TSTP Solution File: LAT385+4 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT385+4 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 17 18:33:40 EDT 2022
% Result : Theorem 10.20s 6.56s
% Output : Proof 10.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : LAT385+4 : TPTP v8.1.0. Released v4.0.0.
% 0.02/0.10 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.09/0.30 % Computer : n013.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Thu Sep 1 16:44:01 EDT 2022
% 0.09/0.30 % CPUTime :
% 0.09/0.30 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.09/0.30 Usage: tptp [options] [-file:]file
% 0.09/0.30 -h, -? prints this message.
% 0.09/0.30 -smt2 print SMT-LIB2 benchmark.
% 0.09/0.30 -m, -model generate model.
% 0.09/0.30 -p, -proof generate proof.
% 0.09/0.30 -c, -core generate unsat core of named formulas.
% 0.09/0.30 -st, -statistics display statistics.
% 0.09/0.30 -t:timeout set timeout (in second).
% 0.09/0.30 -smt2status display status in smt2 format instead of SZS.
% 0.09/0.30 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.09/0.30 -<param>:<value> configuration parameter and value.
% 0.09/0.30 -o:<output-file> file to place output in.
% 10.20/6.56 % SZS status Theorem
% 10.20/6.56 % SZS output start Proof
% 10.20/6.56 tff(sdtlseqdt0_type, type, (
% 10.20/6.56 sdtlseqdt0: ( $i * $i ) > $o)).
% 10.20/6.56 tff(tptp_fun_W1_11_type, type, (
% 10.20/6.56 tptp_fun_W1_11: $i > $i)).
% 10.20/6.56 tff(cS1241_type, type, (
% 10.20/6.56 cS1241: ( $i * $i * $i ) > $i)).
% 10.20/6.56 tff(xT_type, type, (
% 10.20/6.56 xT: $i)).
% 10.20/6.56 tff(xf_type, type, (
% 10.20/6.56 xf: $i)).
% 10.20/6.56 tff(szDzozmdt0_type, type, (
% 10.20/6.56 szDzozmdt0: $i > $i)).
% 10.20/6.56 tff(aElementOf0_type, type, (
% 10.20/6.56 aElementOf0: ( $i * $i ) > $o)).
% 10.20/6.56 tff(sdtlpdtrp0_type, type, (
% 10.20/6.56 sdtlpdtrp0: ( $i * $i ) > $i)).
% 10.20/6.56 tff(aUpperBoundOfIn0_type, type, (
% 10.20/6.56 aUpperBoundOfIn0: ( $i * $i * $i ) > $o)).
% 10.20/6.56 tff(tptp_fun_W1_15_type, type, (
% 10.20/6.56 tptp_fun_W1_15: $i > $i)).
% 10.20/6.56 tff(aSet0_type, type, (
% 10.20/6.56 aSet0: $i > $o)).
% 10.20/6.56 tff(aSubsetOf0_type, type, (
% 10.20/6.56 aSubsetOf0: ( $i * $i ) > $o)).
% 10.20/6.56 tff(tptp_fun_W4_14_type, type, (
% 10.20/6.56 tptp_fun_W4_14: ( $i * $i ) > $i)).
% 10.20/6.56 tff(tptp_fun_W2_13_type, type, (
% 10.20/6.56 tptp_fun_W2_13: $i > $i)).
% 10.20/6.56 tff(aLowerBoundOfIn0_type, type, (
% 10.20/6.56 aLowerBoundOfIn0: ( $i * $i * $i ) > $o)).
% 10.20/6.56 tff(tptp_fun_W3_2_type, type, (
% 10.20/6.56 tptp_fun_W3_2: ( $i * $i ) > $i)).
% 10.20/6.56 tff(tptp_fun_W1_12_type, type, (
% 10.20/6.56 tptp_fun_W1_12: $i > $i)).
% 10.20/6.56 tff(aSupremumOfIn0_type, type, (
% 10.20/6.56 aSupremumOfIn0: ( $i * $i * $i ) > $o)).
% 10.20/6.56 tff(aInfimumOfIn0_type, type, (
% 10.20/6.56 aInfimumOfIn0: ( $i * $i * $i ) > $o)).
% 10.20/6.56 tff(tptp_fun_W1_17_type, type, (
% 10.20/6.56 tptp_fun_W1_17: $i > $i)).
% 10.20/6.56 tff(tptp_fun_W1_16_type, type, (
% 10.20/6.56 tptp_fun_W1_16: $i > $i)).
% 10.20/6.56 tff(szRzazndt0_type, type, (
% 10.20/6.56 szRzazndt0: $i > $i)).
% 10.20/6.56 tff(xU_type, type, (
% 10.20/6.56 xU: $i)).
% 10.20/6.56 tff(xP_type, type, (
% 10.20/6.56 xP: $i)).
% 10.20/6.56 tff(aCompleteLattice0_type, type, (
% 10.20/6.56 aCompleteLattice0: $i > $o)).
% 10.20/6.56 tff(aFunction0_type, type, (
% 10.20/6.56 aFunction0: $i > $o)).
% 10.20/6.56 tff(isMonotone0_type, type, (
% 10.20/6.56 isMonotone0: $i > $o)).
% 10.20/6.56 tff(isOn0_type, type, (
% 10.20/6.56 isOn0: ( $i * $i ) > $o)).
% 10.20/6.56 tff(1,assumption,(aInfimumOfIn0(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | (~((~aElementOf0(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | (~((~((~aElementOf0(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT))), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)), tptp_fun_W1_16(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)))))))) | aLowerBoundOfIn0(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | (~(sdtlseqdt0(tptp_fun_W1_17(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT))), tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT))) | (~aElementOf0(tptp_fun_W1_17(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT))), szDzozmdt0(xf))) | (~aLowerBoundOfIn0(tptp_fun_W1_17(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT))), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT))), W2)))))))), introduced(assumption)).
% 10.20/6.56 tff(2,plain,
% 10.20/6.56 (^[W0: $i] : rewrite((~(aInfimumOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, tptp_fun_W1_16(W0)))))) | aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | (~(sdtlseqdt0(tptp_fun_W1_17(W0), W0) | (~aElementOf0(tptp_fun_W1_17(W0), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2))) | (~aLowerBoundOfIn0(tptp_fun_W1_17(W0), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))))))))) <=> (~(aInfimumOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, tptp_fun_W1_16(W0)))))) | aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | (~(sdtlseqdt0(tptp_fun_W1_17(W0), W0) | (~aElementOf0(tptp_fun_W1_17(W0), szDzozmdt0(xf))) | (~aLowerBoundOfIn0(tptp_fun_W1_17(W0), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2))))))))))),
% 10.20/6.56 inference(bind,[status(th)],[])).
% 10.20/6.56 tff(3,plain,
% 10.20/6.56 (![W0: $i] : (~(aInfimumOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, tptp_fun_W1_16(W0)))))) | aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | (~(sdtlseqdt0(tptp_fun_W1_17(W0), W0) | (~aElementOf0(tptp_fun_W1_17(W0), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2))) | (~aLowerBoundOfIn0(tptp_fun_W1_17(W0), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))))))))) <=> ![W0: $i] : (~(aInfimumOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, tptp_fun_W1_16(W0)))))) | aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | (~(sdtlseqdt0(tptp_fun_W1_17(W0), W0) | (~aElementOf0(tptp_fun_W1_17(W0), szDzozmdt0(xf))) | (~aLowerBoundOfIn0(tptp_fun_W1_17(W0), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2)))))))))),
% 10.20/6.56 inference(quant_intro,[status(thm)],[2])).
% 10.20/6.56 tff(4,plain,
% 10.20/6.56 (^[W0: $i] : refl((~(aInfimumOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, tptp_fun_W1_16(W0)))))) | aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | (~(sdtlseqdt0(tptp_fun_W1_17(W0), W0) | (~aElementOf0(tptp_fun_W1_17(W0), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2))) | (~aLowerBoundOfIn0(tptp_fun_W1_17(W0), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))))))))) <=> (~(aInfimumOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, tptp_fun_W1_16(W0)))))) | aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | (~(sdtlseqdt0(tptp_fun_W1_17(W0), W0) | (~aElementOf0(tptp_fun_W1_17(W0), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2))) | (~aLowerBoundOfIn0(tptp_fun_W1_17(W0), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))))))))))),
% 10.20/6.56 inference(bind,[status(th)],[])).
% 10.20/6.56 tff(5,plain,
% 10.20/6.56 (![W0: $i] : (~(aInfimumOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, tptp_fun_W1_16(W0)))))) | aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | (~(sdtlseqdt0(tptp_fun_W1_17(W0), W0) | (~aElementOf0(tptp_fun_W1_17(W0), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2))) | (~aLowerBoundOfIn0(tptp_fun_W1_17(W0), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))))))))) <=> ![W0: $i] : (~(aInfimumOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, tptp_fun_W1_16(W0)))))) | aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | (~(sdtlseqdt0(tptp_fun_W1_17(W0), W0) | (~aElementOf0(tptp_fun_W1_17(W0), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2))) | (~aLowerBoundOfIn0(tptp_fun_W1_17(W0), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))))))))),
% 10.20/6.56 inference(quant_intro,[status(thm)],[4])).
% 10.20/6.56 tff(6,plain,
% 10.20/6.56 (^[W0: $i] : rewrite((~(aInfimumOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, tptp_fun_W1_16(W0)))))) | aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | (~(sdtlseqdt0(tptp_fun_W1_17(W0), W0) | (~aElementOf0(tptp_fun_W1_17(W0), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2))) | (~aLowerBoundOfIn0(tptp_fun_W1_17(W0), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))))))))) <=> (~(aInfimumOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, tptp_fun_W1_16(W0)))))) | aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | (~(sdtlseqdt0(tptp_fun_W1_17(W0), W0) | (~aElementOf0(tptp_fun_W1_17(W0), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2))) | (~aLowerBoundOfIn0(tptp_fun_W1_17(W0), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))))))))))),
% 10.20/6.56 inference(bind,[status(th)],[])).
% 10.20/6.56 tff(7,plain,
% 10.20/6.56 (![W0: $i] : (~(aInfimumOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, tptp_fun_W1_16(W0)))))) | aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | (~(sdtlseqdt0(tptp_fun_W1_17(W0), W0) | (~aElementOf0(tptp_fun_W1_17(W0), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2))) | (~aLowerBoundOfIn0(tptp_fun_W1_17(W0), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))))))))) <=> ![W0: $i] : (~(aInfimumOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, tptp_fun_W1_16(W0)))))) | aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | (~(sdtlseqdt0(tptp_fun_W1_17(W0), W0) | (~aElementOf0(tptp_fun_W1_17(W0), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2))) | (~aLowerBoundOfIn0(tptp_fun_W1_17(W0), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))))))))),
% 10.20/6.56 inference(quant_intro,[status(thm)],[6])).
% 10.20/6.56 tff(8,plain,
% 10.20/6.56 (![W0: $i] : (~(aInfimumOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, tptp_fun_W1_16(W0)))))) | aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | (~(sdtlseqdt0(tptp_fun_W1_17(W0), W0) | (~aElementOf0(tptp_fun_W1_17(W0), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2))) | (~aLowerBoundOfIn0(tptp_fun_W1_17(W0), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))))))))) <=> ![W0: $i] : (~(aInfimumOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, tptp_fun_W1_16(W0)))))) | aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | (~(sdtlseqdt0(tptp_fun_W1_17(W0), W0) | (~aElementOf0(tptp_fun_W1_17(W0), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2))) | (~aLowerBoundOfIn0(tptp_fun_W1_17(W0), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))))))))),
% 10.20/6.57 inference(transitivity,[status(thm)],[7, 5])).
% 10.20/6.57 tff(9,plain,
% 10.20/6.57 (^[W0: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, tptp_fun_W1_16(W0))))) & (~aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) <=> (~((~((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, tptp_fun_W1_16(W0)))))) | aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))))), rewrite((aElementOf0(tptp_fun_W1_17(W0), szDzozmdt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2)) & aLowerBoundOfIn0(tptp_fun_W1_17(W0), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) & (~sdtlseqdt0(tptp_fun_W1_17(W0), W0))) <=> (~(sdtlseqdt0(tptp_fun_W1_17(W0), W0) | (~aElementOf0(tptp_fun_W1_17(W0), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2))) | (~aLowerBoundOfIn0(tptp_fun_W1_17(W0), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))))), (((~aElementOf0(W0, szDzozmdt0(xf))) | (((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, tptp_fun_W1_16(W0))))) & (~aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | (aElementOf0(tptp_fun_W1_17(W0), szDzozmdt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2)) & aLowerBoundOfIn0(tptp_fun_W1_17(W0), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) & (~sdtlseqdt0(tptp_fun_W1_17(W0), W0)))) <=> ((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, tptp_fun_W1_16(W0)))))) | aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | (~(sdtlseqdt0(tptp_fun_W1_17(W0), W0) | (~aElementOf0(tptp_fun_W1_17(W0), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2))) | (~aLowerBoundOfIn0(tptp_fun_W1_17(W0), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))))))), rewrite(((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, tptp_fun_W1_16(W0)))))) | aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | (~(sdtlseqdt0(tptp_fun_W1_17(W0), W0) | (~aElementOf0(tptp_fun_W1_17(W0), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2))) | (~aLowerBoundOfIn0(tptp_fun_W1_17(W0), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))))) <=> ((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, tptp_fun_W1_16(W0)))))) | aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | (~(sdtlseqdt0(tptp_fun_W1_17(W0), W0) | (~aElementOf0(tptp_fun_W1_17(W0), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2))) | (~aLowerBoundOfIn0(tptp_fun_W1_17(W0), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))))))), (((~aElementOf0(W0, szDzozmdt0(xf))) | (((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, tptp_fun_W1_16(W0))))) & (~aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | (aElementOf0(tptp_fun_W1_17(W0), szDzozmdt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2)) & aLowerBoundOfIn0(tptp_fun_W1_17(W0), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) & (~sdtlseqdt0(tptp_fun_W1_17(W0), W0)))) <=> ((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, tptp_fun_W1_16(W0)))))) | aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | (~(sdtlseqdt0(tptp_fun_W1_17(W0), W0) | (~aElementOf0(tptp_fun_W1_17(W0), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2))) | (~aLowerBoundOfIn0(tptp_fun_W1_17(W0), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))))))), (((~aInfimumOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) & ((~aElementOf0(W0, szDzozmdt0(xf))) | (((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, tptp_fun_W1_16(W0))))) & (~aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | (aElementOf0(tptp_fun_W1_17(W0), szDzozmdt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2)) & aLowerBoundOfIn0(tptp_fun_W1_17(W0), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) & (~sdtlseqdt0(tptp_fun_W1_17(W0), W0))))) <=> ((~aInfimumOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) & ((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, tptp_fun_W1_16(W0)))))) | aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | (~(sdtlseqdt0(tptp_fun_W1_17(W0), W0) | (~aElementOf0(tptp_fun_W1_17(W0), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2))) | (~aLowerBoundOfIn0(tptp_fun_W1_17(W0), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))))))))), rewrite(((~aInfimumOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) & ((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, tptp_fun_W1_16(W0)))))) | aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | (~(sdtlseqdt0(tptp_fun_W1_17(W0), W0) | (~aElementOf0(tptp_fun_W1_17(W0), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2))) | (~aLowerBoundOfIn0(tptp_fun_W1_17(W0), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))))))) <=> (~(aInfimumOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, tptp_fun_W1_16(W0)))))) | aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | (~(sdtlseqdt0(tptp_fun_W1_17(W0), W0) | (~aElementOf0(tptp_fun_W1_17(W0), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2))) | (~aLowerBoundOfIn0(tptp_fun_W1_17(W0), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))))))))), (((~aInfimumOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) & ((~aElementOf0(W0, szDzozmdt0(xf))) | (((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, tptp_fun_W1_16(W0))))) & (~aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | (aElementOf0(tptp_fun_W1_17(W0), szDzozmdt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2)) & aLowerBoundOfIn0(tptp_fun_W1_17(W0), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) & (~sdtlseqdt0(tptp_fun_W1_17(W0), W0))))) <=> (~(aInfimumOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, tptp_fun_W1_16(W0)))))) | aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | (~(sdtlseqdt0(tptp_fun_W1_17(W0), W0) | (~aElementOf0(tptp_fun_W1_17(W0), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2))) | (~aLowerBoundOfIn0(tptp_fun_W1_17(W0), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))))))))))),
% 10.20/6.57 inference(bind,[status(th)],[])).
% 10.20/6.57 tff(10,plain,
% 10.20/6.57 (![W0: $i] : ((~aInfimumOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) & ((~aElementOf0(W0, szDzozmdt0(xf))) | (((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, tptp_fun_W1_16(W0))))) & (~aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | (aElementOf0(tptp_fun_W1_17(W0), szDzozmdt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2)) & aLowerBoundOfIn0(tptp_fun_W1_17(W0), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) & (~sdtlseqdt0(tptp_fun_W1_17(W0), W0))))) <=> ![W0: $i] : (~(aInfimumOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, tptp_fun_W1_16(W0)))))) | aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | (~(sdtlseqdt0(tptp_fun_W1_17(W0), W0) | (~aElementOf0(tptp_fun_W1_17(W0), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2))) | (~aLowerBoundOfIn0(tptp_fun_W1_17(W0), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))))))))),
% 10.20/6.57 inference(quant_intro,[status(thm)],[9])).
% 10.20/6.57 tff(11,plain,
% 10.20/6.57 (^[W0: $i] : rewrite(((~aInfimumOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) & ((~aElementOf0(W0, szDzozmdt0(xf))) | (((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, tptp_fun_W1_16(W0))))) & (~aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | ((aElementOf0(tptp_fun_W1_17(W0), szDzozmdt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2)) & aLowerBoundOfIn0(tptp_fun_W1_17(W0), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) & (~sdtlseqdt0(tptp_fun_W1_17(W0), W0))))) <=> ((~aInfimumOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) & ((~aElementOf0(W0, szDzozmdt0(xf))) | (((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, tptp_fun_W1_16(W0))))) & (~aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | (aElementOf0(tptp_fun_W1_17(W0), szDzozmdt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2)) & aLowerBoundOfIn0(tptp_fun_W1_17(W0), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) & (~sdtlseqdt0(tptp_fun_W1_17(W0), W0))))))),
% 10.20/6.57 inference(bind,[status(th)],[])).
% 10.20/6.57 tff(12,plain,
% 10.20/6.57 (![W0: $i] : ((~aInfimumOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) & ((~aElementOf0(W0, szDzozmdt0(xf))) | (((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, tptp_fun_W1_16(W0))))) & (~aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | ((aElementOf0(tptp_fun_W1_17(W0), szDzozmdt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2)) & aLowerBoundOfIn0(tptp_fun_W1_17(W0), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) & (~sdtlseqdt0(tptp_fun_W1_17(W0), W0))))) <=> ![W0: $i] : ((~aInfimumOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) & ((~aElementOf0(W0, szDzozmdt0(xf))) | (((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, tptp_fun_W1_16(W0))))) & (~aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | (aElementOf0(tptp_fun_W1_17(W0), szDzozmdt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2)) & aLowerBoundOfIn0(tptp_fun_W1_17(W0), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) & (~sdtlseqdt0(tptp_fun_W1_17(W0), W0)))))),
% 10.20/6.58 inference(quant_intro,[status(thm)],[11])).
% 10.20/6.58 tff(13,plain,
% 10.20/6.58 ((~?[W0: $i] : (aInfimumOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | (aElementOf0(W0, szDzozmdt0(xf)) & ((aElementOf0(W0, szDzozmdt0(xf)) & ![W1: $i] : ((~aElementOf0(W1, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) & ![W1: $i] : ((~(aElementOf0(W1, szDzozmdt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | sdtlseqdt0(W1, W0))))) <=> (~?[W0: $i] : (aInfimumOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | (aElementOf0(W0, szDzozmdt0(xf)) & ((aElementOf0(W0, szDzozmdt0(xf)) & ![W1: $i] : ((~aElementOf0(W1, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) & ![W1: $i] : ((~(aElementOf0(W1, szDzozmdt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | sdtlseqdt0(W1, W0)))))),
% 10.20/6.58 inference(rewrite,[status(thm)],[])).
% 10.20/6.58 tff(14,plain,
% 10.20/6.58 ((~?[W0: $i] : (aInfimumOfIn0(W0, cS1241(szRzazndt0(xf), xf, xT), szRzazndt0(xf)) | (aElementOf0(W0, szRzazndt0(xf)) & ((aElementOf0(W0, szRzazndt0(xf)) & ![W1: $i] : ((~aElementOf0(W1, cS1241(szRzazndt0(xf), xf, xT))) | sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, cS1241(szRzazndt0(xf), xf, xT), szRzazndt0(xf))) & ![W1: $i] : ((~(aElementOf0(W1, szRzazndt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, cS1241(szRzazndt0(xf), xf, xT))) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, cS1241(szRzazndt0(xf), xf, xT), szRzazndt0(xf)))) | sdtlseqdt0(W1, W0))))) <=> (~?[W0: $i] : (aInfimumOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | (aElementOf0(W0, szDzozmdt0(xf)) & ((aElementOf0(W0, szDzozmdt0(xf)) & ![W1: $i] : ((~aElementOf0(W1, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) & ![W1: $i] : ((~(aElementOf0(W1, szDzozmdt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | sdtlseqdt0(W1, W0)))))),
% 10.20/6.58 inference(rewrite,[status(thm)],[])).
% 10.20/6.58 tff(15,plain,
% 10.20/6.58 ((~?[W0: $i] : (aInfimumOfIn0(W0, cS1241(szRzazndt0(xf), xf, xT), szRzazndt0(xf)) | (aElementOf0(W0, szRzazndt0(xf)) & ((aElementOf0(W0, szRzazndt0(xf)) & ![W1: $i] : ((~aElementOf0(W1, cS1241(szRzazndt0(xf), xf, xT))) | sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, cS1241(szRzazndt0(xf), xf, xT), szRzazndt0(xf))) & ![W1: $i] : ((~(aElementOf0(W1, szRzazndt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, cS1241(szRzazndt0(xf), xf, xT))) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, cS1241(szRzazndt0(xf), xf, xT), szRzazndt0(xf)))) | sdtlseqdt0(W1, W0))))) <=> (~?[W0: $i] : (aInfimumOfIn0(W0, cS1241(szRzazndt0(xf), xf, xT), szRzazndt0(xf)) | (aElementOf0(W0, szRzazndt0(xf)) & ((aElementOf0(W0, szRzazndt0(xf)) & ![W1: $i] : ((~aElementOf0(W1, cS1241(szRzazndt0(xf), xf, xT))) | sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, cS1241(szRzazndt0(xf), xf, xT), szRzazndt0(xf))) & ![W1: $i] : ((~(aElementOf0(W1, szRzazndt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, cS1241(szRzazndt0(xf), xf, xT))) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, cS1241(szRzazndt0(xf), xf, xT), szRzazndt0(xf)))) | sdtlseqdt0(W1, W0)))))),
% 10.20/6.58 inference(rewrite,[status(thm)],[])).
% 10.20/6.58 tff(16,plain,
% 10.20/6.58 ((~?[W0: $i] : (aInfimumOfIn0(W0, xP, xU) | (aElementOf0(W0, xU) & ((aElementOf0(W0, xU) & ![W1: $i] : ((~aElementOf0(W1, xP)) | sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, xP, xU)) & ![W1: $i] : ((~(aElementOf0(W1, xU) & ![W2: $i] : ((~aElementOf0(W2, xP)) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, xP, xU))) | sdtlseqdt0(W1, W0))))) <=> (~?[W0: $i] : (aInfimumOfIn0(W0, cS1241(szRzazndt0(xf), xf, xT), szRzazndt0(xf)) | (aElementOf0(W0, szRzazndt0(xf)) & ((aElementOf0(W0, szRzazndt0(xf)) & ![W1: $i] : ((~aElementOf0(W1, cS1241(szRzazndt0(xf), xf, xT))) | sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, cS1241(szRzazndt0(xf), xf, xT), szRzazndt0(xf))) & ![W1: $i] : ((~(aElementOf0(W1, szRzazndt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, cS1241(szRzazndt0(xf), xf, xT))) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, cS1241(szRzazndt0(xf), xf, xT), szRzazndt0(xf)))) | sdtlseqdt0(W1, W0)))))),
% 10.20/6.58 inference(rewrite,[status(thm)],[])).
% 10.20/6.58 tff(17,plain,
% 10.20/6.58 ((~?[W0: $i] : (aInfimumOfIn0(W0, xP, xU) | (aElementOf0(W0, xU) & ((aElementOf0(W0, xU) & ![W1: $i] : ((~aElementOf0(W1, xP)) | sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, xP, xU)) & ![W1: $i] : ((~(aElementOf0(W1, xU) & ![W2: $i] : ((~aElementOf0(W2, xP)) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, xP, xU))) | sdtlseqdt0(W1, W0))))) <=> (~?[W0: $i] : (aInfimumOfIn0(W0, xP, xU) | (aElementOf0(W0, xU) & ((aElementOf0(W0, xU) & ![W1: $i] : ((~aElementOf0(W1, xP)) | sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, xP, xU)) & ![W1: $i] : ((~(aElementOf0(W1, xU) & ![W2: $i] : ((~aElementOf0(W2, xP)) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, xP, xU))) | sdtlseqdt0(W1, W0)))))),
% 10.20/6.58 inference(rewrite,[status(thm)],[])).
% 10.20/6.58 tff(18,plain,
% 10.20/6.58 ((~?[W0: $i] : (((aElementOf0(W0, xU) & ((aElementOf0(W0, xU) & ![W1: $i] : (aElementOf0(W1, xP) => sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, xP, xU))) & ![W1: $i] : (((aElementOf0(W1, xU) & ![W2: $i] : (aElementOf0(W2, xP) => sdtlseqdt0(W1, W2))) & aLowerBoundOfIn0(W1, xP, xU)) => sdtlseqdt0(W1, W0))) | aInfimumOfIn0(W0, xP, xU))) <=> (~?[W0: $i] : (aInfimumOfIn0(W0, xP, xU) | (aElementOf0(W0, xU) & ((aElementOf0(W0, xU) & ![W1: $i] : ((~aElementOf0(W1, xP)) | sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, xP, xU)) & ![W1: $i] : ((~(aElementOf0(W1, xU) & ![W2: $i] : ((~aElementOf0(W2, xP)) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, xP, xU))) | sdtlseqdt0(W1, W0)))))),
% 10.20/6.58 inference(rewrite,[status(thm)],[])).
% 10.20/6.58 tff(19,axiom,(~?[W0: $i] : (((aElementOf0(W0, xU) & ((aElementOf0(W0, xU) & ![W1: $i] : (aElementOf0(W1, xP) => sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, xP, xU))) & ![W1: $i] : (((aElementOf0(W1, xU) & ![W2: $i] : (aElementOf0(W2, xP) => sdtlseqdt0(W1, W2))) & aLowerBoundOfIn0(W1, xP, xU)) => sdtlseqdt0(W1, W0))) | aInfimumOfIn0(W0, xP, xU))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__')).
% 10.20/6.58 tff(20,plain,
% 10.20/6.58 (~?[W0: $i] : (aInfimumOfIn0(W0, xP, xU) | (aElementOf0(W0, xU) & ((aElementOf0(W0, xU) & ![W1: $i] : ((~aElementOf0(W1, xP)) | sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, xP, xU)) & ![W1: $i] : ((~(aElementOf0(W1, xU) & ![W2: $i] : ((~aElementOf0(W2, xP)) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, xP, xU))) | sdtlseqdt0(W1, W0))))),
% 10.20/6.58 inference(modus_ponens,[status(thm)],[19, 18])).
% 10.20/6.58 tff(21,plain,
% 10.20/6.58 (~?[W0: $i] : (aInfimumOfIn0(W0, xP, xU) | (aElementOf0(W0, xU) & ((aElementOf0(W0, xU) & ![W1: $i] : ((~aElementOf0(W1, xP)) | sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, xP, xU)) & ![W1: $i] : ((~(aElementOf0(W1, xU) & ![W2: $i] : ((~aElementOf0(W2, xP)) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, xP, xU))) | sdtlseqdt0(W1, W0))))),
% 10.20/6.58 inference(modus_ponens,[status(thm)],[20, 17])).
% 10.20/6.58 tff(22,plain,
% 10.20/6.58 (~?[W0: $i] : (aInfimumOfIn0(W0, xP, xU) | (aElementOf0(W0, xU) & ((aElementOf0(W0, xU) & ![W1: $i] : ((~aElementOf0(W1, xP)) | sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, xP, xU)) & ![W1: $i] : ((~(aElementOf0(W1, xU) & ![W2: $i] : ((~aElementOf0(W2, xP)) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, xP, xU))) | sdtlseqdt0(W1, W0))))),
% 10.20/6.58 inference(modus_ponens,[status(thm)],[21, 17])).
% 10.20/6.58 tff(23,plain,
% 10.20/6.58 (~?[W0: $i] : (aInfimumOfIn0(W0, xP, xU) | (aElementOf0(W0, xU) & ((aElementOf0(W0, xU) & ![W1: $i] : ((~aElementOf0(W1, xP)) | sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, xP, xU)) & ![W1: $i] : ((~(aElementOf0(W1, xU) & ![W2: $i] : ((~aElementOf0(W2, xP)) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, xP, xU))) | sdtlseqdt0(W1, W0))))),
% 10.20/6.58 inference(modus_ponens,[status(thm)],[22, 17])).
% 10.20/6.58 tff(24,plain,
% 10.20/6.58 (~?[W0: $i] : (aInfimumOfIn0(W0, cS1241(szRzazndt0(xf), xf, xT), szRzazndt0(xf)) | (aElementOf0(W0, szRzazndt0(xf)) & ((aElementOf0(W0, szRzazndt0(xf)) & ![W1: $i] : ((~aElementOf0(W1, cS1241(szRzazndt0(xf), xf, xT))) | sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, cS1241(szRzazndt0(xf), xf, xT), szRzazndt0(xf))) & ![W1: $i] : ((~(aElementOf0(W1, szRzazndt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, cS1241(szRzazndt0(xf), xf, xT))) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, cS1241(szRzazndt0(xf), xf, xT), szRzazndt0(xf)))) | sdtlseqdt0(W1, W0))))),
% 10.20/6.58 inference(modus_ponens,[status(thm)],[23, 16])).
% 10.20/6.58 tff(25,plain,
% 10.20/6.58 (~?[W0: $i] : (aInfimumOfIn0(W0, cS1241(szRzazndt0(xf), xf, xT), szRzazndt0(xf)) | (aElementOf0(W0, szRzazndt0(xf)) & ((aElementOf0(W0, szRzazndt0(xf)) & ![W1: $i] : ((~aElementOf0(W1, cS1241(szRzazndt0(xf), xf, xT))) | sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, cS1241(szRzazndt0(xf), xf, xT), szRzazndt0(xf))) & ![W1: $i] : ((~(aElementOf0(W1, szRzazndt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, cS1241(szRzazndt0(xf), xf, xT))) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, cS1241(szRzazndt0(xf), xf, xT), szRzazndt0(xf)))) | sdtlseqdt0(W1, W0))))),
% 10.20/6.58 inference(modus_ponens,[status(thm)],[24, 15])).
% 10.20/6.58 tff(26,plain,
% 10.20/6.58 (~?[W0: $i] : (aInfimumOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | (aElementOf0(W0, szDzozmdt0(xf)) & ((aElementOf0(W0, szDzozmdt0(xf)) & ![W1: $i] : ((~aElementOf0(W1, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) & ![W1: $i] : ((~(aElementOf0(W1, szDzozmdt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | sdtlseqdt0(W1, W0))))),
% 10.20/6.58 inference(modus_ponens,[status(thm)],[25, 14])).
% 10.20/6.58 tff(27,plain,
% 10.20/6.58 (~?[W0: $i] : (aInfimumOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | (aElementOf0(W0, szDzozmdt0(xf)) & ((aElementOf0(W0, szDzozmdt0(xf)) & ![W1: $i] : ((~aElementOf0(W1, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) & ![W1: $i] : ((~(aElementOf0(W1, szDzozmdt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | sdtlseqdt0(W1, W0))))),
% 10.20/6.58 inference(modus_ponens,[status(thm)],[26, 13])).
% 10.20/6.58 tff(28,plain,
% 10.20/6.58 (~?[W0: $i] : (aInfimumOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | (aElementOf0(W0, szDzozmdt0(xf)) & ((aElementOf0(W0, szDzozmdt0(xf)) & ![W1: $i] : ((~aElementOf0(W1, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) & ![W1: $i] : ((~(aElementOf0(W1, szDzozmdt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | sdtlseqdt0(W1, W0))))),
% 10.20/6.58 inference(modus_ponens,[status(thm)],[27, 13])).
% 10.20/6.58 tff(29,plain,
% 10.20/6.58 (~?[W0: $i] : (aInfimumOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | (aElementOf0(W0, szDzozmdt0(xf)) & ((aElementOf0(W0, szDzozmdt0(xf)) & ![W1: $i] : ((~aElementOf0(W1, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) & ![W1: $i] : ((~(aElementOf0(W1, szDzozmdt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | sdtlseqdt0(W1, W0))))),
% 10.20/6.58 inference(modus_ponens,[status(thm)],[28, 13])).
% 10.20/6.58 tff(30,plain,
% 10.20/6.58 (^[W0: $i] : nnf_neg(refl($oeq((~aInfimumOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))), (~aInfimumOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))))), nnf_neg(refl($oeq((~aElementOf0(W0, szDzozmdt0(xf))), (~aElementOf0(W0, szDzozmdt0(xf))))), nnf_neg(nnf_neg(refl($oeq((~aElementOf0(W0, szDzozmdt0(xf))), (~aElementOf0(W0, szDzozmdt0(xf))))), sk($oeq((~![W1: $i] : ((~aElementOf0(W1, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, W1))), (~((~aElementOf0(tptp_fun_W1_16(W0), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, tptp_fun_W1_16(W0)))))), $oeq((~(aElementOf0(W0, szDzozmdt0(xf)) & ![W1: $i] : ((~aElementOf0(W1, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, W1)))), ((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, tptp_fun_W1_16(W0))))))), refl($oeq((~aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))), (~aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))))), $oeq((~((aElementOf0(W0, szDzozmdt0(xf)) & ![W1: $i] : ((~aElementOf0(W1, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))), (((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, tptp_fun_W1_16(W0))))) & (~aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))))), trans(sk($oeq((~![W1: $i] : ((~(aElementOf0(W1, szDzozmdt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | sdtlseqdt0(W1, W0))), (~((~(aElementOf0(tptp_fun_W1_17(W0), szDzozmdt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2)) & aLowerBoundOfIn0(tptp_fun_W1_17(W0), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | sdtlseqdt0(tptp_fun_W1_17(W0), W0))))), nnf_neg(nnf_neg(monotonicity(refl($oeq(aElementOf0(tptp_fun_W1_17(W0), szDzozmdt0(xf)), aElementOf0(tptp_fun_W1_17(W0), szDzozmdt0(xf)))), nnf_pos(proof_bind(^[W2: $i] : refl($oeq(((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2)), ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2))))), $oeq(![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2)), ![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2)))), refl($oeq(aLowerBoundOfIn0(tptp_fun_W1_17(W0), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)), aLowerBoundOfIn0(tptp_fun_W1_17(W0), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))), $oeq((aElementOf0(tptp_fun_W1_17(W0), szDzozmdt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2)) & aLowerBoundOfIn0(tptp_fun_W1_17(W0), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))), (aElementOf0(tptp_fun_W1_17(W0), szDzozmdt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2)) & aLowerBoundOfIn0(tptp_fun_W1_17(W0), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))))), $oeq((~(~(aElementOf0(tptp_fun_W1_17(W0), szDzozmdt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2)) & aLowerBoundOfIn0(tptp_fun_W1_17(W0), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))))), (aElementOf0(tptp_fun_W1_17(W0), szDzozmdt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2)) & aLowerBoundOfIn0(tptp_fun_W1_17(W0), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))))), refl($oeq((~sdtlseqdt0(tptp_fun_W1_17(W0), W0)), (~sdtlseqdt0(tptp_fun_W1_17(W0), W0)))), $oeq((~((~(aElementOf0(tptp_fun_W1_17(W0), szDzozmdt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2)) & aLowerBoundOfIn0(tptp_fun_W1_17(W0), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | sdtlseqdt0(tptp_fun_W1_17(W0), W0))), ((aElementOf0(tptp_fun_W1_17(W0), szDzozmdt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2)) & aLowerBoundOfIn0(tptp_fun_W1_17(W0), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) & (~sdtlseqdt0(tptp_fun_W1_17(W0), W0))))), $oeq((~![W1: $i] : ((~(aElementOf0(W1, szDzozmdt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | sdtlseqdt0(W1, W0))), ((aElementOf0(tptp_fun_W1_17(W0), szDzozmdt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2)) & aLowerBoundOfIn0(tptp_fun_W1_17(W0), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) & (~sdtlseqdt0(tptp_fun_W1_17(W0), W0))))), $oeq((~(aElementOf0(W0, szDzozmdt0(xf)) & ((aElementOf0(W0, szDzozmdt0(xf)) & ![W1: $i] : ((~aElementOf0(W1, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) & ![W1: $i] : ((~(aElementOf0(W1, szDzozmdt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | sdtlseqdt0(W1, W0)))), ((~aElementOf0(W0, szDzozmdt0(xf))) | (((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, tptp_fun_W1_16(W0))))) & (~aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | ((aElementOf0(tptp_fun_W1_17(W0), szDzozmdt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2)) & aLowerBoundOfIn0(tptp_fun_W1_17(W0), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) & (~sdtlseqdt0(tptp_fun_W1_17(W0), W0)))))), $oeq((~(aInfimumOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | (aElementOf0(W0, szDzozmdt0(xf)) & ((aElementOf0(W0, szDzozmdt0(xf)) & ![W1: $i] : ((~aElementOf0(W1, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) & ![W1: $i] : ((~(aElementOf0(W1, szDzozmdt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | sdtlseqdt0(W1, W0))))), ((~aInfimumOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) & ((~aElementOf0(W0, szDzozmdt0(xf))) | (((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, tptp_fun_W1_16(W0))))) & (~aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | ((aElementOf0(tptp_fun_W1_17(W0), szDzozmdt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2)) & aLowerBoundOfIn0(tptp_fun_W1_17(W0), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) & (~sdtlseqdt0(tptp_fun_W1_17(W0), W0)))))))),
% 10.20/6.59 inference(bind,[status(th)],[])).
% 10.20/6.59 tff(31,plain,(
% 10.20/6.59 ![W0: $i] : ((~aInfimumOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) & ((~aElementOf0(W0, szDzozmdt0(xf))) | (((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, tptp_fun_W1_16(W0))))) & (~aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | ((aElementOf0(tptp_fun_W1_17(W0), szDzozmdt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2)) & aLowerBoundOfIn0(tptp_fun_W1_17(W0), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) & (~sdtlseqdt0(tptp_fun_W1_17(W0), W0)))))),
% 10.20/6.59 inference(nnf-neg,[status(sab)],[29, 30])).
% 10.20/6.59 tff(32,plain,
% 10.20/6.59 (![W0: $i] : ((~aInfimumOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) & ((~aElementOf0(W0, szDzozmdt0(xf))) | (((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, tptp_fun_W1_16(W0))))) & (~aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | (aElementOf0(tptp_fun_W1_17(W0), szDzozmdt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2)) & aLowerBoundOfIn0(tptp_fun_W1_17(W0), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) & (~sdtlseqdt0(tptp_fun_W1_17(W0), W0)))))),
% 10.20/6.59 inference(modus_ponens,[status(thm)],[31, 12])).
% 10.20/6.59 tff(33,plain,
% 10.20/6.59 (![W0: $i] : (~(aInfimumOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, tptp_fun_W1_16(W0)))))) | aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | (~(sdtlseqdt0(tptp_fun_W1_17(W0), W0) | (~aElementOf0(tptp_fun_W1_17(W0), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2))) | (~aLowerBoundOfIn0(tptp_fun_W1_17(W0), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))))))))),
% 10.20/6.59 inference(modus_ponens,[status(thm)],[32, 10])).
% 10.20/6.59 tff(34,plain,
% 10.20/6.59 (![W0: $i] : (~(aInfimumOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, tptp_fun_W1_16(W0)))))) | aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | (~(sdtlseqdt0(tptp_fun_W1_17(W0), W0) | (~aElementOf0(tptp_fun_W1_17(W0), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2))) | (~aLowerBoundOfIn0(tptp_fun_W1_17(W0), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))))))))),
% 10.20/6.59 inference(modus_ponens,[status(thm)],[33, 8])).
% 10.20/6.59 tff(35,plain,
% 10.20/6.59 (![W0: $i] : (~(aInfimumOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, tptp_fun_W1_16(W0)))))) | aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | (~(sdtlseqdt0(tptp_fun_W1_17(W0), W0) | (~aElementOf0(tptp_fun_W1_17(W0), szDzozmdt0(xf))) | (~aLowerBoundOfIn0(tptp_fun_W1_17(W0), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2)))))))))),
% 10.20/6.59 inference(modus_ponens,[status(thm)],[34, 3])).
% 10.20/6.59 tff(36,plain,
% 10.20/6.59 ((~![W0: $i] : (~(aInfimumOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~((~aElementOf0(W0, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0, tptp_fun_W1_16(W0)))))) | aLowerBoundOfIn0(W0, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | (~(sdtlseqdt0(tptp_fun_W1_17(W0), W0) | (~aElementOf0(tptp_fun_W1_17(W0), szDzozmdt0(xf))) | (~aLowerBoundOfIn0(tptp_fun_W1_17(W0), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(W0), W2)))))))))) | (~(aInfimumOfIn0(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | (~((~aElementOf0(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | (~((~((~aElementOf0(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT))), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)), tptp_fun_W1_16(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)))))))) | aLowerBoundOfIn0(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | (~(sdtlseqdt0(tptp_fun_W1_17(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT))), tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT))) | (~aElementOf0(tptp_fun_W1_17(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT))), szDzozmdt0(xf))) | (~aLowerBoundOfIn0(tptp_fun_W1_17(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT))), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT))), W2)))))))))),
% 10.20/6.59 inference(quant_inst,[status(thm)],[])).
% 10.20/6.59 tff(37,plain,
% 10.20/6.59 ($false),
% 10.20/6.59 inference(unit_resolution,[status(thm)],[36, 35, 1])).
% 10.27/6.60 tff(38,plain,(~(aInfimumOfIn0(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | (~((~aElementOf0(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | (~((~((~aElementOf0(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT))), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)), tptp_fun_W1_16(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)))))))) | aLowerBoundOfIn0(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | (~(sdtlseqdt0(tptp_fun_W1_17(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT))), tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT))) | (~aElementOf0(tptp_fun_W1_17(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT))), szDzozmdt0(xf))) | (~aLowerBoundOfIn0(tptp_fun_W1_17(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT))), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT))), W2))))))))), inference(lemma,lemma(discharge,[]))).
% 10.27/6.60 tff(39,plain,
% 10.27/6.60 ((aInfimumOfIn0(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | (~((~aElementOf0(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | (~((~((~aElementOf0(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT))), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)), tptp_fun_W1_16(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)))))))) | aLowerBoundOfIn0(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))) | (~(sdtlseqdt0(tptp_fun_W1_17(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT))), tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT))) | (~aElementOf0(tptp_fun_W1_17(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT))), szDzozmdt0(xf))) | (~aLowerBoundOfIn0(tptp_fun_W1_17(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT))), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_17(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT))), W2)))))))) | (~aInfimumOfIn0(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))),
% 10.27/6.60 inference(tautology,[status(thm)],[])).
% 10.27/6.60 tff(40,plain,
% 10.27/6.60 (~aInfimumOfIn0(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))),
% 10.27/6.60 inference(unit_resolution,[status(thm)],[39, 38])).
% 10.27/6.60 tff(41,plain,
% 10.27/6.60 (((~aElementOf0(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | (~aLowerBoundOfIn0(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) | (~aInfimumOfIn0(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) | (~aElementOf0(tptp_fun_W2_13(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | (~aUpperBoundOfIn0(tptp_fun_W2_13(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) | (~aSupremumOfIn0(tptp_fun_W2_13(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)), W2))) | (~![W2: $i] : (sdtlseqdt0(W2, tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT))) | (~((~((~aElementOf0(W2, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W3_2(W2, cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W2, tptp_fun_W3_2(W2, cS1241(szDzozmdt0(xf), xf, xT))))))) | aLowerBoundOfIn0(W2, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))))) | (~![W3: $i] : ((~aElementOf0(W3, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W3, tptp_fun_W2_13(cS1241(szDzozmdt0(xf), xf, xT))))) | (~![W3: $i] : (sdtlseqdt0(tptp_fun_W2_13(cS1241(szDzozmdt0(xf), xf, xT)), W3) | (~((~((~aElementOf0(W3, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W4_14(W3, cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W4_14(W3, cS1241(szDzozmdt0(xf), xf, xT)), W3))))) | aUpperBoundOfIn0(W3, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))))))) | aInfimumOfIn0(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))),
% 10.27/6.60 inference(tautology,[status(thm)],[])).
% 10.27/6.60 tff(42,plain,
% 10.27/6.60 ((~aElementOf0(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | (~aLowerBoundOfIn0(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) | (~aInfimumOfIn0(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) | (~aElementOf0(tptp_fun_W2_13(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | (~aUpperBoundOfIn0(tptp_fun_W2_13(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) | (~aSupremumOfIn0(tptp_fun_W2_13(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)), W2))) | (~![W2: $i] : (sdtlseqdt0(W2, tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT))) | (~((~((~aElementOf0(W2, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W3_2(W2, cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W2, tptp_fun_W3_2(W2, cS1241(szDzozmdt0(xf), xf, xT))))))) | aLowerBoundOfIn0(W2, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))))) | (~![W3: $i] : ((~aElementOf0(W3, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W3, tptp_fun_W2_13(cS1241(szDzozmdt0(xf), xf, xT))))) | (~![W3: $i] : (sdtlseqdt0(tptp_fun_W2_13(cS1241(szDzozmdt0(xf), xf, xT)), W3) | (~((~((~aElementOf0(W3, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W4_14(W3, cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W4_14(W3, cS1241(szDzozmdt0(xf), xf, xT)), W3))))) | aUpperBoundOfIn0(W3, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))))))),
% 10.27/6.60 inference(unit_resolution,[status(thm)],[41, 40])).
% 10.27/6.60 tff(43,plain,
% 10.27/6.60 (^[W0: $i] : rewrite(((~(aSubsetOf0(W0, szDzozmdt0(xf)) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), szDzozmdt0(xf)))))))) | (~((~aElementOf0(tptp_fun_W1_12(W0), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(tptp_fun_W1_12(W0), W2))) | (~aLowerBoundOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf))) | (~![W2: $i] : (sdtlseqdt0(W2, tptp_fun_W1_12(W0)) | (~((~((~aElementOf0(W2, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W3_2(W2, W0), W0)) | sdtlseqdt0(W2, tptp_fun_W3_2(W2, W0)))))) | aLowerBoundOfIn0(W2, W0, szDzozmdt0(xf)))))) | (~aInfimumOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf))) | (~aElementOf0(tptp_fun_W2_13(W0), szDzozmdt0(xf))) | (~![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, tptp_fun_W2_13(W0)))) | (~aUpperBoundOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf))) | (~![W3: $i] : (sdtlseqdt0(tptp_fun_W2_13(W0), W3) | (~((~((~aElementOf0(W3, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W4_14(W3, W0), W0)) | sdtlseqdt0(tptp_fun_W4_14(W3, W0), W3))))) | aUpperBoundOfIn0(W3, W0, szDzozmdt0(xf)))))) | (~aSupremumOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf)))))) <=> ((~(aSubsetOf0(W0, szDzozmdt0(xf)) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), szDzozmdt0(xf)))))))) | (~((~aElementOf0(tptp_fun_W1_12(W0), szDzozmdt0(xf))) | (~aLowerBoundOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf))) | (~aInfimumOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf))) | (~aElementOf0(tptp_fun_W2_13(W0), szDzozmdt0(xf))) | (~aUpperBoundOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf))) | (~aSupremumOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(tptp_fun_W1_12(W0), W2))) | (~![W2: $i] : (sdtlseqdt0(W2, tptp_fun_W1_12(W0)) | (~((~((~aElementOf0(W2, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W3_2(W2, W0), W0)) | sdtlseqdt0(W2, tptp_fun_W3_2(W2, W0)))))) | aLowerBoundOfIn0(W2, W0, szDzozmdt0(xf)))))) | (~![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, tptp_fun_W2_13(W0)))) | (~![W3: $i] : (sdtlseqdt0(tptp_fun_W2_13(W0), W3) | (~((~((~aElementOf0(W3, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W4_14(W3, W0), W0)) | sdtlseqdt0(tptp_fun_W4_14(W3, W0), W3))))) | aUpperBoundOfIn0(W3, W0, szDzozmdt0(xf))))))))))),
% 10.27/6.60 inference(bind,[status(th)],[])).
% 10.27/6.60 tff(44,plain,
% 10.27/6.60 (![W0: $i] : ((~(aSubsetOf0(W0, szDzozmdt0(xf)) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), szDzozmdt0(xf)))))))) | (~((~aElementOf0(tptp_fun_W1_12(W0), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(tptp_fun_W1_12(W0), W2))) | (~aLowerBoundOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf))) | (~![W2: $i] : (sdtlseqdt0(W2, tptp_fun_W1_12(W0)) | (~((~((~aElementOf0(W2, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W3_2(W2, W0), W0)) | sdtlseqdt0(W2, tptp_fun_W3_2(W2, W0)))))) | aLowerBoundOfIn0(W2, W0, szDzozmdt0(xf)))))) | (~aInfimumOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf))) | (~aElementOf0(tptp_fun_W2_13(W0), szDzozmdt0(xf))) | (~![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, tptp_fun_W2_13(W0)))) | (~aUpperBoundOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf))) | (~![W3: $i] : (sdtlseqdt0(tptp_fun_W2_13(W0), W3) | (~((~((~aElementOf0(W3, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W4_14(W3, W0), W0)) | sdtlseqdt0(tptp_fun_W4_14(W3, W0), W3))))) | aUpperBoundOfIn0(W3, W0, szDzozmdt0(xf)))))) | (~aSupremumOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf)))))) <=> ![W0: $i] : ((~(aSubsetOf0(W0, szDzozmdt0(xf)) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), szDzozmdt0(xf)))))))) | (~((~aElementOf0(tptp_fun_W1_12(W0), szDzozmdt0(xf))) | (~aLowerBoundOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf))) | (~aInfimumOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf))) | (~aElementOf0(tptp_fun_W2_13(W0), szDzozmdt0(xf))) | (~aUpperBoundOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf))) | (~aSupremumOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(tptp_fun_W1_12(W0), W2))) | (~![W2: $i] : (sdtlseqdt0(W2, tptp_fun_W1_12(W0)) | (~((~((~aElementOf0(W2, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W3_2(W2, W0), W0)) | sdtlseqdt0(W2, tptp_fun_W3_2(W2, W0)))))) | aLowerBoundOfIn0(W2, W0, szDzozmdt0(xf)))))) | (~![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, tptp_fun_W2_13(W0)))) | (~![W3: $i] : (sdtlseqdt0(tptp_fun_W2_13(W0), W3) | (~((~((~aElementOf0(W3, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W4_14(W3, W0), W0)) | sdtlseqdt0(tptp_fun_W4_14(W3, W0), W3))))) | aUpperBoundOfIn0(W3, W0, szDzozmdt0(xf)))))))))),
% 10.27/6.60 inference(quant_intro,[status(thm)],[43])).
% 10.27/6.60 tff(45,plain,
% 10.27/6.60 (^[W0: $i] : refl(((~(aSubsetOf0(W0, szDzozmdt0(xf)) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), szDzozmdt0(xf)))))))) | (~((~aElementOf0(tptp_fun_W1_12(W0), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(tptp_fun_W1_12(W0), W2))) | (~aLowerBoundOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf))) | (~![W2: $i] : (sdtlseqdt0(W2, tptp_fun_W1_12(W0)) | (~((~((~aElementOf0(W2, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W3_2(W2, W0), W0)) | sdtlseqdt0(W2, tptp_fun_W3_2(W2, W0)))))) | aLowerBoundOfIn0(W2, W0, szDzozmdt0(xf)))))) | (~aInfimumOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf))) | (~aElementOf0(tptp_fun_W2_13(W0), szDzozmdt0(xf))) | (~![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, tptp_fun_W2_13(W0)))) | (~aUpperBoundOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf))) | (~![W3: $i] : (sdtlseqdt0(tptp_fun_W2_13(W0), W3) | (~((~((~aElementOf0(W3, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W4_14(W3, W0), W0)) | sdtlseqdt0(tptp_fun_W4_14(W3, W0), W3))))) | aUpperBoundOfIn0(W3, W0, szDzozmdt0(xf)))))) | (~aSupremumOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf)))))) <=> ((~(aSubsetOf0(W0, szDzozmdt0(xf)) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), szDzozmdt0(xf)))))))) | (~((~aElementOf0(tptp_fun_W1_12(W0), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(tptp_fun_W1_12(W0), W2))) | (~aLowerBoundOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf))) | (~![W2: $i] : (sdtlseqdt0(W2, tptp_fun_W1_12(W0)) | (~((~((~aElementOf0(W2, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W3_2(W2, W0), W0)) | sdtlseqdt0(W2, tptp_fun_W3_2(W2, W0)))))) | aLowerBoundOfIn0(W2, W0, szDzozmdt0(xf)))))) | (~aInfimumOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf))) | (~aElementOf0(tptp_fun_W2_13(W0), szDzozmdt0(xf))) | (~![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, tptp_fun_W2_13(W0)))) | (~aUpperBoundOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf))) | (~![W3: $i] : (sdtlseqdt0(tptp_fun_W2_13(W0), W3) | (~((~((~aElementOf0(W3, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W4_14(W3, W0), W0)) | sdtlseqdt0(tptp_fun_W4_14(W3, W0), W3))))) | aUpperBoundOfIn0(W3, W0, szDzozmdt0(xf)))))) | (~aSupremumOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf)))))))),
% 10.27/6.60 inference(bind,[status(th)],[])).
% 10.27/6.60 tff(46,plain,
% 10.27/6.60 (![W0: $i] : ((~(aSubsetOf0(W0, szDzozmdt0(xf)) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), szDzozmdt0(xf)))))))) | (~((~aElementOf0(tptp_fun_W1_12(W0), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(tptp_fun_W1_12(W0), W2))) | (~aLowerBoundOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf))) | (~![W2: $i] : (sdtlseqdt0(W2, tptp_fun_W1_12(W0)) | (~((~((~aElementOf0(W2, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W3_2(W2, W0), W0)) | sdtlseqdt0(W2, tptp_fun_W3_2(W2, W0)))))) | aLowerBoundOfIn0(W2, W0, szDzozmdt0(xf)))))) | (~aInfimumOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf))) | (~aElementOf0(tptp_fun_W2_13(W0), szDzozmdt0(xf))) | (~![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, tptp_fun_W2_13(W0)))) | (~aUpperBoundOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf))) | (~![W3: $i] : (sdtlseqdt0(tptp_fun_W2_13(W0), W3) | (~((~((~aElementOf0(W3, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W4_14(W3, W0), W0)) | sdtlseqdt0(tptp_fun_W4_14(W3, W0), W3))))) | aUpperBoundOfIn0(W3, W0, szDzozmdt0(xf)))))) | (~aSupremumOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf)))))) <=> ![W0: $i] : ((~(aSubsetOf0(W0, szDzozmdt0(xf)) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), szDzozmdt0(xf)))))))) | (~((~aElementOf0(tptp_fun_W1_12(W0), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(tptp_fun_W1_12(W0), W2))) | (~aLowerBoundOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf))) | (~![W2: $i] : (sdtlseqdt0(W2, tptp_fun_W1_12(W0)) | (~((~((~aElementOf0(W2, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W3_2(W2, W0), W0)) | sdtlseqdt0(W2, tptp_fun_W3_2(W2, W0)))))) | aLowerBoundOfIn0(W2, W0, szDzozmdt0(xf)))))) | (~aInfimumOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf))) | (~aElementOf0(tptp_fun_W2_13(W0), szDzozmdt0(xf))) | (~![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, tptp_fun_W2_13(W0)))) | (~aUpperBoundOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf))) | (~![W3: $i] : (sdtlseqdt0(tptp_fun_W2_13(W0), W3) | (~((~((~aElementOf0(W3, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W4_14(W3, W0), W0)) | sdtlseqdt0(tptp_fun_W4_14(W3, W0), W3))))) | aUpperBoundOfIn0(W3, W0, szDzozmdt0(xf)))))) | (~aSupremumOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf))))))),
% 10.27/6.60 inference(quant_intro,[status(thm)],[45])).
% 10.27/6.60 tff(47,plain,
% 10.27/6.60 (^[W0: $i] : rewrite(((~(aSubsetOf0(W0, szDzozmdt0(xf)) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), szDzozmdt0(xf)))))))) | (~((~aElementOf0(tptp_fun_W1_12(W0), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(tptp_fun_W1_12(W0), W2))) | (~aLowerBoundOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf))) | (~![W2: $i] : (sdtlseqdt0(W2, tptp_fun_W1_12(W0)) | (~((~((~aElementOf0(W2, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W3_2(W2, W0), W0)) | sdtlseqdt0(W2, tptp_fun_W3_2(W2, W0)))))) | aLowerBoundOfIn0(W2, W0, szDzozmdt0(xf)))))) | (~aInfimumOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf))) | (~aElementOf0(tptp_fun_W2_13(W0), szDzozmdt0(xf))) | (~![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, tptp_fun_W2_13(W0)))) | (~aUpperBoundOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf))) | (~![W3: $i] : (sdtlseqdt0(tptp_fun_W2_13(W0), W3) | (~((~((~aElementOf0(W3, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W4_14(W3, W0), W0)) | sdtlseqdt0(tptp_fun_W4_14(W3, W0), W3))))) | aUpperBoundOfIn0(W3, W0, szDzozmdt0(xf)))))) | (~aSupremumOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf)))))) <=> ((~(aSubsetOf0(W0, szDzozmdt0(xf)) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), szDzozmdt0(xf)))))))) | (~((~aElementOf0(tptp_fun_W1_12(W0), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(tptp_fun_W1_12(W0), W2))) | (~aLowerBoundOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf))) | (~![W2: $i] : (sdtlseqdt0(W2, tptp_fun_W1_12(W0)) | (~((~((~aElementOf0(W2, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W3_2(W2, W0), W0)) | sdtlseqdt0(W2, tptp_fun_W3_2(W2, W0)))))) | aLowerBoundOfIn0(W2, W0, szDzozmdt0(xf)))))) | (~aInfimumOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf))) | (~aElementOf0(tptp_fun_W2_13(W0), szDzozmdt0(xf))) | (~![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, tptp_fun_W2_13(W0)))) | (~aUpperBoundOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf))) | (~![W3: $i] : (sdtlseqdt0(tptp_fun_W2_13(W0), W3) | (~((~((~aElementOf0(W3, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W4_14(W3, W0), W0)) | sdtlseqdt0(tptp_fun_W4_14(W3, W0), W3))))) | aUpperBoundOfIn0(W3, W0, szDzozmdt0(xf)))))) | (~aSupremumOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf)))))))),
% 10.27/6.61 inference(bind,[status(th)],[])).
% 10.27/6.61 tff(48,plain,
% 10.27/6.61 (![W0: $i] : ((~(aSubsetOf0(W0, szDzozmdt0(xf)) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), szDzozmdt0(xf)))))))) | (~((~aElementOf0(tptp_fun_W1_12(W0), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(tptp_fun_W1_12(W0), W2))) | (~aLowerBoundOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf))) | (~![W2: $i] : (sdtlseqdt0(W2, tptp_fun_W1_12(W0)) | (~((~((~aElementOf0(W2, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W3_2(W2, W0), W0)) | sdtlseqdt0(W2, tptp_fun_W3_2(W2, W0)))))) | aLowerBoundOfIn0(W2, W0, szDzozmdt0(xf)))))) | (~aInfimumOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf))) | (~aElementOf0(tptp_fun_W2_13(W0), szDzozmdt0(xf))) | (~![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, tptp_fun_W2_13(W0)))) | (~aUpperBoundOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf))) | (~![W3: $i] : (sdtlseqdt0(tptp_fun_W2_13(W0), W3) | (~((~((~aElementOf0(W3, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W4_14(W3, W0), W0)) | sdtlseqdt0(tptp_fun_W4_14(W3, W0), W3))))) | aUpperBoundOfIn0(W3, W0, szDzozmdt0(xf)))))) | (~aSupremumOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf)))))) <=> ![W0: $i] : ((~(aSubsetOf0(W0, szDzozmdt0(xf)) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), szDzozmdt0(xf)))))))) | (~((~aElementOf0(tptp_fun_W1_12(W0), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(tptp_fun_W1_12(W0), W2))) | (~aLowerBoundOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf))) | (~![W2: $i] : (sdtlseqdt0(W2, tptp_fun_W1_12(W0)) | (~((~((~aElementOf0(W2, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W3_2(W2, W0), W0)) | sdtlseqdt0(W2, tptp_fun_W3_2(W2, W0)))))) | aLowerBoundOfIn0(W2, W0, szDzozmdt0(xf)))))) | (~aInfimumOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf))) | (~aElementOf0(tptp_fun_W2_13(W0), szDzozmdt0(xf))) | (~![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, tptp_fun_W2_13(W0)))) | (~aUpperBoundOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf))) | (~![W3: $i] : (sdtlseqdt0(tptp_fun_W2_13(W0), W3) | (~((~((~aElementOf0(W3, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W4_14(W3, W0), W0)) | sdtlseqdt0(tptp_fun_W4_14(W3, W0), W3))))) | aUpperBoundOfIn0(W3, W0, szDzozmdt0(xf)))))) | (~aSupremumOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf))))))),
% 10.27/6.61 inference(quant_intro,[status(thm)],[47])).
% 10.27/6.61 tff(49,plain,
% 10.27/6.61 (![W0: $i] : ((~(aSubsetOf0(W0, szDzozmdt0(xf)) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), szDzozmdt0(xf)))))))) | (~((~aElementOf0(tptp_fun_W1_12(W0), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(tptp_fun_W1_12(W0), W2))) | (~aLowerBoundOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf))) | (~![W2: $i] : (sdtlseqdt0(W2, tptp_fun_W1_12(W0)) | (~((~((~aElementOf0(W2, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W3_2(W2, W0), W0)) | sdtlseqdt0(W2, tptp_fun_W3_2(W2, W0)))))) | aLowerBoundOfIn0(W2, W0, szDzozmdt0(xf)))))) | (~aInfimumOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf))) | (~aElementOf0(tptp_fun_W2_13(W0), szDzozmdt0(xf))) | (~![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, tptp_fun_W2_13(W0)))) | (~aUpperBoundOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf))) | (~![W3: $i] : (sdtlseqdt0(tptp_fun_W2_13(W0), W3) | (~((~((~aElementOf0(W3, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W4_14(W3, W0), W0)) | sdtlseqdt0(tptp_fun_W4_14(W3, W0), W3))))) | aUpperBoundOfIn0(W3, W0, szDzozmdt0(xf)))))) | (~aSupremumOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf)))))) <=> ![W0: $i] : ((~(aSubsetOf0(W0, szDzozmdt0(xf)) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), szDzozmdt0(xf)))))))) | (~((~aElementOf0(tptp_fun_W1_12(W0), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(tptp_fun_W1_12(W0), W2))) | (~aLowerBoundOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf))) | (~![W2: $i] : (sdtlseqdt0(W2, tptp_fun_W1_12(W0)) | (~((~((~aElementOf0(W2, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W3_2(W2, W0), W0)) | sdtlseqdt0(W2, tptp_fun_W3_2(W2, W0)))))) | aLowerBoundOfIn0(W2, W0, szDzozmdt0(xf)))))) | (~aInfimumOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf))) | (~aElementOf0(tptp_fun_W2_13(W0), szDzozmdt0(xf))) | (~![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, tptp_fun_W2_13(W0)))) | (~aUpperBoundOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf))) | (~![W3: $i] : (sdtlseqdt0(tptp_fun_W2_13(W0), W3) | (~((~((~aElementOf0(W3, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W4_14(W3, W0), W0)) | sdtlseqdt0(tptp_fun_W4_14(W3, W0), W3))))) | aUpperBoundOfIn0(W3, W0, szDzozmdt0(xf)))))) | (~aSupremumOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf))))))),
% 10.27/6.61 inference(transitivity,[status(thm)],[48, 46])).
% 10.27/6.61 tff(50,plain,
% 10.27/6.61 (^[W0: $i] : rewrite((((~aSubsetOf0(W0, szDzozmdt0(xf))) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), szDzozmdt0(xf)))))) | (aElementOf0(tptp_fun_W1_12(W0), szDzozmdt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(tptp_fun_W1_12(W0), W2)) & aLowerBoundOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf)) & ![W2: $i] : (sdtlseqdt0(W2, tptp_fun_W1_12(W0)) | (((~aElementOf0(W2, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W3_2(W2, W0), W0)) | sdtlseqdt0(W2, tptp_fun_W3_2(W2, W0))))) & (~aLowerBoundOfIn0(W2, W0, szDzozmdt0(xf))))) & aInfimumOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf)) & aElementOf0(tptp_fun_W2_13(W0), szDzozmdt0(xf)) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, tptp_fun_W2_13(W0))) & aUpperBoundOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf)) & ![W3: $i] : (sdtlseqdt0(tptp_fun_W2_13(W0), W3) | (((~aElementOf0(W3, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W4_14(W3, W0), W0)) | sdtlseqdt0(tptp_fun_W4_14(W3, W0), W3)))) & (~aUpperBoundOfIn0(W3, W0, szDzozmdt0(xf))))) & aSupremumOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf)))) <=> ((~(aSubsetOf0(W0, szDzozmdt0(xf)) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), szDzozmdt0(xf)))))))) | (~((~aElementOf0(tptp_fun_W1_12(W0), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(tptp_fun_W1_12(W0), W2))) | (~aLowerBoundOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf))) | (~![W2: $i] : (sdtlseqdt0(W2, tptp_fun_W1_12(W0)) | (~((~((~aElementOf0(W2, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W3_2(W2, W0), W0)) | sdtlseqdt0(W2, tptp_fun_W3_2(W2, W0)))))) | aLowerBoundOfIn0(W2, W0, szDzozmdt0(xf)))))) | (~aInfimumOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf))) | (~aElementOf0(tptp_fun_W2_13(W0), szDzozmdt0(xf))) | (~![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, tptp_fun_W2_13(W0)))) | (~aUpperBoundOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf))) | (~![W3: $i] : (sdtlseqdt0(tptp_fun_W2_13(W0), W3) | (~((~((~aElementOf0(W3, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W4_14(W3, W0), W0)) | sdtlseqdt0(tptp_fun_W4_14(W3, W0), W3))))) | aUpperBoundOfIn0(W3, W0, szDzozmdt0(xf)))))) | (~aSupremumOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf)))))))),
% 10.27/6.61 inference(bind,[status(th)],[])).
% 10.27/6.61 tff(51,plain,
% 10.27/6.61 (![W0: $i] : (((~aSubsetOf0(W0, szDzozmdt0(xf))) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), szDzozmdt0(xf)))))) | (aElementOf0(tptp_fun_W1_12(W0), szDzozmdt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(tptp_fun_W1_12(W0), W2)) & aLowerBoundOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf)) & ![W2: $i] : (sdtlseqdt0(W2, tptp_fun_W1_12(W0)) | (((~aElementOf0(W2, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W3_2(W2, W0), W0)) | sdtlseqdt0(W2, tptp_fun_W3_2(W2, W0))))) & (~aLowerBoundOfIn0(W2, W0, szDzozmdt0(xf))))) & aInfimumOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf)) & aElementOf0(tptp_fun_W2_13(W0), szDzozmdt0(xf)) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, tptp_fun_W2_13(W0))) & aUpperBoundOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf)) & ![W3: $i] : (sdtlseqdt0(tptp_fun_W2_13(W0), W3) | (((~aElementOf0(W3, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W4_14(W3, W0), W0)) | sdtlseqdt0(tptp_fun_W4_14(W3, W0), W3)))) & (~aUpperBoundOfIn0(W3, W0, szDzozmdt0(xf))))) & aSupremumOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf)))) <=> ![W0: $i] : ((~(aSubsetOf0(W0, szDzozmdt0(xf)) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), szDzozmdt0(xf)))))))) | (~((~aElementOf0(tptp_fun_W1_12(W0), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(tptp_fun_W1_12(W0), W2))) | (~aLowerBoundOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf))) | (~![W2: $i] : (sdtlseqdt0(W2, tptp_fun_W1_12(W0)) | (~((~((~aElementOf0(W2, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W3_2(W2, W0), W0)) | sdtlseqdt0(W2, tptp_fun_W3_2(W2, W0)))))) | aLowerBoundOfIn0(W2, W0, szDzozmdt0(xf)))))) | (~aInfimumOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf))) | (~aElementOf0(tptp_fun_W2_13(W0), szDzozmdt0(xf))) | (~![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, tptp_fun_W2_13(W0)))) | (~aUpperBoundOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf))) | (~![W3: $i] : (sdtlseqdt0(tptp_fun_W2_13(W0), W3) | (~((~((~aElementOf0(W3, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W4_14(W3, W0), W0)) | sdtlseqdt0(tptp_fun_W4_14(W3, W0), W3))))) | aUpperBoundOfIn0(W3, W0, szDzozmdt0(xf)))))) | (~aSupremumOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf))))))),
% 10.27/6.61 inference(quant_intro,[status(thm)],[50])).
% 10.27/6.61 tff(52,plain,
% 10.27/6.61 (^[W0: $i] : rewrite((((~aSubsetOf0(W0, szDzozmdt0(xf))) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), szDzozmdt0(xf)))))) | (aElementOf0(tptp_fun_W1_12(W0), szDzozmdt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(tptp_fun_W1_12(W0), W2)) & aLowerBoundOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf)) & ![W2: $i] : ((((~aElementOf0(W2, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W3_2(W2, W0), W0)) | sdtlseqdt0(W2, tptp_fun_W3_2(W2, W0))))) & (~aLowerBoundOfIn0(W2, W0, szDzozmdt0(xf)))) | sdtlseqdt0(W2, tptp_fun_W1_12(W0))) & aInfimumOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf)) & (aElementOf0(tptp_fun_W2_13(W0), szDzozmdt0(xf)) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, tptp_fun_W2_13(W0))) & aUpperBoundOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf)) & ![W3: $i] : ((((~aElementOf0(W3, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W4_14(W3, W0), W0)) | sdtlseqdt0(tptp_fun_W4_14(W3, W0), W3)))) & (~aUpperBoundOfIn0(W3, W0, szDzozmdt0(xf)))) | sdtlseqdt0(tptp_fun_W2_13(W0), W3)) & aSupremumOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf))))) <=> (((~aSubsetOf0(W0, szDzozmdt0(xf))) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), szDzozmdt0(xf)))))) | (aElementOf0(tptp_fun_W1_12(W0), szDzozmdt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(tptp_fun_W1_12(W0), W2)) & aLowerBoundOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf)) & ![W2: $i] : (sdtlseqdt0(W2, tptp_fun_W1_12(W0)) | (((~aElementOf0(W2, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W3_2(W2, W0), W0)) | sdtlseqdt0(W2, tptp_fun_W3_2(W2, W0))))) & (~aLowerBoundOfIn0(W2, W0, szDzozmdt0(xf))))) & aInfimumOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf)) & aElementOf0(tptp_fun_W2_13(W0), szDzozmdt0(xf)) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, tptp_fun_W2_13(W0))) & aUpperBoundOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf)) & ![W3: $i] : (sdtlseqdt0(tptp_fun_W2_13(W0), W3) | (((~aElementOf0(W3, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W4_14(W3, W0), W0)) | sdtlseqdt0(tptp_fun_W4_14(W3, W0), W3)))) & (~aUpperBoundOfIn0(W3, W0, szDzozmdt0(xf))))) & aSupremumOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf)))))),
% 10.27/6.61 inference(bind,[status(th)],[])).
% 10.27/6.61 tff(53,plain,
% 10.27/6.61 (![W0: $i] : (((~aSubsetOf0(W0, szDzozmdt0(xf))) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), szDzozmdt0(xf)))))) | (aElementOf0(tptp_fun_W1_12(W0), szDzozmdt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(tptp_fun_W1_12(W0), W2)) & aLowerBoundOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf)) & ![W2: $i] : ((((~aElementOf0(W2, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W3_2(W2, W0), W0)) | sdtlseqdt0(W2, tptp_fun_W3_2(W2, W0))))) & (~aLowerBoundOfIn0(W2, W0, szDzozmdt0(xf)))) | sdtlseqdt0(W2, tptp_fun_W1_12(W0))) & aInfimumOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf)) & (aElementOf0(tptp_fun_W2_13(W0), szDzozmdt0(xf)) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, tptp_fun_W2_13(W0))) & aUpperBoundOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf)) & ![W3: $i] : ((((~aElementOf0(W3, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W4_14(W3, W0), W0)) | sdtlseqdt0(tptp_fun_W4_14(W3, W0), W3)))) & (~aUpperBoundOfIn0(W3, W0, szDzozmdt0(xf)))) | sdtlseqdt0(tptp_fun_W2_13(W0), W3)) & aSupremumOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf))))) <=> ![W0: $i] : (((~aSubsetOf0(W0, szDzozmdt0(xf))) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), szDzozmdt0(xf)))))) | (aElementOf0(tptp_fun_W1_12(W0), szDzozmdt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(tptp_fun_W1_12(W0), W2)) & aLowerBoundOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf)) & ![W2: $i] : (sdtlseqdt0(W2, tptp_fun_W1_12(W0)) | (((~aElementOf0(W2, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W3_2(W2, W0), W0)) | sdtlseqdt0(W2, tptp_fun_W3_2(W2, W0))))) & (~aLowerBoundOfIn0(W2, W0, szDzozmdt0(xf))))) & aInfimumOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf)) & aElementOf0(tptp_fun_W2_13(W0), szDzozmdt0(xf)) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, tptp_fun_W2_13(W0))) & aUpperBoundOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf)) & ![W3: $i] : (sdtlseqdt0(tptp_fun_W2_13(W0), W3) | (((~aElementOf0(W3, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W4_14(W3, W0), W0)) | sdtlseqdt0(tptp_fun_W4_14(W3, W0), W3)))) & (~aUpperBoundOfIn0(W3, W0, szDzozmdt0(xf))))) & aSupremumOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf))))),
% 10.27/6.61 inference(quant_intro,[status(thm)],[52])).
% 10.27/6.61 tff(54,plain,
% 10.27/6.61 (^[W0: $i] : rewrite(((~(aSubsetOf0(W0, szRzazndt0(xf)) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, szRzazndt0(xf)))))) | ?[W1: $i] : (aElementOf0(W1, szRzazndt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, W0, szRzazndt0(xf)) & ![W2: $i] : ((~((aElementOf0(W2, szRzazndt0(xf)) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, szRzazndt0(xf)))) | sdtlseqdt0(W2, W1)) & aInfimumOfIn0(W1, W0, szRzazndt0(xf)) & ?[W2: $i] : (aElementOf0(W2, szRzazndt0(xf)) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, W2)) & aUpperBoundOfIn0(W2, W0, szRzazndt0(xf)) & ![W3: $i] : ((~((aElementOf0(W3, szRzazndt0(xf)) & ![W4: $i] : ((~aElementOf0(W4, W0)) | sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, szRzazndt0(xf)))) | sdtlseqdt0(W2, W3)) & aSupremumOfIn0(W2, W0, szRzazndt0(xf))))) <=> ((~(aSubsetOf0(W0, szDzozmdt0(xf)) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, szDzozmdt0(xf)))))) | ?[W1: $i] : (aElementOf0(W1, szDzozmdt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, W0, szDzozmdt0(xf)) & ![W2: $i] : ((~((aElementOf0(W2, szDzozmdt0(xf)) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, szDzozmdt0(xf)))) | sdtlseqdt0(W2, W1)) & aInfimumOfIn0(W1, W0, szDzozmdt0(xf)) & ?[W2: $i] : (aElementOf0(W2, szDzozmdt0(xf)) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, W2)) & aUpperBoundOfIn0(W2, W0, szDzozmdt0(xf)) & ![W3: $i] : ((~((aElementOf0(W3, szDzozmdt0(xf)) & ![W4: $i] : ((~aElementOf0(W4, W0)) | sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, szDzozmdt0(xf)))) | sdtlseqdt0(W2, W3)) & aSupremumOfIn0(W2, W0, szDzozmdt0(xf))))))),
% 10.27/6.61 inference(bind,[status(th)],[])).
% 10.27/6.61 tff(55,plain,
% 10.27/6.61 (![W0: $i] : ((~(aSubsetOf0(W0, szRzazndt0(xf)) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, szRzazndt0(xf)))))) | ?[W1: $i] : (aElementOf0(W1, szRzazndt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, W0, szRzazndt0(xf)) & ![W2: $i] : ((~((aElementOf0(W2, szRzazndt0(xf)) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, szRzazndt0(xf)))) | sdtlseqdt0(W2, W1)) & aInfimumOfIn0(W1, W0, szRzazndt0(xf)) & ?[W2: $i] : (aElementOf0(W2, szRzazndt0(xf)) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, W2)) & aUpperBoundOfIn0(W2, W0, szRzazndt0(xf)) & ![W3: $i] : ((~((aElementOf0(W3, szRzazndt0(xf)) & ![W4: $i] : ((~aElementOf0(W4, W0)) | sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, szRzazndt0(xf)))) | sdtlseqdt0(W2, W3)) & aSupremumOfIn0(W2, W0, szRzazndt0(xf))))) <=> ![W0: $i] : ((~(aSubsetOf0(W0, szDzozmdt0(xf)) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, szDzozmdt0(xf)))))) | ?[W1: $i] : (aElementOf0(W1, szDzozmdt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, W0, szDzozmdt0(xf)) & ![W2: $i] : ((~((aElementOf0(W2, szDzozmdt0(xf)) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, szDzozmdt0(xf)))) | sdtlseqdt0(W2, W1)) & aInfimumOfIn0(W1, W0, szDzozmdt0(xf)) & ?[W2: $i] : (aElementOf0(W2, szDzozmdt0(xf)) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, W2)) & aUpperBoundOfIn0(W2, W0, szDzozmdt0(xf)) & ![W3: $i] : ((~((aElementOf0(W3, szDzozmdt0(xf)) & ![W4: $i] : ((~aElementOf0(W4, W0)) | sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, szDzozmdt0(xf)))) | sdtlseqdt0(W2, W3)) & aSupremumOfIn0(W2, W0, szDzozmdt0(xf)))))),
% 10.27/6.61 inference(quant_intro,[status(thm)],[54])).
% 10.27/6.61 tff(56,plain,
% 10.27/6.61 (^[W0: $i] : rewrite(((~(aSubsetOf0(W0, xU) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xU))))) | ?[W1: $i] : (aElementOf0(W1, xU) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, W0, xU) & ![W2: $i] : ((~((aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU))) | sdtlseqdt0(W2, W1)) & aInfimumOfIn0(W1, W0, xU) & ?[W2: $i] : (aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, W2)) & aUpperBoundOfIn0(W2, W0, xU) & ![W3: $i] : ((~((aElementOf0(W3, xU) & ![W4: $i] : ((~aElementOf0(W4, W0)) | sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU))) | sdtlseqdt0(W2, W3)) & aSupremumOfIn0(W2, W0, xU)))) <=> ((~(aSubsetOf0(W0, szRzazndt0(xf)) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, szRzazndt0(xf)))))) | ?[W1: $i] : (aElementOf0(W1, szRzazndt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, W0, szRzazndt0(xf)) & ![W2: $i] : ((~((aElementOf0(W2, szRzazndt0(xf)) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, szRzazndt0(xf)))) | sdtlseqdt0(W2, W1)) & aInfimumOfIn0(W1, W0, szRzazndt0(xf)) & ?[W2: $i] : (aElementOf0(W2, szRzazndt0(xf)) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, W2)) & aUpperBoundOfIn0(W2, W0, szRzazndt0(xf)) & ![W3: $i] : ((~((aElementOf0(W3, szRzazndt0(xf)) & ![W4: $i] : ((~aElementOf0(W4, W0)) | sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, szRzazndt0(xf)))) | sdtlseqdt0(W2, W3)) & aSupremumOfIn0(W2, W0, szRzazndt0(xf))))))),
% 10.27/6.62 inference(bind,[status(th)],[])).
% 10.27/6.62 tff(57,plain,
% 10.27/6.62 (![W0: $i] : ((~(aSubsetOf0(W0, xU) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xU))))) | ?[W1: $i] : (aElementOf0(W1, xU) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, W0, xU) & ![W2: $i] : ((~((aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU))) | sdtlseqdt0(W2, W1)) & aInfimumOfIn0(W1, W0, xU) & ?[W2: $i] : (aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, W2)) & aUpperBoundOfIn0(W2, W0, xU) & ![W3: $i] : ((~((aElementOf0(W3, xU) & ![W4: $i] : ((~aElementOf0(W4, W0)) | sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU))) | sdtlseqdt0(W2, W3)) & aSupremumOfIn0(W2, W0, xU)))) <=> ![W0: $i] : ((~(aSubsetOf0(W0, szRzazndt0(xf)) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, szRzazndt0(xf)))))) | ?[W1: $i] : (aElementOf0(W1, szRzazndt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, W0, szRzazndt0(xf)) & ![W2: $i] : ((~((aElementOf0(W2, szRzazndt0(xf)) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, szRzazndt0(xf)))) | sdtlseqdt0(W2, W1)) & aInfimumOfIn0(W1, W0, szRzazndt0(xf)) & ?[W2: $i] : (aElementOf0(W2, szRzazndt0(xf)) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, W2)) & aUpperBoundOfIn0(W2, W0, szRzazndt0(xf)) & ![W3: $i] : ((~((aElementOf0(W3, szRzazndt0(xf)) & ![W4: $i] : ((~aElementOf0(W4, W0)) | sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, szRzazndt0(xf)))) | sdtlseqdt0(W2, W3)) & aSupremumOfIn0(W2, W0, szRzazndt0(xf)))))),
% 10.27/6.62 inference(quant_intro,[status(thm)],[56])).
% 10.27/6.62 tff(58,plain,
% 10.27/6.62 (![W0: $i] : ((~(aSubsetOf0(W0, xU) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xU))))) | ?[W1: $i] : (aElementOf0(W1, xU) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, W0, xU) & ![W2: $i] : ((~((aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU))) | sdtlseqdt0(W2, W1)) & aInfimumOfIn0(W1, W0, xU) & ?[W2: $i] : (aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, W2)) & aUpperBoundOfIn0(W2, W0, xU) & ![W3: $i] : ((~((aElementOf0(W3, xU) & ![W4: $i] : ((~aElementOf0(W4, W0)) | sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU))) | sdtlseqdt0(W2, W3)) & aSupremumOfIn0(W2, W0, xU)))) <=> ![W0: $i] : ((~(aSubsetOf0(W0, xU) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xU))))) | ?[W1: $i] : (aElementOf0(W1, xU) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, W0, xU) & ![W2: $i] : ((~((aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU))) | sdtlseqdt0(W2, W1)) & aInfimumOfIn0(W1, W0, xU) & ?[W2: $i] : (aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, W2)) & aUpperBoundOfIn0(W2, W0, xU) & ![W3: $i] : ((~((aElementOf0(W3, xU) & ![W4: $i] : ((~aElementOf0(W4, W0)) | sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU))) | sdtlseqdt0(W2, W3)) & aSupremumOfIn0(W2, W0, xU))))),
% 10.27/6.62 inference(rewrite,[status(thm)],[])).
% 10.27/6.62 tff(59,plain,
% 10.27/6.62 (^[W0: $i] : trans(monotonicity(trans(monotonicity(rewrite((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xU))) <=> (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xU)))), (((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xU))) | aSubsetOf0(W0, xU)) <=> ((aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xU))) | aSubsetOf0(W0, xU)))), rewrite(((aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xU))) | aSubsetOf0(W0, xU)) <=> (aSubsetOf0(W0, xU) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xU))))), (((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xU))) | aSubsetOf0(W0, xU)) <=> (aSubsetOf0(W0, xU) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xU)))))), quant_intro(proof_bind(^[W1: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((aElementOf0(W1, xU) & aElementOf0(W1, xU)) & ![W2: $i] : (aElementOf0(W2, W0) => sdtlseqdt0(W1, W2))) <=> (aElementOf0(W1, xU) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)))), ((((aElementOf0(W1, xU) & aElementOf0(W1, xU)) & ![W2: $i] : (aElementOf0(W2, W0) => sdtlseqdt0(W1, W2))) & aLowerBoundOfIn0(W1, W0, xU)) <=> ((aElementOf0(W1, xU) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))) & aLowerBoundOfIn0(W1, W0, xU)))), rewrite(((aElementOf0(W1, xU) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))) & aLowerBoundOfIn0(W1, W0, xU)) <=> (aElementOf0(W1, xU) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, W0, xU))), ((((aElementOf0(W1, xU) & aElementOf0(W1, xU)) & ![W2: $i] : (aElementOf0(W2, W0) => sdtlseqdt0(W1, W2))) & aLowerBoundOfIn0(W1, W0, xU)) <=> (aElementOf0(W1, xU) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, W0, xU)))), quant_intro(proof_bind(^[W2: $i] : trans(monotonicity(rewrite(((aElementOf0(W2, xU) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU)) <=> ((aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU))), ((((aElementOf0(W2, xU) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU)) => sdtlseqdt0(W2, W1)) <=> (((aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU)) => sdtlseqdt0(W2, W1)))), rewrite((((aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU)) => sdtlseqdt0(W2, W1)) <=> ((~((aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU))) | sdtlseqdt0(W2, W1))), ((((aElementOf0(W2, xU) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU)) => sdtlseqdt0(W2, W1)) <=> ((~((aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU))) | sdtlseqdt0(W2, W1))))), (![W2: $i] : (((aElementOf0(W2, xU) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU)) => sdtlseqdt0(W2, W1)) <=> ![W2: $i] : ((~((aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU))) | sdtlseqdt0(W2, W1)))), (((((aElementOf0(W1, xU) & aElementOf0(W1, xU)) & ![W2: $i] : (aElementOf0(W2, W0) => sdtlseqdt0(W1, W2))) & aLowerBoundOfIn0(W1, W0, xU)) & ![W2: $i] : (((aElementOf0(W2, xU) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU)) => sdtlseqdt0(W2, W1))) <=> ((aElementOf0(W1, xU) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, W0, xU)) & ![W2: $i] : ((~((aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU))) | sdtlseqdt0(W2, W1))))), rewrite(((aElementOf0(W1, xU) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, W0, xU)) & ![W2: $i] : ((~((aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU))) | sdtlseqdt0(W2, W1))) <=> (aElementOf0(W1, xU) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, W0, xU) & ![W2: $i] : ((~((aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU))) | sdtlseqdt0(W2, W1)))), (((((aElementOf0(W1, xU) & aElementOf0(W1, xU)) & ![W2: $i] : (aElementOf0(W2, W0) => sdtlseqdt0(W1, W2))) & aLowerBoundOfIn0(W1, W0, xU)) & ![W2: $i] : (((aElementOf0(W2, xU) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU)) => sdtlseqdt0(W2, W1))) <=> (aElementOf0(W1, xU) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, W0, xU) & ![W2: $i] : ((~((aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU))) | sdtlseqdt0(W2, W1))))), ((((((aElementOf0(W1, xU) & aElementOf0(W1, xU)) & ![W2: $i] : (aElementOf0(W2, W0) => sdtlseqdt0(W1, W2))) & aLowerBoundOfIn0(W1, W0, xU)) & ![W2: $i] : (((aElementOf0(W2, xU) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU)) => sdtlseqdt0(W2, W1))) & aInfimumOfIn0(W1, W0, xU)) <=> ((aElementOf0(W1, xU) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, W0, xU) & ![W2: $i] : ((~((aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU))) | sdtlseqdt0(W2, W1))) & aInfimumOfIn0(W1, W0, xU)))), rewrite(((aElementOf0(W1, xU) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, W0, xU) & ![W2: $i] : ((~((aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU))) | sdtlseqdt0(W2, W1))) & aInfimumOfIn0(W1, W0, xU)) <=> (aElementOf0(W1, xU) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, W0, xU) & ![W2: $i] : ((~((aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU))) | sdtlseqdt0(W2, W1)) & aInfimumOfIn0(W1, W0, xU))), ((((((aElementOf0(W1, xU) & aElementOf0(W1, xU)) & ![W2: $i] : (aElementOf0(W2, W0) => sdtlseqdt0(W1, W2))) & aLowerBoundOfIn0(W1, W0, xU)) & ![W2: $i] : (((aElementOf0(W2, xU) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU)) => sdtlseqdt0(W2, W1))) & aInfimumOfIn0(W1, W0, xU)) <=> (aElementOf0(W1, xU) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, W0, xU) & ![W2: $i] : ((~((aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU))) | sdtlseqdt0(W2, W1)) & aInfimumOfIn0(W1, W0, xU)))), quant_intro(proof_bind(^[W2: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((aElementOf0(W2, xU) & aElementOf0(W2, xU)) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W3, W2))) <=> (aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, W2)))), ((((aElementOf0(W2, xU) & aElementOf0(W2, xU)) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W3, W2))) & aUpperBoundOfIn0(W2, W0, xU)) <=> ((aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, W2))) & aUpperBoundOfIn0(W2, W0, xU)))), rewrite(((aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, W2))) & aUpperBoundOfIn0(W2, W0, xU)) <=> (aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, W2)) & aUpperBoundOfIn0(W2, W0, xU))), ((((aElementOf0(W2, xU) & aElementOf0(W2, xU)) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W3, W2))) & aUpperBoundOfIn0(W2, W0, xU)) <=> (aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, W2)) & aUpperBoundOfIn0(W2, W0, xU)))), quant_intro(proof_bind(^[W3: $i] : trans(monotonicity(rewrite(((aElementOf0(W3, xU) & ![W4: $i] : (aElementOf0(W4, W0) => sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU)) <=> ((aElementOf0(W3, xU) & ![W4: $i] : ((~aElementOf0(W4, W0)) | sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU))), ((((aElementOf0(W3, xU) & ![W4: $i] : (aElementOf0(W4, W0) => sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU)) => sdtlseqdt0(W2, W3)) <=> (((aElementOf0(W3, xU) & ![W4: $i] : ((~aElementOf0(W4, W0)) | sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU)) => sdtlseqdt0(W2, W3)))), rewrite((((aElementOf0(W3, xU) & ![W4: $i] : ((~aElementOf0(W4, W0)) | sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU)) => sdtlseqdt0(W2, W3)) <=> ((~((aElementOf0(W3, xU) & ![W4: $i] : ((~aElementOf0(W4, W0)) | sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU))) | sdtlseqdt0(W2, W3))), ((((aElementOf0(W3, xU) & ![W4: $i] : (aElementOf0(W4, W0) => sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU)) => sdtlseqdt0(W2, W3)) <=> ((~((aElementOf0(W3, xU) & ![W4: $i] : ((~aElementOf0(W4, W0)) | sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU))) | sdtlseqdt0(W2, W3))))), (![W3: $i] : (((aElementOf0(W3, xU) & ![W4: $i] : (aElementOf0(W4, W0) => sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU)) => sdtlseqdt0(W2, W3)) <=> ![W3: $i] : ((~((aElementOf0(W3, xU) & ![W4: $i] : ((~aElementOf0(W4, W0)) | sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU))) | sdtlseqdt0(W2, W3)))), (((((aElementOf0(W2, xU) & aElementOf0(W2, xU)) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W3, W2))) & aUpperBoundOfIn0(W2, W0, xU)) & ![W3: $i] : (((aElementOf0(W3, xU) & ![W4: $i] : (aElementOf0(W4, W0) => sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU)) => sdtlseqdt0(W2, W3))) <=> ((aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, W2)) & aUpperBoundOfIn0(W2, W0, xU)) & ![W3: $i] : ((~((aElementOf0(W3, xU) & ![W4: $i] : ((~aElementOf0(W4, W0)) | sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU))) | sdtlseqdt0(W2, W3))))), rewrite(((aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, W2)) & aUpperBoundOfIn0(W2, W0, xU)) & ![W3: $i] : ((~((aElementOf0(W3, xU) & ![W4: $i] : ((~aElementOf0(W4, W0)) | sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU))) | sdtlseqdt0(W2, W3))) <=> (aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, W2)) & aUpperBoundOfIn0(W2, W0, xU) & ![W3: $i] : ((~((aElementOf0(W3, xU) & ![W4: $i] : ((~aElementOf0(W4, W0)) | sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU))) | sdtlseqdt0(W2, W3)))), (((((aElementOf0(W2, xU) & aElementOf0(W2, xU)) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W3, W2))) & aUpperBoundOfIn0(W2, W0, xU)) & ![W3: $i] : (((aElementOf0(W3, xU) & ![W4: $i] : (aElementOf0(W4, W0) => sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU)) => sdtlseqdt0(W2, W3))) <=> (aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, W2)) & aUpperBoundOfIn0(W2, W0, xU) & ![W3: $i] : ((~((aElementOf0(W3, xU) & ![W4: $i] : ((~aElementOf0(W4, W0)) | sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU))) | sdtlseqdt0(W2, W3))))), ((((((aElementOf0(W2, xU) & aElementOf0(W2, xU)) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W3, W2))) & aUpperBoundOfIn0(W2, W0, xU)) & ![W3: $i] : (((aElementOf0(W3, xU) & ![W4: $i] : (aElementOf0(W4, W0) => sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU)) => sdtlseqdt0(W2, W3))) & aSupremumOfIn0(W2, W0, xU)) <=> ((aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, W2)) & aUpperBoundOfIn0(W2, W0, xU) & ![W3: $i] : ((~((aElementOf0(W3, xU) & ![W4: $i] : ((~aElementOf0(W4, W0)) | sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU))) | sdtlseqdt0(W2, W3))) & aSupremumOfIn0(W2, W0, xU)))), rewrite(((aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, W2)) & aUpperBoundOfIn0(W2, W0, xU) & ![W3: $i] : ((~((aElementOf0(W3, xU) & ![W4: $i] : ((~aElementOf0(W4, W0)) | sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU))) | sdtlseqdt0(W2, W3))) & aSupremumOfIn0(W2, W0, xU)) <=> (aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, W2)) & aUpperBoundOfIn0(W2, W0, xU) & ![W3: $i] : ((~((aElementOf0(W3, xU) & ![W4: $i] : ((~aElementOf0(W4, W0)) | sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU))) | sdtlseqdt0(W2, W3)) & aSupremumOfIn0(W2, W0, xU))), ((((((aElementOf0(W2, xU) & aElementOf0(W2, xU)) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W3, W2))) & aUpperBoundOfIn0(W2, W0, xU)) & ![W3: $i] : (((aElementOf0(W3, xU) & ![W4: $i] : (aElementOf0(W4, W0) => sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU)) => sdtlseqdt0(W2, W3))) & aSupremumOfIn0(W2, W0, xU)) <=> (aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, W2)) & aUpperBoundOfIn0(W2, W0, xU) & ![W3: $i] : ((~((aElementOf0(W3, xU) & ![W4: $i] : ((~aElementOf0(W4, W0)) | sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU))) | sdtlseqdt0(W2, W3)) & aSupremumOfIn0(W2, W0, xU))))), (?[W2: $i] : (((((aElementOf0(W2, xU) & aElementOf0(W2, xU)) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W3, W2))) & aUpperBoundOfIn0(W2, W0, xU)) & ![W3: $i] : (((aElementOf0(W3, xU) & ![W4: $i] : (aElementOf0(W4, W0) => sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU)) => sdtlseqdt0(W2, W3))) & aSupremumOfIn0(W2, W0, xU)) <=> ?[W2: $i] : (aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, W2)) & aUpperBoundOfIn0(W2, W0, xU) & ![W3: $i] : ((~((aElementOf0(W3, xU) & ![W4: $i] : ((~aElementOf0(W4, W0)) | sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU))) | sdtlseqdt0(W2, W3)) & aSupremumOfIn0(W2, W0, xU)))), (((((((aElementOf0(W1, xU) & aElementOf0(W1, xU)) & ![W2: $i] : (aElementOf0(W2, W0) => sdtlseqdt0(W1, W2))) & aLowerBoundOfIn0(W1, W0, xU)) & ![W2: $i] : (((aElementOf0(W2, xU) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU)) => sdtlseqdt0(W2, W1))) & aInfimumOfIn0(W1, W0, xU)) & ?[W2: $i] : (((((aElementOf0(W2, xU) & aElementOf0(W2, xU)) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W3, W2))) & aUpperBoundOfIn0(W2, W0, xU)) & ![W3: $i] : (((aElementOf0(W3, xU) & ![W4: $i] : (aElementOf0(W4, W0) => sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU)) => sdtlseqdt0(W2, W3))) & aSupremumOfIn0(W2, W0, xU))) <=> ((aElementOf0(W1, xU) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, W0, xU) & ![W2: $i] : ((~((aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU))) | sdtlseqdt0(W2, W1)) & aInfimumOfIn0(W1, W0, xU)) & ?[W2: $i] : (aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, W2)) & aUpperBoundOfIn0(W2, W0, xU) & ![W3: $i] : ((~((aElementOf0(W3, xU) & ![W4: $i] : ((~aElementOf0(W4, W0)) | sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU))) | sdtlseqdt0(W2, W3)) & aSupremumOfIn0(W2, W0, xU))))), rewrite(((aElementOf0(W1, xU) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, W0, xU) & ![W2: $i] : ((~((aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU))) | sdtlseqdt0(W2, W1)) & aInfimumOfIn0(W1, W0, xU)) & ?[W2: $i] : (aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, W2)) & aUpperBoundOfIn0(W2, W0, xU) & ![W3: $i] : ((~((aElementOf0(W3, xU) & ![W4: $i] : ((~aElementOf0(W4, W0)) | sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU))) | sdtlseqdt0(W2, W3)) & aSupremumOfIn0(W2, W0, xU))) <=> (aElementOf0(W1, xU) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, W0, xU) & ![W2: $i] : ((~((aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU))) | sdtlseqdt0(W2, W1)) & aInfimumOfIn0(W1, W0, xU) & ?[W2: $i] : (aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, W2)) & aUpperBoundOfIn0(W2, W0, xU) & ![W3: $i] : ((~((aElementOf0(W3, xU) & ![W4: $i] : ((~aElementOf0(W4, W0)) | sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU))) | sdtlseqdt0(W2, W3)) & aSupremumOfIn0(W2, W0, xU)))), (((((((aElementOf0(W1, xU) & aElementOf0(W1, xU)) & ![W2: $i] : (aElementOf0(W2, W0) => sdtlseqdt0(W1, W2))) & aLowerBoundOfIn0(W1, W0, xU)) & ![W2: $i] : (((aElementOf0(W2, xU) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU)) => sdtlseqdt0(W2, W1))) & aInfimumOfIn0(W1, W0, xU)) & ?[W2: $i] : (((((aElementOf0(W2, xU) & aElementOf0(W2, xU)) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W3, W2))) & aUpperBoundOfIn0(W2, W0, xU)) & ![W3: $i] : (((aElementOf0(W3, xU) & ![W4: $i] : (aElementOf0(W4, W0) => sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU)) => sdtlseqdt0(W2, W3))) & aSupremumOfIn0(W2, W0, xU))) <=> (aElementOf0(W1, xU) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, W0, xU) & ![W2: $i] : ((~((aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU))) | sdtlseqdt0(W2, W1)) & aInfimumOfIn0(W1, W0, xU) & ?[W2: $i] : (aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, W2)) & aUpperBoundOfIn0(W2, W0, xU) & ![W3: $i] : ((~((aElementOf0(W3, xU) & ![W4: $i] : ((~aElementOf0(W4, W0)) | sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU))) | sdtlseqdt0(W2, W3)) & aSupremumOfIn0(W2, W0, xU)))))), (?[W1: $i] : ((((((aElementOf0(W1, xU) & aElementOf0(W1, xU)) & ![W2: $i] : (aElementOf0(W2, W0) => sdtlseqdt0(W1, W2))) & aLowerBoundOfIn0(W1, W0, xU)) & ![W2: $i] : (((aElementOf0(W2, xU) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU)) => sdtlseqdt0(W2, W1))) & aInfimumOfIn0(W1, W0, xU)) & ?[W2: $i] : (((((aElementOf0(W2, xU) & aElementOf0(W2, xU)) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W3, W2))) & aUpperBoundOfIn0(W2, W0, xU)) & ![W3: $i] : (((aElementOf0(W3, xU) & ![W4: $i] : (aElementOf0(W4, W0) => sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU)) => sdtlseqdt0(W2, W3))) & aSupremumOfIn0(W2, W0, xU))) <=> ?[W1: $i] : (aElementOf0(W1, xU) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, W0, xU) & ![W2: $i] : ((~((aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU))) | sdtlseqdt0(W2, W1)) & aInfimumOfIn0(W1, W0, xU) & ?[W2: $i] : (aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, W2)) & aUpperBoundOfIn0(W2, W0, xU) & ![W3: $i] : ((~((aElementOf0(W3, xU) & ![W4: $i] : ((~aElementOf0(W4, W0)) | sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU))) | sdtlseqdt0(W2, W3)) & aSupremumOfIn0(W2, W0, xU))))), ((((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xU))) | aSubsetOf0(W0, xU)) => ?[W1: $i] : ((((((aElementOf0(W1, xU) & aElementOf0(W1, xU)) & ![W2: $i] : (aElementOf0(W2, W0) => sdtlseqdt0(W1, W2))) & aLowerBoundOfIn0(W1, W0, xU)) & ![W2: $i] : (((aElementOf0(W2, xU) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU)) => sdtlseqdt0(W2, W1))) & aInfimumOfIn0(W1, W0, xU)) & ?[W2: $i] : (((((aElementOf0(W2, xU) & aElementOf0(W2, xU)) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W3, W2))) & aUpperBoundOfIn0(W2, W0, xU)) & ![W3: $i] : (((aElementOf0(W3, xU) & ![W4: $i] : (aElementOf0(W4, W0) => sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU)) => sdtlseqdt0(W2, W3))) & aSupremumOfIn0(W2, W0, xU)))) <=> ((aSubsetOf0(W0, xU) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xU)))) => ?[W1: $i] : (aElementOf0(W1, xU) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, W0, xU) & ![W2: $i] : ((~((aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU))) | sdtlseqdt0(W2, W1)) & aInfimumOfIn0(W1, W0, xU) & ?[W2: $i] : (aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, W2)) & aUpperBoundOfIn0(W2, W0, xU) & ![W3: $i] : ((~((aElementOf0(W3, xU) & ![W4: $i] : ((~aElementOf0(W4, W0)) | sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU))) | sdtlseqdt0(W2, W3)) & aSupremumOfIn0(W2, W0, xU)))))), rewrite(((aSubsetOf0(W0, xU) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xU)))) => ?[W1: $i] : (aElementOf0(W1, xU) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, W0, xU) & ![W2: $i] : ((~((aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU))) | sdtlseqdt0(W2, W1)) & aInfimumOfIn0(W1, W0, xU) & ?[W2: $i] : (aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, W2)) & aUpperBoundOfIn0(W2, W0, xU) & ![W3: $i] : ((~((aElementOf0(W3, xU) & ![W4: $i] : ((~aElementOf0(W4, W0)) | sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU))) | sdtlseqdt0(W2, W3)) & aSupremumOfIn0(W2, W0, xU)))) <=> ((~(aSubsetOf0(W0, xU) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xU))))) | ?[W1: $i] : (aElementOf0(W1, xU) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, W0, xU) & ![W2: $i] : ((~((aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU))) | sdtlseqdt0(W2, W1)) & aInfimumOfIn0(W1, W0, xU) & ?[W2: $i] : (aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, W2)) & aUpperBoundOfIn0(W2, W0, xU) & ![W3: $i] : ((~((aElementOf0(W3, xU) & ![W4: $i] : ((~aElementOf0(W4, W0)) | sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU))) | sdtlseqdt0(W2, W3)) & aSupremumOfIn0(W2, W0, xU))))), ((((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xU))) | aSubsetOf0(W0, xU)) => ?[W1: $i] : ((((((aElementOf0(W1, xU) & aElementOf0(W1, xU)) & ![W2: $i] : (aElementOf0(W2, W0) => sdtlseqdt0(W1, W2))) & aLowerBoundOfIn0(W1, W0, xU)) & ![W2: $i] : (((aElementOf0(W2, xU) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU)) => sdtlseqdt0(W2, W1))) & aInfimumOfIn0(W1, W0, xU)) & ?[W2: $i] : (((((aElementOf0(W2, xU) & aElementOf0(W2, xU)) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W3, W2))) & aUpperBoundOfIn0(W2, W0, xU)) & ![W3: $i] : (((aElementOf0(W3, xU) & ![W4: $i] : (aElementOf0(W4, W0) => sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU)) => sdtlseqdt0(W2, W3))) & aSupremumOfIn0(W2, W0, xU)))) <=> ((~(aSubsetOf0(W0, xU) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xU))))) | ?[W1: $i] : (aElementOf0(W1, xU) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, W0, xU) & ![W2: $i] : ((~((aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU))) | sdtlseqdt0(W2, W1)) & aInfimumOfIn0(W1, W0, xU) & ?[W2: $i] : (aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, W2)) & aUpperBoundOfIn0(W2, W0, xU) & ![W3: $i] : ((~((aElementOf0(W3, xU) & ![W4: $i] : ((~aElementOf0(W4, W0)) | sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU))) | sdtlseqdt0(W2, W3)) & aSupremumOfIn0(W2, W0, xU))))))),
% 10.27/6.63 inference(bind,[status(th)],[])).
% 10.27/6.63 tff(60,plain,
% 10.27/6.63 (![W0: $i] : (((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xU))) | aSubsetOf0(W0, xU)) => ?[W1: $i] : ((((((aElementOf0(W1, xU) & aElementOf0(W1, xU)) & ![W2: $i] : (aElementOf0(W2, W0) => sdtlseqdt0(W1, W2))) & aLowerBoundOfIn0(W1, W0, xU)) & ![W2: $i] : (((aElementOf0(W2, xU) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU)) => sdtlseqdt0(W2, W1))) & aInfimumOfIn0(W1, W0, xU)) & ?[W2: $i] : (((((aElementOf0(W2, xU) & aElementOf0(W2, xU)) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W3, W2))) & aUpperBoundOfIn0(W2, W0, xU)) & ![W3: $i] : (((aElementOf0(W3, xU) & ![W4: $i] : (aElementOf0(W4, W0) => sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU)) => sdtlseqdt0(W2, W3))) & aSupremumOfIn0(W2, W0, xU)))) <=> ![W0: $i] : ((~(aSubsetOf0(W0, xU) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xU))))) | ?[W1: $i] : (aElementOf0(W1, xU) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, W0, xU) & ![W2: $i] : ((~((aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU))) | sdtlseqdt0(W2, W1)) & aInfimumOfIn0(W1, W0, xU) & ?[W2: $i] : (aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, W2)) & aUpperBoundOfIn0(W2, W0, xU) & ![W3: $i] : ((~((aElementOf0(W3, xU) & ![W4: $i] : ((~aElementOf0(W4, W0)) | sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU))) | sdtlseqdt0(W2, W3)) & aSupremumOfIn0(W2, W0, xU))))),
% 10.27/6.63 inference(quant_intro,[status(thm)],[59])).
% 10.27/6.63 tff(61,axiom,((((((((aSet0(xU) & ![W0: $i] : (((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xU))) | aSubsetOf0(W0, xU)) => ?[W1: $i] : ((((((aElementOf0(W1, xU) & aElementOf0(W1, xU)) & ![W2: $i] : (aElementOf0(W2, W0) => sdtlseqdt0(W1, W2))) & aLowerBoundOfIn0(W1, W0, xU)) & ![W2: $i] : (((aElementOf0(W2, xU) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU)) => sdtlseqdt0(W2, W1))) & aInfimumOfIn0(W1, W0, xU)) & ?[W2: $i] : (((((aElementOf0(W2, xU) & aElementOf0(W2, xU)) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W3, W2))) & aUpperBoundOfIn0(W2, W0, xU)) & ![W3: $i] : (((aElementOf0(W3, xU) & ![W4: $i] : (aElementOf0(W4, W0) => sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU)) => sdtlseqdt0(W2, W3))) & aSupremumOfIn0(W2, W0, xU))))) & aCompleteLattice0(xU)) & aFunction0(xf)) & ![W0: $i, W1: $i] : ((aElementOf0(W0, szDzozmdt0(xf)) & aElementOf0(W1, szDzozmdt0(xf))) => (sdtlseqdt0(W0, W1) => sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1))))) & isMonotone0(xf)) & (szDzozmdt0(xf) = szRzazndt0(xf))) & (szRzazndt0(xf) = xU)) & isOn0(xf, xU)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__1123')).
% 10.27/6.64 tff(62,plain,
% 10.27/6.64 (((((((aSet0(xU) & ![W0: $i] : (((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xU))) | aSubsetOf0(W0, xU)) => ?[W1: $i] : ((((((aElementOf0(W1, xU) & aElementOf0(W1, xU)) & ![W2: $i] : (aElementOf0(W2, W0) => sdtlseqdt0(W1, W2))) & aLowerBoundOfIn0(W1, W0, xU)) & ![W2: $i] : (((aElementOf0(W2, xU) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU)) => sdtlseqdt0(W2, W1))) & aInfimumOfIn0(W1, W0, xU)) & ?[W2: $i] : (((((aElementOf0(W2, xU) & aElementOf0(W2, xU)) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W3, W2))) & aUpperBoundOfIn0(W2, W0, xU)) & ![W3: $i] : (((aElementOf0(W3, xU) & ![W4: $i] : (aElementOf0(W4, W0) => sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU)) => sdtlseqdt0(W2, W3))) & aSupremumOfIn0(W2, W0, xU))))) & aCompleteLattice0(xU)) & aFunction0(xf)) & ![W0: $i, W1: $i] : ((aElementOf0(W0, szDzozmdt0(xf)) & aElementOf0(W1, szDzozmdt0(xf))) => (sdtlseqdt0(W0, W1) => sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1))))) & isMonotone0(xf)) & (szDzozmdt0(xf) = szRzazndt0(xf))) & (szRzazndt0(xf) = xU)),
% 10.27/6.64 inference(and_elim,[status(thm)],[61])).
% 10.27/6.64 tff(63,plain,
% 10.27/6.64 ((((((aSet0(xU) & ![W0: $i] : (((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xU))) | aSubsetOf0(W0, xU)) => ?[W1: $i] : ((((((aElementOf0(W1, xU) & aElementOf0(W1, xU)) & ![W2: $i] : (aElementOf0(W2, W0) => sdtlseqdt0(W1, W2))) & aLowerBoundOfIn0(W1, W0, xU)) & ![W2: $i] : (((aElementOf0(W2, xU) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU)) => sdtlseqdt0(W2, W1))) & aInfimumOfIn0(W1, W0, xU)) & ?[W2: $i] : (((((aElementOf0(W2, xU) & aElementOf0(W2, xU)) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W3, W2))) & aUpperBoundOfIn0(W2, W0, xU)) & ![W3: $i] : (((aElementOf0(W3, xU) & ![W4: $i] : (aElementOf0(W4, W0) => sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU)) => sdtlseqdt0(W2, W3))) & aSupremumOfIn0(W2, W0, xU))))) & aCompleteLattice0(xU)) & aFunction0(xf)) & ![W0: $i, W1: $i] : ((aElementOf0(W0, szDzozmdt0(xf)) & aElementOf0(W1, szDzozmdt0(xf))) => (sdtlseqdt0(W0, W1) => sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1))))) & isMonotone0(xf)) & (szDzozmdt0(xf) = szRzazndt0(xf))),
% 10.27/6.64 inference(and_elim,[status(thm)],[62])).
% 10.27/6.64 tff(64,plain,
% 10.27/6.64 (((((aSet0(xU) & ![W0: $i] : (((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xU))) | aSubsetOf0(W0, xU)) => ?[W1: $i] : ((((((aElementOf0(W1, xU) & aElementOf0(W1, xU)) & ![W2: $i] : (aElementOf0(W2, W0) => sdtlseqdt0(W1, W2))) & aLowerBoundOfIn0(W1, W0, xU)) & ![W2: $i] : (((aElementOf0(W2, xU) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU)) => sdtlseqdt0(W2, W1))) & aInfimumOfIn0(W1, W0, xU)) & ?[W2: $i] : (((((aElementOf0(W2, xU) & aElementOf0(W2, xU)) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W3, W2))) & aUpperBoundOfIn0(W2, W0, xU)) & ![W3: $i] : (((aElementOf0(W3, xU) & ![W4: $i] : (aElementOf0(W4, W0) => sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU)) => sdtlseqdt0(W2, W3))) & aSupremumOfIn0(W2, W0, xU))))) & aCompleteLattice0(xU)) & aFunction0(xf)) & ![W0: $i, W1: $i] : ((aElementOf0(W0, szDzozmdt0(xf)) & aElementOf0(W1, szDzozmdt0(xf))) => (sdtlseqdt0(W0, W1) => sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1))))) & isMonotone0(xf)),
% 10.27/6.64 inference(and_elim,[status(thm)],[63])).
% 10.27/6.64 tff(65,plain,
% 10.27/6.64 ((((aSet0(xU) & ![W0: $i] : (((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xU))) | aSubsetOf0(W0, xU)) => ?[W1: $i] : ((((((aElementOf0(W1, xU) & aElementOf0(W1, xU)) & ![W2: $i] : (aElementOf0(W2, W0) => sdtlseqdt0(W1, W2))) & aLowerBoundOfIn0(W1, W0, xU)) & ![W2: $i] : (((aElementOf0(W2, xU) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU)) => sdtlseqdt0(W2, W1))) & aInfimumOfIn0(W1, W0, xU)) & ?[W2: $i] : (((((aElementOf0(W2, xU) & aElementOf0(W2, xU)) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W3, W2))) & aUpperBoundOfIn0(W2, W0, xU)) & ![W3: $i] : (((aElementOf0(W3, xU) & ![W4: $i] : (aElementOf0(W4, W0) => sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU)) => sdtlseqdt0(W2, W3))) & aSupremumOfIn0(W2, W0, xU))))) & aCompleteLattice0(xU)) & aFunction0(xf)) & ![W0: $i, W1: $i] : ((aElementOf0(W0, szDzozmdt0(xf)) & aElementOf0(W1, szDzozmdt0(xf))) => (sdtlseqdt0(W0, W1) => sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1))))),
% 10.27/6.64 inference(and_elim,[status(thm)],[64])).
% 10.27/6.64 tff(66,plain,
% 10.27/6.64 (((aSet0(xU) & ![W0: $i] : (((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xU))) | aSubsetOf0(W0, xU)) => ?[W1: $i] : ((((((aElementOf0(W1, xU) & aElementOf0(W1, xU)) & ![W2: $i] : (aElementOf0(W2, W0) => sdtlseqdt0(W1, W2))) & aLowerBoundOfIn0(W1, W0, xU)) & ![W2: $i] : (((aElementOf0(W2, xU) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU)) => sdtlseqdt0(W2, W1))) & aInfimumOfIn0(W1, W0, xU)) & ?[W2: $i] : (((((aElementOf0(W2, xU) & aElementOf0(W2, xU)) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W3, W2))) & aUpperBoundOfIn0(W2, W0, xU)) & ![W3: $i] : (((aElementOf0(W3, xU) & ![W4: $i] : (aElementOf0(W4, W0) => sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU)) => sdtlseqdt0(W2, W3))) & aSupremumOfIn0(W2, W0, xU))))) & aCompleteLattice0(xU)) & aFunction0(xf)),
% 10.27/6.64 inference(and_elim,[status(thm)],[65])).
% 10.27/6.64 tff(67,plain,
% 10.27/6.64 ((aSet0(xU) & ![W0: $i] : (((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xU))) | aSubsetOf0(W0, xU)) => ?[W1: $i] : ((((((aElementOf0(W1, xU) & aElementOf0(W1, xU)) & ![W2: $i] : (aElementOf0(W2, W0) => sdtlseqdt0(W1, W2))) & aLowerBoundOfIn0(W1, W0, xU)) & ![W2: $i] : (((aElementOf0(W2, xU) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU)) => sdtlseqdt0(W2, W1))) & aInfimumOfIn0(W1, W0, xU)) & ?[W2: $i] : (((((aElementOf0(W2, xU) & aElementOf0(W2, xU)) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W3, W2))) & aUpperBoundOfIn0(W2, W0, xU)) & ![W3: $i] : (((aElementOf0(W3, xU) & ![W4: $i] : (aElementOf0(W4, W0) => sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU)) => sdtlseqdt0(W2, W3))) & aSupremumOfIn0(W2, W0, xU))))) & aCompleteLattice0(xU)),
% 10.27/6.64 inference(and_elim,[status(thm)],[66])).
% 10.27/6.64 tff(68,plain,
% 10.27/6.64 (aSet0(xU) & ![W0: $i] : (((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xU))) | aSubsetOf0(W0, xU)) => ?[W1: $i] : ((((((aElementOf0(W1, xU) & aElementOf0(W1, xU)) & ![W2: $i] : (aElementOf0(W2, W0) => sdtlseqdt0(W1, W2))) & aLowerBoundOfIn0(W1, W0, xU)) & ![W2: $i] : (((aElementOf0(W2, xU) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU)) => sdtlseqdt0(W2, W1))) & aInfimumOfIn0(W1, W0, xU)) & ?[W2: $i] : (((((aElementOf0(W2, xU) & aElementOf0(W2, xU)) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W3, W2))) & aUpperBoundOfIn0(W2, W0, xU)) & ![W3: $i] : (((aElementOf0(W3, xU) & ![W4: $i] : (aElementOf0(W4, W0) => sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU)) => sdtlseqdt0(W2, W3))) & aSupremumOfIn0(W2, W0, xU))))),
% 10.27/6.64 inference(and_elim,[status(thm)],[67])).
% 10.27/6.64 tff(69,plain,
% 10.27/6.64 (![W0: $i] : (((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xU))) | aSubsetOf0(W0, xU)) => ?[W1: $i] : ((((((aElementOf0(W1, xU) & aElementOf0(W1, xU)) & ![W2: $i] : (aElementOf0(W2, W0) => sdtlseqdt0(W1, W2))) & aLowerBoundOfIn0(W1, W0, xU)) & ![W2: $i] : (((aElementOf0(W2, xU) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU)) => sdtlseqdt0(W2, W1))) & aInfimumOfIn0(W1, W0, xU)) & ?[W2: $i] : (((((aElementOf0(W2, xU) & aElementOf0(W2, xU)) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W3, W2))) & aUpperBoundOfIn0(W2, W0, xU)) & ![W3: $i] : (((aElementOf0(W3, xU) & ![W4: $i] : (aElementOf0(W4, W0) => sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU)) => sdtlseqdt0(W2, W3))) & aSupremumOfIn0(W2, W0, xU))))),
% 10.27/6.64 inference(and_elim,[status(thm)],[68])).
% 10.27/6.64 tff(70,plain,
% 10.27/6.64 (![W0: $i] : ((~(aSubsetOf0(W0, xU) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xU))))) | ?[W1: $i] : (aElementOf0(W1, xU) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, W0, xU) & ![W2: $i] : ((~((aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU))) | sdtlseqdt0(W2, W1)) & aInfimumOfIn0(W1, W0, xU) & ?[W2: $i] : (aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, W2)) & aUpperBoundOfIn0(W2, W0, xU) & ![W3: $i] : ((~((aElementOf0(W3, xU) & ![W4: $i] : ((~aElementOf0(W4, W0)) | sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU))) | sdtlseqdt0(W2, W3)) & aSupremumOfIn0(W2, W0, xU))))),
% 10.27/6.64 inference(modus_ponens,[status(thm)],[69, 60])).
% 10.27/6.64 tff(71,plain,
% 10.27/6.64 (![W0: $i] : ((~(aSubsetOf0(W0, xU) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xU))))) | ?[W1: $i] : (aElementOf0(W1, xU) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, W0, xU) & ![W2: $i] : ((~((aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU))) | sdtlseqdt0(W2, W1)) & aInfimumOfIn0(W1, W0, xU) & ?[W2: $i] : (aElementOf0(W2, xU) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, W2)) & aUpperBoundOfIn0(W2, W0, xU) & ![W3: $i] : ((~((aElementOf0(W3, xU) & ![W4: $i] : ((~aElementOf0(W4, W0)) | sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU))) | sdtlseqdt0(W2, W3)) & aSupremumOfIn0(W2, W0, xU))))),
% 10.27/6.64 inference(modus_ponens,[status(thm)],[70, 58])).
% 10.27/6.64 tff(72,plain,
% 10.27/6.64 (![W0: $i] : ((~(aSubsetOf0(W0, szRzazndt0(xf)) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, szRzazndt0(xf)))))) | ?[W1: $i] : (aElementOf0(W1, szRzazndt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, W0, szRzazndt0(xf)) & ![W2: $i] : ((~((aElementOf0(W2, szRzazndt0(xf)) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, szRzazndt0(xf)))) | sdtlseqdt0(W2, W1)) & aInfimumOfIn0(W1, W0, szRzazndt0(xf)) & ?[W2: $i] : (aElementOf0(W2, szRzazndt0(xf)) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, W2)) & aUpperBoundOfIn0(W2, W0, szRzazndt0(xf)) & ![W3: $i] : ((~((aElementOf0(W3, szRzazndt0(xf)) & ![W4: $i] : ((~aElementOf0(W4, W0)) | sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, szRzazndt0(xf)))) | sdtlseqdt0(W2, W3)) & aSupremumOfIn0(W2, W0, szRzazndt0(xf)))))),
% 10.27/6.64 inference(modus_ponens,[status(thm)],[71, 57])).
% 10.27/6.64 tff(73,plain,
% 10.27/6.64 (![W0: $i] : ((~(aSubsetOf0(W0, szDzozmdt0(xf)) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, szDzozmdt0(xf)))))) | ?[W1: $i] : (aElementOf0(W1, szDzozmdt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)) & aLowerBoundOfIn0(W1, W0, szDzozmdt0(xf)) & ![W2: $i] : ((~((aElementOf0(W2, szDzozmdt0(xf)) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, szDzozmdt0(xf)))) | sdtlseqdt0(W2, W1)) & aInfimumOfIn0(W1, W0, szDzozmdt0(xf)) & ?[W2: $i] : (aElementOf0(W2, szDzozmdt0(xf)) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, W2)) & aUpperBoundOfIn0(W2, W0, szDzozmdt0(xf)) & ![W3: $i] : ((~((aElementOf0(W3, szDzozmdt0(xf)) & ![W4: $i] : ((~aElementOf0(W4, W0)) | sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, szDzozmdt0(xf)))) | sdtlseqdt0(W2, W3)) & aSupremumOfIn0(W2, W0, szDzozmdt0(xf)))))),
% 10.27/6.64 inference(modus_ponens,[status(thm)],[72, 55])).
% 10.27/6.64 tff(74,plain,(
% 10.27/6.64 ![W0: $i] : (((~aSubsetOf0(W0, szDzozmdt0(xf))) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), szDzozmdt0(xf)))))) | (aElementOf0(tptp_fun_W1_12(W0), szDzozmdt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(tptp_fun_W1_12(W0), W2)) & aLowerBoundOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf)) & ![W2: $i] : ((((~aElementOf0(W2, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W3_2(W2, W0), W0)) | sdtlseqdt0(W2, tptp_fun_W3_2(W2, W0))))) & (~aLowerBoundOfIn0(W2, W0, szDzozmdt0(xf)))) | sdtlseqdt0(W2, tptp_fun_W1_12(W0))) & aInfimumOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf)) & (aElementOf0(tptp_fun_W2_13(W0), szDzozmdt0(xf)) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, tptp_fun_W2_13(W0))) & aUpperBoundOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf)) & ![W3: $i] : ((((~aElementOf0(W3, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W4_14(W3, W0), W0)) | sdtlseqdt0(tptp_fun_W4_14(W3, W0), W3)))) & (~aUpperBoundOfIn0(W3, W0, szDzozmdt0(xf)))) | sdtlseqdt0(tptp_fun_W2_13(W0), W3)) & aSupremumOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf)))))),
% 10.27/6.64 inference(skolemize,[status(sab)],[73])).
% 10.27/6.64 tff(75,plain,
% 10.27/6.64 (![W0: $i] : (((~aSubsetOf0(W0, szDzozmdt0(xf))) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), szDzozmdt0(xf)))))) | (aElementOf0(tptp_fun_W1_12(W0), szDzozmdt0(xf)) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(tptp_fun_W1_12(W0), W2)) & aLowerBoundOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf)) & ![W2: $i] : (sdtlseqdt0(W2, tptp_fun_W1_12(W0)) | (((~aElementOf0(W2, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W3_2(W2, W0), W0)) | sdtlseqdt0(W2, tptp_fun_W3_2(W2, W0))))) & (~aLowerBoundOfIn0(W2, W0, szDzozmdt0(xf))))) & aInfimumOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf)) & aElementOf0(tptp_fun_W2_13(W0), szDzozmdt0(xf)) & ![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, tptp_fun_W2_13(W0))) & aUpperBoundOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf)) & ![W3: $i] : (sdtlseqdt0(tptp_fun_W2_13(W0), W3) | (((~aElementOf0(W3, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W4_14(W3, W0), W0)) | sdtlseqdt0(tptp_fun_W4_14(W3, W0), W3)))) & (~aUpperBoundOfIn0(W3, W0, szDzozmdt0(xf))))) & aSupremumOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf))))),
% 10.27/6.64 inference(modus_ponens,[status(thm)],[74, 53])).
% 10.27/6.64 tff(76,plain,
% 10.27/6.64 (![W0: $i] : ((~(aSubsetOf0(W0, szDzozmdt0(xf)) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), szDzozmdt0(xf)))))))) | (~((~aElementOf0(tptp_fun_W1_12(W0), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(tptp_fun_W1_12(W0), W2))) | (~aLowerBoundOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf))) | (~![W2: $i] : (sdtlseqdt0(W2, tptp_fun_W1_12(W0)) | (~((~((~aElementOf0(W2, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W3_2(W2, W0), W0)) | sdtlseqdt0(W2, tptp_fun_W3_2(W2, W0)))))) | aLowerBoundOfIn0(W2, W0, szDzozmdt0(xf)))))) | (~aInfimumOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf))) | (~aElementOf0(tptp_fun_W2_13(W0), szDzozmdt0(xf))) | (~![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, tptp_fun_W2_13(W0)))) | (~aUpperBoundOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf))) | (~![W3: $i] : (sdtlseqdt0(tptp_fun_W2_13(W0), W3) | (~((~((~aElementOf0(W3, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W4_14(W3, W0), W0)) | sdtlseqdt0(tptp_fun_W4_14(W3, W0), W3))))) | aUpperBoundOfIn0(W3, W0, szDzozmdt0(xf)))))) | (~aSupremumOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf))))))),
% 10.27/6.64 inference(modus_ponens,[status(thm)],[75, 51])).
% 10.27/6.64 tff(77,plain,
% 10.27/6.64 (![W0: $i] : ((~(aSubsetOf0(W0, szDzozmdt0(xf)) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), szDzozmdt0(xf)))))))) | (~((~aElementOf0(tptp_fun_W1_12(W0), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(tptp_fun_W1_12(W0), W2))) | (~aLowerBoundOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf))) | (~![W2: $i] : (sdtlseqdt0(W2, tptp_fun_W1_12(W0)) | (~((~((~aElementOf0(W2, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W3_2(W2, W0), W0)) | sdtlseqdt0(W2, tptp_fun_W3_2(W2, W0)))))) | aLowerBoundOfIn0(W2, W0, szDzozmdt0(xf)))))) | (~aInfimumOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf))) | (~aElementOf0(tptp_fun_W2_13(W0), szDzozmdt0(xf))) | (~![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, tptp_fun_W2_13(W0)))) | (~aUpperBoundOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf))) | (~![W3: $i] : (sdtlseqdt0(tptp_fun_W2_13(W0), W3) | (~((~((~aElementOf0(W3, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W4_14(W3, W0), W0)) | sdtlseqdt0(tptp_fun_W4_14(W3, W0), W3))))) | aUpperBoundOfIn0(W3, W0, szDzozmdt0(xf)))))) | (~aSupremumOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf))))))),
% 10.27/6.65 inference(modus_ponens,[status(thm)],[76, 49])).
% 10.27/6.65 tff(78,plain,
% 10.27/6.65 (![W0: $i] : ((~(aSubsetOf0(W0, szDzozmdt0(xf)) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), szDzozmdt0(xf)))))))) | (~((~aElementOf0(tptp_fun_W1_12(W0), szDzozmdt0(xf))) | (~aLowerBoundOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf))) | (~aInfimumOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf))) | (~aElementOf0(tptp_fun_W2_13(W0), szDzozmdt0(xf))) | (~aUpperBoundOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf))) | (~aSupremumOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(tptp_fun_W1_12(W0), W2))) | (~![W2: $i] : (sdtlseqdt0(W2, tptp_fun_W1_12(W0)) | (~((~((~aElementOf0(W2, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W3_2(W2, W0), W0)) | sdtlseqdt0(W2, tptp_fun_W3_2(W2, W0)))))) | aLowerBoundOfIn0(W2, W0, szDzozmdt0(xf)))))) | (~![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, tptp_fun_W2_13(W0)))) | (~![W3: $i] : (sdtlseqdt0(tptp_fun_W2_13(W0), W3) | (~((~((~aElementOf0(W3, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W4_14(W3, W0), W0)) | sdtlseqdt0(tptp_fun_W4_14(W3, W0), W3))))) | aUpperBoundOfIn0(W3, W0, szDzozmdt0(xf)))))))))),
% 10.27/6.65 inference(modus_ponens,[status(thm)],[77, 44])).
% 10.27/6.65 tff(79,plain,
% 10.27/6.65 (((~![W0: $i] : ((~(aSubsetOf0(W0, szDzozmdt0(xf)) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), szDzozmdt0(xf)))))))) | (~((~aElementOf0(tptp_fun_W1_12(W0), szDzozmdt0(xf))) | (~aLowerBoundOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf))) | (~aInfimumOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf))) | (~aElementOf0(tptp_fun_W2_13(W0), szDzozmdt0(xf))) | (~aUpperBoundOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf))) | (~aSupremumOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(tptp_fun_W1_12(W0), W2))) | (~![W2: $i] : (sdtlseqdt0(W2, tptp_fun_W1_12(W0)) | (~((~((~aElementOf0(W2, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W3_2(W2, W0), W0)) | sdtlseqdt0(W2, tptp_fun_W3_2(W2, W0)))))) | aLowerBoundOfIn0(W2, W0, szDzozmdt0(xf)))))) | (~![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, tptp_fun_W2_13(W0)))) | (~![W3: $i] : (sdtlseqdt0(tptp_fun_W2_13(W0), W3) | (~((~((~aElementOf0(W3, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W4_14(W3, W0), W0)) | sdtlseqdt0(tptp_fun_W4_14(W3, W0), W3))))) | aUpperBoundOfIn0(W3, W0, szDzozmdt0(xf)))))))))) | ((~(aSubsetOf0(cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | (~((~aSet0(cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT))) | aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf)))))))) | (~((~aElementOf0(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | (~aLowerBoundOfIn0(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) | (~aInfimumOfIn0(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) | (~aElementOf0(tptp_fun_W2_13(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | (~aUpperBoundOfIn0(tptp_fun_W2_13(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) | (~aSupremumOfIn0(tptp_fun_W2_13(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)), W2))) | (~![W2: $i] : (sdtlseqdt0(W2, tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT))) | (~((~((~aElementOf0(W2, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W3_2(W2, cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W2, tptp_fun_W3_2(W2, cS1241(szDzozmdt0(xf), xf, xT))))))) | aLowerBoundOfIn0(W2, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))))) | (~![W3: $i] : ((~aElementOf0(W3, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W3, tptp_fun_W2_13(cS1241(szDzozmdt0(xf), xf, xT))))) | (~![W3: $i] : (sdtlseqdt0(tptp_fun_W2_13(cS1241(szDzozmdt0(xf), xf, xT)), W3) | (~((~((~aElementOf0(W3, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W4_14(W3, cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W4_14(W3, cS1241(szDzozmdt0(xf), xf, xT)), W3))))) | aUpperBoundOfIn0(W3, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))))))))) <=> ((~![W0: $i] : ((~(aSubsetOf0(W0, szDzozmdt0(xf)) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), szDzozmdt0(xf)))))))) | (~((~aElementOf0(tptp_fun_W1_12(W0), szDzozmdt0(xf))) | (~aLowerBoundOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf))) | (~aInfimumOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf))) | (~aElementOf0(tptp_fun_W2_13(W0), szDzozmdt0(xf))) | (~aUpperBoundOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf))) | (~aSupremumOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(tptp_fun_W1_12(W0), W2))) | (~![W2: $i] : (sdtlseqdt0(W2, tptp_fun_W1_12(W0)) | (~((~((~aElementOf0(W2, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W3_2(W2, W0), W0)) | sdtlseqdt0(W2, tptp_fun_W3_2(W2, W0)))))) | aLowerBoundOfIn0(W2, W0, szDzozmdt0(xf)))))) | (~![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, tptp_fun_W2_13(W0)))) | (~![W3: $i] : (sdtlseqdt0(tptp_fun_W2_13(W0), W3) | (~((~((~aElementOf0(W3, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W4_14(W3, W0), W0)) | sdtlseqdt0(tptp_fun_W4_14(W3, W0), W3))))) | aUpperBoundOfIn0(W3, W0, szDzozmdt0(xf)))))))))) | (~(aSubsetOf0(cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | (~((~aSet0(cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT))) | aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf)))))))) | (~((~aElementOf0(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | (~aLowerBoundOfIn0(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) | (~aInfimumOfIn0(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) | (~aElementOf0(tptp_fun_W2_13(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | (~aUpperBoundOfIn0(tptp_fun_W2_13(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) | (~aSupremumOfIn0(tptp_fun_W2_13(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)), W2))) | (~![W2: $i] : (sdtlseqdt0(W2, tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT))) | (~((~((~aElementOf0(W2, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W3_2(W2, cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W2, tptp_fun_W3_2(W2, cS1241(szDzozmdt0(xf), xf, xT))))))) | aLowerBoundOfIn0(W2, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))))) | (~![W3: $i] : ((~aElementOf0(W3, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W3, tptp_fun_W2_13(cS1241(szDzozmdt0(xf), xf, xT))))) | (~![W3: $i] : (sdtlseqdt0(tptp_fun_W2_13(cS1241(szDzozmdt0(xf), xf, xT)), W3) | (~((~((~aElementOf0(W3, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W4_14(W3, cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W4_14(W3, cS1241(szDzozmdt0(xf), xf, xT)), W3))))) | aUpperBoundOfIn0(W3, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))))))))),
% 10.27/6.65 inference(rewrite,[status(thm)],[])).
% 10.27/6.65 tff(80,plain,
% 10.27/6.65 ((~![W0: $i] : ((~(aSubsetOf0(W0, szDzozmdt0(xf)) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), szDzozmdt0(xf)))))))) | (~((~aElementOf0(tptp_fun_W1_12(W0), szDzozmdt0(xf))) | (~aLowerBoundOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf))) | (~aInfimumOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf))) | (~aElementOf0(tptp_fun_W2_13(W0), szDzozmdt0(xf))) | (~aUpperBoundOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf))) | (~aSupremumOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(tptp_fun_W1_12(W0), W2))) | (~![W2: $i] : (sdtlseqdt0(W2, tptp_fun_W1_12(W0)) | (~((~((~aElementOf0(W2, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W3_2(W2, W0), W0)) | sdtlseqdt0(W2, tptp_fun_W3_2(W2, W0)))))) | aLowerBoundOfIn0(W2, W0, szDzozmdt0(xf)))))) | (~![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, tptp_fun_W2_13(W0)))) | (~![W3: $i] : (sdtlseqdt0(tptp_fun_W2_13(W0), W3) | (~((~((~aElementOf0(W3, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W4_14(W3, W0), W0)) | sdtlseqdt0(tptp_fun_W4_14(W3, W0), W3))))) | aUpperBoundOfIn0(W3, W0, szDzozmdt0(xf)))))))))) | ((~(aSubsetOf0(cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | (~((~aSet0(cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT))) | aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf)))))))) | (~((~aElementOf0(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | (~aLowerBoundOfIn0(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) | (~aInfimumOfIn0(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) | (~aElementOf0(tptp_fun_W2_13(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | (~aUpperBoundOfIn0(tptp_fun_W2_13(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) | (~aSupremumOfIn0(tptp_fun_W2_13(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)), W2))) | (~![W2: $i] : (sdtlseqdt0(W2, tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT))) | (~((~((~aElementOf0(W2, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W3_2(W2, cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W2, tptp_fun_W3_2(W2, cS1241(szDzozmdt0(xf), xf, xT))))))) | aLowerBoundOfIn0(W2, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))))) | (~![W3: $i] : ((~aElementOf0(W3, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W3, tptp_fun_W2_13(cS1241(szDzozmdt0(xf), xf, xT))))) | (~![W3: $i] : (sdtlseqdt0(tptp_fun_W2_13(cS1241(szDzozmdt0(xf), xf, xT)), W3) | (~((~((~aElementOf0(W3, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W4_14(W3, cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W4_14(W3, cS1241(szDzozmdt0(xf), xf, xT)), W3))))) | aUpperBoundOfIn0(W3, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))))))))),
% 10.27/6.65 inference(quant_inst,[status(thm)],[])).
% 10.27/6.65 tff(81,plain,
% 10.27/6.65 ((~![W0: $i] : ((~(aSubsetOf0(W0, szDzozmdt0(xf)) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_11(W0), W0)) | aElementOf0(tptp_fun_W1_11(W0), szDzozmdt0(xf)))))))) | (~((~aElementOf0(tptp_fun_W1_12(W0), szDzozmdt0(xf))) | (~aLowerBoundOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf))) | (~aInfimumOfIn0(tptp_fun_W1_12(W0), W0, szDzozmdt0(xf))) | (~aElementOf0(tptp_fun_W2_13(W0), szDzozmdt0(xf))) | (~aUpperBoundOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf))) | (~aSupremumOfIn0(tptp_fun_W2_13(W0), W0, szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(tptp_fun_W1_12(W0), W2))) | (~![W2: $i] : (sdtlseqdt0(W2, tptp_fun_W1_12(W0)) | (~((~((~aElementOf0(W2, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W3_2(W2, W0), W0)) | sdtlseqdt0(W2, tptp_fun_W3_2(W2, W0)))))) | aLowerBoundOfIn0(W2, W0, szDzozmdt0(xf)))))) | (~![W3: $i] : ((~aElementOf0(W3, W0)) | sdtlseqdt0(W3, tptp_fun_W2_13(W0)))) | (~![W3: $i] : (sdtlseqdt0(tptp_fun_W2_13(W0), W3) | (~((~((~aElementOf0(W3, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W4_14(W3, W0), W0)) | sdtlseqdt0(tptp_fun_W4_14(W3, W0), W3))))) | aUpperBoundOfIn0(W3, W0, szDzozmdt0(xf)))))))))) | (~(aSubsetOf0(cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | (~((~aSet0(cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT))) | aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf)))))))) | (~((~aElementOf0(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | (~aLowerBoundOfIn0(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) | (~aInfimumOfIn0(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) | (~aElementOf0(tptp_fun_W2_13(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | (~aUpperBoundOfIn0(tptp_fun_W2_13(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) | (~aSupremumOfIn0(tptp_fun_W2_13(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)), W2))) | (~![W2: $i] : (sdtlseqdt0(W2, tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT))) | (~((~((~aElementOf0(W2, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W3_2(W2, cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W2, tptp_fun_W3_2(W2, cS1241(szDzozmdt0(xf), xf, xT))))))) | aLowerBoundOfIn0(W2, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))))) | (~![W3: $i] : ((~aElementOf0(W3, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W3, tptp_fun_W2_13(cS1241(szDzozmdt0(xf), xf, xT))))) | (~![W3: $i] : (sdtlseqdt0(tptp_fun_W2_13(cS1241(szDzozmdt0(xf), xf, xT)), W3) | (~((~((~aElementOf0(W3, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W4_14(W3, cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W4_14(W3, cS1241(szDzozmdt0(xf), xf, xT)), W3))))) | aUpperBoundOfIn0(W3, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))))))))),
% 10.33/6.66 inference(modus_ponens,[status(thm)],[80, 79])).
% 10.33/6.66 tff(82,plain,
% 10.33/6.66 ((~(aSubsetOf0(cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | (~((~aSet0(cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT))) | aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf)))))))) | (~((~aElementOf0(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | (~aLowerBoundOfIn0(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) | (~aInfimumOfIn0(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) | (~aElementOf0(tptp_fun_W2_13(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | (~aUpperBoundOfIn0(tptp_fun_W2_13(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) | (~aSupremumOfIn0(tptp_fun_W2_13(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) | (~![W2: $i] : ((~aElementOf0(W2, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT)), W2))) | (~![W2: $i] : (sdtlseqdt0(W2, tptp_fun_W1_12(cS1241(szDzozmdt0(xf), xf, xT))) | (~((~((~aElementOf0(W2, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W3_2(W2, cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W2, tptp_fun_W3_2(W2, cS1241(szDzozmdt0(xf), xf, xT))))))) | aLowerBoundOfIn0(W2, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))))) | (~![W3: $i] : ((~aElementOf0(W3, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W3, tptp_fun_W2_13(cS1241(szDzozmdt0(xf), xf, xT))))) | (~![W3: $i] : (sdtlseqdt0(tptp_fun_W2_13(cS1241(szDzozmdt0(xf), xf, xT)), W3) | (~((~((~aElementOf0(W3, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W4_14(W3, cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(tptp_fun_W4_14(W3, cS1241(szDzozmdt0(xf), xf, xT)), W3))))) | aUpperBoundOfIn0(W3, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))))))))),
% 10.33/6.66 inference(unit_resolution,[status(thm)],[81, 78])).
% 10.33/6.66 tff(83,plain,
% 10.33/6.66 (~(aSubsetOf0(cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | (~((~aSet0(cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT))) | aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf)))))))),
% 10.33/6.66 inference(unit_resolution,[status(thm)],[82, 42])).
% 10.33/6.66 tff(84,plain,
% 10.33/6.66 ((aSubsetOf0(cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | (~((~aSet0(cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT))) | aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))))))) | ((~aSet0(cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT))) | aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf)))))),
% 10.33/6.66 inference(tautology,[status(thm)],[])).
% 10.33/6.66 tff(85,plain,
% 10.33/6.66 ((~aSet0(cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT))) | aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))))),
% 10.33/6.66 inference(unit_resolution,[status(thm)],[84, 83])).
% 10.33/6.66 tff(86,plain,
% 10.33/6.66 (aSet0(cS1241(szRzazndt0(xf), xf, xT)) <=> aSet0(cS1241(szDzozmdt0(xf), xf, xT))),
% 10.33/6.66 inference(rewrite,[status(thm)],[])).
% 10.33/6.66 tff(87,plain,
% 10.33/6.66 (aSet0(xP) <=> aSet0(cS1241(szRzazndt0(xf), xf, xT))),
% 10.33/6.66 inference(rewrite,[status(thm)],[])).
% 10.33/6.66 tff(88,plain,
% 10.33/6.66 (aSet0(xP) <=> aSet0(xP)),
% 10.33/6.66 inference(rewrite,[status(thm)],[])).
% 10.33/6.66 tff(89,axiom,((aSet0(xP) & ![W0: $i] : ((aElementOf0(W0, xP) => (((aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) & ![W1: $i] : (aElementOf0(W1, xT) => sdtlseqdt0(W1, W0))) & aUpperBoundOfIn0(W0, xT, xU))) & (((aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) & (![W1: $i] : (aElementOf0(W1, xT) => sdtlseqdt0(W1, W0)) | aUpperBoundOfIn0(W0, xT, xU))) => aElementOf0(W0, xP)))) & (xP = cS1241(xU, xf, xT))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__1244')).
% 10.33/6.66 tff(90,plain,
% 10.33/6.66 (aSet0(xP) & ![W0: $i] : ((aElementOf0(W0, xP) => (((aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) & ![W1: $i] : (aElementOf0(W1, xT) => sdtlseqdt0(W1, W0))) & aUpperBoundOfIn0(W0, xT, xU))) & (((aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) & (![W1: $i] : (aElementOf0(W1, xT) => sdtlseqdt0(W1, W0)) | aUpperBoundOfIn0(W0, xT, xU))) => aElementOf0(W0, xP)))),
% 10.33/6.66 inference(and_elim,[status(thm)],[89])).
% 10.33/6.66 tff(91,plain,
% 10.33/6.66 (aSet0(xP)),
% 10.33/6.66 inference(and_elim,[status(thm)],[90])).
% 10.33/6.66 tff(92,plain,
% 10.33/6.66 (aSet0(xP)),
% 10.33/6.66 inference(modus_ponens,[status(thm)],[91, 88])).
% 10.33/6.66 tff(93,plain,
% 10.33/6.66 (aSet0(cS1241(szRzazndt0(xf), xf, xT))),
% 10.33/6.66 inference(modus_ponens,[status(thm)],[92, 87])).
% 10.33/6.66 tff(94,plain,
% 10.33/6.66 (aSet0(cS1241(szDzozmdt0(xf), xf, xT))),
% 10.33/6.66 inference(modus_ponens,[status(thm)],[93, 86])).
% 10.33/6.66 tff(95,plain,
% 10.33/6.66 ((~((~aSet0(cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT))) | aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf)))))) | (~aSet0(cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT))) | aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))))),
% 10.33/6.66 inference(tautology,[status(thm)],[])).
% 10.33/6.66 tff(96,plain,
% 10.33/6.66 ((~((~aSet0(cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT))) | aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf)))))) | (~((~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT))) | aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))))),
% 10.33/6.66 inference(unit_resolution,[status(thm)],[95, 94])).
% 10.33/6.66 tff(97,plain,
% 10.33/6.66 (~((~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT))) | aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf)))),
% 10.33/6.66 inference(unit_resolution,[status(thm)],[96, 85])).
% 10.33/6.66 tff(98,plain,
% 10.33/6.66 (((~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT))) | aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | (~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf)))),
% 10.33/6.66 inference(tautology,[status(thm)],[])).
% 10.33/6.66 tff(99,plain,
% 10.33/6.66 (~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))),
% 10.33/6.66 inference(unit_resolution,[status(thm)],[98, 97])).
% 10.33/6.66 tff(100,plain,
% 10.33/6.66 (((~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | (~aUpperBoundOfIn0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), xT, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)))))) | aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))),
% 10.33/6.66 inference(tautology,[status(thm)],[])).
% 10.33/6.66 tff(101,plain,
% 10.33/6.66 ((~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | (~aUpperBoundOfIn0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), xT, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)))))),
% 10.33/6.66 inference(unit_resolution,[status(thm)],[100, 99])).
% 10.33/6.66 tff(102,plain,
% 10.33/6.66 (((~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT))) | aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT))),
% 10.33/6.66 inference(tautology,[status(thm)],[])).
% 10.33/6.66 tff(103,plain,
% 10.33/6.66 (aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT))),
% 10.33/6.66 inference(unit_resolution,[status(thm)],[102, 97])).
% 10.33/6.66 tff(104,plain,
% 10.33/6.66 ((~((~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | (~aUpperBoundOfIn0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), xT, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))))))))) | (~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | (~aUpperBoundOfIn0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), xT, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)))))))),
% 10.33/6.66 inference(tautology,[status(thm)],[])).
% 10.33/6.66 tff(105,plain,
% 10.33/6.66 (~((~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | (~aUpperBoundOfIn0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), xT, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))))))))),
% 10.33/6.66 inference(unit_resolution,[status(thm)],[104, 103, 101])).
% 10.33/6.66 tff(106,plain,
% 10.33/6.67 (((~(aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)))) | (~(aUpperBoundOfIn0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), xT)) | sdtlseqdt0(tptp_fun_W1_15(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))))))) | (~((~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | (~aUpperBoundOfIn0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), xT, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)))))))))) | ((~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | (~aUpperBoundOfIn0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), xT, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))))))))),
% 10.33/6.67 inference(tautology,[status(thm)],[])).
% 10.33/6.67 tff(107,plain,
% 10.33/6.67 ((~(aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)))) | (~(aUpperBoundOfIn0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), xT)) | sdtlseqdt0(tptp_fun_W1_15(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))))))) | (~((~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | (~aUpperBoundOfIn0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), xT, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)))))))))),
% 10.33/6.67 inference(unit_resolution,[status(thm)],[106, 105])).
% 10.33/6.67 tff(108,plain,
% 10.33/6.67 (^[W0: $i] : rewrite((~((~((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))))) | (~(aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))))) <=> (~((~(aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))) | (~((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))))))))),
% 10.33/6.67 inference(bind,[status(th)],[])).
% 10.33/6.67 tff(109,plain,
% 10.33/6.67 (![W0: $i] : (~((~((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))))) | (~(aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))))) <=> ![W0: $i] : (~((~(aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))) | (~((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)))))))))),
% 10.33/6.67 inference(quant_intro,[status(thm)],[108])).
% 10.33/6.67 tff(110,plain,
% 10.33/6.67 (^[W0: $i] : refl((~((~((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))))) | (~(aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))))) <=> (~((~((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))))) | (~(aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))))))),
% 10.33/6.67 inference(bind,[status(th)],[])).
% 10.33/6.67 tff(111,plain,
% 10.33/6.67 (![W0: $i] : (~((~((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))))) | (~(aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))))) <=> ![W0: $i] : (~((~((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))))) | (~(aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0)))))))),
% 10.33/6.67 inference(quant_intro,[status(thm)],[110])).
% 10.33/6.67 tff(112,plain,
% 10.33/6.67 (^[W0: $i] : rewrite((~((~((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))))) | (~(aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))))) <=> (~((~((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))))) | (~(aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))))))),
% 10.33/6.67 inference(bind,[status(th)],[])).
% 10.33/6.67 tff(113,plain,
% 10.33/6.67 (![W0: $i] : (~((~((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))))) | (~(aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))))) <=> ![W0: $i] : (~((~((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))))) | (~(aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0)))))))),
% 10.33/6.67 inference(quant_intro,[status(thm)],[112])).
% 10.33/6.67 tff(114,plain,
% 10.33/6.67 (![W0: $i] : (~((~((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))))) | (~(aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))))) <=> ![W0: $i] : (~((~((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))))) | (~(aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0)))))))),
% 10.33/6.67 inference(transitivity,[status(thm)],[113, 111])).
% 10.33/6.67 tff(115,plain,
% 10.33/6.67 (^[W0: $i] : trans(monotonicity(rewrite(((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | (aElementOf0(W0, szDzozmdt0(xf)) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf)))) <=> ((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))))), trans(monotonicity(rewrite(((~aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf))) & (~((~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0)))) <=> (~(aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0)))), ((aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | ((~aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf))) & (~((~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))) <=> (aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0)))))), rewrite((aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0)))) <=> (aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))), ((aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | ((~aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf))) & (~((~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))) <=> (aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0)))))), ((((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | (aElementOf0(W0, szDzozmdt0(xf)) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf)))) & (aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | ((~aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf))) & (~((~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0)))))) <=> (((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)))))) & (aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))))), rewrite((((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)))))) & (aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))) <=> (~((~((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))))) | (~(aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0)))))))), ((((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | (aElementOf0(W0, szDzozmdt0(xf)) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf)))) & (aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | ((~aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf))) & (~((~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0)))))) <=> (~((~((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))))) | (~(aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0)))))))))),
% 10.33/6.68 inference(bind,[status(th)],[])).
% 10.33/6.68 tff(116,plain,
% 10.33/6.68 (![W0: $i] : (((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | (aElementOf0(W0, szDzozmdt0(xf)) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf)))) & (aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | ((~aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf))) & (~((~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0)))))) <=> ![W0: $i] : (~((~((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))))) | (~(aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0)))))))),
% 10.33/6.68 inference(quant_intro,[status(thm)],[115])).
% 10.33/6.68 tff(117,plain,
% 10.33/6.68 (^[W0: $i] : rewrite((((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | (aElementOf0(W0, szDzozmdt0(xf)) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf)))) & (((~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | ((~aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf))) & (~((~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))) | aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT)))) <=> (((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | (aElementOf0(W0, szDzozmdt0(xf)) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf)))) & (aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | ((~aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf))) & (~((~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0)))))))),
% 10.33/6.68 inference(bind,[status(th)],[])).
% 10.33/6.68 tff(118,plain,
% 10.33/6.68 (![W0: $i] : (((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | (aElementOf0(W0, szDzozmdt0(xf)) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf)))) & (((~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | ((~aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf))) & (~((~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))) | aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT)))) <=> ![W0: $i] : (((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | (aElementOf0(W0, szDzozmdt0(xf)) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf)))) & (aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | ((~aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf))) & (~((~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))))),
% 10.33/6.68 inference(quant_intro,[status(thm)],[117])).
% 10.33/6.68 tff(119,plain,
% 10.33/6.68 (^[W0: $i] : rewrite((((~aElementOf0(W0, cS1241(szRzazndt0(xf), xf, xT))) | (aElementOf0(W0, szRzazndt0(xf)) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, szRzazndt0(xf)))) & ((~(aElementOf0(W0, szRzazndt0(xf)) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & (aUpperBoundOfIn0(W0, xT, szRzazndt0(xf)) | ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))) | aElementOf0(W0, cS1241(szRzazndt0(xf), xf, xT)))) <=> (((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | (aElementOf0(W0, szDzozmdt0(xf)) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf)))) & ((~(aElementOf0(W0, szDzozmdt0(xf)) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & (aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf)) | ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))) | aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT)))))),
% 10.33/6.68 inference(bind,[status(th)],[])).
% 10.33/6.68 tff(120,plain,
% 10.33/6.68 (![W0: $i] : (((~aElementOf0(W0, cS1241(szRzazndt0(xf), xf, xT))) | (aElementOf0(W0, szRzazndt0(xf)) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, szRzazndt0(xf)))) & ((~(aElementOf0(W0, szRzazndt0(xf)) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & (aUpperBoundOfIn0(W0, xT, szRzazndt0(xf)) | ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))) | aElementOf0(W0, cS1241(szRzazndt0(xf), xf, xT)))) <=> ![W0: $i] : (((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | (aElementOf0(W0, szDzozmdt0(xf)) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf)))) & ((~(aElementOf0(W0, szDzozmdt0(xf)) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & (aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf)) | ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))) | aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))))),
% 10.33/6.68 inference(quant_intro,[status(thm)],[119])).
% 10.33/6.68 tff(121,plain,
% 10.33/6.68 (^[W0: $i] : rewrite((((~aElementOf0(W0, xP)) | (aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, xU))) & ((~(aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & (aUpperBoundOfIn0(W0, xT, xU) | ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))) | aElementOf0(W0, xP))) <=> (((~aElementOf0(W0, cS1241(szRzazndt0(xf), xf, xT))) | (aElementOf0(W0, szRzazndt0(xf)) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, szRzazndt0(xf)))) & ((~(aElementOf0(W0, szRzazndt0(xf)) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & (aUpperBoundOfIn0(W0, xT, szRzazndt0(xf)) | ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))) | aElementOf0(W0, cS1241(szRzazndt0(xf), xf, xT)))))),
% 10.33/6.68 inference(bind,[status(th)],[])).
% 10.33/6.68 tff(122,plain,
% 10.33/6.68 (![W0: $i] : (((~aElementOf0(W0, xP)) | (aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, xU))) & ((~(aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & (aUpperBoundOfIn0(W0, xT, xU) | ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))) | aElementOf0(W0, xP))) <=> ![W0: $i] : (((~aElementOf0(W0, cS1241(szRzazndt0(xf), xf, xT))) | (aElementOf0(W0, szRzazndt0(xf)) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, szRzazndt0(xf)))) & ((~(aElementOf0(W0, szRzazndt0(xf)) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & (aUpperBoundOfIn0(W0, xT, szRzazndt0(xf)) | ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))) | aElementOf0(W0, cS1241(szRzazndt0(xf), xf, xT))))),
% 10.33/6.68 inference(quant_intro,[status(thm)],[121])).
% 10.33/6.68 tff(123,plain,
% 10.33/6.68 (![W0: $i] : (((~aElementOf0(W0, xP)) | (aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, xU))) & ((~(aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & (aUpperBoundOfIn0(W0, xT, xU) | ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))) | aElementOf0(W0, xP))) <=> ![W0: $i] : (((~aElementOf0(W0, xP)) | (aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, xU))) & ((~(aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & (aUpperBoundOfIn0(W0, xT, xU) | ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))) | aElementOf0(W0, xP)))),
% 10.33/6.68 inference(rewrite,[status(thm)],[])).
% 10.33/6.68 tff(124,plain,
% 10.33/6.68 (^[W0: $i] : rewrite(((aElementOf0(W0, xP) => (((aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) & ![W1: $i] : (aElementOf0(W1, xT) => sdtlseqdt0(W1, W0))) & aUpperBoundOfIn0(W0, xT, xU))) & (((aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) & (![W1: $i] : (aElementOf0(W1, xT) => sdtlseqdt0(W1, W0)) | aUpperBoundOfIn0(W0, xT, xU))) => aElementOf0(W0, xP))) <=> (((~aElementOf0(W0, xP)) | (aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, xU))) & ((~(aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & (aUpperBoundOfIn0(W0, xT, xU) | ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))) | aElementOf0(W0, xP))))),
% 10.33/6.69 inference(bind,[status(th)],[])).
% 10.33/6.69 tff(125,plain,
% 10.33/6.69 (![W0: $i] : ((aElementOf0(W0, xP) => (((aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) & ![W1: $i] : (aElementOf0(W1, xT) => sdtlseqdt0(W1, W0))) & aUpperBoundOfIn0(W0, xT, xU))) & (((aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) & (![W1: $i] : (aElementOf0(W1, xT) => sdtlseqdt0(W1, W0)) | aUpperBoundOfIn0(W0, xT, xU))) => aElementOf0(W0, xP))) <=> ![W0: $i] : (((~aElementOf0(W0, xP)) | (aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, xU))) & ((~(aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & (aUpperBoundOfIn0(W0, xT, xU) | ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))) | aElementOf0(W0, xP)))),
% 10.33/6.69 inference(quant_intro,[status(thm)],[124])).
% 10.33/6.69 tff(126,plain,
% 10.33/6.69 (![W0: $i] : ((aElementOf0(W0, xP) => (((aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) & ![W1: $i] : (aElementOf0(W1, xT) => sdtlseqdt0(W1, W0))) & aUpperBoundOfIn0(W0, xT, xU))) & (((aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) & (![W1: $i] : (aElementOf0(W1, xT) => sdtlseqdt0(W1, W0)) | aUpperBoundOfIn0(W0, xT, xU))) => aElementOf0(W0, xP)))),
% 10.33/6.69 inference(and_elim,[status(thm)],[90])).
% 10.33/6.69 tff(127,plain,
% 10.33/6.69 (![W0: $i] : (((~aElementOf0(W0, xP)) | (aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, xU))) & ((~(aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & (aUpperBoundOfIn0(W0, xT, xU) | ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))) | aElementOf0(W0, xP)))),
% 10.33/6.69 inference(modus_ponens,[status(thm)],[126, 125])).
% 10.33/6.69 tff(128,plain,
% 10.33/6.69 (![W0: $i] : (((~aElementOf0(W0, xP)) | (aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, xU))) & ((~(aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & (aUpperBoundOfIn0(W0, xT, xU) | ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))) | aElementOf0(W0, xP)))),
% 10.33/6.69 inference(modus_ponens,[status(thm)],[127, 123])).
% 10.33/6.69 tff(129,plain,
% 10.33/6.69 (![W0: $i] : (((~aElementOf0(W0, cS1241(szRzazndt0(xf), xf, xT))) | (aElementOf0(W0, szRzazndt0(xf)) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, szRzazndt0(xf)))) & ((~(aElementOf0(W0, szRzazndt0(xf)) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & (aUpperBoundOfIn0(W0, xT, szRzazndt0(xf)) | ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))) | aElementOf0(W0, cS1241(szRzazndt0(xf), xf, xT))))),
% 10.33/6.69 inference(modus_ponens,[status(thm)],[128, 122])).
% 10.33/6.69 tff(130,plain,
% 10.33/6.69 (![W0: $i] : (((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | (aElementOf0(W0, szDzozmdt0(xf)) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf)))) & ((~(aElementOf0(W0, szDzozmdt0(xf)) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & (aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf)) | ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))) | aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))))),
% 10.33/6.69 inference(modus_ponens,[status(thm)],[129, 120])).
% 10.33/6.69 tff(131,plain,(
% 10.33/6.69 ![W0: $i] : (((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | (aElementOf0(W0, szDzozmdt0(xf)) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf)))) & (((~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | ((~aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf))) & (~((~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))) | aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))))),
% 10.33/6.69 inference(skolemize,[status(sab)],[130])).
% 10.33/6.69 tff(132,plain,
% 10.33/6.69 (![W0: $i] : (((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | (aElementOf0(W0, szDzozmdt0(xf)) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf)))) & (aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | ((~aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf))) & (~((~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))))),
% 10.33/6.69 inference(modus_ponens,[status(thm)],[131, 118])).
% 10.33/6.69 tff(133,plain,
% 10.33/6.69 (![W0: $i] : (~((~((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))))) | (~(aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0)))))))),
% 10.33/6.69 inference(modus_ponens,[status(thm)],[132, 116])).
% 10.33/6.69 tff(134,plain,
% 10.33/6.69 (![W0: $i] : (~((~((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0))))))) | (~(aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0)))))))),
% 10.33/6.69 inference(modus_ponens,[status(thm)],[133, 114])).
% 10.33/6.69 tff(135,plain,
% 10.33/6.69 (![W0: $i] : (~((~(aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))) | (~((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)))))))))),
% 10.33/6.69 inference(modus_ponens,[status(thm)],[134, 109])).
% 10.33/6.69 tff(136,plain,
% 10.33/6.69 (((~![W0: $i] : (~((~(aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))) | (~((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)))))))))) | (~((~(aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)))) | (~(aUpperBoundOfIn0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), xT)) | sdtlseqdt0(tptp_fun_W1_15(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))))))) | (~((~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | (~aUpperBoundOfIn0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), xT, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)))))))))))) <=> ((~![W0: $i] : (~((~(aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))) | (~((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)))))))))) | (~((~(aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)))) | (~(aUpperBoundOfIn0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), xT)) | sdtlseqdt0(tptp_fun_W1_15(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))))))) | (~((~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | (~aUpperBoundOfIn0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), xT, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))))))))))))),
% 10.33/6.69 inference(rewrite,[status(thm)],[])).
% 10.33/6.69 tff(137,plain,
% 10.33/6.69 ((~((~(aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)))) | (~(aUpperBoundOfIn0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), xT)) | sdtlseqdt0(tptp_fun_W1_15(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))))))) | (~((~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)))) | (~aUpperBoundOfIn0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))))))))))) <=> (~((~(aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)))) | (~(aUpperBoundOfIn0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), xT)) | sdtlseqdt0(tptp_fun_W1_15(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))))))) | (~((~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | (~aUpperBoundOfIn0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), xT, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)))))))))))),
% 10.33/6.69 inference(rewrite,[status(thm)],[])).
% 10.33/6.69 tff(138,plain,
% 10.33/6.69 (((~![W0: $i] : (~((~(aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))) | (~((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)))))))))) | (~((~(aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)))) | (~(aUpperBoundOfIn0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), xT)) | sdtlseqdt0(tptp_fun_W1_15(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))))))) | (~((~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)))) | (~aUpperBoundOfIn0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)))))))))))) <=> ((~![W0: $i] : (~((~(aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))) | (~((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)))))))))) | (~((~(aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)))) | (~(aUpperBoundOfIn0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), xT)) | sdtlseqdt0(tptp_fun_W1_15(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))))))) | (~((~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | (~aUpperBoundOfIn0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), xT, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))))))))))))),
% 10.33/6.70 inference(monotonicity,[status(thm)],[137])).
% 10.33/6.70 tff(139,plain,
% 10.33/6.70 (((~![W0: $i] : (~((~(aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))) | (~((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)))))))))) | (~((~(aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)))) | (~(aUpperBoundOfIn0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), xT)) | sdtlseqdt0(tptp_fun_W1_15(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))))))) | (~((~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)))) | (~aUpperBoundOfIn0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)))))))))))) <=> ((~![W0: $i] : (~((~(aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))) | (~((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)))))))))) | (~((~(aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)))) | (~(aUpperBoundOfIn0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), xT)) | sdtlseqdt0(tptp_fun_W1_15(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))))))) | (~((~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | (~aUpperBoundOfIn0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), xT, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))))))))))))),
% 10.33/6.70 inference(transitivity,[status(thm)],[138, 136])).
% 10.33/6.70 tff(140,plain,
% 10.33/6.70 ((~![W0: $i] : (~((~(aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))) | (~((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)))))))))) | (~((~(aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)))) | (~(aUpperBoundOfIn0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), xT)) | sdtlseqdt0(tptp_fun_W1_15(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))))))) | (~((~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)))) | (~aUpperBoundOfIn0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)))))))))))),
% 10.33/6.72 inference(quant_inst,[status(thm)],[])).
% 10.33/6.72 tff(141,plain,
% 10.33/6.72 ((~![W0: $i] : (~((~(aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~(aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0), W0))))) | (~((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)))))))))) | (~((~(aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)))) | (~(aUpperBoundOfIn0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), xT)) | sdtlseqdt0(tptp_fun_W1_15(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))))))) | (~((~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), szDzozmdt0(xf))) | (~aUpperBoundOfIn0(tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)), xT, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT))), tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, tptp_fun_W1_11(cS1241(szDzozmdt0(xf), xf, xT)))))))))))),
% 10.33/6.72 inference(modus_ponens,[status(thm)],[140, 139])).
% 10.33/6.72 tff(142,plain,
% 10.33/6.72 ($false),
% 10.33/6.72 inference(unit_resolution,[status(thm)],[141, 135, 107])).
% 10.33/6.72 % SZS output end Proof
%------------------------------------------------------------------------------