Z3---4.15.1.THM-Prf.s

%------------------------------------------------------------------------------
% File     : Z3---4.15.1
% Problem  : NUM536+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_E %s %d THM

% Computer : n002.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 05:21:19 AM UTC 2025

% Result   : Theorem 0.18s 0.40s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : NUM536+1 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.12  % Command    : run_E %s %d THM
% 0.12/0.33  % Computer : n002.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Fri Jun 20 01:25:31 EDT 2025
% 0.12/0.33  % CPUTime    : 
% 0.18/0.40  % SZS status Theorem
% 0.18/0.40  % SZS output start Proof
% 0.18/0.40  tff(aElementOf0_type, type, (
% 0.18/0.40     aElementOf0: ( $i * $i ) > $o)).
% 0.18/0.40  tff(xS_type, type, (
% 0.18/0.40     xS: $i)).
% 0.18/0.40  tff(tptp_fun_W3_3_type, type, (
% 0.18/0.40     tptp_fun_W3_3: ( $i * $i * $i ) > $i)).
% 0.18/0.40  tff(sdtpldt0_type, type, (
% 0.18/0.40     sdtpldt0: ( $i * $i ) > $i)).
% 0.18/0.40  tff(xx_type, type, (
% 0.18/0.40     xx: $i)).
% 0.18/0.40  tff(aElement0_type, type, (
% 0.18/0.40     aElement0: $i > $o)).
% 0.18/0.40  tff(aSet0_type, type, (
% 0.18/0.40     aSet0: $i > $o)).
% 0.18/0.40  tff(tptp_fun_W3_2_type, type, (
% 0.18/0.40     tptp_fun_W3_2: ( $i * $i * $i ) > $i)).
% 0.18/0.40  tff(sdtmndt0_type, type, (
% 0.18/0.40     sdtmndt0: ( $i * $i ) > $i)).
% 0.18/0.40  tff(1,assumption,((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, sdtpldt0(xS, xx)))))), introduced(assumption)).
% 0.18/0.40  tff(2,plain,
% 0.18/0.40      (aSet0(xS) <=> aSet0(xS)),
% 0.18/0.40      inference(rewrite,[status(thm)],[])).
% 0.18/0.40  tff(3,axiom,(aElement0(xx) & aSet0(xS)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__679')).
% 0.18/0.40  tff(4,plain,
% 0.18/0.40      (aSet0(xS)),
% 0.18/0.40      inference(and_elim,[status(thm)],[3])).
% 0.18/0.40  tff(5,plain,
% 0.18/0.40      (aSet0(xS)),
% 0.18/0.40      inference(modus_ponens,[status(thm)],[4, 2])).
% 0.18/0.40  tff(6,plain,
% 0.18/0.40      (aElement0(xx) <=> aElement0(xx)),
% 0.18/0.40      inference(rewrite,[status(thm)],[])).
% 0.18/0.40  tff(7,plain,
% 0.18/0.40      (aElement0(xx)),
% 0.18/0.40      inference(and_elim,[status(thm)],[3])).
% 0.18/0.40  tff(8,plain,
% 0.18/0.40      (aElement0(xx)),
% 0.18/0.40      inference(modus_ponens,[status(thm)],[7, 6])).
% 0.18/0.40  tff(9,plain,
% 0.18/0.40      (^[W0: $i, W1: $i] : trans(monotonicity(quant_intro(proof_bind(^[W2: $i] : rewrite((~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))))) <=> (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))))))), (![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))))) <=> ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))))))), (((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2))))))))))))), rewrite(((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2))))))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))))))), (((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))))))))),
% 0.18/0.40      inference(bind,[status(th)],[])).
% 0.18/0.40  tff(10,plain,
% 0.18/0.40      (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2))))))) <=> ![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))))))),
% 0.18/0.40      inference(quant_intro,[status(thm)],[9])).
% 0.18/0.40  tff(11,plain,
% 0.18/0.40      (^[W0: $i, W1: $i] : refl(((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2))))))))),
% 0.18/0.40      inference(bind,[status(th)],[])).
% 0.18/0.40  tff(12,plain,
% 0.18/0.40      (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2))))))) <=> ![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))))))),
% 0.18/0.40      inference(quant_intro,[status(thm)],[11])).
% 0.18/0.40  tff(13,plain,
% 0.18/0.40      (^[W0: $i, W1: $i] : rewrite(((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2))))))))),
% 0.18/0.40      inference(bind,[status(th)],[])).
% 0.18/0.40  tff(14,plain,
% 0.18/0.40      (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2))))))) <=> ![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))))))),
% 0.18/0.40      inference(quant_intro,[status(thm)],[13])).
% 0.18/0.40  tff(15,plain,
% 0.18/0.40      (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2))))))) <=> ![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))))))),
% 0.18/0.40      inference(transitivity,[status(thm)],[14, 12])).
% 0.18/0.40  tff(16,plain,
% 0.18/0.40      (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aSet0(W0) & aElement0(W1)) <=> (~((~aSet0(W0)) | (~aElement0(W1))))), ((~(aSet0(W0) & aElement0(W1))) <=> (~(~((~aSet0(W0)) | (~aElement0(W1))))))), rewrite((~(~((~aSet0(W0)) | (~aElement0(W1))))) <=> ((~aSet0(W0)) | (~aElement0(W1)))), ((~(aSet0(W0) & aElement0(W1))) <=> ((~aSet0(W0)) | (~aElement0(W1))))), quant_intro(proof_bind(^[W2: $i] : trans(monotonicity(rewrite(((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) <=> ((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))), trans(monotonicity(trans(monotonicity(trans(trans(monotonicity(rewrite((aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))) <=> (~((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))), ((aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> (aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> (~((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))), rewrite((aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> (~((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))) <=> (~(((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))), ((aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> (~(((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2))))), rewrite((~(((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2))) <=> (~(((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))), ((aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> (~(((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2))))), ((~(aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))) <=> (~(~(((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))))), rewrite((~(~(((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))) <=> (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2))), ((~(aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))) <=> (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))), (((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))) <=> ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2))))), rewrite(((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2))) <=> ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))), (((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))) <=> ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2))))), ((((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) <=> (((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2))))))) & ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))))), rewrite((((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2))))))) & ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))) <=> (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2))))))), ((((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) <=> (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2))))))))), (![W2: $i] : (((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))) <=> ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))))))), (((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))) <=> (((~aSet0(W0)) | (~aElement0(W1))) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2))))))))), rewrite((((~aSet0(W0)) | (~aElement0(W1))) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))))))), (((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))))))))),
% 0.18/0.40      inference(bind,[status(th)],[])).
% 0.18/0.40  tff(17,plain,
% 0.18/0.40      (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))) <=> ![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))))))),
% 0.18/0.40      inference(quant_intro,[status(thm)],[16])).
% 0.18/0.40  tff(18,plain,
% 0.18/0.40      (^[W0: $i, W1: $i] : rewrite(((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | ((~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))))) <=> ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))))),
% 0.18/0.40      inference(bind,[status(th)],[])).
% 0.18/0.40  tff(19,plain,
% 0.18/0.40      (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | ((~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))))) <=> ![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))))),
% 0.18/0.41      inference(quant_intro,[status(thm)],[18])).
% 0.18/0.41  tff(20,plain,
% 0.18/0.41      (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0))))))) <=> ![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))))),
% 0.18/0.41      inference(rewrite,[status(thm)],[])).
% 0.18/0.41  tff(21,plain,
% 0.18/0.41      (^[W0: $i, W1: $i] : trans(monotonicity(quant_intro(proof_bind(^[W2: $i] : rewrite(((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & (aElementOf0(W3, W0) | (W3 = W1)))))) <=> ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))))), (![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & (aElementOf0(W3, W0) | (W3 = W1)))))) <=> ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))))), (((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & (aElementOf0(W3, W0) | (W3 = W1))))))) <=> ((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0))))))))), rewrite(((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0))))))) <=> ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))))), (((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & (aElementOf0(W3, W0) | (W3 = W1))))))) <=> ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))))))),
% 0.18/0.41      inference(bind,[status(th)],[])).
% 0.18/0.41  tff(22,plain,
% 0.18/0.41      (![W0: $i, W1: $i] : ((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & (aElementOf0(W3, W0) | (W3 = W1))))))) <=> ![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))))),
% 0.18/0.41      inference(quant_intro,[status(thm)],[21])).
% 0.18/0.41  tff(23,axiom,(![W0: $i, W1: $i] : ((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & (aElementOf0(W3, W0) | (W3 = W1)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mDefCons')).
% 0.18/0.41  tff(24,plain,
% 0.18/0.41      (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))))),
% 0.18/0.41      inference(modus_ponens,[status(thm)],[23, 22])).
% 0.18/0.41  tff(25,plain,
% 0.18/0.41      (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtpldt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))))),
% 0.18/0.41      inference(modus_ponens,[status(thm)],[24, 20])).
% 0.18/0.41  tff(26,plain,(
% 0.18/0.41      ![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | ((~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))))))))),
% 0.18/0.41      inference(skolemize,[status(sab)],[25])).
% 0.18/0.41  tff(27,plain,
% 0.18/0.41      (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtpldt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & ((W3 = W1) | aElementOf0(W3, W0)))))) & ((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_2(W2, W1, W0)) & ((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0))))))))),
% 0.18/0.41      inference(modus_ponens,[status(thm)],[26, 19])).
% 0.18/0.41  tff(28,plain,
% 0.18/0.41      (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))))))),
% 0.18/0.41      inference(modus_ponens,[status(thm)],[27, 17])).
% 0.18/0.41  tff(29,plain,
% 0.18/0.41      (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))))))),
% 0.18/0.41      inference(modus_ponens,[status(thm)],[28, 15])).
% 0.18/0.41  tff(30,plain,
% 0.18/0.41      (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))))))),
% 0.18/0.41      inference(modus_ponens,[status(thm)],[29, 10])).
% 0.18/0.41  tff(31,plain,
% 0.18/0.41      (((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))))))) | ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2)))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))))))) | (~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2)))))))))))),
% 0.18/0.41      inference(rewrite,[status(thm)],[])).
% 0.18/0.41  tff(32,plain,
% 0.18/0.41      (((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2))))))))))) <=> ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2)))))))))))),
% 0.18/0.41      inference(rewrite,[status(thm)],[])).
% 0.18/0.41  tff(33,plain,
% 0.18/0.41      (^[W2: $i] : rewrite((~((~((W2 = sdtpldt0(xS, xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2)))))))))) <=> (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2)))))))))))),
% 0.18/0.41      inference(bind,[status(th)],[])).
% 0.18/0.41  tff(34,plain,
% 0.18/0.41      (![W2: $i] : (~((~((W2 = sdtpldt0(xS, xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2)))))))))) <=> ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2))))))))))),
% 0.18/0.41      inference(quant_intro,[status(thm)],[33])).
% 0.18/0.41  tff(35,plain,
% 0.18/0.41      (((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtpldt0(xS, xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2))))))))))) <=> ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2)))))))))))),
% 0.18/0.41      inference(monotonicity,[status(thm)],[34])).
% 0.18/0.41  tff(36,plain,
% 0.18/0.41      (((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtpldt0(xS, xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2))))))))))) <=> ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2)))))))))))),
% 0.18/0.41      inference(transitivity,[status(thm)],[35, 32])).
% 0.18/0.41  tff(37,plain,
% 0.18/0.41      (((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))))))) | ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtpldt0(xS, xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2)))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))))))) | ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2))))))))))))),
% 0.18/0.41      inference(monotonicity,[status(thm)],[36])).
% 0.18/0.41  tff(38,plain,
% 0.18/0.41      (((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))))))) | ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtpldt0(xS, xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2)))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))))))) | (~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2)))))))))))),
% 0.20/0.42      inference(transitivity,[status(thm)],[37, 31])).
% 0.20/0.42  tff(39,plain,
% 0.20/0.42      ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))))))) | ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtpldt0(xS, xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2)))))))))))),
% 0.20/0.42      inference(quant_inst,[status(thm)],[])).
% 0.20/0.42  tff(40,plain,
% 0.20/0.42      ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))))))) | (~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2))))))))))),
% 0.20/0.42      inference(modus_ponens,[status(thm)],[39, 38])).
% 0.20/0.42  tff(41,plain,
% 0.20/0.42      (![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2))))))))))),
% 0.20/0.42      inference(unit_resolution,[status(thm)],[40, 30, 8, 5])).
% 0.20/0.42  tff(42,plain,
% 0.20/0.42      (((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2))))))))))) | (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, sdtpldt0(xS, xx)))))))) <=> ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2))))))))))) | (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, sdtpldt0(xS, xx))))))))),
% 0.20/0.42      inference(rewrite,[status(thm)],[])).
% 0.20/0.42  tff(43,plain,
% 0.20/0.42      ((~((~((~aSet0(sdtpldt0(xS, xx))) | (sdtpldt0(xS, xx) = sdtpldt0(xS, xx)) | (((~aElement0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS))) | (~((tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS), sdtpldt0(xS, xx))))) | (~((~(sdtpldt0(xS, xx) = sdtpldt0(xS, xx))) | (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, sdtpldt0(xS, xx))))))))))) <=> (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, sdtpldt0(xS, xx)))))))),
% 0.20/0.42      inference(rewrite,[status(thm)],[])).
% 0.20/0.42  tff(44,plain,
% 0.20/0.42      (((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2))))))))))) | (~((~((~aSet0(sdtpldt0(xS, xx))) | (sdtpldt0(xS, xx) = sdtpldt0(xS, xx)) | (((~aElement0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS))) | (~((tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS), sdtpldt0(xS, xx))))) | (~((~(sdtpldt0(xS, xx) = sdtpldt0(xS, xx))) | (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, sdtpldt0(xS, xx)))))))))))) <=> ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2))))))))))) | (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, sdtpldt0(xS, xx))))))))),
% 0.20/0.42      inference(monotonicity,[status(thm)],[43])).
% 0.20/0.42  tff(45,plain,
% 0.20/0.42      (((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2))))))))))) | (~((~((~aSet0(sdtpldt0(xS, xx))) | (sdtpldt0(xS, xx) = sdtpldt0(xS, xx)) | (((~aElement0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS))) | (~((tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS), sdtpldt0(xS, xx))))) | (~((~(sdtpldt0(xS, xx) = sdtpldt0(xS, xx))) | (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, sdtpldt0(xS, xx)))))))))))) <=> ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2))))))))))) | (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, sdtpldt0(xS, xx))))))))),
% 0.20/0.42      inference(transitivity,[status(thm)],[44, 42])).
% 0.20/0.42  tff(46,plain,
% 0.20/0.42      ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2))))))))))) | (~((~((~aSet0(sdtpldt0(xS, xx))) | (sdtpldt0(xS, xx) = sdtpldt0(xS, xx)) | (((~aElement0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS))) | (~((tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS), sdtpldt0(xS, xx))))) | (~((~(sdtpldt0(xS, xx) = sdtpldt0(xS, xx))) | (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, sdtpldt0(xS, xx)))))))))))),
% 0.20/0.42      inference(quant_inst,[status(thm)],[])).
% 0.20/0.42  tff(47,plain,
% 0.20/0.42      ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2))))))))))) | (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, sdtpldt0(xS, xx)))))))),
% 0.20/0.42      inference(modus_ponens,[status(thm)],[46, 45])).
% 0.20/0.42  tff(48,plain,
% 0.20/0.42      ($false),
% 0.20/0.42      inference(unit_resolution,[status(thm)],[47, 41, 1])).
% 0.20/0.42  tff(49,plain,(~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, sdtpldt0(xS, xx))))))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.42  tff(50,plain,
% 0.20/0.42      (((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, sdtpldt0(xS, xx)))))) | ![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, sdtpldt0(xS, xx))))),
% 0.20/0.42      inference(tautology,[status(thm)],[])).
% 0.20/0.42  tff(51,plain,
% 0.20/0.42      (![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, sdtpldt0(xS, xx))))),
% 0.20/0.42      inference(unit_resolution,[status(thm)],[50, 49])).
% 0.20/0.42  tff(52,plain,
% 0.20/0.42      ((~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, sdtpldt0(xS, xx))))) | (~(((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)))) <=> aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))))),
% 0.20/0.42      inference(quant_inst,[status(thm)],[])).
% 0.20/0.42  tff(53,plain,
% 0.20/0.42      (~(((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)))) <=> aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx)))),
% 0.20/0.42      inference(unit_resolution,[status(thm)],[52, 51])).
% 0.20/0.42  tff(54,assumption,(~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)), introduced(assumption)).
% 0.20/0.42  tff(55,plain,
% 0.20/0.42      (((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, sdtpldt0(xS, xx)))))) | aSet0(sdtpldt0(xS, xx))),
% 0.20/0.42      inference(tautology,[status(thm)],[])).
% 0.20/0.42  tff(56,plain,
% 0.20/0.42      (aSet0(sdtpldt0(xS, xx))),
% 0.20/0.42      inference(unit_resolution,[status(thm)],[55, 49])).
% 0.20/0.42  tff(57,plain,
% 0.20/0.42      (^[W0: $i, W1: $i] : trans(monotonicity(quant_intro(proof_bind(^[W2: $i] : rewrite((~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))))) <=> (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))))))), (![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))))) <=> ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))))))), (((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2))))))))))))), rewrite(((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2))))))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))))))), (((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))))))))),
% 0.20/0.43      inference(bind,[status(th)],[])).
% 0.20/0.43  tff(58,plain,
% 0.20/0.43      (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2))))))) <=> ![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))))))),
% 0.20/0.43      inference(quant_intro,[status(thm)],[57])).
% 0.20/0.43  tff(59,plain,
% 0.20/0.43      (^[W0: $i, W1: $i] : refl(((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2))))))))),
% 0.20/0.43      inference(bind,[status(th)],[])).
% 0.20/0.43  tff(60,plain,
% 0.20/0.43      (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2))))))) <=> ![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))))))),
% 0.20/0.43      inference(quant_intro,[status(thm)],[59])).
% 0.20/0.43  tff(61,plain,
% 0.20/0.43      (^[W0: $i, W1: $i] : rewrite(((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2))))))))),
% 0.20/0.43      inference(bind,[status(th)],[])).
% 0.20/0.43  tff(62,plain,
% 0.20/0.43      (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2))))))) <=> ![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))))))),
% 0.20/0.43      inference(quant_intro,[status(thm)],[61])).
% 0.20/0.43  tff(63,plain,
% 0.20/0.43      (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2))))))) <=> ![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))))))),
% 0.20/0.43      inference(transitivity,[status(thm)],[62, 60])).
% 0.20/0.43  tff(64,plain,
% 0.20/0.43      (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aSet0(W0) & aElement0(W1)) <=> (~((~aSet0(W0)) | (~aElement0(W1))))), ((~(aSet0(W0) & aElement0(W1))) <=> (~(~((~aSet0(W0)) | (~aElement0(W1))))))), rewrite((~(~((~aSet0(W0)) | (~aElement0(W1))))) <=> ((~aSet0(W0)) | (~aElement0(W1)))), ((~(aSet0(W0) & aElement0(W1))) <=> ((~aSet0(W0)) | (~aElement0(W1))))), quant_intro(proof_bind(^[W2: $i] : trans(monotonicity(rewrite(((~(W2 = sdtmndt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))) <=> ((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))), trans(monotonicity(trans(monotonicity(trans(trans(monotonicity(rewrite((aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1))) <=> (~((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)))), ((aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1)))) <=> (aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> (~((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)))))), rewrite((aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> (~((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)))) <=> (~(((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))), ((aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1)))) <=> (~(((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2))))), rewrite((~(((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2))) <=> (~(((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))), ((aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1)))) <=> (~(((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2))))), ((~(aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1))))) <=> (~(~(((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))))), rewrite((~(~(((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))) <=> (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2))), ((~(aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1))))) <=> (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))), (((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1)))))) <=> ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2))))), rewrite(((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2))) <=> ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))), (((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1)))))) <=> ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2))))), ((((~(W2 = sdtmndt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))) & ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1))))))) <=> (((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2))))))) & ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))))), rewrite((((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2))))))) & ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))) <=> (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2))))))), ((((~(W2 = sdtmndt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))) & ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1))))))) <=> (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2))))))))), (![W2: $i] : (((~(W2 = sdtmndt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))) & ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1))))))) <=> ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))))))), (((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtmndt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))) & ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1)))))))) <=> (((~aSet0(W0)) | (~aElement0(W1))) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2))))))))), rewrite((((~aSet0(W0)) | (~aElement0(W1))) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))))))), (((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtmndt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))) & ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1)))))))) <=> ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))))))))),
% 0.20/0.43      inference(bind,[status(th)],[])).
% 0.20/0.43  tff(65,plain,
% 0.20/0.43      (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtmndt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))) & ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1)))))))) <=> ![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))))))),
% 0.20/0.43      inference(quant_intro,[status(thm)],[64])).
% 0.20/0.43  tff(66,plain,
% 0.20/0.43      (^[W0: $i, W1: $i] : rewrite(((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtmndt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))) & ((W2 = sdtmndt0(W0, W1)) | ((~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1))))))))) <=> ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtmndt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))) & ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1)))))))))),
% 0.20/0.43      inference(bind,[status(th)],[])).
% 0.20/0.43  tff(67,plain,
% 0.20/0.43      (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtmndt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))) & ((W2 = sdtmndt0(W0, W1)) | ((~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1))))))))) <=> ![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtmndt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))) & ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1))))))))),
% 0.20/0.43      inference(quant_intro,[status(thm)],[66])).
% 0.20/0.43  tff(68,plain,
% 0.20/0.43      (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1))))))) <=> ![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))))),
% 0.20/0.43      inference(rewrite,[status(thm)],[])).
% 0.20/0.43  tff(69,plain,
% 0.20/0.43      (^[W0: $i, W1: $i] : trans(monotonicity(quant_intro(proof_bind(^[W2: $i] : rewrite(((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> ((aElement0(W3) & aElementOf0(W3, W0)) & (~(W3 = W1)))))) <=> ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))))), (![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> ((aElement0(W3) & aElementOf0(W3, W0)) & (~(W3 = W1)))))) <=> ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))))), (((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> ((aElement0(W3) & aElementOf0(W3, W0)) & (~(W3 = W1))))))) <=> ((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1))))))))), rewrite(((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1))))))) <=> ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))))), (((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> ((aElement0(W3) & aElementOf0(W3, W0)) & (~(W3 = W1))))))) <=> ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))))))),
% 0.20/0.43      inference(bind,[status(th)],[])).
% 0.20/0.43  tff(70,plain,
% 0.20/0.43      (![W0: $i, W1: $i] : ((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> ((aElement0(W3) & aElementOf0(W3, W0)) & (~(W3 = W1))))))) <=> ![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))))),
% 0.20/0.43      inference(quant_intro,[status(thm)],[69])).
% 0.20/0.43  tff(71,axiom,(![W0: $i, W1: $i] : ((aSet0(W0) & aElement0(W1)) => ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> ((aElement0(W3) & aElementOf0(W3, W0)) & (~(W3 = W1)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mDefDiff')).
% 0.20/0.43  tff(72,plain,
% 0.20/0.43      (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))))),
% 0.20/0.43      inference(modus_ponens,[status(thm)],[71, 70])).
% 0.20/0.43  tff(73,plain,
% 0.20/0.43      (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : ((W2 = sdtmndt0(W0, W1)) <=> (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))))),
% 0.20/0.43      inference(modus_ponens,[status(thm)],[72, 68])).
% 0.20/0.43  tff(74,plain,(
% 0.20/0.43      ![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtmndt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))) & ((W2 = sdtmndt0(W0, W1)) | ((~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1)))))))))),
% 0.20/0.43      inference(skolemize,[status(sab)],[73])).
% 0.20/0.43  tff(75,plain,
% 0.20/0.43      (![W0: $i, W1: $i] : ((~(aSet0(W0) & aElement0(W1))) | ![W2: $i] : (((~(W2 = sdtmndt0(W0, W1))) | (aSet0(W2) & ![W3: $i] : (aElementOf0(W3, W2) <=> (aElement0(W3) & aElementOf0(W3, W0) & (~(W3 = W1)))))) & ((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (~(aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2) <=> (aElement0(tptp_fun_W3_3(W2, W1, W0)) & aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0) & (~(tptp_fun_W3_3(W2, W1, W0) = W1))))))))),
% 0.20/0.43      inference(modus_ponens,[status(thm)],[74, 67])).
% 0.20/0.43  tff(76,plain,
% 0.20/0.43      (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))))))),
% 0.20/0.43      inference(modus_ponens,[status(thm)],[75, 65])).
% 0.20/0.43  tff(77,plain,
% 0.20/0.43      (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))) | (~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))))))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[76, 63])).
% 0.20/0.44  tff(78,plain,
% 0.20/0.44      (![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))))))),
% 0.20/0.44      inference(modus_ponens,[status(thm)],[77, 58])).
% 0.20/0.44  tff(79,plain,
% 0.20/0.44      (((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))))))) | ((~aElement0(xx)) | (~aSet0(sdtpldt0(xS, xx))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2)))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, W2)))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))))))) | (~aElement0(xx)) | (~aSet0(sdtpldt0(xS, xx))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2)))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, W2)))))))))))),
% 0.20/0.44      inference(rewrite,[status(thm)],[])).
% 0.20/0.44  tff(80,plain,
% 0.20/0.44      (((~aSet0(sdtpldt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2)))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))) <=> ((~aElement0(xx)) | (~aSet0(sdtpldt0(xS, xx))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2)))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, W2)))))))))))),
% 0.20/0.44      inference(rewrite,[status(thm)],[])).
% 0.20/0.44  tff(81,plain,
% 0.20/0.44      (^[W2: $i] : rewrite((~((~((W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2)))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, W2)))))))))) <=> (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2)))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, W2)))))))))))),
% 0.20/0.44      inference(bind,[status(th)],[])).
% 0.20/0.44  tff(82,plain,
% 0.20/0.44      (![W2: $i] : (~((~((W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2)))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, W2)))))))))) <=> ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2)))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))),
% 0.20/0.44      inference(quant_intro,[status(thm)],[81])).
% 0.20/0.44  tff(83,plain,
% 0.20/0.44      (((~aSet0(sdtpldt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2)))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))) <=> ((~aSet0(sdtpldt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2)))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, W2)))))))))))),
% 0.20/0.44      inference(monotonicity,[status(thm)],[82])).
% 0.20/0.44  tff(84,plain,
% 0.20/0.44      (((~aSet0(sdtpldt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2)))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))) <=> ((~aElement0(xx)) | (~aSet0(sdtpldt0(xS, xx))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2)))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, W2)))))))))))),
% 0.20/0.44      inference(transitivity,[status(thm)],[83, 80])).
% 0.20/0.44  tff(85,plain,
% 0.20/0.44      (((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))))))) | ((~aSet0(sdtpldt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2)))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, W2)))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))))))) | ((~aElement0(xx)) | (~aSet0(sdtpldt0(xS, xx))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2)))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))))),
% 0.20/0.44      inference(monotonicity,[status(thm)],[84])).
% 0.20/0.44  tff(86,plain,
% 0.20/0.44      (((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))))))) | ((~aSet0(sdtpldt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2)))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, W2)))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))))))) | (~aElement0(xx)) | (~aSet0(sdtpldt0(xS, xx))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2)))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, W2)))))))))))),
% 0.20/0.45      inference(transitivity,[status(thm)],[85, 79])).
% 0.20/0.45  tff(87,plain,
% 0.20/0.45      ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))))))) | ((~aSet0(sdtpldt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2)))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, W2)))))))))))),
% 0.20/0.45      inference(quant_inst,[status(thm)],[])).
% 0.20/0.45  tff(88,plain,
% 0.20/0.45      ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))))))) | (~aElement0(xx)) | (~aSet0(sdtpldt0(xS, xx))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2)))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))),
% 0.20/0.45      inference(modus_ponens,[status(thm)],[87, 86])).
% 0.20/0.45  tff(89,plain,
% 0.20/0.45      ((~aSet0(sdtpldt0(xS, xx))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2)))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))),
% 0.20/0.45      inference(unit_resolution,[status(thm)],[88, 78, 8])).
% 0.20/0.45  tff(90,plain,
% 0.20/0.45      (![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2)))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))),
% 0.20/0.45      inference(unit_resolution,[status(thm)],[89, 56])).
% 0.20/0.45  tff(91,plain,
% 0.20/0.45      ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2)))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))) | (~((~((~aSet0(xS)) | (xS = sdtmndt0(sdtpldt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)))) | (~((~(xS = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(xS)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, xS))))))))))),
% 0.20/0.45      inference(quant_inst,[status(thm)],[])).
% 0.20/0.45  tff(92,plain,
% 0.20/0.45      (~((~((~aSet0(xS)) | (xS = sdtmndt0(sdtpldt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)))) | (~((~(xS = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(xS)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, xS)))))))))),
% 0.20/0.45      inference(unit_resolution,[status(thm)],[91, 90])).
% 0.20/0.45  tff(93,plain,
% 0.20/0.45      (((~((~aSet0(xS)) | (xS = sdtmndt0(sdtpldt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)))) | (~((~(xS = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(xS)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, xS))))))))) | ((~aSet0(xS)) | (xS = sdtmndt0(sdtpldt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)))),
% 0.20/0.45      inference(tautology,[status(thm)],[])).
% 0.20/0.45  tff(94,plain,
% 0.20/0.45      ((~aSet0(xS)) | (xS = sdtmndt0(sdtpldt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS))),
% 0.20/0.45      inference(unit_resolution,[status(thm)],[93, 92])).
% 0.20/0.45  tff(95,plain,
% 0.20/0.45      ((xS = sdtmndt0(sdtpldt0(xS, xx), xx)) <=> (sdtmndt0(sdtpldt0(xS, xx), xx) = xS)),
% 0.20/0.45      inference(commutativity,[status(thm)],[])).
% 0.20/0.45  tff(96,plain,
% 0.20/0.45      ((sdtmndt0(sdtpldt0(xS, xx), xx) = xS) <=> (xS = sdtmndt0(sdtpldt0(xS, xx), xx))),
% 0.20/0.45      inference(symmetry,[status(thm)],[95])).
% 0.20/0.45  tff(97,plain,
% 0.20/0.45      ((~(sdtmndt0(sdtpldt0(xS, xx), xx) = xS)) <=> (~(xS = sdtmndt0(sdtpldt0(xS, xx), xx)))),
% 0.20/0.45      inference(monotonicity,[status(thm)],[96])).
% 0.20/0.45  tff(98,plain,
% 0.20/0.45      ((~(sdtmndt0(sdtpldt0(xS, xx), xx) = xS)) <=> (~(sdtmndt0(sdtpldt0(xS, xx), xx) = xS))),
% 0.20/0.45      inference(rewrite,[status(thm)],[])).
% 0.20/0.45  tff(99,axiom,(~(sdtmndt0(sdtpldt0(xS, xx), xx) = xS)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__')).
% 0.20/0.45  tff(100,plain,
% 0.20/0.45      (~(sdtmndt0(sdtpldt0(xS, xx), xx) = xS)),
% 0.20/0.45      inference(modus_ponens,[status(thm)],[99, 98])).
% 0.20/0.45  tff(101,plain,
% 0.20/0.45      (~(xS = sdtmndt0(sdtpldt0(xS, xx), xx))),
% 0.20/0.45      inference(modus_ponens,[status(thm)],[100, 97])).
% 0.20/0.45  tff(102,plain,
% 0.20/0.45      ((~((~aSet0(xS)) | (xS = sdtmndt0(sdtpldt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)))) | (~aSet0(xS)) | (xS = sdtmndt0(sdtpldt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS))),
% 0.20/0.45      inference(tautology,[status(thm)],[])).
% 0.20/0.45  tff(103,plain,
% 0.20/0.45      ((~((~aSet0(xS)) | (xS = sdtmndt0(sdtpldt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)))) | (xS = sdtmndt0(sdtpldt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS))),
% 0.20/0.45      inference(unit_resolution,[status(thm)],[102, 5])).
% 0.20/0.45  tff(104,plain,
% 0.20/0.45      (((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)),
% 0.20/0.45      inference(unit_resolution,[status(thm)],[103, 101, 94])).
% 0.20/0.45  tff(105,plain,
% 0.20/0.45      ((~(((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS))) | (~((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx))) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)),
% 0.20/0.45      inference(tautology,[status(thm)],[])).
% 0.20/0.45  tff(106,plain,
% 0.20/0.45      ((~((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx))) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)),
% 0.20/0.45      inference(unit_resolution,[status(thm)],[105, 104])).
% 0.20/0.45  tff(107,plain,
% 0.20/0.45      (~((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx))),
% 0.20/0.45      inference(unit_resolution,[status(thm)],[106, 54])).
% 0.20/0.45  tff(108,plain,
% 0.20/0.45      (((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx)) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))),
% 0.20/0.45      inference(tautology,[status(thm)],[])).
% 0.20/0.45  tff(109,plain,
% 0.20/0.45      (aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))),
% 0.20/0.45      inference(unit_resolution,[status(thm)],[108, 107])).
% 0.20/0.45  tff(110,plain,
% 0.20/0.45      ((((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)))) <=> aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (~((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS))))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx)))),
% 0.20/0.45      inference(tautology,[status(thm)],[])).
% 0.20/0.45  tff(111,plain,
% 0.20/0.45      (~((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS))))),
% 0.20/0.45      inference(unit_resolution,[status(thm)],[110, 109, 53])).
% 0.20/0.45  tff(112,plain,
% 0.20/0.45      (((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx)) | (~(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx))),
% 0.20/0.45      inference(tautology,[status(thm)],[])).
% 0.20/0.45  tff(113,plain,
% 0.20/0.45      (~(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx)),
% 0.20/0.45      inference(unit_resolution,[status(thm)],[112, 107])).
% 0.20/0.45  tff(114,plain,
% 0.20/0.45      ((~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)),
% 0.20/0.45      inference(tautology,[status(thm)],[])).
% 0.20/0.45  tff(115,plain,
% 0.20/0.45      (~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS))),
% 0.20/0.45      inference(unit_resolution,[status(thm)],[114, 113, 54])).
% 0.20/0.45  tff(116,plain,
% 0.20/0.45      (((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)))) | ((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS))),
% 0.20/0.45      inference(tautology,[status(thm)],[])).
% 0.20/0.45  tff(117,plain,
% 0.20/0.45      ($false),
% 0.20/0.45      inference(unit_resolution,[status(thm)],[116, 115, 111])).
% 0.20/0.45  tff(118,plain,(aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.45  tff(119,plain,
% 0.20/0.45      (^[W0: $i] : refl(((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))))),
% 0.20/0.45      inference(bind,[status(th)],[])).
% 0.20/0.45  tff(120,plain,
% 0.20/0.45      (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.20/0.45      inference(quant_intro,[status(thm)],[119])).
% 0.20/0.45  tff(121,plain,
% 0.20/0.45      (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))))),
% 0.20/0.45      inference(bind,[status(th)],[])).
% 0.20/0.45  tff(122,plain,
% 0.20/0.45      (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.20/0.45      inference(quant_intro,[status(thm)],[121])).
% 0.20/0.45  tff(123,plain,
% 0.20/0.45      (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.20/0.45      inference(transitivity,[status(thm)],[122, 120])).
% 0.20/0.45  tff(124,plain,
% 0.20/0.45      (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.20/0.45      inference(rewrite,[status(thm)],[])).
% 0.20/0.45  tff(125,plain,
% 0.20/0.45      (^[W0: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: $i] : rewrite((aElementOf0(W1, W0) => aElement0(W1)) <=> (aElement0(W1) | (~aElementOf0(W1, W0))))), (![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1)) <=> ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))), ((aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1))) <=> (aSet0(W0) => ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))))), rewrite((aSet0(W0) => ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))), ((aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))))),
% 0.20/0.45      inference(bind,[status(th)],[])).
% 0.20/0.45  tff(126,plain,
% 0.20/0.45      (![W0: $i] : (aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.20/0.45      inference(quant_intro,[status(thm)],[125])).
% 0.20/0.45  tff(127,axiom,(![W0: $i] : (aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mEOfElem')).
% 0.20/0.45  tff(128,plain,
% 0.20/0.45      (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.20/0.45      inference(modus_ponens,[status(thm)],[127, 126])).
% 0.20/0.45  tff(129,plain,
% 0.20/0.45      (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.20/0.45      inference(modus_ponens,[status(thm)],[128, 124])).
% 0.20/0.45  tff(130,plain,(
% 0.20/0.45      ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.20/0.45      inference(skolemize,[status(sab)],[129])).
% 0.20/0.45  tff(131,plain,
% 0.20/0.45      (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.20/0.45      inference(modus_ponens,[status(thm)],[130, 123])).
% 0.20/0.45  tff(132,plain,
% 0.20/0.45      (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | ((~aSet0(xS)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | (~aSet0(xS)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS))))),
% 0.20/0.46      inference(rewrite,[status(thm)],[])).
% 0.20/0.46  tff(133,plain,
% 0.20/0.46      ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | ((~aSet0(xS)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS))))),
% 0.20/0.46      inference(quant_inst,[status(thm)],[])).
% 0.20/0.46  tff(134,plain,
% 0.20/0.46      ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | (~aSet0(xS)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[133, 132])).
% 0.20/0.46  tff(135,plain,
% 0.20/0.46      (![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))),
% 0.20/0.46      inference(unit_resolution,[status(thm)],[134, 131, 5])).
% 0.20/0.46  tff(136,plain,
% 0.20/0.46      (((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | (aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)))) <=> ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)))),
% 0.20/0.46      inference(rewrite,[status(thm)],[])).
% 0.20/0.46  tff(137,plain,
% 0.20/0.46      ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | (aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)))),
% 0.20/0.46      inference(quant_inst,[status(thm)],[])).
% 0.20/0.46  tff(138,plain,
% 0.20/0.46      ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS))),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[137, 136])).
% 0.20/0.46  tff(139,plain,
% 0.20/0.46      (aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS))),
% 0.20/0.46      inference(unit_resolution,[status(thm)],[138, 135])).
% 0.20/0.46  tff(140,plain,
% 0.20/0.46      (aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))),
% 0.20/0.46      inference(unit_resolution,[status(thm)],[139, 118])).
% 0.20/0.46  tff(141,plain,
% 0.20/0.46      ((~(((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS))) | ((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx)) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS))),
% 0.20/0.46      inference(tautology,[status(thm)],[])).
% 0.20/0.46  tff(142,plain,
% 0.20/0.46      (((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx)) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS))),
% 0.20/0.46      inference(unit_resolution,[status(thm)],[141, 104])).
% 0.20/0.46  tff(143,plain,
% 0.20/0.46      ((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx)),
% 0.20/0.46      inference(unit_resolution,[status(thm)],[142, 118])).
% 0.20/0.46  tff(144,plain,
% 0.20/0.46      (((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS))),
% 0.20/0.46      inference(tautology,[status(thm)],[])).
% 0.20/0.46  tff(145,plain,
% 0.20/0.46      ((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)),
% 0.20/0.46      inference(unit_resolution,[status(thm)],[144, 118])).
% 0.20/0.46  tff(146,plain,
% 0.20/0.46      ((~((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS))))) | (~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)))),
% 0.20/0.46      inference(tautology,[status(thm)],[])).
% 0.20/0.46  tff(147,plain,
% 0.20/0.46      (~((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS))))),
% 0.20/0.46      inference(unit_resolution,[status(thm)],[146, 145, 140])).
% 0.20/0.46  tff(148,plain,
% 0.20/0.46      ((((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)))) <=> aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | ((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~((tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)))) | aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))),
% 0.20/0.46      inference(tautology,[status(thm)],[])).
% 0.20/0.46  tff(149,plain,
% 0.20/0.46      (aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))),
% 0.20/0.46      inference(unit_resolution,[status(thm)],[148, 147, 53])).
% 0.20/0.46  tff(150,plain,
% 0.20/0.46      ((~((~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx))) | (~aElement0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx)),
% 0.20/0.46      inference(tautology,[status(thm)],[])).
% 0.20/0.46  tff(151,plain,
% 0.20/0.46      (tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)) = xx),
% 0.20/0.46      inference(unit_resolution,[status(thm)],[150, 149, 143, 140])).
% 0.20/0.46  tff(152,plain,
% 0.20/0.46      (aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS) <=> aElementOf0(xx, xS)),
% 0.20/0.46      inference(monotonicity,[status(thm)],[151])).
% 0.20/0.46  tff(153,plain,
% 0.20/0.46      (aElementOf0(xx, xS) <=> aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)),
% 0.20/0.46      inference(symmetry,[status(thm)],[152])).
% 0.20/0.46  tff(154,plain,
% 0.20/0.46      ((~aElementOf0(xx, xS)) <=> (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS))),
% 0.20/0.46      inference(monotonicity,[status(thm)],[153])).
% 0.20/0.46  tff(155,plain,
% 0.20/0.46      ((~aElementOf0(xx, xS)) <=> (~aElementOf0(xx, xS))),
% 0.20/0.46      inference(rewrite,[status(thm)],[])).
% 0.20/0.46  tff(156,axiom,(~aElementOf0(xx, xS)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__679_02')).
% 0.20/0.46  tff(157,plain,
% 0.20/0.46      (~aElementOf0(xx, xS)),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[156, 155])).
% 0.20/0.46  tff(158,plain,
% 0.20/0.46      (~aElementOf0(tptp_fun_W3_3(xS, xx, sdtpldt0(xS, xx)), xS)),
% 0.20/0.46      inference(modus_ponens,[status(thm)],[157, 154])).
% 0.20/0.46  tff(159,plain,
% 0.20/0.46      ($false),
% 0.20/0.46      inference(unit_resolution,[status(thm)],[118, 158])).
% 0.20/0.46  % SZS output end Proof
% 0.20/0.46  % E exiting
%------------------------------------------------------------------------------