Z3---4.15.1.THM-Prf.s

%------------------------------------------------------------------------------
% File     : Z3---4.15.1
% Problem  : NUM595+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_E %s %d THM

% Computer : n003.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sat Jun 21 05:21:31 AM UTC 2025

% Result   : Theorem 0.62s 0.81s
% Output   : Proof 0.62s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : NUM595+3 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.12  % Command    : run_E %s %d THM
% 0.11/0.33  % Computer : n003.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit   : 300
% 0.11/0.33  % WCLimit    : 300
% 0.11/0.33  % DateTime   : Fri Jun 20 01:33:24 EDT 2025
% 0.11/0.34  % CPUTime    : 
% 0.62/0.81  % SZS status Theorem
% 0.62/0.81  % SZS output start Proof
% 0.62/0.81  tff(aElementOf0_type, type, (
% 0.62/0.81     aElementOf0: ( $i * $i ) > $o)).
% 0.62/0.81  tff(xT_type, type, (
% 0.62/0.81     xT: $i)).
% 0.62/0.81  tff(tptp_fun_W1_37_type, type, (
% 0.62/0.81     tptp_fun_W1_37: $i > $i)).
% 0.62/0.81  tff(xi_type, type, (
% 0.62/0.81     xi: $i)).
% 0.62/0.81  tff(xx_type, type, (
% 0.62/0.81     xx: $i)).
% 0.62/0.81  tff(sdtlpdtrp0_type, type, (
% 0.62/0.81     sdtlpdtrp0: ( $i * $i ) > $i)).
% 0.62/0.81  tff(xd_type, type, (
% 0.62/0.81     xd: $i)).
% 0.62/0.81  tff(szNzAzT0_type, type, (
% 0.62/0.81     szNzAzT0: $i)).
% 0.62/0.81  tff(tptp_fun_W0_43_type, type, (
% 0.62/0.81     tptp_fun_W0_43: $i)).
% 0.62/0.81  tff(xC_type, type, (
% 0.62/0.81     xC: $i)).
% 0.62/0.81  tff(szszuzczcdt0_type, type, (
% 0.62/0.81     szszuzczcdt0: $i > $i)).
% 0.62/0.81  tff(xN_type, type, (
% 0.62/0.81     xN: $i)).
% 0.62/0.81  tff(tptp_fun_W2_39_type, type, (
% 0.62/0.81     tptp_fun_W2_39: ( $i * $i ) > $i)).
% 0.62/0.81  tff(aSubsetOf0_type, type, (
% 0.62/0.81     aSubsetOf0: ( $i * $i ) > $o)).
% 0.62/0.81  tff(xk_type, type, (
% 0.62/0.81     xk: $i)).
% 0.62/0.81  tff(sbrdtbr0_type, type, (
% 0.62/0.81     sbrdtbr0: $i > $i)).
% 0.62/0.81  tff(slbdtsldtrb0_type, type, (
% 0.62/0.81     slbdtsldtrb0: ( $i * $i ) > $i)).
% 0.62/0.81  tff(aSet0_type, type, (
% 0.62/0.81     aSet0: $i > $o)).
% 0.62/0.81  tff(xX_type, type, (
% 0.62/0.81     xX: $i)).
% 0.62/0.81  tff(tptp_fun_W1_42_type, type, (
% 0.62/0.81     tptp_fun_W1_42: $i > $i)).
% 0.62/0.81  tff(szDzozmdt0_type, type, (
% 0.62/0.81     szDzozmdt0: $i > $i)).
% 0.62/0.81  tff(aFunction0_type, type, (
% 0.62/0.81     aFunction0: $i > $o)).
% 0.62/0.81  tff(tptp_fun_W3_38_type, type, (
% 0.62/0.81     tptp_fun_W3_38: ( $i * $i ) > $i)).
% 0.62/0.81  tff(1,plain,
% 0.62/0.81      ((sdtlpdtrp0(xd, xi) = xx) <=> (sdtlpdtrp0(xd, xi) = xx)),
% 0.62/0.81      inference(rewrite,[status(thm)],[])).
% 0.62/0.81  tff(2,axiom,(aElementOf0(xi, szNzAzT0) & (sdtlpdtrp0(xd, xi) = xx)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__4806')).
% 0.62/0.81  tff(3,plain,
% 0.62/0.81      (sdtlpdtrp0(xd, xi) = xx),
% 0.62/0.81      inference(and_elim,[status(thm)],[2])).
% 0.62/0.81  tff(4,plain,
% 0.62/0.81      (sdtlpdtrp0(xd, xi) = xx),
% 0.62/0.81      inference(modus_ponens,[status(thm)],[3, 1])).
% 0.62/0.81  tff(5,plain,
% 0.62/0.81      (^[W0: $i] : refl((~((~((~aElementOf0(W0, xX)) | (~((~aSet0(W0)) | (~(sbrdtbr0(W0) = xk)) | (~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))) | (~(aElementOf0(W0, xX) | (~(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, xX)) | (~((~aSet0(W0)) | (~(sbrdtbr0(W0) = xk)) | (~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))) | (~(aElementOf0(W0, xX) | (~(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))))))))))))))),
% 0.62/0.81      inference(bind,[status(th)],[])).
% 0.62/0.81  tff(6,plain,
% 0.62/0.81      (![W0: $i] : (~((~((~aElementOf0(W0, xX)) | (~((~aSet0(W0)) | (~(sbrdtbr0(W0) = xk)) | (~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))) | (~(aElementOf0(W0, xX) | (~(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, xX)) | (~((~aSet0(W0)) | (~(sbrdtbr0(W0) = xk)) | (~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))) | (~(aElementOf0(W0, xX) | (~(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)))))))))))))),
% 0.62/0.81      inference(quant_intro,[status(thm)],[5])).
% 0.62/0.81  tff(7,plain,
% 0.62/0.81      (^[W0: $i] : rewrite((~((~((~aElementOf0(W0, xX)) | (~((~aSet0(W0)) | (~(sbrdtbr0(W0) = xk)) | (~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))) | (~(aElementOf0(W0, xX) | (~(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, xX)) | (~((~aSet0(W0)) | (~(sbrdtbr0(W0) = xk)) | (~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))) | (~(aElementOf0(W0, xX) | (~(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))))))))))))))),
% 0.62/0.81      inference(bind,[status(th)],[])).
% 0.62/0.81  tff(8,plain,
% 0.62/0.81      (![W0: $i] : (~((~((~aElementOf0(W0, xX)) | (~((~aSet0(W0)) | (~(sbrdtbr0(W0) = xk)) | (~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))) | (~(aElementOf0(W0, xX) | (~(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, xX)) | (~((~aSet0(W0)) | (~(sbrdtbr0(W0) = xk)) | (~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))) | (~(aElementOf0(W0, xX) | (~(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)))))))))))))),
% 0.62/0.81      inference(quant_intro,[status(thm)],[7])).
% 0.62/0.81  tff(9,plain,
% 0.62/0.81      (![W0: $i] : (~((~((~aElementOf0(W0, xX)) | (~((~aSet0(W0)) | (~(sbrdtbr0(W0) = xk)) | (~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))) | (~(aElementOf0(W0, xX) | (~(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, xX)) | (~((~aSet0(W0)) | (~(sbrdtbr0(W0) = xk)) | (~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))) | (~(aElementOf0(W0, xX) | (~(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)))))))))))))),
% 0.62/0.81      inference(transitivity,[status(thm)],[8, 6])).
% 0.62/0.81  tff(10,plain,
% 0.62/0.81      (^[W0: $i] : trans(monotonicity(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))) <=> ((~aElementOf0(W0, xX)) | (~((~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, xX) | (~(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, xX) | (~(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, xX) | (~(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, xX) | (~(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, xX) | (~(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, xX) | (~(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, xX)) | (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) | (~(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, xX)) | (~((~aSet0(W0)) | (~(sbrdtbr0(W0) = xk)) | (~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))))))) & (aElementOf0(W0, xX) | (~(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, xX)) | (~((~aSet0(W0)) | (~(sbrdtbr0(W0) = xk)) | (~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi)))))))) & (aElementOf0(W0, xX) | (~(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, xX)) | (~((~aSet0(W0)) | (~(sbrdtbr0(W0) = xk)) | (~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))) | (~(aElementOf0(W0, xX) | (~(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, xX)) | (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) | (~(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, xX)) | (~((~aSet0(W0)) | (~(sbrdtbr0(W0) = xk)) | (~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))) | (~(aElementOf0(W0, xX) | (~(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)))))))))))))))),
% 0.62/0.81      inference(bind,[status(th)],[])).
% 0.62/0.81  tff(11,plain,
% 0.62/0.81      (![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))) & (aElementOf0(W0, xX) | (~(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, xX)) | (~((~aSet0(W0)) | (~(sbrdtbr0(W0) = xk)) | (~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))) | (~(aElementOf0(W0, xX) | (~(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)))))))))))))),
% 0.62/0.81      inference(quant_intro,[status(thm)],[10])).
% 0.62/0.81  tff(12,plain,
% 0.62/0.81      (^[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)) | (~((~aElementOf0(tptp_fun_W1_42(W0), W0)) | aElementOf0(tptp_fun_W1_42(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))) & (aElementOf0(W0, xX) | (~(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))))))))))),
% 0.62/0.81      inference(bind,[status(th)],[])).
% 0.62/0.81  tff(13,plain,
% 0.62/0.81      (![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)) | (~((~aElementOf0(tptp_fun_W1_42(W0), W0)) | aElementOf0(tptp_fun_W1_42(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))) & (aElementOf0(W0, xX) | (~(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)))))))))),
% 0.62/0.81      inference(quant_intro,[status(thm)],[12])).
% 0.62/0.81  tff(14,plain,
% 0.62/0.81      (![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)))),
% 0.62/0.81      inference(rewrite,[status(thm)],[])).
% 0.62/0.81  tff(15,plain,
% 0.62/0.81      (^[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))))),
% 0.62/0.81      inference(bind,[status(th)],[])).
% 0.62/0.81  tff(16,plain,
% 0.62/0.81      (![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)))),
% 0.62/0.81      inference(quant_intro,[status(thm)],[15])).
% 0.62/0.81  tff(17,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')).
% 0.62/0.81  tff(18,plain,
% 0.62/0.81      ((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))),
% 0.62/0.81      inference(and_elim,[status(thm)],[17])).
% 0.62/0.81  tff(19,plain,
% 0.62/0.81      (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)))),
% 0.62/0.81      inference(and_elim,[status(thm)],[18])).
% 0.62/0.81  tff(20,plain,
% 0.62/0.81      (![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)))),
% 0.62/0.81      inference(and_elim,[status(thm)],[19])).
% 0.62/0.81  tff(21,plain,
% 0.62/0.81      (![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)))),
% 0.62/0.81      inference(modus_ponens,[status(thm)],[20, 16])).
% 0.62/0.81  tff(22,plain,
% 0.62/0.81      (![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)))),
% 0.62/0.81      inference(modus_ponens,[status(thm)],[21, 14])).
% 0.62/0.81  tff(23,plain,(
% 0.62/0.81      ![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)) | (~((~aElementOf0(tptp_fun_W1_42(W0), W0)) | aElementOf0(tptp_fun_W1_42(W0), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))) | (~(sbrdtbr0(W0) = xk))) | aElementOf0(W0, xX)))),
% 0.62/0.81      inference(skolemize,[status(sab)],[22])).
% 0.62/0.81  tff(24,plain,
% 0.62/0.81      (![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))) & (aElementOf0(W0, xX) | (~(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)))))))))),
% 0.62/0.81      inference(modus_ponens,[status(thm)],[23, 13])).
% 0.62/0.81  tff(25,plain,
% 0.62/0.81      (![W0: $i] : (~((~((~aElementOf0(W0, xX)) | (~((~aSet0(W0)) | (~(sbrdtbr0(W0) = xk)) | (~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))) | (~(aElementOf0(W0, xX) | (~(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)))))))))))))),
% 0.62/0.81      inference(modus_ponens,[status(thm)],[24, 11])).
% 0.62/0.81  tff(26,plain,
% 0.62/0.81      (![W0: $i] : (~((~((~aElementOf0(W0, xX)) | (~((~aSet0(W0)) | (~(sbrdtbr0(W0) = xk)) | (~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))) | (~(aElementOf0(W0, xX) | (~(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)))))))))))))),
% 0.62/0.81      inference(modus_ponens,[status(thm)],[25, 9])).
% 0.62/0.81  tff(27,plain,
% 0.62/0.81      (((~![W0: $i] : (~((~((~aElementOf0(W0, xX)) | (~((~aSet0(W0)) | (~(sbrdtbr0(W0) = xk)) | (~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))) | (~(aElementOf0(W0, xX) | (~(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, xX)) | (~((~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, xX) | (~(sbrdtbr0(W0!43) = xk)) | (~((~((~aSet0(W0!43)) | (~((~aElementOf0(tptp_fun_W1_42(W0!43), W0!43)) | aElementOf0(tptp_fun_W1_42(W0!43), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))) | aSubsetOf0(W0!43, sdtlpdtrp0(xN, szszuzczcdt0(xi)))))))))) <=> ((~![W0: $i] : (~((~((~aElementOf0(W0, xX)) | (~((~aSet0(W0)) | (~(sbrdtbr0(W0) = xk)) | (~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))) | (~(aElementOf0(W0, xX) | (~(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, xX)) | (~((~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, xX) | (~(sbrdtbr0(W0!43) = xk)) | (~((~((~aSet0(W0!43)) | (~((~aElementOf0(tptp_fun_W1_42(W0!43), W0!43)) | aElementOf0(tptp_fun_W1_42(W0!43), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))) | aSubsetOf0(W0!43, sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))))),
% 0.62/0.81      inference(rewrite,[status(thm)],[])).
% 0.62/0.81  tff(28,plain,
% 0.62/0.81      ((~((~((~aElementOf0(W0!43, xX)) | (~((~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, xX) | (~(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, xX)) | (~((~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, xX) | (~(sbrdtbr0(W0!43) = xk)) | (~((~((~aSet0(W0!43)) | (~((~aElementOf0(tptp_fun_W1_42(W0!43), W0!43)) | aElementOf0(tptp_fun_W1_42(W0!43), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))) | aSubsetOf0(W0!43, sdtlpdtrp0(xN, szszuzczcdt0(xi)))))))))),
% 0.62/0.81      inference(rewrite,[status(thm)],[])).
% 0.62/0.81  tff(29,plain,
% 0.62/0.81      (((~![W0: $i] : (~((~((~aElementOf0(W0, xX)) | (~((~aSet0(W0)) | (~(sbrdtbr0(W0) = xk)) | (~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))) | (~(aElementOf0(W0, xX) | (~(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, xX)) | (~((~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, xX) | (~(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)))))))))))))) <=> ((~![W0: $i] : (~((~((~aElementOf0(W0, xX)) | (~((~aSet0(W0)) | (~(sbrdtbr0(W0) = xk)) | (~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))) | (~(aElementOf0(W0, xX) | (~(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, xX)) | (~((~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, xX) | (~(sbrdtbr0(W0!43) = xk)) | (~((~((~aSet0(W0!43)) | (~((~aElementOf0(tptp_fun_W1_42(W0!43), W0!43)) | aElementOf0(tptp_fun_W1_42(W0!43), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))) | aSubsetOf0(W0!43, sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))))),
% 0.62/0.81      inference(monotonicity,[status(thm)],[28])).
% 0.62/0.81  tff(30,plain,
% 0.62/0.81      (((~![W0: $i] : (~((~((~aElementOf0(W0, xX)) | (~((~aSet0(W0)) | (~(sbrdtbr0(W0) = xk)) | (~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))) | (~(aElementOf0(W0, xX) | (~(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, xX)) | (~((~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, xX) | (~(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)))))))))))))) <=> ((~![W0: $i] : (~((~((~aElementOf0(W0, xX)) | (~((~aSet0(W0)) | (~(sbrdtbr0(W0) = xk)) | (~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))) | (~(aElementOf0(W0, xX) | (~(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, xX)) | (~((~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, xX) | (~(sbrdtbr0(W0!43) = xk)) | (~((~((~aSet0(W0!43)) | (~((~aElementOf0(tptp_fun_W1_42(W0!43), W0!43)) | aElementOf0(tptp_fun_W1_42(W0!43), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))) | aSubsetOf0(W0!43, sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))))),
% 0.62/0.82      inference(transitivity,[status(thm)],[29, 27])).
% 0.62/0.82  tff(31,plain,
% 0.62/0.82      ((~![W0: $i] : (~((~((~aElementOf0(W0, xX)) | (~((~aSet0(W0)) | (~(sbrdtbr0(W0) = xk)) | (~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))) | (~(aElementOf0(W0, xX) | (~(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, xX)) | (~((~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, xX) | (~(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)))))))))))))),
% 0.62/0.82      inference(quant_inst,[status(thm)],[])).
% 0.62/0.82  tff(32,plain,
% 0.62/0.82      ((~![W0: $i] : (~((~((~aElementOf0(W0, xX)) | (~((~aSet0(W0)) | (~(sbrdtbr0(W0) = xk)) | (~aSubsetOf0(W0, sdtlpdtrp0(xN, szszuzczcdt0(xi)))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))) | (~(aElementOf0(W0, xX) | (~(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, xX)) | (~((~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, xX) | (~(sbrdtbr0(W0!43) = xk)) | (~((~((~aSet0(W0!43)) | (~((~aElementOf0(tptp_fun_W1_42(W0!43), W0!43)) | aElementOf0(tptp_fun_W1_42(W0!43), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))) | aSubsetOf0(W0!43, sdtlpdtrp0(xN, szszuzczcdt0(xi)))))))))),
% 0.62/0.82      inference(modus_ponens,[status(thm)],[31, 30])).
% 0.62/0.82  tff(33,plain,
% 0.62/0.82      (~((~((~aElementOf0(W0!43, xX)) | (~((~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, xX) | (~(sbrdtbr0(W0!43) = xk)) | (~((~((~aSet0(W0!43)) | (~((~aElementOf0(tptp_fun_W1_42(W0!43), W0!43)) | aElementOf0(tptp_fun_W1_42(W0!43), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))) | aSubsetOf0(W0!43, sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))),
% 0.62/0.82      inference(unit_resolution,[status(thm)],[32, 26])).
% 0.62/0.82  tff(34,plain,
% 0.62/0.82      (((~((~aElementOf0(W0!43, xX)) | (~((~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, xX) | (~(sbrdtbr0(W0!43) = xk)) | (~((~((~aSet0(W0!43)) | (~((~aElementOf0(tptp_fun_W1_42(W0!43), W0!43)) | aElementOf0(tptp_fun_W1_42(W0!43), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))) | aSubsetOf0(W0!43, sdtlpdtrp0(xN, szszuzczcdt0(xi)))))))) | ((~aElementOf0(W0!43, xX)) | (~((~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))))))))),
% 0.62/0.82      inference(tautology,[status(thm)],[])).
% 0.62/0.82  tff(35,plain,
% 0.62/0.82      ((~aElementOf0(W0!43, xX)) | (~((~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)))))))),
% 0.62/0.82      inference(unit_resolution,[status(thm)],[34, 33])).
% 0.62/0.82  tff(36,plain,
% 0.62/0.82      (?[W0: $i] : aElementOf0(W0, xX) <=> ?[W0: $i] : aElementOf0(W0, xX)),
% 0.62/0.82      inference(rewrite,[status(thm)],[])).
% 0.62/0.82  tff(37,plain,
% 0.62/0.82      ((~(~?[W0: $i] : aElementOf0(W0, xX))) <=> ?[W0: $i] : aElementOf0(W0, xX)),
% 0.62/0.82      inference(rewrite,[status(thm)],[])).
% 0.62/0.82  tff(38,plain,
% 0.62/0.82      ((~?[W0: $i] : aElementOf0(W0, xX)) <=> (~?[W0: $i] : aElementOf0(W0, xX))),
% 0.62/0.82      inference(rewrite,[status(thm)],[])).
% 0.62/0.82  tff(39,plain,
% 0.62/0.82      ((~(~?[W0: $i] : aElementOf0(W0, xX))) <=> (~(~?[W0: $i] : aElementOf0(W0, xX)))),
% 0.62/0.82      inference(monotonicity,[status(thm)],[38])).
% 0.62/0.82  tff(40,plain,
% 0.62/0.82      ((~(~?[W0: $i] : aElementOf0(W0, xX))) <=> ?[W0: $i] : aElementOf0(W0, xX)),
% 0.62/0.82      inference(transitivity,[status(thm)],[39, 37])).
% 0.62/0.82  tff(41,plain,
% 0.62/0.82      (~(~?[W0: $i] : aElementOf0(W0, xX))),
% 0.62/0.82      inference(and_elim,[status(thm)],[17])).
% 0.62/0.82  tff(42,plain,
% 0.62/0.82      (?[W0: $i] : aElementOf0(W0, xX)),
% 0.62/0.82      inference(modus_ponens,[status(thm)],[41, 40])).
% 0.62/0.82  tff(43,plain,
% 0.62/0.82      (?[W0: $i] : aElementOf0(W0, xX)),
% 0.62/0.82      inference(modus_ponens,[status(thm)],[42, 36])).
% 0.62/0.82  tff(44,plain,(
% 0.62/0.82      aElementOf0(W0!43, xX)),
% 0.62/0.82      inference(skolemize,[status(sab)],[43])).
% 0.62/0.82  tff(45,plain,
% 0.62/0.82      ((~((~aElementOf0(W0!43, xX)) | (~((~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, xX)) | (~((~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)))))))),
% 0.62/0.82      inference(tautology,[status(thm)],[])).
% 0.62/0.82  tff(46,plain,
% 0.62/0.82      ((~((~aElementOf0(W0!43, xX)) | (~((~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)))))))),
% 0.62/0.82      inference(unit_resolution,[status(thm)],[45, 44])).
% 0.62/0.82  tff(47,plain,
% 0.62/0.82      (~((~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))))))),
% 0.62/0.82      inference(unit_resolution,[status(thm)],[46, 35])).
% 0.62/0.82  tff(48,plain,
% 0.62/0.82      (((~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)))))) | aSubsetOf0(W0!43, sdtlpdtrp0(xN, szszuzczcdt0(xi)))),
% 0.62/0.82      inference(tautology,[status(thm)],[])).
% 0.62/0.82  tff(49,plain,
% 0.62/0.82      (aSubsetOf0(W0!43, sdtlpdtrp0(xN, szszuzczcdt0(xi)))),
% 0.62/0.82      inference(unit_resolution,[status(thm)],[48, 47])).
% 0.62/0.82  tff(50,plain,
% 0.62/0.82      ((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)))) | (~aSubsetOf0(W0!43, sdtlpdtrp0(xN, szszuzczcdt0(xi))))),
% 0.62/0.82      inference(tautology,[status(thm)],[])).
% 0.62/0.82  tff(51,plain,
% 0.62/0.82      (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)))),
% 0.62/0.82      inference(unit_resolution,[status(thm)],[50, 49])).
% 0.62/0.82  tff(52,plain,
% 0.62/0.82      (((~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)))))) | (sbrdtbr0(W0!43) = xk)),
% 0.62/0.82      inference(tautology,[status(thm)],[])).
% 0.62/0.82  tff(53,plain,
% 0.62/0.82      (sbrdtbr0(W0!43) = xk),
% 0.62/0.82      inference(unit_resolution,[status(thm)],[52, 47])).
% 0.62/0.82  tff(54,plain,
% 0.62/0.82      ((~((~(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))))))) | (~(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)))))),
% 0.62/0.82      inference(tautology,[status(thm)],[])).
% 0.62/0.82  tff(55,plain,
% 0.62/0.82      (~((~(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))))))),
% 0.62/0.82      inference(unit_resolution,[status(thm)],[54, 53, 51])).
% 0.62/0.82  tff(56,plain,
% 0.62/0.82      ((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)))))))) | ((~(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))))))),
% 0.62/0.82      inference(tautology,[status(thm)],[])).
% 0.62/0.82  tff(57,plain,
% 0.62/0.82      (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)))))))),
% 0.62/0.82      inference(unit_resolution,[status(thm)],[56, 55])).
% 0.62/0.82  tff(58,plain,
% 0.62/0.82      (((~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)),
% 0.62/0.82      inference(tautology,[status(thm)],[])).
% 0.62/0.82  tff(59,plain,
% 0.62/0.82      (aSet0(W0!43)),
% 0.62/0.82      inference(unit_resolution,[status(thm)],[58, 47])).
% 0.62/0.82  tff(60,plain,
% 0.62/0.82      (aElementOf0(xi, szNzAzT0) <=> aElementOf0(xi, szNzAzT0)),
% 0.62/0.82      inference(rewrite,[status(thm)],[])).
% 0.62/0.82  tff(61,plain,
% 0.62/0.82      (aElementOf0(xi, szNzAzT0)),
% 0.62/0.82      inference(and_elim,[status(thm)],[2])).
% 0.62/0.82  tff(62,plain,
% 0.62/0.82      (aElementOf0(xi, szNzAzT0)),
% 0.62/0.82      inference(modus_ponens,[status(thm)],[61, 60])).
% 0.62/0.82  tff(63,plain,
% 0.62/0.82      (^[W0: $i] : refl(((~aElementOf0(W0, szNzAzT0)) | ![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, szNzAzT0)) | ![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))))))))))))),
% 0.62/0.82      inference(bind,[status(th)],[])).
% 0.62/0.82  tff(64,plain,
% 0.62/0.82      (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![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, szNzAzT0)) | ![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)))))))))))),
% 0.62/0.82      inference(quant_intro,[status(thm)],[63])).
% 0.62/0.82  tff(65,plain,
% 0.62/0.82      (^[W0: $i] : rewrite(((~aElementOf0(W0, szNzAzT0)) | ![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, szNzAzT0)) | ![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))))))))))))),
% 0.62/0.82      inference(bind,[status(th)],[])).
% 0.62/0.82  tff(66,plain,
% 0.62/0.82      (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![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, szNzAzT0)) | ![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)))))))))))),
% 0.62/0.82      inference(quant_intro,[status(thm)],[65])).
% 0.62/0.82  tff(67,plain,
% 0.62/0.82      (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![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, szNzAzT0)) | ![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)))))))))))),
% 0.62/0.82      inference(transitivity,[status(thm)],[66, 64])).
% 0.62/0.82  tff(68,plain,
% 0.62/0.82      (^[W0: $i] : rewrite(((~aElementOf0(W0, szNzAzT0)) | ![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, szNzAzT0)) | ![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))))))))))))),
% 0.62/0.82      inference(bind,[status(th)],[])).
% 0.62/0.82  tff(69,plain,
% 0.62/0.82      (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![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, szNzAzT0)) | ![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)))))))))))),
% 0.62/0.82      inference(quant_intro,[status(thm)],[68])).
% 0.62/0.82  tff(70,plain,
% 0.62/0.82      (^[W0: $i] : rewrite(((~aElementOf0(W0, szNzAzT0)) | ![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, szNzAzT0)) | ![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)))))))))))),
% 0.62/0.82      inference(bind,[status(th)],[])).
% 0.62/0.82  tff(71,plain,
% 0.62/0.82      (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![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, szNzAzT0)) | ![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))))))))))),
% 0.62/0.82      inference(quant_intro,[status(thm)],[70])).
% 0.62/0.82  tff(72,plain,
% 0.62/0.82      (![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))))),
% 0.62/0.82      inference(rewrite,[status(thm)],[])).
% 0.62/0.82  tff(73,plain,
% 0.62/0.82      (^[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))))))),
% 0.62/0.82      inference(bind,[status(th)],[])).
% 0.62/0.82  tff(74,plain,
% 0.62/0.82      (![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))))),
% 0.62/0.82      inference(quant_intro,[status(thm)],[73])).
% 0.62/0.82  tff(75,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')).
% 0.62/0.82  tff(76,plain,
% 0.62/0.82      (![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))))),
% 0.62/0.82      inference(and_elim,[status(thm)],[75])).
% 0.62/0.82  tff(77,plain,
% 0.62/0.82      (![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))))),
% 0.62/0.82      inference(modus_ponens,[status(thm)],[76, 74])).
% 0.62/0.82  tff(78,plain,
% 0.62/0.82      (![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))))),
% 0.62/0.82      inference(modus_ponens,[status(thm)],[77, 72])).
% 0.62/0.82  tff(79,plain,(
% 0.62/0.82      ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![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))))),
% 0.62/0.82      inference(skolemize,[status(sab)],[78])).
% 0.62/0.82  tff(80,plain,
% 0.62/0.82      (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![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))))))))))),
% 0.62/0.82      inference(modus_ponens,[status(thm)],[79, 71])).
% 0.62/0.82  tff(81,plain,
% 0.62/0.82      (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![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)))))))))))),
% 0.62/0.82      inference(modus_ponens,[status(thm)],[80, 69])).
% 0.62/0.82  tff(82,plain,
% 0.62/0.82      (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![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)))))))))))),
% 0.62/0.82      inference(modus_ponens,[status(thm)],[81, 67])).
% 0.62/0.82  tff(83,plain,
% 0.62/0.82      (((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![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, szNzAzT0)) | ![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, szNzAzT0)) | ![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, szNzAzT0)) | ![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)))))))))))),
% 0.62/0.82      inference(rewrite,[status(thm)],[])).
% 0.62/0.82  tff(84,plain,
% 0.62/0.82      (((~aElementOf0(xi, szNzAzT0)) | ![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, szNzAzT0)) | ![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)))))))))))),
% 0.62/0.83      inference(rewrite,[status(thm)],[])).
% 0.62/0.83  tff(85,plain,
% 0.62/0.83      (((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![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, szNzAzT0)) | ![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, szNzAzT0)) | ![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, szNzAzT0)) | ![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))))))))))))),
% 0.62/0.83      inference(monotonicity,[status(thm)],[84])).
% 0.62/0.83  tff(86,plain,
% 0.62/0.83      (((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![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, szNzAzT0)) | ![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, szNzAzT0)) | ![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, szNzAzT0)) | ![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)))))))))))),
% 0.62/0.83      inference(transitivity,[status(thm)],[85, 83])).
% 0.62/0.83  tff(87,plain,
% 0.62/0.83      ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![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, szNzAzT0)) | ![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)))))))))))),
% 0.62/0.83      inference(quant_inst,[status(thm)],[])).
% 0.62/0.83  tff(88,plain,
% 0.62/0.83      ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | ![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, szNzAzT0)) | ![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))))))))))),
% 0.62/0.83      inference(modus_ponens,[status(thm)],[87, 86])).
% 0.62/0.83  tff(89,plain,
% 0.62/0.83      (![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))))))))))),
% 0.62/0.83      inference(unit_resolution,[status(thm)],[88, 82, 62])).
% 0.62/0.83  tff(90,plain,
% 0.62/0.83      (((~![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))))))))))),
% 0.62/0.83      inference(rewrite,[status(thm)],[])).
% 0.62/0.83  tff(91,plain,
% 0.62/0.83      ((~![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))))))))))),
% 0.62/0.83      inference(quant_inst,[status(thm)],[])).
% 0.62/0.83  tff(92,plain,
% 0.62/0.83      ((~![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)))))))))),
% 0.62/0.83      inference(modus_ponens,[status(thm)],[91, 90])).
% 0.62/0.83  tff(93,plain,
% 0.62/0.83      (sdtlpdtrp0(xd, xi) = sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0!43)),
% 0.62/0.83      inference(unit_resolution,[status(thm)],[92, 89, 59, 57])).
% 0.62/0.83  tff(94,plain,
% 0.62/0.83      (sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0!43) = sdtlpdtrp0(xd, xi)),
% 0.62/0.83      inference(symmetry,[status(thm)],[93])).
% 0.62/0.83  tff(95,plain,
% 0.62/0.83      ((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)))) | (~aSubsetOf0(W0!43, sdtlpdtrp0(xN, szszuzczcdt0(xi))))),
% 0.62/0.83      inference(tautology,[status(thm)],[])).
% 0.62/0.83  tff(96,plain,
% 0.62/0.83      (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)))),
% 0.62/0.83      inference(unit_resolution,[status(thm)],[95, 49])).
% 0.62/0.83  tff(97,plain,
% 0.62/0.83      ((~((~(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))))))) | (~(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)))))),
% 0.62/0.83      inference(tautology,[status(thm)],[])).
% 0.62/0.83  tff(98,plain,
% 0.62/0.83      (~((~(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))))))),
% 0.62/0.83      inference(unit_resolution,[status(thm)],[97, 53, 96])).
% 0.62/0.83  tff(99,plain,
% 0.62/0.83      ((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)))))))) | ((~(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))))))),
% 0.62/0.83      inference(tautology,[status(thm)],[])).
% 0.62/0.83  tff(100,plain,
% 0.62/0.83      (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)))))))),
% 0.62/0.83      inference(unit_resolution,[status(thm)],[99, 98])).
% 0.62/0.83  tff(101,plain,
% 0.62/0.83      (^[W0: $i] : refl(((~aElementOf0(W0, szNzAzT0)) | (~((~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, szNzAzT0)) | (~((~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)))))))))))))))),
% 0.62/0.83      inference(bind,[status(th)],[])).
% 0.62/0.83  tff(102,plain,
% 0.62/0.83      (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~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, szNzAzT0)) | (~((~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))))))))))))))),
% 0.62/0.83      inference(quant_intro,[status(thm)],[101])).
% 0.62/0.83  tff(103,plain,
% 0.62/0.83      (^[W0: $i] : rewrite(((~aElementOf0(W0, szNzAzT0)) | (~((~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, szNzAzT0)) | (~((~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)))))))))))))))),
% 0.62/0.83      inference(bind,[status(th)],[])).
% 0.62/0.83  tff(104,plain,
% 0.62/0.83      (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~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, szNzAzT0)) | (~((~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))))))))))))))),
% 0.62/0.83      inference(quant_intro,[status(thm)],[103])).
% 0.62/0.83  tff(105,plain,
% 0.62/0.83      (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~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, szNzAzT0)) | (~((~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))))))))))))))),
% 0.62/0.83      inference(transitivity,[status(thm)],[104, 102])).
% 0.62/0.83  tff(106,plain,
% 0.62/0.83      (^[W0: $i] : rewrite(((~aElementOf0(W0, szNzAzT0)) | (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, szNzAzT0)) | (~((~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)))))))))))))))),
% 0.62/0.83      inference(bind,[status(th)],[])).
% 0.62/0.83  tff(107,plain,
% 0.62/0.83      (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (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, szNzAzT0)) | (~((~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))))))))))))))),
% 0.62/0.83      inference(quant_intro,[status(thm)],[106])).
% 0.62/0.83  tff(108,plain,
% 0.62/0.83      (^[W0: $i] : rewrite(((~aElementOf0(W0, szNzAzT0)) | (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, szNzAzT0)) | (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))))))))))))),
% 0.62/0.83      inference(bind,[status(th)],[])).
% 0.62/0.83  tff(109,plain,
% 0.62/0.83      (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (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, szNzAzT0)) | (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)))))))))))),
% 0.62/0.83      inference(quant_intro,[status(thm)],[108])).
% 0.62/0.83  tff(110,plain,
% 0.62/0.83      (![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))))),
% 0.62/0.83      inference(rewrite,[status(thm)],[])).
% 0.62/0.83  tff(111,plain,
% 0.62/0.83      (^[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))))))),
% 0.62/0.83      inference(bind,[status(th)],[])).
% 0.62/0.83  tff(112,plain,
% 0.62/0.83      (![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))))),
% 0.62/0.83      inference(quant_intro,[status(thm)],[111])).
% 0.62/0.83  tff(113,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')).
% 0.62/0.83  tff(114,plain,
% 0.62/0.83      (![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))))),
% 0.62/0.83      inference(modus_ponens,[status(thm)],[113, 112])).
% 0.62/0.83  tff(115,plain,
% 0.62/0.83      (![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))))),
% 0.62/0.83      inference(modus_ponens,[status(thm)],[114, 110])).
% 0.62/0.83  tff(116,plain,(
% 0.62/0.83      ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (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)))))),
% 0.62/0.83      inference(skolemize,[status(sab)],[115])).
% 0.62/0.83  tff(117,plain,
% 0.62/0.83      (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (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)))))))))))),
% 0.62/0.83      inference(modus_ponens,[status(thm)],[116, 109])).
% 0.62/0.83  tff(118,plain,
% 0.62/0.83      (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~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))))))))))))))),
% 0.62/0.83      inference(modus_ponens,[status(thm)],[117, 107])).
% 0.62/0.83  tff(119,plain,
% 0.62/0.83      (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~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))))))))))))))),
% 0.62/0.83      inference(modus_ponens,[status(thm)],[118, 105])).
% 0.62/0.83  tff(120,plain,
% 0.62/0.83      (((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~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, szNzAzT0)) | (~((~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, szNzAzT0)) | (~((~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, szNzAzT0)) | (~((~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))))))))))))))),
% 0.62/0.83      inference(rewrite,[status(thm)],[])).
% 0.62/0.83  tff(121,plain,
% 0.62/0.83      ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~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, szNzAzT0)) | (~((~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))))))))))))))),
% 0.62/0.83      inference(quant_inst,[status(thm)],[])).
% 0.62/0.83  tff(122,plain,
% 0.62/0.83      ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~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, szNzAzT0)) | (~((~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)))))))))))))),
% 0.62/0.84      inference(modus_ponens,[status(thm)],[121, 120])).
% 0.62/0.84  tff(123,plain,
% 0.62/0.84      (~((~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))))))))))))),
% 0.62/0.84      inference(unit_resolution,[status(thm)],[122, 119, 62])).
% 0.62/0.84  tff(124,plain,
% 0.62/0.84      (((~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))))))))))),
% 0.62/0.84      inference(tautology,[status(thm)],[])).
% 0.62/0.84  tff(125,plain,
% 0.62/0.84      (![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))))))))))),
% 0.62/0.84      inference(unit_resolution,[status(thm)],[124, 123])).
% 0.62/0.84  tff(126,plain,
% 0.62/0.84      (((~![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), W0!43)) | aElementOf0(tptp_fun_W3_38(W0!43, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi))))))))))),
% 0.62/0.84      inference(rewrite,[status(thm)],[])).
% 0.62/0.84  tff(127,plain,
% 0.62/0.84      ((~![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))))))))))),
% 0.62/0.84      inference(quant_inst,[status(thm)],[])).
% 0.62/0.84  tff(128,plain,
% 0.62/0.84      ((~![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)))))))))),
% 0.62/0.84      inference(modus_ponens,[status(thm)],[127, 126])).
% 0.62/0.84  tff(129,plain,
% 0.62/0.84      (sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0!43) = tptp_fun_W1_37(xi)),
% 0.62/0.84      inference(unit_resolution,[status(thm)],[128, 125, 59, 100])).
% 0.62/0.84  tff(130,plain,
% 0.62/0.84      (tptp_fun_W1_37(xi) = sdtlpdtrp0(sdtlpdtrp0(xC, xi), W0!43)),
% 0.62/0.84      inference(symmetry,[status(thm)],[129])).
% 0.62/0.84  tff(131,plain,
% 0.62/0.84      (tptp_fun_W1_37(xi) = xx),
% 0.62/0.84      inference(transitivity,[status(thm)],[130, 94, 4])).
% 0.62/0.84  tff(132,plain,
% 0.62/0.84      (aElementOf0(tptp_fun_W1_37(xi), xT) <=> aElementOf0(xx, xT)),
% 0.62/0.84      inference(monotonicity,[status(thm)],[131])).
% 0.62/0.84  tff(133,plain,
% 0.62/0.84      (aElementOf0(xx, xT) <=> aElementOf0(tptp_fun_W1_37(xi), xT)),
% 0.62/0.84      inference(symmetry,[status(thm)],[132])).
% 0.62/0.84  tff(134,plain,
% 0.62/0.84      ((~aElementOf0(xx, xT)) <=> (~aElementOf0(tptp_fun_W1_37(xi), xT))),
% 0.62/0.84      inference(monotonicity,[status(thm)],[133])).
% 0.62/0.84  tff(135,plain,
% 0.62/0.84      ((~aElementOf0(xx, xT)) <=> (~aElementOf0(xx, xT))),
% 0.62/0.84      inference(rewrite,[status(thm)],[])).
% 0.62/0.84  tff(136,axiom,(~aElementOf0(xx, xT)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__')).
% 0.62/0.84  tff(137,plain,
% 0.62/0.84      (~aElementOf0(xx, xT)),
% 0.62/0.84      inference(modus_ponens,[status(thm)],[136, 135])).
% 0.62/0.84  tff(138,plain,
% 0.62/0.84      (~aElementOf0(tptp_fun_W1_37(xi), xT)),
% 0.62/0.84      inference(modus_ponens,[status(thm)],[137, 134])).
% 0.62/0.84  tff(139,plain,
% 0.62/0.84      (((~aElementOf0(tptp_fun_W1_37(xi), xT)) | (~![W2: $i] : ((~aSet0(W2)) | (sdtlpdtrp0(sdtlpdtrp0(xC, xi), W2) = tptp_fun_W1_37(xi)) | (~(aElementOf0(W2, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(xi)), xk)) | (~((~(sbrdtbr0(W2) = xk)) | (~(aSubsetOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(xi))) | (~aElementOf0(tptp_fun_W3_38(W2, xi), W2)) | aElementOf0(tptp_fun_W3_38(W2, xi), sdtlpdtrp0(xN, szszuzczcdt0(xi)))))))))))) | aElementOf0(tptp_fun_W1_37(xi), xT)),
% 0.62/0.84      inference(tautology,[status(thm)],[])).
% 0.62/0.84  tff(140,plain,
% 0.62/0.84      (aElementOf0(tptp_fun_W1_37(xi), xT)),
% 0.62/0.84      inference(unit_resolution,[status(thm)],[139, 123])).
% 0.62/0.84  tff(141,plain,
% 0.62/0.84      ($false),
% 0.62/0.84      inference(unit_resolution,[status(thm)],[140, 138])).
% 0.62/0.84  % SZS output end Proof
% 0.62/0.85  % E exiting
%------------------------------------------------------------------------------