cl (= (forall ((W0 $$unsorted)) (not (and (tptp.aElement0 W0) (or (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xx)) tptp.xI) (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xx tptp.xI)) (or (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xy)) tptp.xJ) (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xy tptp.xJ))))) (forall ((W0 $$unsorted)) (or (not (tptp.aElement0 W0)) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xx)) tptp.xI)) (not (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xx tptp.xI))) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xy)) tptp.xJ)) (not (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xy tptp.xJ))))))) :rule all_simplify)
% 0.38/0.56  (step t153 (cl (= (not (forall ((W0 $$unsorted)) (not (and (tptp.aElement0 W0) (or (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xx)) tptp.xI) (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xx tptp.xI)) (or (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xy)) tptp.xJ) (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xy tptp.xJ)))))) (not (forall ((W0 $$unsorted)) (or (not (tptp.aElement0 W0)) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xx)) tptp.xI)) (not (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xx tptp.xI))) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xy)) tptp.xJ)) (not (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xy tptp.xJ)))))))) :rule cong :premises (t152))
% 0.38/0.56  (step t154 (cl (= (exists ((W0 $$unsorted)) (and (tptp.aElement0 W0) (or (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xx)) tptp.xI) (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xx tptp.xI)) (or (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xy)) tptp.xJ) (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xy tptp.xJ)))) (not (forall ((W0 $$unsorted)) (or (not (tptp.aElement0 W0)) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xx)) tptp.xI)) (not (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xx tptp.xI))) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xy)) tptp.xJ)) (not (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xy tptp.xJ)))))))) :rule trans :premises (t151 t153))
% 0.38/0.56  (step t155 (cl (= (not (exists ((W0 $$unsorted)) (and (tptp.aElement0 W0) (or (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xx)) tptp.xI) (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xx tptp.xI)) (or (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xy)) tptp.xJ) (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xy tptp.xJ))))) (not (not (forall ((W0 $$unsorted)) (or (not (tptp.aElement0 W0)) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xx)) tptp.xI)) (not (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xx tptp.xI))) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xy)) tptp.xJ)) (not (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xy tptp.xJ))))))))) :rule cong :premises (t154))
% 0.38/0.56  (step t156 (cl (= (not (not (forall ((W0 $$unsorted)) (or (not (tptp.aElement0 W0)) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xx)) tptp.xI)) (not (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xx tptp.xI))) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xy)) tptp.xJ)) (not (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xy tptp.xJ))))))) (forall ((W0 $$unsorted)) (or (not (tptp.aElement0 W0)) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xx)) tptp.xI)) (not (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xx tptp.xI))) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xy)) tptp.xJ)) (not (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xy tptp.xJ))))))) :rule all_simplify)
% 0.38/0.56  (step t157 (cl (= (not (exists ((W0 $$unsorted)) (and (tptp.aElement0 W0) (or (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xx)) tptp.xI) (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xx tptp.xI)) (or (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xy)) tptp.xJ) (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xy tptp.xJ))))) (forall ((W0 $$unsorted)) (or (not (tptp.aElement0 W0)) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xx)) tptp.xI)) (not (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xx tptp.xI))) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xy)) tptp.xJ)) (not (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xy tptp.xJ))))))) :rule trans :premises (t155 t156))
% 0.38/0.56  (step t158 (cl (forall ((W0 $$unsorted)) (or (not (tptp.aElement0 W0)) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xx)) tptp.xI)) (not (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xx tptp.xI))) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 W0 (tptp.smndt0 tptp.xy)) tptp.xJ)) (not (tptp.sdteqdtlpzmzozddtrp0 W0 tptp.xy tptp.xJ)))))) :rule resolution :premises (t150 t157 a34))
% 0.38/0.56  (step t159 (cl (or (not (tptp.aElement0 tptp.xw)) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xw (tptp.smndt0 tptp.xx)) tptp.xI)) (not (tptp.sdteqdtlpzmzozddtrp0 tptp.xw tptp.xx tptp.xI))) (and (not (tptp.aElementOf0 (tptp.sdtpldt0 tptp.xw (tptp.smndt0 tptp.xy)) tptp.xJ)) (not (tptp.sdteqdtlpzmzozddtrp0 tptp.xw tptp.xy tptp.xJ))))) :rule resolution :premises (t149 t158))
% 0.38/0.56  (step t160 (cl (not (tptp.aElement0 tptp.xw))) :rule resolution :premises (t136 t139 t142 t159))
% 0.38/0.56  (step t161 (cl) :rule resolution :premises (t35 t134 t160 a31))
% 0.38/0.56  
% 0.38/0.56  % SZS output end Proof for /export/starexec/sandbox/tmp/tmp.R4TOeFgMh0/cvc5---1.0.5_17353.smt2
% 0.38/0.56  % cvc5---1.0.5 exiting
% 0.38/0.57  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------