TSTP Solution File: LAT386+4 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT386+4 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.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 0.18s 0.48s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13 % Problem : LAT386+4 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.35 % Computer : n015.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Thu Sep 1 16:59:53 EDT 2022
% 0.12/0.35 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 0.18/0.48 % SZS status Theorem
% 0.18/0.48 % SZS output start Proof
% 0.18/0.48 tff(sdtlseqdt0_type, type, (
% 0.18/0.48 sdtlseqdt0: ( $i * $i ) > $o)).
% 0.18/0.48 tff(sdtlpdtrp0_type, type, (
% 0.18/0.48 sdtlpdtrp0: ( $i * $i ) > $i)).
% 0.18/0.48 tff(tptp_fun_W0_17_type, type, (
% 0.18/0.48 tptp_fun_W0_17: $i)).
% 0.18/0.48 tff(xf_type, type, (
% 0.18/0.48 xf: $i)).
% 0.18/0.48 tff(xp_type, type, (
% 0.18/0.48 xp: $i)).
% 0.18/0.48 tff(aElement0_type, type, (
% 0.18/0.48 aElement0: $i > $o)).
% 0.18/0.48 tff(aElementOf0_type, type, (
% 0.18/0.48 aElementOf0: ( $i * $i ) > $o)).
% 0.18/0.48 tff(szRzazndt0_type, type, (
% 0.18/0.48 szRzazndt0: $i > $i)).
% 0.18/0.48 tff(szDzozmdt0_type, type, (
% 0.18/0.48 szDzozmdt0: $i > $i)).
% 0.18/0.48 tff(xT_type, type, (
% 0.18/0.48 xT: $i)).
% 0.18/0.48 tff(aUpperBoundOfIn0_type, type, (
% 0.18/0.48 aUpperBoundOfIn0: ( $i * $i * $i ) > $o)).
% 0.18/0.48 tff(cS1241_type, type, (
% 0.18/0.48 cS1241: ( $i * $i * $i ) > $i)).
% 0.18/0.48 tff(tptp_fun_W1_15_type, type, (
% 0.18/0.48 tptp_fun_W1_15: $i > $i)).
% 0.18/0.48 tff(xP_type, type, (
% 0.18/0.48 xP: $i)).
% 0.18/0.48 tff(xU_type, type, (
% 0.18/0.48 xU: $i)).
% 0.18/0.48 tff(aSet0_type, type, (
% 0.18/0.48 aSet0: $i > $o)).
% 0.18/0.48 tff(aLowerBoundOfIn0_type, type, (
% 0.18/0.48 aLowerBoundOfIn0: ( $i * $i * $i ) > $o)).
% 0.18/0.48 tff(tptp_fun_W0_18_type, type, (
% 0.18/0.48 tptp_fun_W0_18: $i)).
% 0.18/0.48 tff(tptp_fun_W1_16_type, type, (
% 0.18/0.48 tptp_fun_W1_16: $i > $i)).
% 0.18/0.48 tff(aFixedPointOf0_type, type, (
% 0.18/0.48 aFixedPointOf0: ( $i * $i ) > $o)).
% 0.18/0.48 tff(cS1142_type, type, (
% 0.18/0.48 cS1142: $i > $i)).
% 0.18/0.48 tff(xS_type, type, (
% 0.18/0.48 xS: $i)).
% 0.18/0.48 tff(aSubsetOf0_type, type, (
% 0.18/0.48 aSubsetOf0: ( $i * $i ) > $o)).
% 0.18/0.48 tff(tptp_fun_W2_1_type, type, (
% 0.18/0.48 tptp_fun_W2_1: ( $i * $i ) > $i)).
% 0.18/0.48 tff(aInfimumOfIn0_type, type, (
% 0.18/0.48 aInfimumOfIn0: ( $i * $i * $i ) > $o)).
% 0.18/0.48 tff(aFunction0_type, type, (
% 0.18/0.48 aFunction0: $i > $o)).
% 0.18/0.48 tff(aCompleteLattice0_type, type, (
% 0.18/0.48 aCompleteLattice0: $i > $o)).
% 0.18/0.48 tff(aSupremumOfIn0_type, type, (
% 0.18/0.48 aSupremumOfIn0: ( $i * $i * $i ) > $o)).
% 0.18/0.48 tff(isMonotone0_type, type, (
% 0.18/0.48 isMonotone0: $i > $o)).
% 0.18/0.48 tff(isOn0_type, type, (
% 0.18/0.48 isOn0: ( $i * $i ) > $o)).
% 0.18/0.48 tff(1,plain,
% 0.18/0.48 (^[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))))))))))),
% 0.18/0.48 inference(bind,[status(th)],[])).
% 0.18/0.48 tff(2,plain,
% 0.18/0.48 (![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)))))))))),
% 0.18/0.48 inference(quant_intro,[status(thm)],[1])).
% 0.18/0.48 tff(3,plain,
% 0.18/0.48 (^[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))))))))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(4,plain,
% 0.18/0.49 (![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)))))))),
% 0.18/0.49 inference(quant_intro,[status(thm)],[3])).
% 0.18/0.49 tff(5,plain,
% 0.18/0.49 (^[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))))))))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(6,plain,
% 0.18/0.49 (![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)))))))),
% 0.18/0.49 inference(quant_intro,[status(thm)],[5])).
% 0.18/0.49 tff(7,plain,
% 0.18/0.49 (![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)))))))),
% 0.18/0.49 inference(transitivity,[status(thm)],[6, 4])).
% 0.18/0.49 tff(8,plain,
% 0.18/0.49 (^[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)))))))))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(9,plain,
% 0.18/0.49 (![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)))))))),
% 0.18/0.49 inference(quant_intro,[status(thm)],[8])).
% 0.18/0.49 tff(10,plain,
% 0.18/0.49 (^[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)))))))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(11,plain,
% 0.18/0.49 (![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))))))),
% 0.18/0.49 inference(quant_intro,[status(thm)],[10])).
% 0.18/0.49 tff(12,plain,
% 0.18/0.49 (^[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)))))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(13,plain,
% 0.18/0.49 (![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))))),
% 0.18/0.49 inference(quant_intro,[status(thm)],[12])).
% 0.18/0.49 tff(14,plain,
% 0.18/0.49 (^[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)))))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(15,plain,
% 0.18/0.49 (![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))))),
% 0.18/0.49 inference(quant_intro,[status(thm)],[14])).
% 0.18/0.49 tff(16,plain,
% 0.18/0.49 (![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)))),
% 0.18/0.49 inference(rewrite,[status(thm)],[])).
% 0.18/0.49 tff(17,plain,
% 0.18/0.49 (^[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))))),
% 0.18/0.49 inference(bind,[status(th)],[])).
% 0.18/0.49 tff(18,plain,
% 0.18/0.49 (![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)))),
% 0.18/0.49 inference(quant_intro,[status(thm)],[17])).
% 0.18/0.49 tff(19,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/sandbox/benchmark/theBenchmark.p','m__1244')).
% 0.18/0.50 tff(20,plain,
% 0.18/0.50 (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)))),
% 0.18/0.50 inference(and_elim,[status(thm)],[19])).
% 0.18/0.50 tff(21,plain,
% 0.18/0.50 (![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)))),
% 0.18/0.50 inference(and_elim,[status(thm)],[20])).
% 0.18/0.50 tff(22,plain,
% 0.18/0.50 (![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)))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[21, 18])).
% 0.18/0.50 tff(23,plain,
% 0.18/0.50 (![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)))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[22, 16])).
% 0.18/0.50 tff(24,plain,
% 0.18/0.50 (![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))))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[23, 15])).
% 0.18/0.50 tff(25,plain,
% 0.18/0.50 (![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))))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[24, 13])).
% 0.18/0.50 tff(26,plain,(
% 0.18/0.50 ![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))))),
% 0.18/0.50 inference(skolemize,[status(sab)],[25])).
% 0.18/0.50 tff(27,plain,
% 0.18/0.50 (![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))))))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[26, 11])).
% 0.18/0.50 tff(28,plain,
% 0.18/0.50 (![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)))))))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[27, 9])).
% 0.18/0.50 tff(29,plain,
% 0.18/0.50 (![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)))))))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[28, 7])).
% 0.18/0.50 tff(30,plain,
% 0.18/0.50 (![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)))))))))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[29, 2])).
% 0.18/0.50 tff(31,plain,
% 0.18/0.50 (((~![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(W0!17, cS1241(szDzozmdt0(xf), xf, xT)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!17), W0!17)) | (~aElementOf0(W0!17, szDzozmdt0(xf))) | (~(aUpperBoundOfIn0(W0!17, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0!17), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0!17), W0!17))))) | (~((~aElementOf0(W0!17, cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(W0!17, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!17), W0!17)) | (~aUpperBoundOfIn0(W0!17, xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!17)))))))))) <=> ((~![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(W0!17, cS1241(szDzozmdt0(xf), xf, xT)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!17), W0!17)) | (~aElementOf0(W0!17, szDzozmdt0(xf))) | (~(aUpperBoundOfIn0(W0!17, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0!17), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0!17), W0!17))))) | (~((~aElementOf0(W0!17, cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(W0!17, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!17), W0!17)) | (~aUpperBoundOfIn0(W0!17, xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!17))))))))))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(32,plain,
% 0.18/0.50 ((~((~(aElementOf0(W0!17, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0!17, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!17), W0!17)) | (~(aUpperBoundOfIn0(W0!17, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0!17), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0!17), W0!17))))) | (~((~aElementOf0(W0!17, cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(W0!17, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!17), W0!17)) | (~aUpperBoundOfIn0(W0!17, xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!17))))))))) <=> (~((~(aElementOf0(W0!17, cS1241(szDzozmdt0(xf), xf, xT)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!17), W0!17)) | (~aElementOf0(W0!17, szDzozmdt0(xf))) | (~(aUpperBoundOfIn0(W0!17, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0!17), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0!17), W0!17))))) | (~((~aElementOf0(W0!17, cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(W0!17, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!17), W0!17)) | (~aUpperBoundOfIn0(W0!17, xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!17)))))))))),
% 0.18/0.50 inference(rewrite,[status(thm)],[])).
% 0.18/0.50 tff(33,plain,
% 0.18/0.50 (((~![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(W0!17, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0!17, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!17), W0!17)) | (~(aUpperBoundOfIn0(W0!17, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0!17), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0!17), W0!17))))) | (~((~aElementOf0(W0!17, cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(W0!17, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!17), W0!17)) | (~aUpperBoundOfIn0(W0!17, xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!17)))))))))) <=> ((~![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(W0!17, cS1241(szDzozmdt0(xf), xf, xT)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!17), W0!17)) | (~aElementOf0(W0!17, szDzozmdt0(xf))) | (~(aUpperBoundOfIn0(W0!17, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0!17), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0!17), W0!17))))) | (~((~aElementOf0(W0!17, cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(W0!17, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!17), W0!17)) | (~aUpperBoundOfIn0(W0!17, xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!17))))))))))),
% 0.18/0.50 inference(monotonicity,[status(thm)],[32])).
% 0.18/0.50 tff(34,plain,
% 0.18/0.50 (((~![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(W0!17, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0!17, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!17), W0!17)) | (~(aUpperBoundOfIn0(W0!17, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0!17), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0!17), W0!17))))) | (~((~aElementOf0(W0!17, cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(W0!17, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!17), W0!17)) | (~aUpperBoundOfIn0(W0!17, xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!17)))))))))) <=> ((~![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(W0!17, cS1241(szDzozmdt0(xf), xf, xT)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!17), W0!17)) | (~aElementOf0(W0!17, szDzozmdt0(xf))) | (~(aUpperBoundOfIn0(W0!17, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0!17), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0!17), W0!17))))) | (~((~aElementOf0(W0!17, cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(W0!17, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!17), W0!17)) | (~aUpperBoundOfIn0(W0!17, xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!17))))))))))),
% 0.18/0.50 inference(transitivity,[status(thm)],[33, 31])).
% 0.18/0.50 tff(35,plain,
% 0.18/0.50 ((~![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(W0!17, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0!17, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!17), W0!17)) | (~(aUpperBoundOfIn0(W0!17, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0!17), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0!17), W0!17))))) | (~((~aElementOf0(W0!17, cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(W0!17, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!17), W0!17)) | (~aUpperBoundOfIn0(W0!17, xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!17)))))))))),
% 0.18/0.50 inference(quant_inst,[status(thm)],[])).
% 0.18/0.50 tff(36,plain,
% 0.18/0.50 ((~![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(W0!17, cS1241(szDzozmdt0(xf), xf, xT)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!17), W0!17)) | (~aElementOf0(W0!17, szDzozmdt0(xf))) | (~(aUpperBoundOfIn0(W0!17, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0!17), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0!17), W0!17))))) | (~((~aElementOf0(W0!17, cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(W0!17, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!17), W0!17)) | (~aUpperBoundOfIn0(W0!17, xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!17)))))))))),
% 0.18/0.50 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.18/0.51 tff(37,plain,
% 0.18/0.51 (~((~(aElementOf0(W0!17, cS1241(szDzozmdt0(xf), xf, xT)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!17), W0!17)) | (~aElementOf0(W0!17, szDzozmdt0(xf))) | (~(aUpperBoundOfIn0(W0!17, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0!17), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0!17), W0!17))))) | (~((~aElementOf0(W0!17, cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(W0!17, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!17), W0!17)) | (~aUpperBoundOfIn0(W0!17, xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!17))))))))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[36, 30])).
% 0.18/0.51 tff(38,plain,
% 0.18/0.51 (((~(aElementOf0(W0!17, cS1241(szDzozmdt0(xf), xf, xT)) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!17), W0!17)) | (~aElementOf0(W0!17, szDzozmdt0(xf))) | (~(aUpperBoundOfIn0(W0!17, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0!17), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0!17), W0!17))))) | (~((~aElementOf0(W0!17, cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(W0!17, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!17), W0!17)) | (~aUpperBoundOfIn0(W0!17, xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!17)))))))) | ((~aElementOf0(W0!17, cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(W0!17, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!17), W0!17)) | (~aUpperBoundOfIn0(W0!17, xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!17))))))),
% 0.18/0.51 inference(tautology,[status(thm)],[])).
% 0.18/0.51 tff(39,plain,
% 0.18/0.51 ((~aElementOf0(W0!17, cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(W0!17, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!17), W0!17)) | (~aUpperBoundOfIn0(W0!17, xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!17)))))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.18/0.51 tff(40,plain,
% 0.18/0.51 ((~![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_16(W0!18), cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(tptp_fun_W1_16(W0!18), szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_16(W0!18)), tptp_fun_W1_16(W0!18))) | (~(aUpperBoundOfIn0(tptp_fun_W1_16(W0!18), xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(tptp_fun_W1_16(W0!18)), xT)) | sdtlseqdt0(tptp_fun_W1_15(tptp_fun_W1_16(W0!18)), tptp_fun_W1_16(W0!18)))))) | (~((~aElementOf0(tptp_fun_W1_16(W0!18), cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(tptp_fun_W1_16(W0!18), szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_16(W0!18)), tptp_fun_W1_16(W0!18))) | (~aUpperBoundOfIn0(tptp_fun_W1_16(W0!18), xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, tptp_fun_W1_16(W0!18))))))))))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(41,plain,
% 0.18/0.51 (~((~(aElementOf0(tptp_fun_W1_16(W0!18), cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(tptp_fun_W1_16(W0!18), szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_16(W0!18)), tptp_fun_W1_16(W0!18))) | (~(aUpperBoundOfIn0(tptp_fun_W1_16(W0!18), xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(tptp_fun_W1_16(W0!18)), xT)) | sdtlseqdt0(tptp_fun_W1_15(tptp_fun_W1_16(W0!18)), tptp_fun_W1_16(W0!18)))))) | (~((~aElementOf0(tptp_fun_W1_16(W0!18), cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(tptp_fun_W1_16(W0!18), szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_16(W0!18)), tptp_fun_W1_16(W0!18))) | (~aUpperBoundOfIn0(tptp_fun_W1_16(W0!18), xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, tptp_fun_W1_16(W0!18)))))))))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[40, 30])).
% 0.18/0.51 tff(42,plain,
% 0.18/0.51 (((~(aElementOf0(tptp_fun_W1_16(W0!18), cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(tptp_fun_W1_16(W0!18), szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_16(W0!18)), tptp_fun_W1_16(W0!18))) | (~(aUpperBoundOfIn0(tptp_fun_W1_16(W0!18), xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(tptp_fun_W1_16(W0!18)), xT)) | sdtlseqdt0(tptp_fun_W1_15(tptp_fun_W1_16(W0!18)), tptp_fun_W1_16(W0!18)))))) | (~((~aElementOf0(tptp_fun_W1_16(W0!18), cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(tptp_fun_W1_16(W0!18), szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_16(W0!18)), tptp_fun_W1_16(W0!18))) | (~aUpperBoundOfIn0(tptp_fun_W1_16(W0!18), xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, tptp_fun_W1_16(W0!18))))))))) | ((~aElementOf0(tptp_fun_W1_16(W0!18), cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(tptp_fun_W1_16(W0!18), szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_16(W0!18)), tptp_fun_W1_16(W0!18))) | (~aUpperBoundOfIn0(tptp_fun_W1_16(W0!18), xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, tptp_fun_W1_16(W0!18)))))))),
% 0.18/0.51 inference(tautology,[status(thm)],[])).
% 0.18/0.51 tff(43,plain,
% 0.18/0.51 ((~aElementOf0(tptp_fun_W1_16(W0!18), cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(tptp_fun_W1_16(W0!18), szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_16(W0!18)), tptp_fun_W1_16(W0!18))) | (~aUpperBoundOfIn0(tptp_fun_W1_16(W0!18), xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, tptp_fun_W1_16(W0!18))))))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.18/0.51 tff(44,plain,
% 0.18/0.51 (^[W0: $i] : refl((~((~((~aElementOf0(W0, cS1142(xf))) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0) = W0)) | (~aFixedPointOf0(W0, xf)))))) | (~((~(aFixedPointOf0(W0, xf) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0) = W0)))))) | aElementOf0(W0, cS1142(xf)))))) <=> (~((~((~aElementOf0(W0, cS1142(xf))) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0) = W0)) | (~aFixedPointOf0(W0, xf)))))) | (~((~(aFixedPointOf0(W0, xf) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0) = W0)))))) | aElementOf0(W0, cS1142(xf)))))))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(45,plain,
% 0.18/0.51 (![W0: $i] : (~((~((~aElementOf0(W0, cS1142(xf))) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0) = W0)) | (~aFixedPointOf0(W0, xf)))))) | (~((~(aFixedPointOf0(W0, xf) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0) = W0)))))) | aElementOf0(W0, cS1142(xf)))))) <=> ![W0: $i] : (~((~((~aElementOf0(W0, cS1142(xf))) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0) = W0)) | (~aFixedPointOf0(W0, xf)))))) | (~((~(aFixedPointOf0(W0, xf) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0) = W0)))))) | aElementOf0(W0, cS1142(xf))))))),
% 0.18/0.51 inference(quant_intro,[status(thm)],[44])).
% 0.18/0.51 tff(46,plain,
% 0.18/0.51 (^[W0: $i] : trans(monotonicity(rewrite(((~aElementOf0(W0, cS1142(xf))) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0) & aFixedPointOf0(W0, xf))) <=> ((~aElementOf0(W0, cS1142(xf))) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0) = W0)) | (~aFixedPointOf0(W0, xf)))))), rewrite(((~(aFixedPointOf0(W0, xf) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0)))) | aElementOf0(W0, cS1142(xf))) <=> ((~(aFixedPointOf0(W0, xf) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0) = W0)))))) | aElementOf0(W0, cS1142(xf)))), ((((~aElementOf0(W0, cS1142(xf))) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0) & aFixedPointOf0(W0, xf))) & ((~(aFixedPointOf0(W0, xf) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0)))) | aElementOf0(W0, cS1142(xf)))) <=> (((~aElementOf0(W0, cS1142(xf))) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0) = W0)) | (~aFixedPointOf0(W0, xf))))) & ((~(aFixedPointOf0(W0, xf) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0) = W0)))))) | aElementOf0(W0, cS1142(xf)))))), rewrite((((~aElementOf0(W0, cS1142(xf))) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0) = W0)) | (~aFixedPointOf0(W0, xf))))) & ((~(aFixedPointOf0(W0, xf) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0) = W0)))))) | aElementOf0(W0, cS1142(xf)))) <=> (~((~((~aElementOf0(W0, cS1142(xf))) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0) = W0)) | (~aFixedPointOf0(W0, xf)))))) | (~((~(aFixedPointOf0(W0, xf) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0) = W0)))))) | aElementOf0(W0, cS1142(xf))))))), ((((~aElementOf0(W0, cS1142(xf))) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0) & aFixedPointOf0(W0, xf))) & ((~(aFixedPointOf0(W0, xf) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0)))) | aElementOf0(W0, cS1142(xf)))) <=> (~((~((~aElementOf0(W0, cS1142(xf))) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0) = W0)) | (~aFixedPointOf0(W0, xf)))))) | (~((~(aFixedPointOf0(W0, xf) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0) = W0)))))) | aElementOf0(W0, cS1142(xf))))))))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(47,plain,
% 0.18/0.51 (![W0: $i] : (((~aElementOf0(W0, cS1142(xf))) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0) & aFixedPointOf0(W0, xf))) & ((~(aFixedPointOf0(W0, xf) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0)))) | aElementOf0(W0, cS1142(xf)))) <=> ![W0: $i] : (~((~((~aElementOf0(W0, cS1142(xf))) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0) = W0)) | (~aFixedPointOf0(W0, xf)))))) | (~((~(aFixedPointOf0(W0, xf) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0) = W0)))))) | aElementOf0(W0, cS1142(xf))))))),
% 0.18/0.51 inference(quant_intro,[status(thm)],[46])).
% 0.18/0.51 tff(48,plain,
% 0.18/0.51 (^[W0: $i] : rewrite((((~aElementOf0(W0, xS)) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0) & aFixedPointOf0(W0, xf))) & ((~(aFixedPointOf0(W0, xf) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0)))) | aElementOf0(W0, xS))) <=> (((~aElementOf0(W0, cS1142(xf))) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0) & aFixedPointOf0(W0, xf))) & ((~(aFixedPointOf0(W0, xf) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0)))) | aElementOf0(W0, cS1142(xf)))))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(49,plain,
% 0.18/0.51 (![W0: $i] : (((~aElementOf0(W0, xS)) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0) & aFixedPointOf0(W0, xf))) & ((~(aFixedPointOf0(W0, xf) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0)))) | aElementOf0(W0, xS))) <=> ![W0: $i] : (((~aElementOf0(W0, cS1142(xf))) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0) & aFixedPointOf0(W0, xf))) & ((~(aFixedPointOf0(W0, xf) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0)))) | aElementOf0(W0, cS1142(xf))))),
% 0.18/0.51 inference(quant_intro,[status(thm)],[48])).
% 0.18/0.51 tff(50,plain,
% 0.18/0.51 (![W0: $i] : (((~aElementOf0(W0, xS)) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0) & aFixedPointOf0(W0, xf))) & ((~(aFixedPointOf0(W0, xf) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0)))) | aElementOf0(W0, xS))) <=> ![W0: $i] : (((~aElementOf0(W0, xS)) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0) & aFixedPointOf0(W0, xf))) & ((~(aFixedPointOf0(W0, xf) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0)))) | aElementOf0(W0, xS)))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(51,plain,
% 0.18/0.51 (^[W0: $i] : rewrite(((aElementOf0(W0, xS) => ((aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0)) & aFixedPointOf0(W0, xf))) & (((aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0)) | aFixedPointOf0(W0, xf)) => aElementOf0(W0, xS))) <=> (((~aElementOf0(W0, xS)) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0) & aFixedPointOf0(W0, xf))) & ((~(aFixedPointOf0(W0, xf) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0)))) | aElementOf0(W0, xS))))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(52,plain,
% 0.18/0.51 (![W0: $i] : ((aElementOf0(W0, xS) => ((aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0)) & aFixedPointOf0(W0, xf))) & (((aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0)) | aFixedPointOf0(W0, xf)) => aElementOf0(W0, xS))) <=> ![W0: $i] : (((~aElementOf0(W0, xS)) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0) & aFixedPointOf0(W0, xf))) & ((~(aFixedPointOf0(W0, xf) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0)))) | aElementOf0(W0, xS)))),
% 0.18/0.51 inference(quant_intro,[status(thm)],[51])).
% 0.18/0.51 tff(53,axiom,((aSet0(xS) & ![W0: $i] : ((aElementOf0(W0, xS) => ((aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0)) & aFixedPointOf0(W0, xf))) & (((aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0)) | aFixedPointOf0(W0, xf)) => aElementOf0(W0, xS)))) & (xS = cS1142(xf))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__1144')).
% 0.18/0.51 tff(54,plain,
% 0.18/0.51 (aSet0(xS) & ![W0: $i] : ((aElementOf0(W0, xS) => ((aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0)) & aFixedPointOf0(W0, xf))) & (((aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0)) | aFixedPointOf0(W0, xf)) => aElementOf0(W0, xS)))),
% 0.18/0.51 inference(and_elim,[status(thm)],[53])).
% 0.18/0.51 tff(55,plain,
% 0.18/0.51 (![W0: $i] : ((aElementOf0(W0, xS) => ((aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0)) & aFixedPointOf0(W0, xf))) & (((aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0)) | aFixedPointOf0(W0, xf)) => aElementOf0(W0, xS)))),
% 0.18/0.51 inference(and_elim,[status(thm)],[54])).
% 0.18/0.51 tff(56,plain,
% 0.18/0.51 (![W0: $i] : (((~aElementOf0(W0, xS)) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0) & aFixedPointOf0(W0, xf))) & ((~(aFixedPointOf0(W0, xf) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0)))) | aElementOf0(W0, xS)))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[55, 52])).
% 0.18/0.51 tff(57,plain,
% 0.18/0.51 (![W0: $i] : (((~aElementOf0(W0, xS)) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0) & aFixedPointOf0(W0, xf))) & ((~(aFixedPointOf0(W0, xf) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0)))) | aElementOf0(W0, xS)))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[56, 50])).
% 0.18/0.51 tff(58,plain,
% 0.18/0.51 (![W0: $i] : (((~aElementOf0(W0, cS1142(xf))) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0) & aFixedPointOf0(W0, xf))) & ((~(aFixedPointOf0(W0, xf) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0)))) | aElementOf0(W0, cS1142(xf))))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[57, 49])).
% 0.18/0.51 tff(59,plain,(
% 0.18/0.51 ![W0: $i] : (((~aElementOf0(W0, cS1142(xf))) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0) & aFixedPointOf0(W0, xf))) & ((~(aFixedPointOf0(W0, xf) | (aElementOf0(W0, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, W0) = W0)))) | aElementOf0(W0, cS1142(xf))))),
% 0.18/0.51 inference(skolemize,[status(sab)],[58])).
% 0.18/0.51 tff(60,plain,
% 0.18/0.51 (![W0: $i] : (~((~((~aElementOf0(W0, cS1142(xf))) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0) = W0)) | (~aFixedPointOf0(W0, xf)))))) | (~((~(aFixedPointOf0(W0, xf) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0) = W0)))))) | aElementOf0(W0, cS1142(xf))))))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[59, 47])).
% 0.18/0.51 tff(61,plain,
% 0.18/0.51 (![W0: $i] : (~((~((~aElementOf0(W0, cS1142(xf))) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0) = W0)) | (~aFixedPointOf0(W0, xf)))))) | (~((~(aFixedPointOf0(W0, xf) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0) = W0)))))) | aElementOf0(W0, cS1142(xf))))))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[60, 45])).
% 0.18/0.51 tff(62,plain,
% 0.18/0.51 ((~![W0: $i] : (~((~((~aElementOf0(W0, cS1142(xf))) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0) = W0)) | (~aFixedPointOf0(W0, xf)))))) | (~((~(aFixedPointOf0(W0, xf) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0) = W0)))))) | aElementOf0(W0, cS1142(xf))))))) | (~((~((~aElementOf0(W0!18, cS1142(xf))) | (~((~aElementOf0(W0!18, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0!18) = W0!18)) | (~aFixedPointOf0(W0!18, xf)))))) | (~((~(aFixedPointOf0(W0!18, xf) | (~((~aElementOf0(W0!18, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0!18) = W0!18)))))) | aElementOf0(W0!18, cS1142(xf))))))),
% 0.18/0.51 inference(quant_inst,[status(thm)],[])).
% 0.18/0.51 tff(63,plain,
% 0.18/0.51 (~((~((~aElementOf0(W0!18, cS1142(xf))) | (~((~aElementOf0(W0!18, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0!18) = W0!18)) | (~aFixedPointOf0(W0!18, xf)))))) | (~((~(aFixedPointOf0(W0!18, xf) | (~((~aElementOf0(W0!18, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0!18) = W0!18)))))) | aElementOf0(W0!18, cS1142(xf)))))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.18/0.51 tff(64,plain,
% 0.18/0.51 (((~((~aElementOf0(W0!18, cS1142(xf))) | (~((~aElementOf0(W0!18, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0!18) = W0!18)) | (~aFixedPointOf0(W0!18, xf)))))) | (~((~(aFixedPointOf0(W0!18, xf) | (~((~aElementOf0(W0!18, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0!18) = W0!18)))))) | aElementOf0(W0!18, cS1142(xf))))) | ((~aElementOf0(W0!18, cS1142(xf))) | (~((~aElementOf0(W0!18, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0!18) = W0!18)) | (~aFixedPointOf0(W0!18, xf)))))),
% 0.18/0.51 inference(tautology,[status(thm)],[])).
% 0.18/0.51 tff(65,plain,
% 0.18/0.51 ((~aElementOf0(W0!18, cS1142(xf))) | (~((~aElementOf0(W0!18, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0!18) = W0!18)) | (~aFixedPointOf0(W0!18, xf))))),
% 0.18/0.51 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.18/0.51 tff(66,plain,
% 0.18/0.51 (aSet0(xS) <=> aSet0(cS1142(xf))),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(67,plain,
% 0.18/0.51 (aSet0(xS) <=> aSet0(xS)),
% 0.18/0.51 inference(rewrite,[status(thm)],[])).
% 0.18/0.51 tff(68,plain,
% 0.18/0.51 (aSet0(xS)),
% 0.18/0.51 inference(and_elim,[status(thm)],[54])).
% 0.18/0.51 tff(69,plain,
% 0.18/0.51 (aSet0(xS)),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.18/0.51 tff(70,plain,
% 0.18/0.51 (aSet0(cS1142(xf))),
% 0.18/0.51 inference(modus_ponens,[status(thm)],[69, 66])).
% 0.18/0.51 tff(71,plain,
% 0.18/0.51 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))))))))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(72,plain,
% 0.18/0.51 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))),
% 0.18/0.51 inference(quant_intro,[status(thm)],[71])).
% 0.18/0.51 tff(73,plain,
% 0.18/0.51 (^[W0: $i] : refl(((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(74,plain,
% 0.18/0.51 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 0.18/0.51 inference(quant_intro,[status(thm)],[73])).
% 0.18/0.51 tff(75,plain,
% 0.18/0.51 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(76,plain,
% 0.18/0.51 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 0.18/0.51 inference(quant_intro,[status(thm)],[75])).
% 0.18/0.51 tff(77,plain,
% 0.18/0.51 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 0.18/0.51 inference(transitivity,[status(thm)],[76, 74])).
% 0.18/0.51 tff(78,plain,
% 0.18/0.51 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))) <=> ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(79,plain,
% 0.18/0.51 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 0.18/0.51 inference(quant_intro,[status(thm)],[78])).
% 0.18/0.51 tff(80,plain,
% 0.18/0.51 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))) <=> ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))),
% 0.18/0.51 inference(bind,[status(th)],[])).
% 0.18/0.51 tff(81,plain,
% 0.18/0.51 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))),
% 0.18/0.52 inference(quant_intro,[status(thm)],[80])).
% 0.18/0.52 tff(82,plain,
% 0.18/0.52 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(83,plain,
% 0.18/0.52 (^[W0: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: $i] : rewrite((aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0)))) <=> (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))), (![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0)))) <=> ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))), ((aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0))))) <=> (aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))), rewrite((aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))) <=> ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))), ((aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0))))) <=> ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))))),
% 0.18/0.52 inference(bind,[status(th)],[])).
% 0.18/0.52 tff(84,plain,
% 0.18/0.52 (![W0: $i] : (aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))),
% 0.18/0.52 inference(quant_intro,[status(thm)],[83])).
% 0.18/0.52 tff(85,axiom,(![W0: $i] : (aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mDefSub')).
% 0.18/0.52 tff(86,plain,
% 0.18/0.52 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.18/0.52 tff(87,plain,
% 0.18/0.52 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[86, 82])).
% 0.18/0.52 tff(88,plain,(
% 0.18/0.52 ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))),
% 0.18/0.52 inference(skolemize,[status(sab)],[87])).
% 0.18/0.52 tff(89,plain,
% 0.18/0.52 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[88, 81])).
% 0.18/0.52 tff(90,plain,
% 0.18/0.52 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[89, 79])).
% 0.18/0.52 tff(91,plain,
% 0.18/0.52 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[90, 77])).
% 0.18/0.52 tff(92,plain,
% 0.18/0.52 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[91, 72])).
% 0.18/0.52 tff(93,plain,
% 0.18/0.52 (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(cS1142(xf))) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, cS1142(xf)) | (~((~aElementOf0(tptp_fun_W2_1(W1, cS1142(xf)), W1)) | aElementOf0(tptp_fun_W2_1(W1, cS1142(xf)), cS1142(xf)))))) | (~((~aSubsetOf0(W1, cS1142(xf))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, cS1142(xf)))))))))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | (~aSet0(cS1142(xf))) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, cS1142(xf)) | (~((~aElementOf0(tptp_fun_W2_1(W1, cS1142(xf)), W1)) | aElementOf0(tptp_fun_W2_1(W1, cS1142(xf)), cS1142(xf)))))) | (~((~aSubsetOf0(W1, cS1142(xf))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, cS1142(xf)))))))))))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(94,plain,
% 0.18/0.52 (((~aSet0(cS1142(xf))) | ![W1: $i] : (~((~(aSubsetOf0(W1, cS1142(xf)) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, cS1142(xf)), W1)) | aElementOf0(tptp_fun_W2_1(W1, cS1142(xf)), cS1142(xf)))))) | (~((~aSubsetOf0(W1, cS1142(xf))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, cS1142(xf))))))))))) <=> ((~aSet0(cS1142(xf))) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, cS1142(xf)) | (~((~aElementOf0(tptp_fun_W2_1(W1, cS1142(xf)), W1)) | aElementOf0(tptp_fun_W2_1(W1, cS1142(xf)), cS1142(xf)))))) | (~((~aSubsetOf0(W1, cS1142(xf))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, cS1142(xf)))))))))))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(95,plain,
% 0.18/0.52 (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(cS1142(xf))) | ![W1: $i] : (~((~(aSubsetOf0(W1, cS1142(xf)) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, cS1142(xf)), W1)) | aElementOf0(tptp_fun_W2_1(W1, cS1142(xf)), cS1142(xf)))))) | (~((~aSubsetOf0(W1, cS1142(xf))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, cS1142(xf)))))))))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(cS1142(xf))) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, cS1142(xf)) | (~((~aElementOf0(tptp_fun_W2_1(W1, cS1142(xf)), W1)) | aElementOf0(tptp_fun_W2_1(W1, cS1142(xf)), cS1142(xf)))))) | (~((~aSubsetOf0(W1, cS1142(xf))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, cS1142(xf))))))))))))),
% 0.18/0.52 inference(monotonicity,[status(thm)],[94])).
% 0.18/0.52 tff(96,plain,
% 0.18/0.52 (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(cS1142(xf))) | ![W1: $i] : (~((~(aSubsetOf0(W1, cS1142(xf)) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, cS1142(xf)), W1)) | aElementOf0(tptp_fun_W2_1(W1, cS1142(xf)), cS1142(xf)))))) | (~((~aSubsetOf0(W1, cS1142(xf))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, cS1142(xf)))))))))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | (~aSet0(cS1142(xf))) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, cS1142(xf)) | (~((~aElementOf0(tptp_fun_W2_1(W1, cS1142(xf)), W1)) | aElementOf0(tptp_fun_W2_1(W1, cS1142(xf)), cS1142(xf)))))) | (~((~aSubsetOf0(W1, cS1142(xf))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, cS1142(xf)))))))))))),
% 0.18/0.52 inference(transitivity,[status(thm)],[95, 93])).
% 0.18/0.52 tff(97,plain,
% 0.18/0.52 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(cS1142(xf))) | ![W1: $i] : (~((~(aSubsetOf0(W1, cS1142(xf)) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, cS1142(xf)), W1)) | aElementOf0(tptp_fun_W2_1(W1, cS1142(xf)), cS1142(xf)))))) | (~((~aSubsetOf0(W1, cS1142(xf))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, cS1142(xf)))))))))))),
% 0.18/0.52 inference(quant_inst,[status(thm)],[])).
% 0.18/0.52 tff(98,plain,
% 0.18/0.52 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | (~aSet0(cS1142(xf))) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, cS1142(xf)) | (~((~aElementOf0(tptp_fun_W2_1(W1, cS1142(xf)), W1)) | aElementOf0(tptp_fun_W2_1(W1, cS1142(xf)), cS1142(xf)))))) | (~((~aSubsetOf0(W1, cS1142(xf))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, cS1142(xf))))))))))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.18/0.52 tff(99,plain,
% 0.18/0.52 (![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, cS1142(xf)) | (~((~aElementOf0(tptp_fun_W2_1(W1, cS1142(xf)), W1)) | aElementOf0(tptp_fun_W2_1(W1, cS1142(xf)), cS1142(xf)))))) | (~((~aSubsetOf0(W1, cS1142(xf))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, cS1142(xf))))))))))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[98, 92, 70])).
% 0.18/0.52 tff(100,plain,
% 0.18/0.52 (((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, cS1142(xf)) | (~((~aElementOf0(tptp_fun_W2_1(W1, cS1142(xf)), W1)) | aElementOf0(tptp_fun_W2_1(W1, cS1142(xf)), cS1142(xf)))))) | (~((~aSubsetOf0(W1, cS1142(xf))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, cS1142(xf))))))))))) | (~((~(aSubsetOf0(xT, cS1142(xf)) | (~aSet0(xT)) | (~((~aElementOf0(tptp_fun_W2_1(xT, cS1142(xf)), xT)) | aElementOf0(tptp_fun_W2_1(xT, cS1142(xf)), cS1142(xf)))))) | (~((~aSubsetOf0(xT, cS1142(xf))) | (~((~aSet0(xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | aElementOf0(W2, cS1142(xf))))))))))) <=> ((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, cS1142(xf)) | (~((~aElementOf0(tptp_fun_W2_1(W1, cS1142(xf)), W1)) | aElementOf0(tptp_fun_W2_1(W1, cS1142(xf)), cS1142(xf)))))) | (~((~aSubsetOf0(W1, cS1142(xf))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, cS1142(xf))))))))))) | (~((~(aSubsetOf0(xT, cS1142(xf)) | (~aSet0(xT)) | (~((~aElementOf0(tptp_fun_W2_1(xT, cS1142(xf)), xT)) | aElementOf0(tptp_fun_W2_1(xT, cS1142(xf)), cS1142(xf)))))) | (~((~aSubsetOf0(xT, cS1142(xf))) | (~((~aSet0(xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | aElementOf0(W2, cS1142(xf)))))))))))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(101,plain,
% 0.18/0.52 ((~((~((~aSet0(xT)) | aSubsetOf0(xT, cS1142(xf)) | (~((~aElementOf0(tptp_fun_W2_1(xT, cS1142(xf)), xT)) | aElementOf0(tptp_fun_W2_1(xT, cS1142(xf)), cS1142(xf)))))) | (~((~aSubsetOf0(xT, cS1142(xf))) | (~((~aSet0(xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | aElementOf0(W2, cS1142(xf)))))))))) <=> (~((~(aSubsetOf0(xT, cS1142(xf)) | (~aSet0(xT)) | (~((~aElementOf0(tptp_fun_W2_1(xT, cS1142(xf)), xT)) | aElementOf0(tptp_fun_W2_1(xT, cS1142(xf)), cS1142(xf)))))) | (~((~aSubsetOf0(xT, cS1142(xf))) | (~((~aSet0(xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | aElementOf0(W2, cS1142(xf))))))))))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(102,plain,
% 0.18/0.52 (((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, cS1142(xf)) | (~((~aElementOf0(tptp_fun_W2_1(W1, cS1142(xf)), W1)) | aElementOf0(tptp_fun_W2_1(W1, cS1142(xf)), cS1142(xf)))))) | (~((~aSubsetOf0(W1, cS1142(xf))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, cS1142(xf))))))))))) | (~((~((~aSet0(xT)) | aSubsetOf0(xT, cS1142(xf)) | (~((~aElementOf0(tptp_fun_W2_1(xT, cS1142(xf)), xT)) | aElementOf0(tptp_fun_W2_1(xT, cS1142(xf)), cS1142(xf)))))) | (~((~aSubsetOf0(xT, cS1142(xf))) | (~((~aSet0(xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | aElementOf0(W2, cS1142(xf))))))))))) <=> ((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, cS1142(xf)) | (~((~aElementOf0(tptp_fun_W2_1(W1, cS1142(xf)), W1)) | aElementOf0(tptp_fun_W2_1(W1, cS1142(xf)), cS1142(xf)))))) | (~((~aSubsetOf0(W1, cS1142(xf))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, cS1142(xf))))))))))) | (~((~(aSubsetOf0(xT, cS1142(xf)) | (~aSet0(xT)) | (~((~aElementOf0(tptp_fun_W2_1(xT, cS1142(xf)), xT)) | aElementOf0(tptp_fun_W2_1(xT, cS1142(xf)), cS1142(xf)))))) | (~((~aSubsetOf0(xT, cS1142(xf))) | (~((~aSet0(xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | aElementOf0(W2, cS1142(xf)))))))))))),
% 0.18/0.52 inference(monotonicity,[status(thm)],[101])).
% 0.18/0.52 tff(103,plain,
% 0.18/0.52 (((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, cS1142(xf)) | (~((~aElementOf0(tptp_fun_W2_1(W1, cS1142(xf)), W1)) | aElementOf0(tptp_fun_W2_1(W1, cS1142(xf)), cS1142(xf)))))) | (~((~aSubsetOf0(W1, cS1142(xf))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, cS1142(xf))))))))))) | (~((~((~aSet0(xT)) | aSubsetOf0(xT, cS1142(xf)) | (~((~aElementOf0(tptp_fun_W2_1(xT, cS1142(xf)), xT)) | aElementOf0(tptp_fun_W2_1(xT, cS1142(xf)), cS1142(xf)))))) | (~((~aSubsetOf0(xT, cS1142(xf))) | (~((~aSet0(xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | aElementOf0(W2, cS1142(xf))))))))))) <=> ((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, cS1142(xf)) | (~((~aElementOf0(tptp_fun_W2_1(W1, cS1142(xf)), W1)) | aElementOf0(tptp_fun_W2_1(W1, cS1142(xf)), cS1142(xf)))))) | (~((~aSubsetOf0(W1, cS1142(xf))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, cS1142(xf))))))))))) | (~((~(aSubsetOf0(xT, cS1142(xf)) | (~aSet0(xT)) | (~((~aElementOf0(tptp_fun_W2_1(xT, cS1142(xf)), xT)) | aElementOf0(tptp_fun_W2_1(xT, cS1142(xf)), cS1142(xf)))))) | (~((~aSubsetOf0(xT, cS1142(xf))) | (~((~aSet0(xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | aElementOf0(W2, cS1142(xf)))))))))))),
% 0.18/0.52 inference(transitivity,[status(thm)],[102, 100])).
% 0.18/0.52 tff(104,plain,
% 0.18/0.52 ((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, cS1142(xf)) | (~((~aElementOf0(tptp_fun_W2_1(W1, cS1142(xf)), W1)) | aElementOf0(tptp_fun_W2_1(W1, cS1142(xf)), cS1142(xf)))))) | (~((~aSubsetOf0(W1, cS1142(xf))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, cS1142(xf))))))))))) | (~((~((~aSet0(xT)) | aSubsetOf0(xT, cS1142(xf)) | (~((~aElementOf0(tptp_fun_W2_1(xT, cS1142(xf)), xT)) | aElementOf0(tptp_fun_W2_1(xT, cS1142(xf)), cS1142(xf)))))) | (~((~aSubsetOf0(xT, cS1142(xf))) | (~((~aSet0(xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | aElementOf0(W2, cS1142(xf))))))))))),
% 0.18/0.52 inference(quant_inst,[status(thm)],[])).
% 0.18/0.52 tff(105,plain,
% 0.18/0.52 ((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, cS1142(xf)) | (~((~aElementOf0(tptp_fun_W2_1(W1, cS1142(xf)), W1)) | aElementOf0(tptp_fun_W2_1(W1, cS1142(xf)), cS1142(xf)))))) | (~((~aSubsetOf0(W1, cS1142(xf))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, cS1142(xf))))))))))) | (~((~(aSubsetOf0(xT, cS1142(xf)) | (~aSet0(xT)) | (~((~aElementOf0(tptp_fun_W2_1(xT, cS1142(xf)), xT)) | aElementOf0(tptp_fun_W2_1(xT, cS1142(xf)), cS1142(xf)))))) | (~((~aSubsetOf0(xT, cS1142(xf))) | (~((~aSet0(xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | aElementOf0(W2, cS1142(xf))))))))))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.18/0.52 tff(106,plain,
% 0.18/0.52 (~((~(aSubsetOf0(xT, cS1142(xf)) | (~aSet0(xT)) | (~((~aElementOf0(tptp_fun_W2_1(xT, cS1142(xf)), xT)) | aElementOf0(tptp_fun_W2_1(xT, cS1142(xf)), cS1142(xf)))))) | (~((~aSubsetOf0(xT, cS1142(xf))) | (~((~aSet0(xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | aElementOf0(W2, cS1142(xf)))))))))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[105, 99])).
% 0.18/0.52 tff(107,plain,
% 0.18/0.52 (((~(aSubsetOf0(xT, cS1142(xf)) | (~aSet0(xT)) | (~((~aElementOf0(tptp_fun_W2_1(xT, cS1142(xf)), xT)) | aElementOf0(tptp_fun_W2_1(xT, cS1142(xf)), cS1142(xf)))))) | (~((~aSubsetOf0(xT, cS1142(xf))) | (~((~aSet0(xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | aElementOf0(W2, cS1142(xf))))))))) | ((~aSubsetOf0(xT, cS1142(xf))) | (~((~aSet0(xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | aElementOf0(W2, cS1142(xf)))))))),
% 0.18/0.52 inference(tautology,[status(thm)],[])).
% 0.18/0.52 tff(108,plain,
% 0.18/0.52 ((~aSubsetOf0(xT, cS1142(xf))) | (~((~aSet0(xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | aElementOf0(W2, cS1142(xf))))))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.18/0.52 tff(109,plain,
% 0.18/0.52 (aSubsetOf0(xT, xS) <=> aSubsetOf0(xT, cS1142(xf))),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(110,plain,
% 0.18/0.52 (aSubsetOf0(xT, xS) <=> aSubsetOf0(xT, xS)),
% 0.18/0.52 inference(rewrite,[status(thm)],[])).
% 0.18/0.52 tff(111,axiom,((aSet0(xT) & ![W0: $i] : (aElementOf0(W0, xT) => aElementOf0(W0, xS))) & aSubsetOf0(xT, xS)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__1173')).
% 0.18/0.52 tff(112,plain,
% 0.18/0.52 (aSubsetOf0(xT, xS)),
% 0.18/0.52 inference(and_elim,[status(thm)],[111])).
% 0.18/0.52 tff(113,plain,
% 0.18/0.52 (aSubsetOf0(xT, xS)),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[112, 110])).
% 0.18/0.52 tff(114,plain,
% 0.18/0.52 (aSubsetOf0(xT, cS1142(xf))),
% 0.18/0.52 inference(modus_ponens,[status(thm)],[113, 109])).
% 0.18/0.52 tff(115,plain,
% 0.18/0.52 ((~((~aSubsetOf0(xT, cS1142(xf))) | (~((~aSet0(xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | aElementOf0(W2, cS1142(xf)))))))) | (~aSubsetOf0(xT, cS1142(xf))) | (~((~aSet0(xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | aElementOf0(W2, cS1142(xf))))))),
% 0.18/0.52 inference(tautology,[status(thm)],[])).
% 0.18/0.52 tff(116,plain,
% 0.18/0.52 ((~((~aSubsetOf0(xT, cS1142(xf))) | (~((~aSet0(xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | aElementOf0(W2, cS1142(xf)))))))) | (~((~aSet0(xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | aElementOf0(W2, cS1142(xf))))))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[115, 114])).
% 0.18/0.52 tff(117,plain,
% 0.18/0.52 (~((~aSet0(xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | aElementOf0(W2, cS1142(xf)))))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[116, 108])).
% 0.18/0.52 tff(118,plain,
% 0.18/0.52 (((~aSet0(xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | aElementOf0(W2, cS1142(xf))))) | ![W2: $i] : ((~aElementOf0(W2, xT)) | aElementOf0(W2, cS1142(xf)))),
% 0.18/0.52 inference(tautology,[status(thm)],[])).
% 0.18/0.52 tff(119,plain,
% 0.18/0.52 (![W2: $i] : ((~aElementOf0(W2, xT)) | aElementOf0(W2, cS1142(xf)))),
% 0.18/0.52 inference(unit_resolution,[status(thm)],[118, 117])).
% 0.18/0.52 tff(120,assumption,(~(aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szDzozmdt0(xf)) | (~aElementOf0(W0!18, xT)) | sdtlseqdt0(W0!18, sdtlpdtrp0(xf, xp)))), introduced(assumption)).
% 0.18/0.52 tff(121,plain,
% 0.18/0.52 ((aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szDzozmdt0(xf)) | (~aElementOf0(W0!18, xT)) | sdtlseqdt0(W0!18, sdtlpdtrp0(xf, xp))) | aElementOf0(W0!18, xT)),
% 0.18/0.53 inference(tautology,[status(thm)],[])).
% 0.18/0.53 tff(122,plain,
% 0.18/0.53 (aElementOf0(W0!18, xT)),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[121, 120])).
% 0.18/0.53 tff(123,plain,
% 0.18/0.53 (((~![W2: $i] : ((~aElementOf0(W2, xT)) | aElementOf0(W2, cS1142(xf)))) | ((~aElementOf0(W0!18, xT)) | aElementOf0(W0!18, cS1142(xf)))) <=> ((~![W2: $i] : ((~aElementOf0(W2, xT)) | aElementOf0(W2, cS1142(xf)))) | (~aElementOf0(W0!18, xT)) | aElementOf0(W0!18, cS1142(xf)))),
% 0.18/0.53 inference(rewrite,[status(thm)],[])).
% 0.18/0.53 tff(124,plain,
% 0.18/0.53 ((~![W2: $i] : ((~aElementOf0(W2, xT)) | aElementOf0(W2, cS1142(xf)))) | ((~aElementOf0(W0!18, xT)) | aElementOf0(W0!18, cS1142(xf)))),
% 0.18/0.53 inference(quant_inst,[status(thm)],[])).
% 0.18/0.53 tff(125,plain,
% 0.18/0.53 ((~![W2: $i] : ((~aElementOf0(W2, xT)) | aElementOf0(W2, cS1142(xf)))) | (~aElementOf0(W0!18, xT)) | aElementOf0(W0!18, cS1142(xf))),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.18/0.53 tff(126,plain,
% 0.18/0.53 (aElementOf0(W0!18, cS1142(xf))),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[125, 122, 119])).
% 0.18/0.53 tff(127,plain,
% 0.18/0.53 ((~((~aElementOf0(W0!18, cS1142(xf))) | (~((~aElementOf0(W0!18, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0!18) = W0!18)) | (~aFixedPointOf0(W0!18, xf)))))) | (~aElementOf0(W0!18, cS1142(xf))) | (~((~aElementOf0(W0!18, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0!18) = W0!18)) | (~aFixedPointOf0(W0!18, xf))))),
% 0.18/0.53 inference(tautology,[status(thm)],[])).
% 0.18/0.53 tff(128,plain,
% 0.18/0.53 ((~((~aElementOf0(W0!18, cS1142(xf))) | (~((~aElementOf0(W0!18, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0!18) = W0!18)) | (~aFixedPointOf0(W0!18, xf)))))) | (~((~aElementOf0(W0!18, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0!18) = W0!18)) | (~aFixedPointOf0(W0!18, xf))))),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[127, 126])).
% 0.18/0.53 tff(129,plain,
% 0.18/0.53 (~((~aElementOf0(W0!18, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0!18) = W0!18)) | (~aFixedPointOf0(W0!18, xf)))),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[128, 65])).
% 0.18/0.53 tff(130,plain,
% 0.18/0.53 (((~aElementOf0(W0!18, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0!18) = W0!18)) | (~aFixedPointOf0(W0!18, xf))) | (sdtlpdtrp0(xf, W0!18) = W0!18)),
% 0.18/0.53 inference(tautology,[status(thm)],[])).
% 0.18/0.53 tff(131,plain,
% 0.18/0.53 (sdtlpdtrp0(xf, W0!18) = W0!18),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[130, 129])).
% 0.18/0.53 tff(132,plain,
% 0.18/0.53 (sdtlseqdt0(sdtlpdtrp0(xf, W0!18), sdtlpdtrp0(xf, xp)) <=> sdtlseqdt0(W0!18, sdtlpdtrp0(xf, xp))),
% 0.18/0.53 inference(monotonicity,[status(thm)],[131])).
% 0.18/0.53 tff(133,plain,
% 0.18/0.53 (sdtlseqdt0(W0!18, sdtlpdtrp0(xf, xp)) <=> sdtlseqdt0(sdtlpdtrp0(xf, W0!18), sdtlpdtrp0(xf, xp))),
% 0.18/0.53 inference(symmetry,[status(thm)],[132])).
% 0.18/0.53 tff(134,plain,
% 0.18/0.53 ((~sdtlseqdt0(W0!18, sdtlpdtrp0(xf, xp))) <=> (~sdtlseqdt0(sdtlpdtrp0(xf, W0!18), sdtlpdtrp0(xf, xp)))),
% 0.18/0.53 inference(monotonicity,[status(thm)],[133])).
% 0.18/0.53 tff(135,plain,
% 0.18/0.53 ((aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szDzozmdt0(xf)) | (~aElementOf0(W0!18, xT)) | sdtlseqdt0(W0!18, sdtlpdtrp0(xf, xp))) | (~sdtlseqdt0(W0!18, sdtlpdtrp0(xf, xp)))),
% 0.18/0.53 inference(tautology,[status(thm)],[])).
% 0.18/0.53 tff(136,plain,
% 0.18/0.53 (~sdtlseqdt0(W0!18, sdtlpdtrp0(xf, xp))),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[135, 120])).
% 0.18/0.53 tff(137,plain,
% 0.18/0.53 (~sdtlseqdt0(sdtlpdtrp0(xf, W0!18), sdtlpdtrp0(xf, xp))),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[136, 134])).
% 0.18/0.53 tff(138,plain,
% 0.18/0.53 (((~aElementOf0(W0!18, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0!18) = W0!18)) | (~aFixedPointOf0(W0!18, xf))) | aElementOf0(W0!18, szDzozmdt0(xf))),
% 0.18/0.53 inference(tautology,[status(thm)],[])).
% 0.18/0.53 tff(139,plain,
% 0.18/0.53 (aElementOf0(W0!18, szDzozmdt0(xf))),
% 0.18/0.53 inference(unit_resolution,[status(thm)],[138, 129])).
% 0.18/0.53 tff(140,plain,
% 0.18/0.53 (aElementOf0(xp, szRzazndt0(xf)) <=> aElementOf0(xp, szDzozmdt0(xf))),
% 0.18/0.53 inference(rewrite,[status(thm)],[])).
% 0.18/0.53 tff(141,plain,
% 0.18/0.53 (aElementOf0(xp, xU) <=> aElementOf0(xp, szRzazndt0(xf))),
% 0.18/0.53 inference(rewrite,[status(thm)],[])).
% 0.18/0.53 tff(142,plain,
% 0.18/0.53 (aElementOf0(xp, xU) <=> aElementOf0(xp, xU)),
% 0.18/0.53 inference(rewrite,[status(thm)],[])).
% 0.18/0.53 tff(143,axiom,(((((aElementOf0(xp, xU) & aElementOf0(xp, xU)) & ![W0: $i] : (aElementOf0(W0, xP) => sdtlseqdt0(xp, W0))) & aLowerBoundOfIn0(xp, xP, xU)) & ![W0: $i] : (((aElementOf0(W0, xU) & ![W1: $i] : (aElementOf0(W1, xP) => sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, xP, xU)) => sdtlseqdt0(W0, xp))) & aInfimumOfIn0(xp, xP, xU)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__1261')).
% 0.18/0.53 tff(144,plain,
% 0.18/0.53 ((((aElementOf0(xp, xU) & aElementOf0(xp, xU)) & ![W0: $i] : (aElementOf0(W0, xP) => sdtlseqdt0(xp, W0))) & aLowerBoundOfIn0(xp, xP, xU)) & ![W0: $i] : (((aElementOf0(W0, xU) & ![W1: $i] : (aElementOf0(W1, xP) => sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, xP, xU)) => sdtlseqdt0(W0, xp))),
% 0.18/0.53 inference(and_elim,[status(thm)],[143])).
% 0.18/0.53 tff(145,plain,
% 0.18/0.53 (((aElementOf0(xp, xU) & aElementOf0(xp, xU)) & ![W0: $i] : (aElementOf0(W0, xP) => sdtlseqdt0(xp, W0))) & aLowerBoundOfIn0(xp, xP, xU)),
% 0.18/0.53 inference(and_elim,[status(thm)],[144])).
% 0.18/0.53 tff(146,plain,
% 0.18/0.53 ((aElementOf0(xp, xU) & aElementOf0(xp, xU)) & ![W0: $i] : (aElementOf0(W0, xP) => sdtlseqdt0(xp, W0))),
% 0.18/0.53 inference(and_elim,[status(thm)],[145])).
% 0.18/0.53 tff(147,plain,
% 0.18/0.53 (aElementOf0(xp, xU) & aElementOf0(xp, xU)),
% 0.18/0.53 inference(and_elim,[status(thm)],[146])).
% 0.18/0.53 tff(148,plain,
% 0.18/0.53 (aElementOf0(xp, xU)),
% 0.18/0.53 inference(and_elim,[status(thm)],[147])).
% 0.18/0.53 tff(149,plain,
% 0.18/0.53 (aElementOf0(xp, xU)),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[148, 142])).
% 0.18/0.53 tff(150,plain,
% 0.18/0.53 (aElementOf0(xp, szRzazndt0(xf))),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[149, 141])).
% 0.18/0.53 tff(151,plain,
% 0.18/0.53 (aElementOf0(xp, szDzozmdt0(xf))),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[150, 140])).
% 0.18/0.53 tff(152,plain,
% 0.18/0.53 (^[W0: $i, W1: $i] : refl((sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1)) | (~sdtlseqdt0(W0, W1)) | (~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W0, szDzozmdt0(xf)))) <=> (sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1)) | (~sdtlseqdt0(W0, W1)) | (~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W0, szDzozmdt0(xf)))))),
% 0.18/0.53 inference(bind,[status(th)],[])).
% 0.18/0.53 tff(153,plain,
% 0.18/0.53 (![W0: $i, W1: $i] : (sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1)) | (~sdtlseqdt0(W0, W1)) | (~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W0, szDzozmdt0(xf)))) <=> ![W0: $i, W1: $i] : (sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1)) | (~sdtlseqdt0(W0, W1)) | (~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W0, szDzozmdt0(xf))))),
% 0.18/0.53 inference(quant_intro,[status(thm)],[152])).
% 0.18/0.53 tff(154,plain,
% 0.18/0.53 (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aElementOf0(W0, szDzozmdt0(xf)) & aElementOf0(W1, szDzozmdt0(xf))) <=> (~((~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W0, szDzozmdt0(xf)))))), ((~(aElementOf0(W0, szDzozmdt0(xf)) & aElementOf0(W1, szDzozmdt0(xf)))) <=> (~(~((~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W0, szDzozmdt0(xf)))))))), rewrite((~(~((~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W0, szDzozmdt0(xf)))))) <=> ((~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W0, szDzozmdt0(xf))))), ((~(aElementOf0(W0, szDzozmdt0(xf)) & aElementOf0(W1, szDzozmdt0(xf)))) <=> ((~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W0, szDzozmdt0(xf)))))), ((sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1)) | (~sdtlseqdt0(W0, W1)) | (~(aElementOf0(W0, szDzozmdt0(xf)) & aElementOf0(W1, szDzozmdt0(xf))))) <=> (sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1)) | (~sdtlseqdt0(W0, W1)) | ((~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W0, szDzozmdt0(xf))))))), rewrite((sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1)) | (~sdtlseqdt0(W0, W1)) | ((~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W0, szDzozmdt0(xf))))) <=> (sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1)) | (~sdtlseqdt0(W0, W1)) | (~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W0, szDzozmdt0(xf))))), ((sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1)) | (~sdtlseqdt0(W0, W1)) | (~(aElementOf0(W0, szDzozmdt0(xf)) & aElementOf0(W1, szDzozmdt0(xf))))) <=> (sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1)) | (~sdtlseqdt0(W0, W1)) | (~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W0, szDzozmdt0(xf))))))),
% 0.18/0.53 inference(bind,[status(th)],[])).
% 0.18/0.53 tff(155,plain,
% 0.18/0.53 (![W0: $i, W1: $i] : (sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1)) | (~sdtlseqdt0(W0, W1)) | (~(aElementOf0(W0, szDzozmdt0(xf)) & aElementOf0(W1, szDzozmdt0(xf))))) <=> ![W0: $i, W1: $i] : (sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1)) | (~sdtlseqdt0(W0, W1)) | (~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W0, szDzozmdt0(xf))))),
% 0.18/0.53 inference(quant_intro,[status(thm)],[154])).
% 0.18/0.53 tff(156,plain,
% 0.18/0.53 (![W0: $i, W1: $i] : (sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1)) | (~sdtlseqdt0(W0, W1)) | (~(aElementOf0(W0, szDzozmdt0(xf)) & aElementOf0(W1, szDzozmdt0(xf))))) <=> ![W0: $i, W1: $i] : (sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1)) | (~sdtlseqdt0(W0, W1)) | (~(aElementOf0(W0, szDzozmdt0(xf)) & aElementOf0(W1, szDzozmdt0(xf)))))),
% 0.18/0.53 inference(rewrite,[status(thm)],[])).
% 0.18/0.53 tff(157,plain,
% 0.18/0.53 (^[W0: $i, W1: $i] : trans(monotonicity(rewrite((sdtlseqdt0(W0, W1) => sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1))) <=> ((~sdtlseqdt0(W0, W1)) | sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1)))), (((aElementOf0(W0, szDzozmdt0(xf)) & aElementOf0(W1, szDzozmdt0(xf))) => (sdtlseqdt0(W0, W1) => sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1)))) <=> ((aElementOf0(W0, szDzozmdt0(xf)) & aElementOf0(W1, szDzozmdt0(xf))) => ((~sdtlseqdt0(W0, W1)) | sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1)))))), rewrite(((aElementOf0(W0, szDzozmdt0(xf)) & aElementOf0(W1, szDzozmdt0(xf))) => ((~sdtlseqdt0(W0, W1)) | sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1)))) <=> (sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1)) | (~sdtlseqdt0(W0, W1)) | (~(aElementOf0(W0, szDzozmdt0(xf)) & aElementOf0(W1, szDzozmdt0(xf)))))), (((aElementOf0(W0, szDzozmdt0(xf)) & aElementOf0(W1, szDzozmdt0(xf))) => (sdtlseqdt0(W0, W1) => sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1)))) <=> (sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1)) | (~sdtlseqdt0(W0, W1)) | (~(aElementOf0(W0, szDzozmdt0(xf)) & aElementOf0(W1, szDzozmdt0(xf)))))))),
% 0.18/0.53 inference(bind,[status(th)],[])).
% 0.18/0.53 tff(158,plain,
% 0.18/0.53 (![W0: $i, W1: $i] : ((aElementOf0(W0, szDzozmdt0(xf)) & aElementOf0(W1, szDzozmdt0(xf))) => (sdtlseqdt0(W0, W1) => sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1)))) <=> ![W0: $i, W1: $i] : (sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1)) | (~sdtlseqdt0(W0, W1)) | (~(aElementOf0(W0, szDzozmdt0(xf)) & aElementOf0(W1, szDzozmdt0(xf)))))),
% 0.18/0.53 inference(quant_intro,[status(thm)],[157])).
% 0.18/0.53 tff(159,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/sandbox/benchmark/theBenchmark.p','m__1123')).
% 0.18/0.53 tff(160,plain,
% 0.18/0.53 (((((((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)),
% 0.18/0.53 inference(and_elim,[status(thm)],[159])).
% 0.18/0.53 tff(161,plain,
% 0.18/0.53 ((((((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))),
% 0.18/0.53 inference(and_elim,[status(thm)],[160])).
% 0.18/0.53 tff(162,plain,
% 0.18/0.53 (((((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)),
% 0.18/0.53 inference(and_elim,[status(thm)],[161])).
% 0.18/0.53 tff(163,plain,
% 0.18/0.53 ((((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))))),
% 0.18/0.53 inference(and_elim,[status(thm)],[162])).
% 0.18/0.53 tff(164,plain,
% 0.18/0.53 (![W0: $i, W1: $i] : ((aElementOf0(W0, szDzozmdt0(xf)) & aElementOf0(W1, szDzozmdt0(xf))) => (sdtlseqdt0(W0, W1) => sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1))))),
% 0.18/0.53 inference(and_elim,[status(thm)],[163])).
% 0.18/0.53 tff(165,plain,
% 0.18/0.53 (![W0: $i, W1: $i] : (sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1)) | (~sdtlseqdt0(W0, W1)) | (~(aElementOf0(W0, szDzozmdt0(xf)) & aElementOf0(W1, szDzozmdt0(xf)))))),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[164, 158])).
% 0.18/0.53 tff(166,plain,
% 0.18/0.53 (![W0: $i, W1: $i] : (sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1)) | (~sdtlseqdt0(W0, W1)) | (~(aElementOf0(W0, szDzozmdt0(xf)) & aElementOf0(W1, szDzozmdt0(xf)))))),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[165, 156])).
% 0.18/0.53 tff(167,plain,(
% 0.18/0.53 ![W0: $i, W1: $i] : (sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1)) | (~sdtlseqdt0(W0, W1)) | (~(aElementOf0(W0, szDzozmdt0(xf)) & aElementOf0(W1, szDzozmdt0(xf)))))),
% 0.18/0.53 inference(skolemize,[status(sab)],[166])).
% 0.18/0.53 tff(168,plain,
% 0.18/0.53 (![W0: $i, W1: $i] : (sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1)) | (~sdtlseqdt0(W0, W1)) | (~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W0, szDzozmdt0(xf))))),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[167, 155])).
% 0.18/0.53 tff(169,plain,
% 0.18/0.53 (![W0: $i, W1: $i] : (sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1)) | (~sdtlseqdt0(W0, W1)) | (~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W0, szDzozmdt0(xf))))),
% 0.18/0.53 inference(modus_ponens,[status(thm)],[168, 153])).
% 0.18/0.53 tff(170,plain,
% 0.18/0.53 (((~![W0: $i, W1: $i] : (sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1)) | (~sdtlseqdt0(W0, W1)) | (~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W0, szDzozmdt0(xf))))) | ((~aElementOf0(xp, szDzozmdt0(xf))) | (~aElementOf0(W0!18, szDzozmdt0(xf))) | sdtlseqdt0(sdtlpdtrp0(xf, W0!18), sdtlpdtrp0(xf, xp)) | (~sdtlseqdt0(W0!18, xp)))) <=> ((~![W0: $i, W1: $i] : (sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1)) | (~sdtlseqdt0(W0, W1)) | (~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W0, szDzozmdt0(xf))))) | (~aElementOf0(xp, szDzozmdt0(xf))) | (~aElementOf0(W0!18, szDzozmdt0(xf))) | sdtlseqdt0(sdtlpdtrp0(xf, W0!18), sdtlpdtrp0(xf, xp)) | (~sdtlseqdt0(W0!18, xp)))),
% 0.18/0.53 inference(rewrite,[status(thm)],[])).
% 0.18/0.53 tff(171,plain,
% 0.18/0.53 ((sdtlseqdt0(sdtlpdtrp0(xf, W0!18), sdtlpdtrp0(xf, xp)) | (~sdtlseqdt0(W0!18, xp)) | (~aElementOf0(xp, szDzozmdt0(xf))) | (~aElementOf0(W0!18, szDzozmdt0(xf)))) <=> ((~aElementOf0(xp, szDzozmdt0(xf))) | (~aElementOf0(W0!18, szDzozmdt0(xf))) | sdtlseqdt0(sdtlpdtrp0(xf, W0!18), sdtlpdtrp0(xf, xp)) | (~sdtlseqdt0(W0!18, xp)))),
% 0.18/0.53 inference(rewrite,[status(thm)],[])).
% 0.18/0.53 tff(172,plain,
% 0.18/0.53 (((~![W0: $i, W1: $i] : (sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1)) | (~sdtlseqdt0(W0, W1)) | (~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W0, szDzozmdt0(xf))))) | (sdtlseqdt0(sdtlpdtrp0(xf, W0!18), sdtlpdtrp0(xf, xp)) | (~sdtlseqdt0(W0!18, xp)) | (~aElementOf0(xp, szDzozmdt0(xf))) | (~aElementOf0(W0!18, szDzozmdt0(xf))))) <=> ((~![W0: $i, W1: $i] : (sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1)) | (~sdtlseqdt0(W0, W1)) | (~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W0, szDzozmdt0(xf))))) | ((~aElementOf0(xp, szDzozmdt0(xf))) | (~aElementOf0(W0!18, szDzozmdt0(xf))) | sdtlseqdt0(sdtlpdtrp0(xf, W0!18), sdtlpdtrp0(xf, xp)) | (~sdtlseqdt0(W0!18, xp))))),
% 0.18/0.53 inference(monotonicity,[status(thm)],[171])).
% 0.18/0.53 tff(173,plain,
% 0.18/0.53 (((~![W0: $i, W1: $i] : (sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1)) | (~sdtlseqdt0(W0, W1)) | (~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W0, szDzozmdt0(xf))))) | (sdtlseqdt0(sdtlpdtrp0(xf, W0!18), sdtlpdtrp0(xf, xp)) | (~sdtlseqdt0(W0!18, xp)) | (~aElementOf0(xp, szDzozmdt0(xf))) | (~aElementOf0(W0!18, szDzozmdt0(xf))))) <=> ((~![W0: $i, W1: $i] : (sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1)) | (~sdtlseqdt0(W0, W1)) | (~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W0, szDzozmdt0(xf))))) | (~aElementOf0(xp, szDzozmdt0(xf))) | (~aElementOf0(W0!18, szDzozmdt0(xf))) | sdtlseqdt0(sdtlpdtrp0(xf, W0!18), sdtlpdtrp0(xf, xp)) | (~sdtlseqdt0(W0!18, xp)))),
% 0.18/0.53 inference(transitivity,[status(thm)],[172, 170])).
% 0.18/0.53 tff(174,plain,
% 0.18/0.53 ((~![W0: $i, W1: $i] : (sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1)) | (~sdtlseqdt0(W0, W1)) | (~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W0, szDzozmdt0(xf))))) | (sdtlseqdt0(sdtlpdtrp0(xf, W0!18), sdtlpdtrp0(xf, xp)) | (~sdtlseqdt0(W0!18, xp)) | (~aElementOf0(xp, szDzozmdt0(xf))) | (~aElementOf0(W0!18, szDzozmdt0(xf))))),
% 0.18/0.54 inference(quant_inst,[status(thm)],[])).
% 0.18/0.54 tff(175,plain,
% 0.18/0.54 ((~![W0: $i, W1: $i] : (sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1)) | (~sdtlseqdt0(W0, W1)) | (~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W0, szDzozmdt0(xf))))) | (~aElementOf0(xp, szDzozmdt0(xf))) | (~aElementOf0(W0!18, szDzozmdt0(xf))) | sdtlseqdt0(sdtlpdtrp0(xf, W0!18), sdtlpdtrp0(xf, xp)) | (~sdtlseqdt0(W0!18, xp))),
% 0.18/0.54 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.18/0.54 tff(176,plain,
% 0.18/0.54 (sdtlseqdt0(sdtlpdtrp0(xf, W0!18), sdtlpdtrp0(xf, xp)) | (~sdtlseqdt0(W0!18, xp))),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[175, 169, 151, 139])).
% 0.18/0.54 tff(177,plain,
% 0.18/0.54 (~sdtlseqdt0(W0!18, xp)),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[176, 137])).
% 0.18/0.54 tff(178,plain,
% 0.18/0.54 (^[W0: $i] : refl((sdtlseqdt0(W0, xp) | (~((~((~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(W0, xp) | (~((~((~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))))))),
% 0.18/0.54 inference(bind,[status(th)],[])).
% 0.18/0.54 tff(179,plain,
% 0.18/0.54 (![W0: $i] : (sdtlseqdt0(W0, xp) | (~((~((~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))))) <=> ![W0: $i] : (sdtlseqdt0(W0, xp) | (~((~((~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)))))),
% 0.18/0.54 inference(quant_intro,[status(thm)],[178])).
% 0.18/0.54 tff(180,plain,
% 0.18/0.54 (^[W0: $i] : 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))))), ((sdtlseqdt0(W0, xp) | (((~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(W0, xp) | (~((~((~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((sdtlseqdt0(W0, xp) | (~((~((~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(W0, xp) | (~((~((~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(W0, xp) | (((~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(W0, xp) | (~((~((~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)))))))),
% 0.18/0.54 inference(bind,[status(th)],[])).
% 0.18/0.54 tff(181,plain,
% 0.18/0.54 (![W0: $i] : (sdtlseqdt0(W0, xp) | (((~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))))) <=> ![W0: $i] : (sdtlseqdt0(W0, xp) | (~((~((~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)))))),
% 0.18/0.54 inference(quant_intro,[status(thm)],[180])).
% 0.18/0.54 tff(182,plain,
% 0.18/0.54 (^[W0: $i] : 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)))) | sdtlseqdt0(W0, xp)) <=> (sdtlseqdt0(W0, xp) | (((~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))))))),
% 0.18/0.54 inference(bind,[status(th)],[])).
% 0.18/0.54 tff(183,plain,
% 0.18/0.54 (![W0: $i] : ((((~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(W0, xp)) <=> ![W0: $i] : (sdtlseqdt0(W0, xp) | (((~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)))))),
% 0.18/0.54 inference(quant_intro,[status(thm)],[182])).
% 0.18/0.54 tff(184,plain,
% 0.18/0.54 (^[W0: $i] : rewrite(((~((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)))) | sdtlseqdt0(W0, xp)) <=> ((~((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)))) | sdtlseqdt0(W0, xp)))),
% 0.18/0.54 inference(bind,[status(th)],[])).
% 0.18/0.54 tff(185,plain,
% 0.18/0.54 (![W0: $i] : ((~((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)))) | sdtlseqdt0(W0, xp)) <=> ![W0: $i] : ((~((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)))) | sdtlseqdt0(W0, xp))),
% 0.18/0.54 inference(quant_intro,[status(thm)],[184])).
% 0.18/0.54 tff(186,plain,
% 0.18/0.54 (^[W0: $i] : rewrite(((~((aElementOf0(W0, xU) & ![W1: $i] : ((~aElementOf0(W1, xP)) | sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, xP, xU))) | sdtlseqdt0(W0, xp)) <=> ((~((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)))) | sdtlseqdt0(W0, xp)))),
% 0.18/0.54 inference(bind,[status(th)],[])).
% 0.18/0.54 tff(187,plain,
% 0.18/0.54 (![W0: $i] : ((~((aElementOf0(W0, xU) & ![W1: $i] : ((~aElementOf0(W1, xP)) | sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, xP, xU))) | sdtlseqdt0(W0, xp)) <=> ![W0: $i] : ((~((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)))) | sdtlseqdt0(W0, xp))),
% 0.18/0.54 inference(quant_intro,[status(thm)],[186])).
% 0.18/0.54 tff(188,plain,
% 0.18/0.54 (![W0: $i] : ((~((aElementOf0(W0, xU) & ![W1: $i] : ((~aElementOf0(W1, xP)) | sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, xP, xU))) | sdtlseqdt0(W0, xp)) <=> ![W0: $i] : ((~((aElementOf0(W0, xU) & ![W1: $i] : ((~aElementOf0(W1, xP)) | sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, xP, xU))) | sdtlseqdt0(W0, xp))),
% 0.18/0.54 inference(rewrite,[status(thm)],[])).
% 0.18/0.54 tff(189,plain,
% 0.18/0.54 (^[W0: $i] : trans(monotonicity(rewrite(((aElementOf0(W0, xU) & ![W1: $i] : (aElementOf0(W1, xP) => sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, xP, xU)) <=> ((aElementOf0(W0, xU) & ![W1: $i] : ((~aElementOf0(W1, xP)) | sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, xP, xU))), ((((aElementOf0(W0, xU) & ![W1: $i] : (aElementOf0(W1, xP) => sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, xP, xU)) => sdtlseqdt0(W0, xp)) <=> (((aElementOf0(W0, xU) & ![W1: $i] : ((~aElementOf0(W1, xP)) | sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, xP, xU)) => sdtlseqdt0(W0, xp)))), rewrite((((aElementOf0(W0, xU) & ![W1: $i] : ((~aElementOf0(W1, xP)) | sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, xP, xU)) => sdtlseqdt0(W0, xp)) <=> ((~((aElementOf0(W0, xU) & ![W1: $i] : ((~aElementOf0(W1, xP)) | sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, xP, xU))) | sdtlseqdt0(W0, xp))), ((((aElementOf0(W0, xU) & ![W1: $i] : (aElementOf0(W1, xP) => sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, xP, xU)) => sdtlseqdt0(W0, xp)) <=> ((~((aElementOf0(W0, xU) & ![W1: $i] : ((~aElementOf0(W1, xP)) | sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, xP, xU))) | sdtlseqdt0(W0, xp))))),
% 0.18/0.54 inference(bind,[status(th)],[])).
% 0.18/0.54 tff(190,plain,
% 0.18/0.54 (![W0: $i] : (((aElementOf0(W0, xU) & ![W1: $i] : (aElementOf0(W1, xP) => sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, xP, xU)) => sdtlseqdt0(W0, xp)) <=> ![W0: $i] : ((~((aElementOf0(W0, xU) & ![W1: $i] : ((~aElementOf0(W1, xP)) | sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, xP, xU))) | sdtlseqdt0(W0, xp))),
% 0.18/0.54 inference(quant_intro,[status(thm)],[189])).
% 0.18/0.54 tff(191,plain,
% 0.18/0.54 (![W0: $i] : (((aElementOf0(W0, xU) & ![W1: $i] : (aElementOf0(W1, xP) => sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, xP, xU)) => sdtlseqdt0(W0, xp))),
% 0.18/0.54 inference(and_elim,[status(thm)],[144])).
% 0.18/0.54 tff(192,plain,
% 0.18/0.54 (![W0: $i] : ((~((aElementOf0(W0, xU) & ![W1: $i] : ((~aElementOf0(W1, xP)) | sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, xP, xU))) | sdtlseqdt0(W0, xp))),
% 0.18/0.54 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.18/0.54 tff(193,plain,
% 0.18/0.54 (![W0: $i] : ((~((aElementOf0(W0, xU) & ![W1: $i] : ((~aElementOf0(W1, xP)) | sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, xP, xU))) | sdtlseqdt0(W0, xp))),
% 0.18/0.54 inference(modus_ponens,[status(thm)],[192, 188])).
% 0.18/0.54 tff(194,plain,
% 0.18/0.54 (![W0: $i] : ((~((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)))) | sdtlseqdt0(W0, xp))),
% 0.18/0.54 inference(modus_ponens,[status(thm)],[193, 187])).
% 0.18/0.54 tff(195,plain,
% 0.18/0.54 (![W0: $i] : ((~((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)))) | sdtlseqdt0(W0, xp))),
% 0.18/0.54 inference(modus_ponens,[status(thm)],[194, 185])).
% 0.18/0.54 tff(196,plain,(
% 0.18/0.54 ![W0: $i] : ((((~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(W0, xp))),
% 0.18/0.54 inference(skolemize,[status(sab)],[195])).
% 0.18/0.54 tff(197,plain,
% 0.18/0.54 (![W0: $i] : (sdtlseqdt0(W0, xp) | (((~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)))))),
% 0.18/0.54 inference(modus_ponens,[status(thm)],[196, 183])).
% 0.18/0.54 tff(198,plain,
% 0.18/0.54 (![W0: $i] : (sdtlseqdt0(W0, xp) | (~((~((~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)))))),
% 0.18/0.54 inference(modus_ponens,[status(thm)],[197, 181])).
% 0.18/0.54 tff(199,plain,
% 0.18/0.54 (![W0: $i] : (sdtlseqdt0(W0, xp) | (~((~((~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)))))),
% 0.18/0.54 inference(modus_ponens,[status(thm)],[198, 179])).
% 0.18/0.54 tff(200,plain,
% 0.18/0.54 (((~![W0: $i] : (sdtlseqdt0(W0, xp) | (~((~((~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(W0!18, xp) | (~((~((~aElementOf0(W0!18, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0!18), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0!18, tptp_fun_W1_16(W0!18)))))) | aLowerBoundOfIn0(W0!18, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))))) <=> ((~![W0: $i] : (sdtlseqdt0(W0, xp) | (~((~((~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(W0!18, xp) | (~((~((~aElementOf0(W0!18, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0!18), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0!18, tptp_fun_W1_16(W0!18)))))) | aLowerBoundOfIn0(W0!18, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))))),
% 0.18/0.54 inference(rewrite,[status(thm)],[])).
% 0.18/0.54 tff(201,plain,
% 0.18/0.54 ((~![W0: $i] : (sdtlseqdt0(W0, xp) | (~((~((~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(W0!18, xp) | (~((~((~aElementOf0(W0!18, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0!18), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0!18, tptp_fun_W1_16(W0!18)))))) | aLowerBoundOfIn0(W0!18, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))))),
% 0.18/0.54 inference(quant_inst,[status(thm)],[])).
% 0.18/0.54 tff(202,plain,
% 0.18/0.54 ((~![W0: $i] : (sdtlseqdt0(W0, xp) | (~((~((~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(W0!18, xp) | (~((~((~aElementOf0(W0!18, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0!18), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0!18, tptp_fun_W1_16(W0!18)))))) | aLowerBoundOfIn0(W0!18, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))))),
% 0.18/0.54 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.18/0.54 tff(203,plain,
% 0.18/0.54 (sdtlseqdt0(W0!18, xp) | (~((~((~aElementOf0(W0!18, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0!18), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0!18, tptp_fun_W1_16(W0!18)))))) | aLowerBoundOfIn0(W0!18, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))))),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[202, 199])).
% 0.18/0.54 tff(204,plain,
% 0.18/0.54 (~((~((~aElementOf0(W0!18, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0!18), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0!18, tptp_fun_W1_16(W0!18)))))) | aLowerBoundOfIn0(W0!18, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[203, 177])).
% 0.18/0.54 tff(205,plain,
% 0.18/0.54 (((~((~aElementOf0(W0!18, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0!18), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0!18, tptp_fun_W1_16(W0!18)))))) | aLowerBoundOfIn0(W0!18, cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) | ((~aElementOf0(W0!18, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0!18), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0!18, tptp_fun_W1_16(W0!18)))))),
% 0.18/0.54 inference(tautology,[status(thm)],[])).
% 0.18/0.54 tff(206,plain,
% 0.18/0.54 ((~aElementOf0(W0!18, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0!18), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0!18, tptp_fun_W1_16(W0!18))))),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[205, 204])).
% 0.18/0.54 tff(207,plain,
% 0.18/0.54 ((~((~aElementOf0(W0!18, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0!18), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0!18, tptp_fun_W1_16(W0!18)))))) | (~aElementOf0(W0!18, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0!18), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0!18, tptp_fun_W1_16(W0!18))))),
% 0.18/0.54 inference(tautology,[status(thm)],[])).
% 0.18/0.54 tff(208,plain,
% 0.18/0.54 ((~((~aElementOf0(W0!18, szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(W0!18), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0!18, tptp_fun_W1_16(W0!18)))))) | (~((~aElementOf0(tptp_fun_W1_16(W0!18), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0!18, tptp_fun_W1_16(W0!18))))),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[207, 139])).
% 0.18/0.54 tff(209,plain,
% 0.18/0.54 (~((~aElementOf0(tptp_fun_W1_16(W0!18), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0!18, tptp_fun_W1_16(W0!18)))),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[208, 206])).
% 0.18/0.54 tff(210,plain,
% 0.18/0.54 (((~aElementOf0(tptp_fun_W1_16(W0!18), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0!18, tptp_fun_W1_16(W0!18))) | aElementOf0(tptp_fun_W1_16(W0!18), cS1241(szDzozmdt0(xf), xf, xT))),
% 0.18/0.54 inference(tautology,[status(thm)],[])).
% 0.18/0.54 tff(211,plain,
% 0.18/0.54 (aElementOf0(tptp_fun_W1_16(W0!18), cS1241(szDzozmdt0(xf), xf, xT))),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[210, 209])).
% 0.18/0.54 tff(212,plain,
% 0.18/0.54 ((~((~aElementOf0(tptp_fun_W1_16(W0!18), cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(tptp_fun_W1_16(W0!18), szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_16(W0!18)), tptp_fun_W1_16(W0!18))) | (~aUpperBoundOfIn0(tptp_fun_W1_16(W0!18), xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, tptp_fun_W1_16(W0!18)))))))) | (~aElementOf0(tptp_fun_W1_16(W0!18), cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(tptp_fun_W1_16(W0!18), szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_16(W0!18)), tptp_fun_W1_16(W0!18))) | (~aUpperBoundOfIn0(tptp_fun_W1_16(W0!18), xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, tptp_fun_W1_16(W0!18))))))),
% 0.18/0.54 inference(tautology,[status(thm)],[])).
% 0.18/0.54 tff(213,plain,
% 0.18/0.54 ((~((~aElementOf0(tptp_fun_W1_16(W0!18), cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(tptp_fun_W1_16(W0!18), szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_16(W0!18)), tptp_fun_W1_16(W0!18))) | (~aUpperBoundOfIn0(tptp_fun_W1_16(W0!18), xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, tptp_fun_W1_16(W0!18)))))))) | (~((~aElementOf0(tptp_fun_W1_16(W0!18), szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_16(W0!18)), tptp_fun_W1_16(W0!18))) | (~aUpperBoundOfIn0(tptp_fun_W1_16(W0!18), xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, tptp_fun_W1_16(W0!18))))))),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[212, 211])).
% 0.18/0.54 tff(214,plain,
% 0.18/0.54 (~((~aElementOf0(tptp_fun_W1_16(W0!18), szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_16(W0!18)), tptp_fun_W1_16(W0!18))) | (~aUpperBoundOfIn0(tptp_fun_W1_16(W0!18), xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, tptp_fun_W1_16(W0!18)))))),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[213, 43])).
% 0.18/0.54 tff(215,plain,
% 0.18/0.54 (((~aElementOf0(tptp_fun_W1_16(W0!18), szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, tptp_fun_W1_16(W0!18)), tptp_fun_W1_16(W0!18))) | (~aUpperBoundOfIn0(tptp_fun_W1_16(W0!18), xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, tptp_fun_W1_16(W0!18))))) | ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, tptp_fun_W1_16(W0!18)))),
% 0.18/0.54 inference(tautology,[status(thm)],[])).
% 0.18/0.54 tff(216,plain,
% 0.18/0.54 (![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, tptp_fun_W1_16(W0!18)))),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[215, 214])).
% 0.18/0.54 tff(217,plain,
% 0.18/0.54 (((~aElementOf0(tptp_fun_W1_16(W0!18), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(W0!18, tptp_fun_W1_16(W0!18))) | (~sdtlseqdt0(W0!18, tptp_fun_W1_16(W0!18)))),
% 0.18/0.54 inference(tautology,[status(thm)],[])).
% 0.18/0.54 tff(218,plain,
% 0.18/0.54 (~sdtlseqdt0(W0!18, tptp_fun_W1_16(W0!18))),
% 0.18/0.54 inference(unit_resolution,[status(thm)],[217, 209])).
% 0.18/0.54 tff(219,plain,
% 0.18/0.54 (((~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, tptp_fun_W1_16(W0!18)))) | ((~aElementOf0(W0!18, xT)) | sdtlseqdt0(W0!18, tptp_fun_W1_16(W0!18)))) <=> ((~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, tptp_fun_W1_16(W0!18)))) | (~aElementOf0(W0!18, xT)) | sdtlseqdt0(W0!18, tptp_fun_W1_16(W0!18)))),
% 0.18/0.55 inference(rewrite,[status(thm)],[])).
% 0.18/0.55 tff(220,plain,
% 0.18/0.55 ((~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, tptp_fun_W1_16(W0!18)))) | ((~aElementOf0(W0!18, xT)) | sdtlseqdt0(W0!18, tptp_fun_W1_16(W0!18)))),
% 0.18/0.55 inference(quant_inst,[status(thm)],[])).
% 0.18/0.55 tff(221,plain,
% 0.18/0.55 ((~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, tptp_fun_W1_16(W0!18)))) | (~aElementOf0(W0!18, xT)) | sdtlseqdt0(W0!18, tptp_fun_W1_16(W0!18))),
% 0.18/0.55 inference(modus_ponens,[status(thm)],[220, 219])).
% 0.18/0.55 tff(222,plain,
% 0.18/0.55 ($false),
% 0.18/0.55 inference(unit_resolution,[status(thm)],[221, 122, 218, 216])).
% 0.18/0.55 tff(223,plain,(aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szDzozmdt0(xf)) | (~aElementOf0(W0!18, xT)) | sdtlseqdt0(W0!18, sdtlpdtrp0(xf, xp))), inference(lemma,lemma(discharge,[]))).
% 0.18/0.55 tff(224,plain,
% 0.18/0.55 (((~(aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | (~aElementOf0(W0!17, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(sdtlpdtrp0(xf, xp), W0!17))) | (~(aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szDzozmdt0(xf)) | (~aElementOf0(W0!18, xT)) | sdtlseqdt0(W0!18, sdtlpdtrp0(xf, xp))))) <=> ((~(aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | (~aElementOf0(W0!17, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(sdtlpdtrp0(xf, xp), W0!17))) | (~(aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szDzozmdt0(xf)) | (~aElementOf0(W0!18, xT)) | sdtlseqdt0(W0!18, sdtlpdtrp0(xf, xp)))))),
% 0.18/0.55 inference(rewrite,[status(thm)],[])).
% 0.18/0.55 tff(225,plain,
% 0.18/0.55 (((~aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szDzozmdt0(xf))) & (~((~aElementOf0(W0!18, xT)) | sdtlseqdt0(W0!18, sdtlpdtrp0(xf, xp))))) <=> (~(aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szDzozmdt0(xf)) | (~aElementOf0(W0!18, xT)) | sdtlseqdt0(W0!18, sdtlpdtrp0(xf, xp))))),
% 0.18/0.55 inference(rewrite,[status(thm)],[])).
% 0.18/0.55 tff(226,plain,
% 0.18/0.55 (((~aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) & (~((~aElementOf0(W0!17, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(sdtlpdtrp0(xf, xp), W0!17)))) <=> (~(aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | (~aElementOf0(W0!17, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(sdtlpdtrp0(xf, xp), W0!17)))),
% 0.18/0.55 inference(rewrite,[status(thm)],[])).
% 0.18/0.55 tff(227,plain,
% 0.18/0.55 ((((~aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) & (~((~aElementOf0(W0!17, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(sdtlpdtrp0(xf, xp), W0!17)))) | ((~aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szDzozmdt0(xf))) & (~((~aElementOf0(W0!18, xT)) | sdtlseqdt0(W0!18, sdtlpdtrp0(xf, xp)))))) <=> ((~(aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | (~aElementOf0(W0!17, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(sdtlpdtrp0(xf, xp), W0!17))) | (~(aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szDzozmdt0(xf)) | (~aElementOf0(W0!18, xT)) | sdtlseqdt0(W0!18, sdtlpdtrp0(xf, xp)))))),
% 0.18/0.55 inference(monotonicity,[status(thm)],[226, 225])).
% 0.18/0.55 tff(228,plain,
% 0.18/0.55 ((((~aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) & (~((~aElementOf0(W0!17, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(sdtlpdtrp0(xf, xp), W0!17)))) | ((~aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szDzozmdt0(xf))) & (~((~aElementOf0(W0!18, xT)) | sdtlseqdt0(W0!18, sdtlpdtrp0(xf, xp)))))) <=> ((~(aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | (~aElementOf0(W0!17, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(sdtlpdtrp0(xf, xp), W0!17))) | (~(aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szDzozmdt0(xf)) | (~aElementOf0(W0!18, xT)) | sdtlseqdt0(W0!18, sdtlpdtrp0(xf, xp)))))),
% 0.18/0.55 inference(transitivity,[status(thm)],[227, 224])).
% 0.18/0.55 tff(229,plain,
% 0.18/0.55 ((((~aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) & (~((~aElementOf0(W0!17, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(sdtlpdtrp0(xf, xp), W0!17)))) | ((~aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szDzozmdt0(xf))) & (~((~aElementOf0(W0!18, xT)) | sdtlseqdt0(W0!18, sdtlpdtrp0(xf, xp)))))) <=> (((~aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) & (~((~aElementOf0(W0!17, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(sdtlpdtrp0(xf, xp), W0!17)))) | ((~aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szDzozmdt0(xf))) & (~((~aElementOf0(W0!18, xT)) | sdtlseqdt0(W0!18, sdtlpdtrp0(xf, xp))))))),
% 0.18/0.55 inference(rewrite,[status(thm)],[])).
% 0.18/0.55 tff(230,plain,
% 0.18/0.55 ((aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szDzozmdt0(xf)) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, sdtlpdtrp0(xf, xp)))) <=> (aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szDzozmdt0(xf)) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, sdtlpdtrp0(xf, xp))))),
% 0.18/0.55 inference(rewrite,[status(thm)],[])).
% 0.18/0.55 tff(231,plain,
% 0.18/0.55 ((aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | ![W0: $i] : ((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(sdtlpdtrp0(xf, xp), W0))) <=> (aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | ![W0: $i] : ((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(sdtlpdtrp0(xf, xp), W0)))),
% 0.18/0.55 inference(rewrite,[status(thm)],[])).
% 0.18/0.55 tff(232,plain,
% 0.18/0.55 (((aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | ![W0: $i] : ((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(sdtlpdtrp0(xf, xp), W0))) & (aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szDzozmdt0(xf)) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, sdtlpdtrp0(xf, xp))))) <=> ((aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | ![W0: $i] : ((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(sdtlpdtrp0(xf, xp), W0))) & (aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szDzozmdt0(xf)) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, sdtlpdtrp0(xf, xp)))))),
% 0.18/0.55 inference(monotonicity,[status(thm)],[231, 230])).
% 0.18/0.55 tff(233,plain,
% 0.18/0.55 ((~((aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | ![W0: $i] : ((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(sdtlpdtrp0(xf, xp), W0))) & (aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szDzozmdt0(xf)) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, sdtlpdtrp0(xf, xp)))))) <=> (~((aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | ![W0: $i] : ((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(sdtlpdtrp0(xf, xp), W0))) & (aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szDzozmdt0(xf)) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, sdtlpdtrp0(xf, xp))))))),
% 0.18/0.55 inference(monotonicity,[status(thm)],[232])).
% 0.18/0.55 tff(234,plain,
% 0.18/0.55 ((~((aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), cS1241(szRzazndt0(xf), xf, xT), szRzazndt0(xf)) | ![W0: $i] : ((~aElementOf0(W0, cS1241(szRzazndt0(xf), xf, xT))) | sdtlseqdt0(sdtlpdtrp0(xf, xp), W0))) & (aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szRzazndt0(xf)) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, sdtlpdtrp0(xf, xp)))))) <=> (~((aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | ![W0: $i] : ((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(sdtlpdtrp0(xf, xp), W0))) & (aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szDzozmdt0(xf)) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, sdtlpdtrp0(xf, xp))))))),
% 0.18/0.55 inference(rewrite,[status(thm)],[])).
% 0.18/0.55 tff(235,plain,
% 0.18/0.55 ((aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szRzazndt0(xf)) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, sdtlpdtrp0(xf, xp)))) <=> (aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szRzazndt0(xf)) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, sdtlpdtrp0(xf, xp))))),
% 0.18/0.55 inference(rewrite,[status(thm)],[])).
% 0.18/0.55 tff(236,plain,
% 0.18/0.55 ((aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), cS1241(szRzazndt0(xf), xf, xT), szRzazndt0(xf)) | ![W0: $i] : ((~aElementOf0(W0, cS1241(szRzazndt0(xf), xf, xT))) | sdtlseqdt0(sdtlpdtrp0(xf, xp), W0))) <=> (aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), cS1241(szRzazndt0(xf), xf, xT), szRzazndt0(xf)) | ![W0: $i] : ((~aElementOf0(W0, cS1241(szRzazndt0(xf), xf, xT))) | sdtlseqdt0(sdtlpdtrp0(xf, xp), W0)))),
% 0.18/0.55 inference(rewrite,[status(thm)],[])).
% 0.18/0.55 tff(237,plain,
% 0.18/0.55 (((aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), cS1241(szRzazndt0(xf), xf, xT), szRzazndt0(xf)) | ![W0: $i] : ((~aElementOf0(W0, cS1241(szRzazndt0(xf), xf, xT))) | sdtlseqdt0(sdtlpdtrp0(xf, xp), W0))) & (aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szRzazndt0(xf)) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, sdtlpdtrp0(xf, xp))))) <=> ((aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), cS1241(szRzazndt0(xf), xf, xT), szRzazndt0(xf)) | ![W0: $i] : ((~aElementOf0(W0, cS1241(szRzazndt0(xf), xf, xT))) | sdtlseqdt0(sdtlpdtrp0(xf, xp), W0))) & (aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szRzazndt0(xf)) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, sdtlpdtrp0(xf, xp)))))),
% 0.18/0.55 inference(monotonicity,[status(thm)],[236, 235])).
% 0.18/0.55 tff(238,plain,
% 0.18/0.55 ((~((aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), cS1241(szRzazndt0(xf), xf, xT), szRzazndt0(xf)) | ![W0: $i] : ((~aElementOf0(W0, cS1241(szRzazndt0(xf), xf, xT))) | sdtlseqdt0(sdtlpdtrp0(xf, xp), W0))) & (aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szRzazndt0(xf)) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, sdtlpdtrp0(xf, xp)))))) <=> (~((aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), cS1241(szRzazndt0(xf), xf, xT), szRzazndt0(xf)) | ![W0: $i] : ((~aElementOf0(W0, cS1241(szRzazndt0(xf), xf, xT))) | sdtlseqdt0(sdtlpdtrp0(xf, xp), W0))) & (aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szRzazndt0(xf)) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, sdtlpdtrp0(xf, xp))))))),
% 0.18/0.55 inference(monotonicity,[status(thm)],[237])).
% 0.18/0.55 tff(239,plain,
% 0.18/0.55 ((~((aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), xP, xU) | ![W0: $i] : ((~aElementOf0(W0, xP)) | sdtlseqdt0(sdtlpdtrp0(xf, xp), W0))) & (aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, sdtlpdtrp0(xf, xp)))))) <=> (~((aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), cS1241(szRzazndt0(xf), xf, xT), szRzazndt0(xf)) | ![W0: $i] : ((~aElementOf0(W0, cS1241(szRzazndt0(xf), xf, xT))) | sdtlseqdt0(sdtlpdtrp0(xf, xp), W0))) & (aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szRzazndt0(xf)) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, sdtlpdtrp0(xf, xp))))))),
% 0.18/0.55 inference(rewrite,[status(thm)],[])).
% 0.18/0.55 tff(240,plain,
% 0.18/0.55 ((aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, sdtlpdtrp0(xf, xp)))) <=> (aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, sdtlpdtrp0(xf, xp))))),
% 0.18/0.55 inference(rewrite,[status(thm)],[])).
% 0.18/0.55 tff(241,plain,
% 0.18/0.55 ((aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), xP, xU) | ![W0: $i] : ((~aElementOf0(W0, xP)) | sdtlseqdt0(sdtlpdtrp0(xf, xp), W0))) <=> (aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), xP, xU) | ![W0: $i] : ((~aElementOf0(W0, xP)) | sdtlseqdt0(sdtlpdtrp0(xf, xp), W0)))),
% 0.18/0.55 inference(rewrite,[status(thm)],[])).
% 0.18/0.55 tff(242,plain,
% 0.18/0.55 (((aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), xP, xU) | ![W0: $i] : ((~aElementOf0(W0, xP)) | sdtlseqdt0(sdtlpdtrp0(xf, xp), W0))) & (aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, sdtlpdtrp0(xf, xp))))) <=> ((aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), xP, xU) | ![W0: $i] : ((~aElementOf0(W0, xP)) | sdtlseqdt0(sdtlpdtrp0(xf, xp), W0))) & (aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, sdtlpdtrp0(xf, xp)))))),
% 0.18/0.55 inference(monotonicity,[status(thm)],[241, 240])).
% 0.18/0.55 tff(243,plain,
% 0.18/0.55 ((~((aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), xP, xU) | ![W0: $i] : ((~aElementOf0(W0, xP)) | sdtlseqdt0(sdtlpdtrp0(xf, xp), W0))) & (aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, sdtlpdtrp0(xf, xp)))))) <=> (~((aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), xP, xU) | ![W0: $i] : ((~aElementOf0(W0, xP)) | sdtlseqdt0(sdtlpdtrp0(xf, xp), W0))) & (aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, sdtlpdtrp0(xf, xp))))))),
% 0.18/0.56 inference(monotonicity,[status(thm)],[242])).
% 0.18/0.56 tff(244,plain,
% 0.18/0.56 ((~((aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), xP, xU) | ![W0: $i] : ((~aElementOf0(W0, xP)) | sdtlseqdt0(sdtlpdtrp0(xf, xp), W0))) & (aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, sdtlpdtrp0(xf, xp)))))) <=> (~((aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), xP, xU) | ![W0: $i] : ((~aElementOf0(W0, xP)) | sdtlseqdt0(sdtlpdtrp0(xf, xp), W0))) & (aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, sdtlpdtrp0(xf, xp))))))),
% 0.18/0.56 inference(rewrite,[status(thm)],[])).
% 0.18/0.56 tff(245,plain,
% 0.18/0.56 ((~((![W0: $i] : (aElementOf0(W0, xP) => sdtlseqdt0(sdtlpdtrp0(xf, xp), W0)) | aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), xP, xU)) & (![W0: $i] : (aElementOf0(W0, xT) => sdtlseqdt0(W0, sdtlpdtrp0(xf, xp))) | aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU)))) <=> (~((aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), xP, xU) | ![W0: $i] : ((~aElementOf0(W0, xP)) | sdtlseqdt0(sdtlpdtrp0(xf, xp), W0))) & (aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, sdtlpdtrp0(xf, xp))))))),
% 0.18/0.56 inference(rewrite,[status(thm)],[])).
% 0.18/0.56 tff(246,axiom,(~((![W0: $i] : (aElementOf0(W0, xP) => sdtlseqdt0(sdtlpdtrp0(xf, xp), W0)) | aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), xP, xU)) & (![W0: $i] : (aElementOf0(W0, xT) => sdtlseqdt0(W0, sdtlpdtrp0(xf, xp))) | aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 0.18/0.56 tff(247,plain,
% 0.18/0.56 (~((aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), xP, xU) | ![W0: $i] : ((~aElementOf0(W0, xP)) | sdtlseqdt0(sdtlpdtrp0(xf, xp), W0))) & (aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, sdtlpdtrp0(xf, xp)))))),
% 0.18/0.56 inference(modus_ponens,[status(thm)],[246, 245])).
% 0.18/0.56 tff(248,plain,
% 0.18/0.56 (~((aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), xP, xU) | ![W0: $i] : ((~aElementOf0(W0, xP)) | sdtlseqdt0(sdtlpdtrp0(xf, xp), W0))) & (aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, sdtlpdtrp0(xf, xp)))))),
% 0.18/0.56 inference(modus_ponens,[status(thm)],[247, 243])).
% 0.18/0.56 tff(249,plain,
% 0.18/0.56 (~((aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), xP, xU) | ![W0: $i] : ((~aElementOf0(W0, xP)) | sdtlseqdt0(sdtlpdtrp0(xf, xp), W0))) & (aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, sdtlpdtrp0(xf, xp)))))),
% 0.18/0.56 inference(modus_ponens,[status(thm)],[248, 244])).
% 0.18/0.56 tff(250,plain,
% 0.18/0.56 (~((aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), xP, xU) | ![W0: $i] : ((~aElementOf0(W0, xP)) | sdtlseqdt0(sdtlpdtrp0(xf, xp), W0))) & (aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, sdtlpdtrp0(xf, xp)))))),
% 0.18/0.56 inference(modus_ponens,[status(thm)],[249, 243])).
% 0.18/0.56 tff(251,plain,
% 0.18/0.56 (~((aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), cS1241(szRzazndt0(xf), xf, xT), szRzazndt0(xf)) | ![W0: $i] : ((~aElementOf0(W0, cS1241(szRzazndt0(xf), xf, xT))) | sdtlseqdt0(sdtlpdtrp0(xf, xp), W0))) & (aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szRzazndt0(xf)) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, sdtlpdtrp0(xf, xp)))))),
% 0.18/0.56 inference(modus_ponens,[status(thm)],[250, 239])).
% 0.18/0.56 tff(252,plain,
% 0.18/0.56 (~((aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), cS1241(szRzazndt0(xf), xf, xT), szRzazndt0(xf)) | ![W0: $i] : ((~aElementOf0(W0, cS1241(szRzazndt0(xf), xf, xT))) | sdtlseqdt0(sdtlpdtrp0(xf, xp), W0))) & (aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szRzazndt0(xf)) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, sdtlpdtrp0(xf, xp)))))),
% 0.18/0.56 inference(modus_ponens,[status(thm)],[251, 238])).
% 0.18/0.56 tff(253,plain,
% 0.18/0.56 (~((aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | ![W0: $i] : ((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(sdtlpdtrp0(xf, xp), W0))) & (aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szDzozmdt0(xf)) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, sdtlpdtrp0(xf, xp)))))),
% 0.18/0.56 inference(modus_ponens,[status(thm)],[252, 234])).
% 0.18/0.56 tff(254,plain,
% 0.18/0.56 (~((aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | ![W0: $i] : ((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(sdtlpdtrp0(xf, xp), W0))) & (aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szDzozmdt0(xf)) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, sdtlpdtrp0(xf, xp)))))),
% 0.18/0.56 inference(modus_ponens,[status(thm)],[253, 233])).
% 0.18/0.56 tff(255,plain,
% 0.18/0.56 (~((aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | ![W0: $i] : ((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(sdtlpdtrp0(xf, xp), W0))) & (aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szDzozmdt0(xf)) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, sdtlpdtrp0(xf, xp)))))),
% 0.18/0.56 inference(modus_ponens,[status(thm)],[254, 233])).
% 0.18/0.56 tff(256,plain,
% 0.18/0.56 (~((aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)) | ![W0: $i] : ((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(sdtlpdtrp0(xf, xp), W0))) & (aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szDzozmdt0(xf)) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, sdtlpdtrp0(xf, xp)))))),
% 0.18/0.56 inference(modus_ponens,[status(thm)],[255, 233])).
% 0.18/0.56 unexpected number of arguments: (let ((a!1 (aLowerBoundOfIn0 (sdtlpdtrp0 xf xp)
% 0.18/0.56 (cS1241 (szDzozmdt0 xf) xf xT)
% 0.18/0.56 (szDzozmdt0 xf)))
% 0.18/0.56 (a!2 (forall ((W0 $i))
% 0.18/0.56 (let ((a!1 (not (aElementOf0 W0 (cS1241 (szDzozmdt0 xf) xf xT)))))
% 0.18/0.56 (or a!1 (sdtlseqdt0 (sdtlpdtrp0 xf xp) W0)))))
% 0.18/0.56 (a!3 (not (aElementOf0 W0!17 (cS1241 (szDzozmdt0 xf) xf xT))))
% 0.18/0.56 (a!6 (~ (not (aUpperBoundOfIn0 (sdtlpdtrp0 xf xp) xT (szDzozmdt0 xf)))
% 0.18/0.56 (not (aUpperBoundOfIn0 (sdtlpdtrp0 xf xp) xT (szDzozmdt0 xf)))))
% 0.18/0.56 (a!7 (forall ((W0 $i))
% 0.18/0.56 (or (not (aElementOf0 W0 xT)) (sdtlseqdt0 W0 (sdtlpdtrp0 xf xp)))))
% 0.18/0.56 (a!8 (not (or (not (aElementOf0 W0!18 xT))
% 0.18/0.56 (sdtlseqdt0 W0!18 (sdtlpdtrp0 xf xp))))))
% 0.18/0.56 (let ((a!4 (not (or a!3 (sdtlseqdt0 (sdtlpdtrp0 xf xp) W0!17))))
% 0.18/0.56 (a!9 (not (or (aUpperBoundOfIn0 (sdtlpdtrp0 xf xp) xT (szDzozmdt0 xf))
% 0.18/0.56 a!7)))
% 0.18/0.56 (a!10 (and (not (aUpperBoundOfIn0 (sdtlpdtrp0 xf xp) xT (szDzozmdt0 xf)))
% 0.18/0.56 a!8))
% 0.18/0.56 (a!12 (and (or a!1 a!2)
% 0.18/0.56 (or (aUpperBoundOfIn0 (sdtlpdtrp0 xf xp) xT (szDzozmdt0 xf))
% 0.18/0.56 a!7))))
% 0.18/0.56 (let ((a!5 (nnf-neg (refl (~ (not a!1) (not a!1)))
% 0.18/0.56 (sk (~ (not a!2) a!4))
% 0.18/0.56 (~ (not (or a!1 a!2)) (and (not a!1) a!4))))
% 0.18/0.56 (a!11 (nnf-neg (refl a!6) (sk (~ (not a!7) a!8)) (~ a!9 a!10)))
% 0.18/0.56 (a!13 (~ (not a!12) (or (and (not a!1) a!4) a!10))))
% 0.18/0.56 (nnf-neg a!5 a!11 a!13))))
% 0.18/0.56 Proof display could not be completed: unexpected number of arguments
%------------------------------------------------------------------------------