TSTP Solution File: NUM585+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM585+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 13:10:41 EDT 2022
% Result : Theorem 1.41s 1.14s
% Output : Proof 1.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM585+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n013.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 : Fri Sep 2 11:59:47 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 1.41/1.14 % SZS status Theorem
% 1.41/1.14 % SZS output start Proof
% 1.41/1.14 tff(tptp_fun_W1_33_type, type, (
% 1.41/1.14 tptp_fun_W1_33: $i)).
% 1.41/1.14 tff(sdtlpdtrp0_type, type, (
% 1.41/1.14 sdtlpdtrp0: ( $i * $i ) > $i)).
% 1.41/1.14 tff(sdtpldt0_type, type, (
% 1.41/1.14 sdtpldt0: ( $i * $i ) > $i)).
% 1.41/1.14 tff(szmzizndt0_type, type, (
% 1.41/1.14 szmzizndt0: $i > $i)).
% 1.41/1.14 tff(tptp_fun_W0_32_type, type, (
% 1.41/1.14 tptp_fun_W0_32: $i)).
% 1.41/1.14 tff(xN_type, type, (
% 1.41/1.14 xN: $i)).
% 1.41/1.14 tff(tptp_fun_W2_34_type, type, (
% 1.41/1.14 tptp_fun_W2_34: $i > $i)).
% 1.41/1.14 tff(xc_type, type, (
% 1.41/1.14 xc: $i)).
% 1.41/1.14 tff(xC_type, type, (
% 1.41/1.14 xC: $i)).
% 1.41/1.14 tff(aElementOf0_type, type, (
% 1.41/1.14 aElementOf0: ( $i * $i ) > $o)).
% 1.41/1.14 tff(szDzozmdt0_type, type, (
% 1.41/1.14 szDzozmdt0: $i > $i)).
% 1.41/1.14 tff(sdtlcdtrc0_type, type, (
% 1.41/1.14 sdtlcdtrc0: ( $i * $i ) > $i)).
% 1.41/1.14 tff(aSet0_type, type, (
% 1.41/1.14 aSet0: $i > $o)).
% 1.41/1.14 tff(xT_type, type, (
% 1.41/1.14 xT: $i)).
% 1.41/1.14 tff(aSubsetOf0_type, type, (
% 1.41/1.14 aSubsetOf0: ( $i * $i ) > $o)).
% 1.41/1.14 tff(szNzAzT0_type, type, (
% 1.41/1.14 szNzAzT0: $i)).
% 1.41/1.14 tff(aElement0_type, type, (
% 1.41/1.14 aElement0: $i > $o)).
% 1.41/1.14 tff(sdtlseqdt0_type, type, (
% 1.41/1.14 sdtlseqdt0: ( $i * $i ) > $o)).
% 1.41/1.14 tff(sdtmndt0_type, type, (
% 1.41/1.14 sdtmndt0: ( $i * $i ) > $i)).
% 1.41/1.14 tff(xk_type, type, (
% 1.41/1.14 xk: $i)).
% 1.41/1.14 tff(sbrdtbr0_type, type, (
% 1.41/1.14 sbrdtbr0: $i > $i)).
% 1.41/1.14 tff(tptp_fun_W2_31_type, type, (
% 1.41/1.14 tptp_fun_W2_31: ( $i * $i ) > $i)).
% 1.41/1.14 tff(slbdtsldtrb0_type, type, (
% 1.41/1.14 slbdtsldtrb0: ( $i * $i ) > $i)).
% 1.41/1.14 tff(aFunction0_type, type, (
% 1.41/1.14 aFunction0: $i > $o)).
% 1.41/1.14 tff(sz00_type, type, (
% 1.41/1.14 sz00: $i)).
% 1.41/1.14 tff(szszuzczcdt0_type, type, (
% 1.41/1.14 szszuzczcdt0: $i > $i)).
% 1.41/1.14 tff(xK_type, type, (
% 1.41/1.14 xK: $i)).
% 1.41/1.14 tff(xS_type, type, (
% 1.41/1.14 xS: $i)).
% 1.41/1.14 tff(tptp_fun_W1_20_type, type, (
% 1.41/1.14 tptp_fun_W1_20: $i > $i)).
% 1.41/1.14 tff(1,plain,
% 1.41/1.14 (^[W1: $i] : refl((~((~((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1)))))) | (~(aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1))))))) <=> (~((~((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1)))))) | (~(aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1))))))))),
% 1.41/1.14 inference(bind,[status(th)],[])).
% 1.41/1.14 tff(2,plain,
% 1.41/1.14 (![W1: $i] : (~((~((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1)))))) | (~(aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1))))))) <=> ![W1: $i] : (~((~((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1)))))) | (~(aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1)))))))),
% 1.41/1.14 inference(quant_intro,[status(thm)],[1])).
% 1.41/1.14 tff(3,plain,
% 1.41/1.14 (^[W1: $i] : rewrite((~((~((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1)))))) | (~(aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1))))))) <=> (~((~((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1)))))) | (~(aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1))))))))),
% 1.41/1.15 inference(bind,[status(th)],[])).
% 1.41/1.15 tff(4,plain,
% 1.41/1.15 (![W1: $i] : (~((~((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1)))))) | (~(aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1))))))) <=> ![W1: $i] : (~((~((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1)))))) | (~(aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1)))))))),
% 1.41/1.15 inference(quant_intro,[status(thm)],[3])).
% 1.41/1.15 tff(5,plain,
% 1.41/1.15 (![W1: $i] : (~((~((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1)))))) | (~(aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1))))))) <=> ![W1: $i] : (~((~((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1)))))) | (~(aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1)))))))),
% 1.41/1.15 inference(transitivity,[status(thm)],[4, 2])).
% 1.41/1.15 tff(6,plain,
% 1.41/1.15 (^[W1: $i] : trans(monotonicity(rewrite(((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1))) <=> ((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1)))))), rewrite((aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : (~(aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1)))) <=> (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1))))), ((((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1))) & (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : (~(aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1))))) <=> (((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1))))) & (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1))))))), rewrite((((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1))))) & (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1))))) <=> (~((~((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1)))))) | (~(aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1)))))))), ((((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1))) & (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : (~(aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1))))) <=> (~((~((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1)))))) | (~(aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1)))))))))),
% 1.41/1.15 inference(bind,[status(th)],[])).
% 1.41/1.15 tff(7,plain,
% 1.41/1.15 (![W1: $i] : (((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1))) & (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : (~(aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1))))) <=> ![W1: $i] : (~((~((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1)))))) | (~(aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1)))))))),
% 1.41/1.15 inference(quant_intro,[status(thm)],[6])).
% 1.41/1.15 tff(8,plain,
% 1.41/1.15 (((~aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))), xT)) & (~((~aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | aElementOf0(W1!33, xT))) & (aSet0(sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) & ![W1: $i] : (((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1))) & (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : (~(aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1)))))) & aElementOf0(W0!32, szDzozmdt0(xN))) <=> ((~aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))), xT)) & (~((~aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | aElementOf0(W1!33, xT))) & aSet0(sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) & ![W1: $i] : (((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1))) & (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : (~(aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1))))) & aElementOf0(W0!32, szDzozmdt0(xN)))),
% 1.41/1.15 inference(rewrite,[status(thm)],[])).
% 1.41/1.15 tff(9,plain,
% 1.41/1.15 ((~(~aElementOf0(W0!32, szDzozmdt0(xN)))) <=> aElementOf0(W0!32, szDzozmdt0(xN))),
% 1.41/1.15 inference(rewrite,[status(thm)],[])).
% 1.41/1.15 tff(10,plain,
% 1.41/1.15 ((aSet0(sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) & ![W1: $i] : (((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1))) & (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : (~(aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1)))))) <=> (aSet0(sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) & ![W1: $i] : (((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1))) & (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : (~(aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1))))))),
% 1.41/1.15 inference(rewrite,[status(thm)],[])).
% 1.41/1.15 tff(11,plain,
% 1.41/1.15 (((~aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))), xT)) & (~((~aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | aElementOf0(W1!33, xT))) & (aSet0(sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) & ![W1: $i] : (((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1))) & (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : (~(aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1)))))) & (~(~aElementOf0(W0!32, szDzozmdt0(xN))))) <=> ((~aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))), xT)) & (~((~aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | aElementOf0(W1!33, xT))) & (aSet0(sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) & ![W1: $i] : (((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1))) & (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : (~(aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1)))))) & aElementOf0(W0!32, szDzozmdt0(xN)))),
% 1.41/1.15 inference(monotonicity,[status(thm)],[10, 9])).
% 1.41/1.15 tff(12,plain,
% 1.41/1.15 (((~aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))), xT)) & (~((~aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | aElementOf0(W1!33, xT))) & (aSet0(sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) & ![W1: $i] : (((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1))) & (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : (~(aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1)))))) & (~(~aElementOf0(W0!32, szDzozmdt0(xN))))) <=> ((~aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))), xT)) & (~((~aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | aElementOf0(W1!33, xT))) & aSet0(sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) & ![W1: $i] : (((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1))) & (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : (~(aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1))))) & aElementOf0(W0!32, szDzozmdt0(xN)))),
% 1.41/1.15 inference(transitivity,[status(thm)],[11, 8])).
% 1.41/1.15 tff(13,plain,
% 1.41/1.15 ((~![W0: $i] : (aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0))), xT) | ![W1: $i] : ((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0))))) | aElementOf0(W1, xT)) | (~(aSet0(sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) <=> ?[W2: $i] : (aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = W1))))) | (~aElementOf0(W0, szDzozmdt0(xN))))) <=> (~![W0: $i] : (aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0))), xT) | ![W1: $i] : ((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0))))) | aElementOf0(W1, xT)) | (~(aSet0(sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) <=> ?[W2: $i] : (aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = W1))))) | (~aElementOf0(W0, szDzozmdt0(xN)))))),
% 1.41/1.15 inference(rewrite,[status(thm)],[])).
% 1.41/1.15 tff(14,plain,
% 1.41/1.15 ((~![W0: $i] : (aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0))), xT) | (~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0))))) | aElementOf0(W1, xT)) | (~(aSet0(sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) <=> ?[W2: $i] : (aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = W1))))))) <=> (~![W0: $i] : (aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0))), xT) | ![W1: $i] : ((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0))))) | aElementOf0(W1, xT)) | (~(aSet0(sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) <=> ?[W2: $i] : (aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = W1))))) | (~aElementOf0(W0, szDzozmdt0(xN)))))),
% 1.41/1.15 inference(rewrite,[status(thm)],[])).
% 1.41/1.15 tff(15,plain,
% 1.41/1.15 ((~![W0: $i] : (aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0))), xT) | (~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0))))) | aElementOf0(W1, xT)) | (~(aSet0(sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) <=> ?[W2: $i] : (aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = W1))))))) <=> (~![W0: $i] : (aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0))), xT) | (~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0))))) | aElementOf0(W1, xT)) | (~(aSet0(sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) <=> ?[W2: $i] : (aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = W1)))))))),
% 1.41/1.15 inference(rewrite,[status(thm)],[])).
% 1.41/1.15 tff(16,plain,
% 1.41/1.15 ((~![W0: $i] : (aElementOf0(W0, szNzAzT0) => ((aSet0(sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) <=> ?[W2: $i] : (aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = W1)))) => (![W1: $i] : (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) => aElementOf0(W1, xT)) | aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0))), xT))))) <=> (~![W0: $i] : (aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0))), xT) | (~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0))))) | aElementOf0(W1, xT)) | (~(aSet0(sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) <=> ?[W2: $i] : (aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = W1)))))))),
% 1.41/1.15 inference(rewrite,[status(thm)],[])).
% 1.41/1.15 tff(17,axiom,(~![W0: $i] : (aElementOf0(W0, szNzAzT0) => ((aSet0(sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) <=> ?[W2: $i] : (aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = W1)))) => (![W1: $i] : (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) => aElementOf0(W1, xT)) | aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0))), xT))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 1.41/1.15 tff(18,plain,
% 1.41/1.15 (~![W0: $i] : (aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0))), xT) | (~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0))))) | aElementOf0(W1, xT)) | (~(aSet0(sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) <=> ?[W2: $i] : (aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = W1))))))),
% 1.41/1.15 inference(modus_ponens,[status(thm)],[17, 16])).
% 1.41/1.15 tff(19,plain,
% 1.41/1.15 (~![W0: $i] : (aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0))), xT) | (~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0))))) | aElementOf0(W1, xT)) | (~(aSet0(sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) <=> ?[W2: $i] : (aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = W1))))))),
% 1.41/1.15 inference(modus_ponens,[status(thm)],[18, 15])).
% 1.41/1.15 tff(20,plain,
% 1.41/1.15 (~![W0: $i] : (aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0))), xT) | (~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0))))) | aElementOf0(W1, xT)) | (~(aSet0(sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) <=> ?[W2: $i] : (aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = W1))))))),
% 1.41/1.15 inference(modus_ponens,[status(thm)],[19, 15])).
% 1.41/1.15 tff(21,plain,
% 1.41/1.15 (~![W0: $i] : (aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0))), xT) | (~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0))))) | aElementOf0(W1, xT)) | (~(aSet0(sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) <=> ?[W2: $i] : (aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = W1))))))),
% 1.41/1.15 inference(modus_ponens,[status(thm)],[20, 15])).
% 1.41/1.15 tff(22,plain,
% 1.41/1.15 (~![W0: $i] : (aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0))), xT) | ![W1: $i] : ((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0))))) | aElementOf0(W1, xT)) | (~(aSet0(sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) <=> ?[W2: $i] : (aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = W1))))) | (~aElementOf0(W0, szDzozmdt0(xN))))),
% 1.41/1.15 inference(modus_ponens,[status(thm)],[21, 14])).
% 1.41/1.15 tff(23,plain,
% 1.41/1.15 (~![W0: $i] : (aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0))), xT) | ![W1: $i] : ((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0))))) | aElementOf0(W1, xT)) | (~(aSet0(sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) <=> ?[W2: $i] : (aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = W1))))) | (~aElementOf0(W0, szDzozmdt0(xN))))),
% 1.41/1.15 inference(modus_ponens,[status(thm)],[22, 13])).
% 1.41/1.15 tff(24,plain,
% 1.41/1.15 (~![W0: $i] : (aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0))), xT) | ![W1: $i] : ((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0))))) | aElementOf0(W1, xT)) | (~(aSet0(sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) <=> ?[W2: $i] : (aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = W1))))) | (~aElementOf0(W0, szDzozmdt0(xN))))),
% 1.41/1.15 inference(modus_ponens,[status(thm)],[23, 13])).
% 1.41/1.15 tff(25,plain,
% 1.41/1.15 (~![W0: $i] : (aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0))), xT) | ![W1: $i] : ((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0))))) | aElementOf0(W1, xT)) | (~(aSet0(sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0), szDzozmdt0(sdtlpdtrp0(xC, W0)))) <=> ?[W2: $i] : (aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = W1))))) | (~aElementOf0(W0, szDzozmdt0(xN))))),
% 1.41/1.15 inference(modus_ponens,[status(thm)],[24, 13])).
% 1.41/1.15 tff(26,plain,
% 1.41/1.15 ((~aSubsetOf0(sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))), xT)) & (~((~aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | aElementOf0(W1!33, xT))) & aSet0(sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) & ![W1: $i] : (((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1))) & (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : (~(aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1))))) & aElementOf0(W0!32, szDzozmdt0(xN))),
% 1.41/1.15 inference(modus_ponens,[status(thm)],[25, 12])).
% 1.41/1.15 tff(27,plain,
% 1.41/1.15 (![W1: $i] : (((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1))) & (aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : (~(aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1)))))),
% 1.41/1.15 inference(and_elim,[status(thm)],[26])).
% 1.41/1.15 tff(28,plain,
% 1.41/1.15 (![W1: $i] : (~((~((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1)))))) | (~(aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1)))))))),
% 1.41/1.15 inference(modus_ponens,[status(thm)],[27, 7])).
% 1.41/1.15 tff(29,plain,
% 1.41/1.15 (![W1: $i] : (~((~((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1)))))) | (~(aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1)))))))),
% 1.41/1.15 inference(modus_ponens,[status(thm)],[28, 5])).
% 1.41/1.15 tff(30,plain,
% 1.41/1.15 ((~![W1: $i] : (~((~((~aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1)) = W1)))))) | (~(aElementOf0(W1, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1)))))))) | (~((~((~aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = W1!33)))))) | (~(aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1!33)))))))),
% 1.41/1.15 inference(quant_inst,[status(thm)],[])).
% 1.41/1.15 tff(31,plain,
% 1.41/1.15 (~((~((~aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = W1!33)))))) | (~(aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1!33))))))),
% 1.41/1.15 inference(unit_resolution,[status(thm)],[30, 29])).
% 1.41/1.15 tff(32,plain,
% 1.41/1.15 (((~((~aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = W1!33)))))) | (~(aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | ![W2: $i] : ((~aElementOf0(W2, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W2) = W1!33)))))) | ((~aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = W1!33)))))),
% 1.41/1.15 inference(tautology,[status(thm)],[])).
% 1.41/1.15 tff(33,plain,
% 1.41/1.15 ((~aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = W1!33))))),
% 1.41/1.15 inference(unit_resolution,[status(thm)],[32, 31])).
% 1.41/1.15 tff(34,plain,
% 1.41/1.15 (~((~aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | aElementOf0(W1!33, xT))),
% 1.41/1.15 inference(and_elim,[status(thm)],[26])).
% 1.41/1.15 tff(35,plain,
% 1.41/1.15 (aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))),
% 1.46/1.16 inference(or_elim,[status(thm)],[34])).
% 1.46/1.16 tff(36,plain,
% 1.46/1.16 ((~((~aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = W1!33)))))) | (~aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = W1!33))))),
% 1.46/1.16 inference(tautology,[status(thm)],[])).
% 1.46/1.16 tff(37,plain,
% 1.46/1.16 ((~((~aElementOf0(W1!33, sdtlcdtrc0(sdtlpdtrp0(xC, W0!32), szDzozmdt0(sdtlpdtrp0(xC, W0!32))))) | (~((~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = W1!33)))))) | (~((~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = W1!33))))),
% 1.46/1.16 inference(unit_resolution,[status(thm)],[36, 35])).
% 1.46/1.16 tff(38,plain,
% 1.46/1.16 (~((~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = W1!33)))),
% 1.46/1.16 inference(unit_resolution,[status(thm)],[37, 33])).
% 1.46/1.16 tff(39,plain,
% 1.46/1.16 (((~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = W1!33))) | (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = W1!33)),
% 1.46/1.16 inference(tautology,[status(thm)],[])).
% 1.46/1.16 tff(40,plain,
% 1.46/1.16 (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = W1!33),
% 1.46/1.16 inference(unit_resolution,[status(thm)],[39, 38])).
% 1.46/1.16 tff(41,plain,
% 1.46/1.16 (aElementOf0(W0!32, szDzozmdt0(xN))),
% 1.46/1.16 inference(and_elim,[status(thm)],[26])).
% 1.46/1.16 tff(42,plain,
% 1.46/1.16 (^[W0: $i] : rewrite(((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~(sbrdtbr0(W1) = xk)))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))) <=> ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))))))))))))),
% 1.46/1.16 inference(bind,[status(th)],[])).
% 1.46/1.16 tff(43,plain,
% 1.46/1.16 (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~(sbrdtbr0(W1) = xk)))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))))),
% 1.46/1.16 inference(quant_intro,[status(thm)],[42])).
% 1.46/1.16 tff(44,plain,
% 1.46/1.16 (^[W0: $i] : refl(((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~(sbrdtbr0(W1) = xk)))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))) <=> ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~(sbrdtbr0(W1) = xk)))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))),
% 1.46/1.16 inference(bind,[status(th)],[])).
% 1.46/1.16 tff(45,plain,
% 1.46/1.16 (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~(sbrdtbr0(W1) = xk)))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~(sbrdtbr0(W1) = xk)))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))))))))),
% 1.46/1.16 inference(quant_intro,[status(thm)],[44])).
% 1.46/1.16 tff(46,plain,
% 1.46/1.16 (^[W0: $i] : rewrite(((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~(sbrdtbr0(W1) = xk)))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))) <=> ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~(sbrdtbr0(W1) = xk)))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))),
% 1.46/1.16 inference(bind,[status(th)],[])).
% 1.46/1.16 tff(47,plain,
% 1.46/1.16 (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~(sbrdtbr0(W1) = xk)))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~(sbrdtbr0(W1) = xk)))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))))))))),
% 1.46/1.17 inference(quant_intro,[status(thm)],[46])).
% 1.46/1.17 tff(48,plain,
% 1.46/1.17 (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~(sbrdtbr0(W1) = xk)))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~(sbrdtbr0(W1) = xk)))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))))))))),
% 1.46/1.17 inference(transitivity,[status(thm)],[47, 45])).
% 1.46/1.17 tff(49,plain,
% 1.46/1.17 (^[W0: $i] : rewrite(((~aElementOf0(W0, szDzozmdt0(xN))) | (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & (aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | ((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) & ![W1: $i] : ((~aSet0(W1)) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))) | ((~aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & (((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sbrdtbr0(W1) = xk))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) <=> ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~(sbrdtbr0(W1) = xk)))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))),
% 1.46/1.17 inference(bind,[status(th)],[])).
% 1.46/1.17 tff(50,plain,
% 1.46/1.17 (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & (aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | ((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) & ![W1: $i] : ((~aSet0(W1)) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))) | ((~aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & (((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sbrdtbr0(W1) = xk))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~(sbrdtbr0(W1) = xk)))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))))))))),
% 1.46/1.17 inference(quant_intro,[status(thm)],[49])).
% 1.46/1.17 tff(51,plain,
% 1.46/1.17 (^[W0: $i] : rewrite(((~aElementOf0(W0, szDzozmdt0(xN))) | (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~(sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) & ![W1: $i] : (((~aSet0(W1)) | ((~aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) & (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & (((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sbrdtbr0(W1) = xk))) & (aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))) <=> ((~aElementOf0(W0, szDzozmdt0(xN))) | (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & (aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | ((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) & ![W1: $i] : ((~aSet0(W1)) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))) | ((~aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & (((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sbrdtbr0(W1) = xk))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))))))),
% 1.46/1.17 inference(bind,[status(th)],[])).
% 1.46/1.17 tff(52,plain,
% 1.46/1.17 (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~(sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) & ![W1: $i] : (((~aSet0(W1)) | ((~aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) & (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & (((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sbrdtbr0(W1) = xk))) & (aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & (aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | ((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) & ![W1: $i] : ((~aSet0(W1)) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))) | ((~aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & (((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sbrdtbr0(W1) = xk))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))),
% 1.46/1.17 inference(quant_intro,[status(thm)],[51])).
% 1.46/1.17 tff(53,plain,
% 1.46/1.17 (^[W0: $i] : rewrite(((~aElementOf0(W0, szNzAzT0)) | (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) & ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))) <=> ((~aElementOf0(W0, szDzozmdt0(xN))) | (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) & ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))))),
% 1.46/1.17 inference(bind,[status(th)],[])).
% 1.46/1.17 tff(54,plain,
% 1.46/1.17 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) & ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) & ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))))),
% 1.46/1.18 inference(quant_intro,[status(thm)],[53])).
% 1.46/1.18 tff(55,plain,
% 1.46/1.18 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) & ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) & ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))))),
% 1.46/1.18 inference(rewrite,[status(thm)],[])).
% 1.46/1.18 tff(56,plain,
% 1.46/1.18 (^[W0: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[W1: $i] : rewrite((aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) <=> ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)))), (![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) <=> ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)))), (((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) <=> ((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))))), rewrite(((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) <=> (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)))), (((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) <=> (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))))), ((((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) <=> ((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))), rewrite(((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) <=> (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))), ((((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) <=> (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))), quant_intro(proof_bind(^[W1: $i] : rewrite((aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))), (![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))), (((((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) <=> ((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))), rewrite(((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) <=> (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))), (((((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) <=> (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))), quant_intro(proof_bind(^[W1: $i] : rewrite(((aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) => (((aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk))) & ((((aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) => aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))) <=> (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))))), (![W1: $i] : ((aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) => (((aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk))) & ((((aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) => aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))) <=> ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))))), ((((((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W1: $i] : ((aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) => (((aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk))) & ((((aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) => aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))))) <=> ((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))))))), rewrite(((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))))) <=> (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))))), ((((((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W1: $i] : ((aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) => (((aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk))) & ((((aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) => aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))))) <=> (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))))))), (((((((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W1: $i] : ((aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) => (((aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk))) & ((((aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) => aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) <=> ((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))))), rewrite(((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) <=> (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)))), (((((((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W1: $i] : ((aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) => (((aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk))) & ((((aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) => aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) <=> (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))))), quant_intro(proof_bind(^[W1: $i] : trans(monotonicity(rewrite((aSet0(W1) & ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) => ((aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0))) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) => (((![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)))))) <=> (aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))), trans(monotonicity(trans(monotonicity(rewrite((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))), (((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) <=> ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))), rewrite(((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))), (((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))), ((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))), rewrite(((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))), ((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))), (((aSet0(W1) & ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) => ((aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0))) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) => (((![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)))))) => (((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) <=> ((aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) => (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))), rewrite(((aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) => (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) <=> ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))), (((aSet0(W1) & ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) => ((aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0))) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) => (((![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)))))) => (((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) <=> ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))))), (![W1: $i] : ((aSet0(W1) & ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) => ((aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0))) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) => (((![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)))))) => (((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))) <=> ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))), ((((((((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W1: $i] : ((aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) => (((aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk))) & ((((aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) => aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) & ![W1: $i] : ((aSet0(W1) & ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) => ((aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0))) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) => (((![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)))))) => (((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))) <=> ((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) & ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))))), rewrite(((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) & ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))) <=> (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) & ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))), ((((((((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W1: $i] : ((aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) => (((aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk))) & ((((aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) => aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) & ![W1: $i] : ((aSet0(W1) & ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) => ((aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0))) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) => (((![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)))))) => (((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))) <=> (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) & ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))))), ((aElementOf0(W0, szNzAzT0) => (((((((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W1: $i] : ((aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) => (((aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk))) & ((((aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) => aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) & ![W1: $i] : ((aSet0(W1) & ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) => ((aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0))) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) => (((![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)))))) => (((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))) <=> (aElementOf0(W0, szNzAzT0) => (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) & ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))))), rewrite((aElementOf0(W0, szNzAzT0) => (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) & ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))) <=> ((~aElementOf0(W0, szNzAzT0)) | (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) & ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))))), ((aElementOf0(W0, szNzAzT0) => (((((((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W1: $i] : ((aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) => (((aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk))) & ((((aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) => aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) & ![W1: $i] : ((aSet0(W1) & ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) => ((aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0))) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) => (((![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)))))) => (((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))) <=> ((~aElementOf0(W0, szNzAzT0)) | (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) & ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))))))),
% 1.46/1.20 inference(bind,[status(th)],[])).
% 1.46/1.20 tff(57,plain,
% 1.46/1.20 (![W0: $i] : (aElementOf0(W0, szNzAzT0) => (((((((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W1: $i] : ((aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) => (((aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk))) & ((((aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) => aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) & ![W1: $i] : ((aSet0(W1) & ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) => ((aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0))) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) => (((![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)))))) => (((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) & ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))))),
% 1.46/1.20 inference(quant_intro,[status(thm)],[56])).
% 1.46/1.20 tff(58,axiom,((aFunction0(xC) & (szDzozmdt0(xC) = szNzAzT0)) & ![W0: $i] : (aElementOf0(W0, szNzAzT0) => (((((((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W1: $i] : ((aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) => (((aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk))) & ((((aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) => aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) & ![W1: $i] : ((aSet0(W1) & ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) => ((aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0))) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) => (((![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)))))) => (((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__4151')).
% 1.46/1.20 tff(59,plain,
% 1.46/1.20 (![W0: $i] : (aElementOf0(W0, szNzAzT0) => (((((((aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) & ![W1: $i] : (aElementOf0(W1, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0))) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W1: $i] : ((aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) => (((aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk))) & ((((aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) => aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) & ![W1: $i] : ((aSet0(W1) & ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) => ((aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0))) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) => (((![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)))))) => (((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))))),
% 1.46/1.20 inference(and_elim,[status(thm)],[58])).
% 1.46/1.20 tff(60,plain,
% 1.46/1.20 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) & ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))))),
% 1.46/1.20 inference(modus_ponens,[status(thm)],[59, 57])).
% 1.46/1.20 tff(61,plain,
% 1.46/1.20 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) & ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))))),
% 1.46/1.20 inference(modus_ponens,[status(thm)],[60, 55])).
% 1.46/1.20 tff(62,plain,
% 1.46/1.20 (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((~((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) & (sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) & ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))))),
% 1.46/1.20 inference(modus_ponens,[status(thm)],[61, 54])).
% 1.46/1.20 tff(63,plain,(
% 1.46/1.20 ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & ((((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~(sbrdtbr0(W1) = xk))) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) & ![W1: $i] : (((~aSet0(W1)) | ((~aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) & (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & (((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sbrdtbr0(W1) = xk))) & (aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))))),
% 1.46/1.20 inference(skolemize,[status(sab)],[62])).
% 1.46/1.20 tff(64,plain,
% 1.46/1.20 (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (aFunction0(sdtlpdtrp0(xC, W0)) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1)) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W1) & aElementOf0(W1, sdtlpdtrp0(xN, W0)) & (~(W1 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W1: $i] : (((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & (sbrdtbr0(W1) = xk))) & (aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | ((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) & (szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) & ![W1: $i] : ((~aSet0(W1)) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))) | ((~aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & (((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sbrdtbr0(W1) = xk))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))),
% 1.46/1.20 inference(modus_ponens,[status(thm)],[63, 52])).
% 1.46/1.20 tff(65,plain,
% 1.46/1.20 (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~(sbrdtbr0(W1) = xk)))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))))))))),
% 1.46/1.20 inference(modus_ponens,[status(thm)],[64, 50])).
% 1.46/1.20 tff(66,plain,
% 1.46/1.20 (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~(sbrdtbr0(W1) = xk)))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))))))))))),
% 1.46/1.20 inference(modus_ponens,[status(thm)],[65, 48])).
% 1.46/1.20 tff(67,plain,
% 1.46/1.20 (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))))),
% 1.46/1.20 inference(modus_ponens,[status(thm)],[66, 43])).
% 1.46/1.20 tff(68,plain,
% 1.46/1.20 (((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))))) | ((~aElementOf0(W0!32, szDzozmdt0(xN))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aFunction0(sdtlpdtrp0(xC, W0!32))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0!32)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0!32))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~((~(sbrdtbr0(W1) = xk)) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))))) | (~aElementOf0(W0!32, szDzozmdt0(xN))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aFunction0(sdtlpdtrp0(xC, W0!32))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0!32)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0!32))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~((~(sbrdtbr0(W1) = xk)) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))))),
% 1.46/1.21 inference(rewrite,[status(thm)],[])).
% 1.46/1.21 tff(69,plain,
% 1.46/1.21 (((~aElementOf0(W0!32, szDzozmdt0(xN))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aFunction0(sdtlpdtrp0(xC, W0!32))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0!32)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0!32))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))))))))) <=> ((~aElementOf0(W0!32, szDzozmdt0(xN))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aFunction0(sdtlpdtrp0(xC, W0!32))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0!32)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0!32))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~((~(sbrdtbr0(W1) = xk)) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))))),
% 1.46/1.21 inference(rewrite,[status(thm)],[])).
% 1.46/1.21 tff(70,plain,
% 1.46/1.21 (((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))))) | ((~aElementOf0(W0!32, szDzozmdt0(xN))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aFunction0(sdtlpdtrp0(xC, W0!32))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0!32)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0!32))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))))) | ((~aElementOf0(W0!32, szDzozmdt0(xN))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aFunction0(sdtlpdtrp0(xC, W0!32))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0!32)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0!32))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~((~(sbrdtbr0(W1) = xk)) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))))))))))),
% 1.46/1.21 inference(monotonicity,[status(thm)],[69])).
% 1.46/1.21 tff(71,plain,
% 1.46/1.21 (((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))))) | ((~aElementOf0(W0!32, szDzozmdt0(xN))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aFunction0(sdtlpdtrp0(xC, W0!32))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0!32)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0!32))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))))) | (~aElementOf0(W0!32, szDzozmdt0(xN))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aFunction0(sdtlpdtrp0(xC, W0!32))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0!32)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0!32))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~((~(sbrdtbr0(W1) = xk)) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))))),
% 1.46/1.22 inference(transitivity,[status(thm)],[70, 68])).
% 1.46/1.22 tff(72,plain,
% 1.46/1.22 ((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))))) | ((~aElementOf0(W0!32, szDzozmdt0(xN))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aFunction0(sdtlpdtrp0(xC, W0!32))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0!32)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0!32))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))))),
% 1.46/1.22 inference(quant_inst,[status(thm)],[])).
% 1.46/1.22 tff(73,plain,
% 1.46/1.22 ((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aFunction0(sdtlpdtrp0(xC, W0))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0)))) | (~((~aSet0(W1)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~(sbrdtbr0(W1) = xk)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) | (~(aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0))) | (~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))))))) | (~aElementOf0(W0!32, szDzozmdt0(xN))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aFunction0(sdtlpdtrp0(xC, W0!32))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0!32)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0!32))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~((~(sbrdtbr0(W1) = xk)) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))))))))),
% 1.46/1.22 inference(modus_ponens,[status(thm)],[72, 71])).
% 1.46/1.22 tff(74,plain,
% 1.46/1.22 (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aFunction0(sdtlpdtrp0(xC, W0!32))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0!32)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0!32))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~((~(sbrdtbr0(W1) = xk)) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))),
% 1.46/1.22 inference(unit_resolution,[status(thm)],[73, 67, 41])).
% 1.46/1.22 tff(75,plain,
% 1.46/1.22 (((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aFunction0(sdtlpdtrp0(xC, W0!32))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0!32)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0!32))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~((~(sbrdtbr0(W1) = xk)) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))))))) | ![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~((~(sbrdtbr0(W1) = xk)) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))),
% 1.46/1.22 inference(tautology,[status(thm)],[])).
% 1.46/1.22 tff(76,plain,
% 1.46/1.22 (![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~((~(sbrdtbr0(W1) = xk)) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))),
% 1.46/1.22 inference(unit_resolution,[status(thm)],[75, 74])).
% 1.46/1.22 tff(77,plain,
% 1.46/1.22 (((~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~((~(sbrdtbr0(W1) = xk)) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))) | (~((~((~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, tptp_fun_W2_34(W1!33))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~(aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~((~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))) <=> ((~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~((~(sbrdtbr0(W1) = xk)) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))) | (~((~((~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, tptp_fun_W2_34(W1!33))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~(aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~((~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))))))))),
% 1.46/1.23 inference(rewrite,[status(thm)],[])).
% 1.46/1.23 tff(78,plain,
% 1.46/1.23 ((~((~((~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, tptp_fun_W2_34(W1!33))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~((~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))))))) <=> (~((~((~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, tptp_fun_W2_34(W1!33))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~(aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~((~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))),
% 1.46/1.23 inference(rewrite,[status(thm)],[])).
% 1.46/1.23 tff(79,plain,
% 1.46/1.23 (((~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~((~(sbrdtbr0(W1) = xk)) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))) | (~((~((~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, tptp_fun_W2_34(W1!33))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~((~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))) <=> ((~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~((~(sbrdtbr0(W1) = xk)) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))) | (~((~((~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, tptp_fun_W2_34(W1!33))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~(aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~((~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))))))))),
% 1.46/1.23 inference(monotonicity,[status(thm)],[78])).
% 1.46/1.23 tff(80,plain,
% 1.46/1.23 (((~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~((~(sbrdtbr0(W1) = xk)) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))) | (~((~((~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, tptp_fun_W2_34(W1!33))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~((~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))) <=> ((~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~((~(sbrdtbr0(W1) = xk)) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))) | (~((~((~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, tptp_fun_W2_34(W1!33))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~(aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~((~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))))))))),
% 1.46/1.23 inference(transitivity,[status(thm)],[79, 77])).
% 1.46/1.23 tff(81,plain,
% 1.46/1.23 ((~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~((~(sbrdtbr0(W1) = xk)) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))) | (~((~((~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, tptp_fun_W2_34(W1!33))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~((~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))),
% 1.46/1.23 inference(quant_inst,[status(thm)],[])).
% 1.46/1.23 tff(82,plain,
% 1.46/1.23 ((~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~((~(sbrdtbr0(W1) = xk)) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))) | (~((~((~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, tptp_fun_W2_34(W1!33))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~(aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~((~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))),
% 1.54/1.23 inference(modus_ponens,[status(thm)],[81, 80])).
% 1.54/1.23 tff(83,plain,
% 1.54/1.23 (~((~((~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, tptp_fun_W2_34(W1!33))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~(aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~((~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))))))),
% 1.54/1.23 inference(unit_resolution,[status(thm)],[82, 76])).
% 1.54/1.23 tff(84,plain,
% 1.54/1.23 (((~((~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, tptp_fun_W2_34(W1!33))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~(aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~((~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))) | ((~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, tptp_fun_W2_34(W1!33))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))),
% 1.54/1.23 inference(tautology,[status(thm)],[])).
% 1.54/1.23 tff(85,plain,
% 1.54/1.23 ((~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, tptp_fun_W2_34(W1!33))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))),
% 1.54/1.23 inference(unit_resolution,[status(thm)],[84, 83])).
% 1.54/1.23 tff(86,plain,
% 1.54/1.23 (((~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = W1!33))) | aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))),
% 1.54/1.23 inference(tautology,[status(thm)],[])).
% 1.54/1.23 tff(87,plain,
% 1.54/1.23 (aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))),
% 1.54/1.23 inference(unit_resolution,[status(thm)],[86, 38])).
% 1.54/1.23 tff(88,plain,
% 1.54/1.23 ((~((~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, tptp_fun_W2_34(W1!33))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, tptp_fun_W2_34(W1!33))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))),
% 1.54/1.23 inference(tautology,[status(thm)],[])).
% 1.54/1.23 tff(89,plain,
% 1.54/1.23 ((~((~aElementOf0(tptp_fun_W2_34(W1!33), szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, tptp_fun_W2_34(W1!33))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, tptp_fun_W2_34(W1!33))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))),
% 1.54/1.23 inference(unit_resolution,[status(thm)],[88, 87])).
% 1.54/1.23 tff(90,plain,
% 1.54/1.23 (~((~aSet0(tptp_fun_W2_34(W1!33))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, tptp_fun_W2_34(W1!33))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))),
% 1.54/1.23 inference(unit_resolution,[status(thm)],[89, 85])).
% 1.54/1.23 tff(91,plain,
% 1.54/1.23 (((~aSet0(tptp_fun_W2_34(W1!33))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, tptp_fun_W2_34(W1!33))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | aSet0(tptp_fun_W2_34(W1!33))),
% 1.54/1.23 inference(tautology,[status(thm)],[])).
% 1.54/1.23 tff(92,plain,
% 1.54/1.23 (aSet0(tptp_fun_W2_34(W1!33))),
% 1.54/1.23 inference(unit_resolution,[status(thm)],[91, 90])).
% 1.54/1.23 tff(93,plain,
% 1.54/1.23 (((~aSet0(tptp_fun_W2_34(W1!33))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, tptp_fun_W2_34(W1!33))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)),
% 1.54/1.23 inference(tautology,[status(thm)],[])).
% 1.54/1.23 tff(94,plain,
% 1.54/1.23 (sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk),
% 1.54/1.23 inference(unit_resolution,[status(thm)],[93, 90])).
% 1.54/1.23 tff(95,plain,
% 1.54/1.23 (((~aSet0(tptp_fun_W2_34(W1!33))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, tptp_fun_W2_34(W1!33))) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))),
% 1.54/1.23 inference(tautology,[status(thm)],[])).
% 1.54/1.23 tff(96,plain,
% 1.54/1.23 (aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))),
% 1.54/1.23 inference(unit_resolution,[status(thm)],[95, 90])).
% 1.54/1.23 tff(97,plain,
% 1.54/1.23 ((aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))),
% 1.54/1.23 inference(tautology,[status(thm)],[])).
% 1.54/1.23 tff(98,plain,
% 1.54/1.23 (aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))),
% 1.54/1.23 inference(unit_resolution,[status(thm)],[97, 96])).
% 1.54/1.23 tff(99,plain,
% 1.54/1.23 ((~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))),
% 1.54/1.23 inference(tautology,[status(thm)],[])).
% 1.54/1.23 tff(100,plain,
% 1.54/1.23 (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))),
% 1.54/1.23 inference(unit_resolution,[status(thm)],[99, 98, 94])).
% 1.54/1.23 tff(101,plain,
% 1.54/1.23 (((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | aElementOf0(tptp_fun_W2_34(W1!33), slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | ((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))),
% 1.54/1.23 inference(tautology,[status(thm)],[])).
% 1.54/1.23 tff(102,plain,
% 1.54/1.23 ((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | aElementOf0(tptp_fun_W2_34(W1!33), slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[101, 100])).
% 1.54/1.24 tff(103,plain,
% 1.54/1.24 (((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aFunction0(sdtlpdtrp0(xC, W0!32))) | (~(szDzozmdt0(sdtlpdtrp0(xC, W0!32)) = slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk))) | (~![W1: $i] : ((~aElementOf0(W1, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W1))) | (~![W1: $i] : (aElementOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W1)) | (~aElementOf0(W1, sdtlpdtrp0(xN, W0!32))) | (W1 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | (~![W1: $i] : (~((~((~aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32)))) | (~((~aSet0(W1)) | (~(sbrdtbr0(W1) = xk)) | (~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~((~(sbrdtbr0(W1) = xk)) | aElementOf0(W1, szDzozmdt0(sdtlpdtrp0(xC, W0!32))) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))))) | (~![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))))))) | ![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))),
% 1.54/1.24 inference(tautology,[status(thm)],[])).
% 1.54/1.24 tff(104,plain,
% 1.54/1.24 (![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))),
% 1.54/1.24 inference(unit_resolution,[status(thm)],[103, 74])).
% 1.54/1.24 tff(105,plain,
% 1.54/1.24 (((~![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))) | ((~aSet0(tptp_fun_W2_34(W1!33))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | aElementOf0(tptp_fun_W2_34(W1!33), slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = sdtlpdtrp0(xc, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, tptp_fun_W2_34(W1!33)) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))) <=> ((~![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))) | (~aSet0(tptp_fun_W2_34(W1!33))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | aElementOf0(tptp_fun_W2_34(W1!33), slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = sdtlpdtrp0(xc, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, tptp_fun_W2_34(W1!33)) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))),
% 1.54/1.24 inference(rewrite,[status(thm)],[])).
% 1.54/1.24 tff(106,plain,
% 1.54/1.24 (((~aSet0(tptp_fun_W2_34(W1!33))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(tptp_fun_W2_34(W1!33), slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = sdtlpdtrp0(xc, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, tptp_fun_W2_34(W1!33)) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))))) <=> ((~aSet0(tptp_fun_W2_34(W1!33))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | aElementOf0(tptp_fun_W2_34(W1!33), slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = sdtlpdtrp0(xc, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, tptp_fun_W2_34(W1!33)) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))),
% 1.54/1.24 inference(rewrite,[status(thm)],[])).
% 1.54/1.24 tff(107,plain,
% 1.54/1.24 (((~![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))) | ((~aSet0(tptp_fun_W2_34(W1!33))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(tptp_fun_W2_34(W1!33), slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = sdtlpdtrp0(xc, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, tptp_fun_W2_34(W1!33)) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))) <=> ((~![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))) | ((~aSet0(tptp_fun_W2_34(W1!33))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | aElementOf0(tptp_fun_W2_34(W1!33), slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = sdtlpdtrp0(xc, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, tptp_fun_W2_34(W1!33)) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))))))),
% 1.54/1.24 inference(monotonicity,[status(thm)],[106])).
% 1.54/1.24 tff(108,plain,
% 1.54/1.24 (((~![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))) | ((~aSet0(tptp_fun_W2_34(W1!33))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(tptp_fun_W2_34(W1!33), slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = sdtlpdtrp0(xc, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, tptp_fun_W2_34(W1!33)) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))) <=> ((~![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))) | (~aSet0(tptp_fun_W2_34(W1!33))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | aElementOf0(tptp_fun_W2_34(W1!33), slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = sdtlpdtrp0(xc, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, tptp_fun_W2_34(W1!33)) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))),
% 1.54/1.25 inference(transitivity,[status(thm)],[107, 105])).
% 1.54/1.25 tff(109,plain,
% 1.54/1.25 ((~![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))) | ((~aSet0(tptp_fun_W2_34(W1!33))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(tptp_fun_W2_34(W1!33), slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = sdtlpdtrp0(xc, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, tptp_fun_W2_34(W1!33)) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))),
% 1.54/1.25 inference(quant_inst,[status(thm)],[])).
% 1.54/1.25 tff(110,plain,
% 1.54/1.25 ((~![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), W1) = sdtlpdtrp0(xc, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))))) | (~aSet0(tptp_fun_W2_34(W1!33))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | aElementOf0(tptp_fun_W2_34(W1!33), slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = sdtlpdtrp0(xc, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, tptp_fun_W2_34(W1!33)) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))))),
% 1.54/1.25 inference(modus_ponens,[status(thm)],[109, 108])).
% 1.54/1.25 tff(111,plain,
% 1.54/1.25 ((~aSet0(tptp_fun_W2_34(W1!33))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | aElementOf0(tptp_fun_W2_34(W1!33), slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = sdtlpdtrp0(xc, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, tptp_fun_W2_34(W1!33)) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))))),
% 1.54/1.25 inference(unit_resolution,[status(thm)],[110, 104])).
% 1.54/1.25 tff(112,plain,
% 1.54/1.25 (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = sdtlpdtrp0(xc, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, tptp_fun_W2_34(W1!33)) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))),
% 1.54/1.25 inference(unit_resolution,[status(thm)],[111, 102, 92])).
% 1.54/1.25 tff(113,plain,
% 1.54/1.25 (((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~(sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = sdtlpdtrp0(xc, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, tptp_fun_W2_34(W1!33)) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = sdtlpdtrp0(xc, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))),
% 1.54/1.25 inference(tautology,[status(thm)],[])).
% 1.54/1.25 tff(114,plain,
% 1.54/1.25 (sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33)) = sdtlpdtrp0(xc, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))),
% 1.54/1.25 inference(unit_resolution,[status(thm)],[113, 112])).
% 1.54/1.25 tff(115,plain,
% 1.54/1.25 (sdtlpdtrp0(xc, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = sdtlpdtrp0(sdtlpdtrp0(xC, W0!32), tptp_fun_W2_34(W1!33))),
% 1.54/1.25 inference(symmetry,[status(thm)],[114])).
% 1.54/1.25 tff(116,plain,
% 1.54/1.25 (sdtlpdtrp0(xc, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = W1!33),
% 1.54/1.25 inference(transitivity,[status(thm)],[115, 40])).
% 1.54/1.25 tff(117,plain,
% 1.54/1.25 (^[W0: $i] : rewrite(((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), szDzozmdt0(xc))))) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) <=> ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), szDzozmdt0(xc))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))),
% 1.54/1.25 inference(bind,[status(th)],[])).
% 1.54/1.25 tff(118,plain,
% 1.54/1.25 (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), szDzozmdt0(xc))))) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), szDzozmdt0(xc))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))))))),
% 1.54/1.25 inference(quant_intro,[status(thm)],[117])).
% 1.54/1.25 tff(119,plain,
% 1.54/1.25 (^[W0: $i] : refl(((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), szDzozmdt0(xc))))) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) <=> ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), szDzozmdt0(xc))))) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))),
% 1.54/1.25 inference(bind,[status(th)],[])).
% 1.54/1.25 tff(120,plain,
% 1.54/1.25 (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), szDzozmdt0(xc))))) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), szDzozmdt0(xc))))) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))))))),
% 1.54/1.25 inference(quant_intro,[status(thm)],[119])).
% 1.54/1.25 tff(121,plain,
% 1.54/1.25 (^[W0: $i] : rewrite(((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), szDzozmdt0(xc))))) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) <=> ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), szDzozmdt0(xc))))) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))),
% 1.54/1.25 inference(bind,[status(th)],[])).
% 1.54/1.25 tff(122,plain,
% 1.54/1.25 (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), szDzozmdt0(xc))))) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), szDzozmdt0(xc))))) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))))))),
% 1.54/1.25 inference(quant_intro,[status(thm)],[121])).
% 1.54/1.25 tff(123,plain,
% 1.54/1.25 (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), szDzozmdt0(xc))))) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), szDzozmdt0(xc))))) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))))))),
% 1.54/1.25 inference(transitivity,[status(thm)],[122, 120])).
% 1.54/1.25 tff(124,plain,
% 1.54/1.25 (^[W0: $i] : rewrite(((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((~aSet0(W1)) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00))) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), sdtlpdtrp0(xN, sz00)) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = szszuzczcdt0(xk)) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), szDzozmdt0(xc))) | ((~aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & (((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sbrdtbr0(W1) = xk))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) <=> ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), szDzozmdt0(xc))))) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))))),
% 1.54/1.26 inference(bind,[status(th)],[])).
% 1.54/1.26 tff(125,plain,
% 1.54/1.26 (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((~aSet0(W1)) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00))) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), sdtlpdtrp0(xN, sz00)) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = szszuzczcdt0(xk)) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), szDzozmdt0(xc))) | ((~aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & (((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sbrdtbr0(W1) = xk))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), szDzozmdt0(xc))))) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))))))),
% 1.54/1.26 inference(quant_intro,[status(thm)],[124])).
% 1.54/1.26 tff(126,plain,
% 1.54/1.26 (^[W0: $i] : rewrite(((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : (((~aSet0(W1)) | ((~aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) & (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & (((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sbrdtbr0(W1) = xk))) & (aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00))) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), sdtlpdtrp0(xN, sz00)) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = szszuzczcdt0(xk)) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), szDzozmdt0(xc))))) <=> ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((~aSet0(W1)) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00))) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), sdtlpdtrp0(xN, sz00)) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = szszuzczcdt0(xk)) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), szDzozmdt0(xc))) | ((~aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & (((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sbrdtbr0(W1) = xk))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))),
% 1.54/1.26 inference(bind,[status(th)],[])).
% 1.54/1.26 tff(127,plain,
% 1.54/1.26 (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : (((~aSet0(W1)) | ((~aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) & (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & (((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sbrdtbr0(W1) = xk))) & (aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00))) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), sdtlpdtrp0(xN, sz00)) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = szszuzczcdt0(xk)) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), szDzozmdt0(xc))))) <=> ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((~aSet0(W1)) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00))) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), sdtlpdtrp0(xN, sz00)) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = szszuzczcdt0(xk)) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), szDzozmdt0(xc))) | ((~aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & (((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sbrdtbr0(W1) = xk))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))))),
% 1.54/1.26 inference(quant_intro,[status(thm)],[126])).
% 1.54/1.26 tff(128,plain,
% 1.54/1.26 (^[W0: $i] : rewrite(((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00))) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), sdtlpdtrp0(xN, sz00)) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = szszuzczcdt0(xk)) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(sdtlpdtrp0(xN, sz00), szszuzczcdt0(xk)))))) <=> ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00))) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), sdtlpdtrp0(xN, sz00)) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = szszuzczcdt0(xk)) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), szDzozmdt0(xc))))))),
% 1.54/1.26 inference(bind,[status(th)],[])).
% 1.54/1.26 tff(129,plain,
% 1.54/1.26 (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00))) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), sdtlpdtrp0(xN, sz00)) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = szszuzczcdt0(xk)) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(sdtlpdtrp0(xN, sz00), szszuzczcdt0(xk)))))) <=> ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00))) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), sdtlpdtrp0(xN, sz00)) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = szszuzczcdt0(xk)) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), szDzozmdt0(xc)))))),
% 1.54/1.26 inference(quant_intro,[status(thm)],[128])).
% 1.54/1.26 tff(130,plain,
% 1.54/1.26 (^[W0: $i] : rewrite(((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK))))) <=> ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00))) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), sdtlpdtrp0(xN, sz00)) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = szszuzczcdt0(xk)) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(sdtlpdtrp0(xN, sz00), szszuzczcdt0(xk)))))))),
% 1.54/1.26 inference(bind,[status(th)],[])).
% 1.54/1.26 tff(131,plain,
% 1.54/1.26 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK))))) <=> ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00))) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), sdtlpdtrp0(xN, sz00)) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = szszuzczcdt0(xk)) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(sdtlpdtrp0(xN, sz00), szszuzczcdt0(xk))))))),
% 1.54/1.26 inference(quant_intro,[status(thm)],[130])).
% 1.54/1.26 tff(132,plain,
% 1.54/1.26 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK)))))),
% 1.54/1.26 inference(rewrite,[status(thm)],[])).
% 1.54/1.26 tff(133,plain,
% 1.54/1.26 (^[W0: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: $i] : trans(monotonicity(rewrite((aSet0(W1) & ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) => ((aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0))) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) => (((![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)))))) <=> (aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))), trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))), (((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) <=> ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))), rewrite(((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))))), (((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))))), ((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) <=> ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))), rewrite(((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))), ((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))), quant_intro(proof_bind(^[W2: $i] : rewrite((aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) => aElementOf0(W2, xS)) <=> ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)))), (![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) => aElementOf0(W2, xS)) <=> ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)))), (((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) => aElementOf0(W2, xS))) <=> ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS))))), rewrite(((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS))) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)))), (((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) => aElementOf0(W2, xS))) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS))))), ((((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) => aElementOf0(W2, xS))) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) <=> ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS))) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)))), rewrite(((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS))) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS))), ((((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) => aElementOf0(W2, xS))) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)))), (((((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) => aElementOf0(W2, xS))) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)) <=> ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)))), rewrite(((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK))), (((((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) => aElementOf0(W2, xS))) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)))), ((((((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) => aElementOf0(W2, xS))) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK))) <=> ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK))))), rewrite(((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK))) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK)))), ((((((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) => aElementOf0(W2, xS))) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK))) <=> (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK))))), (((aSet0(W1) & ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) => ((aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0))) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) => (((![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)))))) => (((((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) => aElementOf0(W2, xS))) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK)))) <=> ((aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) => (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK)))))), rewrite(((aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))))) => (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK)))) <=> ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK))))), (((aSet0(W1) & ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) => ((aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0))) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) => (((![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)))))) => (((((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) => aElementOf0(W2, xS))) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK)))) <=> ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK))))))), (![W1: $i] : ((aSet0(W1) & ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) => ((aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0))) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) => (((![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)))))) => (((((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) => aElementOf0(W2, xS))) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK)))) <=> ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK)))))), ((aElementOf0(W0, szNzAzT0) => ![W1: $i] : ((aSet0(W1) & ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) => ((aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0))) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) => (((![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)))))) => (((((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) => aElementOf0(W2, xS))) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK))))) <=> (aElementOf0(W0, szNzAzT0) => ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK))))))), rewrite((aElementOf0(W0, szNzAzT0) => ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK))))) <=> ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK)))))), ((aElementOf0(W0, szNzAzT0) => ![W1: $i] : ((aSet0(W1) & ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) => ((aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0))) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) => (((![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)))))) => (((((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) => aElementOf0(W2, xS))) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK))))) <=> ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK)))))))),
% 1.58/1.28 inference(bind,[status(th)],[])).
% 1.58/1.28 tff(134,plain,
% 1.58/1.28 (![W0: $i] : (aElementOf0(W0, szNzAzT0) => ![W1: $i] : ((aSet0(W1) & ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) => ((aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0))) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) => (((![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)))))) => (((((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) => aElementOf0(W2, xS))) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK))))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK)))))),
% 1.58/1.28 inference(quant_intro,[status(thm)],[133])).
% 1.58/1.28 tff(135,axiom,(![W0: $i] : (aElementOf0(W0, szNzAzT0) => ![W1: $i] : ((aSet0(W1) & ((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) => ((aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> ((aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0))) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) => (((![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (sbrdtbr0(W1) = xk)) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)))))) => (((((((aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : (aElementOf0(W2, sdtlpdtrp0(xN, W0)) => sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) => aElementOf0(W2, xS))) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS)) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK)) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__3965')).
% 1.58/1.28 tff(136,plain,
% 1.58/1.28 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK)))))),
% 1.58/1.28 inference(modus_ponens,[status(thm)],[135, 134])).
% 1.58/1.28 tff(137,plain,
% 1.58/1.28 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, xS)) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), xS) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = xK) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(xS, xK)))))),
% 1.58/1.28 inference(modus_ponens,[status(thm)],[136, 132])).
% 1.58/1.28 tff(138,plain,
% 1.58/1.28 (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00))) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), sdtlpdtrp0(xN, sz00)) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = szszuzczcdt0(xk)) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), slbdtsldtrb0(sdtlpdtrp0(xN, sz00), szszuzczcdt0(xk))))))),
% 1.58/1.28 inference(modus_ponens,[status(thm)],[137, 131])).
% 1.58/1.28 tff(139,plain,
% 1.58/1.28 (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~(aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)))) | ((aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))) & (sbrdtbr0(W1) = xk)) | (~(aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00))) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), sdtlpdtrp0(xN, sz00)) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = szszuzczcdt0(xk)) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), szDzozmdt0(xc)))))),
% 1.58/1.28 inference(modus_ponens,[status(thm)],[138, 129])).
% 1.58/1.28 tff(140,plain,(
% 1.58/1.28 ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : (((~aSet0(W1)) | ((~aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) & (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) & (((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sbrdtbr0(W1) = xk))) & (aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00))) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), sdtlpdtrp0(xN, sz00)) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = szszuzczcdt0(xk)) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), szDzozmdt0(xc)))))),
% 1.58/1.28 inference(skolemize,[status(sab)],[139])).
% 1.58/1.28 tff(141,plain,
% 1.58/1.28 (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((~aSet0(W1)) | (aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & (aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))) & ![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00))) & aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), sdtlpdtrp0(xN, sz00)) & (sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = szszuzczcdt0(xk)) & aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), szDzozmdt0(xc))) | ((~aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk))) & aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0)) & ![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2)) & (((~aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) & (~((~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))))) | (~(sbrdtbr0(W1) = xk))) & aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) & ![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (aElement0(W2) & aElementOf0(W2, sdtlpdtrp0(xN, W0)) & (~(W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))))),
% 1.58/1.28 inference(modus_ponens,[status(thm)],[140, 127])).
% 1.58/1.28 tff(142,plain,
% 1.58/1.28 (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), szDzozmdt0(xc))))) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))))))),
% 1.58/1.28 inference(modus_ponens,[status(thm)],[141, 125])).
% 1.58/1.28 tff(143,plain,
% 1.58/1.28 (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), szDzozmdt0(xc))))) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))))))),
% 1.58/1.28 inference(modus_ponens,[status(thm)],[142, 123])).
% 1.58/1.28 tff(144,plain,
% 1.58/1.28 (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), szDzozmdt0(xc))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))))))),
% 1.58/1.28 inference(modus_ponens,[status(thm)],[143, 118])).
% 1.58/1.28 tff(145,plain,
% 1.58/1.28 (((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), szDzozmdt0(xc))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))))))) | ((~aElementOf0(W0!32, szDzozmdt0(xN))) | ![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00))))))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), szDzozmdt0(xc))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))))))) | (~aElementOf0(W0!32, szDzozmdt0(xN))) | ![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00))))))))),
% 1.58/1.28 inference(rewrite,[status(thm)],[])).
% 1.58/1.28 tff(146,plain,
% 1.58/1.28 (((~aElementOf0(W0!32, szDzozmdt0(xN))) | ![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))))) <=> ((~aElementOf0(W0!32, szDzozmdt0(xN))) | ![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00))))))))),
% 1.58/1.28 inference(rewrite,[status(thm)],[])).
% 1.58/1.28 tff(147,plain,
% 1.58/1.28 (((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), szDzozmdt0(xc))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))))))) | ((~aElementOf0(W0!32, szDzozmdt0(xN))) | ![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), szDzozmdt0(xc))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))))))) | ((~aElementOf0(W0!32, szDzozmdt0(xN))) | ![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))))))),
% 1.58/1.29 inference(monotonicity,[status(thm)],[146])).
% 1.58/1.29 tff(148,plain,
% 1.58/1.29 (((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), szDzozmdt0(xc))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))))))) | ((~aElementOf0(W0!32, szDzozmdt0(xN))) | ![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), szDzozmdt0(xc))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))))))) | (~aElementOf0(W0!32, szDzozmdt0(xN))) | ![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00))))))))),
% 1.58/1.29 inference(transitivity,[status(thm)],[147, 145])).
% 1.58/1.29 tff(149,plain,
% 1.58/1.29 ((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), szDzozmdt0(xc))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))))))) | ((~aElementOf0(W0!32, szDzozmdt0(xN))) | ![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))))),
% 1.58/1.29 inference(quant_inst,[status(thm)],[])).
% 1.58/1.29 tff(150,plain,
% 1.58/1.29 ((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))), szDzozmdt0(xc))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0))))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))) | (~(aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))), xk)) | (~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0)), sdtlpdtrp0(xN, W0))) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0), sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))))))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0), szmzizndt0(sdtlpdtrp0(xN, W0)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0)))))))))))) | (~aElementOf0(W0!32, szDzozmdt0(xN))) | ![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))))),
% 1.58/1.29 inference(modus_ponens,[status(thm)],[149, 148])).
% 1.58/1.29 tff(151,plain,
% 1.58/1.29 (![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))))),
% 1.58/1.29 inference(unit_resolution,[status(thm)],[150, 144, 41])).
% 1.58/1.29 tff(152,plain,
% 1.58/1.29 (((~![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))))) | ((~aSet0(tptp_fun_W2_34(W1!33))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | aElementOf0(tptp_fun_W2_34(W1!33), slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, tptp_fun_W2_34(W1!33)) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))))) <=> ((~![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))))) | (~aSet0(tptp_fun_W2_34(W1!33))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | aElementOf0(tptp_fun_W2_34(W1!33), slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, tptp_fun_W2_34(W1!33)) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))))),
% 1.58/1.30 inference(rewrite,[status(thm)],[])).
% 1.58/1.30 tff(153,plain,
% 1.58/1.30 (((~aSet0(tptp_fun_W2_34(W1!33))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(tptp_fun_W2_34(W1!33), slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, tptp_fun_W2_34(W1!33)) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00))))))) <=> ((~aSet0(tptp_fun_W2_34(W1!33))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | aElementOf0(tptp_fun_W2_34(W1!33), slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, tptp_fun_W2_34(W1!33)) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))))),
% 1.58/1.30 inference(rewrite,[status(thm)],[])).
% 1.58/1.30 tff(154,plain,
% 1.58/1.30 (((~![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))))) | ((~aSet0(tptp_fun_W2_34(W1!33))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(tptp_fun_W2_34(W1!33), slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, tptp_fun_W2_34(W1!33)) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))))) <=> ((~![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))))) | ((~aSet0(tptp_fun_W2_34(W1!33))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | aElementOf0(tptp_fun_W2_34(W1!33), slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, tptp_fun_W2_34(W1!33)) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00))))))))),
% 1.58/1.30 inference(monotonicity,[status(thm)],[153])).
% 1.58/1.30 tff(155,plain,
% 1.58/1.30 (((~![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))))) | ((~aSet0(tptp_fun_W2_34(W1!33))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(tptp_fun_W2_34(W1!33), slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, tptp_fun_W2_34(W1!33)) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))))) <=> ((~![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))))) | (~aSet0(tptp_fun_W2_34(W1!33))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | aElementOf0(tptp_fun_W2_34(W1!33), slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, tptp_fun_W2_34(W1!33)) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))))),
% 1.58/1.30 inference(transitivity,[status(thm)],[154, 152])).
% 1.58/1.30 tff(156,plain,
% 1.58/1.30 ((~![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))))) | ((~aSet0(tptp_fun_W2_34(W1!33))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(tptp_fun_W2_34(W1!33), slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, tptp_fun_W2_34(W1!33)) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))))),
% 1.58/1.30 inference(quant_inst,[status(thm)],[])).
% 1.58/1.30 tff(157,plain,
% 1.58/1.30 ((~![W1: $i] : ((~aSet0(W1)) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W1, slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(W1, W0!32), W1)) | aElementOf0(tptp_fun_W2_31(W1, W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, W1) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~aSet0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(W1, szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))))) | (~aSet0(tptp_fun_W2_34(W1!33))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | aElementOf0(tptp_fun_W2_34(W1!33), slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, tptp_fun_W2_34(W1!33)) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00))))))),
% 1.58/1.31 inference(modus_ponens,[status(thm)],[156, 155])).
% 1.58/1.31 tff(158,plain,
% 1.58/1.31 ((~aSet0(tptp_fun_W2_34(W1!33))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~aSet0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))) | aElementOf0(tptp_fun_W2_34(W1!33), slbdtsldtrb0(sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32))), xk)) | (~((~(sbrdtbr0(tptp_fun_W2_34(W1!33)) = xk)) | (~(aSubsetOf0(tptp_fun_W2_34(W1!33), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) | (~aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), tptp_fun_W2_34(W1!33))) | aElementOf0(tptp_fun_W2_31(tptp_fun_W2_34(W1!33), W0!32), sdtmndt0(sdtlpdtrp0(xN, W0!32), szmzizndt0(sdtlpdtrp0(xN, W0!32)))))))))) | (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, tptp_fun_W2_34(W1!33)) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00))))))),
% 1.58/1.31 inference(unit_resolution,[status(thm)],[157, 151])).
% 1.58/1.31 tff(159,plain,
% 1.58/1.31 (~((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, tptp_fun_W2_34(W1!33)) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00)))))),
% 1.58/1.31 inference(unit_resolution,[status(thm)],[158, 102, 92])).
% 1.58/1.31 tff(160,plain,
% 1.58/1.31 (((~aElementOf0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), sdtlpdtrp0(xN, W0!32))) | (~![W2: $i] : ((~aElementOf0(W2, sdtlpdtrp0(xN, W0!32))) | sdtlseqdt0(szmzizndt0(sdtlpdtrp0(xN, W0!32)), W2))) | (~![W2: $i] : (aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) <=> (~((~aElement0(W2)) | (~(aElementOf0(W2, tptp_fun_W2_34(W1!33)) | (W2 = szmzizndt0(sdtlpdtrp0(xN, W0!32))))))))) | (~aSet0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | (~aSubsetOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), sdtlpdtrp0(xN, sz00))) | (~(sbrdtbr0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = szszuzczcdt0(xk))) | (~aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))) | (~![W2: $i] : ((~aElementOf0(W2, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))))) | aElementOf0(W2, sdtlpdtrp0(xN, sz00))))) | aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))),
% 1.58/1.31 inference(tautology,[status(thm)],[])).
% 1.58/1.31 tff(161,plain,
% 1.58/1.31 (aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))),
% 1.58/1.31 inference(unit_resolution,[status(thm)],[160, 159])).
% 1.58/1.31 tff(162,plain,
% 1.58/1.31 (^[W0: $i] : refl((~((~((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W0))))))) <=> (~((~((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W0))))))))),
% 1.58/1.31 inference(bind,[status(th)],[])).
% 1.58/1.31 tff(163,plain,
% 1.58/1.31 (![W0: $i] : (~((~((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W0))))))) <=> ![W0: $i] : (~((~((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W0)))))))),
% 1.58/1.31 inference(quant_intro,[status(thm)],[162])).
% 1.58/1.31 tff(164,plain,
% 1.58/1.31 (^[W0: $i] : rewrite((~((~((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W0))))))) <=> (~((~((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W0))))))))),
% 1.58/1.31 inference(bind,[status(th)],[])).
% 1.58/1.31 tff(165,plain,
% 1.58/1.31 (![W0: $i] : (~((~((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W0))))))) <=> ![W0: $i] : (~((~((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W0)))))))),
% 1.58/1.31 inference(quant_intro,[status(thm)],[164])).
% 1.58/1.31 tff(166,plain,
% 1.58/1.31 (![W0: $i] : (~((~((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W0))))))) <=> ![W0: $i] : (~((~((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W0)))))))),
% 1.58/1.31 inference(transitivity,[status(thm)],[165, 163])).
% 1.58/1.31 tff(167,plain,
% 1.58/1.31 (^[W0: $i] : trans(monotonicity(rewrite(((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc)) & (sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0))) <=> ((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0)))))), rewrite((aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : (~(aElementOf0(W1, szDzozmdt0(xc)) & (sdtlpdtrp0(xc, W1) = W0)))) <=> (aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W0))))), ((((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc)) & (sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0))) & (aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : (~(aElementOf0(W1, szDzozmdt0(xc)) & (sdtlpdtrp0(xc, W1) = W0))))) <=> (((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0))))) & (aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W0))))))), rewrite((((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0))))) & (aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W0))))) <=> (~((~((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W0)))))))), ((((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc)) & (sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0))) & (aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : (~(aElementOf0(W1, szDzozmdt0(xc)) & (sdtlpdtrp0(xc, W1) = W0))))) <=> (~((~((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W0)))))))))),
% 1.58/1.31 inference(bind,[status(th)],[])).
% 1.58/1.31 tff(168,plain,
% 1.58/1.31 (![W0: $i] : (((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc)) & (sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0))) & (aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : (~(aElementOf0(W1, szDzozmdt0(xc)) & (sdtlpdtrp0(xc, W1) = W0))))) <=> ![W0: $i] : (~((~((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W0)))))))),
% 1.58/1.31 inference(quant_intro,[status(thm)],[167])).
% 1.58/1.31 tff(169,plain,
% 1.58/1.31 (![W0: $i] : (aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) <=> ?[W1: $i] : (aElementOf0(W1, szDzozmdt0(xc)) & (sdtlpdtrp0(xc, W1) = W0))) <=> ![W0: $i] : (aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) <=> ?[W1: $i] : (aElementOf0(W1, szDzozmdt0(xc)) & (sdtlpdtrp0(xc, W1) = W0)))),
% 1.58/1.31 inference(rewrite,[status(thm)],[])).
% 1.58/1.31 tff(170,axiom,((((((aFunction0(xc) & ![W0: $i] : ((aElementOf0(W0, szDzozmdt0(xc)) => (((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xS))) & aSubsetOf0(W0, xS)) & (sbrdtbr0(W0) = xK))) & ((((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xS))) | aSubsetOf0(W0, xS)) & (sbrdtbr0(W0) = xK)) => aElementOf0(W0, szDzozmdt0(xc))))) & (szDzozmdt0(xc) = slbdtsldtrb0(xS, xK))) & aSet0(sdtlcdtrc0(xc, szDzozmdt0(xc)))) & ![W0: $i] : (aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) <=> ?[W1: $i] : (aElementOf0(W1, szDzozmdt0(xc)) & (sdtlpdtrp0(xc, W1) = W0)))) & ![W0: $i] : (aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) => aElementOf0(W0, xT))) & aSubsetOf0(sdtlcdtrc0(xc, szDzozmdt0(xc)), xT)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__3453')).
% 1.58/1.31 tff(171,plain,
% 1.58/1.31 (((((aFunction0(xc) & ![W0: $i] : ((aElementOf0(W0, szDzozmdt0(xc)) => (((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xS))) & aSubsetOf0(W0, xS)) & (sbrdtbr0(W0) = xK))) & ((((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xS))) | aSubsetOf0(W0, xS)) & (sbrdtbr0(W0) = xK)) => aElementOf0(W0, szDzozmdt0(xc))))) & (szDzozmdt0(xc) = slbdtsldtrb0(xS, xK))) & aSet0(sdtlcdtrc0(xc, szDzozmdt0(xc)))) & ![W0: $i] : (aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) <=> ?[W1: $i] : (aElementOf0(W1, szDzozmdt0(xc)) & (sdtlpdtrp0(xc, W1) = W0)))) & ![W0: $i] : (aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) => aElementOf0(W0, xT))),
% 1.58/1.31 inference(and_elim,[status(thm)],[170])).
% 1.58/1.31 tff(172,plain,
% 1.58/1.31 ((((aFunction0(xc) & ![W0: $i] : ((aElementOf0(W0, szDzozmdt0(xc)) => (((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xS))) & aSubsetOf0(W0, xS)) & (sbrdtbr0(W0) = xK))) & ((((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xS))) | aSubsetOf0(W0, xS)) & (sbrdtbr0(W0) = xK)) => aElementOf0(W0, szDzozmdt0(xc))))) & (szDzozmdt0(xc) = slbdtsldtrb0(xS, xK))) & aSet0(sdtlcdtrc0(xc, szDzozmdt0(xc)))) & ![W0: $i] : (aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) <=> ?[W1: $i] : (aElementOf0(W1, szDzozmdt0(xc)) & (sdtlpdtrp0(xc, W1) = W0)))),
% 1.58/1.31 inference(and_elim,[status(thm)],[171])).
% 1.58/1.31 tff(173,plain,
% 1.58/1.31 (![W0: $i] : (aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) <=> ?[W1: $i] : (aElementOf0(W1, szDzozmdt0(xc)) & (sdtlpdtrp0(xc, W1) = W0)))),
% 1.58/1.31 inference(and_elim,[status(thm)],[172])).
% 1.58/1.31 tff(174,plain,
% 1.58/1.31 (![W0: $i] : (aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) <=> ?[W1: $i] : (aElementOf0(W1, szDzozmdt0(xc)) & (sdtlpdtrp0(xc, W1) = W0)))),
% 1.58/1.31 inference(modus_ponens,[status(thm)],[173, 169])).
% 1.58/1.31 tff(175,plain,(
% 1.58/1.31 ![W0: $i] : (((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc)) & (sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0))) & (aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : (~(aElementOf0(W1, szDzozmdt0(xc)) & (sdtlpdtrp0(xc, W1) = W0)))))),
% 1.58/1.31 inference(skolemize,[status(sab)],[174])).
% 1.58/1.31 tff(176,plain,
% 1.58/1.31 (![W0: $i] : (~((~((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W0)))))))),
% 1.58/1.31 inference(modus_ponens,[status(thm)],[175, 168])).
% 1.58/1.31 tff(177,plain,
% 1.58/1.31 (![W0: $i] : (~((~((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W0)))))))),
% 1.58/1.31 inference(modus_ponens,[status(thm)],[176, 166])).
% 1.58/1.31 tff(178,plain,
% 1.58/1.31 ((~![W0: $i] : (~((~((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W0), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W0)))))))) | (~((~((~aElementOf0(W1!33, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W1!33), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W1!33)) = W1!33)))))) | (~(aElementOf0(W1!33, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W1!33)))))))),
% 1.58/1.31 inference(quant_inst,[status(thm)],[])).
% 1.58/1.31 tff(179,plain,
% 1.58/1.31 (~((~((~aElementOf0(W1!33, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W1!33), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W1!33)) = W1!33)))))) | (~(aElementOf0(W1!33, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W1!33))))))),
% 1.58/1.31 inference(unit_resolution,[status(thm)],[178, 177])).
% 1.58/1.31 tff(180,plain,
% 1.58/1.31 (((~((~aElementOf0(W1!33, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | (~((~aElementOf0(tptp_fun_W1_20(W1!33), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, tptp_fun_W1_20(W1!33)) = W1!33)))))) | (~(aElementOf0(W1!33, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W1!33)))))) | (aElementOf0(W1!33, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W1!33))))),
% 1.58/1.31 inference(tautology,[status(thm)],[])).
% 1.58/1.31 tff(181,plain,
% 1.58/1.31 (aElementOf0(W1!33, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W1!33)))),
% 1.58/1.31 inference(unit_resolution,[status(thm)],[180, 179])).
% 1.58/1.31 tff(182,plain,
% 1.58/1.31 (~aElementOf0(W1!33, xT)),
% 1.58/1.31 inference(or_elim,[status(thm)],[34])).
% 1.58/1.31 tff(183,plain,
% 1.58/1.31 (^[W0: $i] : refl(((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W0, xT)) <=> ((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W0, xT)))),
% 1.58/1.31 inference(bind,[status(th)],[])).
% 1.58/1.31 tff(184,plain,
% 1.58/1.31 (![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W0, xT)) <=> ![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W0, xT))),
% 1.58/1.31 inference(quant_intro,[status(thm)],[183])).
% 1.58/1.31 tff(185,plain,
% 1.58/1.31 (![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W0, xT)) <=> ![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W0, xT))),
% 1.58/1.31 inference(rewrite,[status(thm)],[])).
% 1.58/1.31 tff(186,plain,
% 1.58/1.31 (^[W0: $i] : rewrite((aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) => aElementOf0(W0, xT)) <=> ((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W0, xT)))),
% 1.58/1.31 inference(bind,[status(th)],[])).
% 1.58/1.31 tff(187,plain,
% 1.58/1.31 (![W0: $i] : (aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) => aElementOf0(W0, xT)) <=> ![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W0, xT))),
% 1.58/1.31 inference(quant_intro,[status(thm)],[186])).
% 1.58/1.31 tff(188,plain,
% 1.58/1.31 (![W0: $i] : (aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc))) => aElementOf0(W0, xT))),
% 1.58/1.31 inference(and_elim,[status(thm)],[171])).
% 1.58/1.31 tff(189,plain,
% 1.58/1.31 (![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W0, xT))),
% 1.58/1.31 inference(modus_ponens,[status(thm)],[188, 187])).
% 1.58/1.31 tff(190,plain,
% 1.58/1.31 (![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W0, xT))),
% 1.58/1.32 inference(modus_ponens,[status(thm)],[189, 185])).
% 1.58/1.32 tff(191,plain,(
% 1.58/1.32 ![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W0, xT))),
% 1.58/1.32 inference(skolemize,[status(sab)],[190])).
% 1.58/1.32 tff(192,plain,
% 1.58/1.32 (![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W0, xT))),
% 1.58/1.32 inference(modus_ponens,[status(thm)],[191, 184])).
% 1.58/1.32 tff(193,plain,
% 1.58/1.32 (((~![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W0, xT))) | ((~aElementOf0(W1!33, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W1!33, xT))) <=> ((~![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W0, xT))) | (~aElementOf0(W1!33, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W1!33, xT))),
% 1.58/1.32 inference(rewrite,[status(thm)],[])).
% 1.58/1.32 tff(194,plain,
% 1.58/1.32 ((~![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W0, xT))) | ((~aElementOf0(W1!33, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W1!33, xT))),
% 1.58/1.32 inference(quant_inst,[status(thm)],[])).
% 1.58/1.32 tff(195,plain,
% 1.58/1.32 ((~![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W0, xT))) | (~aElementOf0(W1!33, sdtlcdtrc0(xc, szDzozmdt0(xc)))) | aElementOf0(W1!33, xT)),
% 1.58/1.32 inference(modus_ponens,[status(thm)],[194, 193])).
% 1.58/1.32 tff(196,plain,
% 1.58/1.32 (~aElementOf0(W1!33, sdtlcdtrc0(xc, szDzozmdt0(xc)))),
% 1.58/1.32 inference(unit_resolution,[status(thm)],[195, 192, 182])).
% 1.58/1.32 tff(197,plain,
% 1.58/1.32 ((~(aElementOf0(W1!33, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W1!33))))) | aElementOf0(W1!33, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W1!33)))),
% 1.58/1.32 inference(tautology,[status(thm)],[])).
% 1.58/1.32 tff(198,plain,
% 1.58/1.32 ((~(aElementOf0(W1!33, sdtlcdtrc0(xc, szDzozmdt0(xc))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W1!33))))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W1!33)))),
% 1.58/1.32 inference(unit_resolution,[status(thm)],[197, 196])).
% 1.58/1.32 tff(199,plain,
% 1.58/1.32 (![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W1!33)))),
% 1.58/1.32 inference(unit_resolution,[status(thm)],[198, 181])).
% 1.58/1.32 tff(200,plain,
% 1.58/1.32 (((~![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W1!33)))) | ((~aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = W1!33)))) <=> ((~![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W1!33)))) | (~aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = W1!33)))),
% 1.58/1.32 inference(rewrite,[status(thm)],[])).
% 1.58/1.32 tff(201,plain,
% 1.58/1.32 ((~![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W1!33)))) | ((~aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = W1!33)))),
% 1.58/1.32 inference(quant_inst,[status(thm)],[])).
% 1.58/1.32 tff(202,plain,
% 1.58/1.32 ((~![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, W1) = W1!33)))) | (~aElementOf0(sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32))), szDzozmdt0(xc))) | (~(sdtlpdtrp0(xc, sdtpldt0(tptp_fun_W2_34(W1!33), szmzizndt0(sdtlpdtrp0(xN, W0!32)))) = W1!33))),
% 1.58/1.32 inference(modus_ponens,[status(thm)],[201, 200])).
% 1.58/1.32 tff(203,plain,
% 1.58/1.32 ($false),
% 1.58/1.32 inference(unit_resolution,[status(thm)],[202, 199, 161, 116])).
% 1.58/1.32 % SZS output end Proof
%------------------------------------------------------------------------------