TSTP Solution File: LAT381+1 by cvc5---1.0.5
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- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : LAT381+1 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n010.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 17:23:05 EDT 2024
% Result : Theorem 0.21s 0.55s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13 % Problem : LAT381+1 : TPTP v8.2.0. Released v4.0.0.
% 0.06/0.14 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n010.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 : Mon May 27 14:38:24 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.21/0.50 %----Proving TF0_NAR, FOF, or CNF
% 0.21/0.55 --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.21/0.55 % SZS status Theorem for /export/starexec/sandbox/tmp/tmp.WXacSnhyMK/cvc5---1.0.5_28887.smt2
% 0.21/0.55 % SZS output start Proof for /export/starexec/sandbox/tmp/tmp.WXacSnhyMK/cvc5---1.0.5_28887.smt2
% 0.21/0.55 (assume a0 (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) true)))
% 0.21/0.55 (assume a1 (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) true)))
% 0.21/0.55 (assume a2 (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElement0 W1))))))
% 0.21/0.55 (assume a3 (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (= (tptp.isEmpty0 W0) (not (exists ((W1 $$unsorted)) (tptp.aElementOf0 W1 W0)))))))
% 0.21/0.55 (assume a4 (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (= (tptp.aSubsetOf0 W1 W0) (and (tptp.aSet0 W1) (forall ((W2 $$unsorted)) (=> (tptp.aElementOf0 W2 W1) (tptp.aElementOf0 W2 W0)))))))))
% 0.21/0.55 (assume a5 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (=> (tptp.sdtlseqdt0 W0 W1) true))))
% 0.21/0.55 (assume a6 (forall ((W0 $$unsorted)) (=> (tptp.aElement0 W0) (tptp.sdtlseqdt0 W0 W0))))
% 0.21/0.55 (assume a7 (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W0)) (= W0 W1)))))
% 0.21/0.55 (assume a8 (forall ((W0 $$unsorted) (W1 $$unsorted) (W2 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1) (tptp.aElement0 W2)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W2)) (tptp.sdtlseqdt0 W0 W2)))))
% 0.21/0.55 (assume a9 (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aSubsetOf0 W1 W0) (forall ((W2 $$unsorted)) (= (tptp.aLowerBoundOfIn0 W2 W1 W0) (and (tptp.aElementOf0 W2 W0) (forall ((W3 $$unsorted)) (=> (tptp.aElementOf0 W3 W1) (tptp.sdtlseqdt0 W2 W3)))))))))))
% 0.21/0.55 (assume a10 (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aSubsetOf0 W1 W0) (forall ((W2 $$unsorted)) (= (tptp.aUpperBoundOfIn0 W2 W1 W0) (and (tptp.aElementOf0 W2 W0) (forall ((W3 $$unsorted)) (=> (tptp.aElementOf0 W3 W1) (tptp.sdtlseqdt0 W3 W2)))))))))))
% 0.21/0.55 (assume a11 (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aSubsetOf0 W1 W0) (forall ((W2 $$unsorted)) (= (tptp.aInfimumOfIn0 W2 W1 W0) (and (tptp.aElementOf0 W2 W0) (tptp.aLowerBoundOfIn0 W2 W1 W0) (forall ((W3 $$unsorted)) (=> (tptp.aLowerBoundOfIn0 W3 W1 W0) (tptp.sdtlseqdt0 W3 W2)))))))))))
% 0.21/0.55 (assume a12 (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aSubsetOf0 W1 W0) (forall ((W2 $$unsorted)) (= (tptp.aSupremumOfIn0 W2 W1 W0) (and (tptp.aElementOf0 W2 W0) (tptp.aUpperBoundOfIn0 W2 W1 W0) (forall ((W3 $$unsorted)) (=> (tptp.aUpperBoundOfIn0 W3 W1 W0) (tptp.sdtlseqdt0 W2 W3)))))))))))
% 0.21/0.55 (assume a13 (tptp.aSet0 tptp.xT))
% 0.21/0.55 (assume a14 (tptp.aSubsetOf0 tptp.xS tptp.xT))
% 0.21/0.55 (assume a15 (and (tptp.aSupremumOfIn0 tptp.xu tptp.xS tptp.xT) (tptp.aSupremumOfIn0 tptp.xv tptp.xS tptp.xT)))
% 0.21/0.55 (assume a16 (not (= tptp.xu tptp.xv)))
% 0.21/0.55 (assume a17 true)
% 0.21/0.55 (step t1 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (not (tptp.sdtlseqdt0 W1 W0)) (= W0 W1))) (or (not (tptp.aElement0 tptp.xu)) (not (tptp.aElement0 tptp.xv)) (not (tptp.sdtlseqdt0 tptp.xu tptp.xv)) (not (tptp.sdtlseqdt0 tptp.xv tptp.xu)) (= tptp.xu tptp.xv))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (not (tptp.sdtlseqdt0 W1 W0)) (= W0 W1)))) :rule implies_neg1)
% 0.21/0.55 (anchor :step t2)
% 0.21/0.55 (assume t2.a0 (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (not (tptp.sdtlseqdt0 W1 W0)) (= W0 W1))))
% 0.21/0.55 (step t2.t1 (cl (or (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (not (tptp.sdtlseqdt0 W1 W0)) (= W0 W1)))) (or (not (tptp.aElement0 tptp.xu)) (not (tptp.aElement0 tptp.xv)) (not (tptp.sdtlseqdt0 tptp.xu tptp.xv)) (not (tptp.sdtlseqdt0 tptp.xv tptp.xu)) (= tptp.xu tptp.xv)))) :rule forall_inst :args ((:= W0 tptp.xu) (:= W1 tptp.xv)))
% 0.21/0.55 (step t2.t2 (cl (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (not (tptp.sdtlseqdt0 W1 W0)) (= W0 W1)))) (or (not (tptp.aElement0 tptp.xu)) (not (tptp.aElement0 tptp.xv)) (not (tptp.sdtlseqdt0 tptp.xu tptp.xv)) (not (tptp.sdtlseqdt0 tptp.xv tptp.xu)) (= tptp.xu tptp.xv))) :rule or :premises (t2.t1))
% 0.21/0.55 (step t2.t3 (cl (or (not (tptp.aElement0 tptp.xu)) (not (tptp.aElement0 tptp.xv)) (not (tptp.sdtlseqdt0 tptp.xu tptp.xv)) (not (tptp.sdtlseqdt0 tptp.xv tptp.xu)) (= tptp.xu tptp.xv))) :rule resolution :premises (t2.t2 t2.a0))
% 0.21/0.55 (step t2 (cl (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (not (tptp.sdtlseqdt0 W1 W0)) (= W0 W1)))) (or (not (tptp.aElement0 tptp.xu)) (not (tptp.aElement0 tptp.xv)) (not (tptp.sdtlseqdt0 tptp.xu tptp.xv)) (not (tptp.sdtlseqdt0 tptp.xv tptp.xu)) (= tptp.xu tptp.xv))) :rule subproof :discharge (t2.a0))
% 0.21/0.55 (step t3 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (not (tptp.sdtlseqdt0 W1 W0)) (= W0 W1))) (or (not (tptp.aElement0 tptp.xu)) (not (tptp.aElement0 tptp.xv)) (not (tptp.sdtlseqdt0 tptp.xu tptp.xv)) (not (tptp.sdtlseqdt0 tptp.xv tptp.xu)) (= tptp.xu tptp.xv))) (or (not (tptp.aElement0 tptp.xu)) (not (tptp.aElement0 tptp.xv)) (not (tptp.sdtlseqdt0 tptp.xu tptp.xv)) (not (tptp.sdtlseqdt0 tptp.xv tptp.xu)) (= tptp.xu tptp.xv))) :rule resolution :premises (t1 t2))
% 0.21/0.55 (step t4 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (not (tptp.sdtlseqdt0 W1 W0)) (= W0 W1))) (or (not (tptp.aElement0 tptp.xu)) (not (tptp.aElement0 tptp.xv)) (not (tptp.sdtlseqdt0 tptp.xu tptp.xv)) (not (tptp.sdtlseqdt0 tptp.xv tptp.xu)) (= tptp.xu tptp.xv))) (not (or (not (tptp.aElement0 tptp.xu)) (not (tptp.aElement0 tptp.xv)) (not (tptp.sdtlseqdt0 tptp.xu tptp.xv)) (not (tptp.sdtlseqdt0 tptp.xv tptp.xu)) (= tptp.xu tptp.xv)))) :rule implies_neg2)
% 0.21/0.55 (step t5 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (not (tptp.sdtlseqdt0 W1 W0)) (= W0 W1))) (or (not (tptp.aElement0 tptp.xu)) (not (tptp.aElement0 tptp.xv)) (not (tptp.sdtlseqdt0 tptp.xu tptp.xv)) (not (tptp.sdtlseqdt0 tptp.xv tptp.xu)) (= tptp.xu tptp.xv))) (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (not (tptp.sdtlseqdt0 W1 W0)) (= W0 W1))) (or (not (tptp.aElement0 tptp.xu)) (not (tptp.aElement0 tptp.xv)) (not (tptp.sdtlseqdt0 tptp.xu tptp.xv)) (not (tptp.sdtlseqdt0 tptp.xv tptp.xu)) (= tptp.xu tptp.xv)))) :rule resolution :premises (t3 t4))
% 0.21/0.55 (step t6 (cl (=> (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (not (tptp.sdtlseqdt0 W1 W0)) (= W0 W1))) (or (not (tptp.aElement0 tptp.xu)) (not (tptp.aElement0 tptp.xv)) (not (tptp.sdtlseqdt0 tptp.xu tptp.xv)) (not (tptp.sdtlseqdt0 tptp.xv tptp.xu)) (= tptp.xu tptp.xv)))) :rule contraction :premises (t5))
% 0.21/0.55 (step t7 (cl (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (not (tptp.sdtlseqdt0 W1 W0)) (= W0 W1)))) (or (not (tptp.aElement0 tptp.xu)) (not (tptp.aElement0 tptp.xv)) (not (tptp.sdtlseqdt0 tptp.xu tptp.xv)) (not (tptp.sdtlseqdt0 tptp.xv tptp.xu)) (= tptp.xu tptp.xv))) :rule implies :premises (t6))
% 0.21/0.55 (step t8 (cl (not (or (not (tptp.aElement0 tptp.xu)) (not (tptp.aElement0 tptp.xv)) (not (tptp.sdtlseqdt0 tptp.xu tptp.xv)) (not (tptp.sdtlseqdt0 tptp.xv tptp.xu)) (= tptp.xu tptp.xv))) (not (tptp.aElement0 tptp.xu)) (not (tptp.aElement0 tptp.xv)) (not (tptp.sdtlseqdt0 tptp.xu tptp.xv)) (not (tptp.sdtlseqdt0 tptp.xv tptp.xu)) (= tptp.xu tptp.xv)) :rule or_pos)
% 0.21/0.55 (step t9 (cl (= tptp.xu tptp.xv) (not (tptp.aElement0 tptp.xu)) (not (tptp.aElement0 tptp.xv)) (not (tptp.sdtlseqdt0 tptp.xu tptp.xv)) (not (tptp.sdtlseqdt0 tptp.xv tptp.xu)) (not (or (not (tptp.aElement0 tptp.xu)) (not (tptp.aElement0 tptp.xv)) (not (tptp.sdtlseqdt0 tptp.xu tptp.xv)) (not (tptp.sdtlseqdt0 tptp.xv tptp.xu)) (= tptp.xu tptp.xv)))) :rule reordering :premises (t8))
% 0.21/0.55 (step t10 (cl (not (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aElementOf0 tptp.xu tptp.xT)) (tptp.aElement0 tptp.xu))) (not (tptp.aSet0 tptp.xT)) (not (tptp.aElementOf0 tptp.xu tptp.xT)) (tptp.aElement0 tptp.xu)) :rule or_pos)
% 0.21/0.55 (step t11 (cl (not (tptp.aSet0 tptp.xT)) (not (tptp.aElementOf0 tptp.xu tptp.xT)) (tptp.aElement0 tptp.xu) (not (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aElementOf0 tptp.xu tptp.xT)) (tptp.aElement0 tptp.xu)))) :rule reordering :premises (t10))
% 0.21/0.55 (step t12 (cl (not (and (tptp.aElementOf0 tptp.xu tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xu tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu W3))))) (tptp.aElementOf0 tptp.xu tptp.xT)) :rule and_pos)
% 0.21/0.55 (step t13 (cl (tptp.aElementOf0 tptp.xu tptp.xT) (not (and (tptp.aElementOf0 tptp.xu tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xu tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu W3)))))) :rule reordering :premises (t12))
% 0.21/0.55 (step t14 (cl (not (= (tptp.aSupremumOfIn0 tptp.xu tptp.xS tptp.xT) (and (tptp.aElementOf0 tptp.xu tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xu tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu W3)))))) (not (tptp.aSupremumOfIn0 tptp.xu tptp.xS tptp.xT)) (and (tptp.aElementOf0 tptp.xu tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xu tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu W3))))) :rule equiv_pos2)
% 0.21/0.55 (step t15 (cl (not (tptp.aSupremumOfIn0 tptp.xu tptp.xS tptp.xT)) (and (tptp.aElementOf0 tptp.xu tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xu tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu W3)))) (not (= (tptp.aSupremumOfIn0 tptp.xu tptp.xS tptp.xT) (and (tptp.aElementOf0 tptp.xu tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xu tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu W3))))))) :rule reordering :premises (t14))
% 0.21/0.55 (step t16 (cl (tptp.aSupremumOfIn0 tptp.xu tptp.xS tptp.xT)) :rule and :premises (a15))
% 0.21/0.55 (step t17 (cl (not (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aSubsetOf0 tptp.xS tptp.xT)) (= (tptp.aSupremumOfIn0 tptp.xu tptp.xS tptp.xT) (and (tptp.aElementOf0 tptp.xu tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xu tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu W3))))))) (not (tptp.aSet0 tptp.xT)) (not (tptp.aSubsetOf0 tptp.xS tptp.xT)) (= (tptp.aSupremumOfIn0 tptp.xu tptp.xS tptp.xT) (and (tptp.aElementOf0 tptp.xu tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xu tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu W3)))))) :rule or_pos)
% 0.21/0.55 (step t18 (cl (not (tptp.aSet0 tptp.xT)) (not (tptp.aSubsetOf0 tptp.xS tptp.xT)) (= (tptp.aSupremumOfIn0 tptp.xu tptp.xS tptp.xT) (and (tptp.aElementOf0 tptp.xu tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xu tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu W3))))) (not (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aSubsetOf0 tptp.xS tptp.xT)) (= (tptp.aSupremumOfIn0 tptp.xu tptp.xS tptp.xT) (and (tptp.aElementOf0 tptp.xu tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xu tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu W3)))))))) :rule reordering :premises (t17))
% 0.21/0.55 (step t19 (cl (=> (forall ((W0 $$unsorted) (BOUND_VARIABLE_1061 $$unsorted) (BOUND_VARIABLE_1059 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aSubsetOf0 BOUND_VARIABLE_1059 W0)) (= (tptp.aSupremumOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (and (tptp.aElementOf0 BOUND_VARIABLE_1061 W0) (tptp.aUpperBoundOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 BOUND_VARIABLE_1059 W0)) (tptp.sdtlseqdt0 BOUND_VARIABLE_1061 W3))))))) (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aSubsetOf0 tptp.xS tptp.xT)) (= (tptp.aSupremumOfIn0 tptp.xu tptp.xS tptp.xT) (and (tptp.aElementOf0 tptp.xu tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xu tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu W3))))))) (forall ((W0 $$unsorted) (BOUND_VARIABLE_1061 $$unsorted) (BOUND_VARIABLE_1059 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aSubsetOf0 BOUND_VARIABLE_1059 W0)) (= (tptp.aSupremumOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (and (tptp.aElementOf0 BOUND_VARIABLE_1061 W0) (tptp.aUpperBoundOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 BOUND_VARIABLE_1059 W0)) (tptp.sdtlseqdt0 BOUND_VARIABLE_1061 W3)))))))) :rule implies_neg1)
% 0.21/0.55 (anchor :step t20)
% 0.21/0.55 (assume t20.a0 (forall ((W0 $$unsorted) (BOUND_VARIABLE_1061 $$unsorted) (BOUND_VARIABLE_1059 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aSubsetOf0 BOUND_VARIABLE_1059 W0)) (= (tptp.aSupremumOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (and (tptp.aElementOf0 BOUND_VARIABLE_1061 W0) (tptp.aUpperBoundOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 BOUND_VARIABLE_1059 W0)) (tptp.sdtlseqdt0 BOUND_VARIABLE_1061 W3))))))))
% 0.21/0.55 (step t20.t1 (cl (or (not (forall ((W0 $$unsorted) (BOUND_VARIABLE_1061 $$unsorted) (BOUND_VARIABLE_1059 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aSubsetOf0 BOUND_VARIABLE_1059 W0)) (= (tptp.aSupremumOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (and (tptp.aElementOf0 BOUND_VARIABLE_1061 W0) (tptp.aUpperBoundOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 BOUND_VARIABLE_1059 W0)) (tptp.sdtlseqdt0 BOUND_VARIABLE_1061 W3)))))))) (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aSubsetOf0 tptp.xS tptp.xT)) (= (tptp.aSupremumOfIn0 tptp.xu tptp.xS tptp.xT) (and (tptp.aElementOf0 tptp.xu tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xu tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu W3)))))))) :rule forall_inst :args ((:= W0 tptp.xT) (:= BOUND_VARIABLE_1061 tptp.xu) (:= BOUND_VARIABLE_1059 tptp.xS)))
% 0.21/0.55 (step t20.t2 (cl (not (forall ((W0 $$unsorted) (BOUND_VARIABLE_1061 $$unsorted) (BOUND_VARIABLE_1059 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aSubsetOf0 BOUND_VARIABLE_1059 W0)) (= (tptp.aSupremumOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (and (tptp.aElementOf0 BOUND_VARIABLE_1061 W0) (tptp.aUpperBoundOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 BOUND_VARIABLE_1059 W0)) (tptp.sdtlseqdt0 BOUND_VARIABLE_1061 W3)))))))) (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aSubsetOf0 tptp.xS tptp.xT)) (= (tptp.aSupremumOfIn0 tptp.xu tptp.xS tptp.xT) (and (tptp.aElementOf0 tptp.xu tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xu tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu W3))))))) :rule or :premises (t20.t1))
% 0.21/0.55 (step t20.t3 (cl (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aSubsetOf0 tptp.xS tptp.xT)) (= (tptp.aSupremumOfIn0 tptp.xu tptp.xS tptp.xT) (and (tptp.aElementOf0 tptp.xu tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xu tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu W3))))))) :rule resolution :premises (t20.t2 t20.a0))
% 0.21/0.55 (step t20 (cl (not (forall ((W0 $$unsorted) (BOUND_VARIABLE_1061 $$unsorted) (BOUND_VARIABLE_1059 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aSubsetOf0 BOUND_VARIABLE_1059 W0)) (= (tptp.aSupremumOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (and (tptp.aElementOf0 BOUND_VARIABLE_1061 W0) (tptp.aUpperBoundOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 BOUND_VARIABLE_1059 W0)) (tptp.sdtlseqdt0 BOUND_VARIABLE_1061 W3)))))))) (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aSubsetOf0 tptp.xS tptp.xT)) (= (tptp.aSupremumOfIn0 tptp.xu tptp.xS tptp.xT) (and (tptp.aElementOf0 tptp.xu tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xu tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu W3))))))) :rule subproof :discharge (t20.a0))
% 0.21/0.55 (step t21 (cl (=> (forall ((W0 $$unsorted) (BOUND_VARIABLE_1061 $$unsorted) (BOUND_VARIABLE_1059 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aSubsetOf0 BOUND_VARIABLE_1059 W0)) (= (tptp.aSupremumOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (and (tptp.aElementOf0 BOUND_VARIABLE_1061 W0) (tptp.aUpperBoundOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 BOUND_VARIABLE_1059 W0)) (tptp.sdtlseqdt0 BOUND_VARIABLE_1061 W3))))))) (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aSubsetOf0 tptp.xS tptp.xT)) (= (tptp.aSupremumOfIn0 tptp.xu tptp.xS tptp.xT) (and (tptp.aElementOf0 tptp.xu tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xu tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu W3))))))) (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aSubsetOf0 tptp.xS tptp.xT)) (= (tptp.aSupremumOfIn0 tptp.xu tptp.xS tptp.xT) (and (tptp.aElementOf0 tptp.xu tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xu tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu W3))))))) :rule resolution :premises (t19 t20))
% 0.21/0.55 (step t22 (cl (=> (forall ((W0 $$unsorted) (BOUND_VARIABLE_1061 $$unsorted) (BOUND_VARIABLE_1059 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aSubsetOf0 BOUND_VARIABLE_1059 W0)) (= (tptp.aSupremumOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (and (tptp.aElementOf0 BOUND_VARIABLE_1061 W0) (tptp.aUpperBoundOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 BOUND_VARIABLE_1059 W0)) (tptp.sdtlseqdt0 BOUND_VARIABLE_1061 W3))))))) (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aSubsetOf0 tptp.xS tptp.xT)) (= (tptp.aSupremumOfIn0 tptp.xu tptp.xS tptp.xT) (and (tptp.aElementOf0 tptp.xu tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xu tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu W3))))))) (not (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aSubsetOf0 tptp.xS tptp.xT)) (= (tptp.aSupremumOfIn0 tptp.xu tptp.xS tptp.xT) (and (tptp.aElementOf0 tptp.xu tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xu tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu W3)))))))) :rule implies_neg2)
% 0.21/0.55 (step t23 (cl (=> (forall ((W0 $$unsorted) (BOUND_VARIABLE_1061 $$unsorted) (BOUND_VARIABLE_1059 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aSubsetOf0 BOUND_VARIABLE_1059 W0)) (= (tptp.aSupremumOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (and (tptp.aElementOf0 BOUND_VARIABLE_1061 W0) (tptp.aUpperBoundOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 BOUND_VARIABLE_1059 W0)) (tptp.sdtlseqdt0 BOUND_VARIABLE_1061 W3))))))) (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aSubsetOf0 tptp.xS tptp.xT)) (= (tptp.aSupremumOfIn0 tptp.xu tptp.xS tptp.xT) (and (tptp.aElementOf0 tptp.xu tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xu tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu W3))))))) (=> (forall ((W0 $$unsorted) (BOUND_VARIABLE_1061 $$unsorted) (BOUND_VARIABLE_1059 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aSubsetOf0 BOUND_VARIABLE_1059 W0)) (= (tptp.aSupremumOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (and (tptp.aElementOf0 BOUND_VARIABLE_1061 W0) (tptp.aUpperBoundOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 BOUND_VARIABLE_1059 W0)) (tptp.sdtlseqdt0 BOUND_VARIABLE_1061 W3))))))) (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aSubsetOf0 tptp.xS tptp.xT)) (= (tptp.aSupremumOfIn0 tptp.xu tptp.xS tptp.xT) (and (tptp.aElementOf0 tptp.xu tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xu tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu W3)))))))) :rule resolution :premises (t21 t22))
% 0.21/0.55 (step t24 (cl (=> (forall ((W0 $$unsorted) (BOUND_VARIABLE_1061 $$unsorted) (BOUND_VARIABLE_1059 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aSubsetOf0 BOUND_VARIABLE_1059 W0)) (= (tptp.aSupremumOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (and (tptp.aElementOf0 BOUND_VARIABLE_1061 W0) (tptp.aUpperBoundOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 BOUND_VARIABLE_1059 W0)) (tptp.sdtlseqdt0 BOUND_VARIABLE_1061 W3))))))) (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aSubsetOf0 tptp.xS tptp.xT)) (= (tptp.aSupremumOfIn0 tptp.xu tptp.xS tptp.xT) (and (tptp.aElementOf0 tptp.xu tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xu tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu W3)))))))) :rule contraction :premises (t23))
% 0.21/0.55 (step t25 (cl (not (forall ((W0 $$unsorted) (BOUND_VARIABLE_1061 $$unsorted) (BOUND_VARIABLE_1059 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aSubsetOf0 BOUND_VARIABLE_1059 W0)) (= (tptp.aSupremumOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (and (tptp.aElementOf0 BOUND_VARIABLE_1061 W0) (tptp.aUpperBoundOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 BOUND_VARIABLE_1059 W0)) (tptp.sdtlseqdt0 BOUND_VARIABLE_1061 W3)))))))) (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aSubsetOf0 tptp.xS tptp.xT)) (= (tptp.aSupremumOfIn0 tptp.xu tptp.xS tptp.xT) (and (tptp.aElementOf0 tptp.xu tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xu tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu W3))))))) :rule implies :premises (t24))
% 0.21/0.55 (step t26 (cl (not (= (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aSubsetOf0 W1 W0) (forall ((W2 $$unsorted)) (= (tptp.aSupremumOfIn0 W2 W1 W0) (and (tptp.aElementOf0 W2 W0) (tptp.aUpperBoundOfIn0 W2 W1 W0) (forall ((W3 $$unsorted)) (=> (tptp.aUpperBoundOfIn0 W3 W1 W0) (tptp.sdtlseqdt0 W2 W3)))))))))) (forall ((W0 $$unsorted) (BOUND_VARIABLE_1061 $$unsorted) (BOUND_VARIABLE_1059 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aSubsetOf0 BOUND_VARIABLE_1059 W0)) (= (tptp.aSupremumOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (and (tptp.aElementOf0 BOUND_VARIABLE_1061 W0) (tptp.aUpperBoundOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 BOUND_VARIABLE_1059 W0)) (tptp.sdtlseqdt0 BOUND_VARIABLE_1061 W3))))))))) (not (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aSubsetOf0 W1 W0) (forall ((W2 $$unsorted)) (= (tptp.aSupremumOfIn0 W2 W1 W0) (and (tptp.aElementOf0 W2 W0) (tptp.aUpperBoundOfIn0 W2 W1 W0) (forall ((W3 $$unsorted)) (=> (tptp.aUpperBoundOfIn0 W3 W1 W0) (tptp.sdtlseqdt0 W2 W3))))))))))) (forall ((W0 $$unsorted) (BOUND_VARIABLE_1061 $$unsorted) (BOUND_VARIABLE_1059 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aSubsetOf0 BOUND_VARIABLE_1059 W0)) (= (tptp.aSupremumOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (and (tptp.aElementOf0 BOUND_VARIABLE_1061 W0) (tptp.aUpperBoundOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 BOUND_VARIABLE_1059 W0)) (tptp.sdtlseqdt0 BOUND_VARIABLE_1061 W3)))))))) :rule equiv_pos2)
% 0.21/0.55 (anchor :step t27 :args ((W0 $$unsorted) (:= W0 W0)))
% 0.21/0.55 (step t27.t1 (cl (= W0 W0)) :rule refl)
% 0.21/0.55 (step t27.t2 (cl (= (tptp.aSet0 W0) (tptp.aSet0 W0))) :rule refl)
% 0.21/0.55 (anchor :step t27.t3 :args ((W1 $$unsorted) (:= W1 W1)))
% 0.21/0.55 (step t27.t3.t1 (cl (= W1 W1)) :rule refl)
% 0.21/0.55 (step t27.t3.t2 (cl (= (tptp.aSubsetOf0 W1 W0) (tptp.aSubsetOf0 W1 W0))) :rule refl)
% 0.21/0.55 (anchor :step t27.t3.t3 :args ((W2 $$unsorted) (:= W2 W2)))
% 0.21/0.55 (step t27.t3.t3.t1 (cl (= W2 W2)) :rule refl)
% 0.21/0.55 (step t27.t3.t3.t2 (cl (= (tptp.aSupremumOfIn0 W2 W1 W0) (tptp.aSupremumOfIn0 W2 W1 W0))) :rule refl)
% 0.21/0.55 (step t27.t3.t3.t3 (cl (= (tptp.aElementOf0 W2 W0) (tptp.aElementOf0 W2 W0))) :rule refl)
% 0.21/0.55 (step t27.t3.t3.t4 (cl (= (tptp.aUpperBoundOfIn0 W2 W1 W0) (tptp.aUpperBoundOfIn0 W2 W1 W0))) :rule refl)
% 0.21/0.55 (step t27.t3.t3.t5 (cl (= (forall ((W3 $$unsorted)) (=> (tptp.aUpperBoundOfIn0 W3 W1 W0) (tptp.sdtlseqdt0 W2 W3))) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 W1 W0)) (tptp.sdtlseqdt0 W2 W3))))) :rule all_simplify)
% 0.21/0.55 (step t27.t3.t3.t6 (cl (= (and (tptp.aElementOf0 W2 W0) (tptp.aUpperBoundOfIn0 W2 W1 W0) (forall ((W3 $$unsorted)) (=> (tptp.aUpperBoundOfIn0 W3 W1 W0) (tptp.sdtlseqdt0 W2 W3)))) (and (tptp.aElementOf0 W2 W0) (tptp.aUpperBoundOfIn0 W2 W1 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 W1 W0)) (tptp.sdtlseqdt0 W2 W3)))))) :rule cong :premises (t27.t3.t3.t3 t27.t3.t3.t4 t27.t3.t3.t5))
% 0.21/0.55 (step t27.t3.t3.t7 (cl (= (= (tptp.aSupremumOfIn0 W2 W1 W0) (and (tptp.aElementOf0 W2 W0) (tptp.aUpperBoundOfIn0 W2 W1 W0) (forall ((W3 $$unsorted)) (=> (tptp.aUpperBoundOfIn0 W3 W1 W0) (tptp.sdtlseqdt0 W2 W3))))) (= (tptp.aSupremumOfIn0 W2 W1 W0) (and (tptp.aElementOf0 W2 W0) (tptp.aUpperBoundOfIn0 W2 W1 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 W1 W0)) (tptp.sdtlseqdt0 W2 W3))))))) :rule cong :premises (t27.t3.t3.t2 t27.t3.t3.t6))
% 0.21/0.55 (step t27.t3.t3 (cl (= (forall ((W2 $$unsorted)) (= (tptp.aSupremumOfIn0 W2 W1 W0) (and (tptp.aElementOf0 W2 W0) (tptp.aUpperBoundOfIn0 W2 W1 W0) (forall ((W3 $$unsorted)) (=> (tptp.aUpperBoundOfIn0 W3 W1 W0) (tptp.sdtlseqdt0 W2 W3)))))) (forall ((W2 $$unsorted)) (= (tptp.aSupremumOfIn0 W2 W1 W0) (and (tptp.aElementOf0 W2 W0) (tptp.aUpperBoundOfIn0 W2 W1 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 W1 W0)) (tptp.sdtlseqdt0 W2 W3)))))))) :rule bind)
% 0.21/0.55 (step t27.t3.t4 (cl (= (=> (tptp.aSubsetOf0 W1 W0) (forall ((W2 $$unsorted)) (= (tptp.aSupremumOfIn0 W2 W1 W0) (and (tptp.aElementOf0 W2 W0) (tptp.aUpperBoundOfIn0 W2 W1 W0) (forall ((W3 $$unsorted)) (=> (tptp.aUpperBoundOfIn0 W3 W1 W0) (tptp.sdtlseqdt0 W2 W3))))))) (=> (tptp.aSubsetOf0 W1 W0) (forall ((W2 $$unsorted)) (= (tptp.aSupremumOfIn0 W2 W1 W0) (and (tptp.aElementOf0 W2 W0) (tptp.aUpperBoundOfIn0 W2 W1 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 W1 W0)) (tptp.sdtlseqdt0 W2 W3))))))))) :rule cong :premises (t27.t3.t2 t27.t3.t3))
% 0.21/0.55 (step t27.t3 (cl (= (forall ((W1 $$unsorted)) (=> (tptp.aSubsetOf0 W1 W0) (forall ((W2 $$unsorted)) (= (tptp.aSupremumOfIn0 W2 W1 W0) (and (tptp.aElementOf0 W2 W0) (tptp.aUpperBoundOfIn0 W2 W1 W0) (forall ((W3 $$unsorted)) (=> (tptp.aUpperBoundOfIn0 W3 W1 W0) (tptp.sdtlseqdt0 W2 W3)))))))) (forall ((W1 $$unsorted)) (=> (tptp.aSubsetOf0 W1 W0) (forall ((W2 $$unsorted)) (= (tptp.aSupremumOfIn0 W2 W1 W0) (and (tptp.aElementOf0 W2 W0) (tptp.aUpperBoundOfIn0 W2 W1 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 W1 W0)) (tptp.sdtlseqdt0 W2 W3)))))))))) :rule bind)
% 0.21/0.55 (step t27.t4 (cl (= (forall ((W1 $$unsorted)) (=> (tptp.aSubsetOf0 W1 W0) (forall ((W2 $$unsorted)) (= (tptp.aSupremumOfIn0 W2 W1 W0) (and (tptp.aElementOf0 W2 W0) (tptp.aUpperBoundOfIn0 W2 W1 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 W1 W0)) (tptp.sdtlseqdt0 W2 W3)))))))) (forall ((W1 $$unsorted)) (or (not (tptp.aSubsetOf0 W1 W0)) (forall ((W2 $$unsorted)) (= (tptp.aSupremumOfIn0 W2 W1 W0) (and (tptp.aElementOf0 W2 W0) (tptp.aUpperBoundOfIn0 W2 W1 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 W1 W0)) (tptp.sdtlseqdt0 W2 W3)))))))))) :rule all_simplify)
% 0.21/0.55 (step t27.t5 (cl (= (forall ((W1 $$unsorted)) (or (not (tptp.aSubsetOf0 W1 W0)) (forall ((W2 $$unsorted)) (= (tptp.aSupremumOfIn0 W2 W1 W0) (and (tptp.aElementOf0 W2 W0) (tptp.aUpperBoundOfIn0 W2 W1 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 W1 W0)) (tptp.sdtlseqdt0 W2 W3)))))))) (forall ((W1 $$unsorted) (BOUND_VARIABLE_1041 $$unsorted)) (or (not (tptp.aSubsetOf0 W1 W0)) (= (tptp.aSupremumOfIn0 BOUND_VARIABLE_1041 W1 W0) (and (tptp.aElementOf0 BOUND_VARIABLE_1041 W0) (tptp.aUpperBoundOfIn0 BOUND_VARIABLE_1041 W1 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 W1 W0)) (tptp.sdtlseqdt0 BOUND_VARIABLE_1041 W3))))))))) :rule all_simplify)
% 0.21/0.55 (step t27.t6 (cl (= (forall ((W1 $$unsorted)) (=> (tptp.aSubsetOf0 W1 W0) (forall ((W2 $$unsorted)) (= (tptp.aSupremumOfIn0 W2 W1 W0) (and (tptp.aElementOf0 W2 W0) (tptp.aUpperBoundOfIn0 W2 W1 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 W1 W0)) (tptp.sdtlseqdt0 W2 W3)))))))) (forall ((W1 $$unsorted) (BOUND_VARIABLE_1041 $$unsorted)) (or (not (tptp.aSubsetOf0 W1 W0)) (= (tptp.aSupremumOfIn0 BOUND_VARIABLE_1041 W1 W0) (and (tptp.aElementOf0 BOUND_VARIABLE_1041 W0) (tptp.aUpperBoundOfIn0 BOUND_VARIABLE_1041 W1 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 W1 W0)) (tptp.sdtlseqdt0 BOUND_VARIABLE_1041 W3))))))))) :rule trans :premises (t27.t4 t27.t5))
% 0.21/0.55 (step t27.t7 (cl (= (forall ((W1 $$unsorted)) (=> (tptp.aSubsetOf0 W1 W0) (forall ((W2 $$unsorted)) (= (tptp.aSupremumOfIn0 W2 W1 W0) (and (tptp.aElementOf0 W2 W0) (tptp.aUpperBoundOfIn0 W2 W1 W0) (forall ((W3 $$unsorted)) (=> (tptp.aUpperBoundOfIn0 W3 W1 W0) (tptp.sdtlseqdt0 W2 W3)))))))) (forall ((W1 $$unsorted) (BOUND_VARIABLE_1041 $$unsorted)) (or (not (tptp.aSubsetOf0 W1 W0)) (= (tptp.aSupremumOfIn0 BOUND_VARIABLE_1041 W1 W0) (and (tptp.aElementOf0 BOUND_VARIABLE_1041 W0) (tptp.aUpperBoundOfIn0 BOUND_VARIABLE_1041 W1 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 W1 W0)) (tptp.sdtlseqdt0 BOUND_VARIABLE_1041 W3))))))))) :rule trans :premises (t27.t3 t27.t6))
% 0.21/0.55 (step t27.t8 (cl (= (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aSubsetOf0 W1 W0) (forall ((W2 $$unsorted)) (= (tptp.aSupremumOfIn0 W2 W1 W0) (and (tptp.aElementOf0 W2 W0) (tptp.aUpperBoundOfIn0 W2 W1 W0) (forall ((W3 $$unsorted)) (=> (tptp.aUpperBoundOfIn0 W3 W1 W0) (tptp.sdtlseqdt0 W2 W3))))))))) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted) (BOUND_VARIABLE_1041 $$unsorted)) (or (not (tptp.aSubsetOf0 W1 W0)) (= (tptp.aSupremumOfIn0 BOUND_VARIABLE_1041 W1 W0) (and (tptp.aElementOf0 BOUND_VARIABLE_1041 W0) (tptp.aUpperBoundOfIn0 BOUND_VARIABLE_1041 W1 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 W1 W0)) (tptp.sdtlseqdt0 BOUND_VARIABLE_1041 W3)))))))))) :rule cong :premises (t27.t2 t27.t7))
% 0.21/0.55 (step t27 (cl (= (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aSubsetOf0 W1 W0) (forall ((W2 $$unsorted)) (= (tptp.aSupremumOfIn0 W2 W1 W0) (and (tptp.aElementOf0 W2 W0) (tptp.aUpperBoundOfIn0 W2 W1 W0) (forall ((W3 $$unsorted)) (=> (tptp.aUpperBoundOfIn0 W3 W1 W0) (tptp.sdtlseqdt0 W2 W3)))))))))) (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted) (BOUND_VARIABLE_1041 $$unsorted)) (or (not (tptp.aSubsetOf0 W1 W0)) (= (tptp.aSupremumOfIn0 BOUND_VARIABLE_1041 W1 W0) (and (tptp.aElementOf0 BOUND_VARIABLE_1041 W0) (tptp.aUpperBoundOfIn0 BOUND_VARIABLE_1041 W1 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 W1 W0)) (tptp.sdtlseqdt0 BOUND_VARIABLE_1041 W3))))))))))) :rule bind)
% 0.21/0.55 (step t28 (cl (= (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted) (BOUND_VARIABLE_1041 $$unsorted)) (or (not (tptp.aSubsetOf0 W1 W0)) (= (tptp.aSupremumOfIn0 BOUND_VARIABLE_1041 W1 W0) (and (tptp.aElementOf0 BOUND_VARIABLE_1041 W0) (tptp.aUpperBoundOfIn0 BOUND_VARIABLE_1041 W1 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 W1 W0)) (tptp.sdtlseqdt0 BOUND_VARIABLE_1041 W3))))))))) (forall ((W0 $$unsorted)) (or (not (tptp.aSet0 W0)) (forall ((W1 $$unsorted) (BOUND_VARIABLE_1041 $$unsorted)) (or (not (tptp.aSubsetOf0 W1 W0)) (= (tptp.aSupremumOfIn0 BOUND_VARIABLE_1041 W1 W0) (and (tptp.aElementOf0 BOUND_VARIABLE_1041 W0) (tptp.aUpperBoundOfIn0 BOUND_VARIABLE_1041 W1 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 W1 W0)) (tptp.sdtlseqdt0 BOUND_VARIABLE_1041 W3))))))))))) :rule all_simplify)
% 0.21/0.55 (step t29 (cl (= (forall ((W0 $$unsorted)) (or (not (tptp.aSet0 W0)) (forall ((W1 $$unsorted) (BOUND_VARIABLE_1041 $$unsorted)) (or (not (tptp.aSubsetOf0 W1 W0)) (= (tptp.aSupremumOfIn0 BOUND_VARIABLE_1041 W1 W0) (and (tptp.aElementOf0 BOUND_VARIABLE_1041 W0) (tptp.aUpperBoundOfIn0 BOUND_VARIABLE_1041 W1 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 W1 W0)) (tptp.sdtlseqdt0 BOUND_VARIABLE_1041 W3))))))))) (forall ((W0 $$unsorted) (BOUND_VARIABLE_1061 $$unsorted) (BOUND_VARIABLE_1059 $$unsorted)) (or (not (tptp.aSet0 W0)) (or (not (tptp.aSubsetOf0 BOUND_VARIABLE_1059 W0)) (= (tptp.aSupremumOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (and (tptp.aElementOf0 BOUND_VARIABLE_1061 W0) (tptp.aUpperBoundOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 BOUND_VARIABLE_1059 W0)) (tptp.sdtlseqdt0 BOUND_VARIABLE_1061 W3)))))))))) :rule all_simplify)
% 0.21/0.55 (anchor :step t30 :args ((W0 $$unsorted) (:= W0 W0) (BOUND_VARIABLE_1061 $$unsorted) (:= BOUND_VARIABLE_1061 BOUND_VARIABLE_1061) (BOUND_VARIABLE_1059 $$unsorted) (:= BOUND_VARIABLE_1059 BOUND_VARIABLE_1059)))
% 0.21/0.55 (step t30.t1 (cl (= W0 W0)) :rule refl)
% 0.21/0.55 (step t30.t2 (cl (= BOUND_VARIABLE_1061 BOUND_VARIABLE_1061)) :rule refl)
% 0.21/0.55 (step t30.t3 (cl (= BOUND_VARIABLE_1059 BOUND_VARIABLE_1059)) :rule refl)
% 0.21/0.55 (step t30.t4 (cl (= (or (not (tptp.aSet0 W0)) (or (not (tptp.aSubsetOf0 BOUND_VARIABLE_1059 W0)) (= (tptp.aSupremumOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (and (tptp.aElementOf0 BOUND_VARIABLE_1061 W0) (tptp.aUpperBoundOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 BOUND_VARIABLE_1059 W0)) (tptp.sdtlseqdt0 BOUND_VARIABLE_1061 W3))))))) (or (not (tptp.aSet0 W0)) (not (tptp.aSubsetOf0 BOUND_VARIABLE_1059 W0)) (= (tptp.aSupremumOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (and (tptp.aElementOf0 BOUND_VARIABLE_1061 W0) (tptp.aUpperBoundOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 BOUND_VARIABLE_1059 W0)) (tptp.sdtlseqdt0 BOUND_VARIABLE_1061 W3)))))))) :rule all_simplify)
% 0.21/0.55 (step t30 (cl (= (forall ((W0 $$unsorted) (BOUND_VARIABLE_1061 $$unsorted) (BOUND_VARIABLE_1059 $$unsorted)) (or (not (tptp.aSet0 W0)) (or (not (tptp.aSubsetOf0 BOUND_VARIABLE_1059 W0)) (= (tptp.aSupremumOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (and (tptp.aElementOf0 BOUND_VARIABLE_1061 W0) (tptp.aUpperBoundOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 BOUND_VARIABLE_1059 W0)) (tptp.sdtlseqdt0 BOUND_VARIABLE_1061 W3)))))))) (forall ((W0 $$unsorted) (BOUND_VARIABLE_1061 $$unsorted) (BOUND_VARIABLE_1059 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aSubsetOf0 BOUND_VARIABLE_1059 W0)) (= (tptp.aSupremumOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (and (tptp.aElementOf0 BOUND_VARIABLE_1061 W0) (tptp.aUpperBoundOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 BOUND_VARIABLE_1059 W0)) (tptp.sdtlseqdt0 BOUND_VARIABLE_1061 W3))))))))) :rule bind)
% 0.21/0.55 (step t31 (cl (= (forall ((W0 $$unsorted)) (or (not (tptp.aSet0 W0)) (forall ((W1 $$unsorted) (BOUND_VARIABLE_1041 $$unsorted)) (or (not (tptp.aSubsetOf0 W1 W0)) (= (tptp.aSupremumOfIn0 BOUND_VARIABLE_1041 W1 W0) (and (tptp.aElementOf0 BOUND_VARIABLE_1041 W0) (tptp.aUpperBoundOfIn0 BOUND_VARIABLE_1041 W1 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 W1 W0)) (tptp.sdtlseqdt0 BOUND_VARIABLE_1041 W3))))))))) (forall ((W0 $$unsorted) (BOUND_VARIABLE_1061 $$unsorted) (BOUND_VARIABLE_1059 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aSubsetOf0 BOUND_VARIABLE_1059 W0)) (= (tptp.aSupremumOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (and (tptp.aElementOf0 BOUND_VARIABLE_1061 W0) (tptp.aUpperBoundOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 BOUND_VARIABLE_1059 W0)) (tptp.sdtlseqdt0 BOUND_VARIABLE_1061 W3))))))))) :rule trans :premises (t29 t30))
% 0.21/0.55 (step t32 (cl (= (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted) (BOUND_VARIABLE_1041 $$unsorted)) (or (not (tptp.aSubsetOf0 W1 W0)) (= (tptp.aSupremumOfIn0 BOUND_VARIABLE_1041 W1 W0) (and (tptp.aElementOf0 BOUND_VARIABLE_1041 W0) (tptp.aUpperBoundOfIn0 BOUND_VARIABLE_1041 W1 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 W1 W0)) (tptp.sdtlseqdt0 BOUND_VARIABLE_1041 W3))))))))) (forall ((W0 $$unsorted) (BOUND_VARIABLE_1061 $$unsorted) (BOUND_VARIABLE_1059 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aSubsetOf0 BOUND_VARIABLE_1059 W0)) (= (tptp.aSupremumOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (and (tptp.aElementOf0 BOUND_VARIABLE_1061 W0) (tptp.aUpperBoundOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 BOUND_VARIABLE_1059 W0)) (tptp.sdtlseqdt0 BOUND_VARIABLE_1061 W3))))))))) :rule trans :premises (t28 t31))
% 0.21/0.55 (step t33 (cl (= (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aSubsetOf0 W1 W0) (forall ((W2 $$unsorted)) (= (tptp.aSupremumOfIn0 W2 W1 W0) (and (tptp.aElementOf0 W2 W0) (tptp.aUpperBoundOfIn0 W2 W1 W0) (forall ((W3 $$unsorted)) (=> (tptp.aUpperBoundOfIn0 W3 W1 W0) (tptp.sdtlseqdt0 W2 W3)))))))))) (forall ((W0 $$unsorted) (BOUND_VARIABLE_1061 $$unsorted) (BOUND_VARIABLE_1059 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aSubsetOf0 BOUND_VARIABLE_1059 W0)) (= (tptp.aSupremumOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (and (tptp.aElementOf0 BOUND_VARIABLE_1061 W0) (tptp.aUpperBoundOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 BOUND_VARIABLE_1059 W0)) (tptp.sdtlseqdt0 BOUND_VARIABLE_1061 W3))))))))) :rule trans :premises (t27 t32))
% 0.21/0.55 (step t34 (cl (forall ((W0 $$unsorted) (BOUND_VARIABLE_1061 $$unsorted) (BOUND_VARIABLE_1059 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aSubsetOf0 BOUND_VARIABLE_1059 W0)) (= (tptp.aSupremumOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (and (tptp.aElementOf0 BOUND_VARIABLE_1061 W0) (tptp.aUpperBoundOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 BOUND_VARIABLE_1059 W0)) (tptp.sdtlseqdt0 BOUND_VARIABLE_1061 W3)))))))) :rule resolution :premises (t26 t33 a12))
% 0.21/0.55 (step t35 (cl (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aSubsetOf0 tptp.xS tptp.xT)) (= (tptp.aSupremumOfIn0 tptp.xu tptp.xS tptp.xT) (and (tptp.aElementOf0 tptp.xu tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xu tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu W3))))))) :rule resolution :premises (t25 t34))
% 0.21/0.55 (step t36 (cl (= (tptp.aSupremumOfIn0 tptp.xu tptp.xS tptp.xT) (and (tptp.aElementOf0 tptp.xu tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xu tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu W3)))))) :rule resolution :premises (t18 a13 a14 t35))
% 0.21/0.55 (step t37 (cl (and (tptp.aElementOf0 tptp.xu tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xu tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu W3))))) :rule resolution :premises (t15 t16 t36))
% 0.21/0.55 (step t38 (cl (tptp.aElementOf0 tptp.xu tptp.xT)) :rule resolution :premises (t13 t37))
% 0.21/0.55 (step t39 (cl (=> (forall ((W0 $$unsorted) (BOUND_VARIABLE_798 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_798 W0)) (tptp.aElement0 BOUND_VARIABLE_798))) (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aElementOf0 tptp.xu tptp.xT)) (tptp.aElement0 tptp.xu))) (forall ((W0 $$unsorted) (BOUND_VARIABLE_798 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_798 W0)) (tptp.aElement0 BOUND_VARIABLE_798)))) :rule implies_neg1)
% 0.21/0.55 (anchor :step t40)
% 0.21/0.55 (assume t40.a0 (forall ((W0 $$unsorted) (BOUND_VARIABLE_798 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_798 W0)) (tptp.aElement0 BOUND_VARIABLE_798))))
% 0.21/0.55 (step t40.t1 (cl (or (not (forall ((W0 $$unsorted) (BOUND_VARIABLE_798 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_798 W0)) (tptp.aElement0 BOUND_VARIABLE_798)))) (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aElementOf0 tptp.xu tptp.xT)) (tptp.aElement0 tptp.xu)))) :rule forall_inst :args ((:= W0 tptp.xT) (:= BOUND_VARIABLE_798 tptp.xu)))
% 0.21/0.55 (step t40.t2 (cl (not (forall ((W0 $$unsorted) (BOUND_VARIABLE_798 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_798 W0)) (tptp.aElement0 BOUND_VARIABLE_798)))) (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aElementOf0 tptp.xu tptp.xT)) (tptp.aElement0 tptp.xu))) :rule or :premises (t40.t1))
% 0.21/0.55 (step t40.t3 (cl (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aElementOf0 tptp.xu tptp.xT)) (tptp.aElement0 tptp.xu))) :rule resolution :premises (t40.t2 t40.a0))
% 0.21/0.55 (step t40 (cl (not (forall ((W0 $$unsorted) (BOUND_VARIABLE_798 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_798 W0)) (tptp.aElement0 BOUND_VARIABLE_798)))) (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aElementOf0 tptp.xu tptp.xT)) (tptp.aElement0 tptp.xu))) :rule subproof :discharge (t40.a0))
% 0.21/0.55 (step t41 (cl (=> (forall ((W0 $$unsorted) (BOUND_VARIABLE_798 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_798 W0)) (tptp.aElement0 BOUND_VARIABLE_798))) (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aElementOf0 tptp.xu tptp.xT)) (tptp.aElement0 tptp.xu))) (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aElementOf0 tptp.xu tptp.xT)) (tptp.aElement0 tptp.xu))) :rule resolution :premises (t39 t40))
% 0.21/0.55 (step t42 (cl (=> (forall ((W0 $$unsorted) (BOUND_VARIABLE_798 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_798 W0)) (tptp.aElement0 BOUND_VARIABLE_798))) (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aElementOf0 tptp.xu tptp.xT)) (tptp.aElement0 tptp.xu))) (not (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aElementOf0 tptp.xu tptp.xT)) (tptp.aElement0 tptp.xu)))) :rule implies_neg2)
% 0.21/0.55 (step t43 (cl (=> (forall ((W0 $$unsorted) (BOUND_VARIABLE_798 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_798 W0)) (tptp.aElement0 BOUND_VARIABLE_798))) (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aElementOf0 tptp.xu tptp.xT)) (tptp.aElement0 tptp.xu))) (=> (forall ((W0 $$unsorted) (BOUND_VARIABLE_798 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_798 W0)) (tptp.aElement0 BOUND_VARIABLE_798))) (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aElementOf0 tptp.xu tptp.xT)) (tptp.aElement0 tptp.xu)))) :rule resolution :premises (t41 t42))
% 0.21/0.55 (step t44 (cl (=> (forall ((W0 $$unsorted) (BOUND_VARIABLE_798 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_798 W0)) (tptp.aElement0 BOUND_VARIABLE_798))) (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aElementOf0 tptp.xu tptp.xT)) (tptp.aElement0 tptp.xu)))) :rule contraction :premises (t43))
% 0.21/0.55 (step t45 (cl (not (forall ((W0 $$unsorted) (BOUND_VARIABLE_798 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_798 W0)) (tptp.aElement0 BOUND_VARIABLE_798)))) (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aElementOf0 tptp.xu tptp.xT)) (tptp.aElement0 tptp.xu))) :rule implies :premises (t44))
% 0.21/0.55 (step t46 (cl (not (= (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElement0 W1))))) (forall ((W0 $$unsorted) (BOUND_VARIABLE_798 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_798 W0)) (tptp.aElement0 BOUND_VARIABLE_798))))) (not (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElement0 W1)))))) (forall ((W0 $$unsorted) (BOUND_VARIABLE_798 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_798 W0)) (tptp.aElement0 BOUND_VARIABLE_798)))) :rule equiv_pos2)
% 0.21/0.55 (anchor :step t47 :args ((W0 $$unsorted) (:= W0 W0)))
% 0.21/0.55 (step t47.t1 (cl (= W0 W0)) :rule refl)
% 0.21/0.55 (step t47.t2 (cl (= (tptp.aSet0 W0) (tptp.aSet0 W0))) :rule refl)
% 0.21/0.55 (step t47.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)
% 0.21/0.55 (step t47.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 (t47.t2 t47.t3))
% 0.21/0.55 (step t47 (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)
% 0.21/0.55 (step t48 (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)
% 0.21/0.55 (step t49 (cl (= (forall ((W0 $$unsorted)) (or (not (tptp.aSet0 W0)) (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 W0)) (tptp.aElement0 W1))))) (forall ((W0 $$unsorted) (BOUND_VARIABLE_798 $$unsorted)) (or (not (tptp.aSet0 W0)) (or (not (tptp.aElementOf0 BOUND_VARIABLE_798 W0)) (tptp.aElement0 BOUND_VARIABLE_798)))))) :rule all_simplify)
% 0.21/0.55 (anchor :step t50 :args ((W0 $$unsorted) (:= W0 W0) (BOUND_VARIABLE_798 $$unsorted) (:= BOUND_VARIABLE_798 BOUND_VARIABLE_798)))
% 0.21/0.55 (step t50.t1 (cl (= W0 W0)) :rule refl)
% 0.21/0.55 (step t50.t2 (cl (= BOUND_VARIABLE_798 BOUND_VARIABLE_798)) :rule refl)
% 0.21/0.55 (step t50.t3 (cl (= (or (not (tptp.aSet0 W0)) (or (not (tptp.aElementOf0 BOUND_VARIABLE_798 W0)) (tptp.aElement0 BOUND_VARIABLE_798))) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_798 W0)) (tptp.aElement0 BOUND_VARIABLE_798)))) :rule all_simplify)
% 0.21/0.55 (step t50 (cl (= (forall ((W0 $$unsorted) (BOUND_VARIABLE_798 $$unsorted)) (or (not (tptp.aSet0 W0)) (or (not (tptp.aElementOf0 BOUND_VARIABLE_798 W0)) (tptp.aElement0 BOUND_VARIABLE_798)))) (forall ((W0 $$unsorted) (BOUND_VARIABLE_798 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_798 W0)) (tptp.aElement0 BOUND_VARIABLE_798))))) :rule bind)
% 0.21/0.55 (step t51 (cl (= (forall ((W0 $$unsorted)) (or (not (tptp.aSet0 W0)) (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 W0)) (tptp.aElement0 W1))))) (forall ((W0 $$unsorted) (BOUND_VARIABLE_798 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_798 W0)) (tptp.aElement0 BOUND_VARIABLE_798))))) :rule trans :premises (t49 t50))
% 0.21/0.55 (step t52 (cl (= (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (or (not (tptp.aElementOf0 W1 W0)) (tptp.aElement0 W1))))) (forall ((W0 $$unsorted) (BOUND_VARIABLE_798 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_798 W0)) (tptp.aElement0 BOUND_VARIABLE_798))))) :rule trans :premises (t48 t51))
% 0.21/0.55 (step t53 (cl (= (forall ((W0 $$unsorted)) (=> (tptp.aSet0 W0) (forall ((W1 $$unsorted)) (=> (tptp.aElementOf0 W1 W0) (tptp.aElement0 W1))))) (forall ((W0 $$unsorted) (BOUND_VARIABLE_798 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_798 W0)) (tptp.aElement0 BOUND_VARIABLE_798))))) :rule trans :premises (t47 t52))
% 0.21/0.55 (step t54 (cl (forall ((W0 $$unsorted) (BOUND_VARIABLE_798 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_798 W0)) (tptp.aElement0 BOUND_VARIABLE_798)))) :rule resolution :premises (t46 t53 a2))
% 0.21/0.55 (step t55 (cl (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aElementOf0 tptp.xu tptp.xT)) (tptp.aElement0 tptp.xu))) :rule resolution :premises (t45 t54))
% 0.21/0.55 (step t56 (cl (tptp.aElement0 tptp.xu)) :rule resolution :premises (t11 a13 t38 t55))
% 0.21/0.55 (step t57 (cl (not (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aElementOf0 tptp.xv tptp.xT)) (tptp.aElement0 tptp.xv))) (not (tptp.aSet0 tptp.xT)) (not (tptp.aElementOf0 tptp.xv tptp.xT)) (tptp.aElement0 tptp.xv)) :rule or_pos)
% 0.21/0.55 (step t58 (cl (not (tptp.aSet0 tptp.xT)) (not (tptp.aElementOf0 tptp.xv tptp.xT)) (tptp.aElement0 tptp.xv) (not (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aElementOf0 tptp.xv tptp.xT)) (tptp.aElement0 tptp.xv)))) :rule reordering :premises (t57))
% 0.21/0.55 (step t59 (cl (not (and (tptp.aElementOf0 tptp.xv tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xv tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv W3))))) (tptp.aElementOf0 tptp.xv tptp.xT)) :rule and_pos)
% 0.21/0.55 (step t60 (cl (tptp.aElementOf0 tptp.xv tptp.xT) (not (and (tptp.aElementOf0 tptp.xv tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xv tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv W3)))))) :rule reordering :premises (t59))
% 0.21/0.55 (step t61 (cl (not (= (tptp.aSupremumOfIn0 tptp.xv tptp.xS tptp.xT) (and (tptp.aElementOf0 tptp.xv tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xv tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv W3)))))) (not (tptp.aSupremumOfIn0 tptp.xv tptp.xS tptp.xT)) (and (tptp.aElementOf0 tptp.xv tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xv tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv W3))))) :rule equiv_pos2)
% 0.21/0.55 (step t62 (cl (not (tptp.aSupremumOfIn0 tptp.xv tptp.xS tptp.xT)) (and (tptp.aElementOf0 tptp.xv tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xv tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv W3)))) (not (= (tptp.aSupremumOfIn0 tptp.xv tptp.xS tptp.xT) (and (tptp.aElementOf0 tptp.xv tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xv tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv W3))))))) :rule reordering :premises (t61))
% 0.21/0.55 (step t63 (cl (tptp.aSupremumOfIn0 tptp.xv tptp.xS tptp.xT)) :rule and :premises (a15))
% 0.21/0.55 (step t64 (cl (not (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aSubsetOf0 tptp.xS tptp.xT)) (= (tptp.aSupremumOfIn0 tptp.xv tptp.xS tptp.xT) (and (tptp.aElementOf0 tptp.xv tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xv tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv W3))))))) (not (tptp.aSet0 tptp.xT)) (not (tptp.aSubsetOf0 tptp.xS tptp.xT)) (= (tptp.aSupremumOfIn0 tptp.xv tptp.xS tptp.xT) (and (tptp.aElementOf0 tptp.xv tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xv tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv W3)))))) :rule or_pos)
% 0.21/0.55 (step t65 (cl (not (tptp.aSet0 tptp.xT)) (not (tptp.aSubsetOf0 tptp.xS tptp.xT)) (= (tptp.aSupremumOfIn0 tptp.xv tptp.xS tptp.xT) (and (tptp.aElementOf0 tptp.xv tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xv tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv W3))))) (not (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aSubsetOf0 tptp.xS tptp.xT)) (= (tptp.aSupremumOfIn0 tptp.xv tptp.xS tptp.xT) (and (tptp.aElementOf0 tptp.xv tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xv tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv W3)))))))) :rule reordering :premises (t64))
% 0.21/0.55 (step t66 (cl (=> (forall ((W0 $$unsorted) (BOUND_VARIABLE_1061 $$unsorted) (BOUND_VARIABLE_1059 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aSubsetOf0 BOUND_VARIABLE_1059 W0)) (= (tptp.aSupremumOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (and (tptp.aElementOf0 BOUND_VARIABLE_1061 W0) (tptp.aUpperBoundOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 BOUND_VARIABLE_1059 W0)) (tptp.sdtlseqdt0 BOUND_VARIABLE_1061 W3))))))) (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aSubsetOf0 tptp.xS tptp.xT)) (= (tptp.aSupremumOfIn0 tptp.xv tptp.xS tptp.xT) (and (tptp.aElementOf0 tptp.xv tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xv tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv W3))))))) (forall ((W0 $$unsorted) (BOUND_VARIABLE_1061 $$unsorted) (BOUND_VARIABLE_1059 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aSubsetOf0 BOUND_VARIABLE_1059 W0)) (= (tptp.aSupremumOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (and (tptp.aElementOf0 BOUND_VARIABLE_1061 W0) (tptp.aUpperBoundOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 BOUND_VARIABLE_1059 W0)) (tptp.sdtlseqdt0 BOUND_VARIABLE_1061 W3)))))))) :rule implies_neg1)
% 0.21/0.55 (anchor :step t67)
% 0.21/0.55 (assume t67.a0 (forall ((W0 $$unsorted) (BOUND_VARIABLE_1061 $$unsorted) (BOUND_VARIABLE_1059 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aSubsetOf0 BOUND_VARIABLE_1059 W0)) (= (tptp.aSupremumOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (and (tptp.aElementOf0 BOUND_VARIABLE_1061 W0) (tptp.aUpperBoundOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 BOUND_VARIABLE_1059 W0)) (tptp.sdtlseqdt0 BOUND_VARIABLE_1061 W3))))))))
% 0.21/0.55 (step t67.t1 (cl (or (not (forall ((W0 $$unsorted) (BOUND_VARIABLE_1061 $$unsorted) (BOUND_VARIABLE_1059 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aSubsetOf0 BOUND_VARIABLE_1059 W0)) (= (tptp.aSupremumOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (and (tptp.aElementOf0 BOUND_VARIABLE_1061 W0) (tptp.aUpperBoundOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 BOUND_VARIABLE_1059 W0)) (tptp.sdtlseqdt0 BOUND_VARIABLE_1061 W3)))))))) (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aSubsetOf0 tptp.xS tptp.xT)) (= (tptp.aSupremumOfIn0 tptp.xv tptp.xS tptp.xT) (and (tptp.aElementOf0 tptp.xv tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xv tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv W3)))))))) :rule forall_inst :args ((:= W0 tptp.xT) (:= BOUND_VARIABLE_1061 tptp.xv) (:= BOUND_VARIABLE_1059 tptp.xS)))
% 0.21/0.55 (step t67.t2 (cl (not (forall ((W0 $$unsorted) (BOUND_VARIABLE_1061 $$unsorted) (BOUND_VARIABLE_1059 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aSubsetOf0 BOUND_VARIABLE_1059 W0)) (= (tptp.aSupremumOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (and (tptp.aElementOf0 BOUND_VARIABLE_1061 W0) (tptp.aUpperBoundOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 BOUND_VARIABLE_1059 W0)) (tptp.sdtlseqdt0 BOUND_VARIABLE_1061 W3)))))))) (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aSubsetOf0 tptp.xS tptp.xT)) (= (tptp.aSupremumOfIn0 tptp.xv tptp.xS tptp.xT) (and (tptp.aElementOf0 tptp.xv tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xv tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv W3))))))) :rule or :premises (t67.t1))
% 0.21/0.55 (step t67.t3 (cl (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aSubsetOf0 tptp.xS tptp.xT)) (= (tptp.aSupremumOfIn0 tptp.xv tptp.xS tptp.xT) (and (tptp.aElementOf0 tptp.xv tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xv tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv W3))))))) :rule resolution :premises (t67.t2 t67.a0))
% 0.21/0.55 (step t67 (cl (not (forall ((W0 $$unsorted) (BOUND_VARIABLE_1061 $$unsorted) (BOUND_VARIABLE_1059 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aSubsetOf0 BOUND_VARIABLE_1059 W0)) (= (tptp.aSupremumOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (and (tptp.aElementOf0 BOUND_VARIABLE_1061 W0) (tptp.aUpperBoundOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 BOUND_VARIABLE_1059 W0)) (tptp.sdtlseqdt0 BOUND_VARIABLE_1061 W3)))))))) (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aSubsetOf0 tptp.xS tptp.xT)) (= (tptp.aSupremumOfIn0 tptp.xv tptp.xS tptp.xT) (and (tptp.aElementOf0 tptp.xv tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xv tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv W3))))))) :rule subproof :discharge (t67.a0))
% 0.21/0.55 (step t68 (cl (=> (forall ((W0 $$unsorted) (BOUND_VARIABLE_1061 $$unsorted) (BOUND_VARIABLE_1059 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aSubsetOf0 BOUND_VARIABLE_1059 W0)) (= (tptp.aSupremumOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (and (tptp.aElementOf0 BOUND_VARIABLE_1061 W0) (tptp.aUpperBoundOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 BOUND_VARIABLE_1059 W0)) (tptp.sdtlseqdt0 BOUND_VARIABLE_1061 W3))))))) (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aSubsetOf0 tptp.xS tptp.xT)) (= (tptp.aSupremumOfIn0 tptp.xv tptp.xS tptp.xT) (and (tptp.aElementOf0 tptp.xv tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xv tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv W3))))))) (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aSubsetOf0 tptp.xS tptp.xT)) (= (tptp.aSupremumOfIn0 tptp.xv tptp.xS tptp.xT) (and (tptp.aElementOf0 tptp.xv tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xv tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv W3))))))) :rule resolution :premises (t66 t67))
% 0.21/0.55 (step t69 (cl (=> (forall ((W0 $$unsorted) (BOUND_VARIABLE_1061 $$unsorted) (BOUND_VARIABLE_1059 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aSubsetOf0 BOUND_VARIABLE_1059 W0)) (= (tptp.aSupremumOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (and (tptp.aElementOf0 BOUND_VARIABLE_1061 W0) (tptp.aUpperBoundOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 BOUND_VARIABLE_1059 W0)) (tptp.sdtlseqdt0 BOUND_VARIABLE_1061 W3))))))) (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aSubsetOf0 tptp.xS tptp.xT)) (= (tptp.aSupremumOfIn0 tptp.xv tptp.xS tptp.xT) (and (tptp.aElementOf0 tptp.xv tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xv tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv W3))))))) (not (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aSubsetOf0 tptp.xS tptp.xT)) (= (tptp.aSupremumOfIn0 tptp.xv tptp.xS tptp.xT) (and (tptp.aElementOf0 tptp.xv tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xv tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv W3)))))))) :rule implies_neg2)
% 0.21/0.55 (step t70 (cl (=> (forall ((W0 $$unsorted) (BOUND_VARIABLE_1061 $$unsorted) (BOUND_VARIABLE_1059 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aSubsetOf0 BOUND_VARIABLE_1059 W0)) (= (tptp.aSupremumOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (and (tptp.aElementOf0 BOUND_VARIABLE_1061 W0) (tptp.aUpperBoundOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 BOUND_VARIABLE_1059 W0)) (tptp.sdtlseqdt0 BOUND_VARIABLE_1061 W3))))))) (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aSubsetOf0 tptp.xS tptp.xT)) (= (tptp.aSupremumOfIn0 tptp.xv tptp.xS tptp.xT) (and (tptp.aElementOf0 tptp.xv tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xv tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv W3))))))) (=> (forall ((W0 $$unsorted) (BOUND_VARIABLE_1061 $$unsorted) (BOUND_VARIABLE_1059 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aSubsetOf0 BOUND_VARIABLE_1059 W0)) (= (tptp.aSupremumOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (and (tptp.aElementOf0 BOUND_VARIABLE_1061 W0) (tptp.aUpperBoundOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 BOUND_VARIABLE_1059 W0)) (tptp.sdtlseqdt0 BOUND_VARIABLE_1061 W3))))))) (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aSubsetOf0 tptp.xS tptp.xT)) (= (tptp.aSupremumOfIn0 tptp.xv tptp.xS tptp.xT) (and (tptp.aElementOf0 tptp.xv tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xv tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv W3)))))))) :rule resolution :premises (t68 t69))
% 0.21/0.55 (step t71 (cl (=> (forall ((W0 $$unsorted) (BOUND_VARIABLE_1061 $$unsorted) (BOUND_VARIABLE_1059 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aSubsetOf0 BOUND_VARIABLE_1059 W0)) (= (tptp.aSupremumOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (and (tptp.aElementOf0 BOUND_VARIABLE_1061 W0) (tptp.aUpperBoundOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 BOUND_VARIABLE_1059 W0)) (tptp.sdtlseqdt0 BOUND_VARIABLE_1061 W3))))))) (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aSubsetOf0 tptp.xS tptp.xT)) (= (tptp.aSupremumOfIn0 tptp.xv tptp.xS tptp.xT) (and (tptp.aElementOf0 tptp.xv tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xv tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv W3)))))))) :rule contraction :premises (t70))
% 0.21/0.55 (step t72 (cl (not (forall ((W0 $$unsorted) (BOUND_VARIABLE_1061 $$unsorted) (BOUND_VARIABLE_1059 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aSubsetOf0 BOUND_VARIABLE_1059 W0)) (= (tptp.aSupremumOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (and (tptp.aElementOf0 BOUND_VARIABLE_1061 W0) (tptp.aUpperBoundOfIn0 BOUND_VARIABLE_1061 BOUND_VARIABLE_1059 W0) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 BOUND_VARIABLE_1059 W0)) (tptp.sdtlseqdt0 BOUND_VARIABLE_1061 W3)))))))) (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aSubsetOf0 tptp.xS tptp.xT)) (= (tptp.aSupremumOfIn0 tptp.xv tptp.xS tptp.xT) (and (tptp.aElementOf0 tptp.xv tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xv tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv W3))))))) :rule implies :premises (t71))
% 0.21/0.55 (step t73 (cl (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aSubsetOf0 tptp.xS tptp.xT)) (= (tptp.aSupremumOfIn0 tptp.xv tptp.xS tptp.xT) (and (tptp.aElementOf0 tptp.xv tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xv tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv W3))))))) :rule resolution :premises (t72 t34))
% 0.21/0.55 (step t74 (cl (= (tptp.aSupremumOfIn0 tptp.xv tptp.xS tptp.xT) (and (tptp.aElementOf0 tptp.xv tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xv tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv W3)))))) :rule resolution :premises (t65 a13 a14 t73))
% 0.21/0.55 (step t75 (cl (and (tptp.aElementOf0 tptp.xv tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xv tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv W3))))) :rule resolution :premises (t62 t63 t74))
% 0.21/0.55 (step t76 (cl (tptp.aElementOf0 tptp.xv tptp.xT)) :rule resolution :premises (t60 t75))
% 0.21/0.55 (step t77 (cl (=> (forall ((W0 $$unsorted) (BOUND_VARIABLE_798 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_798 W0)) (tptp.aElement0 BOUND_VARIABLE_798))) (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aElementOf0 tptp.xv tptp.xT)) (tptp.aElement0 tptp.xv))) (forall ((W0 $$unsorted) (BOUND_VARIABLE_798 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_798 W0)) (tptp.aElement0 BOUND_VARIABLE_798)))) :rule implies_neg1)
% 0.21/0.55 (anchor :step t78)
% 0.21/0.55 (assume t78.a0 (forall ((W0 $$unsorted) (BOUND_VARIABLE_798 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_798 W0)) (tptp.aElement0 BOUND_VARIABLE_798))))
% 0.21/0.55 (step t78.t1 (cl (or (not (forall ((W0 $$unsorted) (BOUND_VARIABLE_798 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_798 W0)) (tptp.aElement0 BOUND_VARIABLE_798)))) (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aElementOf0 tptp.xv tptp.xT)) (tptp.aElement0 tptp.xv)))) :rule forall_inst :args ((:= W0 tptp.xT) (:= BOUND_VARIABLE_798 tptp.xv)))
% 0.21/0.55 (step t78.t2 (cl (not (forall ((W0 $$unsorted) (BOUND_VARIABLE_798 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_798 W0)) (tptp.aElement0 BOUND_VARIABLE_798)))) (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aElementOf0 tptp.xv tptp.xT)) (tptp.aElement0 tptp.xv))) :rule or :premises (t78.t1))
% 0.21/0.55 (step t78.t3 (cl (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aElementOf0 tptp.xv tptp.xT)) (tptp.aElement0 tptp.xv))) :rule resolution :premises (t78.t2 t78.a0))
% 0.21/0.55 (step t78 (cl (not (forall ((W0 $$unsorted) (BOUND_VARIABLE_798 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_798 W0)) (tptp.aElement0 BOUND_VARIABLE_798)))) (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aElementOf0 tptp.xv tptp.xT)) (tptp.aElement0 tptp.xv))) :rule subproof :discharge (t78.a0))
% 0.21/0.55 (step t79 (cl (=> (forall ((W0 $$unsorted) (BOUND_VARIABLE_798 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_798 W0)) (tptp.aElement0 BOUND_VARIABLE_798))) (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aElementOf0 tptp.xv tptp.xT)) (tptp.aElement0 tptp.xv))) (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aElementOf0 tptp.xv tptp.xT)) (tptp.aElement0 tptp.xv))) :rule resolution :premises (t77 t78))
% 0.21/0.55 (step t80 (cl (=> (forall ((W0 $$unsorted) (BOUND_VARIABLE_798 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_798 W0)) (tptp.aElement0 BOUND_VARIABLE_798))) (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aElementOf0 tptp.xv tptp.xT)) (tptp.aElement0 tptp.xv))) (not (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aElementOf0 tptp.xv tptp.xT)) (tptp.aElement0 tptp.xv)))) :rule implies_neg2)
% 0.21/0.55 (step t81 (cl (=> (forall ((W0 $$unsorted) (BOUND_VARIABLE_798 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_798 W0)) (tptp.aElement0 BOUND_VARIABLE_798))) (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aElementOf0 tptp.xv tptp.xT)) (tptp.aElement0 tptp.xv))) (=> (forall ((W0 $$unsorted) (BOUND_VARIABLE_798 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_798 W0)) (tptp.aElement0 BOUND_VARIABLE_798))) (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aElementOf0 tptp.xv tptp.xT)) (tptp.aElement0 tptp.xv)))) :rule resolution :premises (t79 t80))
% 0.21/0.55 (step t82 (cl (=> (forall ((W0 $$unsorted) (BOUND_VARIABLE_798 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_798 W0)) (tptp.aElement0 BOUND_VARIABLE_798))) (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aElementOf0 tptp.xv tptp.xT)) (tptp.aElement0 tptp.xv)))) :rule contraction :premises (t81))
% 0.21/0.55 (step t83 (cl (not (forall ((W0 $$unsorted) (BOUND_VARIABLE_798 $$unsorted)) (or (not (tptp.aSet0 W0)) (not (tptp.aElementOf0 BOUND_VARIABLE_798 W0)) (tptp.aElement0 BOUND_VARIABLE_798)))) (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aElementOf0 tptp.xv tptp.xT)) (tptp.aElement0 tptp.xv))) :rule implies :premises (t82))
% 0.21/0.55 (step t84 (cl (or (not (tptp.aSet0 tptp.xT)) (not (tptp.aElementOf0 tptp.xv tptp.xT)) (tptp.aElement0 tptp.xv))) :rule resolution :premises (t83 t54))
% 0.21/0.55 (step t85 (cl (tptp.aElement0 tptp.xv)) :rule resolution :premises (t58 a13 t76 t84))
% 0.21/0.55 (step t86 (cl (not (or (not (tptp.aUpperBoundOfIn0 tptp.xv tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu tptp.xv))) (not (tptp.aUpperBoundOfIn0 tptp.xv tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu tptp.xv)) :rule or_pos)
% 0.21/0.55 (step t87 (cl (not (tptp.aUpperBoundOfIn0 tptp.xv tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu tptp.xv) (not (or (not (tptp.aUpperBoundOfIn0 tptp.xv tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu tptp.xv)))) :rule reordering :premises (t86))
% 0.21/0.55 (step t88 (cl (not (and (tptp.aElementOf0 tptp.xv tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xv tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv W3))))) (tptp.aUpperBoundOfIn0 tptp.xv tptp.xS tptp.xT)) :rule and_pos)
% 0.21/0.55 (step t89 (cl (tptp.aUpperBoundOfIn0 tptp.xv tptp.xS tptp.xT) (not (and (tptp.aElementOf0 tptp.xv tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xv tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv W3)))))) :rule reordering :premises (t88))
% 0.21/0.55 (step t90 (cl (tptp.aUpperBoundOfIn0 tptp.xv tptp.xS tptp.xT)) :rule resolution :premises (t89 t75))
% 0.21/0.55 (step t91 (cl (=> (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu W3))) (or (not (tptp.aUpperBoundOfIn0 tptp.xv tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu tptp.xv))) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu W3)))) :rule implies_neg1)
% 0.21/0.55 (anchor :step t92)
% 0.21/0.55 (assume t92.a0 (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu W3))))
% 0.21/0.55 (step t92.t1 (cl (or (not (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu W3)))) (or (not (tptp.aUpperBoundOfIn0 tptp.xv tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu tptp.xv)))) :rule forall_inst :args ((:= W3 tptp.xv)))
% 0.21/0.55 (step t92.t2 (cl (not (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu W3)))) (or (not (tptp.aUpperBoundOfIn0 tptp.xv tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu tptp.xv))) :rule or :premises (t92.t1))
% 0.21/0.55 (step t92.t3 (cl (or (not (tptp.aUpperBoundOfIn0 tptp.xv tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu tptp.xv))) :rule resolution :premises (t92.t2 t92.a0))
% 0.21/0.55 (step t92 (cl (not (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu W3)))) (or (not (tptp.aUpperBoundOfIn0 tptp.xv tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu tptp.xv))) :rule subproof :discharge (t92.a0))
% 0.21/0.55 (step t93 (cl (=> (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu W3))) (or (not (tptp.aUpperBoundOfIn0 tptp.xv tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu tptp.xv))) (or (not (tptp.aUpperBoundOfIn0 tptp.xv tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu tptp.xv))) :rule resolution :premises (t91 t92))
% 0.21/0.55 (step t94 (cl (=> (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu W3))) (or (not (tptp.aUpperBoundOfIn0 tptp.xv tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu tptp.xv))) (not (or (not (tptp.aUpperBoundOfIn0 tptp.xv tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu tptp.xv)))) :rule implies_neg2)
% 0.21/0.55 (step t95 (cl (=> (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu W3))) (or (not (tptp.aUpperBoundOfIn0 tptp.xv tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu tptp.xv))) (=> (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu W3))) (or (not (tptp.aUpperBoundOfIn0 tptp.xv tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu tptp.xv)))) :rule resolution :premises (t93 t94))
% 0.21/0.55 (step t96 (cl (=> (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu W3))) (or (not (tptp.aUpperBoundOfIn0 tptp.xv tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu tptp.xv)))) :rule contraction :premises (t95))
% 0.21/0.55 (step t97 (cl (not (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu W3)))) (or (not (tptp.aUpperBoundOfIn0 tptp.xv tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu tptp.xv))) :rule implies :premises (t96))
% 0.21/0.55 (step t98 (cl (not (and (tptp.aElementOf0 tptp.xu tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xu tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu W3))))) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu W3)))) :rule and_pos)
% 0.21/0.55 (step t99 (cl (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu W3))) (not (and (tptp.aElementOf0 tptp.xu tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xu tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu W3)))))) :rule reordering :premises (t98))
% 0.21/0.55 (step t100 (cl (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu W3)))) :rule resolution :premises (t99 t37))
% 0.21/0.55 (step t101 (cl (or (not (tptp.aUpperBoundOfIn0 tptp.xv tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu tptp.xv))) :rule resolution :premises (t97 t100))
% 0.21/0.55 (step t102 (cl (tptp.sdtlseqdt0 tptp.xu tptp.xv)) :rule resolution :premises (t87 t90 t101))
% 0.21/0.55 (step t103 (cl (not (or (not (tptp.aUpperBoundOfIn0 tptp.xu tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv tptp.xu))) (not (tptp.aUpperBoundOfIn0 tptp.xu tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv tptp.xu)) :rule or_pos)
% 0.21/0.55 (step t104 (cl (not (tptp.aUpperBoundOfIn0 tptp.xu tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv tptp.xu) (not (or (not (tptp.aUpperBoundOfIn0 tptp.xu tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv tptp.xu)))) :rule reordering :premises (t103))
% 0.21/0.55 (step t105 (cl (not (and (tptp.aElementOf0 tptp.xu tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xu tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu W3))))) (tptp.aUpperBoundOfIn0 tptp.xu tptp.xS tptp.xT)) :rule and_pos)
% 0.21/0.55 (step t106 (cl (tptp.aUpperBoundOfIn0 tptp.xu tptp.xS tptp.xT) (not (and (tptp.aElementOf0 tptp.xu tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xu tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xu W3)))))) :rule reordering :premises (t105))
% 0.21/0.55 (step t107 (cl (tptp.aUpperBoundOfIn0 tptp.xu tptp.xS tptp.xT)) :rule resolution :premises (t106 t37))
% 0.21/0.55 (step t108 (cl (=> (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv W3))) (or (not (tptp.aUpperBoundOfIn0 tptp.xu tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv tptp.xu))) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv W3)))) :rule implies_neg1)
% 0.21/0.55 (anchor :step t109)
% 0.21/0.55 (assume t109.a0 (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv W3))))
% 0.21/0.55 (step t109.t1 (cl (or (not (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv W3)))) (or (not (tptp.aUpperBoundOfIn0 tptp.xu tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv tptp.xu)))) :rule forall_inst :args ((:= W3 tptp.xu)))
% 0.21/0.55 (step t109.t2 (cl (not (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv W3)))) (or (not (tptp.aUpperBoundOfIn0 tptp.xu tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv tptp.xu))) :rule or :premises (t109.t1))
% 0.21/0.55 (step t109.t3 (cl (or (not (tptp.aUpperBoundOfIn0 tptp.xu tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv tptp.xu))) :rule resolution :premises (t109.t2 t109.a0))
% 0.21/0.55 (step t109 (cl (not (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv W3)))) (or (not (tptp.aUpperBoundOfIn0 tptp.xu tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv tptp.xu))) :rule subproof :discharge (t109.a0))
% 0.21/0.55 (step t110 (cl (=> (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv W3))) (or (not (tptp.aUpperBoundOfIn0 tptp.xu tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv tptp.xu))) (or (not (tptp.aUpperBoundOfIn0 tptp.xu tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv tptp.xu))) :rule resolution :premises (t108 t109))
% 0.21/0.55 (step t111 (cl (=> (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv W3))) (or (not (tptp.aUpperBoundOfIn0 tptp.xu tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv tptp.xu))) (not (or (not (tptp.aUpperBoundOfIn0 tptp.xu tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv tptp.xu)))) :rule implies_neg2)
% 0.21/0.55 (step t112 (cl (=> (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv W3))) (or (not (tptp.aUpperBoundOfIn0 tptp.xu tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv tptp.xu))) (=> (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv W3))) (or (not (tptp.aUpperBoundOfIn0 tptp.xu tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv tptp.xu)))) :rule resolution :premises (t110 t111))
% 0.21/0.55 (step t113 (cl (=> (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv W3))) (or (not (tptp.aUpperBoundOfIn0 tptp.xu tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv tptp.xu)))) :rule contraction :premises (t112))
% 0.21/0.55 (step t114 (cl (not (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv W3)))) (or (not (tptp.aUpperBoundOfIn0 tptp.xu tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv tptp.xu))) :rule implies :premises (t113))
% 0.21/0.56 (step t115 (cl (not (and (tptp.aElementOf0 tptp.xv tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xv tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv W3))))) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv W3)))) :rule and_pos)
% 0.21/0.56 (step t116 (cl (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv W3))) (not (and (tptp.aElementOf0 tptp.xv tptp.xT) (tptp.aUpperBoundOfIn0 tptp.xv tptp.xS tptp.xT) (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv W3)))))) :rule reordering :premises (t115))
% 0.21/0.56 (step t117 (cl (forall ((W3 $$unsorted)) (or (not (tptp.aUpperBoundOfIn0 W3 tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv W3)))) :rule resolution :premises (t116 t75))
% 0.21/0.56 (step t118 (cl (or (not (tptp.aUpperBoundOfIn0 tptp.xu tptp.xS tptp.xT)) (tptp.sdtlseqdt0 tptp.xv tptp.xu))) :rule resolution :premises (t114 t117))
% 0.21/0.56 (step t119 (cl (tptp.sdtlseqdt0 tptp.xv tptp.xu)) :rule resolution :premises (t104 t107 t118))
% 0.21/0.56 (step t120 (cl (not (or (not (tptp.aElement0 tptp.xu)) (not (tptp.aElement0 tptp.xv)) (not (tptp.sdtlseqdt0 tptp.xu tptp.xv)) (not (tptp.sdtlseqdt0 tptp.xv tptp.xu)) (= tptp.xu tptp.xv)))) :rule resolution :premises (t9 a16 t56 t85 t102 t119))
% 0.21/0.56 (step t121 (cl (not (= (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W0)) (= W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (not (tptp.sdtlseqdt0 W1 W0)) (= W0 W1))))) (not (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W0)) (= W0 W1))))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (not (tptp.sdtlseqdt0 W1 W0)) (= W0 W1)))) :rule equiv_pos2)
% 0.21/0.56 (step t122 (cl (= (forall ((W0 $$unsorted) (W1 $$unsorted)) (=> (and (tptp.aElement0 W0) (tptp.aElement0 W1)) (=> (and (tptp.sdtlseqdt0 W0 W1) (tptp.sdtlseqdt0 W1 W0)) (= W0 W1)))) (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (not (tptp.sdtlseqdt0 W1 W0)) (= W0 W1))))) :rule all_simplify)
% 0.21/0.56 (step t123 (cl (forall ((W0 $$unsorted) (W1 $$unsorted)) (or (not (tptp.aElement0 W0)) (not (tptp.aElement0 W1)) (not (tptp.sdtlseqdt0 W0 W1)) (not (tptp.sdtlseqdt0 W1 W0)) (= W0 W1)))) :rule resolution :premises (t121 t122 a7))
% 0.21/0.56 (step t124 (cl) :rule resolution :premises (t7 t120 t123))
% 0.21/0.56
% 0.21/0.56 % SZS output end Proof for /export/starexec/sandbox/tmp/tmp.WXacSnhyMK/cvc5---1.0.5_28887.smt2
% 0.21/0.56 % cvc5---1.0.5 exiting
% 0.21/0.56 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------