%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM536+2 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 0.12s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM536+2 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 01:25:20 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.40 % SZS status Theorem
% 0.12/0.40 % SZS output start Proof
% 0.12/0.40 tff(aElementOf0_type, type, (
% 0.12/0.40 aElementOf0: ( $i * $i ) > $o)).
% 0.12/0.40 tff(xS_type, type, (
% 0.12/0.40 xS: $i)).
% 0.12/0.40 tff(tptp_fun_W2_1_type, type, (
% 0.12/0.40 tptp_fun_W2_1: ( $i * $i ) > $i)).
% 0.12/0.40 tff(sdtmndt0_type, type, (
% 0.12/0.40 sdtmndt0: ( $i * $i ) > $i)).
% 0.12/0.40 tff(xx_type, type, (
% 0.12/0.40 xx: $i)).
% 0.12/0.40 tff(sdtpldt0_type, type, (
% 0.12/0.40 sdtpldt0: ( $i * $i ) > $i)).
% 0.12/0.40 tff(aElement0_type, type, (
% 0.12/0.40 aElement0: $i > $o)).
% 0.12/0.40 tff(aSet0_type, type, (
% 0.12/0.40 aSet0: $i > $o)).
% 0.12/0.40 tff(tptp_fun_W3_3_type, type, (
% 0.12/0.40 tptp_fun_W3_3: ( $i * $i * $i ) > $i)).
% 0.12/0.40 tff(aSubsetOf0_type, type, (
% 0.12/0.40 aSubsetOf0: ( $i * $i ) > $o)).
% 0.12/0.40 tff(tptp_fun_W3_2_type, type, (
% 0.12/0.40 tptp_fun_W3_2: ( $i * $i * $i ) > $i)).
% 0.12/0.40 tff(1,plain,
% 0.12/0.40 (aSet0(sdtpldt0(xS, xx)) <=> aSet0(sdtpldt0(xS, xx))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(2,plain,
% 0.12/0.40 ((~((aSet0(sdtpldt0(xS, xx)) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(xS, xx)) <=> (aElement0(W0) & (aElementOf0(W0, xS) | (W0 = xx))))) => ((aSet0(sdtmndt0(sdtpldt0(xS, xx), xx)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtpldt0(xS, xx), xx)) <=> ((aElement0(W0) & aElementOf0(W0, sdtpldt0(xS, xx))) & (~(W0 = xx))))) => (sdtmndt0(sdtpldt0(xS, xx), xx) = xS)))) <=> (~((sdtmndt0(sdtpldt0(xS, xx), xx) = xS) | (~(aSet0(sdtmndt0(sdtpldt0(xS, xx), xx)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtpldt0(xS, xx), xx)) <=> (aElement0(W0) & aElementOf0(W0, sdtpldt0(xS, xx)) & (~(W0 = xx)))))) | (~(aSet0(sdtpldt0(xS, xx)) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(xS, xx)) <=> (aElement0(W0) & ((W0 = xx) | aElementOf0(W0, xS))))))))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(3,axiom,(~((aSet0(sdtpldt0(xS, xx)) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(xS, xx)) <=> (aElement0(W0) & (aElementOf0(W0, xS) | (W0 = xx))))) => ((aSet0(sdtmndt0(sdtpldt0(xS, xx), xx)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtpldt0(xS, xx), xx)) <=> ((aElement0(W0) & aElementOf0(W0, sdtpldt0(xS, xx))) & (~(W0 = xx))))) => (sdtmndt0(sdtpldt0(xS, xx), xx) = xS)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__')).
% 0.12/0.40 tff(4,plain,
% 0.12/0.40 (~((sdtmndt0(sdtpldt0(xS, xx), xx) = xS) | (~(aSet0(sdtmndt0(sdtpldt0(xS, xx), xx)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtpldt0(xS, xx), xx)) <=> (aElement0(W0) & aElementOf0(W0, sdtpldt0(xS, xx)) & (~(W0 = xx)))))) | (~(aSet0(sdtpldt0(xS, xx)) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(xS, xx)) <=> (aElement0(W0) & ((W0 = xx) | aElementOf0(W0, xS)))))))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.12/0.40 tff(5,plain,
% 0.12/0.40 (aSet0(sdtpldt0(xS, xx)) & ![W0: $i] : (aElementOf0(W0, sdtpldt0(xS, xx)) <=> (aElement0(W0) & ((W0 = xx) | aElementOf0(W0, xS))))),
% 0.12/0.40 inference(or_elim,[status(thm)],[4])).
% 0.12/0.40 tff(6,plain,
% 0.12/0.40 (aSet0(sdtpldt0(xS, xx))),
% 0.12/0.40 inference(and_elim,[status(thm)],[5])).
% 0.12/0.40 tff(7,plain,
% 0.12/0.40 (aSet0(sdtpldt0(xS, xx))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.12/0.40 tff(8,plain,
% 0.12/0.40 (aElement0(xx) <=> aElement0(xx)),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(9,axiom,(aElement0(xx) & aSet0(xS)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__679')).
% 0.12/0.40 tff(10,plain,
% 0.12/0.40 (aElement0(xx)),
% 0.12/0.40 inference(and_elim,[status(thm)],[9])).
% 0.12/0.40 tff(11,plain,
% 0.12/0.40 (aElement0(xx)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[10, 8])).
% 0.12/0.40 tff(12,plain,
% 0.12/0.40 (^[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)))))))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(13,plain,
% 0.12/0.40 (![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)))))))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[12])).
% 0.12/0.40 tff(14,plain,
% 0.12/0.40 (^[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))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(15,plain,
% 0.12/0.40 (![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)))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[14])).
% 0.12/0.40 tff(16,plain,
% 0.12/0.40 (^[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))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(17,plain,
% 0.12/0.40 (![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)))))))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[16])).
% 0.12/0.40 tff(18,plain,
% 0.12/0.40 (![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)))))))),
% 0.12/0.40 inference(transitivity,[status(thm)],[17, 15])).
% 0.12/0.40 tff(19,plain,
% 0.12/0.40 (^[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 = 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)))))))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(20,plain,
% 0.12/0.40 (![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)))))))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[19])).
% 0.12/0.41 tff(21,plain,
% 0.12/0.41 (^[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)))))))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(22,plain,
% 0.12/0.41 (![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))))))))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[21])).
% 0.12/0.41 tff(23,plain,
% 0.12/0.41 (![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)))))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(24,plain,
% 0.12/0.41 (^[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)))))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(25,plain,
% 0.21/0.41 (![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)))))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[24])).
% 0.21/0.41 tff(26,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')).
% 0.21/0.41 tff(27,plain,
% 0.21/0.41 (![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)))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.21/0.41 tff(28,plain,
% 0.21/0.41 (![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)))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.21/0.41 tff(29,plain,(
% 0.21/0.41 ![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)))))))))),
% 0.21/0.41 inference(skolemize,[status(sab)],[28])).
% 0.21/0.41 tff(30,plain,
% 0.21/0.41 (![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))))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.21/0.41 tff(31,plain,
% 0.21/0.41 (![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)))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[30, 20])).
% 0.21/0.41 tff(32,plain,
% 0.21/0.41 (![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)))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[31, 18])).
% 0.21/0.41 tff(33,plain,
% 0.21/0.41 (![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)))))))))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[32, 13])).
% 0.21/0.41 tff(34,plain,
% 0.21/0.41 (((~![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] : (~((~((~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)))))))))))) | (~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)))))))))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(35,plain,
% 0.21/0.41 (((~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))))))))))) <=> ((~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)))))))))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(36,plain,
% 0.21/0.41 (^[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)))))))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(37,plain,
% 0.21/0.41 (![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))))))))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[36])).
% 0.21/0.41 tff(38,plain,
% 0.21/0.41 (((~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)))))))))))),
% 0.21/0.41 inference(monotonicity,[status(thm)],[37])).
% 0.21/0.41 tff(39,plain,
% 0.21/0.41 (((~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)))))))))))),
% 0.21/0.41 inference(transitivity,[status(thm)],[38, 35])).
% 0.21/0.42 tff(40,plain,
% 0.21/0.42 (((~![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)))))))))))) | ((~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))))))))))))),
% 0.21/0.42 inference(monotonicity,[status(thm)],[39])).
% 0.21/0.42 tff(41,plain,
% 0.21/0.42 (((~![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)))))))))))) | (~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)))))))))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[40, 34])).
% 0.21/0.42 tff(42,plain,
% 0.21/0.42 ((~![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)))))))))))),
% 0.21/0.42 inference(quant_inst,[status(thm)],[])).
% 0.21/0.42 tff(43,plain,
% 0.21/0.42 ((~![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] : (~((~((~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))))))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.21/0.42 tff(44,plain,
% 0.21/0.42 (![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))))))))))),
% 0.21/0.42 inference(unit_resolution,[status(thm)],[43, 33, 11, 7])).
% 0.21/0.42 tff(45,plain,
% 0.21/0.42 (((~![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(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), 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))))))))))) | (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx))))))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(46,plain,
% 0.21/0.43 ((~((~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (sdtmndt0(sdtpldt0(xS, xx), xx) = sdtmndt0(sdtpldt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_3(sdtmndt0(sdtpldt0(xS, xx), xx), xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(sdtmndt0(sdtpldt0(xS, xx), xx), xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(sdtmndt0(sdtpldt0(xS, xx), xx), xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(sdtmndt0(sdtpldt0(xS, xx), xx), xx, sdtpldt0(xS, xx)), sdtmndt0(sdtpldt0(xS, xx), xx))))) | (~((~(sdtmndt0(sdtpldt0(xS, xx), xx) = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx))))))))))) <=> (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)))))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(47,plain,
% 0.21/0.43 (((~![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(sdtmndt0(sdtpldt0(xS, xx), xx))) | (sdtmndt0(sdtpldt0(xS, xx), xx) = sdtmndt0(sdtpldt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_3(sdtmndt0(sdtpldt0(xS, xx), xx), xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(sdtmndt0(sdtpldt0(xS, xx), xx), xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(sdtmndt0(sdtpldt0(xS, xx), xx), xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(sdtmndt0(sdtpldt0(xS, xx), xx), xx, sdtpldt0(xS, xx)), sdtmndt0(sdtpldt0(xS, xx), xx))))) | (~((~(sdtmndt0(sdtpldt0(xS, xx), xx) = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), 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))))))))))) | (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx))))))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[46])).
% 0.21/0.43 tff(48,plain,
% 0.21/0.43 (((~![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(sdtmndt0(sdtpldt0(xS, xx), xx))) | (sdtmndt0(sdtpldt0(xS, xx), xx) = sdtmndt0(sdtpldt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_3(sdtmndt0(sdtpldt0(xS, xx), xx), xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(sdtmndt0(sdtpldt0(xS, xx), xx), xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(sdtmndt0(sdtpldt0(xS, xx), xx), xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(sdtmndt0(sdtpldt0(xS, xx), xx), xx, sdtpldt0(xS, xx)), sdtmndt0(sdtpldt0(xS, xx), xx))))) | (~((~(sdtmndt0(sdtpldt0(xS, xx), xx) = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), 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))))))))))) | (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx))))))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[47, 45])).
% 0.21/0.43 tff(49,plain,
% 0.21/0.43 ((~![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(sdtmndt0(sdtpldt0(xS, xx), xx))) | (sdtmndt0(sdtpldt0(xS, xx), xx) = sdtmndt0(sdtpldt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_3(sdtmndt0(sdtpldt0(xS, xx), xx), xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(sdtmndt0(sdtpldt0(xS, xx), xx), xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(sdtmndt0(sdtpldt0(xS, xx), xx), xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(sdtmndt0(sdtpldt0(xS, xx), xx), xx, sdtpldt0(xS, xx)), sdtmndt0(sdtpldt0(xS, xx), xx))))) | (~((~(sdtmndt0(sdtpldt0(xS, xx), xx) = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)))))))))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(50,plain,
% 0.21/0.43 ((~![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(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.21/0.43 tff(51,plain,
% 0.21/0.43 (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx))))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[50, 44])).
% 0.21/0.43 tff(52,plain,
% 0.21/0.43 (((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)))))) | ![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx))))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(53,plain,
% 0.21/0.43 (![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[52, 51])).
% 0.21/0.43 tff(54,plain,
% 0.21/0.43 ((~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx))))) | (~(((~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtpldt0(xS, xx))) | (tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx)) <=> aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(55,plain,
% 0.21/0.43 (~(((~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtpldt0(xS, xx))) | (tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx)) <=> aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.21/0.43 tff(56,plain,
% 0.21/0.43 (aSet0(xS) <=> aSet0(xS)),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(57,plain,
% 0.21/0.43 (aSet0(xS)),
% 0.21/0.43 inference(and_elim,[status(thm)],[9])).
% 0.21/0.43 tff(58,plain,
% 0.21/0.43 (aSet0(xS)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.21/0.43 tff(59,plain,
% 0.21/0.43 (^[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)))))))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(60,plain,
% 0.21/0.43 (![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)))))))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[59])).
% 0.21/0.43 tff(61,plain,
% 0.21/0.43 (^[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))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(62,plain,
% 0.21/0.43 (![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)))))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[61])).
% 0.21/0.44 tff(63,plain,
% 0.21/0.44 (^[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))))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(64,plain,
% 0.21/0.44 (![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)))))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[63])).
% 0.21/0.44 tff(65,plain,
% 0.21/0.44 (![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)))))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[64, 62])).
% 0.21/0.44 tff(66,plain,
% 0.21/0.44 (^[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)))))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(67,plain,
% 0.21/0.44 (![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)))))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[66])).
% 0.21/0.44 tff(68,plain,
% 0.21/0.44 (^[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)))))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(69,plain,
% 0.21/0.44 (![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))))))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[68])).
% 0.21/0.44 tff(70,plain,
% 0.21/0.44 (![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)))))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(71,plain,
% 0.21/0.44 (^[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)))))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(72,plain,
% 0.21/0.44 (![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)))))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[71])).
% 0.21/0.44 tff(73,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')).
% 0.21/0.44 tff(74,plain,
% 0.21/0.44 (![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)))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.21/0.44 tff(75,plain,
% 0.21/0.44 (![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)))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.21/0.44 tff(76,plain,(
% 0.21/0.44 ![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)))))))))),
% 0.21/0.44 inference(skolemize,[status(sab)],[75])).
% 0.21/0.44 tff(77,plain,
% 0.21/0.44 (![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))))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[76, 69])).
% 0.21/0.44 tff(78,plain,
% 0.21/0.44 (![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)))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[77, 67])).
% 0.21/0.44 tff(79,plain,
% 0.21/0.44 (![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)))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[78, 65])).
% 0.21/0.44 tff(80,plain,
% 0.21/0.44 (![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)))))))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[79, 60])).
% 0.21/0.44 tff(81,plain,
% 0.21/0.44 (((~![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)))))))))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(82,plain,
% 0.21/0.45 (((~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)))))))))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(83,plain,
% 0.21/0.45 (^[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)))))))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(84,plain,
% 0.21/0.45 (![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))))))))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[83])).
% 0.21/0.45 tff(85,plain,
% 0.21/0.45 (((~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)))))))))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[84])).
% 0.21/0.45 tff(86,plain,
% 0.21/0.45 (((~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)))))))))))),
% 0.21/0.45 inference(transitivity,[status(thm)],[85, 82])).
% 0.21/0.45 tff(87,plain,
% 0.21/0.45 (((~![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))))))))))))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[86])).
% 0.21/0.45 tff(88,plain,
% 0.21/0.45 (((~![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)))))))))))),
% 0.21/0.45 inference(transitivity,[status(thm)],[87, 81])).
% 0.21/0.45 tff(89,plain,
% 0.21/0.45 ((~![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)))))))))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(90,plain,
% 0.21/0.45 ((~![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))))))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.21/0.45 tff(91,plain,
% 0.21/0.45 (![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))))))))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[90, 80, 11, 58])).
% 0.21/0.45 tff(92,plain,
% 0.21/0.45 (((~![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))))))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(93,plain,
% 0.21/0.46 ((~((~((~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)))))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(94,plain,
% 0.21/0.46 (((~![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))))))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[93])).
% 0.21/0.46 tff(95,plain,
% 0.21/0.46 (((~![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))))))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[94, 92])).
% 0.21/0.46 tff(96,plain,
% 0.21/0.46 ((~![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)))))))))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(97,plain,
% 0.21/0.46 ((~![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)))))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.21/0.46 tff(98,plain,
% 0.21/0.46 (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, sdtpldt0(xS, xx))))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[97, 91])).
% 0.21/0.46 tff(99,plain,
% 0.21/0.46 (((~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))))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(100,plain,
% 0.21/0.46 (![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, sdtpldt0(xS, xx))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.21/0.46 tff(101,plain,
% 0.21/0.46 ((~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, sdtpldt0(xS, xx))))) | (~(((~aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) | (~((tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS)))) <=> aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtpldt0(xS, xx))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(102,plain,
% 0.21/0.46 (~(((~aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) | (~((tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS)))) <=> aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtpldt0(xS, xx)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[101, 100])).
% 0.21/0.46 tff(103,plain,
% 0.21/0.46 ((~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx))))) | (~(((~aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) | (~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtpldt0(xS, xx))) | (tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx)) <=> aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(104,plain,
% 0.21/0.46 (~(((~aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) | (~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtpldt0(xS, xx))) | (tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx)) <=> aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[103, 53])).
% 0.21/0.46 tff(105,assumption,(~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))), introduced(assumption)).
% 0.21/0.46 tff(106,plain,
% 0.21/0.46 (((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS)) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(107,plain,
% 0.21/0.46 (aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[106, 105])).
% 0.21/0.46 tff(108,plain,
% 0.21/0.46 ((((~aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) | (~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtpldt0(xS, xx))) | (tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx)) <=> aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) | (~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtpldt0(xS, xx))) | (tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx))) | (~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx)))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(109,plain,
% 0.21/0.46 ((((~aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) | (~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtpldt0(xS, xx))) | (tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx)) <=> aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) | (~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtpldt0(xS, xx))) | (tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[108, 107])).
% 0.21/0.46 tff(110,plain,
% 0.21/0.46 (~((~aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) | (~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtpldt0(xS, xx))) | (tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[109, 104])).
% 0.21/0.46 tff(111,plain,
% 0.21/0.46 (((~aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) | (~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtpldt0(xS, xx))) | (tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx)) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtpldt0(xS, xx))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(112,plain,
% 0.21/0.46 (aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtpldt0(xS, xx))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.21/0.46 tff(113,plain,
% 0.21/0.46 ((((~aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) | (~((tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS)))) <=> aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtpldt0(xS, xx))) | (~((~aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) | (~((tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))))) | (~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtpldt0(xS, xx)))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(114,plain,
% 0.21/0.46 (~((~aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) | (~((tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[113, 112, 102])).
% 0.21/0.46 tff(115,plain,
% 0.21/0.46 (((~aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) | (~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtpldt0(xS, xx))) | (tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx)) | (~(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(116,plain,
% 0.21/0.46 (~(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx)),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[115, 110])).
% 0.21/0.46 tff(117,plain,
% 0.21/0.47 (((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS)) | (~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(118,plain,
% 0.21/0.47 (~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[117, 105])).
% 0.21/0.47 tff(119,plain,
% 0.21/0.47 ((~((tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))) | (tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS)),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(120,plain,
% 0.21/0.47 ((~((tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))) | (tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[119, 118])).
% 0.21/0.47 tff(121,plain,
% 0.21/0.47 (~((tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[120, 116])).
% 0.21/0.47 tff(122,plain,
% 0.21/0.47 (((~aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) | (~((tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS)))) | ((tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(123,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[122, 121, 114])).
% 0.21/0.47 tff(124,plain,((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.47 tff(125,plain,
% 0.21/0.47 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(126,plain,
% 0.21/0.47 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[125])).
% 0.21/0.47 tff(127,plain,
% 0.21/0.47 (^[W0: $i] : refl(((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(128,plain,
% 0.21/0.47 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[127])).
% 0.21/0.47 tff(129,plain,
% 0.21/0.47 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(130,plain,
% 0.21/0.47 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[129])).
% 0.21/0.47 tff(131,plain,
% 0.21/0.47 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 0.21/0.47 inference(transitivity,[status(thm)],[130, 128])).
% 0.21/0.47 tff(132,plain,
% 0.21/0.47 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))) <=> ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(133,plain,
% 0.21/0.47 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[132])).
% 0.21/0.47 tff(134,plain,
% 0.21/0.47 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))) <=> ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(135,plain,
% 0.21/0.47 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[134])).
% 0.21/0.47 tff(136,plain,
% 0.21/0.47 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(137,plain,
% 0.21/0.47 (^[W0: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: $i] : rewrite((aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0)))) <=> (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))), (![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0)))) <=> ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))), ((aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0))))) <=> (aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))), rewrite((aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))) <=> ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))), ((aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0))))) <=> ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(138,plain,
% 0.21/0.47 (![W0: $i] : (aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[137])).
% 0.21/0.47 tff(139,axiom,(![W0: $i] : (aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mDefSub')).
% 0.21/0.47 tff(140,plain,
% 0.21/0.47 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.21/0.47 tff(141,plain,
% 0.21/0.47 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[140, 136])).
% 0.21/0.47 tff(142,plain,(
% 0.21/0.47 ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))),
% 0.21/0.47 inference(skolemize,[status(sab)],[141])).
% 0.21/0.47 tff(143,plain,
% 0.21/0.47 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[142, 135])).
% 0.21/0.47 tff(144,plain,
% 0.21/0.47 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[143, 133])).
% 0.21/0.47 tff(145,plain,
% 0.21/0.47 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[144, 131])).
% 0.21/0.47 tff(146,plain,
% 0.21/0.47 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[145, 126])).
% 0.21/0.47 tff(147,plain,
% 0.21/0.47 (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(xS)) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS))))))))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | (~aSet0(xS)) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS))))))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(148,plain,
% 0.21/0.47 (((~aSet0(xS)) | ![W1: $i] : (~((~(aSubsetOf0(W1, xS) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS)))))))))) <=> ((~aSet0(xS)) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS))))))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(149,plain,
% 0.21/0.47 (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(xS)) | ![W1: $i] : (~((~(aSubsetOf0(W1, xS) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS))))))))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(xS)) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS)))))))))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[148])).
% 0.21/0.48 tff(150,plain,
% 0.21/0.48 (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(xS)) | ![W1: $i] : (~((~(aSubsetOf0(W1, xS) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS))))))))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | (~aSet0(xS)) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS))))))))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[149, 147])).
% 0.21/0.48 tff(151,plain,
% 0.21/0.48 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(xS)) | ![W1: $i] : (~((~(aSubsetOf0(W1, xS) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS))))))))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(152,plain,
% 0.21/0.48 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | (~aSet0(xS)) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS)))))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[151, 150])).
% 0.21/0.48 tff(153,plain,
% 0.21/0.48 (![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS)))))))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[152, 146, 58])).
% 0.21/0.48 tff(154,plain,
% 0.21/0.48 ((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS)))))))))) | (~((~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))))) | (~((~aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS)) | (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W2: $i] : ((~aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(W2, xS)))))))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(155,plain,
% 0.21/0.48 (~((~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))))) | (~((~aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS)) | (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W2: $i] : ((~aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(W2, xS))))))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[154, 153])).
% 0.21/0.48 tff(156,plain,
% 0.21/0.48 (((~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))))) | (~((~aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS)) | (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W2: $i] : ((~aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(W2, xS)))))))) | ((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(157,plain,
% 0.21/0.48 ((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[156, 155])).
% 0.21/0.48 tff(158,plain,
% 0.21/0.48 (aSet0(sdtmndt0(sdtpldt0(xS, xx), xx)) <=> aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(159,plain,
% 0.21/0.48 (aSet0(sdtmndt0(sdtpldt0(xS, xx), xx)) & ![W0: $i] : (aElementOf0(W0, sdtmndt0(sdtpldt0(xS, xx), xx)) <=> (aElement0(W0) & aElementOf0(W0, sdtpldt0(xS, xx)) & (~(W0 = xx))))),
% 0.21/0.48 inference(or_elim,[status(thm)],[4])).
% 0.21/0.48 tff(160,plain,
% 0.21/0.48 (aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))),
% 0.21/0.48 inference(and_elim,[status(thm)],[159])).
% 0.21/0.48 tff(161,plain,
% 0.21/0.48 (aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[160, 158])).
% 0.21/0.48 tff(162,plain,
% 0.21/0.48 ((~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))))) | (~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS)))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(163,plain,
% 0.21/0.48 ((~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))))) | aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[162, 161])).
% 0.21/0.48 tff(164,plain,
% 0.21/0.48 (aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[163, 157])).
% 0.21/0.48 tff(165,plain,
% 0.21/0.48 (aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[164, 124])).
% 0.21/0.48 tff(166,plain,
% 0.21/0.48 ((~(sdtmndt0(sdtpldt0(xS, xx), xx) = xS)) <=> (~(sdtmndt0(sdtpldt0(xS, xx), xx) = xS))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(167,plain,
% 0.21/0.48 (~(sdtmndt0(sdtpldt0(xS, xx), xx) = xS)),
% 0.21/0.48 inference(or_elim,[status(thm)],[4])).
% 0.21/0.48 tff(168,plain,
% 0.21/0.48 (~(sdtmndt0(sdtpldt0(xS, xx), xx) = xS)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.21/0.48 tff(169,plain,
% 0.21/0.48 (^[W0: $i, W1: $i] : refl(((W0 = W1) | (~aSet0(W1)) | (~aSubsetOf0(W1, W0)) | (~aSubsetOf0(W0, W1)) | (~aSet0(W0))) <=> ((W0 = W1) | (~aSet0(W1)) | (~aSubsetOf0(W1, W0)) | (~aSubsetOf0(W0, W1)) | (~aSet0(W0))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(170,plain,
% 0.21/0.48 (![W0: $i, W1: $i] : ((W0 = W1) | (~aSet0(W1)) | (~aSubsetOf0(W1, W0)) | (~aSubsetOf0(W0, W1)) | (~aSet0(W0))) <=> ![W0: $i, W1: $i] : ((W0 = W1) | (~aSet0(W1)) | (~aSubsetOf0(W1, W0)) | (~aSubsetOf0(W0, W1)) | (~aSet0(W0)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[169])).
% 0.21/0.48 tff(171,plain,
% 0.21/0.48 (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aSubsetOf0(W0, W1) & aSubsetOf0(W1, W0)) <=> (~((~aSubsetOf0(W1, W0)) | (~aSubsetOf0(W0, W1))))), ((~(aSubsetOf0(W0, W1) & aSubsetOf0(W1, W0))) <=> (~(~((~aSubsetOf0(W1, W0)) | (~aSubsetOf0(W0, W1))))))), rewrite((~(~((~aSubsetOf0(W1, W0)) | (~aSubsetOf0(W0, W1))))) <=> ((~aSubsetOf0(W1, W0)) | (~aSubsetOf0(W0, W1)))), ((~(aSubsetOf0(W0, W1) & aSubsetOf0(W1, W0))) <=> ((~aSubsetOf0(W1, W0)) | (~aSubsetOf0(W0, W1))))), trans(monotonicity(rewrite((aSet0(W0) & aSet0(W1)) <=> (~((~aSet0(W1)) | (~aSet0(W0))))), ((~(aSet0(W0) & aSet0(W1))) <=> (~(~((~aSet0(W1)) | (~aSet0(W0))))))), rewrite((~(~((~aSet0(W1)) | (~aSet0(W0))))) <=> ((~aSet0(W1)) | (~aSet0(W0)))), ((~(aSet0(W0) & aSet0(W1))) <=> ((~aSet0(W1)) | (~aSet0(W0))))), (((W0 = W1) | (~(aSubsetOf0(W0, W1) & aSubsetOf0(W1, W0))) | (~(aSet0(W0) & aSet0(W1)))) <=> ((W0 = W1) | ((~aSubsetOf0(W1, W0)) | (~aSubsetOf0(W0, W1))) | ((~aSet0(W1)) | (~aSet0(W0)))))), rewrite(((W0 = W1) | ((~aSubsetOf0(W1, W0)) | (~aSubsetOf0(W0, W1))) | ((~aSet0(W1)) | (~aSet0(W0)))) <=> ((W0 = W1) | (~aSet0(W1)) | (~aSubsetOf0(W1, W0)) | (~aSubsetOf0(W0, W1)) | (~aSet0(W0)))), (((W0 = W1) | (~(aSubsetOf0(W0, W1) & aSubsetOf0(W1, W0))) | (~(aSet0(W0) & aSet0(W1)))) <=> ((W0 = W1) | (~aSet0(W1)) | (~aSubsetOf0(W1, W0)) | (~aSubsetOf0(W0, W1)) | (~aSet0(W0)))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(172,plain,
% 0.21/0.48 (![W0: $i, W1: $i] : ((W0 = W1) | (~(aSubsetOf0(W0, W1) & aSubsetOf0(W1, W0))) | (~(aSet0(W0) & aSet0(W1)))) <=> ![W0: $i, W1: $i] : ((W0 = W1) | (~aSet0(W1)) | (~aSubsetOf0(W1, W0)) | (~aSubsetOf0(W0, W1)) | (~aSet0(W0)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[171])).
% 0.21/0.48 tff(173,plain,
% 0.21/0.48 (![W0: $i, W1: $i] : ((W0 = W1) | (~(aSubsetOf0(W0, W1) & aSubsetOf0(W1, W0))) | (~(aSet0(W0) & aSet0(W1)))) <=> ![W0: $i, W1: $i] : ((W0 = W1) | (~(aSubsetOf0(W0, W1) & aSubsetOf0(W1, W0))) | (~(aSet0(W0) & aSet0(W1))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(174,plain,
% 0.21/0.48 (^[W0: $i, W1: $i] : trans(monotonicity(rewrite(((aSubsetOf0(W0, W1) & aSubsetOf0(W1, W0)) => (W0 = W1)) <=> ((~(aSubsetOf0(W0, W1) & aSubsetOf0(W1, W0))) | (W0 = W1))), (((aSet0(W0) & aSet0(W1)) => ((aSubsetOf0(W0, W1) & aSubsetOf0(W1, W0)) => (W0 = W1))) <=> ((aSet0(W0) & aSet0(W1)) => ((~(aSubsetOf0(W0, W1) & aSubsetOf0(W1, W0))) | (W0 = W1))))), rewrite(((aSet0(W0) & aSet0(W1)) => ((~(aSubsetOf0(W0, W1) & aSubsetOf0(W1, W0))) | (W0 = W1))) <=> ((W0 = W1) | (~(aSubsetOf0(W0, W1) & aSubsetOf0(W1, W0))) | (~(aSet0(W0) & aSet0(W1))))), (((aSet0(W0) & aSet0(W1)) => ((aSubsetOf0(W0, W1) & aSubsetOf0(W1, W0)) => (W0 = W1))) <=> ((W0 = W1) | (~(aSubsetOf0(W0, W1) & aSubsetOf0(W1, W0))) | (~(aSet0(W0) & aSet0(W1))))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(175,plain,
% 0.21/0.48 (![W0: $i, W1: $i] : ((aSet0(W0) & aSet0(W1)) => ((aSubsetOf0(W0, W1) & aSubsetOf0(W1, W0)) => (W0 = W1))) <=> ![W0: $i, W1: $i] : ((W0 = W1) | (~(aSubsetOf0(W0, W1) & aSubsetOf0(W1, W0))) | (~(aSet0(W0) & aSet0(W1))))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[174])).
% 0.21/0.48 tff(176,axiom,(![W0: $i, W1: $i] : ((aSet0(W0) & aSet0(W1)) => ((aSubsetOf0(W0, W1) & aSubsetOf0(W1, W0)) => (W0 = W1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mSubASymm')).
% 0.21/0.48 tff(177,plain,
% 0.21/0.48 (![W0: $i, W1: $i] : ((W0 = W1) | (~(aSubsetOf0(W0, W1) & aSubsetOf0(W1, W0))) | (~(aSet0(W0) & aSet0(W1))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.21/0.48 tff(178,plain,
% 0.21/0.48 (![W0: $i, W1: $i] : ((W0 = W1) | (~(aSubsetOf0(W0, W1) & aSubsetOf0(W1, W0))) | (~(aSet0(W0) & aSet0(W1))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[177, 173])).
% 0.21/0.48 tff(179,plain,(
% 0.21/0.48 ![W0: $i, W1: $i] : ((W0 = W1) | (~(aSubsetOf0(W0, W1) & aSubsetOf0(W1, W0))) | (~(aSet0(W0) & aSet0(W1))))),
% 0.21/0.48 inference(skolemize,[status(sab)],[178])).
% 0.21/0.48 tff(180,plain,
% 0.21/0.48 (![W0: $i, W1: $i] : ((W0 = W1) | (~aSet0(W1)) | (~aSubsetOf0(W1, W0)) | (~aSubsetOf0(W0, W1)) | (~aSet0(W0)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[179, 172])).
% 0.21/0.48 tff(181,plain,
% 0.21/0.48 (![W0: $i, W1: $i] : ((W0 = W1) | (~aSet0(W1)) | (~aSubsetOf0(W1, W0)) | (~aSubsetOf0(W0, W1)) | (~aSet0(W0)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[180, 170])).
% 0.21/0.48 tff(182,plain,
% 0.21/0.48 (((~![W0: $i, W1: $i] : ((W0 = W1) | (~aSet0(W1)) | (~aSubsetOf0(W1, W0)) | (~aSubsetOf0(W0, W1)) | (~aSet0(W0)))) | ((sdtmndt0(sdtpldt0(xS, xx), xx) = xS) | (~aSet0(xS)) | (~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS)))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aSet0(W1)) | (~aSubsetOf0(W1, W0)) | (~aSubsetOf0(W0, W1)) | (~aSet0(W0)))) | (sdtmndt0(sdtpldt0(xS, xx), xx) = xS) | (~aSet0(xS)) | (~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(183,plain,
% 0.21/0.48 (((sdtmndt0(sdtpldt0(xS, xx), xx) = xS) | (~aSet0(xS)) | (~aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS)) | (~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx)))) <=> ((sdtmndt0(sdtpldt0(xS, xx), xx) = xS) | (~aSet0(xS)) | (~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(184,plain,
% 0.21/0.48 (((~![W0: $i, W1: $i] : ((W0 = W1) | (~aSet0(W1)) | (~aSubsetOf0(W1, W0)) | (~aSubsetOf0(W0, W1)) | (~aSet0(W0)))) | ((sdtmndt0(sdtpldt0(xS, xx), xx) = xS) | (~aSet0(xS)) | (~aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS)) | (~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aSet0(W1)) | (~aSubsetOf0(W1, W0)) | (~aSubsetOf0(W0, W1)) | (~aSet0(W0)))) | ((sdtmndt0(sdtpldt0(xS, xx), xx) = xS) | (~aSet0(xS)) | (~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[183])).
% 0.21/0.48 tff(185,plain,
% 0.21/0.48 (((~![W0: $i, W1: $i] : ((W0 = W1) | (~aSet0(W1)) | (~aSubsetOf0(W1, W0)) | (~aSubsetOf0(W0, W1)) | (~aSet0(W0)))) | ((sdtmndt0(sdtpldt0(xS, xx), xx) = xS) | (~aSet0(xS)) | (~aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS)) | (~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aSet0(W1)) | (~aSubsetOf0(W1, W0)) | (~aSubsetOf0(W0, W1)) | (~aSet0(W0)))) | (sdtmndt0(sdtpldt0(xS, xx), xx) = xS) | (~aSet0(xS)) | (~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS)))),
% 0.21/0.48 inference(transitivity,[status(thm)],[184, 182])).
% 0.21/0.48 tff(186,plain,
% 0.21/0.48 ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aSet0(W1)) | (~aSubsetOf0(W1, W0)) | (~aSubsetOf0(W0, W1)) | (~aSet0(W0)))) | ((sdtmndt0(sdtpldt0(xS, xx), xx) = xS) | (~aSet0(xS)) | (~aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS)) | (~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(187,plain,
% 0.21/0.48 ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aSet0(W1)) | (~aSubsetOf0(W1, W0)) | (~aSubsetOf0(W0, W1)) | (~aSet0(W0)))) | (sdtmndt0(sdtpldt0(xS, xx), xx) = xS) | (~aSet0(xS)) | (~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.21/0.48 tff(188,plain,
% 0.21/0.48 (~aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[187, 181, 58, 168, 161, 165])).
% 0.21/0.48 tff(189,plain,
% 0.21/0.48 (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx)) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx)))))))))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | (~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx)) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx)))))))))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(190,plain,
% 0.21/0.49 (((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | ![W1: $i] : (~((~(aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx)) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx))))))))))) <=> ((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx)) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx)))))))))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(191,plain,
% 0.21/0.49 (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | ![W1: $i] : (~((~(aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx)) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx)))))))))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx)) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx))))))))))))),
% 0.21/0.49 inference(monotonicity,[status(thm)],[190])).
% 0.21/0.49 tff(192,plain,
% 0.21/0.49 (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | ![W1: $i] : (~((~(aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx)) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx)))))))))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | (~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx)) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx)))))))))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[191, 189])).
% 0.21/0.49 tff(193,plain,
% 0.21/0.49 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | ![W1: $i] : (~((~(aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx)) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx)))))))))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(194,plain,
% 0.21/0.49 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | (~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx)) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx))))))))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.21/0.49 tff(195,plain,
% 0.21/0.49 (![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx)) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx))))))))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[194, 146, 161])).
% 0.21/0.49 tff(196,plain,
% 0.21/0.49 ((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx)) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx))))))))))) | (~((~((~aSet0(xS)) | aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) | (~((~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))) | (~((~aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx))))))))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(197,plain,
% 0.21/0.49 (~((~((~aSet0(xS)) | aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) | (~((~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))) | (~((~aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx)))))))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[196, 195])).
% 0.21/0.49 tff(198,plain,
% 0.21/0.49 (((~((~aSet0(xS)) | aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) | (~((~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))) | (~((~aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx))))))))) | ((~aSet0(xS)) | aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) | (~((~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(199,plain,
% 0.21/0.49 ((~aSet0(xS)) | aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) | (~((~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[198, 197])).
% 0.21/0.49 tff(200,plain,
% 0.21/0.49 ((~((~aSet0(xS)) | aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) | (~((~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))) | (~aSet0(xS)) | aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) | (~((~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx))))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(201,plain,
% 0.21/0.49 ((~((~aSet0(xS)) | aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) | (~((~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))) | aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) | (~((~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[200, 58])).
% 0.21/0.49 tff(202,plain,
% 0.21/0.49 (aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) | (~((~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx))))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[201, 199])).
% 0.21/0.49 tff(203,plain,
% 0.21/0.49 (~((~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[202, 188])).
% 0.21/0.49 tff(204,plain,
% 0.21/0.49 (((~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(205,plain,
% 0.21/0.49 (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[204, 203])).
% 0.21/0.49 tff(206,plain,
% 0.21/0.49 ((((~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtpldt0(xS, xx))) | (tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx)) <=> aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx))) | ((~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtpldt0(xS, xx))) | (tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx)) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx))),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(207,plain,
% 0.21/0.49 ((((~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtpldt0(xS, xx))) | (tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx)) <=> aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx))) | ((~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtpldt0(xS, xx))) | (tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[206, 205])).
% 0.21/0.49 tff(208,plain,
% 0.21/0.49 ((~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtpldt0(xS, xx))) | (tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[207, 55])).
% 0.21/0.49 tff(209,plain,
% 0.21/0.49 (((~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)),
% 0.21/0.49 inference(tautology,[status(thm)],[])).
% 0.21/0.49 tff(210,plain,
% 0.21/0.49 (aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[209, 203])).
% 0.21/0.49 tff(211,plain,
% 0.21/0.49 (^[W0: $i] : refl(((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(212,plain,
% 0.21/0.49 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[211])).
% 0.21/0.49 tff(213,plain,
% 0.21/0.49 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(214,plain,
% 0.21/0.49 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[213])).
% 0.21/0.49 tff(215,plain,
% 0.21/0.49 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.21/0.49 inference(transitivity,[status(thm)],[214, 212])).
% 0.21/0.49 tff(216,plain,
% 0.21/0.49 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(217,plain,
% 0.21/0.49 (^[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))))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(218,plain,
% 0.21/0.49 (![W0: $i] : (aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[217])).
% 0.21/0.49 tff(219,axiom,(![W0: $i] : (aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mEOfElem')).
% 0.21/0.49 tff(220,plain,
% 0.21/0.49 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.21/0.49 tff(221,plain,
% 0.21/0.49 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[220, 216])).
% 0.21/0.49 tff(222,plain,(
% 0.21/0.49 ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.21/0.49 inference(skolemize,[status(sab)],[221])).
% 0.21/0.49 tff(223,plain,
% 0.21/0.49 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[222, 215])).
% 0.21/0.49 tff(224,plain,
% 0.21/0.49 (((~![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))))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(225,plain,
% 0.21/0.49 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | ((~aSet0(xS)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(226,plain,
% 0.21/0.49 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | (~aSet0(xS)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.21/0.49 tff(227,plain,
% 0.21/0.49 (![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[226, 223, 58])).
% 0.21/0.49 tff(228,plain,
% 0.21/0.49 (((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | (aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)))) <=> ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(229,plain,
% 0.21/0.49 ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | (aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(230,plain,
% 0.21/0.49 ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[229, 228])).
% 0.21/0.49 tff(231,plain,
% 0.21/0.49 (aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[230, 227, 210])).
% 0.21/0.49 tff(232,plain,
% 0.21/0.49 ((~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, sdtpldt0(xS, xx))))) | (~(((~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)))) <=> aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtpldt0(xS, xx))))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(233,plain,
% 0.21/0.49 (~(((~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)))) <=> aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtpldt0(xS, xx)))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[232, 100])).
% 0.21/0.50 tff(234,plain,
% 0.21/0.50 (((tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)) | (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(235,plain,
% 0.21/0.50 ((tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[234, 210])).
% 0.21/0.50 tff(236,plain,
% 0.21/0.50 ((~((~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS))))) | (~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(237,plain,
% 0.21/0.50 ((~((~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS))))) | (~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[236, 235])).
% 0.21/0.50 tff(238,plain,
% 0.21/0.50 (~((~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS))))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[237, 231])).
% 0.21/0.50 tff(239,plain,
% 0.21/0.50 ((((~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)))) <=> aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtpldt0(xS, xx))) | ((~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)))) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtpldt0(xS, xx))),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(240,plain,
% 0.21/0.50 (aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtpldt0(xS, xx))),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[239, 238, 233])).
% 0.21/0.50 tff(241,plain,
% 0.21/0.50 ((~((~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtpldt0(xS, xx))) | (tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx))) | (~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtpldt0(xS, xx))) | (tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx)),
% 0.21/0.50 inference(tautology,[status(thm)],[])).
% 0.21/0.50 tff(242,plain,
% 0.21/0.50 (tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[241, 240, 231, 208])).
% 0.21/0.50 tff(243,plain,
% 0.21/0.50 (aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS) <=> aElementOf0(xx, xS)),
% 0.21/0.50 inference(monotonicity,[status(thm)],[242])).
% 0.21/0.50 tff(244,plain,
% 0.21/0.50 (aElementOf0(xx, xS) <=> aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)),
% 0.21/0.50 inference(symmetry,[status(thm)],[243])).
% 0.21/0.50 tff(245,plain,
% 0.21/0.50 ((~aElementOf0(xx, xS)) <=> (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS))),
% 0.21/0.50 inference(monotonicity,[status(thm)],[244])).
% 0.21/0.50 tff(246,plain,
% 0.21/0.50 ((~aElementOf0(xx, xS)) <=> (~aElementOf0(xx, xS))),
% 0.21/0.50 inference(rewrite,[status(thm)],[])).
% 0.21/0.50 tff(247,axiom,(~aElementOf0(xx, xS)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__679_02')).
% 0.21/0.50 tff(248,plain,
% 0.21/0.50 (~aElementOf0(xx, xS)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[247, 246])).
% 0.21/0.50 tff(249,plain,
% 0.21/0.50 (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)),
% 0.21/0.50 inference(modus_ponens,[status(thm)],[248, 245])).
% 0.21/0.50 tff(250,plain,
% 0.21/0.50 ($false),
% 0.21/0.50 inference(unit_resolution,[status(thm)],[210, 249])).
% 0.21/0.50 % SZS output end Proof
% 0.21/0.50 % E exiting
%------------------------------------------------------------------------------