TSTP Solution File: NUM597+3 by Z3---4.8.9.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : NUM597+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n015.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun Sep 18 13:10:46 EDT 2022

% Result   : Theorem 2.27s 1.76s
% Output   : Proof 2.40s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : NUM597+3 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33  % Computer : n015.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Fri Sep  2 12:23:54 EDT 2022
% 0.12/0.33  % 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.
% 2.27/1.76  % SZS status Theorem
% 2.27/1.76  % SZS output start Proof
% 2.27/1.76  tff(szDzizrdt0_type, type, (
% 2.27/1.76     szDzizrdt0: $i > $i)).
% 2.27/1.76  tff(xd_type, type, (
% 2.27/1.76     xd: $i)).
% 2.27/1.76  tff(sdtlpdtrp0_type, type, (
% 2.27/1.76     sdtlpdtrp0: ( $i * $i ) > $i)).
% 2.27/1.76  tff(aElementOf0_type, type, (
% 2.27/1.76     aElementOf0: ( $i * $i ) > $o)).
% 2.27/1.76  tff(szDzozmdt0_type, type, (
% 2.27/1.76     szDzozmdt0: $i > $i)).
% 2.27/1.76  tff(xN_type, type, (
% 2.27/1.76     xN: $i)).
% 2.27/1.76  tff(sdtlcdtrc0_type, type, (
% 2.27/1.76     sdtlcdtrc0: ( $i * $i ) > $i)).
% 2.27/1.76  tff(tptp_fun_W1_40_type, type, (
% 2.27/1.76     tptp_fun_W1_40: $i > $i)).
% 2.27/1.76  tff(aSet0_type, type, (
% 2.27/1.76     aSet0: $i > $o)).
% 2.27/1.76  tff(xT_type, type, (
% 2.27/1.76     xT: $i)).
% 2.27/1.76  tff(aSubsetOf0_type, type, (
% 2.27/1.76     aSubsetOf0: ( $i * $i ) > $o)).
% 2.27/1.76  tff(tptp_fun_W0_41_type, type, (
% 2.27/1.76     tptp_fun_W0_41: $i)).
% 2.27/1.76  tff(sdtlbdtrb0_type, type, (
% 2.27/1.76     sdtlbdtrb0: ( $i * $i ) > $i)).
% 2.27/1.76  tff(1,plain,
% 2.27/1.76      (^[W0: $i] : refl((~((~((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN)))) | (~((~aElementOf0(tptp_fun_W1_40(W0), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_40(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W1) = W0))))))) <=> (~((~((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN)))) | (~((~aElementOf0(tptp_fun_W1_40(W0), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_40(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W1) = W0))))))))),
% 2.27/1.76      inference(bind,[status(th)],[])).
% 2.27/1.76  tff(2,plain,
% 2.27/1.76      (![W0: $i] : (~((~((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN)))) | (~((~aElementOf0(tptp_fun_W1_40(W0), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_40(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W1) = W0))))))) <=> ![W0: $i] : (~((~((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN)))) | (~((~aElementOf0(tptp_fun_W1_40(W0), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_40(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W1) = W0)))))))),
% 2.27/1.76      inference(quant_intro,[status(thm)],[1])).
% 2.27/1.76  tff(3,plain,
% 2.27/1.76      (^[W0: $i] : rewrite((~((~((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN)))) | (~((~aElementOf0(tptp_fun_W1_40(W0), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_40(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W1) = W0))))))) <=> (~((~((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN)))) | (~((~aElementOf0(tptp_fun_W1_40(W0), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_40(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W1) = W0))))))))),
% 2.27/1.76      inference(bind,[status(th)],[])).
% 2.27/1.76  tff(4,plain,
% 2.27/1.76      (![W0: $i] : (~((~((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN)))) | (~((~aElementOf0(tptp_fun_W1_40(W0), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_40(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W1) = W0))))))) <=> ![W0: $i] : (~((~((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN)))) | (~((~aElementOf0(tptp_fun_W1_40(W0), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_40(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W1) = W0)))))))),
% 2.27/1.76      inference(quant_intro,[status(thm)],[3])).
% 2.27/1.76  tff(5,plain,
% 2.27/1.76      (![W0: $i] : (~((~((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN)))) | (~((~aElementOf0(tptp_fun_W1_40(W0), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_40(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W1) = W0))))))) <=> ![W0: $i] : (~((~((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN)))) | (~((~aElementOf0(tptp_fun_W1_40(W0), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_40(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W1) = W0)))))))),
% 2.27/1.76      inference(transitivity,[status(thm)],[4, 2])).
% 2.27/1.76  tff(6,plain,
% 2.27/1.76      (^[W0: $i] : trans(monotonicity(rewrite(((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN)))) | (aElementOf0(tptp_fun_W1_40(W0), szDzozmdt0(xN)) & (sdtlpdtrp0(xd, tptp_fun_W1_40(W0)) = W0))) <=> ((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN)))) | (~((~aElementOf0(tptp_fun_W1_40(W0), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_40(W0)) = W0)))))), rewrite((aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN))) | ![W1: $i] : (~(aElementOf0(W1, szDzozmdt0(xN)) & (sdtlpdtrp0(xd, W1) = W0)))) <=> (aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W1) = W0))))), ((((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN)))) | (aElementOf0(tptp_fun_W1_40(W0), szDzozmdt0(xN)) & (sdtlpdtrp0(xd, tptp_fun_W1_40(W0)) = W0))) & (aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN))) | ![W1: $i] : (~(aElementOf0(W1, szDzozmdt0(xN)) & (sdtlpdtrp0(xd, W1) = W0))))) <=> (((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN)))) | (~((~aElementOf0(tptp_fun_W1_40(W0), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_40(W0)) = W0))))) & (aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W1) = W0))))))), rewrite((((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN)))) | (~((~aElementOf0(tptp_fun_W1_40(W0), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_40(W0)) = W0))))) & (aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W1) = W0))))) <=> (~((~((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN)))) | (~((~aElementOf0(tptp_fun_W1_40(W0), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_40(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W1) = W0)))))))), ((((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN)))) | (aElementOf0(tptp_fun_W1_40(W0), szDzozmdt0(xN)) & (sdtlpdtrp0(xd, tptp_fun_W1_40(W0)) = W0))) & (aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN))) | ![W1: $i] : (~(aElementOf0(W1, szDzozmdt0(xN)) & (sdtlpdtrp0(xd, W1) = W0))))) <=> (~((~((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN)))) | (~((~aElementOf0(tptp_fun_W1_40(W0), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_40(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W1) = W0)))))))))),
% 2.27/1.76      inference(bind,[status(th)],[])).
% 2.27/1.76  tff(7,plain,
% 2.27/1.76      (![W0: $i] : (((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN)))) | (aElementOf0(tptp_fun_W1_40(W0), szDzozmdt0(xN)) & (sdtlpdtrp0(xd, tptp_fun_W1_40(W0)) = W0))) & (aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN))) | ![W1: $i] : (~(aElementOf0(W1, szDzozmdt0(xN)) & (sdtlpdtrp0(xd, W1) = W0))))) <=> ![W0: $i] : (~((~((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN)))) | (~((~aElementOf0(tptp_fun_W1_40(W0), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_40(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W1) = W0)))))))),
% 2.27/1.76      inference(quant_intro,[status(thm)],[6])).
% 2.27/1.76  tff(8,plain,
% 2.27/1.76      (^[W0: $i] : rewrite((aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xd))) <=> ?[W1: $i] : (aElementOf0(W1, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W1) = W0))) <=> (aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN))) <=> ?[W1: $i] : (aElementOf0(W1, szDzozmdt0(xN)) & (sdtlpdtrp0(xd, W1) = W0))))),
% 2.27/1.76      inference(bind,[status(th)],[])).
% 2.27/1.76  tff(9,plain,
% 2.27/1.76      (![W0: $i] : (aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xd))) <=> ?[W1: $i] : (aElementOf0(W1, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W1) = W0))) <=> ![W0: $i] : (aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN))) <=> ?[W1: $i] : (aElementOf0(W1, szDzozmdt0(xN)) & (sdtlpdtrp0(xd, W1) = W0)))),
% 2.27/1.76      inference(quant_intro,[status(thm)],[8])).
% 2.27/1.76  tff(10,plain,
% 2.27/1.76      (![W0: $i] : (aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xd))) <=> ?[W1: $i] : (aElementOf0(W1, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W1) = W0))) <=> ![W0: $i] : (aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xd))) <=> ?[W1: $i] : (aElementOf0(W1, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W1) = W0)))),
% 2.27/1.76      inference(rewrite,[status(thm)],[])).
% 2.27/1.76  tff(11,axiom,(((aSet0(sdtlcdtrc0(xd, szDzozmdt0(xd))) & ![W0: $i] : (aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xd))) <=> ?[W1: $i] : (aElementOf0(W1, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W1) = W0)))) & ![W0: $i] : (aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xd))) => aElementOf0(W0, xT))) & aSubsetOf0(sdtlcdtrc0(xd, szDzozmdt0(xd)), xT)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__4758')).
% 2.27/1.76  tff(12,plain,
% 2.27/1.76      ((aSet0(sdtlcdtrc0(xd, szDzozmdt0(xd))) & ![W0: $i] : (aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xd))) <=> ?[W1: $i] : (aElementOf0(W1, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W1) = W0)))) & ![W0: $i] : (aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xd))) => aElementOf0(W0, xT))),
% 2.27/1.76      inference(and_elim,[status(thm)],[11])).
% 2.27/1.76  tff(13,plain,
% 2.27/1.76      (aSet0(sdtlcdtrc0(xd, szDzozmdt0(xd))) & ![W0: $i] : (aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xd))) <=> ?[W1: $i] : (aElementOf0(W1, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W1) = W0)))),
% 2.27/1.76      inference(and_elim,[status(thm)],[12])).
% 2.27/1.76  tff(14,plain,
% 2.27/1.76      (![W0: $i] : (aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xd))) <=> ?[W1: $i] : (aElementOf0(W1, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W1) = W0)))),
% 2.27/1.76      inference(and_elim,[status(thm)],[13])).
% 2.27/1.76  tff(15,plain,
% 2.27/1.76      (![W0: $i] : (aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xd))) <=> ?[W1: $i] : (aElementOf0(W1, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W1) = W0)))),
% 2.27/1.76      inference(modus_ponens,[status(thm)],[14, 10])).
% 2.27/1.76  tff(16,plain,
% 2.27/1.76      (![W0: $i] : (aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN))) <=> ?[W1: $i] : (aElementOf0(W1, szDzozmdt0(xN)) & (sdtlpdtrp0(xd, W1) = W0)))),
% 2.27/1.76      inference(modus_ponens,[status(thm)],[15, 9])).
% 2.27/1.76  tff(17,plain,(
% 2.27/1.76      ![W0: $i] : (((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN)))) | (aElementOf0(tptp_fun_W1_40(W0), szDzozmdt0(xN)) & (sdtlpdtrp0(xd, tptp_fun_W1_40(W0)) = W0))) & (aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN))) | ![W1: $i] : (~(aElementOf0(W1, szDzozmdt0(xN)) & (sdtlpdtrp0(xd, W1) = W0)))))),
% 2.27/1.76      inference(skolemize,[status(sab)],[16])).
% 2.27/1.76  tff(18,plain,
% 2.27/1.76      (![W0: $i] : (~((~((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN)))) | (~((~aElementOf0(tptp_fun_W1_40(W0), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_40(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W1) = W0)))))))),
% 2.27/1.76      inference(modus_ponens,[status(thm)],[17, 7])).
% 2.27/1.76  tff(19,plain,
% 2.27/1.76      (![W0: $i] : (~((~((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN)))) | (~((~aElementOf0(tptp_fun_W1_40(W0), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_40(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W1) = W0)))))))),
% 2.27/1.76      inference(modus_ponens,[status(thm)],[18, 5])).
% 2.27/1.76  tff(20,plain,
% 2.27/1.76      ((~![W0: $i] : (~((~((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN)))) | (~((~aElementOf0(tptp_fun_W1_40(W0), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_40(W0)) = W0)))))) | (~(aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W1) = W0)))))))) | (~((~((~aElementOf0(szDzizrdt0(xd), sdtlcdtrc0(xd, szDzozmdt0(xN)))) | (~((~aElementOf0(tptp_fun_W1_40(szDzizrdt0(xd)), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_40(szDzizrdt0(xd))) = szDzizrdt0(xd))))))) | (~(aElementOf0(szDzizrdt0(xd), sdtlcdtrc0(xd, szDzozmdt0(xN))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W1) = szDzizrdt0(xd))))))))),
% 2.27/1.76      inference(quant_inst,[status(thm)],[])).
% 2.27/1.76  tff(21,plain,
% 2.27/1.76      (~((~((~aElementOf0(szDzizrdt0(xd), sdtlcdtrc0(xd, szDzozmdt0(xN)))) | (~((~aElementOf0(tptp_fun_W1_40(szDzizrdt0(xd)), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_40(szDzizrdt0(xd))) = szDzizrdt0(xd))))))) | (~(aElementOf0(szDzizrdt0(xd), sdtlcdtrc0(xd, szDzozmdt0(xN))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)))))))),
% 2.27/1.76      inference(unit_resolution,[status(thm)],[20, 19])).
% 2.27/1.76  tff(22,plain,
% 2.27/1.76      (((~((~aElementOf0(szDzizrdt0(xd), sdtlcdtrc0(xd, szDzozmdt0(xN)))) | (~((~aElementOf0(tptp_fun_W1_40(szDzizrdt0(xd)), szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, tptp_fun_W1_40(szDzizrdt0(xd))) = szDzizrdt0(xd))))))) | (~(aElementOf0(szDzizrdt0(xd), sdtlcdtrc0(xd, szDzozmdt0(xN))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W1) = szDzizrdt0(xd))))))) | (aElementOf0(szDzizrdt0(xd), sdtlcdtrc0(xd, szDzozmdt0(xN))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)))))),
% 2.27/1.76      inference(tautology,[status(thm)],[])).
% 2.27/1.76  tff(23,plain,
% 2.27/1.76      (aElementOf0(szDzizrdt0(xd), sdtlcdtrc0(xd, szDzozmdt0(xN))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W1) = szDzizrdt0(xd))))),
% 2.27/1.76      inference(unit_resolution,[status(thm)],[22, 21])).
% 2.27/1.76  tff(24,plain,
% 2.27/1.76      ((~aElementOf0(szDzizrdt0(xd), xT)) <=> (~aElementOf0(szDzizrdt0(xd), xT))),
% 2.27/1.76      inference(rewrite,[status(thm)],[])).
% 2.27/1.76  tff(25,axiom,(~aElementOf0(szDzizrdt0(xd), xT)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 2.27/1.76  tff(26,plain,
% 2.27/1.76      (~aElementOf0(szDzizrdt0(xd), xT)),
% 2.27/1.76      inference(modus_ponens,[status(thm)],[25, 24])).
% 2.27/1.76  tff(27,plain,
% 2.27/1.76      (^[W0: $i] : refl(((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN)))) | aElementOf0(W0, xT)) <=> ((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN)))) | aElementOf0(W0, xT)))),
% 2.27/1.76      inference(bind,[status(th)],[])).
% 2.27/1.76  tff(28,plain,
% 2.27/1.76      (![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN)))) | aElementOf0(W0, xT)) <=> ![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN)))) | aElementOf0(W0, xT))),
% 2.27/1.76      inference(quant_intro,[status(thm)],[27])).
% 2.27/1.76  tff(29,plain,
% 2.27/1.76      (^[W0: $i] : rewrite(((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xd)))) | aElementOf0(W0, xT)) <=> ((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN)))) | aElementOf0(W0, xT)))),
% 2.27/1.76      inference(bind,[status(th)],[])).
% 2.27/1.76  tff(30,plain,
% 2.27/1.76      (![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xd)))) | aElementOf0(W0, xT)) <=> ![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN)))) | aElementOf0(W0, xT))),
% 2.27/1.76      inference(quant_intro,[status(thm)],[29])).
% 2.27/1.76  tff(31,plain,
% 2.27/1.76      (![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xd)))) | aElementOf0(W0, xT)) <=> ![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xd)))) | aElementOf0(W0, xT))),
% 2.27/1.76      inference(rewrite,[status(thm)],[])).
% 2.27/1.76  tff(32,plain,
% 2.27/1.76      (^[W0: $i] : rewrite((aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xd))) => aElementOf0(W0, xT)) <=> ((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xd)))) | aElementOf0(W0, xT)))),
% 2.27/1.76      inference(bind,[status(th)],[])).
% 2.27/1.76  tff(33,plain,
% 2.27/1.76      (![W0: $i] : (aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xd))) => aElementOf0(W0, xT)) <=> ![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xd)))) | aElementOf0(W0, xT))),
% 2.27/1.76      inference(quant_intro,[status(thm)],[32])).
% 2.27/1.76  tff(34,plain,
% 2.27/1.76      (![W0: $i] : (aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xd))) => aElementOf0(W0, xT))),
% 2.27/1.76      inference(and_elim,[status(thm)],[12])).
% 2.27/1.76  tff(35,plain,
% 2.27/1.76      (![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xd)))) | aElementOf0(W0, xT))),
% 2.27/1.76      inference(modus_ponens,[status(thm)],[34, 33])).
% 2.27/1.76  tff(36,plain,
% 2.27/1.76      (![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xd)))) | aElementOf0(W0, xT))),
% 2.27/1.76      inference(modus_ponens,[status(thm)],[35, 31])).
% 2.27/1.76  tff(37,plain,
% 2.27/1.76      (![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN)))) | aElementOf0(W0, xT))),
% 2.27/1.76      inference(modus_ponens,[status(thm)],[36, 30])).
% 2.27/1.76  tff(38,plain,(
% 2.27/1.76      ![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN)))) | aElementOf0(W0, xT))),
% 2.27/1.76      inference(skolemize,[status(sab)],[37])).
% 2.27/1.76  tff(39,plain,
% 2.27/1.76      (![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN)))) | aElementOf0(W0, xT))),
% 2.27/1.76      inference(modus_ponens,[status(thm)],[38, 28])).
% 2.27/1.76  tff(40,plain,
% 2.27/1.76      (((~![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN)))) | aElementOf0(W0, xT))) | ((~aElementOf0(szDzizrdt0(xd), sdtlcdtrc0(xd, szDzozmdt0(xN)))) | aElementOf0(szDzizrdt0(xd), xT))) <=> ((~![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN)))) | aElementOf0(W0, xT))) | (~aElementOf0(szDzizrdt0(xd), sdtlcdtrc0(xd, szDzozmdt0(xN)))) | aElementOf0(szDzizrdt0(xd), xT))),
% 2.27/1.76      inference(rewrite,[status(thm)],[])).
% 2.27/1.76  tff(41,plain,
% 2.27/1.76      ((~![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN)))) | aElementOf0(W0, xT))) | ((~aElementOf0(szDzizrdt0(xd), sdtlcdtrc0(xd, szDzozmdt0(xN)))) | aElementOf0(szDzizrdt0(xd), xT))),
% 2.27/1.76      inference(quant_inst,[status(thm)],[])).
% 2.27/1.76  tff(42,plain,
% 2.27/1.76      ((~![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xN)))) | aElementOf0(W0, xT))) | (~aElementOf0(szDzizrdt0(xd), sdtlcdtrc0(xd, szDzozmdt0(xN)))) | aElementOf0(szDzizrdt0(xd), xT)),
% 2.27/1.76      inference(modus_ponens,[status(thm)],[41, 40])).
% 2.27/1.76  tff(43,plain,
% 2.27/1.76      (~aElementOf0(szDzizrdt0(xd), sdtlcdtrc0(xd, szDzozmdt0(xN)))),
% 2.27/1.76      inference(unit_resolution,[status(thm)],[42, 39, 26])).
% 2.27/1.76  tff(44,plain,
% 2.27/1.76      ((~(aElementOf0(szDzizrdt0(xd), sdtlcdtrc0(xd, szDzozmdt0(xN))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)))))) | aElementOf0(szDzizrdt0(xd), sdtlcdtrc0(xd, szDzozmdt0(xN))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W1) = szDzizrdt0(xd))))),
% 2.27/1.76      inference(tautology,[status(thm)],[])).
% 2.27/1.76  tff(45,plain,
% 2.27/1.76      ((~(aElementOf0(szDzizrdt0(xd), sdtlcdtrc0(xd, szDzozmdt0(xN))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)))))) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W1) = szDzizrdt0(xd))))),
% 2.27/1.76      inference(unit_resolution,[status(thm)],[44, 43])).
% 2.27/1.76  tff(46,plain,
% 2.27/1.76      (![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W1) = szDzizrdt0(xd))))),
% 2.27/1.76      inference(unit_resolution,[status(thm)],[45, 23])).
% 2.27/1.76  tff(47,plain,
% 2.27/1.76      (^[W0: $i] : refl((aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (~((~aElementOf0(W0, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd)))))) <=> (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (~((~aElementOf0(W0, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd)))))))),
% 2.27/1.76      inference(bind,[status(th)],[])).
% 2.27/1.76  tff(48,plain,
% 2.27/1.76      (![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (~((~aElementOf0(W0, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd)))))) <=> ![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (~((~aElementOf0(W0, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))))),
% 2.27/1.76      inference(quant_intro,[status(thm)],[47])).
% 2.27/1.76  tff(49,plain,
% 2.27/1.76      (^[W0: $i] : rewrite((aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xN)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd)))) <=> (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (~((~aElementOf0(W0, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd)))))))),
% 2.27/1.76      inference(bind,[status(th)],[])).
% 2.27/1.76  tff(50,plain,
% 2.27/1.76      (![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xN)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd)))) <=> ![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (~((~aElementOf0(W0, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))))),
% 2.27/1.76      inference(quant_intro,[status(thm)],[49])).
% 2.27/1.76  tff(51,plain,
% 2.27/1.76      (^[W0: $i] : rewrite((aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd)))) <=> (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xN)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd)))))),
% 2.27/1.76      inference(bind,[status(th)],[])).
% 2.27/1.76  tff(52,plain,
% 2.27/1.76      (![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd)))) <=> ![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xN)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))),
% 2.27/1.76      inference(quant_intro,[status(thm)],[51])).
% 2.27/1.76  tff(53,plain,
% 2.27/1.76      (![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd)))) <=> ![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))),
% 2.27/1.77      inference(rewrite,[status(thm)],[])).
% 2.27/1.77  tff(54,plain,
% 2.27/1.77      ((~((aSet0(sdtlbdtrb0(xd, szDzizrdt0(xd))) & ![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))) => (~?[W0: $i] : aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))))) <=> (~((~?[W0: $i] : aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(aSet0(sdtlbdtrb0(xd, szDzizrdt0(xd))) & ![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))))))),
% 2.27/1.77      inference(rewrite,[status(thm)],[])).
% 2.27/1.77  tff(55,axiom,(~((aSet0(sdtlbdtrb0(xd, szDzizrdt0(xd))) & ![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))) => (~?[W0: $i] : aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__4868')).
% 2.27/1.77  tff(56,plain,
% 2.27/1.77      (~((~?[W0: $i] : aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(aSet0(sdtlbdtrb0(xd, szDzizrdt0(xd))) & ![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd)))))))),
% 2.27/1.77      inference(modus_ponens,[status(thm)],[55, 54])).
% 2.27/1.77  tff(57,plain,
% 2.27/1.77      (aSet0(sdtlbdtrb0(xd, szDzizrdt0(xd))) & ![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))),
% 2.27/1.77      inference(or_elim,[status(thm)],[56])).
% 2.27/1.77  tff(58,plain,
% 2.27/1.77      (![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))),
% 2.27/1.77      inference(and_elim,[status(thm)],[57])).
% 2.27/1.77  tff(59,plain,
% 2.27/1.77      (![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))),
% 2.27/1.77      inference(modus_ponens,[status(thm)],[58, 53])).
% 2.27/1.77  tff(60,plain,
% 2.27/1.77      (![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xN)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))),
% 2.27/1.77      inference(modus_ponens,[status(thm)],[59, 52])).
% 2.27/1.77  tff(61,plain,(
% 2.27/1.77      ![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xN)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))),
% 2.27/1.77      inference(skolemize,[status(sab)],[60])).
% 2.27/1.77  tff(62,plain,
% 2.27/1.77      (![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (~((~aElementOf0(W0, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))))),
% 2.27/1.77      inference(modus_ponens,[status(thm)],[61, 50])).
% 2.27/1.77  tff(63,plain,
% 2.27/1.77      (![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (~((~aElementOf0(W0, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))))),
% 2.27/1.77      inference(modus_ponens,[status(thm)],[62, 48])).
% 2.27/1.77  tff(64,plain,
% 2.27/1.77      ((~![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (~((~aElementOf0(W0, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))))) | (aElementOf0(W0!41, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (~((~aElementOf0(W0!41, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0!41) = szDzizrdt0(xd))))))),
% 2.27/1.77      inference(quant_inst,[status(thm)],[])).
% 2.27/1.77  tff(65,plain,
% 2.27/1.77      (aElementOf0(W0!41, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (~((~aElementOf0(W0!41, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0!41) = szDzizrdt0(xd)))))),
% 2.27/1.77      inference(unit_resolution,[status(thm)],[64, 63])).
% 2.27/1.77  tff(66,plain,
% 2.27/1.77      (?[W0: $i] : aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> ?[W0: $i] : aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))),
% 2.27/1.77      inference(rewrite,[status(thm)],[])).
% 2.27/1.77  tff(67,plain,
% 2.27/1.77      (?[W0: $i] : aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))),
% 2.27/1.77      inference(or_elim,[status(thm)],[56])).
% 2.27/1.77  tff(68,plain,
% 2.27/1.77      (?[W0: $i] : aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))),
% 2.27/1.77      inference(modus_ponens,[status(thm)],[67, 66])).
% 2.27/1.77  tff(69,plain,(
% 2.27/1.77      aElementOf0(W0!41, sdtlbdtrb0(xd, szDzizrdt0(xd)))),
% 2.27/1.77      inference(skolemize,[status(sab)],[68])).
% 2.40/1.78  tff(70,plain,
% 2.40/1.78      ((~(aElementOf0(W0!41, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (~((~aElementOf0(W0!41, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0!41) = szDzizrdt0(xd))))))) | (~aElementOf0(W0!41, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~((~aElementOf0(W0!41, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0!41) = szDzizrdt0(xd)))))),
% 2.40/1.78      inference(tautology,[status(thm)],[])).
% 2.40/1.78  tff(71,plain,
% 2.40/1.78      ((~(aElementOf0(W0!41, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (~((~aElementOf0(W0!41, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0!41) = szDzizrdt0(xd))))))) | (~((~aElementOf0(W0!41, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0!41) = szDzizrdt0(xd)))))),
% 2.40/1.78      inference(unit_resolution,[status(thm)],[70, 69])).
% 2.40/1.78  tff(72,plain,
% 2.40/1.78      (~((~aElementOf0(W0!41, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0!41) = szDzizrdt0(xd))))),
% 2.40/1.78      inference(unit_resolution,[status(thm)],[71, 65])).
% 2.40/1.78  tff(73,plain,
% 2.40/1.78      (((~aElementOf0(W0!41, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0!41) = szDzizrdt0(xd)))) | (sdtlpdtrp0(xd, W0!41) = szDzizrdt0(xd))),
% 2.40/1.78      inference(tautology,[status(thm)],[])).
% 2.40/1.78  tff(74,plain,
% 2.40/1.78      (sdtlpdtrp0(xd, W0!41) = szDzizrdt0(xd)),
% 2.40/1.78      inference(unit_resolution,[status(thm)],[73, 72])).
% 2.40/1.78  tff(75,plain,
% 2.40/1.78      (((~aElementOf0(W0!41, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0!41) = szDzizrdt0(xd)))) | aElementOf0(W0!41, szDzozmdt0(xN))),
% 2.40/1.78      inference(tautology,[status(thm)],[])).
% 2.40/1.78  tff(76,plain,
% 2.40/1.78      (aElementOf0(W0!41, szDzozmdt0(xN))),
% 2.40/1.78      inference(unit_resolution,[status(thm)],[75, 72])).
% 2.40/1.78  tff(77,plain,
% 2.40/1.78      (((~![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W1) = szDzizrdt0(xd))))) | ((~aElementOf0(W0!41, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0!41) = szDzizrdt0(xd))))) <=> ((~![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W1) = szDzizrdt0(xd))))) | (~aElementOf0(W0!41, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0!41) = szDzizrdt0(xd))))),
% 2.40/1.78      inference(rewrite,[status(thm)],[])).
% 2.40/1.78  tff(78,plain,
% 2.40/1.78      ((~![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W1) = szDzizrdt0(xd))))) | ((~aElementOf0(W0!41, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0!41) = szDzizrdt0(xd))))),
% 2.40/1.78      inference(quant_inst,[status(thm)],[])).
% 2.40/1.78  tff(79,plain,
% 2.40/1.78      ((~![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W1) = szDzizrdt0(xd))))) | (~aElementOf0(W0!41, szDzozmdt0(xN))) | (~(sdtlpdtrp0(xd, W0!41) = szDzizrdt0(xd)))),
% 2.40/1.78      inference(modus_ponens,[status(thm)],[78, 77])).
% 2.40/1.78  tff(80,plain,
% 2.40/1.78      ($false),
% 2.40/1.78      inference(unit_resolution,[status(thm)],[79, 76, 74, 46])).
% 2.40/1.78  % SZS output end Proof
%------------------------------------------------------------------------------