%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM534+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:21:18 AM UTC 2025
% Result : Theorem 0.21s 0.41s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.13 % Problem : NUM534+1 : TPTP v9.0.0. Released v4.0.0.
% 0.05/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 01:23:20 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.21/0.41 % SZS status Theorem
% 0.21/0.41 % SZS output start Proof
% 0.21/0.41 tff(aElementOf0_type, type, (
% 0.21/0.41 aElementOf0: ( $i * $i ) > $o)).
% 0.21/0.41 tff(xS_type, type, (
% 0.21/0.41 xS: $i)).
% 0.21/0.41 tff(tptp_fun_W3_2_type, type, (
% 0.21/0.41 tptp_fun_W3_2: ( $i * $i * $i ) > $i)).
% 0.21/0.41 tff(sdtmndt0_type, type, (
% 0.21/0.41 sdtmndt0: ( $i * $i ) > $i)).
% 0.21/0.41 tff(xx_type, type, (
% 0.21/0.41 xx: $i)).
% 0.21/0.41 tff(aElement0_type, type, (
% 0.21/0.41 aElement0: $i > $o)).
% 0.21/0.41 tff(aSet0_type, type, (
% 0.21/0.41 aSet0: $i > $o)).
% 0.21/0.41 tff(tptp_fun_W3_3_type, type, (
% 0.21/0.41 tptp_fun_W3_3: ( $i * $i * $i ) > $i)).
% 0.21/0.41 tff(sdtpldt0_type, type, (
% 0.21/0.41 sdtpldt0: ( $i * $i ) > $i)).
% 0.21/0.41 tff(1,assumption,(~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))), introduced(assumption)).
% 0.21/0.41 tff(2,plain,
% 0.21/0.41 (((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))),
% 0.21/0.41 inference(tautology,[status(thm)],[])).
% 0.21/0.41 tff(3,plain,
% 0.21/0.41 (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[2, 1])).
% 0.21/0.41 tff(4,assumption,((~aSet0(sdtmndt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(xS, xx)))))), introduced(assumption)).
% 0.21/0.41 tff(5,plain,
% 0.21/0.41 (aSet0(xS) <=> aSet0(xS)),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(6,axiom,(aSet0(xS)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__617')).
% 0.21/0.41 tff(7,plain,
% 0.21/0.41 (aSet0(xS)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.21/0.41 tff(8,plain,
% 0.21/0.41 (^[W0: $i] : refl(((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(9,plain,
% 0.21/0.41 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[8])).
% 0.21/0.41 tff(10,plain,
% 0.21/0.41 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(11,plain,
% 0.21/0.41 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[10])).
% 0.21/0.41 tff(12,plain,
% 0.21/0.41 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.21/0.41 inference(transitivity,[status(thm)],[11, 9])).
% 0.21/0.41 tff(13,plain,
% 0.21/0.41 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(14,plain,
% 0.21/0.41 (^[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))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 0.21/0.41 tff(15,plain,
% 0.21/0.41 (![W0: $i] : (aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[14])).
% 0.21/0.41 tff(16,axiom,(![W0: $i] : (aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mEOfElem')).
% 0.21/0.41 tff(17,plain,
% 0.21/0.41 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[16, 15])).
% 0.21/0.41 tff(18,plain,
% 0.21/0.41 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[17, 13])).
% 0.21/0.41 tff(19,plain,(
% 0.21/0.41 ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.21/0.41 inference(skolemize,[status(sab)],[18])).
% 0.21/0.41 tff(20,plain,
% 0.21/0.41 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.21/0.41 tff(21,plain,
% 0.21/0.41 (((~![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))))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(22,plain,
% 0.21/0.41 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | ((~aSet0(xS)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS))))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(23,plain,
% 0.21/0.41 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | (~aSet0(xS)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.21/0.41 tff(24,plain,
% 0.21/0.41 (![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[23, 20, 7])).
% 0.21/0.41 tff(25,plain,
% 0.21/0.41 (aElementOf0(xx, xS) <=> aElementOf0(xx, xS)),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(26,axiom,(aElementOf0(xx, xS)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__617_02')).
% 0.21/0.41 tff(27,plain,
% 0.21/0.41 (aElementOf0(xx, xS)),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.21/0.41 tff(28,plain,
% 0.21/0.41 (((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | (aElement0(xx) | (~aElementOf0(xx, xS)))) <=> ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | aElement0(xx) | (~aElementOf0(xx, xS)))),
% 0.21/0.41 inference(rewrite,[status(thm)],[])).
% 0.21/0.41 tff(29,plain,
% 0.21/0.41 ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | (aElement0(xx) | (~aElementOf0(xx, xS)))),
% 0.21/0.41 inference(quant_inst,[status(thm)],[])).
% 0.21/0.41 tff(30,plain,
% 0.21/0.41 ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | aElement0(xx) | (~aElementOf0(xx, xS))),
% 0.21/0.41 inference(modus_ponens,[status(thm)],[29, 28])).
% 0.21/0.41 tff(31,plain,
% 0.21/0.41 (aElement0(xx)),
% 0.21/0.41 inference(unit_resolution,[status(thm)],[30, 27, 24])).
% 0.21/0.41 tff(32,plain,
% 0.21/0.41 (^[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)))))))))))))),
% 0.21/0.41 inference(bind,[status(th)],[])).
% 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)) | (~![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)))))))))))),
% 0.21/0.41 inference(quant_intro,[status(thm)],[32])).
% 0.21/0.41 tff(34,plain,
% 0.21/0.41 (^[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))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(35,plain,
% 0.21/0.42 (![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)))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[34])).
% 0.21/0.42 tff(36,plain,
% 0.21/0.42 (^[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))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(37,plain,
% 0.21/0.42 (![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)))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[36])).
% 0.21/0.42 tff(38,plain,
% 0.21/0.42 (![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)))))))),
% 0.21/0.42 inference(transitivity,[status(thm)],[37, 35])).
% 0.21/0.42 tff(39,plain,
% 0.21/0.42 (^[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)))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 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) & ![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)))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[39])).
% 0.21/0.42 tff(41,plain,
% 0.21/0.42 (^[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)))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 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) & ![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))))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[41])).
% 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) & ![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)))))))),
% 0.21/0.42 inference(rewrite,[status(thm)],[])).
% 0.21/0.42 tff(44,plain,
% 0.21/0.42 (^[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)))))))))),
% 0.21/0.42 inference(bind,[status(th)],[])).
% 0.21/0.42 tff(45,plain,
% 0.21/0.42 (![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)))))))),
% 0.21/0.42 inference(quant_intro,[status(thm)],[44])).
% 0.21/0.42 tff(46,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/sandbox/benchmark/theBenchmark.p','mDefDiff')).
% 0.21/0.42 tff(47,plain,
% 0.21/0.42 (![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)))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.21/0.42 tff(48,plain,
% 0.21/0.42 (![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)))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.21/0.42 tff(49,plain,(
% 0.21/0.42 ![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)))))))))),
% 0.21/0.42 inference(skolemize,[status(sab)],[48])).
% 0.21/0.42 tff(50,plain,
% 0.21/0.42 (![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))))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.21/0.42 tff(51,plain,
% 0.21/0.42 (![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)))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[50, 40])).
% 0.21/0.42 tff(52,plain,
% 0.21/0.42 (![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)))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[51, 38])).
% 0.21/0.42 tff(53,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)))))))))))),
% 0.21/0.42 inference(modus_ponens,[status(thm)],[52, 33])).
% 0.21/0.42 tff(54,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(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (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(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, W2)))))))))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(55,plain,
% 0.21/0.43 (((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))) <=> ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, W2)))))))))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(56,plain,
% 0.21/0.43 (^[W2: $i] : rewrite((~((~((W2 = sdtmndt0(xS, xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, W2)))))))))) <=> (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, W2)))))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(57,plain,
% 0.21/0.43 (![W2: $i] : (~((~((W2 = sdtmndt0(xS, xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, W2)))))))))) <=> ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[56])).
% 0.21/0.43 tff(58,plain,
% 0.21/0.43 (((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtmndt0(xS, xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))) <=> ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, W2)))))))))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[57])).
% 0.21/0.43 tff(59,plain,
% 0.21/0.43 (((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtmndt0(xS, xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))) <=> ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, W2)))))))))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[58, 55])).
% 0.21/0.43 tff(60,plain,
% 0.21/0.43 (((~![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(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtmndt0(xS, xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (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(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))))),
% 0.21/0.43 inference(monotonicity,[status(thm)],[59])).
% 0.21/0.43 tff(61,plain,
% 0.21/0.43 (((~![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(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtmndt0(xS, xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (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(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, W2)))))))))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[60, 54])).
% 0.21/0.43 tff(62,plain,
% 0.21/0.43 ((~![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(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtmndt0(xS, xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, W2)))))))))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(63,plain,
% 0.21/0.43 ((~![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(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.21/0.43 tff(64,plain,
% 0.21/0.43 ((~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[63, 53, 7])).
% 0.21/0.43 tff(65,plain,
% 0.21/0.43 (![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[64, 31])).
% 0.21/0.44 tff(66,plain,
% 0.21/0.44 (((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))) | (~((~aSet0(sdtmndt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(xS, xx)))))))) <=> ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))) | (~((~aSet0(sdtmndt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(xS, xx))))))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(67,plain,
% 0.21/0.44 ((~((~((~aSet0(sdtmndt0(xS, xx))) | (sdtmndt0(xS, xx) = sdtmndt0(xS, xx)) | (((~aElement0(tptp_fun_W3_3(sdtmndt0(xS, xx), xx, xS))) | (~aElementOf0(tptp_fun_W3_3(sdtmndt0(xS, xx), xx, xS), xS)) | (tptp_fun_W3_3(sdtmndt0(xS, xx), xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(sdtmndt0(xS, xx), xx, xS), sdtmndt0(xS, xx))))) | (~((~(sdtmndt0(xS, xx) = sdtmndt0(xS, xx))) | (~((~aSet0(sdtmndt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(xS, xx))))))))))) <=> (~((~aSet0(sdtmndt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(xS, xx)))))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(68,plain,
% 0.21/0.44 (((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))) | (~((~((~aSet0(sdtmndt0(xS, xx))) | (sdtmndt0(xS, xx) = sdtmndt0(xS, xx)) | (((~aElement0(tptp_fun_W3_3(sdtmndt0(xS, xx), xx, xS))) | (~aElementOf0(tptp_fun_W3_3(sdtmndt0(xS, xx), xx, xS), xS)) | (tptp_fun_W3_3(sdtmndt0(xS, xx), xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(sdtmndt0(xS, xx), xx, xS), sdtmndt0(xS, xx))))) | (~((~(sdtmndt0(xS, xx) = sdtmndt0(xS, xx))) | (~((~aSet0(sdtmndt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(xS, xx)))))))))))) <=> ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))) | (~((~aSet0(sdtmndt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(xS, xx))))))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[67])).
% 0.21/0.44 tff(69,plain,
% 0.21/0.44 (((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))) | (~((~((~aSet0(sdtmndt0(xS, xx))) | (sdtmndt0(xS, xx) = sdtmndt0(xS, xx)) | (((~aElement0(tptp_fun_W3_3(sdtmndt0(xS, xx), xx, xS))) | (~aElementOf0(tptp_fun_W3_3(sdtmndt0(xS, xx), xx, xS), xS)) | (tptp_fun_W3_3(sdtmndt0(xS, xx), xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(sdtmndt0(xS, xx), xx, xS), sdtmndt0(xS, xx))))) | (~((~(sdtmndt0(xS, xx) = sdtmndt0(xS, xx))) | (~((~aSet0(sdtmndt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(xS, xx)))))))))))) <=> ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))) | (~((~aSet0(sdtmndt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(xS, xx))))))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[68, 66])).
% 0.21/0.44 tff(70,plain,
% 0.21/0.44 ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))) | (~((~((~aSet0(sdtmndt0(xS, xx))) | (sdtmndt0(xS, xx) = sdtmndt0(xS, xx)) | (((~aElement0(tptp_fun_W3_3(sdtmndt0(xS, xx), xx, xS))) | (~aElementOf0(tptp_fun_W3_3(sdtmndt0(xS, xx), xx, xS), xS)) | (tptp_fun_W3_3(sdtmndt0(xS, xx), xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(sdtmndt0(xS, xx), xx, xS), sdtmndt0(xS, xx))))) | (~((~(sdtmndt0(xS, xx) = sdtmndt0(xS, xx))) | (~((~aSet0(sdtmndt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(xS, xx)))))))))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(71,plain,
% 0.21/0.44 ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(xS, xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, xS))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, xS), xS)) | (tptp_fun_W3_3(W2, xx, xS) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, xS), W2)))) | (~((~(W2 = sdtmndt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))) | (~((~aSet0(sdtmndt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(xS, xx)))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.21/0.44 tff(72,plain,
% 0.21/0.44 ($false),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[71, 65, 4])).
% 0.21/0.44 tff(73,plain,(~((~aSet0(sdtmndt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(xS, xx))))))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.44 tff(74,plain,
% 0.21/0.44 (((~aSet0(sdtmndt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(xS, xx)))))) | ![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(xS, xx))))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(75,plain,
% 0.21/0.44 (![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(xS, xx))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.21/0.44 tff(76,plain,
% 0.21/0.44 ((~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(xS, xx))))) | (~(((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)) | (tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(77,plain,
% 0.21/0.44 (~(((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)) | (tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[76, 75])).
% 0.21/0.44 tff(78,plain,
% 0.21/0.44 ((((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)) | (tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))) | ((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)) | (tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx)) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(79,plain,
% 0.21/0.44 (((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)) | (tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx)) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.21/0.44 tff(80,plain,
% 0.21/0.44 ((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)) | (tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[79, 3])).
% 0.21/0.44 tff(81,plain,
% 0.21/0.44 (((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))) | (~(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(82,plain,
% 0.21/0.44 (~(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx)),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[81, 1])).
% 0.21/0.44 tff(83,plain,
% 0.21/0.44 (((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) | ((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(84,plain,
% 0.21/0.44 ((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[83, 1])).
% 0.21/0.44 tff(85,plain,
% 0.21/0.44 (((~aSet0(sdtmndt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, xS)) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(xS, xx)))))) | aSet0(sdtmndt0(xS, xx))),
% 0.21/0.44 inference(tautology,[status(thm)],[])).
% 0.21/0.44 tff(86,plain,
% 0.21/0.44 (aSet0(sdtmndt0(xS, xx))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[85, 73])).
% 0.21/0.44 tff(87,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] : (~(((~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)))))))))))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(88,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)) | (((~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(quant_intro,[status(thm)],[87])).
% 0.21/0.44 tff(89,plain,
% 0.21/0.44 (^[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))))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 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)) | (~![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)))))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[89])).
% 0.21/0.45 tff(91,plain,
% 0.21/0.45 (^[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))))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(92,plain,
% 0.21/0.45 (![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)))))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[91])).
% 0.21/0.45 tff(93,plain,
% 0.21/0.45 (![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)))))))),
% 0.21/0.45 inference(transitivity,[status(thm)],[92, 90])).
% 0.21/0.45 tff(94,plain,
% 0.21/0.45 (^[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)))))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(95,plain,
% 0.21/0.45 (![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)))))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[94])).
% 0.21/0.45 tff(96,plain,
% 0.21/0.45 (^[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)))))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(97,plain,
% 0.21/0.45 (![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))))))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[96])).
% 0.21/0.45 tff(98,plain,
% 0.21/0.45 (![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)))))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(99,plain,
% 0.21/0.45 (^[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)))))))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(100,plain,
% 0.21/0.45 (![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)))))))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[99])).
% 0.21/0.45 tff(101,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/sandbox/benchmark/theBenchmark.p','mDefCons')).
% 0.21/0.45 tff(102,plain,
% 0.21/0.45 (![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)))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.21/0.45 tff(103,plain,
% 0.21/0.45 (![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)))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[102, 98])).
% 0.21/0.45 tff(104,plain,(
% 0.21/0.45 ![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)))))))))),
% 0.21/0.45 inference(skolemize,[status(sab)],[103])).
% 0.21/0.45 tff(105,plain,
% 0.21/0.45 (![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))))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[104, 97])).
% 0.21/0.45 tff(106,plain,
% 0.21/0.45 (![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)))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[105, 95])).
% 0.21/0.45 tff(107,plain,
% 0.21/0.45 (![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)))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[106, 93])).
% 0.21/0.45 tff(108,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)))))))))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[107, 88])).
% 0.21/0.46 tff(109,plain,
% 0.21/0.46 (((~![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)))))))))))) | ((~aElement0(xx)) | (~aSet0(sdtmndt0(xS, xx))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2)))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))) <=> 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)))))))))))) | (~aElement0(xx)) | (~aSet0(sdtmndt0(xS, xx))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2)))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))) <=> aElementOf0(W3, W2)))))))))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(110,plain,
% 0.21/0.46 (((~aSet0(sdtmndt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2)))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))) <=> aElementOf0(W3, W2))))))))))) <=> ((~aElement0(xx)) | (~aSet0(sdtmndt0(xS, xx))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2)))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))) <=> aElementOf0(W3, W2)))))))))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(111,plain,
% 0.21/0.46 (^[W2: $i] : rewrite((~((~((W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2)))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))) <=> aElementOf0(W3, W2)))))))))) <=> (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2)))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))) <=> aElementOf0(W3, W2)))))))))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(112,plain,
% 0.21/0.46 (![W2: $i] : (~((~((W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2)))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))) <=> aElementOf0(W3, W2)))))))))) <=> ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2)))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))) <=> aElementOf0(W3, W2))))))))))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[111])).
% 0.21/0.46 tff(113,plain,
% 0.21/0.46 (((~aSet0(sdtmndt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2)))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))) <=> aElementOf0(W3, W2))))))))))) <=> ((~aSet0(sdtmndt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2)))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))) <=> aElementOf0(W3, W2)))))))))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[112])).
% 0.21/0.46 tff(114,plain,
% 0.21/0.46 (((~aSet0(sdtmndt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2)))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))) <=> aElementOf0(W3, W2))))))))))) <=> ((~aElement0(xx)) | (~aSet0(sdtmndt0(xS, xx))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2)))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))) <=> aElementOf0(W3, W2)))))))))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[113, 110])).
% 0.21/0.46 tff(115,plain,
% 0.21/0.46 (((~![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(sdtmndt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2)))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))) <=> 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)))))))))))) | ((~aElement0(xx)) | (~aSet0(sdtmndt0(xS, xx))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2)))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))) <=> aElementOf0(W3, W2))))))))))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[114])).
% 0.21/0.46 tff(116,plain,
% 0.21/0.46 (((~![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(sdtmndt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2)))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))) <=> 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)))))))))))) | (~aElement0(xx)) | (~aSet0(sdtmndt0(xS, xx))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2)))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))) <=> aElementOf0(W3, W2)))))))))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[115, 109])).
% 0.21/0.46 tff(117,plain,
% 0.21/0.46 ((~![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(sdtmndt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2)))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))) <=> aElementOf0(W3, W2)))))))))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(118,plain,
% 0.21/0.47 ((~![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)))))))))))) | (~aElement0(xx)) | (~aSet0(sdtmndt0(xS, xx))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2)))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))) <=> aElementOf0(W3, W2))))))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.21/0.47 tff(119,plain,
% 0.21/0.47 ((~aElement0(xx)) | (~aSet0(sdtmndt0(xS, xx))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2)))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))) <=> aElementOf0(W3, W2))))))))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[118, 108])).
% 0.21/0.47 tff(120,plain,
% 0.21/0.47 ((~aSet0(sdtmndt0(xS, xx))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2)))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))) <=> aElementOf0(W3, W2))))))))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[119, 31])).
% 0.21/0.47 tff(121,plain,
% 0.21/0.47 (![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2)))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))) <=> aElementOf0(W3, W2))))))))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[120, 86])).
% 0.21/0.47 tff(122,plain,
% 0.21/0.47 ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(sdtmndt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, sdtmndt0(xS, xx)), W2)))) | (~((~(W2 = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))) <=> aElementOf0(W3, W2))))))))))) | (~((~((~aSet0(xS)) | (xS = sdtpldt0(sdtmndt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)))) | (~((~(xS = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(xS)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))) <=> aElementOf0(W3, xS))))))))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(123,plain,
% 0.21/0.47 (~((~((~aSet0(xS)) | (xS = sdtpldt0(sdtmndt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)))) | (~((~(xS = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(xS)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))) <=> aElementOf0(W3, xS)))))))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[122, 121])).
% 0.21/0.47 tff(124,plain,
% 0.21/0.47 (((~((~aSet0(xS)) | (xS = sdtpldt0(sdtmndt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)))) | (~((~(xS = sdtpldt0(sdtmndt0(xS, xx), xx))) | (~((~aSet0(xS)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, sdtmndt0(xS, xx))))) <=> aElementOf0(W3, xS))))))))) | ((~aSet0(xS)) | (xS = sdtpldt0(sdtmndt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(125,plain,
% 0.21/0.47 ((~aSet0(xS)) | (xS = sdtpldt0(sdtmndt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[124, 123])).
% 0.21/0.47 tff(126,plain,
% 0.21/0.47 ((xS = sdtpldt0(sdtmndt0(xS, xx), xx)) <=> (sdtpldt0(sdtmndt0(xS, xx), xx) = xS)),
% 0.21/0.47 inference(commutativity,[status(thm)],[])).
% 0.21/0.47 tff(127,plain,
% 0.21/0.47 ((sdtpldt0(sdtmndt0(xS, xx), xx) = xS) <=> (xS = sdtpldt0(sdtmndt0(xS, xx), xx))),
% 0.21/0.47 inference(symmetry,[status(thm)],[126])).
% 0.21/0.47 tff(128,plain,
% 0.21/0.47 ((~(sdtpldt0(sdtmndt0(xS, xx), xx) = xS)) <=> (~(xS = sdtpldt0(sdtmndt0(xS, xx), xx)))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[127])).
% 0.21/0.47 tff(129,plain,
% 0.21/0.47 ((~(sdtpldt0(sdtmndt0(xS, xx), xx) = xS)) <=> (~(sdtpldt0(sdtmndt0(xS, xx), xx) = xS))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(130,axiom,(~(sdtpldt0(sdtmndt0(xS, xx), xx) = xS)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 0.21/0.47 tff(131,plain,
% 0.21/0.47 (~(sdtpldt0(sdtmndt0(xS, xx), xx) = xS)),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[130, 129])).
% 0.21/0.47 tff(132,plain,
% 0.21/0.47 (~(xS = sdtpldt0(sdtmndt0(xS, xx), xx))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[131, 128])).
% 0.21/0.47 tff(133,plain,
% 0.21/0.47 ((~((~aSet0(xS)) | (xS = sdtpldt0(sdtmndt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)))) | (~aSet0(xS)) | (xS = sdtpldt0(sdtmndt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(134,plain,
% 0.21/0.47 ((~((~aSet0(xS)) | (xS = sdtpldt0(sdtmndt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)))) | (xS = sdtpldt0(sdtmndt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[133, 7])).
% 0.21/0.47 tff(135,plain,
% 0.21/0.47 (((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[134, 132, 125])).
% 0.21/0.47 tff(136,plain,
% 0.21/0.47 ((~(((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS))) | (~((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))))) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(137,plain,
% 0.21/0.47 ((~((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))))) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[136, 135])).
% 0.21/0.47 tff(138,plain,
% 0.21/0.47 (aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[137, 84])).
% 0.21/0.47 tff(139,plain,
% 0.21/0.47 (((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | (aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)))) <=> ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(140,plain,
% 0.21/0.47 ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | (aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(141,plain,
% 0.21/0.47 ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[140, 139])).
% 0.21/0.47 tff(142,plain,
% 0.21/0.47 (aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[141, 24])).
% 0.21/0.47 tff(143,plain,
% 0.21/0.47 (aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[142, 138])).
% 0.21/0.47 tff(144,plain,
% 0.21/0.47 ((~((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)) | (tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx))) | (~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)) | (tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx)),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(145,plain,
% 0.21/0.47 ($false),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[144, 143, 138, 82, 80])).
% 0.21/0.47 tff(146,plain,((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(147,assumption,(~((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)) | (tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx))), introduced(assumption)).
% 0.21/0.48 tff(148,plain,
% 0.21/0.48 (((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)) | (tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx)) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(149,plain,
% 0.21/0.48 (aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[148, 147])).
% 0.21/0.48 tff(150,plain,
% 0.21/0.48 (((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)) | (tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx)) | aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(151,plain,
% 0.21/0.48 (aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[150, 147])).
% 0.21/0.48 tff(152,plain,
% 0.21/0.48 ((~((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))))) | (~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(153,plain,
% 0.21/0.48 (~((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[152, 151, 146])).
% 0.21/0.48 tff(154,plain,
% 0.21/0.48 ((~(((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) <=> aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS))) | ((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(155,plain,
% 0.21/0.48 (((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[154, 135])).
% 0.21/0.48 tff(156,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[155, 153, 149])).
% 0.21/0.48 tff(157,plain,((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)) | (tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx)), inference(lemma,lemma(discharge,[]))).
% 0.21/0.48 tff(158,plain,
% 0.21/0.48 ((((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)) | (tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))) | (~((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)) | (tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(159,plain,
% 0.21/0.48 ((~((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)) | (tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx))) | (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[158, 77])).
% 0.21/0.48 tff(160,plain,
% 0.21/0.48 (~aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[159, 157])).
% 0.21/0.48 tff(161,plain,
% 0.21/0.48 ((~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))) | (tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(162,plain,
% 0.21/0.48 (tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[161, 160, 146])).
% 0.21/0.48 tff(163,plain,
% 0.21/0.48 (aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS) <=> aElementOf0(xx, xS)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[162])).
% 0.21/0.48 tff(164,plain,
% 0.21/0.48 (aElementOf0(xx, xS) <=> aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)),
% 0.21/0.48 inference(symmetry,[status(thm)],[163])).
% 0.21/0.48 tff(165,plain,
% 0.21/0.48 (aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), xS)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[27, 164])).
% 0.21/0.48 tff(166,plain,
% 0.21/0.48 (aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx))) <=> aElement0(xx)),
% 0.21/0.48 inference(monotonicity,[status(thm)],[162])).
% 0.21/0.48 tff(167,plain,
% 0.21/0.48 (aElement0(xx) <=> aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))),
% 0.21/0.48 inference(symmetry,[status(thm)],[166])).
% 0.21/0.48 tff(168,plain,
% 0.21/0.48 (aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[31, 167])).
% 0.21/0.48 tff(169,plain,
% 0.21/0.48 (~((~aElement0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)))) | (~((tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)) = xx) | aElementOf0(tptp_fun_W3_2(xS, xx, sdtmndt0(xS, xx)), sdtmndt0(xS, xx)))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[152, 168, 146])).
% 0.21/0.48 tff(170,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[155, 169, 165])).
% 0.21/0.48 % SZS output end Proof
% 0.21/0.48 % E exiting
%------------------------------------------------------------------------------