%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM537+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:21:19 AM UTC 2025
% Result : Theorem 0.20s 0.50s
% Output : Proof 0.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : NUM537+1 : TPTP v9.0.0. Released v4.0.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n013.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Jun 20 01:24:08 EDT 2025
% 0.13/0.33 % CPUTime :
% 0.20/0.50 % SZS status Theorem
% 0.20/0.50 % SZS output start Proof
% 0.20/0.50 tff(aElementOf0_type, type, (
% 0.20/0.50 aElementOf0: ( $i * $i ) > $o)).
% 0.20/0.50 tff(xS_type, type, (
% 0.20/0.50 xS: $i)).
% 0.20/0.50 tff(tptp_fun_W2_1_type, type, (
% 0.20/0.50 tptp_fun_W2_1: ( $i * $i ) > $i)).
% 0.20/0.50 tff(sdtmndt0_type, type, (
% 0.20/0.50 sdtmndt0: ( $i * $i ) > $i)).
% 0.20/0.50 tff(xx_type, type, (
% 0.20/0.50 xx: $i)).
% 0.20/0.50 tff(sdtpldt0_type, type, (
% 0.20/0.50 sdtpldt0: ( $i * $i ) > $i)).
% 0.20/0.50 tff(aElement0_type, type, (
% 0.20/0.50 aElement0: $i > $o)).
% 0.20/0.50 tff(aSet0_type, type, (
% 0.20/0.50 aSet0: $i > $o)).
% 0.20/0.50 tff(tptp_fun_W3_3_type, type, (
% 0.20/0.50 tptp_fun_W3_3: ( $i * $i * $i ) > $i)).
% 0.20/0.50 tff(tptp_fun_W3_2_type, type, (
% 0.20/0.50 tptp_fun_W3_2: ( $i * $i * $i ) > $i)).
% 0.20/0.50 tff(aSubsetOf0_type, type, (
% 0.20/0.50 aSubsetOf0: ( $i * $i ) > $o)).
% 0.20/0.50 tff(1,assumption,((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)))))), introduced(assumption)).
% 0.20/0.50 tff(2,assumption,((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, sdtpldt0(xS, xx)))))), introduced(assumption)).
% 0.20/0.50 tff(3,plain,
% 0.20/0.50 (aSet0(xS) <=> aSet0(xS)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(4,axiom,(aElement0(xx) & aSet0(xS)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__679')).
% 0.20/0.50 tff(5,plain,
% 0.20/0.50 (aSet0(xS)),
% 0.20/0.50 inference(and_elim,[status(thm)],[4])).
% 0.20/0.50 tff(6,plain,
% 0.20/0.50 (aSet0(xS)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[5, 3])).
% 0.20/0.50 tff(7,plain,
% 0.20/0.50 (aElement0(xx) <=> aElement0(xx)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(8,plain,
% 0.20/0.50 (aElement0(xx)),
% 0.20/0.50 inference(and_elim,[status(thm)],[4])).
% 0.20/0.50 tff(9,plain,
% 0.20/0.50 (aElement0(xx)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.20/0.50 tff(10,plain,
% 0.20/0.50 (^[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)))))))))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(11,plain,
% 0.20/0.50 (![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)))))))))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[10])).
% 0.20/0.50 tff(12,plain,
% 0.20/0.50 (^[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))))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(13,plain,
% 0.20/0.50 (![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)))))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[12])).
% 0.20/0.50 tff(14,plain,
% 0.20/0.50 (^[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))))))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(15,plain,
% 0.20/0.50 (![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)))))))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[14])).
% 0.20/0.50 tff(16,plain,
% 0.20/0.50 (![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)))))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[15, 13])).
% 0.20/0.50 tff(17,plain,
% 0.20/0.50 (^[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)))))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(18,plain,
% 0.20/0.51 (![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)))))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[17])).
% 0.20/0.51 tff(19,plain,
% 0.20/0.51 (^[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)))))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(20,plain,
% 0.20/0.51 (![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))))))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[19])).
% 0.20/0.51 tff(21,plain,
% 0.20/0.51 (![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)))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(22,plain,
% 0.20/0.51 (^[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)))))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(23,plain,
% 0.20/0.51 (![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)))))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[22])).
% 0.20/0.51 tff(24,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')).
% 0.20/0.51 tff(25,plain,
% 0.20/0.51 (![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)))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.20/0.51 tff(26,plain,
% 0.20/0.51 (![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)))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.20/0.51 tff(27,plain,(
% 0.20/0.51 ![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)))))))))),
% 0.20/0.51 inference(skolemize,[status(sab)],[26])).
% 0.20/0.51 tff(28,plain,
% 0.20/0.51 (![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))))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[27, 20])).
% 0.20/0.51 tff(29,plain,
% 0.20/0.51 (![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)))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[28, 18])).
% 0.20/0.51 tff(30,plain,
% 0.20/0.51 (![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)))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[29, 16])).
% 0.20/0.51 tff(31,plain,
% 0.20/0.51 (![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)))))))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[30, 11])).
% 0.20/0.51 tff(32,plain,
% 0.20/0.51 (((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))))))) | ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2)))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))))))) | (~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2)))))))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(33,plain,
% 0.20/0.51 (((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2))))))))))) <=> ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2)))))))))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(34,plain,
% 0.20/0.51 (^[W2: $i] : rewrite((~((~((W2 = sdtpldt0(xS, xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2)))))))))) <=> (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2)))))))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(35,plain,
% 0.20/0.51 (![W2: $i] : (~((~((W2 = sdtpldt0(xS, xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2)))))))))) <=> ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2))))))))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[34])).
% 0.20/0.51 tff(36,plain,
% 0.20/0.51 (((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtpldt0(xS, xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2))))))))))) <=> ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2)))))))))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[35])).
% 0.20/0.51 tff(37,plain,
% 0.20/0.51 (((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtpldt0(xS, xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2))))))))))) <=> ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2)))))))))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[36, 33])).
% 0.20/0.51 tff(38,plain,
% 0.20/0.51 (((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))))))) | ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtpldt0(xS, xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2)))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))))))) | ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2))))))))))))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[37])).
% 0.20/0.51 tff(39,plain,
% 0.20/0.51 (((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))))))) | ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtpldt0(xS, xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2)))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))))))) | (~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2)))))))))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[38, 32])).
% 0.20/0.51 tff(40,plain,
% 0.20/0.51 ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))))))) | ((~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtpldt0(xS, xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2)))))))))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(41,plain,
% 0.20/0.51 ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtpldt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_2(W2, W1, W0))) | (~((tptp_fun_W3_2(W2, W1, W0) = W1) | aElementOf0(tptp_fun_W3_2(W2, W1, W0), W0)))) <=> aElementOf0(tptp_fun_W3_2(W2, W1, W0), W2)))) | (~((~(W2 = sdtpldt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = W1) | aElementOf0(W3, W0)))) <=> aElementOf0(W3, W2)))))))))))) | (~aSet0(xS)) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2))))))))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.20/0.51 tff(42,plain,
% 0.20/0.51 (![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2))))))))))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[41, 31, 9, 6])).
% 0.20/0.51 tff(43,plain,
% 0.20/0.51 (((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2))))))))))) | (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, sdtpldt0(xS, xx)))))))) <=> ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2))))))))))) | (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, sdtpldt0(xS, xx))))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(44,plain,
% 0.20/0.52 ((~((~((~aSet0(sdtpldt0(xS, xx))) | (sdtpldt0(xS, xx) = sdtpldt0(xS, xx)) | (((~aElement0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS))) | (~((tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS), sdtpldt0(xS, xx))))) | (~((~(sdtpldt0(xS, xx) = sdtpldt0(xS, xx))) | (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, sdtpldt0(xS, xx))))))))))) <=> (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, sdtpldt0(xS, xx)))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(45,plain,
% 0.20/0.52 (((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2))))))))))) | (~((~((~aSet0(sdtpldt0(xS, xx))) | (sdtpldt0(xS, xx) = sdtpldt0(xS, xx)) | (((~aElement0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS))) | (~((tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS), sdtpldt0(xS, xx))))) | (~((~(sdtpldt0(xS, xx) = sdtpldt0(xS, xx))) | (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, sdtpldt0(xS, xx)))))))))))) <=> ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2))))))))))) | (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, sdtpldt0(xS, xx))))))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[44])).
% 0.20/0.52 tff(46,plain,
% 0.20/0.52 (((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2))))))))))) | (~((~((~aSet0(sdtpldt0(xS, xx))) | (sdtpldt0(xS, xx) = sdtpldt0(xS, xx)) | (((~aElement0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS))) | (~((tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS), sdtpldt0(xS, xx))))) | (~((~(sdtpldt0(xS, xx) = sdtpldt0(xS, xx))) | (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, sdtpldt0(xS, xx)))))))))))) <=> ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2))))))))))) | (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, sdtpldt0(xS, xx))))))))),
% 0.36/0.52 inference(transitivity,[status(thm)],[45, 43])).
% 0.36/0.52 tff(47,plain,
% 0.36/0.52 ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2))))))))))) | (~((~((~aSet0(sdtpldt0(xS, xx))) | (sdtpldt0(xS, xx) = sdtpldt0(xS, xx)) | (((~aElement0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS))) | (~((tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(sdtpldt0(xS, xx), xx, xS), sdtpldt0(xS, xx))))) | (~((~(sdtpldt0(xS, xx) = sdtpldt0(xS, xx))) | (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, sdtpldt0(xS, xx)))))))))))),
% 0.36/0.52 inference(quant_inst,[status(thm)],[])).
% 0.36/0.52 tff(48,plain,
% 0.36/0.52 ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtpldt0(xS, xx)) | (((~aElement0(tptp_fun_W3_2(W2, xx, xS))) | (~((tptp_fun_W3_2(W2, xx, xS) = xx) | aElementOf0(tptp_fun_W3_2(W2, xx, xS), xS)))) <=> aElementOf0(tptp_fun_W3_2(W2, xx, xS), W2)))) | (~((~(W2 = sdtpldt0(xS, xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, W2))))))))))) | (~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, sdtpldt0(xS, xx)))))))),
% 0.36/0.52 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.36/0.52 tff(49,plain,
% 0.36/0.52 ($false),
% 0.36/0.52 inference(unit_resolution,[status(thm)],[48, 42, 2])).
% 0.36/0.52 tff(50,plain,(~((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, sdtpldt0(xS, xx))))))), inference(lemma,lemma(discharge,[]))).
% 0.36/0.52 tff(51,plain,
% 0.36/0.52 (((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, sdtpldt0(xS, xx)))))) | aSet0(sdtpldt0(xS, xx))),
% 0.36/0.52 inference(tautology,[status(thm)],[])).
% 0.36/0.52 tff(52,plain,
% 0.36/0.52 (aSet0(sdtpldt0(xS, xx))),
% 0.36/0.52 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.36/0.52 tff(53,plain,
% 0.36/0.52 (^[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)))))))))))))),
% 0.36/0.52 inference(bind,[status(th)],[])).
% 0.36/0.52 tff(54,plain,
% 0.36/0.52 (![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)))))))))))),
% 0.36/0.52 inference(quant_intro,[status(thm)],[53])).
% 0.36/0.52 tff(55,plain,
% 0.36/0.52 (^[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))))))))),
% 0.36/0.52 inference(bind,[status(th)],[])).
% 0.36/0.52 tff(56,plain,
% 0.36/0.52 (![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)))))))),
% 0.36/0.52 inference(quant_intro,[status(thm)],[55])).
% 0.36/0.52 tff(57,plain,
% 0.36/0.52 (^[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))))))))),
% 0.36/0.52 inference(bind,[status(th)],[])).
% 0.36/0.52 tff(58,plain,
% 0.36/0.52 (![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)))))))),
% 0.36/0.52 inference(quant_intro,[status(thm)],[57])).
% 0.36/0.52 tff(59,plain,
% 0.36/0.52 (![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)))))))),
% 0.36/0.52 inference(transitivity,[status(thm)],[58, 56])).
% 0.36/0.52 tff(60,plain,
% 0.36/0.52 (^[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)))))))))),
% 0.36/0.52 inference(bind,[status(th)],[])).
% 0.36/0.52 tff(61,plain,
% 0.36/0.52 (![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)))))))),
% 0.36/0.52 inference(quant_intro,[status(thm)],[60])).
% 0.36/0.52 tff(62,plain,
% 0.36/0.52 (^[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)))))))))),
% 0.36/0.52 inference(bind,[status(th)],[])).
% 0.36/0.52 tff(63,plain,
% 0.36/0.52 (![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))))))))),
% 0.36/0.52 inference(quant_intro,[status(thm)],[62])).
% 0.36/0.52 tff(64,plain,
% 0.36/0.52 (![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)))))))),
% 0.36/0.52 inference(rewrite,[status(thm)],[])).
% 0.36/0.52 tff(65,plain,
% 0.36/0.52 (^[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)))))))))),
% 0.36/0.52 inference(bind,[status(th)],[])).
% 0.36/0.52 tff(66,plain,
% 0.36/0.52 (![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)))))))),
% 0.36/0.52 inference(quant_intro,[status(thm)],[65])).
% 0.36/0.52 tff(67,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')).
% 0.36/0.52 tff(68,plain,
% 0.36/0.52 (![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)))))))),
% 0.36/0.52 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.36/0.52 tff(69,plain,
% 0.36/0.52 (![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)))))))),
% 0.36/0.52 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.36/0.52 tff(70,plain,(
% 0.36/0.52 ![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)))))))))),
% 0.36/0.52 inference(skolemize,[status(sab)],[69])).
% 0.36/0.52 tff(71,plain,
% 0.36/0.52 (![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))))))))),
% 0.36/0.52 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.36/0.52 tff(72,plain,
% 0.36/0.52 (![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)))))))),
% 0.36/0.52 inference(modus_ponens,[status(thm)],[71, 61])).
% 0.36/0.52 tff(73,plain,
% 0.36/0.52 (![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)))))))),
% 0.36/0.52 inference(modus_ponens,[status(thm)],[72, 59])).
% 0.36/0.52 tff(74,plain,
% 0.36/0.52 (![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)))))))))))),
% 0.36/0.52 inference(modus_ponens,[status(thm)],[73, 54])).
% 0.36/0.52 tff(75,plain,
% 0.36/0.52 (((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))))))) | ((~aElement0(xx)) | (~aSet0(sdtpldt0(xS, xx))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2)))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, W2)))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))))))) | (~aElement0(xx)) | (~aSet0(sdtpldt0(xS, xx))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2)))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, W2)))))))))))),
% 0.36/0.52 inference(rewrite,[status(thm)],[])).
% 0.36/0.52 tff(76,plain,
% 0.36/0.52 (((~aSet0(sdtpldt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2)))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))) <=> ((~aElement0(xx)) | (~aSet0(sdtpldt0(xS, xx))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2)))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, W2)))))))))))),
% 0.36/0.52 inference(rewrite,[status(thm)],[])).
% 0.36/0.52 tff(77,plain,
% 0.36/0.52 (^[W2: $i] : rewrite((~((~((W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2)))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, W2)))))))))) <=> (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2)))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, W2)))))))))))),
% 0.36/0.52 inference(bind,[status(th)],[])).
% 0.36/0.52 tff(78,plain,
% 0.36/0.52 (![W2: $i] : (~((~((W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2)))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, W2)))))))))) <=> ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2)))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))),
% 0.36/0.53 inference(quant_intro,[status(thm)],[77])).
% 0.36/0.53 tff(79,plain,
% 0.36/0.53 (((~aSet0(sdtpldt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2)))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))) <=> ((~aSet0(sdtpldt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2)))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, W2)))))))))))),
% 0.36/0.53 inference(monotonicity,[status(thm)],[78])).
% 0.36/0.53 tff(80,plain,
% 0.36/0.53 (((~aSet0(sdtpldt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2)))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))) <=> ((~aElement0(xx)) | (~aSet0(sdtpldt0(xS, xx))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2)))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, W2)))))))))))),
% 0.36/0.53 inference(transitivity,[status(thm)],[79, 76])).
% 0.36/0.53 tff(81,plain,
% 0.36/0.53 (((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))))))) | ((~aSet0(sdtpldt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2)))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, W2)))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))))))) | ((~aElement0(xx)) | (~aSet0(sdtpldt0(xS, xx))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2)))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))))),
% 0.36/0.53 inference(monotonicity,[status(thm)],[80])).
% 0.36/0.53 tff(82,plain,
% 0.36/0.53 (((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))))))) | ((~aSet0(sdtpldt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2)))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, W2)))))))))))) <=> ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))))))) | (~aElement0(xx)) | (~aSet0(sdtpldt0(xS, xx))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2)))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, W2)))))))))))),
% 0.36/0.53 inference(transitivity,[status(thm)],[81, 75])).
% 0.36/0.53 tff(83,plain,
% 0.36/0.53 ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))))))) | ((~aSet0(sdtpldt0(xS, xx))) | (~aElement0(xx)) | ![W2: $i] : (~((~((W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2)))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, W2)))))))))))),
% 0.36/0.53 inference(quant_inst,[status(thm)],[])).
% 0.36/0.53 tff(84,plain,
% 0.36/0.53 ((~![W0: $i, W1: $i] : ((~aSet0(W0)) | (~aElement0(W1)) | ![W2: $i] : (~((~((W2 = sdtmndt0(W0, W1)) | (~aSet0(W2)) | (((~aElement0(tptp_fun_W3_3(W2, W1, W0))) | (~aElementOf0(tptp_fun_W3_3(W2, W1, W0), W0)) | (tptp_fun_W3_3(W2, W1, W0) = W1)) <=> aElementOf0(tptp_fun_W3_3(W2, W1, W0), W2)))) | (~((~(W2 = sdtmndt0(W0, W1))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, W0)) | (W3 = W1)) <=> aElementOf0(W3, W2)))))))))))) | (~aElement0(xx)) | (~aSet0(sdtpldt0(xS, xx))) | ![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2)))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))),
% 0.36/0.53 inference(modus_ponens,[status(thm)],[83, 82])).
% 0.36/0.53 tff(85,plain,
% 0.36/0.53 (![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2)))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))),
% 0.36/0.53 inference(unit_resolution,[status(thm)],[84, 74, 9, 52])).
% 0.36/0.53 tff(86,plain,
% 0.36/0.53 (((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2)))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))) | (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)))))))) <=> ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2)))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))) | (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx))))))))),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(87,plain,
% 0.36/0.53 ((~((~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (sdtmndt0(sdtpldt0(xS, xx), xx) = sdtmndt0(sdtpldt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_3(sdtmndt0(sdtpldt0(xS, xx), xx), xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(sdtmndt0(sdtpldt0(xS, xx), xx), xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(sdtmndt0(sdtpldt0(xS, xx), xx), xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(sdtmndt0(sdtpldt0(xS, xx), xx), xx, sdtpldt0(xS, xx)), sdtmndt0(sdtpldt0(xS, xx), xx))))) | (~((~(sdtmndt0(sdtpldt0(xS, xx), xx) = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx))))))))))) <=> (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)))))))),
% 0.36/0.53 inference(rewrite,[status(thm)],[])).
% 0.36/0.53 tff(88,plain,
% 0.36/0.53 (((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2)))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))) | (~((~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (sdtmndt0(sdtpldt0(xS, xx), xx) = sdtmndt0(sdtpldt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_3(sdtmndt0(sdtpldt0(xS, xx), xx), xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(sdtmndt0(sdtpldt0(xS, xx), xx), xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(sdtmndt0(sdtpldt0(xS, xx), xx), xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(sdtmndt0(sdtpldt0(xS, xx), xx), xx, sdtpldt0(xS, xx)), sdtmndt0(sdtpldt0(xS, xx), xx))))) | (~((~(sdtmndt0(sdtpldt0(xS, xx), xx) = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)))))))))))) <=> ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2)))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))) | (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx))))))))),
% 0.36/0.53 inference(monotonicity,[status(thm)],[87])).
% 0.36/0.53 tff(89,plain,
% 0.36/0.53 (((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2)))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))) | (~((~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (sdtmndt0(sdtpldt0(xS, xx), xx) = sdtmndt0(sdtpldt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_3(sdtmndt0(sdtpldt0(xS, xx), xx), xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(sdtmndt0(sdtpldt0(xS, xx), xx), xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(sdtmndt0(sdtpldt0(xS, xx), xx), xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(sdtmndt0(sdtpldt0(xS, xx), xx), xx, sdtpldt0(xS, xx)), sdtmndt0(sdtpldt0(xS, xx), xx))))) | (~((~(sdtmndt0(sdtpldt0(xS, xx), xx) = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)))))))))))) <=> ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2)))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))) | (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx))))))))),
% 0.38/0.54 inference(transitivity,[status(thm)],[88, 86])).
% 0.38/0.54 tff(90,plain,
% 0.38/0.54 ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2)))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))) | (~((~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (sdtmndt0(sdtpldt0(xS, xx), xx) = sdtmndt0(sdtpldt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_3(sdtmndt0(sdtpldt0(xS, xx), xx), xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(sdtmndt0(sdtpldt0(xS, xx), xx), xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(sdtmndt0(sdtpldt0(xS, xx), xx), xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(sdtmndt0(sdtpldt0(xS, xx), xx), xx, sdtpldt0(xS, xx)), sdtmndt0(sdtpldt0(xS, xx), xx))))) | (~((~(sdtmndt0(sdtpldt0(xS, xx), xx) = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)))))))))))),
% 0.38/0.54 inference(quant_inst,[status(thm)],[])).
% 0.38/0.54 tff(91,plain,
% 0.38/0.54 ((~![W2: $i] : (~((~((~aSet0(W2)) | (W2 = sdtmndt0(sdtpldt0(xS, xx), xx)) | (((~aElement0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)))) | (~aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), sdtpldt0(xS, xx))) | (tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)) = xx)) <=> aElementOf0(tptp_fun_W3_3(W2, xx, sdtpldt0(xS, xx)), W2)))) | (~((~(W2 = sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W2)) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, W2))))))))))) | (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)))))))),
% 0.38/0.54 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.38/0.54 tff(92,plain,
% 0.38/0.54 ($false),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[91, 85, 1])).
% 0.38/0.54 tff(93,plain,(~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx))))))), inference(lemma,lemma(discharge,[]))).
% 0.38/0.54 tff(94,plain,
% 0.38/0.54 (((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)))))) | ![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx))))),
% 0.38/0.54 inference(tautology,[status(thm)],[])).
% 0.38/0.54 tff(95,plain,
% 0.38/0.54 (![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx))))),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.38/0.54 tff(96,plain,
% 0.38/0.54 ((~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx))))) | (~(((~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtpldt0(xS, xx))) | (tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx)) <=> aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx))))),
% 0.38/0.54 inference(quant_inst,[status(thm)],[])).
% 0.38/0.54 tff(97,plain,
% 0.38/0.54 (~(((~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtpldt0(xS, xx))) | (tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx)) <=> aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.38/0.54 tff(98,plain,
% 0.38/0.54 (((~aSet0(sdtpldt0(xS, xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, sdtpldt0(xS, xx)))))) | ![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, sdtpldt0(xS, xx))))),
% 0.38/0.54 inference(tautology,[status(thm)],[])).
% 0.38/0.54 tff(99,plain,
% 0.38/0.54 (![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, sdtpldt0(xS, xx))))),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[98, 50])).
% 0.38/0.54 tff(100,plain,
% 0.38/0.54 ((~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, sdtpldt0(xS, xx))))) | (~(((~aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) | (~((tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS)))) <=> aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtpldt0(xS, xx))))),
% 0.38/0.54 inference(quant_inst,[status(thm)],[])).
% 0.38/0.54 tff(101,plain,
% 0.38/0.54 (~(((~aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) | (~((tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS)))) <=> aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtpldt0(xS, xx)))),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.38/0.54 tff(102,plain,
% 0.38/0.54 ((~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx))))) | (~(((~aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) | (~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtpldt0(xS, xx))) | (tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx)) <=> aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))))),
% 0.38/0.54 inference(quant_inst,[status(thm)],[])).
% 0.38/0.54 tff(103,plain,
% 0.38/0.54 (~(((~aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) | (~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtpldt0(xS, xx))) | (tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx)) <=> aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx)))),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[102, 95])).
% 0.38/0.54 tff(104,assumption,(~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))), introduced(assumption)).
% 0.38/0.54 tff(105,plain,
% 0.38/0.54 (((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS)) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))),
% 0.38/0.54 inference(tautology,[status(thm)],[])).
% 0.38/0.54 tff(106,plain,
% 0.38/0.54 (aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.38/0.54 tff(107,plain,
% 0.38/0.54 ((((~aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) | (~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtpldt0(xS, xx))) | (tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx)) <=> aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) | (~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtpldt0(xS, xx))) | (tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx))) | (~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx)))),
% 0.38/0.54 inference(tautology,[status(thm)],[])).
% 0.38/0.54 tff(108,plain,
% 0.38/0.54 ((((~aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) | (~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtpldt0(xS, xx))) | (tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx)) <=> aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) | (~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtpldt0(xS, xx))) | (tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx)))),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.38/0.54 tff(109,plain,
% 0.38/0.54 (~((~aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) | (~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtpldt0(xS, xx))) | (tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx))),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[108, 103])).
% 0.38/0.54 tff(110,plain,
% 0.38/0.54 (((~aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) | (~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtpldt0(xS, xx))) | (tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx)) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtpldt0(xS, xx))),
% 0.38/0.54 inference(tautology,[status(thm)],[])).
% 0.38/0.54 tff(111,plain,
% 0.38/0.54 (aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtpldt0(xS, xx))),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[110, 109])).
% 0.38/0.54 tff(112,plain,
% 0.38/0.54 ((((~aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) | (~((tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS)))) <=> aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtpldt0(xS, xx))) | (~((~aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) | (~((tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))))) | (~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtpldt0(xS, xx)))),
% 0.38/0.54 inference(tautology,[status(thm)],[])).
% 0.38/0.54 tff(113,plain,
% 0.38/0.54 (~((~aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) | (~((tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))))),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[112, 111, 101])).
% 0.38/0.54 tff(114,plain,
% 0.38/0.54 (((~aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) | (~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtpldt0(xS, xx))) | (tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx)) | (~(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx))),
% 0.38/0.54 inference(tautology,[status(thm)],[])).
% 0.38/0.54 tff(115,plain,
% 0.38/0.54 (~(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx)),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[114, 109])).
% 0.38/0.54 tff(116,plain,
% 0.38/0.54 (((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS)) | (~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))),
% 0.38/0.54 inference(tautology,[status(thm)],[])).
% 0.38/0.54 tff(117,plain,
% 0.38/0.54 (~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS)),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[116, 104])).
% 0.38/0.54 tff(118,plain,
% 0.38/0.54 ((~((tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))) | (tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS)),
% 0.38/0.54 inference(tautology,[status(thm)],[])).
% 0.38/0.54 tff(119,plain,
% 0.38/0.54 ((~((tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))) | (tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx)),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[118, 117])).
% 0.38/0.54 tff(120,plain,
% 0.38/0.54 (~((tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[119, 115])).
% 0.38/0.54 tff(121,plain,
% 0.38/0.54 (((~aElement0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) | (~((tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS)))) | ((tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS) = xx) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))),
% 0.38/0.54 inference(tautology,[status(thm)],[])).
% 0.38/0.54 tff(122,plain,
% 0.38/0.54 ($false),
% 0.38/0.54 inference(unit_resolution,[status(thm)],[121, 120, 113])).
% 0.38/0.54 tff(123,plain,((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS)), inference(lemma,lemma(discharge,[]))).
% 0.38/0.54 tff(124,plain,
% 0.38/0.54 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))))))))),
% 0.38/0.54 inference(bind,[status(th)],[])).
% 0.38/0.54 tff(125,plain,
% 0.38/0.54 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))),
% 0.38/0.54 inference(quant_intro,[status(thm)],[124])).
% 0.38/0.54 tff(126,plain,
% 0.38/0.54 (^[W0: $i] : refl(((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))))),
% 0.38/0.54 inference(bind,[status(th)],[])).
% 0.38/0.54 tff(127,plain,
% 0.38/0.54 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 0.38/0.54 inference(quant_intro,[status(thm)],[126])).
% 0.38/0.54 tff(128,plain,
% 0.38/0.54 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))))),
% 0.38/0.54 inference(bind,[status(th)],[])).
% 0.38/0.54 tff(129,plain,
% 0.38/0.54 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 0.38/0.54 inference(quant_intro,[status(thm)],[128])).
% 0.38/0.54 tff(130,plain,
% 0.38/0.54 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 0.38/0.54 inference(transitivity,[status(thm)],[129, 127])).
% 0.38/0.54 tff(131,plain,
% 0.38/0.54 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))) <=> ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))))),
% 0.38/0.54 inference(bind,[status(th)],[])).
% 0.38/0.54 tff(132,plain,
% 0.38/0.54 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 0.38/0.54 inference(quant_intro,[status(thm)],[131])).
% 0.38/0.54 tff(133,plain,
% 0.38/0.54 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))) <=> ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))),
% 0.38/0.54 inference(bind,[status(th)],[])).
% 0.38/0.54 tff(134,plain,
% 0.38/0.54 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))),
% 0.38/0.54 inference(quant_intro,[status(thm)],[133])).
% 0.38/0.54 tff(135,plain,
% 0.38/0.54 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))),
% 0.38/0.54 inference(rewrite,[status(thm)],[])).
% 0.38/0.54 tff(136,plain,
% 0.38/0.54 (^[W0: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: $i] : rewrite((aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0)))) <=> (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))), (![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0)))) <=> ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))), ((aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0))))) <=> (aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))), rewrite((aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))) <=> ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))), ((aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0))))) <=> ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))))),
% 0.38/0.54 inference(bind,[status(th)],[])).
% 0.38/0.54 tff(137,plain,
% 0.38/0.54 (![W0: $i] : (aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))),
% 0.38/0.54 inference(quant_intro,[status(thm)],[136])).
% 0.38/0.54 tff(138,axiom,(![W0: $i] : (aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mDefSub')).
% 0.38/0.54 tff(139,plain,
% 0.38/0.54 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))),
% 0.38/0.54 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.38/0.54 tff(140,plain,
% 0.38/0.54 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))),
% 0.38/0.54 inference(modus_ponens,[status(thm)],[139, 135])).
% 0.38/0.54 tff(141,plain,(
% 0.38/0.54 ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))),
% 0.38/0.54 inference(skolemize,[status(sab)],[140])).
% 0.38/0.54 tff(142,plain,
% 0.38/0.54 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))),
% 0.38/0.54 inference(modus_ponens,[status(thm)],[141, 134])).
% 0.38/0.54 tff(143,plain,
% 0.38/0.54 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 0.38/0.54 inference(modus_ponens,[status(thm)],[142, 132])).
% 0.38/0.54 tff(144,plain,
% 0.38/0.54 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 0.38/0.54 inference(modus_ponens,[status(thm)],[143, 130])).
% 0.38/0.54 tff(145,plain,
% 0.38/0.54 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))),
% 0.38/0.54 inference(modus_ponens,[status(thm)],[144, 125])).
% 0.38/0.54 tff(146,plain,
% 0.38/0.54 (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(xS)) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS))))))))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | (~aSet0(xS)) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS))))))))))),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(147,plain,
% 0.38/0.55 (((~aSet0(xS)) | ![W1: $i] : (~((~(aSubsetOf0(W1, xS) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS)))))))))) <=> ((~aSet0(xS)) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS))))))))))),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(148,plain,
% 0.38/0.55 (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(xS)) | ![W1: $i] : (~((~(aSubsetOf0(W1, xS) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS))))))))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(xS)) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS)))))))))))),
% 0.38/0.55 inference(monotonicity,[status(thm)],[147])).
% 0.38/0.55 tff(149,plain,
% 0.38/0.55 (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(xS)) | ![W1: $i] : (~((~(aSubsetOf0(W1, xS) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS))))))))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | (~aSet0(xS)) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS))))))))))),
% 0.38/0.55 inference(transitivity,[status(thm)],[148, 146])).
% 0.38/0.55 tff(150,plain,
% 0.38/0.55 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(xS)) | ![W1: $i] : (~((~(aSubsetOf0(W1, xS) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS))))))))))),
% 0.38/0.55 inference(quant_inst,[status(thm)],[])).
% 0.38/0.55 tff(151,plain,
% 0.38/0.55 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | (~aSet0(xS)) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS)))))))))),
% 0.38/0.55 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.38/0.55 tff(152,plain,
% 0.38/0.55 (![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS)))))))))),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[151, 145, 6])).
% 0.38/0.55 tff(153,plain,
% 0.38/0.55 (((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS)))))))))) | (~((~(aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS) | (~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))))) | (~((~aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS)) | (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W2: $i] : ((~aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(W2, xS)))))))))) <=> ((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS)))))))))) | (~((~(aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS) | (~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))))) | (~((~aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS)) | (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W2: $i] : ((~aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(W2, xS))))))))))),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(154,plain,
% 0.38/0.55 ((~((~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))))) | (~((~aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS)) | (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W2: $i] : ((~aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(W2, xS))))))))) <=> (~((~(aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS) | (~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))))) | (~((~aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS)) | (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W2: $i] : ((~aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(W2, xS)))))))))),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(155,plain,
% 0.38/0.55 (((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS)))))))))) | (~((~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))))) | (~((~aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS)) | (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W2: $i] : ((~aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(W2, xS)))))))))) <=> ((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS)))))))))) | (~((~(aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS) | (~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))))) | (~((~aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS)) | (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W2: $i] : ((~aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(W2, xS))))))))))),
% 0.38/0.55 inference(monotonicity,[status(thm)],[154])).
% 0.38/0.55 tff(156,plain,
% 0.38/0.55 (((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS)))))))))) | (~((~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))))) | (~((~aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS)) | (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W2: $i] : ((~aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(W2, xS)))))))))) <=> ((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS)))))))))) | (~((~(aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS) | (~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))))) | (~((~aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS)) | (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W2: $i] : ((~aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(W2, xS))))))))))),
% 0.38/0.55 inference(transitivity,[status(thm)],[155, 153])).
% 0.38/0.55 tff(157,plain,
% 0.38/0.55 ((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS)))))))))) | (~((~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))))) | (~((~aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS)) | (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W2: $i] : ((~aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(W2, xS)))))))))),
% 0.38/0.55 inference(quant_inst,[status(thm)],[])).
% 0.38/0.55 tff(158,plain,
% 0.38/0.55 ((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, xS) | (~((~aElementOf0(tptp_fun_W2_1(W1, xS), W1)) | aElementOf0(tptp_fun_W2_1(W1, xS), xS))))) | (~((~aSubsetOf0(W1, xS)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, xS)))))))))) | (~((~(aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS) | (~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))))) | (~((~aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS)) | (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W2: $i] : ((~aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(W2, xS)))))))))),
% 0.38/0.55 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.38/0.55 tff(159,plain,
% 0.38/0.55 (~((~(aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS) | (~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))))) | (~((~aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS)) | (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W2: $i] : ((~aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(W2, xS))))))))),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[158, 152])).
% 0.38/0.55 tff(160,plain,
% 0.38/0.55 (((~(aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS) | (~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))))) | (~((~aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS)) | (~((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W2: $i] : ((~aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(W2, xS)))))))) | (aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS) | (~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))))),
% 0.38/0.55 inference(tautology,[status(thm)],[])).
% 0.38/0.55 tff(161,plain,
% 0.38/0.55 (aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS) | (~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS)))),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[160, 159])).
% 0.38/0.55 tff(162,plain,
% 0.38/0.55 (((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~![W3: $i] : (~(((~aElement0(W3)) | (~aElementOf0(W3, sdtpldt0(xS, xx))) | (W3 = xx)) <=> aElementOf0(W3, sdtmndt0(sdtpldt0(xS, xx), xx)))))) | aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))),
% 0.38/0.55 inference(tautology,[status(thm)],[])).
% 0.38/0.55 tff(163,plain,
% 0.38/0.55 (aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[162, 93])).
% 0.38/0.55 tff(164,plain,
% 0.38/0.55 ((~(aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS) | (~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))))) | aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS) | (~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS)))),
% 0.38/0.55 inference(tautology,[status(thm)],[])).
% 0.38/0.55 tff(165,plain,
% 0.38/0.55 ((~(aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS) | (~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS))))) | aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS)))),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[164, 163])).
% 0.38/0.55 tff(166,plain,
% 0.38/0.55 (aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS) | (~((~aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(sdtmndt0(sdtpldt0(xS, xx), xx), xS), xS)))),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[165, 161])).
% 0.38/0.55 tff(167,plain,
% 0.38/0.55 (aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS)),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[166, 123])).
% 0.38/0.55 tff(168,plain,
% 0.38/0.55 ((~(~((~aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS))))) <=> ((~aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS)))),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(169,plain,
% 0.38/0.55 ((aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) & aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS)) <=> (~((~aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS))))),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(170,plain,
% 0.38/0.55 ((~(aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) & aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) <=> (~(~((~aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS)))))),
% 0.38/0.55 inference(monotonicity,[status(thm)],[169])).
% 0.38/0.55 tff(171,plain,
% 0.38/0.55 ((~(aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) & aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) <=> ((~aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS)))),
% 0.38/0.55 inference(transitivity,[status(thm)],[170, 168])).
% 0.38/0.55 tff(172,plain,
% 0.38/0.55 ((~(aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) & aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS))) <=> (~(aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) & aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS)))),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(173,axiom,(~(aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) & aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 0.38/0.55 tff(174,plain,
% 0.38/0.55 (~(aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) & aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS))),
% 0.38/0.55 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.38/0.55 tff(175,plain,
% 0.38/0.55 ((~aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS))),
% 0.38/0.55 inference(modus_ponens,[status(thm)],[174, 171])).
% 0.38/0.55 tff(176,plain,
% 0.38/0.55 (~aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx))),
% 0.38/0.55 inference(unit_resolution,[status(thm)],[175, 167])).
% 0.38/0.55 tff(177,plain,
% 0.38/0.55 (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | ![W1: $i] : (~((~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))) | aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx)))))))))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | (~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | ![W1: $i] : (~((~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))) | aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx)))))))))))),
% 0.38/0.55 inference(rewrite,[status(thm)],[])).
% 0.38/0.55 tff(178,plain,
% 0.38/0.55 (((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | ![W1: $i] : (~((~(aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx)) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx))))))))))) <=> ((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | ![W1: $i] : (~((~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))) | aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx)))))))))))),
% 0.38/0.56 inference(rewrite,[status(thm)],[])).
% 0.38/0.56 tff(179,plain,
% 0.38/0.56 (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | ![W1: $i] : (~((~(aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx)) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx)))))))))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | ![W1: $i] : (~((~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))) | aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx))))))))))))),
% 0.38/0.56 inference(monotonicity,[status(thm)],[178])).
% 0.38/0.56 tff(180,plain,
% 0.38/0.56 (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | ![W1: $i] : (~((~(aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx)) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx)))))))))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | (~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | ![W1: $i] : (~((~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))) | aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx)))))))))))),
% 0.38/0.56 inference(transitivity,[status(thm)],[179, 177])).
% 0.38/0.56 tff(181,plain,
% 0.38/0.56 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | ![W1: $i] : (~((~(aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx)) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx)))))))))))),
% 0.38/0.56 inference(quant_inst,[status(thm)],[])).
% 0.38/0.56 tff(182,plain,
% 0.38/0.56 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | (~aSet0(sdtmndt0(sdtpldt0(xS, xx), xx))) | ![W1: $i] : (~((~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))) | aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx))))))))))),
% 0.38/0.56 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.38/0.56 tff(183,plain,
% 0.38/0.56 (![W1: $i] : (~((~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))) | aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx))))))))))),
% 0.38/0.56 inference(unit_resolution,[status(thm)],[182, 145, 163])).
% 0.38/0.56 tff(184,plain,
% 0.38/0.56 ((~![W1: $i] : (~((~((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), W1)) | aElementOf0(tptp_fun_W2_1(W1, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))) | aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((~aSubsetOf0(W1, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx))))))))))) | (~((~((~aSet0(xS)) | (~((~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))) | aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((~aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx))))))))))),
% 0.38/0.56 inference(quant_inst,[status(thm)],[])).
% 0.38/0.56 tff(185,plain,
% 0.38/0.56 (~((~((~aSet0(xS)) | (~((~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))) | aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((~aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx)))))))))),
% 0.38/0.56 inference(unit_resolution,[status(thm)],[184, 183])).
% 0.38/0.56 tff(186,plain,
% 0.38/0.56 (((~((~aSet0(xS)) | (~((~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))) | aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((~aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~((~aSet0(xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | aElementOf0(W2, sdtmndt0(sdtpldt0(xS, xx), xx))))))))) | ((~aSet0(xS)) | (~((~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))) | aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))),
% 0.38/0.56 inference(tautology,[status(thm)],[])).
% 0.38/0.56 tff(187,plain,
% 0.38/0.56 ((~aSet0(xS)) | (~((~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))) | aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx))),
% 0.38/0.56 inference(unit_resolution,[status(thm)],[186, 185])).
% 0.38/0.56 tff(188,plain,
% 0.38/0.56 ((~((~aSet0(xS)) | (~((~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))) | aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~aSet0(xS)) | (~((~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))) | aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx))),
% 0.38/0.56 inference(tautology,[status(thm)],[])).
% 0.38/0.56 tff(189,plain,
% 0.38/0.56 ((~((~aSet0(xS)) | (~((~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))) | aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))) | aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx))),
% 0.38/0.56 inference(unit_resolution,[status(thm)],[188, 6])).
% 0.38/0.56 tff(190,plain,
% 0.38/0.56 ((~((~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))) | aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx))),
% 0.38/0.56 inference(unit_resolution,[status(thm)],[189, 187])).
% 0.38/0.56 tff(191,plain,
% 0.38/0.56 (~((~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))),
% 0.38/0.56 inference(unit_resolution,[status(thm)],[190, 176])).
% 0.38/0.56 tff(192,plain,
% 0.38/0.56 (((~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx)))),
% 0.38/0.56 inference(tautology,[status(thm)],[])).
% 0.38/0.56 tff(193,plain,
% 0.38/0.56 (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx))),
% 0.38/0.56 inference(unit_resolution,[status(thm)],[192, 191])).
% 0.38/0.56 tff(194,plain,
% 0.38/0.56 ((((~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtpldt0(xS, xx))) | (tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx)) <=> aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx))) | ((~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtpldt0(xS, xx))) | (tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx)) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx))),
% 0.38/0.56 inference(tautology,[status(thm)],[])).
% 0.38/0.56 tff(195,plain,
% 0.38/0.56 ((((~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtpldt0(xS, xx))) | (tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx)) <=> aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx))) | ((~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtpldt0(xS, xx))) | (tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx))),
% 0.38/0.56 inference(unit_resolution,[status(thm)],[194, 193])).
% 0.38/0.56 tff(196,plain,
% 0.38/0.56 ((~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtpldt0(xS, xx))) | (tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx)),
% 0.38/0.56 inference(unit_resolution,[status(thm)],[195, 97])).
% 0.38/0.56 tff(197,plain,
% 0.38/0.56 (((~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtmndt0(sdtpldt0(xS, xx), xx))) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)),
% 0.38/0.56 inference(tautology,[status(thm)],[])).
% 0.38/0.56 tff(198,plain,
% 0.38/0.56 (aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)),
% 0.38/0.56 inference(unit_resolution,[status(thm)],[197, 191])).
% 0.38/0.56 tff(199,plain,
% 0.38/0.56 (^[W0: $i] : refl(((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))))),
% 0.38/0.56 inference(bind,[status(th)],[])).
% 0.38/0.56 tff(200,plain,
% 0.38/0.56 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.38/0.56 inference(quant_intro,[status(thm)],[199])).
% 0.38/0.56 tff(201,plain,
% 0.38/0.56 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))))),
% 0.38/0.56 inference(bind,[status(th)],[])).
% 0.38/0.56 tff(202,plain,
% 0.38/0.56 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.38/0.56 inference(quant_intro,[status(thm)],[201])).
% 0.38/0.56 tff(203,plain,
% 0.38/0.56 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.38/0.56 inference(transitivity,[status(thm)],[202, 200])).
% 0.38/0.56 tff(204,plain,
% 0.38/0.56 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0)))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.38/0.56 inference(rewrite,[status(thm)],[])).
% 0.38/0.56 tff(205,plain,
% 0.38/0.56 (^[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))))))),
% 0.38/0.56 inference(bind,[status(th)],[])).
% 0.38/0.56 tff(206,plain,
% 0.38/0.56 (![W0: $i] : (aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.38/0.56 inference(quant_intro,[status(thm)],[205])).
% 0.38/0.56 tff(207,axiom,(![W0: $i] : (aSet0(W0) => ![W1: $i] : (aElementOf0(W1, W0) => aElement0(W1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mEOfElem')).
% 0.38/0.56 tff(208,plain,
% 0.38/0.56 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.38/0.56 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.38/0.56 tff(209,plain,
% 0.38/0.56 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.38/0.56 inference(modus_ponens,[status(thm)],[208, 204])).
% 0.38/0.56 tff(210,plain,(
% 0.38/0.56 ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.38/0.56 inference(skolemize,[status(sab)],[209])).
% 0.38/0.56 tff(211,plain,
% 0.38/0.56 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))),
% 0.38/0.56 inference(modus_ponens,[status(thm)],[210, 203])).
% 0.38/0.56 tff(212,plain,
% 0.38/0.56 (((~![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))))),
% 0.38/0.56 inference(rewrite,[status(thm)],[])).
% 0.38/0.56 tff(213,plain,
% 0.38/0.56 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | ((~aSet0(xS)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS))))),
% 0.38/0.56 inference(quant_inst,[status(thm)],[])).
% 0.38/0.56 tff(214,plain,
% 0.38/0.56 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, W0))))) | (~aSet0(xS)) | ![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))),
% 0.38/0.56 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.38/0.56 tff(215,plain,
% 0.38/0.56 (![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))),
% 0.38/0.56 inference(unit_resolution,[status(thm)],[214, 211, 6])).
% 0.38/0.56 tff(216,plain,
% 0.38/0.56 (((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | (aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)))) <=> ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)))),
% 0.38/0.56 inference(rewrite,[status(thm)],[])).
% 0.38/0.56 tff(217,plain,
% 0.38/0.56 ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | (aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)))),
% 0.38/0.56 inference(quant_inst,[status(thm)],[])).
% 0.38/0.56 tff(218,plain,
% 0.38/0.56 ((~![W1: $i] : (aElement0(W1) | (~aElementOf0(W1, xS)))) | aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx))) | (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS))),
% 0.38/0.56 inference(modus_ponens,[status(thm)],[217, 216])).
% 0.38/0.56 tff(219,plain,
% 0.38/0.56 (aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))),
% 0.38/0.56 inference(unit_resolution,[status(thm)],[218, 215, 198])).
% 0.38/0.56 tff(220,plain,
% 0.38/0.56 ((~![W3: $i] : (~(((~aElement0(W3)) | (~((W3 = xx) | aElementOf0(W3, xS)))) <=> aElementOf0(W3, sdtpldt0(xS, xx))))) | (~(((~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)))) <=> aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtpldt0(xS, xx))))),
% 0.38/0.56 inference(quant_inst,[status(thm)],[])).
% 0.38/0.56 tff(221,plain,
% 0.38/0.56 (~(((~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)))) <=> aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtpldt0(xS, xx)))),
% 0.38/0.56 inference(unit_resolution,[status(thm)],[220, 99])).
% 0.38/0.56 tff(222,plain,
% 0.38/0.56 (((tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)) | (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS))),
% 0.38/0.56 inference(tautology,[status(thm)],[])).
% 0.38/0.56 tff(223,plain,
% 0.38/0.56 ((tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)),
% 0.38/0.56 inference(unit_resolution,[status(thm)],[222, 198])).
% 0.38/0.56 tff(224,plain,
% 0.38/0.56 ((~((~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS))))) | (~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)))),
% 0.38/0.56 inference(tautology,[status(thm)],[])).
% 0.38/0.56 tff(225,plain,
% 0.38/0.56 ((~((~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS))))) | (~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx))))),
% 0.38/0.56 inference(unit_resolution,[status(thm)],[224, 223])).
% 0.38/0.56 tff(226,plain,
% 0.38/0.56 (~((~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS))))),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[225, 219])).
% 0.38/0.57 tff(227,plain,
% 0.38/0.57 ((((~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)))) <=> aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtpldt0(xS, xx))) | ((~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~((tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)))) | aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtpldt0(xS, xx))),
% 0.38/0.57 inference(tautology,[status(thm)],[])).
% 0.38/0.57 tff(228,plain,
% 0.38/0.57 (aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtpldt0(xS, xx))),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[227, 226, 221])).
% 0.38/0.57 tff(229,plain,
% 0.38/0.57 ((~((~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtpldt0(xS, xx))) | (tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx))) | (~aElement0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)))) | (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), sdtpldt0(xS, xx))) | (tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx)),
% 0.38/0.57 inference(tautology,[status(thm)],[])).
% 0.38/0.57 tff(230,plain,
% 0.38/0.57 (tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)) = xx),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[229, 228, 219, 196])).
% 0.38/0.57 tff(231,plain,
% 0.38/0.57 (aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS) <=> aElementOf0(xx, xS)),
% 0.38/0.57 inference(monotonicity,[status(thm)],[230])).
% 0.38/0.57 tff(232,plain,
% 0.38/0.57 (aElementOf0(xx, xS) <=> aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)),
% 0.38/0.57 inference(symmetry,[status(thm)],[231])).
% 0.38/0.57 tff(233,plain,
% 0.38/0.57 ((~aElementOf0(xx, xS)) <=> (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS))),
% 0.38/0.57 inference(monotonicity,[status(thm)],[232])).
% 0.38/0.57 tff(234,plain,
% 0.38/0.57 ((~aElementOf0(xx, xS)) <=> (~aElementOf0(xx, xS))),
% 0.38/0.57 inference(rewrite,[status(thm)],[])).
% 0.38/0.57 tff(235,axiom,(~aElementOf0(xx, xS)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__679_02')).
% 0.38/0.57 tff(236,plain,
% 0.38/0.57 (~aElementOf0(xx, xS)),
% 0.38/0.57 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.38/0.57 tff(237,plain,
% 0.38/0.57 (~aElementOf0(tptp_fun_W2_1(xS, sdtmndt0(sdtpldt0(xS, xx), xx)), xS)),
% 0.38/0.57 inference(modus_ponens,[status(thm)],[236, 233])).
% 0.38/0.57 tff(238,plain,
% 0.38/0.57 ($false),
% 0.38/0.57 inference(unit_resolution,[status(thm)],[198, 237])).
% 0.38/0.57 % SZS output end Proof
% 0.38/0.57 % E exiting
%------------------------------------------------------------------------------