TSTP Solution File: LAT387+4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT387+4 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 18:33:41 EDT 2022
% Result : Theorem 0.20s 0.48s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LAT387+4 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Sep 1 17:11:04 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.48 % SZS status Theorem
% 0.20/0.48 % SZS output start Proof
% 0.20/0.48 tff(sdtlseqdt0_type, type, (
% 0.20/0.48 sdtlseqdt0: ( $i * $i ) > $o)).
% 0.20/0.48 tff(sdtlpdtrp0_type, type, (
% 0.20/0.48 sdtlpdtrp0: ( $i * $i ) > $i)).
% 0.20/0.48 tff(xp_type, type, (
% 0.20/0.48 xp: $i)).
% 0.20/0.48 tff(xf_type, type, (
% 0.20/0.48 xf: $i)).
% 0.20/0.48 tff(tptp_fun_W0_17_type, type, (
% 0.20/0.48 tptp_fun_W0_17: $i)).
% 0.20/0.48 tff(aElementOf0_type, type, (
% 0.20/0.48 aElementOf0: ( $i * $i ) > $o)).
% 0.20/0.48 tff(cS1241_type, type, (
% 0.20/0.48 cS1241: ( $i * $i * $i ) > $i)).
% 0.20/0.48 tff(xT_type, type, (
% 0.20/0.48 xT: $i)).
% 0.20/0.48 tff(szDzozmdt0_type, type, (
% 0.20/0.48 szDzozmdt0: $i > $i)).
% 0.20/0.48 tff(szRzazndt0_type, type, (
% 0.20/0.48 szRzazndt0: $i > $i)).
% 0.20/0.48 tff(isMonotone0_type, type, (
% 0.20/0.48 isMonotone0: $i > $o)).
% 0.20/0.48 tff(aFunction0_type, type, (
% 0.20/0.48 aFunction0: $i > $o)).
% 0.20/0.48 tff(aCompleteLattice0_type, type, (
% 0.20/0.48 aCompleteLattice0: $i > $o)).
% 0.20/0.48 tff(xU_type, type, (
% 0.20/0.48 xU: $i)).
% 0.20/0.48 tff(aSupremumOfIn0_type, type, (
% 0.20/0.48 aSupremumOfIn0: ( $i * $i * $i ) > $o)).
% 0.20/0.48 tff(aUpperBoundOfIn0_type, type, (
% 0.20/0.48 aUpperBoundOfIn0: ( $i * $i * $i ) > $o)).
% 0.20/0.48 tff(aInfimumOfIn0_type, type, (
% 0.20/0.48 aInfimumOfIn0: ( $i * $i * $i ) > $o)).
% 0.20/0.48 tff(aLowerBoundOfIn0_type, type, (
% 0.20/0.48 aLowerBoundOfIn0: ( $i * $i * $i ) > $o)).
% 0.20/0.48 tff(aSubsetOf0_type, type, (
% 0.20/0.48 aSubsetOf0: ( $i * $i ) > $o)).
% 0.20/0.48 tff(aSet0_type, type, (
% 0.20/0.48 aSet0: $i > $o)).
% 0.20/0.48 tff(isOn0_type, type, (
% 0.20/0.48 isOn0: ( $i * $i ) > $o)).
% 0.20/0.48 tff(xP_type, type, (
% 0.20/0.48 xP: $i)).
% 0.20/0.48 tff(tptp_fun_W1_16_type, type, (
% 0.20/0.48 tptp_fun_W1_16: $i > $i)).
% 0.20/0.48 tff(tptp_fun_W1_15_type, type, (
% 0.20/0.48 tptp_fun_W1_15: $i > $i)).
% 0.20/0.48 tff(aElement0_type, type, (
% 0.20/0.48 aElement0: $i > $o)).
% 0.20/0.48 tff(cS1142_type, type, (
% 0.20/0.48 cS1142: $i > $i)).
% 0.20/0.48 tff(tptp_fun_W0_18_type, type, (
% 0.20/0.48 tptp_fun_W0_18: $i)).
% 0.20/0.48 tff(aFixedPointOf0_type, type, (
% 0.20/0.48 aFixedPointOf0: ( $i * $i ) > $o)).
% 0.20/0.48 tff(xS_type, type, (
% 0.20/0.48 xS: $i)).
% 0.20/0.48 tff(1,assumption,(~sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp))), introduced(assumption)).
% 0.20/0.48 tff(2,plain,
% 0.20/0.48 ((szDzozmdt0(xf) = szRzazndt0(xf)) <=> (szDzozmdt0(xf) = szRzazndt0(xf))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(3,axiom,((((((((aSet0(xU) & ![W0: $i] : (((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xU))) | aSubsetOf0(W0, xU)) => ?[W1: $i] : ((((((aElementOf0(W1, xU) & aElementOf0(W1, xU)) & ![W2: $i] : (aElementOf0(W2, W0) => sdtlseqdt0(W1, W2))) & aLowerBoundOfIn0(W1, W0, xU)) & ![W2: $i] : (((aElementOf0(W2, xU) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W2, W3))) | aLowerBoundOfIn0(W2, W0, xU)) => sdtlseqdt0(W2, W1))) & aInfimumOfIn0(W1, W0, xU)) & ?[W2: $i] : (((((aElementOf0(W2, xU) & aElementOf0(W2, xU)) & ![W3: $i] : (aElementOf0(W3, W0) => sdtlseqdt0(W3, W2))) & aUpperBoundOfIn0(W2, W0, xU)) & ![W3: $i] : (((aElementOf0(W3, xU) & ![W4: $i] : (aElementOf0(W4, W0) => sdtlseqdt0(W4, W3))) | aUpperBoundOfIn0(W3, W0, xU)) => sdtlseqdt0(W2, W3))) & aSupremumOfIn0(W2, W0, xU))))) & aCompleteLattice0(xU)) & aFunction0(xf)) & ![W0: $i, W1: $i] : ((aElementOf0(W0, szDzozmdt0(xf)) & aElementOf0(W1, szDzozmdt0(xf))) => (sdtlseqdt0(W0, W1) => sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1))))) & isMonotone0(xf)) & (szDzozmdt0(xf) = szRzazndt0(xf))) & (szRzazndt0(xf) = xU)) & isOn0(xf, xU)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__1123')).
% 0.20/0.48 tff(4,plain,
% 0.20/0.48 (((((((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)),
% 0.20/0.49 inference(and_elim,[status(thm)],[3])).
% 0.20/0.49 tff(5,plain,
% 0.20/0.49 ((((((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))),
% 0.20/0.49 inference(and_elim,[status(thm)],[4])).
% 0.20/0.49 tff(6,plain,
% 0.20/0.49 (szDzozmdt0(xf) = szRzazndt0(xf)),
% 0.20/0.49 inference(and_elim,[status(thm)],[5])).
% 0.20/0.49 tff(7,plain,
% 0.20/0.49 (szDzozmdt0(xf) = szRzazndt0(xf)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.49 tff(8,plain,
% 0.20/0.49 (szRzazndt0(xf) = szDzozmdt0(xf)),
% 0.20/0.49 inference(symmetry,[status(thm)],[7])).
% 0.20/0.49 tff(9,plain,
% 0.20/0.49 (aElementOf0(sdtlpdtrp0(xf, xp), szRzazndt0(xf)) <=> aElementOf0(sdtlpdtrp0(xf, xp), szDzozmdt0(xf))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[8])).
% 0.20/0.49 tff(10,plain,
% 0.20/0.49 (aFunction0(xf) <=> aFunction0(xf)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(11,plain,
% 0.20/0.49 (((((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)),
% 0.20/0.49 inference(and_elim,[status(thm)],[5])).
% 0.20/0.49 tff(12,plain,
% 0.20/0.49 ((((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))))),
% 0.20/0.49 inference(and_elim,[status(thm)],[11])).
% 0.20/0.49 tff(13,plain,
% 0.20/0.49 (((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)),
% 0.20/0.49 inference(and_elim,[status(thm)],[12])).
% 0.20/0.49 tff(14,plain,
% 0.20/0.49 (aFunction0(xf)),
% 0.20/0.49 inference(and_elim,[status(thm)],[13])).
% 0.20/0.49 tff(15,plain,
% 0.20/0.49 (aFunction0(xf)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.20/0.49 tff(16,plain,
% 0.20/0.49 (^[W0: $i] : refl(((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0)))) <=> ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0)))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(17,plain,
% 0.20/0.49 (![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0)))) <=> ![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[16])).
% 0.20/0.49 tff(18,plain,
% 0.20/0.49 (^[W0: $i] : rewrite(((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0)))) <=> ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0)))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(19,plain,
% 0.20/0.49 (![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0)))) <=> ![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[18])).
% 0.20/0.49 tff(20,plain,
% 0.20/0.49 (![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0)))) <=> ![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[19, 17])).
% 0.20/0.49 tff(21,plain,
% 0.20/0.49 (![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0)))) <=> ![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(22,plain,
% 0.20/0.49 (^[W0: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: $i] : rewrite((aElementOf0(W1, szDzozmdt0(W0)) => aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0))) <=> ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0))))), (![W1: $i] : (aElementOf0(W1, szDzozmdt0(W0)) => aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0))) <=> ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0))))), ((aFunction0(W0) => ![W1: $i] : (aElementOf0(W1, szDzozmdt0(W0)) => aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0)))) <=> (aFunction0(W0) => ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0)))))), rewrite((aFunction0(W0) => ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0)))) <=> ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0))))), ((aFunction0(W0) => ![W1: $i] : (aElementOf0(W1, szDzozmdt0(W0)) => aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0)))) <=> ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(23,plain,
% 0.20/0.49 (![W0: $i] : (aFunction0(W0) => ![W1: $i] : (aElementOf0(W1, szDzozmdt0(W0)) => aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0)))) <=> ![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[22])).
% 0.20/0.49 tff(24,axiom,(![W0: $i] : (aFunction0(W0) => ![W1: $i] : (aElementOf0(W1, szDzozmdt0(W0)) => aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mImgSort')).
% 0.20/0.49 tff(25,plain,
% 0.20/0.49 (![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.20/0.49 tff(26,plain,
% 0.20/0.49 (![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.20/0.49 tff(27,plain,(
% 0.20/0.49 ![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0))))),
% 0.20/0.49 inference(skolemize,[status(sab)],[26])).
% 0.20/0.49 tff(28,plain,
% 0.20/0.49 (![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.20/0.49 tff(29,plain,
% 0.20/0.49 (((~![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0))))) | ((~aFunction0(xf)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xf))) | aElementOf0(sdtlpdtrp0(xf, W1), szRzazndt0(xf))))) <=> ((~![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0))))) | (~aFunction0(xf)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xf))) | aElementOf0(sdtlpdtrp0(xf, W1), szRzazndt0(xf))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(30,plain,
% 0.20/0.49 ((~![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0))))) | ((~aFunction0(xf)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xf))) | aElementOf0(sdtlpdtrp0(xf, W1), szRzazndt0(xf))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(31,plain,
% 0.20/0.49 ((~![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), szRzazndt0(W0))))) | (~aFunction0(xf)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xf))) | aElementOf0(sdtlpdtrp0(xf, W1), szRzazndt0(xf)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.20/0.49 tff(32,plain,
% 0.20/0.49 (![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xf))) | aElementOf0(sdtlpdtrp0(xf, W1), szRzazndt0(xf)))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[31, 28, 15])).
% 0.20/0.49 tff(33,plain,
% 0.20/0.49 (aElementOf0(xp, szRzazndt0(xf)) <=> aElementOf0(xp, szDzozmdt0(xf))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(34,plain,
% 0.20/0.49 (aElementOf0(xp, xU) <=> aElementOf0(xp, szRzazndt0(xf))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(35,plain,
% 0.20/0.49 (aElementOf0(xp, xU) <=> aElementOf0(xp, xU)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(36,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/sandbox2/benchmark/theBenchmark.p','m__1261')).
% 0.20/0.49 tff(37,plain,
% 0.20/0.49 ((((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))),
% 0.20/0.49 inference(and_elim,[status(thm)],[36])).
% 0.20/0.49 tff(38,plain,
% 0.20/0.49 (((aElementOf0(xp, xU) & aElementOf0(xp, xU)) & ![W0: $i] : (aElementOf0(W0, xP) => sdtlseqdt0(xp, W0))) & aLowerBoundOfIn0(xp, xP, xU)),
% 0.20/0.49 inference(and_elim,[status(thm)],[37])).
% 0.20/0.49 tff(39,plain,
% 0.20/0.49 ((aElementOf0(xp, xU) & aElementOf0(xp, xU)) & ![W0: $i] : (aElementOf0(W0, xP) => sdtlseqdt0(xp, W0))),
% 0.20/0.49 inference(and_elim,[status(thm)],[38])).
% 0.20/0.49 tff(40,plain,
% 0.20/0.49 (aElementOf0(xp, xU) & aElementOf0(xp, xU)),
% 0.20/0.49 inference(and_elim,[status(thm)],[39])).
% 0.20/0.49 tff(41,plain,
% 0.20/0.49 (aElementOf0(xp, xU)),
% 0.20/0.49 inference(and_elim,[status(thm)],[40])).
% 0.20/0.49 tff(42,plain,
% 0.20/0.49 (aElementOf0(xp, xU)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[41, 35])).
% 0.20/0.49 tff(43,plain,
% 0.20/0.49 (aElementOf0(xp, szRzazndt0(xf))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[42, 34])).
% 0.20/0.49 tff(44,plain,
% 0.20/0.49 (aElementOf0(xp, szDzozmdt0(xf))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[43, 33])).
% 0.20/0.49 tff(45,plain,
% 0.20/0.49 (((~![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xf))) | aElementOf0(sdtlpdtrp0(xf, W1), szRzazndt0(xf)))) | ((~aElementOf0(xp, szDzozmdt0(xf))) | aElementOf0(sdtlpdtrp0(xf, xp), szRzazndt0(xf)))) <=> ((~![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xf))) | aElementOf0(sdtlpdtrp0(xf, W1), szRzazndt0(xf)))) | (~aElementOf0(xp, szDzozmdt0(xf))) | aElementOf0(sdtlpdtrp0(xf, xp), szRzazndt0(xf)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(46,plain,
% 0.20/0.49 ((~![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xf))) | aElementOf0(sdtlpdtrp0(xf, W1), szRzazndt0(xf)))) | ((~aElementOf0(xp, szDzozmdt0(xf))) | aElementOf0(sdtlpdtrp0(xf, xp), szRzazndt0(xf)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(47,plain,
% 0.20/0.49 ((~![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xf))) | aElementOf0(sdtlpdtrp0(xf, W1), szRzazndt0(xf)))) | (~aElementOf0(xp, szDzozmdt0(xf))) | aElementOf0(sdtlpdtrp0(xf, xp), szRzazndt0(xf))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.20/0.49 tff(48,plain,
% 0.20/0.49 (aElementOf0(sdtlpdtrp0(xf, xp), szRzazndt0(xf))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[47, 44, 32])).
% 0.20/0.49 tff(49,plain,
% 0.20/0.49 (aElementOf0(sdtlpdtrp0(xf, xp), szDzozmdt0(xf))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[48, 9])).
% 0.20/0.49 tff(50,plain,
% 0.20/0.49 (aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), cS1241(szRzazndt0(xf), xf, xT), szRzazndt0(xf)) <=> aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(51,plain,
% 0.20/0.49 (aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), xP, xU) <=> aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), cS1241(szRzazndt0(xf), xf, xT), szRzazndt0(xf))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(52,plain,
% 0.20/0.49 (aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), xP, xU) <=> aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), xP, xU)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(53,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/sandbox2/benchmark/theBenchmark.p','m__1299')).
% 0.20/0.49 tff(54,plain,
% 0.20/0.49 ((![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)))),
% 0.20/0.49 inference(and_elim,[status(thm)],[53])).
% 0.20/0.49 tff(55,plain,
% 0.20/0.49 (![W0: $i] : (aElementOf0(W0, xP) => sdtlseqdt0(sdtlpdtrp0(xf, xp), W0)) & aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), xP, xU)),
% 0.20/0.49 inference(and_elim,[status(thm)],[54])).
% 0.20/0.49 tff(56,plain,
% 0.20/0.49 (aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), xP, xU)),
% 0.20/0.49 inference(and_elim,[status(thm)],[55])).
% 0.20/0.49 tff(57,plain,
% 0.20/0.49 (aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), xP, xU)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.20/0.49 tff(58,plain,
% 0.20/0.49 (aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), cS1241(szRzazndt0(xf), xf, xT), szRzazndt0(xf))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[57, 51])).
% 0.20/0.49 tff(59,plain,
% 0.20/0.49 (aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[58, 50])).
% 0.20/0.49 tff(60,plain,
% 0.20/0.49 (((~((~aElementOf0(sdtlpdtrp0(xf, xp), szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(sdtlpdtrp0(xf, xp)), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(sdtlpdtrp0(xf, xp), tptp_fun_W1_16(sdtlpdtrp0(xf, xp))))))) | aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))) | (~aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(61,plain,
% 0.20/0.49 ((~((~aElementOf0(sdtlpdtrp0(xf, xp), szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(sdtlpdtrp0(xf, xp)), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(sdtlpdtrp0(xf, xp), tptp_fun_W1_16(sdtlpdtrp0(xf, xp))))))) | aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[60, 59])).
% 0.20/0.49 tff(62,plain,
% 0.20/0.49 (^[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))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(63,plain,
% 0.20/0.49 (![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)))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[62])).
% 0.20/0.49 tff(64,plain,
% 0.20/0.49 (^[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)))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(65,plain,
% 0.20/0.49 (![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)))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[64])).
% 0.20/0.49 tff(66,plain,
% 0.20/0.49 (^[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))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(67,plain,
% 0.20/0.49 (![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)))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[66])).
% 0.20/0.49 tff(68,plain,
% 0.20/0.49 (^[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)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(69,plain,
% 0.20/0.49 (![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))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[68])).
% 0.20/0.49 tff(70,plain,
% 0.20/0.49 (^[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)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(71,plain,
% 0.20/0.49 (![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))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[70])).
% 0.20/0.49 tff(72,plain,
% 0.20/0.49 (![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))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(73,plain,
% 0.20/0.49 (^[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))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(74,plain,
% 0.20/0.50 (![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))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[73])).
% 0.20/0.50 tff(75,plain,
% 0.20/0.50 (![W0: $i] : (((aElementOf0(W0, xU) & ![W1: $i] : (aElementOf0(W1, xP) => sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, xP, xU)) => sdtlseqdt0(W0, xp))),
% 0.20/0.50 inference(and_elim,[status(thm)],[37])).
% 0.20/0.50 tff(76,plain,
% 0.20/0.50 (![W0: $i] : ((~((aElementOf0(W0, xU) & ![W1: $i] : ((~aElementOf0(W1, xP)) | sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, xP, xU))) | sdtlseqdt0(W0, xp))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.20/0.50 tff(77,plain,
% 0.20/0.50 (![W0: $i] : ((~((aElementOf0(W0, xU) & ![W1: $i] : ((~aElementOf0(W1, xP)) | sdtlseqdt0(W0, W1))) | aLowerBoundOfIn0(W0, xP, xU))) | sdtlseqdt0(W0, xp))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[76, 72])).
% 0.20/0.50 tff(78,plain,
% 0.20/0.50 (![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))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[77, 71])).
% 0.20/0.50 tff(79,plain,
% 0.20/0.50 (![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))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[78, 69])).
% 0.20/0.50 tff(80,plain,(
% 0.20/0.50 ![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))),
% 0.20/0.50 inference(skolemize,[status(sab)],[79])).
% 0.20/0.50 tff(81,plain,
% 0.20/0.50 (![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)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[80, 67])).
% 0.20/0.50 tff(82,plain,
% 0.20/0.50 (![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)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[81, 65])).
% 0.20/0.50 tff(83,plain,
% 0.20/0.50 (![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)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[82, 63])).
% 0.20/0.50 tff(84,plain,
% 0.20/0.50 (((~![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(sdtlpdtrp0(xf, xp), xp) | (~((~((~aElementOf0(sdtlpdtrp0(xf, xp), szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(sdtlpdtrp0(xf, xp)), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(sdtlpdtrp0(xf, xp), tptp_fun_W1_16(sdtlpdtrp0(xf, xp))))))) | aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), 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(sdtlpdtrp0(xf, xp), xp) | (~((~((~aElementOf0(sdtlpdtrp0(xf, xp), szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(sdtlpdtrp0(xf, xp)), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(sdtlpdtrp0(xf, xp), tptp_fun_W1_16(sdtlpdtrp0(xf, xp))))))) | aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(85,plain,
% 0.20/0.50 ((~![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(sdtlpdtrp0(xf, xp), xp) | (~((~((~aElementOf0(sdtlpdtrp0(xf, xp), szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(sdtlpdtrp0(xf, xp)), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(sdtlpdtrp0(xf, xp), tptp_fun_W1_16(sdtlpdtrp0(xf, xp))))))) | aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf)))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(86,plain,
% 0.20/0.50 ((~![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(sdtlpdtrp0(xf, xp), xp) | (~((~((~aElementOf0(sdtlpdtrp0(xf, xp), szDzozmdt0(xf))) | (~((~aElementOf0(tptp_fun_W1_16(sdtlpdtrp0(xf, xp)), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(sdtlpdtrp0(xf, xp), tptp_fun_W1_16(sdtlpdtrp0(xf, xp))))))) | aLowerBoundOfIn0(sdtlpdtrp0(xf, xp), cS1241(szDzozmdt0(xf), xf, xT), szDzozmdt0(xf))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.20/0.50 tff(87,plain,
% 0.20/0.50 (sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[86, 83, 61])).
% 0.20/0.50 tff(88,plain,
% 0.20/0.50 (^[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)))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(89,plain,
% 0.20/0.50 (![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))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[88])).
% 0.20/0.50 tff(90,plain,
% 0.20/0.50 (^[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))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(91,plain,
% 0.20/0.50 (![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))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[90])).
% 0.20/0.50 tff(92,plain,
% 0.20/0.50 (![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)))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(93,plain,
% 0.20/0.50 (^[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)))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(94,plain,
% 0.20/0.50 (![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)))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[93])).
% 0.20/0.50 tff(95,plain,
% 0.20/0.50 (![W0: $i, W1: $i] : ((aElementOf0(W0, szDzozmdt0(xf)) & aElementOf0(W1, szDzozmdt0(xf))) => (sdtlseqdt0(W0, W1) => sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1))))),
% 0.20/0.50 inference(and_elim,[status(thm)],[12])).
% 0.20/0.50 tff(96,plain,
% 0.20/0.50 (![W0: $i, W1: $i] : (sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1)) | (~sdtlseqdt0(W0, W1)) | (~(aElementOf0(W0, szDzozmdt0(xf)) & aElementOf0(W1, szDzozmdt0(xf)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.20/0.50 tff(97,plain,
% 0.20/0.50 (![W0: $i, W1: $i] : (sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1)) | (~sdtlseqdt0(W0, W1)) | (~(aElementOf0(W0, szDzozmdt0(xf)) & aElementOf0(W1, szDzozmdt0(xf)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.20/0.50 tff(98,plain,(
% 0.20/0.50 ![W0: $i, W1: $i] : (sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1)) | (~sdtlseqdt0(W0, W1)) | (~(aElementOf0(W0, szDzozmdt0(xf)) & aElementOf0(W1, szDzozmdt0(xf)))))),
% 0.20/0.50 inference(skolemize,[status(sab)],[97])).
% 0.20/0.50 tff(99,plain,
% 0.20/0.50 (![W0: $i, W1: $i] : (sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1)) | (~sdtlseqdt0(W0, W1)) | (~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W0, szDzozmdt0(xf))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[98, 91])).
% 0.20/0.50 tff(100,plain,
% 0.20/0.50 (![W0: $i, W1: $i] : (sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1)) | (~sdtlseqdt0(W0, W1)) | (~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W0, szDzozmdt0(xf))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[99, 89])).
% 0.20/0.50 tff(101,plain,
% 0.20/0.50 (((~![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))) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (~aElementOf0(sdtlpdtrp0(xf, xp), szDzozmdt0(xf))) | sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, 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))) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (~aElementOf0(sdtlpdtrp0(xf, xp), szDzozmdt0(xf))) | sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(102,plain,
% 0.20/0.50 ((sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp)) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (~aElementOf0(xp, szDzozmdt0(xf))) | (~aElementOf0(sdtlpdtrp0(xf, xp), szDzozmdt0(xf)))) <=> ((~aElementOf0(xp, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (~aElementOf0(sdtlpdtrp0(xf, xp), szDzozmdt0(xf))) | sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(103,plain,
% 0.20/0.50 (((~![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, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp)) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (~aElementOf0(xp, szDzozmdt0(xf))) | (~aElementOf0(sdtlpdtrp0(xf, xp), 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))) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (~aElementOf0(sdtlpdtrp0(xf, xp), szDzozmdt0(xf))) | sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[102])).
% 0.20/0.50 tff(104,plain,
% 0.20/0.50 (((~![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, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp)) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (~aElementOf0(xp, szDzozmdt0(xf))) | (~aElementOf0(sdtlpdtrp0(xf, xp), 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))) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (~aElementOf0(sdtlpdtrp0(xf, xp), szDzozmdt0(xf))) | sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp)))),
% 0.20/0.50 inference(transitivity,[status(thm)],[103, 101])).
% 0.20/0.50 tff(105,plain,
% 0.20/0.50 ((~![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, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp)) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (~aElementOf0(xp, szDzozmdt0(xf))) | (~aElementOf0(sdtlpdtrp0(xf, xp), szDzozmdt0(xf))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(106,plain,
% 0.20/0.50 ((~![W0: $i, W1: $i] : (sdtlseqdt0(sdtlpdtrp0(xf, W0), sdtlpdtrp0(xf, W1)) | (~sdtlseqdt0(W0, W1)) | (~aElementOf0(W1, szDzozmdt0(xf))) | (~aElementOf0(W0, szDzozmdt0(xf))))) | (~aElementOf0(xp, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (~aElementOf0(sdtlpdtrp0(xf, xp), szDzozmdt0(xf))) | sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.20/0.50 tff(107,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[106, 100, 44, 87, 49, 1])).
% 0.20/0.50 tff(108,plain,(sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.50 tff(109,plain,
% 0.20/0.50 (^[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))))))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(110,plain,
% 0.20/0.50 (![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))))))) <=> ![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)))))))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[109])).
% 0.20/0.50 tff(111,plain,
% 0.20/0.50 (^[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))))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(112,plain,
% 0.20/0.51 (![W0: $i] : (~((~((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf))) | (~![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)))))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[111])).
% 0.20/0.51 tff(113,plain,
% 0.20/0.51 (^[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))))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(114,plain,
% 0.20/0.51 (![W0: $i] : (~((~((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf))) | (~![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)))))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[113])).
% 0.20/0.51 tff(115,plain,
% 0.20/0.51 (![W0: $i] : (~((~((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf))) | (~![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)))))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[114, 112])).
% 0.20/0.51 tff(116,plain,
% 0.20/0.51 (^[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)))))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(117,plain,
% 0.20/0.51 (![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)))))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[116])).
% 0.20/0.51 tff(118,plain,
% 0.20/0.51 (^[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)))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(119,plain,
% 0.20/0.51 (![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))))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[118])).
% 0.20/0.51 tff(120,plain,
% 0.20/0.51 (^[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)))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(121,plain,
% 0.20/0.51 (![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))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[120])).
% 0.20/0.51 tff(122,plain,
% 0.20/0.51 (^[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)))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(123,plain,
% 0.20/0.51 (![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))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[122])).
% 0.20/0.51 tff(124,plain,
% 0.20/0.51 (![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)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(125,plain,
% 0.20/0.51 (^[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))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(126,plain,
% 0.20/0.51 (![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)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[125])).
% 0.20/0.51 tff(127,axiom,((aSet0(xP) & ![W0: $i] : ((aElementOf0(W0, xP) => (((aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) & ![W1: $i] : (aElementOf0(W1, xT) => sdtlseqdt0(W1, W0))) & aUpperBoundOfIn0(W0, xT, xU))) & (((aElementOf0(W0, xU) & sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) & (![W1: $i] : (aElementOf0(W1, xT) => sdtlseqdt0(W1, W0)) | aUpperBoundOfIn0(W0, xT, xU))) => aElementOf0(W0, xP)))) & (xP = cS1241(xU, xf, xT))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__1244')).
% 0.20/0.51 tff(128,plain,
% 0.20/0.51 (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)))),
% 0.20/0.51 inference(and_elim,[status(thm)],[127])).
% 0.20/0.51 tff(129,plain,
% 0.20/0.51 (![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)))),
% 0.20/0.51 inference(and_elim,[status(thm)],[128])).
% 0.20/0.51 tff(130,plain,
% 0.20/0.51 (![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)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[129, 126])).
% 0.20/0.51 tff(131,plain,
% 0.20/0.51 (![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)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[130, 124])).
% 0.20/0.51 tff(132,plain,
% 0.20/0.51 (![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))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[131, 123])).
% 0.20/0.51 tff(133,plain,
% 0.20/0.51 (![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))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[132, 121])).
% 0.20/0.51 tff(134,plain,(
% 0.20/0.51 ![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))))),
% 0.20/0.51 inference(skolemize,[status(sab)],[133])).
% 0.20/0.51 tff(135,plain,
% 0.20/0.51 (![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))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[134, 119])).
% 0.20/0.51 tff(136,plain,
% 0.20/0.51 (![W0: $i] : (~((~((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(W0, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0), W0)) | (~aUpperBoundOfIn0(W0, xT, szDzozmdt0(xf))) | (~![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)))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[135, 117])).
% 0.20/0.52 tff(137,plain,
% 0.20/0.52 (![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)))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[136, 115])).
% 0.20/0.52 tff(138,plain,
% 0.20/0.52 (![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)))))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[137, 110])).
% 0.20/0.52 tff(139,plain,
% 0.20/0.52 ((~![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(sdtlpdtrp0(xf, xp), cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(sdtlpdtrp0(xf, xp), szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp))) | (~(aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), xT)) | sdtlseqdt0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp)))))) | (~((~aElementOf0(sdtlpdtrp0(xf, xp), cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(sdtlpdtrp0(xf, xp), szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp))) | (~aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, sdtlpdtrp0(xf, xp))))))))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(140,plain,
% 0.20/0.52 (~((~(aElementOf0(sdtlpdtrp0(xf, xp), cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(sdtlpdtrp0(xf, xp), szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp))) | (~(aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), xT)) | sdtlseqdt0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp)))))) | (~((~aElementOf0(sdtlpdtrp0(xf, xp), cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(sdtlpdtrp0(xf, xp), szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp))) | (~aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, sdtlpdtrp0(xf, xp)))))))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[139, 138])).
% 0.20/0.52 tff(141,plain,
% 0.20/0.52 (((~(aElementOf0(sdtlpdtrp0(xf, xp), cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(sdtlpdtrp0(xf, xp), szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp))) | (~(aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), xT)) | sdtlseqdt0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp)))))) | (~((~aElementOf0(sdtlpdtrp0(xf, xp), cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(sdtlpdtrp0(xf, xp), szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp))) | (~aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, sdtlpdtrp0(xf, xp))))))))) | (aElementOf0(sdtlpdtrp0(xf, xp), cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(sdtlpdtrp0(xf, xp), szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp))) | (~(aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), xT)) | sdtlseqdt0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp)))))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(142,plain,
% 0.20/0.52 (aElementOf0(sdtlpdtrp0(xf, xp), cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(sdtlpdtrp0(xf, xp), szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp))) | (~(aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), xT)) | sdtlseqdt0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[141, 140])).
% 0.20/0.52 tff(143,plain,
% 0.20/0.52 (aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szRzazndt0(xf)) <=> aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szDzozmdt0(xf))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(144,plain,
% 0.20/0.52 (aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU) <=> aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szRzazndt0(xf))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(145,plain,
% 0.20/0.52 (aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU) <=> aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU)),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(146,plain,
% 0.20/0.52 (aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU)),
% 0.20/0.52 inference(and_elim,[status(thm)],[53])).
% 0.20/0.52 tff(147,plain,
% 0.20/0.52 (aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, xU)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.20/0.52 tff(148,plain,
% 0.20/0.52 (aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szRzazndt0(xf))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[147, 144])).
% 0.20/0.52 tff(149,plain,
% 0.20/0.52 (aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szDzozmdt0(xf))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[148, 143])).
% 0.20/0.52 tff(150,plain,
% 0.20/0.52 ((aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), xT)) | sdtlseqdt0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp))) | (~aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szDzozmdt0(xf)))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(151,plain,
% 0.20/0.52 (aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), xT)) | sdtlseqdt0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[150, 149])).
% 0.20/0.52 tff(152,plain,
% 0.20/0.52 ((~(aElementOf0(sdtlpdtrp0(xf, xp), cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(sdtlpdtrp0(xf, xp), szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp))) | (~(aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), xT)) | sdtlseqdt0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp)))))) | aElementOf0(sdtlpdtrp0(xf, xp), cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(sdtlpdtrp0(xf, xp), szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp))) | (~(aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), xT)) | sdtlseqdt0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp))))),
% 0.20/0.52 inference(tautology,[status(thm)],[])).
% 0.20/0.52 tff(153,plain,
% 0.20/0.52 ((~(aElementOf0(sdtlpdtrp0(xf, xp), cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(sdtlpdtrp0(xf, xp), szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp))) | (~(aUpperBoundOfIn0(sdtlpdtrp0(xf, xp), xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), xT)) | sdtlseqdt0(tptp_fun_W1_15(sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp)))))) | aElementOf0(sdtlpdtrp0(xf, xp), cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(sdtlpdtrp0(xf, xp), szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[152, 151])).
% 0.20/0.52 tff(154,plain,
% 0.20/0.52 (aElementOf0(sdtlpdtrp0(xf, xp), cS1241(szDzozmdt0(xf), xf, xT)) | (~sdtlseqdt0(sdtlpdtrp0(xf, sdtlpdtrp0(xf, xp)), sdtlpdtrp0(xf, xp)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[153, 49, 142])).
% 0.20/0.52 tff(155,plain,
% 0.20/0.52 (aElementOf0(sdtlpdtrp0(xf, xp), cS1241(szDzozmdt0(xf), xf, xT))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[154, 108])).
% 0.20/0.52 tff(156,plain,
% 0.20/0.52 (^[W0: $i] : refl(((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(xp, W0)) <=> ((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(xp, W0)))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(157,plain,
% 0.20/0.52 (![W0: $i] : ((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(xp, W0)) <=> ![W0: $i] : ((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(xp, W0))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[156])).
% 0.20/0.52 tff(158,plain,
% 0.20/0.52 (^[W0: $i] : rewrite(((~aElementOf0(W0, cS1241(szRzazndt0(xf), xf, xT))) | sdtlseqdt0(xp, W0)) <=> ((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(xp, W0)))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(159,plain,
% 0.20/0.52 (![W0: $i] : ((~aElementOf0(W0, cS1241(szRzazndt0(xf), xf, xT))) | sdtlseqdt0(xp, W0)) <=> ![W0: $i] : ((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(xp, W0))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[158])).
% 0.20/0.52 tff(160,plain,
% 0.20/0.52 (^[W0: $i] : rewrite(((~aElementOf0(W0, xP)) | sdtlseqdt0(xp, W0)) <=> ((~aElementOf0(W0, cS1241(szRzazndt0(xf), xf, xT))) | sdtlseqdt0(xp, W0)))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(161,plain,
% 0.20/0.52 (![W0: $i] : ((~aElementOf0(W0, xP)) | sdtlseqdt0(xp, W0)) <=> ![W0: $i] : ((~aElementOf0(W0, cS1241(szRzazndt0(xf), xf, xT))) | sdtlseqdt0(xp, W0))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[160])).
% 0.20/0.52 tff(162,plain,
% 0.20/0.52 (![W0: $i] : ((~aElementOf0(W0, xP)) | sdtlseqdt0(xp, W0)) <=> ![W0: $i] : ((~aElementOf0(W0, xP)) | sdtlseqdt0(xp, W0))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(163,plain,
% 0.20/0.52 (^[W0: $i] : rewrite((aElementOf0(W0, xP) => sdtlseqdt0(xp, W0)) <=> ((~aElementOf0(W0, xP)) | sdtlseqdt0(xp, W0)))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(164,plain,
% 0.20/0.52 (![W0: $i] : (aElementOf0(W0, xP) => sdtlseqdt0(xp, W0)) <=> ![W0: $i] : ((~aElementOf0(W0, xP)) | sdtlseqdt0(xp, W0))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[163])).
% 0.20/0.52 tff(165,plain,
% 0.20/0.52 (![W0: $i] : (aElementOf0(W0, xP) => sdtlseqdt0(xp, W0))),
% 0.20/0.52 inference(and_elim,[status(thm)],[39])).
% 0.20/0.52 tff(166,plain,
% 0.20/0.52 (![W0: $i] : ((~aElementOf0(W0, xP)) | sdtlseqdt0(xp, W0))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.20/0.52 tff(167,plain,
% 0.20/0.52 (![W0: $i] : ((~aElementOf0(W0, xP)) | sdtlseqdt0(xp, W0))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[166, 162])).
% 0.20/0.52 tff(168,plain,
% 0.20/0.52 (![W0: $i] : ((~aElementOf0(W0, cS1241(szRzazndt0(xf), xf, xT))) | sdtlseqdt0(xp, W0))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[167, 161])).
% 0.20/0.52 tff(169,plain,
% 0.20/0.52 (![W0: $i] : ((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(xp, W0))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[168, 159])).
% 0.20/0.52 tff(170,plain,(
% 0.20/0.52 ![W0: $i] : ((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(xp, W0))),
% 0.20/0.52 inference(skolemize,[status(sab)],[169])).
% 0.20/0.52 tff(171,plain,
% 0.20/0.52 (![W0: $i] : ((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(xp, W0))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[170, 157])).
% 0.20/0.52 tff(172,plain,
% 0.20/0.52 (((~![W0: $i] : ((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(xp, W0))) | ((~aElementOf0(sdtlpdtrp0(xf, xp), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(xp, sdtlpdtrp0(xf, xp)))) <=> ((~![W0: $i] : ((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(xp, W0))) | (~aElementOf0(sdtlpdtrp0(xf, xp), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(xp, sdtlpdtrp0(xf, xp)))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(173,plain,
% 0.20/0.52 ((~![W0: $i] : ((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(xp, W0))) | ((~aElementOf0(sdtlpdtrp0(xf, xp), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(xp, sdtlpdtrp0(xf, xp)))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(174,plain,
% 0.20/0.52 ((~![W0: $i] : ((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(xp, W0))) | (~aElementOf0(sdtlpdtrp0(xf, xp), cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(xp, sdtlpdtrp0(xf, xp))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.20/0.52 tff(175,plain,
% 0.20/0.52 (sdtlseqdt0(xp, sdtlpdtrp0(xf, xp))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[174, 171, 155])).
% 0.20/0.52 tff(176,plain,
% 0.20/0.52 (aElementOf0(xp, szRzazndt0(xf)) <=> aElementOf0(xp, szDzozmdt0(xf))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[8])).
% 0.20/0.52 tff(177,plain,
% 0.20/0.52 (aElementOf0(xp, szDzozmdt0(xf)) <=> aElementOf0(xp, szRzazndt0(xf))),
% 0.20/0.52 inference(symmetry,[status(thm)],[176])).
% 0.20/0.52 tff(178,plain,
% 0.20/0.52 (aElementOf0(xp, szRzazndt0(xf))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[44, 177])).
% 0.20/0.52 tff(179,plain,
% 0.20/0.52 (aSet0(szRzazndt0(xf)) <=> aSet0(szDzozmdt0(xf))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[8])).
% 0.20/0.52 tff(180,plain,
% 0.20/0.52 (aSet0(szDzozmdt0(xf)) <=> aSet0(szRzazndt0(xf))),
% 0.20/0.52 inference(symmetry,[status(thm)],[179])).
% 0.20/0.52 tff(181,plain,
% 0.20/0.52 (aSet0(szRzazndt0(xf)) <=> aSet0(szDzozmdt0(xf))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(182,plain,
% 0.20/0.52 (aSet0(xU) <=> aSet0(szRzazndt0(xf))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(183,plain,
% 0.20/0.52 (aSet0(xU) <=> aSet0(xU)),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(184,plain,
% 0.20/0.52 ((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)),
% 0.20/0.52 inference(and_elim,[status(thm)],[13])).
% 0.20/0.52 tff(185,plain,
% 0.20/0.52 (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))))),
% 0.20/0.52 inference(and_elim,[status(thm)],[184])).
% 0.20/0.52 tff(186,plain,
% 0.20/0.52 (aSet0(xU)),
% 0.20/0.52 inference(and_elim,[status(thm)],[185])).
% 0.20/0.52 tff(187,plain,
% 0.20/0.52 (aSet0(xU)),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[186, 183])).
% 0.20/0.52 tff(188,plain,
% 0.20/0.52 (aSet0(szRzazndt0(xf))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[187, 182])).
% 0.20/0.52 tff(189,plain,
% 0.20/0.52 (aSet0(szDzozmdt0(xf))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[188, 181])).
% 0.20/0.52 tff(190,plain,
% 0.20/0.52 (aSet0(szRzazndt0(xf))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[189, 180])).
% 0.20/0.52 tff(191,plain,
% 0.20/0.52 (^[W0: $i] : refl(((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(192,plain,
% 0.20/0.52 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[191])).
% 0.20/0.52 tff(193,plain,
% 0.20/0.52 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(194,plain,
% 0.20/0.52 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[193])).
% 0.20/0.52 tff(195,plain,
% 0.20/0.52 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[194, 192])).
% 0.20/0.52 tff(196,plain,
% 0.20/0.52 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(197,plain,
% 0.20/0.52 (^[W0: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: $i] : rewrite((aElementOf0(W1, W0) => aElement0(W1)) <=> (aElement0(W1) | (~aElementOf0(W1, W0))))), (![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1)) <=> ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))), ((aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1))) <=> (aSet0(W0) => ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))))), rewrite((aSet0(W0) => ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))), ((aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(198,plain,
% 0.20/0.52 (![W0: $i] : (aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[197])).
% 0.20/0.52 tff(199,axiom,(![W0: $i] : (aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mEOfElem')).
% 0.20/0.52 tff(200,plain,
% 0.20/0.52 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.20/0.52 tff(201,plain,
% 0.20/0.52 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[200, 196])).
% 0.20/0.52 tff(202,plain,(
% 0.20/0.52 ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.20/0.52 inference(skolemize,[status(sab)],[201])).
% 0.20/0.52 tff(203,plain,
% 0.20/0.52 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[202, 195])).
% 0.20/0.52 tff(204,plain,
% 0.20/0.52 (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | ((~aSet0(szRzazndt0(xf))) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, szRzazndt0(xf)))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | (~aSet0(szRzazndt0(xf))) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, szRzazndt0(xf)))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(205,plain,
% 0.20/0.52 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | ((~aSet0(szRzazndt0(xf))) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, szRzazndt0(xf)))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(206,plain,
% 0.20/0.52 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | (~aSet0(szRzazndt0(xf))) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, szRzazndt0(xf))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[205, 204])).
% 0.20/0.52 tff(207,plain,
% 0.20/0.52 ((~aSet0(szRzazndt0(xf))) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, szRzazndt0(xf))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[206, 203])).
% 0.20/0.52 tff(208,plain,
% 0.20/0.52 (![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, szRzazndt0(xf))))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[207, 190])).
% 0.20/0.52 tff(209,plain,
% 0.20/0.52 (((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, szRzazndt0(xf))))) | (aElement0(xp) | (~aElementOf0(xp, szRzazndt0(xf))))) <=> ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, szRzazndt0(xf))))) | aElement0(xp) | (~aElementOf0(xp, szRzazndt0(xf))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(210,plain,
% 0.20/0.52 ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, szRzazndt0(xf))))) | (aElement0(xp) | (~aElementOf0(xp, szRzazndt0(xf))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(211,plain,
% 0.20/0.52 ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, szRzazndt0(xf))))) | aElement0(xp) | (~aElementOf0(xp, szRzazndt0(xf)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.20/0.52 tff(212,plain,
% 0.20/0.52 (aElement0(xp) | (~aElementOf0(xp, szRzazndt0(xf)))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[211, 208])).
% 0.20/0.52 tff(213,plain,
% 0.20/0.52 (aElement0(xp)),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[212, 178])).
% 0.20/0.52 tff(214,plain,
% 0.20/0.52 (((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, szRzazndt0(xf))))) | (aElement0(sdtlpdtrp0(xf, xp)) | (~aElementOf0(sdtlpdtrp0(xf, xp), szRzazndt0(xf))))) <=> ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, szRzazndt0(xf))))) | aElement0(sdtlpdtrp0(xf, xp)) | (~aElementOf0(sdtlpdtrp0(xf, xp), szRzazndt0(xf))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(215,plain,
% 0.20/0.52 ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, szRzazndt0(xf))))) | (aElement0(sdtlpdtrp0(xf, xp)) | (~aElementOf0(sdtlpdtrp0(xf, xp), szRzazndt0(xf))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(216,plain,
% 0.20/0.52 ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, szRzazndt0(xf))))) | aElement0(sdtlpdtrp0(xf, xp)) | (~aElementOf0(sdtlpdtrp0(xf, xp), szRzazndt0(xf)))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[215, 214])).
% 0.20/0.52 tff(217,plain,
% 0.20/0.52 (aElement0(sdtlpdtrp0(xf, xp))),
% 0.20/0.52 inference(unit_resolution,[status(thm)],[216, 208, 48])).
% 0.20/0.52 tff(218,plain,
% 0.20/0.52 (^[W0: $i, W1: $i] : refl(((W0 = W1) | (~aElement0(W1)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)) | (~aElement0(W0))) <=> ((W0 = W1) | (~aElement0(W1)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)) | (~aElement0(W0))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(219,plain,
% 0.20/0.52 (![W0: $i, W1: $i] : ((W0 = W1) | (~aElement0(W1)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)) | (~aElement0(W0))) <=> ![W0: $i, W1: $i] : ((W0 = W1) | (~aElement0(W1)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)) | (~aElement0(W0)))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[218])).
% 0.20/0.52 tff(220,plain,
% 0.20/0.52 (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)) <=> (~((~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0))))), ((~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))) <=> (~(~((~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0))))))), rewrite((~(~((~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0))))) <=> ((~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)))), ((~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))) <=> ((~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0))))), trans(monotonicity(rewrite((aElement0(W0) & aElement0(W1)) <=> (~((~aElement0(W1)) | (~aElement0(W0))))), ((~(aElement0(W0) & aElement0(W1))) <=> (~(~((~aElement0(W1)) | (~aElement0(W0))))))), rewrite((~(~((~aElement0(W1)) | (~aElement0(W0))))) <=> ((~aElement0(W1)) | (~aElement0(W0)))), ((~(aElement0(W0) & aElement0(W1))) <=> ((~aElement0(W1)) | (~aElement0(W0))))), (((W0 = W1) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))) | (~(aElement0(W0) & aElement0(W1)))) <=> ((W0 = W1) | ((~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0))) | ((~aElement0(W1)) | (~aElement0(W0)))))), rewrite(((W0 = W1) | ((~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0))) | ((~aElement0(W1)) | (~aElement0(W0)))) <=> ((W0 = W1) | (~aElement0(W1)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)) | (~aElement0(W0)))), (((W0 = W1) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))) | (~(aElement0(W0) & aElement0(W1)))) <=> ((W0 = W1) | (~aElement0(W1)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)) | (~aElement0(W0)))))),
% 0.20/0.52 inference(bind,[status(th)],[])).
% 0.20/0.52 tff(221,plain,
% 0.20/0.52 (![W0: $i, W1: $i] : ((W0 = W1) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))) | (~(aElement0(W0) & aElement0(W1)))) <=> ![W0: $i, W1: $i] : ((W0 = W1) | (~aElement0(W1)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)) | (~aElement0(W0)))),
% 0.20/0.52 inference(quant_intro,[status(thm)],[220])).
% 0.20/0.53 tff(222,plain,
% 0.20/0.53 (![W0: $i, W1: $i] : ((W0 = W1) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))) | (~(aElement0(W0) & aElement0(W1)))) <=> ![W0: $i, W1: $i] : ((W0 = W1) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))) | (~(aElement0(W0) & aElement0(W1))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(223,plain,
% 0.20/0.53 (^[W0: $i, W1: $i] : trans(monotonicity(rewrite(((sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)) => (W0 = W1)) <=> ((~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))) | (W0 = W1))), (((aElement0(W0) & aElement0(W1)) => ((sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)) => (W0 = W1))) <=> ((aElement0(W0) & aElement0(W1)) => ((~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))) | (W0 = W1))))), rewrite(((aElement0(W0) & aElement0(W1)) => ((~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))) | (W0 = W1))) <=> ((W0 = W1) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))) | (~(aElement0(W0) & aElement0(W1))))), (((aElement0(W0) & aElement0(W1)) => ((sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)) => (W0 = W1))) <=> ((W0 = W1) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))) | (~(aElement0(W0) & aElement0(W1))))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(224,plain,
% 0.20/0.53 (![W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) => ((sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)) => (W0 = W1))) <=> ![W0: $i, W1: $i] : ((W0 = W1) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))) | (~(aElement0(W0) & aElement0(W1))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[223])).
% 0.20/0.53 tff(225,axiom,(![W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) => ((sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0)) => (W0 = W1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mASymm')).
% 0.20/0.53 tff(226,plain,
% 0.20/0.53 (![W0: $i, W1: $i] : ((W0 = W1) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))) | (~(aElement0(W0) & aElement0(W1))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.20/0.53 tff(227,plain,
% 0.20/0.53 (![W0: $i, W1: $i] : ((W0 = W1) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))) | (~(aElement0(W0) & aElement0(W1))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[226, 222])).
% 0.20/0.53 tff(228,plain,(
% 0.20/0.53 ![W0: $i, W1: $i] : ((W0 = W1) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W0))) | (~(aElement0(W0) & aElement0(W1))))),
% 0.20/0.53 inference(skolemize,[status(sab)],[227])).
% 0.20/0.53 tff(229,plain,
% 0.20/0.53 (![W0: $i, W1: $i] : ((W0 = W1) | (~aElement0(W1)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)) | (~aElement0(W0)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[228, 221])).
% 0.20/0.53 tff(230,plain,
% 0.20/0.53 (![W0: $i, W1: $i] : ((W0 = W1) | (~aElement0(W1)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)) | (~aElement0(W0)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[229, 219])).
% 0.20/0.53 tff(231,plain,
% 0.20/0.53 (((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElement0(W1)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)) | (~aElement0(W0)))) | ((~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (xp = sdtlpdtrp0(xf, xp)) | (~aElement0(sdtlpdtrp0(xf, xp))) | (~sdtlseqdt0(xp, sdtlpdtrp0(xf, xp))) | (~aElement0(xp)))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElement0(W1)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)) | (~aElement0(W0)))) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (xp = sdtlpdtrp0(xf, xp)) | (~aElement0(sdtlpdtrp0(xf, xp))) | (~sdtlseqdt0(xp, sdtlpdtrp0(xf, xp))) | (~aElement0(xp)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(232,plain,
% 0.20/0.53 (((xp = sdtlpdtrp0(xf, xp)) | (~aElement0(sdtlpdtrp0(xf, xp))) | (~sdtlseqdt0(xp, sdtlpdtrp0(xf, xp))) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (~aElement0(xp))) <=> ((~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (xp = sdtlpdtrp0(xf, xp)) | (~aElement0(sdtlpdtrp0(xf, xp))) | (~sdtlseqdt0(xp, sdtlpdtrp0(xf, xp))) | (~aElement0(xp)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(233,plain,
% 0.20/0.53 (((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElement0(W1)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)) | (~aElement0(W0)))) | ((xp = sdtlpdtrp0(xf, xp)) | (~aElement0(sdtlpdtrp0(xf, xp))) | (~sdtlseqdt0(xp, sdtlpdtrp0(xf, xp))) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (~aElement0(xp)))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElement0(W1)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)) | (~aElement0(W0)))) | ((~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (xp = sdtlpdtrp0(xf, xp)) | (~aElement0(sdtlpdtrp0(xf, xp))) | (~sdtlseqdt0(xp, sdtlpdtrp0(xf, xp))) | (~aElement0(xp))))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[232])).
% 0.20/0.53 tff(234,plain,
% 0.20/0.53 (((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElement0(W1)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)) | (~aElement0(W0)))) | ((xp = sdtlpdtrp0(xf, xp)) | (~aElement0(sdtlpdtrp0(xf, xp))) | (~sdtlseqdt0(xp, sdtlpdtrp0(xf, xp))) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (~aElement0(xp)))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElement0(W1)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)) | (~aElement0(W0)))) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (xp = sdtlpdtrp0(xf, xp)) | (~aElement0(sdtlpdtrp0(xf, xp))) | (~sdtlseqdt0(xp, sdtlpdtrp0(xf, xp))) | (~aElement0(xp)))),
% 0.20/0.53 inference(transitivity,[status(thm)],[233, 231])).
% 0.20/0.53 tff(235,plain,
% 0.20/0.53 ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElement0(W1)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)) | (~aElement0(W0)))) | ((xp = sdtlpdtrp0(xf, xp)) | (~aElement0(sdtlpdtrp0(xf, xp))) | (~sdtlseqdt0(xp, sdtlpdtrp0(xf, xp))) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (~aElement0(xp)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(236,plain,
% 0.20/0.53 ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElement0(W1)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)) | (~aElement0(W0)))) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (xp = sdtlpdtrp0(xf, xp)) | (~aElement0(sdtlpdtrp0(xf, xp))) | (~sdtlseqdt0(xp, sdtlpdtrp0(xf, xp))) | (~aElement0(xp))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.20/0.53 tff(237,plain,
% 0.20/0.53 ((xp = sdtlpdtrp0(xf, xp)) | (~aElement0(sdtlpdtrp0(xf, xp))) | (~sdtlseqdt0(xp, sdtlpdtrp0(xf, xp))) | (~aElement0(xp))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[236, 230, 87])).
% 0.20/0.53 tff(238,plain,
% 0.20/0.53 ((xp = sdtlpdtrp0(xf, xp)) | (~sdtlseqdt0(xp, sdtlpdtrp0(xf, xp)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[237, 217, 213])).
% 0.20/0.53 tff(239,plain,
% 0.20/0.53 (xp = sdtlpdtrp0(xf, xp)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[238, 175])).
% 0.20/0.53 tff(240,plain,
% 0.20/0.53 (sdtlpdtrp0(xf, xp) = xp),
% 0.20/0.53 inference(symmetry,[status(thm)],[239])).
% 0.20/0.53 tff(241,plain,
% 0.20/0.53 (sdtlseqdt0(W0!17, sdtlpdtrp0(xf, xp)) <=> sdtlseqdt0(W0!17, xp)),
% 0.20/0.53 inference(monotonicity,[status(thm)],[240])).
% 0.20/0.53 tff(242,plain,
% 0.20/0.53 (sdtlseqdt0(W0!17, xp) <=> sdtlseqdt0(W0!17, sdtlpdtrp0(xf, xp))),
% 0.20/0.53 inference(symmetry,[status(thm)],[241])).
% 0.20/0.53 tff(243,plain,
% 0.20/0.53 ((~sdtlseqdt0(W0!17, xp)) <=> (~sdtlseqdt0(W0!17, sdtlpdtrp0(xf, xp)))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[242])).
% 0.20/0.53 tff(244,plain,
% 0.20/0.53 ((~![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!18, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0!18, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!18), W0!18)) | (~(aUpperBoundOfIn0(W0!18, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0!18), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0!18), W0!18))))) | (~((~aElementOf0(W0!18, cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(W0!18, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!18), W0!18)) | (~aUpperBoundOfIn0(W0!18, xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!18)))))))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(245,plain,
% 0.20/0.53 (~((~(aElementOf0(W0!18, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0!18, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!18), W0!18)) | (~(aUpperBoundOfIn0(W0!18, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0!18), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0!18), W0!18))))) | (~((~aElementOf0(W0!18, cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(W0!18, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!18), W0!18)) | (~aUpperBoundOfIn0(W0!18, xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!18))))))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[244, 138])).
% 0.20/0.53 tff(246,plain,
% 0.20/0.53 (((~(aElementOf0(W0!18, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0!18, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!18), W0!18)) | (~(aUpperBoundOfIn0(W0!18, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0!18), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0!18), W0!18))))) | (~((~aElementOf0(W0!18, cS1241(szDzozmdt0(xf), xf, xT))) | (~((~aElementOf0(W0!18, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!18), W0!18)) | (~aUpperBoundOfIn0(W0!18, xT, szDzozmdt0(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!18)))))))) | (aElementOf0(W0!18, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0!18, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!18), W0!18)) | (~(aUpperBoundOfIn0(W0!18, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0!18), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0!18), W0!18))))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(247,plain,
% 0.20/0.53 (aElementOf0(W0!18, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0!18, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!18), W0!18)) | (~(aUpperBoundOfIn0(W0!18, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0!18), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0!18), W0!18)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[246, 245])).
% 0.20/0.53 tff(248,plain,
% 0.20/0.53 (^[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)))))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(249,plain,
% 0.20/0.53 (![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))))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[248])).
% 0.20/0.53 tff(250,plain,
% 0.20/0.53 (^[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))))))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(251,plain,
% 0.20/0.53 (![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))))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[250])).
% 0.20/0.53 tff(252,plain,
% 0.20/0.53 (^[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)))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(253,plain,
% 0.20/0.53 (![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))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[252])).
% 0.20/0.53 tff(254,plain,
% 0.20/0.53 (![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)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(255,plain,
% 0.20/0.53 (^[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))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(256,plain,
% 0.20/0.53 (![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)))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[255])).
% 0.20/0.53 tff(257,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/sandbox2/benchmark/theBenchmark.p','m__1144')).
% 0.20/0.53 tff(258,plain,
% 0.20/0.53 (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)))),
% 0.20/0.53 inference(and_elim,[status(thm)],[257])).
% 0.20/0.53 tff(259,plain,
% 0.20/0.53 (![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)))),
% 0.20/0.53 inference(and_elim,[status(thm)],[258])).
% 0.20/0.53 tff(260,plain,
% 0.20/0.53 (![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)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[259, 256])).
% 0.20/0.53 tff(261,plain,
% 0.20/0.53 (![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)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[260, 254])).
% 0.20/0.53 tff(262,plain,
% 0.20/0.53 (![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))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[261, 253])).
% 0.20/0.53 tff(263,plain,(
% 0.20/0.53 ![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))))),
% 0.20/0.53 inference(skolemize,[status(sab)],[262])).
% 0.20/0.53 tff(264,plain,
% 0.20/0.53 (![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))))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[263, 251])).
% 0.20/0.53 tff(265,plain,
% 0.20/0.53 (![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))))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[264, 249])).
% 0.20/0.53 tff(266,plain,
% 0.20/0.53 ((~![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))))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(267,plain,
% 0.20/0.53 (~((~((~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)))))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[266, 265])).
% 0.20/0.54 tff(268,plain,
% 0.20/0.54 (((~((~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)))))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(269,plain,
% 0.20/0.54 ((~aElementOf0(W0!18, cS1142(xf))) | (~((~aElementOf0(W0!18, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0!18) = W0!18)) | (~aFixedPointOf0(W0!18, xf))))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[268, 267])).
% 0.20/0.54 tff(270,assumption,(~(sdtlseqdt0(xp, W0!18) | (~aElementOf0(W0!18, cS1142(xf))) | (~aUpperBoundOfIn0(W0!18, xT, cS1142(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!18))))), introduced(assumption)).
% 0.20/0.54 tff(271,plain,
% 0.20/0.54 ((sdtlseqdt0(xp, W0!18) | (~aElementOf0(W0!18, cS1142(xf))) | (~aUpperBoundOfIn0(W0!18, xT, cS1142(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!18)))) | aElementOf0(W0!18, cS1142(xf))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(272,plain,
% 0.20/0.54 (aElementOf0(W0!18, cS1142(xf))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[271, 270])).
% 0.20/0.54 tff(273,plain,
% 0.20/0.54 ((~((~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))))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(274,plain,
% 0.20/0.54 ((~((~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))))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[273, 272])).
% 0.20/0.54 tff(275,plain,
% 0.20/0.54 (~((~aElementOf0(W0!18, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0!18) = W0!18)) | (~aFixedPointOf0(W0!18, xf)))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[274, 269])).
% 0.20/0.54 tff(276,plain,
% 0.20/0.54 (((~aElementOf0(W0!18, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0!18) = W0!18)) | (~aFixedPointOf0(W0!18, xf))) | (sdtlpdtrp0(xf, W0!18) = W0!18)),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(277,plain,
% 0.20/0.54 (sdtlpdtrp0(xf, W0!18) = W0!18),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[276, 275])).
% 0.20/0.54 tff(278,plain,
% 0.20/0.54 (W0!18 = sdtlpdtrp0(xf, W0!18)),
% 0.20/0.54 inference(symmetry,[status(thm)],[277])).
% 0.20/0.54 tff(279,plain,
% 0.20/0.54 (sdtlseqdt0(W0!18, W0!18) <=> sdtlseqdt0(sdtlpdtrp0(xf, W0!18), W0!18)),
% 0.20/0.54 inference(monotonicity,[status(thm)],[278])).
% 0.20/0.54 tff(280,plain,
% 0.20/0.54 (aSet0(xS) <=> aSet0(cS1142(xf))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(281,plain,
% 0.20/0.54 (aSet0(xS) <=> aSet0(xS)),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(282,plain,
% 0.20/0.54 (aSet0(xS)),
% 0.20/0.54 inference(and_elim,[status(thm)],[258])).
% 0.20/0.54 tff(283,plain,
% 0.20/0.54 (aSet0(xS)),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[282, 281])).
% 0.20/0.54 tff(284,plain,
% 0.20/0.54 (aSet0(cS1142(xf))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[283, 280])).
% 0.20/0.54 tff(285,plain,
% 0.20/0.54 (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | ((~aSet0(cS1142(xf))) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, cS1142(xf)))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | (~aSet0(cS1142(xf))) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, cS1142(xf)))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(286,plain,
% 0.20/0.54 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | ((~aSet0(cS1142(xf))) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, cS1142(xf)))))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(287,plain,
% 0.20/0.54 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | (~aSet0(cS1142(xf))) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, cS1142(xf))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[286, 285])).
% 0.20/0.54 tff(288,plain,
% 0.20/0.54 (![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, cS1142(xf))))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[287, 203, 284])).
% 0.20/0.54 tff(289,plain,
% 0.20/0.54 (((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, cS1142(xf))))) | (aElement0(W0!18) | (~aElementOf0(W0!18, cS1142(xf))))) <=> ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, cS1142(xf))))) | aElement0(W0!18) | (~aElementOf0(W0!18, cS1142(xf))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(290,plain,
% 0.20/0.54 ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, cS1142(xf))))) | (aElement0(W0!18) | (~aElementOf0(W0!18, cS1142(xf))))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(291,plain,
% 0.20/0.54 ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, cS1142(xf))))) | aElement0(W0!18) | (~aElementOf0(W0!18, cS1142(xf)))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[290, 289])).
% 0.20/0.54 tff(292,plain,
% 0.20/0.54 (aElement0(W0!18)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[291, 272, 288])).
% 0.20/0.54 tff(293,plain,
% 0.20/0.54 (^[W0: $i] : refl(((~aElement0(W0)) | sdtlseqdt0(W0, W0)) <=> ((~aElement0(W0)) | sdtlseqdt0(W0, W0)))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(294,plain,
% 0.20/0.54 (![W0: $i] : ((~aElement0(W0)) | sdtlseqdt0(W0, W0)) <=> ![W0: $i] : ((~aElement0(W0)) | sdtlseqdt0(W0, W0))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[293])).
% 0.20/0.54 tff(295,plain,
% 0.20/0.54 (![W0: $i] : ((~aElement0(W0)) | sdtlseqdt0(W0, W0)) <=> ![W0: $i] : ((~aElement0(W0)) | sdtlseqdt0(W0, W0))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(296,plain,
% 0.20/0.54 (^[W0: $i] : rewrite((aElement0(W0) => sdtlseqdt0(W0, W0)) <=> ((~aElement0(W0)) | sdtlseqdt0(W0, W0)))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(297,plain,
% 0.20/0.54 (![W0: $i] : (aElement0(W0) => sdtlseqdt0(W0, W0)) <=> ![W0: $i] : ((~aElement0(W0)) | sdtlseqdt0(W0, W0))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[296])).
% 0.20/0.54 tff(298,axiom,(![W0: $i] : (aElement0(W0) => sdtlseqdt0(W0, W0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mARefl')).
% 0.20/0.54 tff(299,plain,
% 0.20/0.54 (![W0: $i] : ((~aElement0(W0)) | sdtlseqdt0(W0, W0))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[298, 297])).
% 0.20/0.54 tff(300,plain,
% 0.20/0.54 (![W0: $i] : ((~aElement0(W0)) | sdtlseqdt0(W0, W0))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[299, 295])).
% 0.20/0.54 tff(301,plain,(
% 0.20/0.54 ![W0: $i] : ((~aElement0(W0)) | sdtlseqdt0(W0, W0))),
% 0.20/0.54 inference(skolemize,[status(sab)],[300])).
% 0.20/0.54 tff(302,plain,
% 0.20/0.54 (![W0: $i] : ((~aElement0(W0)) | sdtlseqdt0(W0, W0))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[301, 294])).
% 0.20/0.54 tff(303,plain,
% 0.20/0.54 (((~![W0: $i] : ((~aElement0(W0)) | sdtlseqdt0(W0, W0))) | ((~aElement0(W0!18)) | sdtlseqdt0(W0!18, W0!18))) <=> ((~![W0: $i] : ((~aElement0(W0)) | sdtlseqdt0(W0, W0))) | (~aElement0(W0!18)) | sdtlseqdt0(W0!18, W0!18))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(304,plain,
% 0.20/0.54 ((~![W0: $i] : ((~aElement0(W0)) | sdtlseqdt0(W0, W0))) | ((~aElement0(W0!18)) | sdtlseqdt0(W0!18, W0!18))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(305,plain,
% 0.20/0.54 ((~![W0: $i] : ((~aElement0(W0)) | sdtlseqdt0(W0, W0))) | (~aElement0(W0!18)) | sdtlseqdt0(W0!18, W0!18)),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[304, 303])).
% 0.20/0.54 tff(306,plain,
% 0.20/0.54 (sdtlseqdt0(W0!18, W0!18)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[305, 302, 292])).
% 0.20/0.54 tff(307,plain,
% 0.20/0.54 (sdtlseqdt0(sdtlpdtrp0(xf, W0!18), W0!18)),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[306, 279])).
% 0.20/0.54 tff(308,plain,
% 0.20/0.54 (((~aElementOf0(W0!18, szDzozmdt0(xf))) | (~(sdtlpdtrp0(xf, W0!18) = W0!18)) | (~aFixedPointOf0(W0!18, xf))) | aElementOf0(W0!18, szDzozmdt0(xf))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(309,plain,
% 0.20/0.54 (aElementOf0(W0!18, szDzozmdt0(xf))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[308, 275])).
% 0.20/0.54 tff(310,plain,
% 0.20/0.54 ((sdtlseqdt0(xp, W0!18) | (~aElementOf0(W0!18, cS1142(xf))) | (~aUpperBoundOfIn0(W0!18, xT, cS1142(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!18)))) | (~sdtlseqdt0(xp, W0!18))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(311,plain,
% 0.20/0.54 (~sdtlseqdt0(xp, W0!18)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[310, 270])).
% 0.20/0.54 tff(312,plain,
% 0.20/0.54 (((~![W0: $i] : ((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(xp, W0))) | ((~aElementOf0(W0!18, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(xp, W0!18))) <=> ((~![W0: $i] : ((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(xp, W0))) | (~aElementOf0(W0!18, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(xp, W0!18))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(313,plain,
% 0.20/0.54 ((~![W0: $i] : ((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(xp, W0))) | ((~aElementOf0(W0!18, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(xp, W0!18))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(314,plain,
% 0.20/0.54 ((~![W0: $i] : ((~aElementOf0(W0, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(xp, W0))) | (~aElementOf0(W0!18, cS1241(szDzozmdt0(xf), xf, xT))) | sdtlseqdt0(xp, W0!18)),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[313, 312])).
% 0.20/0.54 tff(315,plain,
% 0.20/0.54 (~aElementOf0(W0!18, cS1241(szDzozmdt0(xf), xf, xT))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[314, 171, 311])).
% 0.20/0.54 tff(316,plain,
% 0.20/0.54 ((~(aElementOf0(W0!18, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0!18, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!18), W0!18)) | (~(aUpperBoundOfIn0(W0!18, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0!18), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0!18), W0!18))))) | aElementOf0(W0!18, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0!18, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!18), W0!18)) | (~(aUpperBoundOfIn0(W0!18, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0!18), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0!18), W0!18)))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(317,plain,
% 0.20/0.54 ((~(aElementOf0(W0!18, cS1241(szDzozmdt0(xf), xf, xT)) | (~aElementOf0(W0!18, szDzozmdt0(xf))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!18), W0!18)) | (~(aUpperBoundOfIn0(W0!18, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0!18), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0!18), W0!18))))) | (~sdtlseqdt0(sdtlpdtrp0(xf, W0!18), W0!18)) | (~(aUpperBoundOfIn0(W0!18, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0!18), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0!18), W0!18)))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[316, 315, 309])).
% 0.20/0.54 tff(318,plain,
% 0.20/0.54 (~(aUpperBoundOfIn0(W0!18, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0!18), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0!18), W0!18))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[317, 307, 247])).
% 0.20/0.54 tff(319,plain,
% 0.20/0.54 ((aUpperBoundOfIn0(W0!18, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0!18), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0!18), W0!18)) | (~sdtlseqdt0(tptp_fun_W1_15(W0!18), W0!18))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(320,plain,
% 0.20/0.54 (~sdtlseqdt0(tptp_fun_W1_15(W0!18), W0!18)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[319, 318])).
% 0.20/0.54 tff(321,plain,
% 0.20/0.54 ((aUpperBoundOfIn0(W0!18, xT, szDzozmdt0(xf)) | (~aElementOf0(tptp_fun_W1_15(W0!18), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0!18), W0!18)) | aElementOf0(tptp_fun_W1_15(W0!18), xT)),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(322,plain,
% 0.20/0.54 (aElementOf0(tptp_fun_W1_15(W0!18), xT)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[321, 318])).
% 0.20/0.54 tff(323,plain,
% 0.20/0.54 ((sdtlseqdt0(xp, W0!18) | (~aElementOf0(W0!18, cS1142(xf))) | (~aUpperBoundOfIn0(W0!18, xT, cS1142(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!18)))) | ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!18))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(324,plain,
% 0.20/0.54 (![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!18))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[323, 270])).
% 0.20/0.54 tff(325,plain,
% 0.20/0.54 (((~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!18))) | ((~aElementOf0(tptp_fun_W1_15(W0!18), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0!18), W0!18))) <=> ((~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!18))) | (~aElementOf0(tptp_fun_W1_15(W0!18), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0!18), W0!18))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(326,plain,
% 0.20/0.54 ((~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!18))) | ((~aElementOf0(tptp_fun_W1_15(W0!18), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0!18), W0!18))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(327,plain,
% 0.20/0.54 ((~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!18))) | (~aElementOf0(tptp_fun_W1_15(W0!18), xT)) | sdtlseqdt0(tptp_fun_W1_15(W0!18), W0!18)),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[326, 325])).
% 0.20/0.54 tff(328,plain,
% 0.20/0.54 ($false),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[327, 324, 322, 320])).
% 0.20/0.54 tff(329,plain,(sdtlseqdt0(xp, W0!18) | (~aElementOf0(W0!18, cS1142(xf))) | (~aUpperBoundOfIn0(W0!18, xT, cS1142(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!18)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.54 tff(330,plain,
% 0.20/0.54 (((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElement0(W1)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)) | (~aElement0(W0)))) | ((sdtlpdtrp0(xf, xp) = xp) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (~aElement0(sdtlpdtrp0(xf, xp))) | (~sdtlseqdt0(xp, sdtlpdtrp0(xf, xp))) | (~aElement0(xp)))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElement0(W1)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)) | (~aElement0(W0)))) | (sdtlpdtrp0(xf, xp) = xp) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (~aElement0(sdtlpdtrp0(xf, xp))) | (~sdtlseqdt0(xp, sdtlpdtrp0(xf, xp))) | (~aElement0(xp)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(331,plain,
% 0.20/0.54 (((sdtlpdtrp0(xf, xp) = xp) | (~aElement0(xp)) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (~sdtlseqdt0(xp, sdtlpdtrp0(xf, xp))) | (~aElement0(sdtlpdtrp0(xf, xp)))) <=> ((sdtlpdtrp0(xf, xp) = xp) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (~aElement0(sdtlpdtrp0(xf, xp))) | (~sdtlseqdt0(xp, sdtlpdtrp0(xf, xp))) | (~aElement0(xp)))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(332,plain,
% 0.20/0.54 (((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElement0(W1)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)) | (~aElement0(W0)))) | ((sdtlpdtrp0(xf, xp) = xp) | (~aElement0(xp)) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (~sdtlseqdt0(xp, sdtlpdtrp0(xf, xp))) | (~aElement0(sdtlpdtrp0(xf, xp))))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElement0(W1)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)) | (~aElement0(W0)))) | ((sdtlpdtrp0(xf, xp) = xp) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (~aElement0(sdtlpdtrp0(xf, xp))) | (~sdtlseqdt0(xp, sdtlpdtrp0(xf, xp))) | (~aElement0(xp))))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[331])).
% 0.20/0.54 tff(333,plain,
% 0.20/0.54 (((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElement0(W1)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)) | (~aElement0(W0)))) | ((sdtlpdtrp0(xf, xp) = xp) | (~aElement0(xp)) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (~sdtlseqdt0(xp, sdtlpdtrp0(xf, xp))) | (~aElement0(sdtlpdtrp0(xf, xp))))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElement0(W1)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)) | (~aElement0(W0)))) | (sdtlpdtrp0(xf, xp) = xp) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (~aElement0(sdtlpdtrp0(xf, xp))) | (~sdtlseqdt0(xp, sdtlpdtrp0(xf, xp))) | (~aElement0(xp)))),
% 0.20/0.54 inference(transitivity,[status(thm)],[332, 330])).
% 0.20/0.54 tff(334,plain,
% 0.20/0.54 ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElement0(W1)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)) | (~aElement0(W0)))) | ((sdtlpdtrp0(xf, xp) = xp) | (~aElement0(xp)) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (~sdtlseqdt0(xp, sdtlpdtrp0(xf, xp))) | (~aElement0(sdtlpdtrp0(xf, xp))))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(335,plain,
% 0.20/0.54 ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElement0(W1)) | (~sdtlseqdt0(W0, W1)) | (~sdtlseqdt0(W1, W0)) | (~aElement0(W0)))) | (sdtlpdtrp0(xf, xp) = xp) | (~sdtlseqdt0(sdtlpdtrp0(xf, xp), xp)) | (~aElement0(sdtlpdtrp0(xf, xp))) | (~sdtlseqdt0(xp, sdtlpdtrp0(xf, xp))) | (~aElement0(xp))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[334, 333])).
% 0.20/0.54 tff(336,plain,
% 0.20/0.54 ((sdtlpdtrp0(xf, xp) = xp) | (~aElement0(sdtlpdtrp0(xf, xp))) | (~sdtlseqdt0(xp, sdtlpdtrp0(xf, xp))) | (~aElement0(xp))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[335, 230, 87])).
% 0.20/0.54 tff(337,plain,
% 0.20/0.54 ((sdtlpdtrp0(xf, xp) = xp) | (~sdtlseqdt0(xp, sdtlpdtrp0(xf, xp)))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[336, 217, 213])).
% 0.20/0.54 tff(338,plain,
% 0.20/0.54 (sdtlpdtrp0(xf, xp) = xp),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[337, 175])).
% 0.20/0.54 tff(339,plain,
% 0.20/0.54 (((sdtlpdtrp0(xf, xp) = xp) | aFixedPointOf0(xp, xf)) | (~(sdtlpdtrp0(xf, xp) = xp))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(340,plain,
% 0.20/0.54 ((sdtlpdtrp0(xf, xp) = xp) | aFixedPointOf0(xp, xf)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[339, 338])).
% 0.20/0.54 tff(341,plain,
% 0.20/0.54 (((~((sdtlpdtrp0(xf, xp) = xp) | aFixedPointOf0(xp, xf))) | (~((~((~(aUpperBoundOfIn0(xp, xT, cS1142(xf)) | (~aElementOf0(W0!17, xT)) | sdtlseqdt0(W0!17, xp))) | (~(sdtlseqdt0(xp, W0!18) | (~aElementOf0(W0!18, cS1142(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!18))) | (~aUpperBoundOfIn0(W0!18, xT, cS1142(xf))))))) | aSupremumOfIn0(xp, xT, cS1142(xf))))) <=> ((~((sdtlpdtrp0(xf, xp) = xp) | aFixedPointOf0(xp, xf))) | (~((~((~(aUpperBoundOfIn0(xp, xT, cS1142(xf)) | (~aElementOf0(W0!17, xT)) | sdtlseqdt0(W0!17, xp))) | (~(sdtlseqdt0(xp, W0!18) | (~aElementOf0(W0!18, cS1142(xf))) | (~aUpperBoundOfIn0(W0!18, xT, cS1142(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!18))))))) | aSupremumOfIn0(xp, xT, cS1142(xf)))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(342,plain,
% 0.20/0.54 (((~((sdtlpdtrp0(xf, xp) = xp) | aFixedPointOf0(xp, xf))) | (~((~((~(aUpperBoundOfIn0(xp, xT, cS1142(xf)) | (~aElementOf0(W0!17, xT)) | sdtlseqdt0(W0!17, xp))) | (~(sdtlseqdt0(xp, W0!18) | (~aElementOf0(W0!18, cS1142(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!18))) | (~aUpperBoundOfIn0(W0!18, xT, cS1142(xf))))))) | aSupremumOfIn0(xp, xT, cS1142(xf))))) <=> ((~((sdtlpdtrp0(xf, xp) = xp) | aFixedPointOf0(xp, xf))) | (~((~((~(aUpperBoundOfIn0(xp, xT, cS1142(xf)) | (~aElementOf0(W0!17, xT)) | sdtlseqdt0(W0!17, xp))) | (~(sdtlseqdt0(xp, W0!18) | (~aElementOf0(W0!18, cS1142(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!18))) | (~aUpperBoundOfIn0(W0!18, xT, cS1142(xf))))))) | aSupremumOfIn0(xp, xT, cS1142(xf)))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(343,plain,
% 0.20/0.54 (((~((sdtlpdtrp0(xf, xp) = xp) | aFixedPointOf0(xp, xf))) | ((((~aUpperBoundOfIn0(xp, xT, cS1142(xf))) & (~((~aElementOf0(W0!17, xT)) | sdtlseqdt0(W0!17, xp)))) | (aElementOf0(W0!18, cS1142(xf)) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!18)) & aUpperBoundOfIn0(W0!18, xT, cS1142(xf)) & (~sdtlseqdt0(xp, W0!18)))) & (~aSupremumOfIn0(xp, xT, cS1142(xf))))) <=> ((~((sdtlpdtrp0(xf, xp) = xp) | aFixedPointOf0(xp, xf))) | (~((~((~(aUpperBoundOfIn0(xp, xT, cS1142(xf)) | (~aElementOf0(W0!17, xT)) | sdtlseqdt0(W0!17, xp))) | (~(sdtlseqdt0(xp, W0!18) | (~aElementOf0(W0!18, cS1142(xf))) | (~![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!18))) | (~aUpperBoundOfIn0(W0!18, xT, cS1142(xf))))))) | aSupremumOfIn0(xp, xT, cS1142(xf)))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(344,plain,
% 0.20/0.54 (((~((sdtlpdtrp0(xf, xp) = xp) | aFixedPointOf0(xp, xf))) | ((((~aUpperBoundOfIn0(xp, xT, cS1142(xf))) & (~((~aElementOf0(W0!17, xT)) | sdtlseqdt0(W0!17, xp)))) | ((aElementOf0(W0!18, cS1142(xf)) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!18)) & aUpperBoundOfIn0(W0!18, xT, cS1142(xf))) & (~sdtlseqdt0(xp, W0!18)))) & (~aSupremumOfIn0(xp, xT, cS1142(xf))))) <=> ((~((sdtlpdtrp0(xf, xp) = xp) | aFixedPointOf0(xp, xf))) | ((((~aUpperBoundOfIn0(xp, xT, cS1142(xf))) & (~((~aElementOf0(W0!17, xT)) | sdtlseqdt0(W0!17, xp)))) | (aElementOf0(W0!18, cS1142(xf)) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0!18)) & aUpperBoundOfIn0(W0!18, xT, cS1142(xf)) & (~sdtlseqdt0(xp, W0!18)))) & (~aSupremumOfIn0(xp, xT, cS1142(xf)))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(345,plain,
% 0.20/0.54 ((((sdtlpdtrp0(xf, xp) = xp) | aFixedPointOf0(xp, xf)) & (((aUpperBoundOfIn0(xp, xT, cS1142(xf)) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, xp))) & ![W0: $i] : ((~(aElementOf0(W0, cS1142(xf)) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, cS1142(xf)))) | sdtlseqdt0(xp, W0))) | aSupremumOfIn0(xp, xT, cS1142(xf)))) <=> (((sdtlpdtrp0(xf, xp) = xp) | aFixedPointOf0(xp, xf)) & (((aUpperBoundOfIn0(xp, xT, cS1142(xf)) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, xp))) & ![W0: $i] : ((~(aElementOf0(W0, cS1142(xf)) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, cS1142(xf)))) | sdtlseqdt0(xp, W0))) | aSupremumOfIn0(xp, xT, cS1142(xf))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(346,plain,
% 0.20/0.55 ((~(((sdtlpdtrp0(xf, xp) = xp) | aFixedPointOf0(xp, xf)) & (((aUpperBoundOfIn0(xp, xT, cS1142(xf)) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, xp))) & ![W0: $i] : ((~(aElementOf0(W0, cS1142(xf)) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, cS1142(xf)))) | sdtlseqdt0(xp, W0))) | aSupremumOfIn0(xp, xT, cS1142(xf))))) <=> (~(((sdtlpdtrp0(xf, xp) = xp) | aFixedPointOf0(xp, xf)) & (((aUpperBoundOfIn0(xp, xT, cS1142(xf)) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, xp))) & ![W0: $i] : ((~(aElementOf0(W0, cS1142(xf)) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, cS1142(xf)))) | sdtlseqdt0(xp, W0))) | aSupremumOfIn0(xp, xT, cS1142(xf)))))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[345])).
% 0.20/0.55 tff(347,plain,
% 0.20/0.55 ((~(((aElementOf0(xp, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, xp) = xp)) | aFixedPointOf0(xp, xf)) & (((aUpperBoundOfIn0(xp, xT, cS1142(xf)) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, xp))) & ![W0: $i] : ((~(aElementOf0(W0, cS1142(xf)) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, cS1142(xf)))) | sdtlseqdt0(xp, W0))) | aSupremumOfIn0(xp, xT, cS1142(xf))))) <=> (~(((sdtlpdtrp0(xf, xp) = xp) | aFixedPointOf0(xp, xf)) & (((aUpperBoundOfIn0(xp, xT, cS1142(xf)) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, xp))) & ![W0: $i] : ((~(aElementOf0(W0, cS1142(xf)) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, cS1142(xf)))) | sdtlseqdt0(xp, W0))) | aSupremumOfIn0(xp, xT, cS1142(xf)))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(348,plain,
% 0.20/0.55 ((((aElementOf0(xp, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, xp) = xp)) | aFixedPointOf0(xp, xf)) & (((aUpperBoundOfIn0(xp, xT, cS1142(xf)) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, xp))) & ![W0: $i] : ((~(aElementOf0(W0, cS1142(xf)) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, cS1142(xf)))) | sdtlseqdt0(xp, W0))) | aSupremumOfIn0(xp, xT, cS1142(xf)))) <=> (((aElementOf0(xp, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, xp) = xp)) | aFixedPointOf0(xp, xf)) & (((aUpperBoundOfIn0(xp, xT, cS1142(xf)) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, xp))) & ![W0: $i] : ((~(aElementOf0(W0, cS1142(xf)) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, cS1142(xf)))) | sdtlseqdt0(xp, W0))) | aSupremumOfIn0(xp, xT, cS1142(xf))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(349,plain,
% 0.20/0.55 ((~(((aElementOf0(xp, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, xp) = xp)) | aFixedPointOf0(xp, xf)) & (((aUpperBoundOfIn0(xp, xT, cS1142(xf)) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, xp))) & ![W0: $i] : ((~(aElementOf0(W0, cS1142(xf)) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, cS1142(xf)))) | sdtlseqdt0(xp, W0))) | aSupremumOfIn0(xp, xT, cS1142(xf))))) <=> (~(((aElementOf0(xp, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, xp) = xp)) | aFixedPointOf0(xp, xf)) & (((aUpperBoundOfIn0(xp, xT, cS1142(xf)) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, xp))) & ![W0: $i] : ((~(aElementOf0(W0, cS1142(xf)) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, cS1142(xf)))) | sdtlseqdt0(xp, W0))) | aSupremumOfIn0(xp, xT, cS1142(xf)))))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[348])).
% 0.20/0.55 tff(350,plain,
% 0.20/0.55 ((~(((aElementOf0(xp, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, xp) = xp)) | aFixedPointOf0(xp, xf)) & (((aUpperBoundOfIn0(xp, xT, xS) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, xp))) & ![W0: $i] : ((~(aElementOf0(W0, xS) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, xS))) | sdtlseqdt0(xp, W0))) | aSupremumOfIn0(xp, xT, xS)))) <=> (~(((aElementOf0(xp, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, xp) = xp)) | aFixedPointOf0(xp, xf)) & (((aUpperBoundOfIn0(xp, xT, cS1142(xf)) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, xp))) & ![W0: $i] : ((~(aElementOf0(W0, cS1142(xf)) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, cS1142(xf)))) | sdtlseqdt0(xp, W0))) | aSupremumOfIn0(xp, xT, cS1142(xf)))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(351,plain,
% 0.20/0.55 ((((aElementOf0(xp, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, xp) = xp)) | aFixedPointOf0(xp, xf)) & (((aUpperBoundOfIn0(xp, xT, xS) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, xp))) & ![W0: $i] : ((~(aElementOf0(W0, xS) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, xS))) | sdtlseqdt0(xp, W0))) | aSupremumOfIn0(xp, xT, xS))) <=> (((aElementOf0(xp, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, xp) = xp)) | aFixedPointOf0(xp, xf)) & (((aUpperBoundOfIn0(xp, xT, xS) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, xp))) & ![W0: $i] : ((~(aElementOf0(W0, xS) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, xS))) | sdtlseqdt0(xp, W0))) | aSupremumOfIn0(xp, xT, xS)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(352,plain,
% 0.20/0.55 ((~(((aElementOf0(xp, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, xp) = xp)) | aFixedPointOf0(xp, xf)) & (((aUpperBoundOfIn0(xp, xT, xS) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, xp))) & ![W0: $i] : ((~(aElementOf0(W0, xS) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, xS))) | sdtlseqdt0(xp, W0))) | aSupremumOfIn0(xp, xT, xS)))) <=> (~(((aElementOf0(xp, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, xp) = xp)) | aFixedPointOf0(xp, xf)) & (((aUpperBoundOfIn0(xp, xT, xS) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, xp))) & ![W0: $i] : ((~(aElementOf0(W0, xS) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, xS))) | sdtlseqdt0(xp, W0))) | aSupremumOfIn0(xp, xT, xS))))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[351])).
% 0.20/0.55 tff(353,plain,
% 0.20/0.55 ((~(((aElementOf0(xp, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, xp) = xp)) | aFixedPointOf0(xp, xf)) & (((aUpperBoundOfIn0(xp, xT, xS) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, xp))) & ![W0: $i] : ((~(aElementOf0(W0, xS) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, xS))) | sdtlseqdt0(xp, W0))) | aSupremumOfIn0(xp, xT, xS)))) <=> (~(((aElementOf0(xp, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, xp) = xp)) | aFixedPointOf0(xp, xf)) & (((aUpperBoundOfIn0(xp, xT, xS) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, xp))) & ![W0: $i] : ((~(aElementOf0(W0, xS) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, xS))) | sdtlseqdt0(xp, W0))) | aSupremumOfIn0(xp, xT, xS))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(354,plain,
% 0.20/0.55 ((~(((aElementOf0(xp, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, xp) = xp)) | aFixedPointOf0(xp, xf)) & (((![W0: $i] : (aElementOf0(W0, xT) => sdtlseqdt0(W0, xp)) | aUpperBoundOfIn0(xp, xT, xS)) & ![W0: $i] : (((aElementOf0(W0, xS) & ![W1: $i] : (aElementOf0(W1, xT) => sdtlseqdt0(W1, W0))) & aUpperBoundOfIn0(W0, xT, xS)) => sdtlseqdt0(xp, W0))) | aSupremumOfIn0(xp, xT, xS)))) <=> (~(((aElementOf0(xp, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, xp) = xp)) | aFixedPointOf0(xp, xf)) & (((aUpperBoundOfIn0(xp, xT, xS) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, xp))) & ![W0: $i] : ((~(aElementOf0(W0, xS) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, xS))) | sdtlseqdt0(xp, W0))) | aSupremumOfIn0(xp, xT, xS))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(355,axiom,(~(((aElementOf0(xp, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, xp) = xp)) | aFixedPointOf0(xp, xf)) & (((![W0: $i] : (aElementOf0(W0, xT) => sdtlseqdt0(W0, xp)) | aUpperBoundOfIn0(xp, xT, xS)) & ![W0: $i] : (((aElementOf0(W0, xS) & ![W1: $i] : (aElementOf0(W1, xT) => sdtlseqdt0(W1, W0))) & aUpperBoundOfIn0(W0, xT, xS)) => sdtlseqdt0(xp, W0))) | aSupremumOfIn0(xp, xT, xS)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__')).
% 0.20/0.55 tff(356,plain,
% 0.20/0.55 (~(((aElementOf0(xp, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, xp) = xp)) | aFixedPointOf0(xp, xf)) & (((aUpperBoundOfIn0(xp, xT, xS) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, xp))) & ![W0: $i] : ((~(aElementOf0(W0, xS) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, xS))) | sdtlseqdt0(xp, W0))) | aSupremumOfIn0(xp, xT, xS)))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[355, 354])).
% 0.20/0.55 tff(357,plain,
% 0.20/0.55 (~(((aElementOf0(xp, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, xp) = xp)) | aFixedPointOf0(xp, xf)) & (((aUpperBoundOfIn0(xp, xT, xS) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, xp))) & ![W0: $i] : ((~(aElementOf0(W0, xS) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, xS))) | sdtlseqdt0(xp, W0))) | aSupremumOfIn0(xp, xT, xS)))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[356, 352])).
% 0.20/0.55 tff(358,plain,
% 0.20/0.55 (~(((aElementOf0(xp, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, xp) = xp)) | aFixedPointOf0(xp, xf)) & (((aUpperBoundOfIn0(xp, xT, xS) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, xp))) & ![W0: $i] : ((~(aElementOf0(W0, xS) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, xS))) | sdtlseqdt0(xp, W0))) | aSupremumOfIn0(xp, xT, xS)))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[357, 353])).
% 0.20/0.55 tff(359,plain,
% 0.20/0.55 (~(((aElementOf0(xp, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, xp) = xp)) | aFixedPointOf0(xp, xf)) & (((aUpperBoundOfIn0(xp, xT, xS) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, xp))) & ![W0: $i] : ((~(aElementOf0(W0, xS) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, xS))) | sdtlseqdt0(xp, W0))) | aSupremumOfIn0(xp, xT, xS)))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[358, 352])).
% 0.20/0.55 tff(360,plain,
% 0.20/0.55 (~(((aElementOf0(xp, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, xp) = xp)) | aFixedPointOf0(xp, xf)) & (((aUpperBoundOfIn0(xp, xT, cS1142(xf)) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, xp))) & ![W0: $i] : ((~(aElementOf0(W0, cS1142(xf)) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, cS1142(xf)))) | sdtlseqdt0(xp, W0))) | aSupremumOfIn0(xp, xT, cS1142(xf))))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[359, 350])).
% 0.20/0.55 tff(361,plain,
% 0.20/0.55 (~(((aElementOf0(xp, szDzozmdt0(xf)) & (sdtlpdtrp0(xf, xp) = xp)) | aFixedPointOf0(xp, xf)) & (((aUpperBoundOfIn0(xp, xT, cS1142(xf)) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, xp))) & ![W0: $i] : ((~(aElementOf0(W0, cS1142(xf)) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, cS1142(xf)))) | sdtlseqdt0(xp, W0))) | aSupremumOfIn0(xp, xT, cS1142(xf))))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[360, 349])).
% 0.20/0.55 tff(362,plain,
% 0.20/0.55 (~(((sdtlpdtrp0(xf, xp) = xp) | aFixedPointOf0(xp, xf)) & (((aUpperBoundOfIn0(xp, xT, cS1142(xf)) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, xp))) & ![W0: $i] : ((~(aElementOf0(W0, cS1142(xf)) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, cS1142(xf)))) | sdtlseqdt0(xp, W0))) | aSupremumOfIn0(xp, xT, cS1142(xf))))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[361, 347])).
% 0.20/0.55 tff(363,plain,
% 0.20/0.55 (~(((sdtlpdtrp0(xf, xp) = xp) | aFixedPointOf0(xp, xf)) & (((aUpperBoundOfIn0(xp, xT, cS1142(xf)) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, xp))) & ![W0: $i] : ((~(aElementOf0(W0, cS1142(xf)) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, cS1142(xf)))) | sdtlseqdt0(xp, W0))) | aSupremumOfIn0(xp, xT, cS1142(xf))))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[362, 346])).
% 0.20/0.55 tff(364,plain,
% 0.20/0.55 (~(((sdtlpdtrp0(xf, xp) = xp) | aFixedPointOf0(xp, xf)) & (((aUpperBoundOfIn0(xp, xT, cS1142(xf)) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, xp))) & ![W0: $i] : ((~(aElementOf0(W0, cS1142(xf)) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, cS1142(xf)))) | sdtlseqdt0(xp, W0))) | aSupremumOfIn0(xp, xT, cS1142(xf))))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[363, 346])).
% 0.20/0.56 tff(365,plain,
% 0.20/0.56 (~(((sdtlpdtrp0(xf, xp) = xp) | aFixedPointOf0(xp, xf)) & (((aUpperBoundOfIn0(xp, xT, cS1142(xf)) | ![W0: $i] : ((~aElementOf0(W0, xT)) | sdtlseqdt0(W0, xp))) & ![W0: $i] : ((~(aElementOf0(W0, cS1142(xf)) & ![W1: $i] : ((~aElementOf0(W1, xT)) | sdtlseqdt0(W1, W0)) & aUpperBoundOfIn0(W0, xT, cS1142(xf)))) | sdtlseqdt0(xp, W0))) | aSupremumOfIn0(xp, xT, cS1142(xf))))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[364, 346])).
% 0.20/0.56 unexpected number of arguments: (let ((a!1 (not (or (= (sdtlpdtrp0 xf xp) xp) (aFixedPointOf0 xp xf))))
% 0.20/0.56 (a!2 (~ (not (aUpperBoundOfIn0 xp xT (cS1142 xf)))
% 0.20/0.56 (not (aUpperBoundOfIn0 xp xT (cS1142 xf)))))
% 0.20/0.56 (a!3 (forall ((W0 $i)) (or (not (aElementOf0 W0 xT)) (sdtlseqdt0 W0 xp))))
% 0.20/0.56 (a!4 (not (or (not (aElementOf0 W0!17 xT)) (sdtlseqdt0 W0!17 xp))))
% 0.20/0.56 (a!8 (forall ((W0 $i))
% 0.20/0.56 (let ((a!1 (forall ((W1 $i))
% 0.20/0.56 (or (not (aElementOf0 W1 xT)) (sdtlseqdt0 W1 W0)))))
% 0.20/0.56 (let ((a!2 (not (and (aElementOf0 W0 (cS1142 xf))
% 0.20/0.56 a!1
% 0.20/0.56 (aUpperBoundOfIn0 W0 xT (cS1142 xf))))))
% 0.20/0.56 (or a!2 (sdtlseqdt0 xp W0))))))
% 0.20/0.56 (a!9 (forall ((W1 $i))
% 0.20/0.56 (or (not (aElementOf0 W1 xT)) (sdtlseqdt0 W1 W0!18))))
% 0.20/0.56 (a!12 (refl (~ (aElementOf0 W0!18 (cS1142 xf))
% 0.20/0.56 (aElementOf0 W0!18 (cS1142 xf)))))
% 0.20/0.56 (a!14 (refl (~ (aUpperBoundOfIn0 W0!18 xT (cS1142 xf))
% 0.20/0.56 (aUpperBoundOfIn0 W0!18 xT (cS1142 xf)))))
% 0.20/0.56 (a!16 (refl (~ (not (sdtlseqdt0 xp W0!18)) (not (sdtlseqdt0 xp W0!18)))))
% 0.20/0.56 (a!21 (~ (not (aSupremumOfIn0 xp xT (cS1142 xf)))
% 0.20/0.56 (not (aSupremumOfIn0 xp xT (cS1142 xf))))))
% 0.20/0.56 (let ((a!5 (not (or (aUpperBoundOfIn0 xp xT (cS1142 xf)) a!3)))
% 0.20/0.56 (a!6 (and (not (aUpperBoundOfIn0 xp xT (cS1142 xf))) a!4))
% 0.20/0.56 (a!10 (and (aElementOf0 W0!18 (cS1142 xf))
% 0.20/0.56 a!9
% 0.20/0.56 (aUpperBoundOfIn0 W0!18 xT (cS1142 xf))))
% 0.20/0.56 (a!13 (nnf-pos (proof-bind (lambda ((W1 $i))
% 0.20/0.56 (let ((a!1 (~ (or (not (aElementOf0 W1 xT))
% 0.20/0.56 (sdtlseqdt0 W1 W0!18))
% 0.20/0.56 (or (not (aElementOf0 W1 xT))
% 0.20/0.56 (sdtlseqdt0 W1 W0!18)))))
% 0.20/0.56 (refl a!1))))
% 0.20/0.56 (~ a!9 a!9)))
% 0.20/0.56 (a!19 (and (or (aUpperBoundOfIn0 xp xT (cS1142 xf)) a!3) a!8)))
% 0.20/0.56 (let ((a!7 (nnf-neg (refl a!2) (sk (~ (not a!3) a!4)) (~ a!5 a!6)))
% 0.20/0.56 (a!11 (~ (not a!8) (not (or (not a!10) (sdtlseqdt0 xp W0!18)))))
% 0.20/0.56 (a!15 (nnf-neg (monotonicity a!12 a!13 a!14 (~ a!10 a!10))
% 0.20/0.56 (~ (not (not a!10)) a!10)))
% 0.20/0.56 (a!17 (~ (not (or (not a!10) (sdtlseqdt0 xp W0!18)))
% 0.20/0.56 (and a!10 (not (sdtlseqdt0 xp W0!18)))))
% 0.20/0.56 (a!18 (~ (not a!8) (and a!10 (not (sdtlseqdt0 xp W0!18)))))
% 0.20/0.56 (a!20 (or a!6 (and a!10 (not (sdtlseqdt0 xp W0!18)))))
% 0.20/0.56 (a!22 (not (or a!19 (aSupremumOfIn0 xp xT (cS1142 xf)))))
% 0.20/0.56 (a!25 (and (or (= (sdtlpdtrp0 xf xp) xp) (aFixedPointOf0 xp xf))
% 0.20/0.56 (or a!19 (aSupremumOfIn0 xp xT (cS1142 xf))))))
% 0.20/0.56 (let ((a!23 (and a!20 (not (aSupremumOfIn0 xp xT (cS1142 xf))))))
% 0.20/0.56 (let ((a!24 (nnf-neg (nnf-neg a!7
% 0.20/0.56 (trans (sk a!11) (nnf-neg a!15 a!16 a!17) a!18)
% 0.20/0.56 (~ (not a!19) a!20))
% 0.20/0.56 (refl a!21)
% 0.20/0.56 (~ a!22 a!23))))
% 0.20/0.56 (nnf-neg (refl (~ a!1 a!1)) a!24 (~ (not a!25) (or a!1 a!23))))))))
% 0.20/0.56 Proof display could not be completed: unexpected number of arguments
%------------------------------------------------------------------------------