TSTP Solution File: NUM595+3 by Z3---4.8.9.0

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : NUM595+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n012.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 13:10:45 EDT 2022

% Result   : Theorem 0.92s 0.88s
% Output   : Proof 0.92s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : NUM595+3 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34  % Computer : n012.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Fri Sep  2 12:09:34 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34  Usage: tptp [options] [-file:]file
% 0.12/0.34    -h, -?       prints this message.
% 0.12/0.34    -smt2        print SMT-LIB2 benchmark.
% 0.12/0.34    -m, -model   generate model.
% 0.12/0.34    -p, -proof   generate proof.
% 0.12/0.34    -c, -core    generate unsat core of named formulas.
% 0.12/0.34    -st, -statistics display statistics.
% 0.12/0.34    -t:timeout   set timeout (in second).
% 0.12/0.34    -smt2status  display status in smt2 format instead of SZS.
% 0.12/0.34    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34    -<param>:<value> configuration parameter and value.
% 0.12/0.34    -o:<output-file> file to place output in.
% 0.92/0.88  % SZS status Theorem
% 0.92/0.88  % SZS output start Proof
% 0.92/0.88  tff(aElementOf0_type, type, (
% 0.92/0.88     aElementOf0: ( $i * $i ) > $o)).
% 0.92/0.88  tff(xT_type, type, (
% 0.92/0.88     xT: $i)).
% 0.92/0.88  tff(tptp_fun_W1_37_type, type, (
% 0.92/0.88     tptp_fun_W1_37: $i > $i)).
% 0.92/0.88  tff(xi_type, type, (
% 0.92/0.88     xi: $i)).
% 0.92/0.88  tff(sdtlpdtrp0_type, type, (
% 0.92/0.88     sdtlpdtrp0: ( $i * $i ) > $i)).
% 0.92/0.88  tff(xd_type, type, (
% 0.92/0.88     xd: $i)).
% 0.92/0.88  tff(tptp_fun_W0_43_type, type, (
% 0.92/0.88     tptp_fun_W0_43: $i)).
% 0.92/0.88  tff(xC_type, type, (
% 0.92/0.88     xC: $i)).
% 0.92/0.88  tff(szszuzczcdt0_type, type, (
% 0.92/0.88     szszuzczcdt0: $i > $i)).
% 0.92/0.88  tff(xN_type, type, (
% 0.92/0.88     xN: $i)).
% 0.92/0.88  tff(tptp_fun_W2_39_type, type, (
% 0.92/0.88     tptp_fun_W2_39: ( $i * $i ) > $i)).
% 0.92/0.88  tff(aSubsetOf0_type, type, (
% 0.92/0.88     aSubsetOf0: ( $i * $i ) > $o)).
% 0.92/0.88  tff(xk_type, type, (
% 0.92/0.88     xk: $i)).
% 0.92/0.88  tff(sbrdtbr0_type, type, (
% 0.92/0.88     sbrdtbr0: $i > $i)).
% 0.92/0.88  tff(slbdtsldtrb0_type, type, (
% 0.92/0.88     slbdtsldtrb0: ( $i * $i ) > $i)).
% 0.92/0.88  tff(xX_type, type, (
% 0.92/0.88     xX: $i)).
% 0.92/0.88  tff(aSet0_type, type, (
% 0.92/0.88     aSet0: $i > $o)).
% 0.92/0.88  tff(tptp_fun_W1_42_type, type, (
% 0.92/0.88     tptp_fun_W1_42: $i > $i)).
% 0.92/0.88  tff(szDzozmdt0_type, type, (
% 0.92/0.88     szDzozmdt0: $i > $i)).
% 0.92/0.88  tff(szNzAzT0_type, type, (
% 0.92/0.88     szNzAzT0: $i)).
% 0.92/0.88  tff(xx_type, type, (
% 0.92/0.88     xx: $i)).
% 0.92/0.88  tff(aFunction0_type, type, (
% 0.92/0.88     aFunction0: $i > $o)).
% 0.92/0.88  tff(tptp_fun_W3_38_type, type, (
% 0.92/0.88     tptp_fun_W3_38: ( $i * $i ) > $i)).
% 0.92/0.88  tff(1,plain,
% 0.92/0.88      (^[W0: $i] : rewrite(aElementOf0(W0, xX) <=> aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)))),
% 0.92/0.88      inference(bind,[status(th)],[])).
% 0.92/0.88  tff(2,plain,
% 0.92/0.88      (?[W0: $i] : aElementOf0(W0, xX) <=> ?[W0: $i] : aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk))),
% 0.92/0.88      inference(quant_intro,[status(thm)],[1])).
% 0.92/0.88  tff(3,plain,
% 0.92/0.88      (?[W0: $i] : aElementOf0(W0, xX) <=> ?[W0: $i] : aElementOf0(W0, xX)),
% 0.92/0.88      inference(rewrite,[status(thm)],[])).
% 0.92/0.88  tff(4,plain,
% 0.92/0.88      ((~(~?[W0: $i] : aElementOf0(W0, xX))) <=> ?[W0: $i] : aElementOf0(W0, xX)),
% 0.92/0.88      inference(rewrite,[status(thm)],[])).
% 0.92/0.88  tff(5,plain,
% 0.92/0.88      ((~?[W0: $i] : aElementOf0(W0, xX)) <=> (~?[W0: $i] : aElementOf0(W0, xX))),
% 0.92/0.88      inference(rewrite,[status(thm)],[])).
% 0.92/0.88  tff(6,plain,
% 0.92/0.88      ((~(~?[W0: $i] : aElementOf0(W0, xX))) <=> (~(~?[W0: $i] : aElementOf0(W0, xX)))),
% 0.92/0.88      inference(monotonicity,[status(thm)],[5])).
% 0.92/0.88  tff(7,plain,
% 0.92/0.88      ((~(~?[W0: $i] : aElementOf0(W0, xX))) <=> ?[W0: $i] : aElementOf0(W0, xX)),
% 0.92/0.88      inference(transitivity,[status(thm)],[6, 4])).
% 0.92/0.88  tff(8,axiom,(((aSet0(xX) & ![W0: $i] : ((aElementOf0(W0, xX) => (((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))) & aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) & (sbrdtbr0(W0) = xk))) & ((((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))) | aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) & (sbrdtbr0(W0) = xk)) => aElementOf0(W0, xX)))) & (xX = slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk))) & (~(~?[W0: $i] : aElementOf0(W0, xX)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__4826')).
% 0.92/0.88  tff(9,plain,
% 0.92/0.88      (~(~?[W0: $i] : aElementOf0(W0, xX))),
% 0.92/0.88      inference(and_elim,[status(thm)],[8])).
% 0.92/0.88  tff(10,plain,
% 0.92/0.88      (?[W0: $i] : aElementOf0(W0, xX)),
% 0.92/0.88      inference(modus_ponens,[status(thm)],[9, 7])).
% 0.92/0.88  tff(11,plain,
% 0.92/0.88      (?[W0: $i] : aElementOf0(W0, xX)),
% 0.92/0.88      inference(modus_ponens,[status(thm)],[10, 3])).
% 0.92/0.88  tff(12,plain,
% 0.92/0.88      (?[W0: $i] : aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk))),
% 0.92/0.88      inference(modus_ponens,[status(thm)],[11, 2])).
% 0.92/0.88  tff(13,plain,(
% 0.92/0.88      aElementOf0(W0!43, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk))),
% 0.92/0.88      inference(skolemize,[status(sab)],[12])).
% 0.92/0.88  tff(14,plain,
% 0.92/0.88      ((aElementOf0(W0!43, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W0!43) = xk)) | (~(aSubsetOf0(W0!43, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W2_39(W0!43, xi), W0!43)) | aElementOf0(tptp_fun_W2_39(W0!43, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi)))))))) | (~aElementOf0(W0!43, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)))),
% 0.92/0.88      inference(tautology,[status(thm)],[])).
% 0.92/0.88  tff(15,plain,
% 0.92/0.88      (aElementOf0(W0!43, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W0!43) = xk)) | (~(aSubsetOf0(W0!43, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W2_39(W0!43, xi), W0!43)) | aElementOf0(tptp_fun_W2_39(W0!43, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi)))))))),
% 0.92/0.88      inference(unit_resolution,[status(thm)],[14, 13])).
% 0.92/0.88  tff(16,plain,
% 0.92/0.88      (^[W0: $i] : refl((~((~((~aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk))) | (~((~aSet0(W0)) | (~(sbrdtbr0(W0) = xk)) | (~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))) | (~(aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_42(W0), W0)) | aElementOf0(tptp_fun_W1_42(W0), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))))))) <=> (~((~((~aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk))) | (~((~aSet0(W0)) | (~(sbrdtbr0(W0) = xk)) | (~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))) | (~(aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_42(W0), W0)) | aElementOf0(tptp_fun_W1_42(W0), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))))))))),
% 0.92/0.88      inference(bind,[status(th)],[])).
% 0.92/0.88  tff(17,plain,
% 0.92/0.88      (![W0: $i] : (~((~((~aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk))) | (~((~aSet0(W0)) | (~(sbrdtbr0(W0) = xk)) | (~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))) | (~(aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_42(W0), W0)) | aElementOf0(tptp_fun_W1_42(W0), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))))))) <=> ![W0: $i] : (~((~((~aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk))) | (~((~aSet0(W0)) | (~(sbrdtbr0(W0) = xk)) | (~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))) | (~(aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_42(W0), W0)) | aElementOf0(tptp_fun_W1_42(W0), sdtlpdtrp0(xN, szszuzczcdt0(xi)))))))))))))),
% 0.92/0.88      inference(quant_intro,[status(thm)],[16])).
% 0.92/0.88  tff(18,plain,
% 0.92/0.88      (^[W0: $i] : rewrite((~((~((~aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk))) | (~((~aSet0(W0)) | (~(sbrdtbr0(W0) = xk)) | (~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))) | (~(aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_42(W0), W0)) | aElementOf0(tptp_fun_W1_42(W0), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))))))) <=> (~((~((~aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk))) | (~((~aSet0(W0)) | (~(sbrdtbr0(W0) = xk)) | (~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))) | (~(aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_42(W0), W0)) | aElementOf0(tptp_fun_W1_42(W0), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))))))))),
% 0.92/0.88      inference(bind,[status(th)],[])).
% 0.92/0.88  tff(19,plain,
% 0.92/0.88      (![W0: $i] : (~((~((~aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk))) | (~((~aSet0(W0)) | (~(sbrdtbr0(W0) = xk)) | (~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))) | (~(aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_42(W0), W0)) | aElementOf0(tptp_fun_W1_42(W0), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))))))) <=> ![W0: $i] : (~((~((~aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk))) | (~((~aSet0(W0)) | (~(sbrdtbr0(W0) = xk)) | (~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))) | (~(aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_42(W0), W0)) | aElementOf0(tptp_fun_W1_42(W0), sdtlpdtrp0(xN, szszuzczcdt0(xi)))))))))))))),
% 0.92/0.88      inference(quant_intro,[status(thm)],[18])).
% 0.92/0.88  tff(20,plain,
% 0.92/0.88      (![W0: $i] : (~((~((~aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk))) | (~((~aSet0(W0)) | (~(sbrdtbr0(W0) = xk)) | (~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))) | (~(aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_42(W0), W0)) | aElementOf0(tptp_fun_W1_42(W0), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))))))) <=> ![W0: $i] : (~((~((~aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk))) | (~((~aSet0(W0)) | (~(sbrdtbr0(W0) = xk)) | (~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))) | (~(aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_42(W0), W0)) | aElementOf0(tptp_fun_W1_42(W0), sdtlpdtrp0(xN, szszuzczcdt0(xi)))))))))))))),
% 0.92/0.88      inference(transitivity,[status(thm)],[19, 17])).
% 0.92/0.88  tff(21,plain,
% 0.92/0.88      (^[W0: $i] : trans(monotonicity(rewrite(((~aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk))) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) & aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) & (sbrdtbr0(W0) = xk))) <=> ((~aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk))) | (~((~aSet0(W0)) | (~(sbrdtbr0(W0) = xk)) | (~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))), trans(monotonicity(rewrite(((~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_42(W0), W0)) | aElementOf0(tptp_fun_W1_42(W0), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))) <=> (~(aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_42(W0), W0)) | aElementOf0(tptp_fun_W1_42(W0), sdtlpdtrp0(xN, szszuzczcdt0(xi)))))))))), ((aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~(sbrdtbr0(W0) = xk)) | ((~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_42(W0), W0)) | aElementOf0(tptp_fun_W1_42(W0), sdtlpdtrp0(xN, szszuzczcdt0(xi)))))))) <=> (aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_42(W0), W0)) | aElementOf0(tptp_fun_W1_42(W0), sdtlpdtrp0(xN, szszuzczcdt0(xi)))))))))))), rewrite((aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_42(W0), W0)) | aElementOf0(tptp_fun_W1_42(W0), sdtlpdtrp0(xN, szszuzczcdt0(xi)))))))))) <=> (aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_42(W0), W0)) | aElementOf0(tptp_fun_W1_42(W0), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))))), ((aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~(sbrdtbr0(W0) = xk)) | ((~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_42(W0), W0)) | aElementOf0(tptp_fun_W1_42(W0), sdtlpdtrp0(xN, szszuzczcdt0(xi)))))))) <=> (aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_42(W0), W0)) | aElementOf0(tptp_fun_W1_42(W0), sdtlpdtrp0(xN, szszuzczcdt0(xi)))))))))))), ((((~aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk))) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) & aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) & (sbrdtbr0(W0) = xk))) & (aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~(sbrdtbr0(W0) = xk)) | ((~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_42(W0), W0)) | aElementOf0(tptp_fun_W1_42(W0), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))) <=> (((~aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk))) | (~((~aSet0(W0)) | (~(sbrdtbr0(W0) = xk)) | (~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))))))) & (aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_42(W0), W0)) | aElementOf0(tptp_fun_W1_42(W0), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))))))), rewrite((((~aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk))) | (~((~aSet0(W0)) | (~(sbrdtbr0(W0) = xk)) | (~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))))))) & (aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_42(W0), W0)) | aElementOf0(tptp_fun_W1_42(W0), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))))) <=> (~((~((~aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk))) | (~((~aSet0(W0)) | (~(sbrdtbr0(W0) = xk)) | (~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))) | (~(aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_42(W0), W0)) | aElementOf0(tptp_fun_W1_42(W0), sdtlpdtrp0(xN, szszuzczcdt0(xi)))))))))))))), ((((~aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk))) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) & aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) & (sbrdtbr0(W0) = xk))) & (aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~(sbrdtbr0(W0) = xk)) | ((~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_42(W0), W0)) | aElementOf0(tptp_fun_W1_42(W0), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))) <=> (~((~((~aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk))) | (~((~aSet0(W0)) | (~(sbrdtbr0(W0) = xk)) | (~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))) | (~(aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_42(W0), W0)) | aElementOf0(tptp_fun_W1_42(W0), sdtlpdtrp0(xN, szszuzczcdt0(xi)))))))))))))))),
% 0.92/0.89      inference(bind,[status(th)],[])).
% 0.92/0.89  tff(22,plain,
% 0.92/0.89      (![W0: $i] : (((~aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk))) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) & aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) & (sbrdtbr0(W0) = xk))) & (aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~(sbrdtbr0(W0) = xk)) | ((~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_42(W0), W0)) | aElementOf0(tptp_fun_W1_42(W0), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))) <=> ![W0: $i] : (~((~((~aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk))) | (~((~aSet0(W0)) | (~(sbrdtbr0(W0) = xk)) | (~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))) | (~(aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_42(W0), W0)) | aElementOf0(tptp_fun_W1_42(W0), sdtlpdtrp0(xN, szszuzczcdt0(xi)))))))))))))),
% 0.92/0.89      inference(quant_intro,[status(thm)],[21])).
% 0.92/0.89  tff(23,plain,
% 0.92/0.89      (^[W0: $i] : rewrite((((~aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk))) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) & aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) & (sbrdtbr0(W0) = xk))) & ((((~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_42(W0), W0)) | aElementOf0(tptp_fun_W1_42(W0), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))) | (~(sbrdtbr0(W0) = xk))) | aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)))) <=> (((~aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk))) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) & aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) & (sbrdtbr0(W0) = xk))) & (aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~(sbrdtbr0(W0) = xk)) | ((~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_42(W0), W0)) | aElementOf0(tptp_fun_W1_42(W0), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))))),
% 0.92/0.89      inference(bind,[status(th)],[])).
% 0.92/0.89  tff(24,plain,
% 0.92/0.89      (![W0: $i] : (((~aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk))) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) & aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) & (sbrdtbr0(W0) = xk))) & ((((~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_42(W0), W0)) | aElementOf0(tptp_fun_W1_42(W0), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))) | (~(sbrdtbr0(W0) = xk))) | aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)))) <=> ![W0: $i] : (((~aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk))) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) & aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) & (sbrdtbr0(W0) = xk))) & (aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~(sbrdtbr0(W0) = xk)) | ((~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_42(W0), W0)) | aElementOf0(tptp_fun_W1_42(W0), sdtlpdtrp0(xN, szszuzczcdt0(xi)))))))))),
% 0.92/0.89      inference(quant_intro,[status(thm)],[23])).
% 0.92/0.89  tff(25,plain,
% 0.92/0.89      (^[W0: $i] : rewrite((((~aElementOf0(W0, xX)) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) & aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) & (sbrdtbr0(W0) = xk))) & ((~((aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))))) & (sbrdtbr0(W0) = xk))) | aElementOf0(W0, xX))) <=> (((~aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk))) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) & aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) & (sbrdtbr0(W0) = xk))) & ((~((aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))))) & (sbrdtbr0(W0) = xk))) | aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)))))),
% 0.92/0.89      inference(bind,[status(th)],[])).
% 0.92/0.89  tff(26,plain,
% 0.92/0.89      (![W0: $i] : (((~aElementOf0(W0, xX)) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) & aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) & (sbrdtbr0(W0) = xk))) & ((~((aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))))) & (sbrdtbr0(W0) = xk))) | aElementOf0(W0, xX))) <=> ![W0: $i] : (((~aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk))) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) & aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) & (sbrdtbr0(W0) = xk))) & ((~((aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))))) & (sbrdtbr0(W0) = xk))) | aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk))))),
% 0.92/0.89      inference(quant_intro,[status(thm)],[25])).
% 0.92/0.89  tff(27,plain,
% 0.92/0.89      (![W0: $i] : (((~aElementOf0(W0, xX)) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) & aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) & (sbrdtbr0(W0) = xk))) & ((~((aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))))) & (sbrdtbr0(W0) = xk))) | aElementOf0(W0, xX))) <=> ![W0: $i] : (((~aElementOf0(W0, xX)) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) & aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) & (sbrdtbr0(W0) = xk))) & ((~((aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))))) & (sbrdtbr0(W0) = xk))) | aElementOf0(W0, xX)))),
% 0.92/0.89      inference(rewrite,[status(thm)],[])).
% 0.92/0.89  tff(28,plain,
% 0.92/0.89      (^[W0: $i] : rewrite(((aElementOf0(W0, xX) => (((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))) & aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) & (sbrdtbr0(W0) = xk))) & ((((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))) | aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) & (sbrdtbr0(W0) = xk)) => aElementOf0(W0, xX))) <=> (((~aElementOf0(W0, xX)) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) & aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) & (sbrdtbr0(W0) = xk))) & ((~((aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))))) & (sbrdtbr0(W0) = xk))) | aElementOf0(W0, xX))))),
% 0.92/0.89      inference(bind,[status(th)],[])).
% 0.92/0.89  tff(29,plain,
% 0.92/0.89      (![W0: $i] : ((aElementOf0(W0, xX) => (((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))) & aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) & (sbrdtbr0(W0) = xk))) & ((((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))) | aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) & (sbrdtbr0(W0) = xk)) => aElementOf0(W0, xX))) <=> ![W0: $i] : (((~aElementOf0(W0, xX)) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) & aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) & (sbrdtbr0(W0) = xk))) & ((~((aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))))) & (sbrdtbr0(W0) = xk))) | aElementOf0(W0, xX)))),
% 0.92/0.89      inference(quant_intro,[status(thm)],[28])).
% 0.92/0.89  tff(30,plain,
% 0.92/0.89      ((aSet0(xX) & ![W0: $i] : ((aElementOf0(W0, xX) => (((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))) & aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) & (sbrdtbr0(W0) = xk))) & ((((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))) | aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) & (sbrdtbr0(W0) = xk)) => aElementOf0(W0, xX)))) & (xX = slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk))),
% 0.92/0.89      inference(and_elim,[status(thm)],[8])).
% 0.92/0.89  tff(31,plain,
% 0.92/0.89      (aSet0(xX) & ![W0: $i] : ((aElementOf0(W0, xX) => (((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))) & aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) & (sbrdtbr0(W0) = xk))) & ((((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))) | aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) & (sbrdtbr0(W0) = xk)) => aElementOf0(W0, xX)))),
% 0.92/0.89      inference(and_elim,[status(thm)],[30])).
% 0.92/0.89  tff(32,plain,
% 0.92/0.89      (![W0: $i] : ((aElementOf0(W0, xX) => (((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))) & aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) & (sbrdtbr0(W0) = xk))) & ((((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))) | aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) & (sbrdtbr0(W0) = xk)) => aElementOf0(W0, xX)))),
% 0.92/0.89      inference(and_elim,[status(thm)],[31])).
% 0.92/0.89  tff(33,plain,
% 0.92/0.89      (![W0: $i] : (((~aElementOf0(W0, xX)) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) & aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) & (sbrdtbr0(W0) = xk))) & ((~((aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))))) & (sbrdtbr0(W0) = xk))) | aElementOf0(W0, xX)))),
% 0.92/0.89      inference(modus_ponens,[status(thm)],[32, 29])).
% 0.92/0.89  tff(34,plain,
% 0.92/0.89      (![W0: $i] : (((~aElementOf0(W0, xX)) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) & aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) & (sbrdtbr0(W0) = xk))) & ((~((aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))))) & (sbrdtbr0(W0) = xk))) | aElementOf0(W0, xX)))),
% 0.92/0.89      inference(modus_ponens,[status(thm)],[33, 27])).
% 0.92/0.89  tff(35,plain,
% 0.92/0.89      (![W0: $i] : (((~aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk))) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) & aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) & (sbrdtbr0(W0) = xk))) & ((~((aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))))) & (sbrdtbr0(W0) = xk))) | aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk))))),
% 0.92/0.89      inference(modus_ponens,[status(thm)],[34, 26])).
% 0.92/0.89  tff(36,plain,(
% 0.92/0.89      ![W0: $i] : (((~aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk))) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) & aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) & (sbrdtbr0(W0) = xk))) & ((((~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_42(W0), W0)) | aElementOf0(tptp_fun_W1_42(W0), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))) | (~(sbrdtbr0(W0) = xk))) | aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk))))),
% 0.92/0.89      inference(skolemize,[status(sab)],[35])).
% 0.92/0.89  tff(37,plain,
% 0.92/0.89      (![W0: $i] : (((~aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk))) | (aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) & aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) & (sbrdtbr0(W0) = xk))) & (aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~(sbrdtbr0(W0) = xk)) | ((~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) & ((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_42(W0), W0)) | aElementOf0(tptp_fun_W1_42(W0), sdtlpdtrp0(xN, szszuzczcdt0(xi)))))))))),
% 0.92/0.89      inference(modus_ponens,[status(thm)],[36, 24])).
% 0.92/0.89  tff(38,plain,
% 0.92/0.89      (![W0: $i] : (~((~((~aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk))) | (~((~aSet0(W0)) | (~(sbrdtbr0(W0) = xk)) | (~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))) | (~(aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_42(W0), W0)) | aElementOf0(tptp_fun_W1_42(W0), sdtlpdtrp0(xN, szszuzczcdt0(xi)))))))))))))),
% 0.92/0.89      inference(modus_ponens,[status(thm)],[37, 22])).
% 0.92/0.89  tff(39,plain,
% 0.92/0.89      (![W0: $i] : (~((~((~aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk))) | (~((~aSet0(W0)) | (~(sbrdtbr0(W0) = xk)) | (~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))) | (~(aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_42(W0), W0)) | aElementOf0(tptp_fun_W1_42(W0), sdtlpdtrp0(xN, szszuzczcdt0(xi)))))))))))))),
% 0.92/0.89      inference(modus_ponens,[status(thm)],[38, 20])).
% 0.92/0.89  tff(40,plain,
% 0.92/0.89      ((~![W0: $i] : (~((~((~aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk))) | (~((~aSet0(W0)) | (~(sbrdtbr0(W0) = xk)) | (~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))) | (~(aElementOf0(W0, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~(sbrdtbr0(W0) = xk)) | (~(aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~((~aSet0(W0)) | (~((~aElementOf0(tptp_fun_W1_42(W0), W0)) | aElementOf0(tptp_fun_W1_42(W0), sdtlpdtrp0(xN, szszuzczcdt0(xi)))))))))))))) | (~((~((~aElementOf0(W0!43, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk))) | (~((~aSet0(W0!43)) | (~(sbrdtbr0(W0!43) = xk)) | (~aSubsetOf0(W0!43, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0!43)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))) | (~(aElementOf0(W0!43, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~(sbrdtbr0(W0!43) = xk)) | (~(aSubsetOf0(W0!43, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~((~aSet0(W0!43)) | (~((~aElementOf0(tptp_fun_W1_42(W0!43), W0!43)) | aElementOf0(tptp_fun_W1_42(W0!43), sdtlpdtrp0(xN, szszuzczcdt0(xi)))))))))))))),
% 0.92/0.89      inference(quant_inst,[status(thm)],[])).
% 0.92/0.89  tff(41,plain,
% 0.92/0.89      (~((~((~aElementOf0(W0!43, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk))) | (~((~aSet0(W0!43)) | (~(sbrdtbr0(W0!43) = xk)) | (~aSubsetOf0(W0!43, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0!43)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))) | (~(aElementOf0(W0!43, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~(sbrdtbr0(W0!43) = xk)) | (~(aSubsetOf0(W0!43, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~((~aSet0(W0!43)) | (~((~aElementOf0(tptp_fun_W1_42(W0!43), W0!43)) | aElementOf0(tptp_fun_W1_42(W0!43), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))))))),
% 0.92/0.89      inference(unit_resolution,[status(thm)],[40, 39])).
% 0.92/0.89  tff(42,plain,
% 0.92/0.89      (((~((~aElementOf0(W0!43, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk))) | (~((~aSet0(W0!43)) | (~(sbrdtbr0(W0!43) = xk)) | (~aSubsetOf0(W0!43, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0!43)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))) | (~(aElementOf0(W0!43, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~(sbrdtbr0(W0!43) = xk)) | (~(aSubsetOf0(W0!43, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~((~aSet0(W0!43)) | (~((~aElementOf0(tptp_fun_W1_42(W0!43), W0!43)) | aElementOf0(tptp_fun_W1_42(W0!43), sdtlpdtrp0(xN, szszuzczcdt0(xi)))))))))))) | ((~aElementOf0(W0!43, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk))) | (~((~aSet0(W0!43)) | (~(sbrdtbr0(W0!43) = xk)) | (~aSubsetOf0(W0!43, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0!43)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))),
% 0.92/0.89      inference(tautology,[status(thm)],[])).
% 0.92/0.89  tff(43,plain,
% 0.92/0.89      ((~aElementOf0(W0!43, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk))) | (~((~aSet0(W0!43)) | (~(sbrdtbr0(W0!43) = xk)) | (~aSubsetOf0(W0!43, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0!43)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))))))),
% 0.92/0.89      inference(unit_resolution,[status(thm)],[42, 41])).
% 0.92/0.89  tff(44,plain,
% 0.92/0.89      ((~((~aElementOf0(W0!43, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk))) | (~((~aSet0(W0!43)) | (~(sbrdtbr0(W0!43) = xk)) | (~aSubsetOf0(W0!43, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0!43)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))) | (~aElementOf0(W0!43, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk))) | (~((~aSet0(W0!43)) | (~(sbrdtbr0(W0!43) = xk)) | (~aSubsetOf0(W0!43, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0!43)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))))))),
% 0.92/0.89      inference(tautology,[status(thm)],[])).
% 0.92/0.89  tff(45,plain,
% 0.92/0.89      ((~((~aElementOf0(W0!43, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk))) | (~((~aSet0(W0!43)) | (~(sbrdtbr0(W0!43) = xk)) | (~aSubsetOf0(W0!43, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0!43)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))) | (~((~aSet0(W0!43)) | (~(sbrdtbr0(W0!43) = xk)) | (~aSubsetOf0(W0!43, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0!43)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))))))),
% 0.92/0.89      inference(unit_resolution,[status(thm)],[44, 13])).
% 0.92/0.89  tff(46,plain,
% 0.92/0.89      (~((~aSet0(W0!43)) | (~(sbrdtbr0(W0!43) = xk)) | (~aSubsetOf0(W0!43, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0!43)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))))),
% 0.92/0.89      inference(unit_resolution,[status(thm)],[45, 43])).
% 0.92/0.89  tff(47,plain,
% 0.92/0.89      (((~aSet0(W0!43)) | (~(sbrdtbr0(W0!43) = xk)) | (~aSubsetOf0(W0!43, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0!43)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))))) | aSet0(W0!43)),
% 0.92/0.89      inference(tautology,[status(thm)],[])).
% 0.92/0.89  tff(48,plain,
% 0.92/0.89      (aSet0(W0!43)),
% 0.92/0.89      inference(unit_resolution,[status(thm)],[47, 46])).
% 0.92/0.89  tff(49,plain,
% 0.92/0.89      (aElementOf0(xi, szNzAzT0) <=> aElementOf0(xi, szDzozmdt0(xN))),
% 0.92/0.89      inference(rewrite,[status(thm)],[])).
% 0.92/0.89  tff(50,plain,
% 0.92/0.89      (aElementOf0(xi, szNzAzT0) <=> aElementOf0(xi, szNzAzT0)),
% 0.92/0.89      inference(rewrite,[status(thm)],[])).
% 0.92/0.89  tff(51,axiom,(aElementOf0(xi, szNzAzT0) & (sdtlpdtrp0(xd, xi) = xx)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__4806')).
% 0.92/0.89  tff(52,plain,
% 0.92/0.89      (aElementOf0(xi, szNzAzT0)),
% 0.92/0.89      inference(and_elim,[status(thm)],[51])).
% 0.92/0.89  tff(53,plain,
% 0.92/0.89      (aElementOf0(xi, szNzAzT0)),
% 0.92/0.89      inference(modus_ponens,[status(thm)],[52, 50])).
% 0.92/0.89  tff(54,plain,
% 0.92/0.89      (aElementOf0(xi, szDzozmdt0(xN))),
% 0.92/0.89      inference(modus_ponens,[status(thm)],[53, 49])).
% 0.92/0.89  tff(55,plain,
% 0.92/0.89      (^[W0: $i] : refl(((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1)) | (~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | (~aElementOf0(tptp_fun_W2_39(W1, W0), W1)) | aElementOf0(tptp_fun_W2_39(W1, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0))))))))))) <=> ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1)) | (~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | (~aElementOf0(tptp_fun_W2_39(W1, W0), W1)) | aElementOf0(tptp_fun_W2_39(W1, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0))))))))))))),
% 0.92/0.89      inference(bind,[status(th)],[])).
% 0.92/0.89  tff(56,plain,
% 0.92/0.89      (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1)) | (~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | (~aElementOf0(tptp_fun_W2_39(W1, W0), W1)) | aElementOf0(tptp_fun_W2_39(W1, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0))))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1)) | (~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | (~aElementOf0(tptp_fun_W2_39(W1, W0), W1)) | aElementOf0(tptp_fun_W2_39(W1, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0)))))))))))),
% 0.92/0.89      inference(quant_intro,[status(thm)],[55])).
% 0.92/0.89  tff(57,plain,
% 0.92/0.89      (^[W0: $i] : rewrite(((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1)) | (~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | (~aElementOf0(tptp_fun_W2_39(W1, W0), W1)) | aElementOf0(tptp_fun_W2_39(W1, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0))))))))))) <=> ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1)) | (~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | (~aElementOf0(tptp_fun_W2_39(W1, W0), W1)) | aElementOf0(tptp_fun_W2_39(W1, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0))))))))))))),
% 0.92/0.89      inference(bind,[status(th)],[])).
% 0.92/0.89  tff(58,plain,
% 0.92/0.89      (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1)) | (~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | (~aElementOf0(tptp_fun_W2_39(W1, W0), W1)) | aElementOf0(tptp_fun_W2_39(W1, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0))))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1)) | (~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | (~aElementOf0(tptp_fun_W2_39(W1, W0), W1)) | aElementOf0(tptp_fun_W2_39(W1, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0)))))))))))),
% 0.92/0.89      inference(quant_intro,[status(thm)],[57])).
% 0.92/0.89  tff(59,plain,
% 0.92/0.89      (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1)) | (~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | (~aElementOf0(tptp_fun_W2_39(W1, W0), W1)) | aElementOf0(tptp_fun_W2_39(W1, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0))))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1)) | (~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | (~aElementOf0(tptp_fun_W2_39(W1, W0), W1)) | aElementOf0(tptp_fun_W2_39(W1, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0)))))))))))),
% 0.92/0.89      inference(transitivity,[status(thm)],[58, 56])).
% 0.92/0.89  tff(60,plain,
% 0.92/0.89      (^[W0: $i] : rewrite(((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1)) | (~aSet0(W1)) | ((~aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk))) & ((~(sbrdtbr0(W1) = xk)) | ((~aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & (~((~aElementOf0(tptp_fun_W2_39(W1, W0), W1)) | aElementOf0(tptp_fun_W2_39(W1, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0)))))))))) <=> ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1)) | (~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | (~aElementOf0(tptp_fun_W2_39(W1, W0), W1)) | aElementOf0(tptp_fun_W2_39(W1, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0))))))))))))),
% 0.92/0.89      inference(bind,[status(th)],[])).
% 0.92/0.89  tff(61,plain,
% 0.92/0.89      (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1)) | (~aSet0(W1)) | ((~aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk))) & ((~(sbrdtbr0(W1) = xk)) | ((~aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & (~((~aElementOf0(tptp_fun_W2_39(W1, W0), W1)) | aElementOf0(tptp_fun_W2_39(W1, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0)))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1)) | (~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | (~aElementOf0(tptp_fun_W2_39(W1, W0), W1)) | aElementOf0(tptp_fun_W2_39(W1, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0)))))))))))),
% 0.92/0.89      inference(quant_intro,[status(thm)],[60])).
% 0.92/0.89  tff(62,plain,
% 0.92/0.89      (^[W0: $i] : rewrite(((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : (((~aSet0(W1)) | ((~aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk))) & (((~aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & (~((~aElementOf0(tptp_fun_W2_39(W1, W0), W1)) | aElementOf0(tptp_fun_W2_39(W1, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) | (~(sbrdtbr0(W1) = xk))))) | (sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1)))) <=> ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1)) | (~aSet0(W1)) | ((~aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk))) & ((~(sbrdtbr0(W1) = xk)) | ((~aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & (~((~aElementOf0(tptp_fun_W2_39(W1, W0), W1)) | aElementOf0(tptp_fun_W2_39(W1, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0)))))))))))),
% 0.92/0.89      inference(bind,[status(th)],[])).
% 0.92/0.89  tff(63,plain,
% 0.92/0.89      (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : (((~aSet0(W1)) | ((~aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk))) & (((~aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & (~((~aElementOf0(tptp_fun_W2_39(W1, W0), W1)) | aElementOf0(tptp_fun_W2_39(W1, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) | (~(sbrdtbr0(W1) = xk))))) | (sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1)))) <=> ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1)) | (~aSet0(W1)) | ((~aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk))) & ((~(sbrdtbr0(W1) = xk)) | ((~aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & (~((~aElementOf0(tptp_fun_W2_39(W1, W0), W1)) | aElementOf0(tptp_fun_W2_39(W1, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0))))))))))),
% 0.92/0.89      inference(quant_intro,[status(thm)],[62])).
% 0.92/0.89  tff(64,plain,
% 0.92/0.89      (^[W0: $i] : rewrite(((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | ((aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))))) & (sbrdtbr0(W1) = xk))))) | (sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1)))) <=> ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | ((aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))))) & (sbrdtbr0(W1) = xk))))) | (sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1)))))),
% 0.92/0.90      inference(bind,[status(th)],[])).
% 0.92/0.90  tff(65,plain,
% 0.92/0.90      (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | ((aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))))) & (sbrdtbr0(W1) = xk))))) | (sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1)))) <=> ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | ((aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))))) & (sbrdtbr0(W1) = xk))))) | (sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1))))),
% 0.92/0.90      inference(quant_intro,[status(thm)],[64])).
% 0.92/0.90  tff(66,plain,
% 0.92/0.90      (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | ((aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))))) & (sbrdtbr0(W1) = xk))))) | (sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1)))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | ((aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))))) & (sbrdtbr0(W1) = xk))))) | (sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1))))),
% 0.92/0.90      inference(rewrite,[status(thm)],[])).
% 0.92/0.90  tff(67,plain,
% 0.92/0.90      (^[W0: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: $i] : trans(monotonicity(rewrite((aSet0(W1) & (((![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & (sbrdtbr0(W1) = xk)) | aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)))) <=> (aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | ((aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))))) & (sbrdtbr0(W1) = xk))))), (((aSet0(W1) & (((![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & (sbrdtbr0(W1) = xk)) | aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)))) => (sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1))) <=> ((aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | ((aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))))) & (sbrdtbr0(W1) = xk)))) => (sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1))))), rewrite(((aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | ((aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))))) & (sbrdtbr0(W1) = xk)))) => (sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1))) <=> ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | ((aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))))) & (sbrdtbr0(W1) = xk))))) | (sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1)))), (((aSet0(W1) & (((![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & (sbrdtbr0(W1) = xk)) | aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)))) => (sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1))) <=> ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | ((aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))))) & (sbrdtbr0(W1) = xk))))) | (sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1)))))), (![W1: $i] : ((aSet0(W1) & (((![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & (sbrdtbr0(W1) = xk)) | aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)))) => (sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1))) <=> ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | ((aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))))) & (sbrdtbr0(W1) = xk))))) | (sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1))))), ((aElementOf0(W0, szNzAzT0) => ![W1: $i] : ((aSet0(W1) & (((![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & (sbrdtbr0(W1) = xk)) | aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)))) => (sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1)))) <=> (aElementOf0(W0, szNzAzT0) => ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | ((aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))))) & (sbrdtbr0(W1) = xk))))) | (sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1)))))), rewrite((aElementOf0(W0, szNzAzT0) => ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | ((aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))))) & (sbrdtbr0(W1) = xk))))) | (sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1)))) <=> ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | ((aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))))) & (sbrdtbr0(W1) = xk))))) | (sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1))))), ((aElementOf0(W0, szNzAzT0) => ![W1: $i] : ((aSet0(W1) & (((![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & (sbrdtbr0(W1) = xk)) | aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)))) => (sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1)))) <=> ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | ((aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))))) & (sbrdtbr0(W1) = xk))))) | (sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1))))))),
% 0.92/0.90      inference(bind,[status(th)],[])).
% 0.92/0.90  tff(68,plain,
% 0.92/0.90      (![W0: $i] : (aElementOf0(W0, szNzAzT0) => ![W1: $i] : ((aSet0(W1) & (((![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & (sbrdtbr0(W1) = xk)) | aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)))) => (sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1)))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | ((aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))))) & (sbrdtbr0(W1) = xk))))) | (sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1))))),
% 0.92/0.90      inference(quant_intro,[status(thm)],[67])).
% 0.92/0.90  tff(69,axiom,((aFunction0(xd) & (szDzozmdt0(xd) = szNzAzT0)) & ![W0: $i] : (aElementOf0(W0, szNzAzT0) => ![W1: $i] : ((aSet0(W1) & (((![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & (sbrdtbr0(W1) = xk)) | aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)))) => (sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__4730')).
% 0.92/0.90  tff(70,plain,
% 0.92/0.90      (![W0: $i] : (aElementOf0(W0, szNzAzT0) => ![W1: $i] : ((aSet0(W1) & (((![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & (sbrdtbr0(W1) = xk)) | aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)))) => (sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1))))),
% 0.92/0.90      inference(and_elim,[status(thm)],[69])).
% 0.92/0.90  tff(71,plain,
% 0.92/0.90      (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | ((aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))))) & (sbrdtbr0(W1) = xk))))) | (sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1))))),
% 0.92/0.90      inference(modus_ponens,[status(thm)],[70, 68])).
% 0.92/0.90  tff(72,plain,
% 0.92/0.90      (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | ((aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))))) & (sbrdtbr0(W1) = xk))))) | (sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1))))),
% 0.92/0.90      inference(modus_ponens,[status(thm)],[71, 66])).
% 0.92/0.90  tff(73,plain,
% 0.92/0.90      (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((~(aSet0(W1) & (aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | ((aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))))) & (sbrdtbr0(W1) = xk))))) | (sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1))))),
% 0.92/0.90      inference(modus_ponens,[status(thm)],[72, 65])).
% 0.92/0.90  tff(74,plain,(
% 0.92/0.90      ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : (((~aSet0(W1)) | ((~aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk))) & (((~aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & (~((~aElementOf0(tptp_fun_W2_39(W1, W0), W1)) | aElementOf0(tptp_fun_W2_39(W1, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) | (~(sbrdtbr0(W1) = xk))))) | (sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1))))),
% 0.92/0.90      inference(skolemize,[status(sab)],[73])).
% 0.92/0.90  tff(75,plain,
% 0.92/0.90      (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1)) | (~aSet0(W1)) | ((~aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk))) & ((~(sbrdtbr0(W1) = xk)) | ((~aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & (~((~aElementOf0(tptp_fun_W2_39(W1, W0), W1)) | aElementOf0(tptp_fun_W2_39(W1, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0))))))))))),
% 0.92/0.90      inference(modus_ponens,[status(thm)],[74, 63])).
% 0.92/0.90  tff(76,plain,
% 0.92/0.90      (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1)) | (~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | (~aElementOf0(tptp_fun_W2_39(W1, W0), W1)) | aElementOf0(tptp_fun_W2_39(W1, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0)))))))))))),
% 0.92/0.90      inference(modus_ponens,[status(thm)],[75, 61])).
% 0.92/0.90  tff(77,plain,
% 0.92/0.90      (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1)) | (~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | (~aElementOf0(tptp_fun_W2_39(W1, W0), W1)) | aElementOf0(tptp_fun_W2_39(W1, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0)))))))))))),
% 0.92/0.90      inference(modus_ponens,[status(thm)],[76, 59])).
% 0.92/0.90  tff(78,plain,
% 0.92/0.90      (((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1)) | (~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | (~aElementOf0(tptp_fun_W2_39(W1, W0), W1)) | aElementOf0(tptp_fun_W2_39(W1, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0)))))))))))) | ((~aElementOf0(xi, szDzozmdt0(xN))) | ![W1: $i] : ((~aSet0(W1)) | (sdtlpdtrp0(xd, xi) = sdtlpdtrp0(sdtlpdtrp0(xC, xi), W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W2_39(W1, xi), W1)) | aElementOf0(tptp_fun_W2_39(W1, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi)))))))))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1)) | (~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | (~aElementOf0(tptp_fun_W2_39(W1, W0), W1)) | aElementOf0(tptp_fun_W2_39(W1, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0)))))))))))) | (~aElementOf0(xi, szDzozmdt0(xN))) | ![W1: $i] : ((~aSet0(W1)) | (sdtlpdtrp0(xd, xi) = sdtlpdtrp0(sdtlpdtrp0(xC, xi), W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W2_39(W1, xi), W1)) | aElementOf0(tptp_fun_W2_39(W1, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi)))))))))))),
% 0.92/0.90      inference(rewrite,[status(thm)],[])).
% 0.92/0.90  tff(79,plain,
% 0.92/0.90      (((~aElementOf0(xi, szDzozmdt0(xN))) | ![W1: $i] : ((sdtlpdtrp0(xd, xi) = sdtlpdtrp0(sdtlpdtrp0(xC, xi), W1)) | (~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W2_39(W1, xi), W1)) | aElementOf0(tptp_fun_W2_39(W1, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))))) <=> ((~aElementOf0(xi, szDzozmdt0(xN))) | ![W1: $i] : ((~aSet0(W1)) | (sdtlpdtrp0(xd, xi) = sdtlpdtrp0(sdtlpdtrp0(xC, xi), W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W2_39(W1, xi), W1)) | aElementOf0(tptp_fun_W2_39(W1, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi)))))))))))),
% 0.92/0.90      inference(rewrite,[status(thm)],[])).
% 0.92/0.90  tff(80,plain,
% 0.92/0.90      (((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1)) | (~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | (~aElementOf0(tptp_fun_W2_39(W1, W0), W1)) | aElementOf0(tptp_fun_W2_39(W1, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0)))))))))))) | ((~aElementOf0(xi, szDzozmdt0(xN))) | ![W1: $i] : ((sdtlpdtrp0(xd, xi) = sdtlpdtrp0(sdtlpdtrp0(xC, xi), W1)) | (~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W2_39(W1, xi), W1)) | aElementOf0(tptp_fun_W2_39(W1, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi)))))))))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1)) | (~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | (~aElementOf0(tptp_fun_W2_39(W1, W0), W1)) | aElementOf0(tptp_fun_W2_39(W1, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0)))))))))))) | ((~aElementOf0(xi, szDzozmdt0(xN))) | ![W1: $i] : ((~aSet0(W1)) | (sdtlpdtrp0(xd, xi) = sdtlpdtrp0(sdtlpdtrp0(xC, xi), W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W2_39(W1, xi), W1)) | aElementOf0(tptp_fun_W2_39(W1, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))))))),
% 0.92/0.90      inference(monotonicity,[status(thm)],[79])).
% 0.92/0.90  tff(81,plain,
% 0.92/0.90      (((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1)) | (~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | (~aElementOf0(tptp_fun_W2_39(W1, W0), W1)) | aElementOf0(tptp_fun_W2_39(W1, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0)))))))))))) | ((~aElementOf0(xi, szDzozmdt0(xN))) | ![W1: $i] : ((sdtlpdtrp0(xd, xi) = sdtlpdtrp0(sdtlpdtrp0(xC, xi), W1)) | (~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W2_39(W1, xi), W1)) | aElementOf0(tptp_fun_W2_39(W1, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi)))))))))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1)) | (~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | (~aElementOf0(tptp_fun_W2_39(W1, W0), W1)) | aElementOf0(tptp_fun_W2_39(W1, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0)))))))))))) | (~aElementOf0(xi, szDzozmdt0(xN))) | ![W1: $i] : ((~aSet0(W1)) | (sdtlpdtrp0(xd, xi) = sdtlpdtrp0(sdtlpdtrp0(xC, xi), W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W2_39(W1, xi), W1)) | aElementOf0(tptp_fun_W2_39(W1, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi)))))))))))),
% 0.92/0.90      inference(transitivity,[status(thm)],[80, 78])).
% 0.92/0.90  tff(82,plain,
% 0.92/0.90      ((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1)) | (~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | (~aElementOf0(tptp_fun_W2_39(W1, W0), W1)) | aElementOf0(tptp_fun_W2_39(W1, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0)))))))))))) | ((~aElementOf0(xi, szDzozmdt0(xN))) | ![W1: $i] : ((sdtlpdtrp0(xd, xi) = sdtlpdtrp0(sdtlpdtrp0(xC, xi), W1)) | (~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W2_39(W1, xi), W1)) | aElementOf0(tptp_fun_W2_39(W1, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi)))))))))))),
% 0.92/0.90      inference(quant_inst,[status(thm)],[])).
% 0.92/0.90  tff(83,plain,
% 0.92/0.90      ((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ![W1: $i] : ((sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1)) | (~aSet0(W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | (~aElementOf0(tptp_fun_W2_39(W1, W0), W1)) | aElementOf0(tptp_fun_W2_39(W1, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0)))))))))))) | (~aElementOf0(xi, szDzozmdt0(xN))) | ![W1: $i] : ((~aSet0(W1)) | (sdtlpdtrp0(xd, xi) = sdtlpdtrp0(sdtlpdtrp0(xC, xi), W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W2_39(W1, xi), W1)) | aElementOf0(tptp_fun_W2_39(W1, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))))),
% 0.92/0.90      inference(modus_ponens,[status(thm)],[82, 81])).
% 0.92/0.90  tff(84,plain,
% 0.92/0.90      (![W1: $i] : ((~aSet0(W1)) | (sdtlpdtrp0(xd, xi) = sdtlpdtrp0(sdtlpdtrp0(xC, xi), W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W2_39(W1, xi), W1)) | aElementOf0(tptp_fun_W2_39(W1, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))))),
% 0.92/0.90      inference(unit_resolution,[status(thm)],[83, 77, 54])).
% 0.92/0.90  tff(85,plain,
% 0.92/0.90      (((~![W1: $i] : ((~aSet0(W1)) | (sdtlpdtrp0(xd, xi) = sdtlpdtrp0(sdtlpdtrp0(xC, xi), W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W2_39(W1, xi), W1)) | aElementOf0(tptp_fun_W2_39(W1, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))))) | ((~aSet0(W0!43)) | (sdtlpdtrp0(xd, xi) = sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0!43)) | (~(aElementOf0(W0!43, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W0!43) = xk)) | (~(aSubsetOf0(W0!43, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W2_39(W0!43, xi), W0!43)) | aElementOf0(tptp_fun_W2_39(W0!43, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))))) <=> ((~![W1: $i] : ((~aSet0(W1)) | (sdtlpdtrp0(xd, xi) = sdtlpdtrp0(sdtlpdtrp0(xC, xi), W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W2_39(W1, xi), W1)) | aElementOf0(tptp_fun_W2_39(W1, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))))) | (~aSet0(W0!43)) | (sdtlpdtrp0(xd, xi) = sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0!43)) | (~(aElementOf0(W0!43, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W0!43) = xk)) | (~(aSubsetOf0(W0!43, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W2_39(W0!43, xi), W0!43)) | aElementOf0(tptp_fun_W2_39(W0!43, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))))),
% 0.92/0.90      inference(rewrite,[status(thm)],[])).
% 0.92/0.90  tff(86,plain,
% 0.92/0.90      ((~![W1: $i] : ((~aSet0(W1)) | (sdtlpdtrp0(xd, xi) = sdtlpdtrp0(sdtlpdtrp0(xC, xi), W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W2_39(W1, xi), W1)) | aElementOf0(tptp_fun_W2_39(W1, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))))) | ((~aSet0(W0!43)) | (sdtlpdtrp0(xd, xi) = sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0!43)) | (~(aElementOf0(W0!43, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W0!43) = xk)) | (~(aSubsetOf0(W0!43, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W2_39(W0!43, xi), W0!43)) | aElementOf0(tptp_fun_W2_39(W0!43, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))))),
% 0.92/0.90      inference(quant_inst,[status(thm)],[])).
% 0.92/0.90  tff(87,plain,
% 0.92/0.90      ((~![W1: $i] : ((~aSet0(W1)) | (sdtlpdtrp0(xd, xi) = sdtlpdtrp0(sdtlpdtrp0(xC, xi), W1)) | (~(aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W1) = xk)) | (~(aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W2_39(W1, xi), W1)) | aElementOf0(tptp_fun_W2_39(W1, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))))) | (~aSet0(W0!43)) | (sdtlpdtrp0(xd, xi) = sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0!43)) | (~(aElementOf0(W0!43, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W0!43) = xk)) | (~(aSubsetOf0(W0!43, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W2_39(W0!43, xi), W0!43)) | aElementOf0(tptp_fun_W2_39(W0!43, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi)))))))))),
% 0.92/0.90      inference(modus_ponens,[status(thm)],[86, 85])).
% 0.92/0.90  tff(88,plain,
% 0.92/0.90      (sdtlpdtrp0(xd, xi) = sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0!43)),
% 0.92/0.90      inference(unit_resolution,[status(thm)],[87, 84, 48, 15])).
% 0.92/0.90  tff(89,plain,
% 0.92/0.90      (sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0!43) = sdtlpdtrp0(xd, xi)),
% 0.92/0.90      inference(symmetry,[status(thm)],[88])).
% 0.92/0.90  tff(90,plain,
% 0.92/0.90      ((aElementOf0(W0!43, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W0!43) = xk)) | (~(aSubsetOf0(W0!43, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | aElementOf0(tptp_fun_W3_38(W0!43, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W3_38(W0!43, xi), W0!43))))))) | (~aElementOf0(W0!43, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)))),
% 0.92/0.90      inference(tautology,[status(thm)],[])).
% 0.92/0.90  tff(91,plain,
% 0.92/0.90      (aElementOf0(W0!43, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W0!43) = xk)) | (~(aSubsetOf0(W0!43, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | aElementOf0(tptp_fun_W3_38(W0!43, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W3_38(W0!43, xi), W0!43))))))),
% 0.92/0.90      inference(unit_resolution,[status(thm)],[90, 13])).
% 0.92/0.90  tff(92,plain,
% 0.92/0.90      (^[W0: $i] : refl(((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(tptp_fun_W1_37(W0), xT)) | (~![W2: $i] : ((~aSet0(W2)) | (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = tptp_fun_W1_37(W0)) | (~(aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | (~((~(sbrdtbr0(W2) = xk)) | (~(aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | (~aElementOf0(tptp_fun_W3_38(W2, W0), W2)) | aElementOf0(tptp_fun_W3_38(W2, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0)))))))))))))) <=> ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(tptp_fun_W1_37(W0), xT)) | (~![W2: $i] : ((~aSet0(W2)) | (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = tptp_fun_W1_37(W0)) | (~(aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | (~((~(sbrdtbr0(W2) = xk)) | (~(aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | (~aElementOf0(tptp_fun_W3_38(W2, W0), W2)) | aElementOf0(tptp_fun_W3_38(W2, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0)))))))))))))))),
% 0.92/0.90      inference(bind,[status(th)],[])).
% 0.92/0.90  tff(93,plain,
% 0.92/0.90      (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(tptp_fun_W1_37(W0), xT)) | (~![W2: $i] : ((~aSet0(W2)) | (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = tptp_fun_W1_37(W0)) | (~(aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | (~((~(sbrdtbr0(W2) = xk)) | (~(aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | (~aElementOf0(tptp_fun_W3_38(W2, W0), W2)) | aElementOf0(tptp_fun_W3_38(W2, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0)))))))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(tptp_fun_W1_37(W0), xT)) | (~![W2: $i] : ((~aSet0(W2)) | (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = tptp_fun_W1_37(W0)) | (~(aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | (~((~(sbrdtbr0(W2) = xk)) | (~(aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | (~aElementOf0(tptp_fun_W3_38(W2, W0), W2)) | aElementOf0(tptp_fun_W3_38(W2, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0))))))))))))))),
% 0.92/0.90      inference(quant_intro,[status(thm)],[92])).
% 0.92/0.90  tff(94,plain,
% 0.92/0.90      (^[W0: $i] : rewrite(((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(tptp_fun_W1_37(W0), xT)) | (~![W2: $i] : ((~aSet0(W2)) | (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = tptp_fun_W1_37(W0)) | (~(aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | (~((~(sbrdtbr0(W2) = xk)) | (~(aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | (~aElementOf0(tptp_fun_W3_38(W2, W0), W2)) | aElementOf0(tptp_fun_W3_38(W2, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0)))))))))))))) <=> ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(tptp_fun_W1_37(W0), xT)) | (~![W2: $i] : ((~aSet0(W2)) | (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = tptp_fun_W1_37(W0)) | (~(aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | (~((~(sbrdtbr0(W2) = xk)) | (~(aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | (~aElementOf0(tptp_fun_W3_38(W2, W0), W2)) | aElementOf0(tptp_fun_W3_38(W2, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0)))))))))))))))),
% 0.92/0.90      inference(bind,[status(th)],[])).
% 0.92/0.90  tff(95,plain,
% 0.92/0.90      (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(tptp_fun_W1_37(W0), xT)) | (~![W2: $i] : ((~aSet0(W2)) | (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = tptp_fun_W1_37(W0)) | (~(aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | (~((~(sbrdtbr0(W2) = xk)) | (~(aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | (~aElementOf0(tptp_fun_W3_38(W2, W0), W2)) | aElementOf0(tptp_fun_W3_38(W2, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0)))))))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(tptp_fun_W1_37(W0), xT)) | (~![W2: $i] : ((~aSet0(W2)) | (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = tptp_fun_W1_37(W0)) | (~(aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | (~((~(sbrdtbr0(W2) = xk)) | (~(aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | (~aElementOf0(tptp_fun_W3_38(W2, W0), W2)) | aElementOf0(tptp_fun_W3_38(W2, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0))))))))))))))),
% 0.92/0.90      inference(quant_intro,[status(thm)],[94])).
% 0.92/0.90  tff(96,plain,
% 0.92/0.90      (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(tptp_fun_W1_37(W0), xT)) | (~![W2: $i] : ((~aSet0(W2)) | (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = tptp_fun_W1_37(W0)) | (~(aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | (~((~(sbrdtbr0(W2) = xk)) | (~(aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | (~aElementOf0(tptp_fun_W3_38(W2, W0), W2)) | aElementOf0(tptp_fun_W3_38(W2, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0)))))))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(tptp_fun_W1_37(W0), xT)) | (~![W2: $i] : ((~aSet0(W2)) | (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = tptp_fun_W1_37(W0)) | (~(aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | (~((~(sbrdtbr0(W2) = xk)) | (~(aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | (~aElementOf0(tptp_fun_W3_38(W2, W0), W2)) | aElementOf0(tptp_fun_W3_38(W2, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0))))))))))))))),
% 0.92/0.90      inference(transitivity,[status(thm)],[95, 93])).
% 0.92/0.90  tff(97,plain,
% 0.92/0.90      (^[W0: $i] : rewrite(((~aElementOf0(W0, szDzozmdt0(xN))) | (aElementOf0(tptp_fun_W1_37(W0), xT) & ![W2: $i] : ((~aSet0(W2)) | (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = tptp_fun_W1_37(W0)) | ((~aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk))) & ((~(sbrdtbr0(W2) = xk)) | ((~aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & (~((~aElementOf0(tptp_fun_W3_38(W2, W0), W2)) | aElementOf0(tptp_fun_W3_38(W2, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0))))))))))) <=> ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(tptp_fun_W1_37(W0), xT)) | (~![W2: $i] : ((~aSet0(W2)) | (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = tptp_fun_W1_37(W0)) | (~(aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | (~((~(sbrdtbr0(W2) = xk)) | (~(aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | (~aElementOf0(tptp_fun_W3_38(W2, W0), W2)) | aElementOf0(tptp_fun_W3_38(W2, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0)))))))))))))))),
% 0.92/0.90      inference(bind,[status(th)],[])).
% 0.92/0.90  tff(98,plain,
% 0.92/0.90      (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (aElementOf0(tptp_fun_W1_37(W0), xT) & ![W2: $i] : ((~aSet0(W2)) | (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = tptp_fun_W1_37(W0)) | ((~aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk))) & ((~(sbrdtbr0(W2) = xk)) | ((~aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & (~((~aElementOf0(tptp_fun_W3_38(W2, W0), W2)) | aElementOf0(tptp_fun_W3_38(W2, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0))))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(tptp_fun_W1_37(W0), xT)) | (~![W2: $i] : ((~aSet0(W2)) | (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = tptp_fun_W1_37(W0)) | (~(aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | (~((~(sbrdtbr0(W2) = xk)) | (~(aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | (~aElementOf0(tptp_fun_W3_38(W2, W0), W2)) | aElementOf0(tptp_fun_W3_38(W2, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0))))))))))))))),
% 0.92/0.90      inference(quant_intro,[status(thm)],[97])).
% 0.92/0.90  tff(99,plain,
% 0.92/0.90      (^[W0: $i] : rewrite(((~aElementOf0(W0, szDzozmdt0(xN))) | (aElementOf0(tptp_fun_W1_37(W0), xT) & ![W2: $i] : (((~aSet0(W2)) | ((~aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk))) & (((~aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & (~((~aElementOf0(tptp_fun_W3_38(W2, W0), W2)) | aElementOf0(tptp_fun_W3_38(W2, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) | (~(sbrdtbr0(W2) = xk))))) | (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = tptp_fun_W1_37(W0))))) <=> ((~aElementOf0(W0, szDzozmdt0(xN))) | (aElementOf0(tptp_fun_W1_37(W0), xT) & ![W2: $i] : ((~aSet0(W2)) | (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = tptp_fun_W1_37(W0)) | ((~aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk))) & ((~(sbrdtbr0(W2) = xk)) | ((~aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & (~((~aElementOf0(tptp_fun_W3_38(W2, W0), W2)) | aElementOf0(tptp_fun_W3_38(W2, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0))))))))))))),
% 0.92/0.90      inference(bind,[status(th)],[])).
% 0.92/0.90  tff(100,plain,
% 0.92/0.90      (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (aElementOf0(tptp_fun_W1_37(W0), xT) & ![W2: $i] : (((~aSet0(W2)) | ((~aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk))) & (((~aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & (~((~aElementOf0(tptp_fun_W3_38(W2, W0), W2)) | aElementOf0(tptp_fun_W3_38(W2, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) | (~(sbrdtbr0(W2) = xk))))) | (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = tptp_fun_W1_37(W0))))) <=> ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (aElementOf0(tptp_fun_W1_37(W0), xT) & ![W2: $i] : ((~aSet0(W2)) | (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = tptp_fun_W1_37(W0)) | ((~aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk))) & ((~(sbrdtbr0(W2) = xk)) | ((~aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & (~((~aElementOf0(tptp_fun_W3_38(W2, W0), W2)) | aElementOf0(tptp_fun_W3_38(W2, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0)))))))))))),
% 0.92/0.90      inference(quant_intro,[status(thm)],[99])).
% 0.92/0.90  tff(101,plain,
% 0.92/0.90      (^[W0: $i] : rewrite(((~aElementOf0(W0, szNzAzT0)) | ?[W1: $i] : (aElementOf0(W1, xT) & ![W2: $i] : ((~(aSet0(W2) & (aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | ((aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | ![W3: $i] : ((~aElementOf0(W3, W2)) | aElementOf0(W3, sdtlpdtrp0(xN, szszuzczcdt0(W0))))) & (sbrdtbr0(W2) = xk))))) | (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = W1)))) <=> ((~aElementOf0(W0, szDzozmdt0(xN))) | ?[W1: $i] : (aElementOf0(W1, xT) & ![W2: $i] : ((~(aSet0(W2) & (aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | ((aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | ![W3: $i] : ((~aElementOf0(W3, W2)) | aElementOf0(W3, sdtlpdtrp0(xN, szszuzczcdt0(W0))))) & (sbrdtbr0(W2) = xk))))) | (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = W1)))))),
% 0.92/0.90      inference(bind,[status(th)],[])).
% 0.92/0.90  tff(102,plain,
% 0.92/0.90      (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ?[W1: $i] : (aElementOf0(W1, xT) & ![W2: $i] : ((~(aSet0(W2) & (aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | ((aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | ![W3: $i] : ((~aElementOf0(W3, W2)) | aElementOf0(W3, sdtlpdtrp0(xN, szszuzczcdt0(W0))))) & (sbrdtbr0(W2) = xk))))) | (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = W1)))) <=> ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ?[W1: $i] : (aElementOf0(W1, xT) & ![W2: $i] : ((~(aSet0(W2) & (aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | ((aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | ![W3: $i] : ((~aElementOf0(W3, W2)) | aElementOf0(W3, sdtlpdtrp0(xN, szszuzczcdt0(W0))))) & (sbrdtbr0(W2) = xk))))) | (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = W1))))),
% 0.92/0.90      inference(quant_intro,[status(thm)],[101])).
% 0.92/0.90  tff(103,plain,
% 0.92/0.90      (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ?[W1: $i] : (aElementOf0(W1, xT) & ![W2: $i] : ((~(aSet0(W2) & (aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | ((aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | ![W3: $i] : ((~aElementOf0(W3, W2)) | aElementOf0(W3, sdtlpdtrp0(xN, szszuzczcdt0(W0))))) & (sbrdtbr0(W2) = xk))))) | (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = W1)))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ?[W1: $i] : (aElementOf0(W1, xT) & ![W2: $i] : ((~(aSet0(W2) & (aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | ((aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | ![W3: $i] : ((~aElementOf0(W3, W2)) | aElementOf0(W3, sdtlpdtrp0(xN, szszuzczcdt0(W0))))) & (sbrdtbr0(W2) = xk))))) | (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = W1))))),
% 0.92/0.90      inference(rewrite,[status(thm)],[])).
% 0.92/0.90  tff(104,plain,
% 0.92/0.90      (^[W0: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: $i] : rewrite((aElementOf0(W1, xT) & ![W2: $i] : ((aSet0(W2) & (((![W3: $i] : (aElementOf0(W3, W2) => aElementOf0(W3, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & (sbrdtbr0(W2) = xk)) | aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)))) => (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = W1))) <=> (aElementOf0(W1, xT) & ![W2: $i] : ((~(aSet0(W2) & (aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | ((aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | ![W3: $i] : ((~aElementOf0(W3, W2)) | aElementOf0(W3, sdtlpdtrp0(xN, szszuzczcdt0(W0))))) & (sbrdtbr0(W2) = xk))))) | (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = W1))))), (?[W1: $i] : (aElementOf0(W1, xT) & ![W2: $i] : ((aSet0(W2) & (((![W3: $i] : (aElementOf0(W3, W2) => aElementOf0(W3, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & (sbrdtbr0(W2) = xk)) | aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)))) => (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = W1))) <=> ?[W1: $i] : (aElementOf0(W1, xT) & ![W2: $i] : ((~(aSet0(W2) & (aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | ((aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | ![W3: $i] : ((~aElementOf0(W3, W2)) | aElementOf0(W3, sdtlpdtrp0(xN, szszuzczcdt0(W0))))) & (sbrdtbr0(W2) = xk))))) | (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = W1))))), ((aElementOf0(W0, szNzAzT0) => ?[W1: $i] : (aElementOf0(W1, xT) & ![W2: $i] : ((aSet0(W2) & (((![W3: $i] : (aElementOf0(W3, W2) => aElementOf0(W3, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & (sbrdtbr0(W2) = xk)) | aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)))) => (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = W1)))) <=> (aElementOf0(W0, szNzAzT0) => ?[W1: $i] : (aElementOf0(W1, xT) & ![W2: $i] : ((~(aSet0(W2) & (aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | ((aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | ![W3: $i] : ((~aElementOf0(W3, W2)) | aElementOf0(W3, sdtlpdtrp0(xN, szszuzczcdt0(W0))))) & (sbrdtbr0(W2) = xk))))) | (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = W1)))))), rewrite((aElementOf0(W0, szNzAzT0) => ?[W1: $i] : (aElementOf0(W1, xT) & ![W2: $i] : ((~(aSet0(W2) & (aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | ((aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | ![W3: $i] : ((~aElementOf0(W3, W2)) | aElementOf0(W3, sdtlpdtrp0(xN, szszuzczcdt0(W0))))) & (sbrdtbr0(W2) = xk))))) | (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = W1)))) <=> ((~aElementOf0(W0, szNzAzT0)) | ?[W1: $i] : (aElementOf0(W1, xT) & ![W2: $i] : ((~(aSet0(W2) & (aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | ((aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | ![W3: $i] : ((~aElementOf0(W3, W2)) | aElementOf0(W3, sdtlpdtrp0(xN, szszuzczcdt0(W0))))) & (sbrdtbr0(W2) = xk))))) | (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = W1))))), ((aElementOf0(W0, szNzAzT0) => ?[W1: $i] : (aElementOf0(W1, xT) & ![W2: $i] : ((aSet0(W2) & (((![W3: $i] : (aElementOf0(W3, W2) => aElementOf0(W3, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & (sbrdtbr0(W2) = xk)) | aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)))) => (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = W1)))) <=> ((~aElementOf0(W0, szNzAzT0)) | ?[W1: $i] : (aElementOf0(W1, xT) & ![W2: $i] : ((~(aSet0(W2) & (aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | ((aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | ![W3: $i] : ((~aElementOf0(W3, W2)) | aElementOf0(W3, sdtlpdtrp0(xN, szszuzczcdt0(W0))))) & (sbrdtbr0(W2) = xk))))) | (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = W1))))))),
% 0.92/0.91      inference(bind,[status(th)],[])).
% 0.92/0.91  tff(105,plain,
% 0.92/0.91      (![W0: $i] : (aElementOf0(W0, szNzAzT0) => ?[W1: $i] : (aElementOf0(W1, xT) & ![W2: $i] : ((aSet0(W2) & (((![W3: $i] : (aElementOf0(W3, W2) => aElementOf0(W3, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & (sbrdtbr0(W2) = xk)) | aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)))) => (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = W1)))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ?[W1: $i] : (aElementOf0(W1, xT) & ![W2: $i] : ((~(aSet0(W2) & (aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | ((aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | ![W3: $i] : ((~aElementOf0(W3, W2)) | aElementOf0(W3, sdtlpdtrp0(xN, szszuzczcdt0(W0))))) & (sbrdtbr0(W2) = xk))))) | (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = W1))))),
% 0.92/0.91      inference(quant_intro,[status(thm)],[104])).
% 0.92/0.91  tff(106,axiom,(![W0: $i] : (aElementOf0(W0, szNzAzT0) => ?[W1: $i] : (aElementOf0(W1, xT) & ![W2: $i] : ((aSet0(W2) & (((![W3: $i] : (aElementOf0(W3, W2) => aElementOf0(W3, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & (sbrdtbr0(W2) = xk)) | aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)))) => (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = W1))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__4618')).
% 0.92/0.91  tff(107,plain,
% 0.92/0.91      (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ?[W1: $i] : (aElementOf0(W1, xT) & ![W2: $i] : ((~(aSet0(W2) & (aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | ((aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | ![W3: $i] : ((~aElementOf0(W3, W2)) | aElementOf0(W3, sdtlpdtrp0(xN, szszuzczcdt0(W0))))) & (sbrdtbr0(W2) = xk))))) | (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = W1))))),
% 0.92/0.91      inference(modus_ponens,[status(thm)],[106, 105])).
% 0.92/0.91  tff(108,plain,
% 0.92/0.91      (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ?[W1: $i] : (aElementOf0(W1, xT) & ![W2: $i] : ((~(aSet0(W2) & (aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | ((aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | ![W3: $i] : ((~aElementOf0(W3, W2)) | aElementOf0(W3, sdtlpdtrp0(xN, szszuzczcdt0(W0))))) & (sbrdtbr0(W2) = xk))))) | (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = W1))))),
% 0.92/0.91      inference(modus_ponens,[status(thm)],[107, 103])).
% 0.92/0.91  tff(109,plain,
% 0.92/0.91      (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | ?[W1: $i] : (aElementOf0(W1, xT) & ![W2: $i] : ((~(aSet0(W2) & (aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | ((aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | ![W3: $i] : ((~aElementOf0(W3, W2)) | aElementOf0(W3, sdtlpdtrp0(xN, szszuzczcdt0(W0))))) & (sbrdtbr0(W2) = xk))))) | (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = W1))))),
% 0.92/0.91      inference(modus_ponens,[status(thm)],[108, 102])).
% 0.92/0.91  tff(110,plain,(
% 0.92/0.91      ![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (aElementOf0(tptp_fun_W1_37(W0), xT) & ![W2: $i] : (((~aSet0(W2)) | ((~aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk))) & (((~aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & (~((~aElementOf0(tptp_fun_W3_38(W2, W0), W2)) | aElementOf0(tptp_fun_W3_38(W2, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0)))))) | (~(sbrdtbr0(W2) = xk))))) | (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = tptp_fun_W1_37(W0)))))),
% 0.92/0.91      inference(skolemize,[status(sab)],[109])).
% 0.92/0.91  tff(111,plain,
% 0.92/0.91      (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (aElementOf0(tptp_fun_W1_37(W0), xT) & ![W2: $i] : ((~aSet0(W2)) | (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = tptp_fun_W1_37(W0)) | ((~aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk))) & ((~(sbrdtbr0(W2) = xk)) | ((~aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & (~((~aElementOf0(tptp_fun_W3_38(W2, W0), W2)) | aElementOf0(tptp_fun_W3_38(W2, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0)))))))))))),
% 0.92/0.91      inference(modus_ponens,[status(thm)],[110, 100])).
% 0.92/0.91  tff(112,plain,
% 0.92/0.91      (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(tptp_fun_W1_37(W0), xT)) | (~![W2: $i] : ((~aSet0(W2)) | (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = tptp_fun_W1_37(W0)) | (~(aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | (~((~(sbrdtbr0(W2) = xk)) | (~(aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | (~aElementOf0(tptp_fun_W3_38(W2, W0), W2)) | aElementOf0(tptp_fun_W3_38(W2, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0))))))))))))))),
% 0.92/0.91      inference(modus_ponens,[status(thm)],[111, 98])).
% 0.92/0.91  tff(113,plain,
% 0.92/0.91      (![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(tptp_fun_W1_37(W0), xT)) | (~![W2: $i] : ((~aSet0(W2)) | (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = tptp_fun_W1_37(W0)) | (~(aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | (~((~(sbrdtbr0(W2) = xk)) | (~(aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | (~aElementOf0(tptp_fun_W3_38(W2, W0), W2)) | aElementOf0(tptp_fun_W3_38(W2, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0))))))))))))))),
% 0.92/0.91      inference(modus_ponens,[status(thm)],[112, 96])).
% 0.92/0.91  tff(114,plain,
% 0.92/0.91      (((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(tptp_fun_W1_37(W0), xT)) | (~![W2: $i] : ((~aSet0(W2)) | (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = tptp_fun_W1_37(W0)) | (~(aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | (~((~(sbrdtbr0(W2) = xk)) | (~(aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | (~aElementOf0(tptp_fun_W3_38(W2, W0), W2)) | aElementOf0(tptp_fun_W3_38(W2, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0))))))))))))))) | ((~aElementOf0(xi, szDzozmdt0(xN))) | (~((~aElementOf0(tptp_fun_W1_37(xi), xT)) | (~![W2: $i] : ((~aSet0(W2)) | (sdtlpdtrp0(sdtlpdtrp0(xC, xi), W2) = tptp_fun_W1_37(xi)) | (~(aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W2) = xk)) | (~(aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W3_38(W2, xi), W2)) | aElementOf0(tptp_fun_W3_38(W2, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))))))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(tptp_fun_W1_37(W0), xT)) | (~![W2: $i] : ((~aSet0(W2)) | (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = tptp_fun_W1_37(W0)) | (~(aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | (~((~(sbrdtbr0(W2) = xk)) | (~(aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | (~aElementOf0(tptp_fun_W3_38(W2, W0), W2)) | aElementOf0(tptp_fun_W3_38(W2, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0))))))))))))))) | (~aElementOf0(xi, szDzozmdt0(xN))) | (~((~aElementOf0(tptp_fun_W1_37(xi), xT)) | (~![W2: $i] : ((~aSet0(W2)) | (sdtlpdtrp0(sdtlpdtrp0(xC, xi), W2) = tptp_fun_W1_37(xi)) | (~(aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W2) = xk)) | (~(aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W3_38(W2, xi), W2)) | aElementOf0(tptp_fun_W3_38(W2, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))))))))),
% 0.92/0.91      inference(rewrite,[status(thm)],[])).
% 0.92/0.91  tff(115,plain,
% 0.92/0.91      ((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(tptp_fun_W1_37(W0), xT)) | (~![W2: $i] : ((~aSet0(W2)) | (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = tptp_fun_W1_37(W0)) | (~(aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | (~((~(sbrdtbr0(W2) = xk)) | (~(aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | (~aElementOf0(tptp_fun_W3_38(W2, W0), W2)) | aElementOf0(tptp_fun_W3_38(W2, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0))))))))))))))) | ((~aElementOf0(xi, szDzozmdt0(xN))) | (~((~aElementOf0(tptp_fun_W1_37(xi), xT)) | (~![W2: $i] : ((~aSet0(W2)) | (sdtlpdtrp0(sdtlpdtrp0(xC, xi), W2) = tptp_fun_W1_37(xi)) | (~(aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W2) = xk)) | (~(aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W3_38(W2, xi), W2)) | aElementOf0(tptp_fun_W3_38(W2, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))))))))),
% 0.92/0.91      inference(quant_inst,[status(thm)],[])).
% 0.92/0.91  tff(116,plain,
% 0.92/0.91      ((~![W0: $i] : ((~aElementOf0(W0, szDzozmdt0(xN))) | (~((~aElementOf0(tptp_fun_W1_37(W0), xT)) | (~![W2: $i] : ((~aSet0(W2)) | (sdtlpdtrp0(sdtlpdtrp0(xC, W0), W2) = tptp_fun_W1_37(W0)) | (~(aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)) | (~((~(sbrdtbr0(W2) = xk)) | (~(aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0))) | (~aElementOf0(tptp_fun_W3_38(W2, W0), W2)) | aElementOf0(tptp_fun_W3_38(W2, W0), sdtlpdtrp0(xN, szszuzczcdt0(W0))))))))))))))) | (~aElementOf0(xi, szDzozmdt0(xN))) | (~((~aElementOf0(tptp_fun_W1_37(xi), xT)) | (~![W2: $i] : ((~aSet0(W2)) | (sdtlpdtrp0(sdtlpdtrp0(xC, xi), W2) = tptp_fun_W1_37(xi)) | (~(aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W2) = xk)) | (~(aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W3_38(W2, xi), W2)) | aElementOf0(tptp_fun_W3_38(W2, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi)))))))))))))),
% 0.92/0.91      inference(modus_ponens,[status(thm)],[115, 114])).
% 0.92/0.91  tff(117,plain,
% 0.92/0.91      (~((~aElementOf0(tptp_fun_W1_37(xi), xT)) | (~![W2: $i] : ((~aSet0(W2)) | (sdtlpdtrp0(sdtlpdtrp0(xC, xi), W2) = tptp_fun_W1_37(xi)) | (~(aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W2) = xk)) | (~(aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W3_38(W2, xi), W2)) | aElementOf0(tptp_fun_W3_38(W2, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))))))),
% 0.92/0.91      inference(unit_resolution,[status(thm)],[116, 113, 54])).
% 0.92/0.91  tff(118,plain,
% 0.92/0.91      (((~aElementOf0(tptp_fun_W1_37(xi), xT)) | (~![W2: $i] : ((~aSet0(W2)) | (sdtlpdtrp0(sdtlpdtrp0(xC, xi), W2) = tptp_fun_W1_37(xi)) | (~(aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W2) = xk)) | (~(aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W3_38(W2, xi), W2)) | aElementOf0(tptp_fun_W3_38(W2, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi)))))))))))) | ![W2: $i] : ((~aSet0(W2)) | (sdtlpdtrp0(sdtlpdtrp0(xC, xi), W2) = tptp_fun_W1_37(xi)) | (~(aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W2) = xk)) | (~(aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W3_38(W2, xi), W2)) | aElementOf0(tptp_fun_W3_38(W2, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))))),
% 0.92/0.91      inference(tautology,[status(thm)],[])).
% 0.92/0.91  tff(119,plain,
% 0.92/0.91      (![W2: $i] : ((~aSet0(W2)) | (sdtlpdtrp0(sdtlpdtrp0(xC, xi), W2) = tptp_fun_W1_37(xi)) | (~(aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W2) = xk)) | (~(aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W3_38(W2, xi), W2)) | aElementOf0(tptp_fun_W3_38(W2, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))))),
% 0.92/0.91      inference(unit_resolution,[status(thm)],[118, 117])).
% 0.92/0.91  tff(120,plain,
% 0.92/0.91      (((~![W2: $i] : ((~aSet0(W2)) | (sdtlpdtrp0(sdtlpdtrp0(xC, xi), W2) = tptp_fun_W1_37(xi)) | (~(aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W2) = xk)) | (~(aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W3_38(W2, xi), W2)) | aElementOf0(tptp_fun_W3_38(W2, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))))) | ((~aSet0(W0!43)) | (sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0!43) = tptp_fun_W1_37(xi)) | (~(aElementOf0(W0!43, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W0!43) = xk)) | (~(aSubsetOf0(W0!43, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | aElementOf0(tptp_fun_W3_38(W0!43, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W3_38(W0!43, xi), W0!43)))))))))) <=> ((~![W2: $i] : ((~aSet0(W2)) | (sdtlpdtrp0(sdtlpdtrp0(xC, xi), W2) = tptp_fun_W1_37(xi)) | (~(aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W2) = xk)) | (~(aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W3_38(W2, xi), W2)) | aElementOf0(tptp_fun_W3_38(W2, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))))) | (~aSet0(W0!43)) | (sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0!43) = tptp_fun_W1_37(xi)) | (~(aElementOf0(W0!43, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W0!43) = xk)) | (~(aSubsetOf0(W0!43, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | aElementOf0(tptp_fun_W3_38(W0!43, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W3_38(W0!43, xi), W0!43)))))))))),
% 0.92/0.91      inference(rewrite,[status(thm)],[])).
% 0.92/0.91  tff(121,plain,
% 0.92/0.91      (((~aSet0(W0!43)) | (sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0!43) = tptp_fun_W1_37(xi)) | (~(aElementOf0(W0!43, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W0!43) = xk)) | (~(aSubsetOf0(W0!43, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | aElementOf0(tptp_fun_W3_38(W0!43, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W3_38(W0!43, xi), W0!43))))))))) <=> ((~aSet0(W0!43)) | (sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0!43) = tptp_fun_W1_37(xi)) | (~(aElementOf0(W0!43, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W0!43) = xk)) | (~(aSubsetOf0(W0!43, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | aElementOf0(tptp_fun_W3_38(W0!43, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W3_38(W0!43, xi), W0!43)))))))))),
% 0.92/0.91      inference(rewrite,[status(thm)],[])).
% 0.92/0.91  tff(122,plain,
% 0.92/0.91      ((~(aElementOf0(W0!43, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W0!43) = xk)) | (~(aSubsetOf0(W0!43, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W3_38(W0!43, xi), W0!43)) | aElementOf0(tptp_fun_W3_38(W0!43, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))) <=> (~(aElementOf0(W0!43, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W0!43) = xk)) | (~(aSubsetOf0(W0!43, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | aElementOf0(tptp_fun_W3_38(W0!43, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W3_38(W0!43, xi), W0!43))))))))),
% 0.92/0.91      inference(rewrite,[status(thm)],[])).
% 0.92/0.91  tff(123,plain,
% 0.92/0.91      (((~aSet0(W0!43)) | (sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0!43) = tptp_fun_W1_37(xi)) | (~(aElementOf0(W0!43, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W0!43) = xk)) | (~(aSubsetOf0(W0!43, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W3_38(W0!43, xi), W0!43)) | aElementOf0(tptp_fun_W3_38(W0!43, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi)))))))))) <=> ((~aSet0(W0!43)) | (sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0!43) = tptp_fun_W1_37(xi)) | (~(aElementOf0(W0!43, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W0!43) = xk)) | (~(aSubsetOf0(W0!43, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | aElementOf0(tptp_fun_W3_38(W0!43, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W3_38(W0!43, xi), W0!43)))))))))),
% 0.92/0.91      inference(monotonicity,[status(thm)],[122])).
% 0.92/0.91  tff(124,plain,
% 0.92/0.91      (((~aSet0(W0!43)) | (sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0!43) = tptp_fun_W1_37(xi)) | (~(aElementOf0(W0!43, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W0!43) = xk)) | (~(aSubsetOf0(W0!43, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W3_38(W0!43, xi), W0!43)) | aElementOf0(tptp_fun_W3_38(W0!43, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi)))))))))) <=> ((~aSet0(W0!43)) | (sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0!43) = tptp_fun_W1_37(xi)) | (~(aElementOf0(W0!43, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W0!43) = xk)) | (~(aSubsetOf0(W0!43, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | aElementOf0(tptp_fun_W3_38(W0!43, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W3_38(W0!43, xi), W0!43)))))))))),
% 0.92/0.91      inference(transitivity,[status(thm)],[123, 121])).
% 0.92/0.91  tff(125,plain,
% 0.92/0.91      (((~![W2: $i] : ((~aSet0(W2)) | (sdtlpdtrp0(sdtlpdtrp0(xC, xi), W2) = tptp_fun_W1_37(xi)) | (~(aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W2) = xk)) | (~(aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W3_38(W2, xi), W2)) | aElementOf0(tptp_fun_W3_38(W2, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))))) | ((~aSet0(W0!43)) | (sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0!43) = tptp_fun_W1_37(xi)) | (~(aElementOf0(W0!43, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W0!43) = xk)) | (~(aSubsetOf0(W0!43, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W3_38(W0!43, xi), W0!43)) | aElementOf0(tptp_fun_W3_38(W0!43, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))))) <=> ((~![W2: $i] : ((~aSet0(W2)) | (sdtlpdtrp0(sdtlpdtrp0(xC, xi), W2) = tptp_fun_W1_37(xi)) | (~(aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W2) = xk)) | (~(aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W3_38(W2, xi), W2)) | aElementOf0(tptp_fun_W3_38(W2, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))))) | ((~aSet0(W0!43)) | (sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0!43) = tptp_fun_W1_37(xi)) | (~(aElementOf0(W0!43, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W0!43) = xk)) | (~(aSubsetOf0(W0!43, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | aElementOf0(tptp_fun_W3_38(W0!43, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W3_38(W0!43, xi), W0!43))))))))))),
% 0.92/0.91      inference(monotonicity,[status(thm)],[124])).
% 0.92/0.91  tff(126,plain,
% 0.92/0.91      (((~![W2: $i] : ((~aSet0(W2)) | (sdtlpdtrp0(sdtlpdtrp0(xC, xi), W2) = tptp_fun_W1_37(xi)) | (~(aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W2) = xk)) | (~(aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W3_38(W2, xi), W2)) | aElementOf0(tptp_fun_W3_38(W2, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))))) | ((~aSet0(W0!43)) | (sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0!43) = tptp_fun_W1_37(xi)) | (~(aElementOf0(W0!43, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W0!43) = xk)) | (~(aSubsetOf0(W0!43, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W3_38(W0!43, xi), W0!43)) | aElementOf0(tptp_fun_W3_38(W0!43, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))))) <=> ((~![W2: $i] : ((~aSet0(W2)) | (sdtlpdtrp0(sdtlpdtrp0(xC, xi), W2) = tptp_fun_W1_37(xi)) | (~(aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W2) = xk)) | (~(aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W3_38(W2, xi), W2)) | aElementOf0(tptp_fun_W3_38(W2, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))))) | (~aSet0(W0!43)) | (sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0!43) = tptp_fun_W1_37(xi)) | (~(aElementOf0(W0!43, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W0!43) = xk)) | (~(aSubsetOf0(W0!43, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | aElementOf0(tptp_fun_W3_38(W0!43, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W3_38(W0!43, xi), W0!43)))))))))),
% 0.92/0.91      inference(transitivity,[status(thm)],[125, 120])).
% 0.92/0.91  tff(127,plain,
% 0.92/0.91      ((~![W2: $i] : ((~aSet0(W2)) | (sdtlpdtrp0(sdtlpdtrp0(xC, xi), W2) = tptp_fun_W1_37(xi)) | (~(aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W2) = xk)) | (~(aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W3_38(W2, xi), W2)) | aElementOf0(tptp_fun_W3_38(W2, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))))) | ((~aSet0(W0!43)) | (sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0!43) = tptp_fun_W1_37(xi)) | (~(aElementOf0(W0!43, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W0!43) = xk)) | (~(aSubsetOf0(W0!43, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W3_38(W0!43, xi), W0!43)) | aElementOf0(tptp_fun_W3_38(W0!43, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))))),
% 0.92/0.91      inference(quant_inst,[status(thm)],[])).
% 0.92/0.91  tff(128,plain,
% 0.92/0.91      ((~![W2: $i] : ((~aSet0(W2)) | (sdtlpdtrp0(sdtlpdtrp0(xC, xi), W2) = tptp_fun_W1_37(xi)) | (~(aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W2) = xk)) | (~(aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W3_38(W2, xi), W2)) | aElementOf0(tptp_fun_W3_38(W2, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))))) | (~aSet0(W0!43)) | (sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0!43) = tptp_fun_W1_37(xi)) | (~(aElementOf0(W0!43, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W0!43) = xk)) | (~(aSubsetOf0(W0!43, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | aElementOf0(tptp_fun_W3_38(W0!43, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W3_38(W0!43, xi), W0!43))))))))),
% 0.92/0.91      inference(modus_ponens,[status(thm)],[127, 126])).
% 0.92/0.91  tff(129,plain,
% 0.92/0.91      (sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0!43) = tptp_fun_W1_37(xi)),
% 0.92/0.91      inference(unit_resolution,[status(thm)],[128, 119, 48, 91])).
% 0.92/0.91  tff(130,plain,
% 0.92/0.91      (tptp_fun_W1_37(xi) = sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0!43)),
% 0.92/0.91      inference(symmetry,[status(thm)],[129])).
% 0.92/0.91  tff(131,plain,
% 0.92/0.91      (tptp_fun_W1_37(xi) = sdtlpdtrp0(xd, xi)),
% 0.92/0.91      inference(transitivity,[status(thm)],[130, 89])).
% 0.92/0.91  tff(132,plain,
% 0.92/0.91      (aElementOf0(tptp_fun_W1_37(xi), xT) <=> aElementOf0(sdtlpdtrp0(xd, xi), xT)),
% 0.92/0.91      inference(monotonicity,[status(thm)],[131])).
% 0.92/0.91  tff(133,plain,
% 0.92/0.91      (aElementOf0(sdtlpdtrp0(xd, xi), xT) <=> aElementOf0(tptp_fun_W1_37(xi), xT)),
% 0.92/0.91      inference(symmetry,[status(thm)],[132])).
% 0.92/0.91  tff(134,plain,
% 0.92/0.91      ((~aElementOf0(sdtlpdtrp0(xd, xi), xT)) <=> (~aElementOf0(tptp_fun_W1_37(xi), xT))),
% 0.92/0.91      inference(monotonicity,[status(thm)],[133])).
% 0.92/0.91  tff(135,plain,
% 0.92/0.91      ((~aElementOf0(xx, xT)) <=> (~aElementOf0(sdtlpdtrp0(xd, xi), xT))),
% 0.92/0.91      inference(rewrite,[status(thm)],[])).
% 0.92/0.91  tff(136,plain,
% 0.92/0.91      ((~aElementOf0(xx, xT)) <=> (~aElementOf0(xx, xT))),
% 0.92/0.91      inference(rewrite,[status(thm)],[])).
% 0.92/0.91  tff(137,axiom,(~aElementOf0(xx, xT)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__')).
% 0.92/0.91  tff(138,plain,
% 0.92/0.91      (~aElementOf0(xx, xT)),
% 0.92/0.91      inference(modus_ponens,[status(thm)],[137, 136])).
% 0.92/0.92  tff(139,plain,
% 0.92/0.92      (~aElementOf0(sdtlpdtrp0(xd, xi), xT)),
% 0.92/0.92      inference(modus_ponens,[status(thm)],[138, 135])).
% 0.92/0.92  tff(140,plain,
% 0.92/0.92      (~aElementOf0(tptp_fun_W1_37(xi), xT)),
% 0.92/0.92      inference(modus_ponens,[status(thm)],[139, 134])).
% 0.92/0.92  tff(141,plain,
% 0.92/0.92      (((~aElementOf0(tptp_fun_W1_37(xi), xT)) | (~![W2: $i] : ((~aSet0(W2)) | (sdtlpdtrp0(sdtlpdtrp0(xC, xi), W2) = tptp_fun_W1_37(xi)) | (~(aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W2) = xk)) | (~(aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W3_38(W2, xi), W2)) | aElementOf0(tptp_fun_W3_38(W2, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi)))))))))))) | aElementOf0(tptp_fun_W1_37(xi), xT)),
% 0.92/0.92      inference(tautology,[status(thm)],[])).
% 0.92/0.92  tff(142,plain,
% 0.92/0.92      (aElementOf0(tptp_fun_W1_37(xi), xT)),
% 0.92/0.92      inference(unit_resolution,[status(thm)],[141, 117])).
% 0.92/0.92  tff(143,plain,
% 0.92/0.92      ($false),
% 0.92/0.92      inference(unit_resolution,[status(thm)],[142, 140])).
% 0.92/0.92  % SZS output end Proof
%------------------------------------------------------------------------------