%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM437+5 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:20:59 AM UTC 2025
% Result : Theorem 18.50s 24.99s
% Output : Proof 18.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/5.62 % Problem : NUM437+5 : TPTP v9.0.0. Released v4.0.0.
% 0.12/5.62 % Command : run_E %s %d THM
% 0.15/6.65 % Computer : n007.cluster.edu
% 0.15/6.65 % Model : x86_64 x86_64
% 0.15/6.65 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/6.65 % Memory : 8042.1875MB
% 0.15/6.65 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/6.65 % CPULimit : 300
% 0.15/6.65 % WCLimit : 300
% 0.15/6.65 % DateTime : Fri Jun 20 01:08:43 EDT 2025
% 0.15/6.65 % CPUTime :
% 18.50/24.99 % SZS status Theorem
% 18.50/24.99 % SZS output start Proof
% 18.50/24.99 tff(aElementOf0_type, type, (
% 18.50/24.99 aElementOf0: ( $i * $i ) > $o)).
% 18.50/24.99 tff(tptp_fun_W1_18_type, type, (
% 18.50/24.99 tptp_fun_W1_18: $i > $i)).
% 18.50/24.99 tff(tptp_fun_W0_15_type, type, (
% 18.50/24.99 tptp_fun_W0_15: $i)).
% 18.50/24.99 tff(tptp_fun_W2_17_type, type, (
% 18.50/24.99 tptp_fun_W2_17: $i > $i)).
% 18.50/24.99 tff(tptp_fun_W2_13_type, type, (
% 18.50/24.99 tptp_fun_W2_13: ( $i * $i ) > $i)).
% 18.50/24.99 tff(szAzrzSzezqlpdtcmdtrp0_type, type, (
% 18.50/24.99 szAzrzSzezqlpdtcmdtrp0: ( $i * $i ) > $i)).
% 18.50/24.99 tff(aSet0_type, type, (
% 18.50/24.99 aSet0: $i > $o)).
% 18.50/24.99 tff(aSubsetOf0_type, type, (
% 18.50/24.99 aSubsetOf0: ( $i * $i ) > $o)).
% 18.50/24.99 tff(tptp_fun_W2_2_type, type, (
% 18.50/24.99 tptp_fun_W2_2: ( $i * $i ) > $i)).
% 18.50/24.99 tff(aDivisorOf0_type, type, (
% 18.50/24.99 aDivisorOf0: ( $i * $i ) > $o)).
% 18.50/24.99 tff(sdtpldt0_type, type, (
% 18.50/24.99 sdtpldt0: ( $i * $i ) > $i)).
% 18.50/24.99 tff(smndt0_type, type, (
% 18.50/24.99 smndt0: $i > $i)).
% 18.50/24.99 tff(sdteqdtlpzmzozddtrp0_type, type, (
% 18.50/24.99 sdteqdtlpzmzozddtrp0: ( $i * $i * $i ) > $o)).
% 18.50/24.99 tff(sdtasdt0_type, type, (
% 18.50/24.99 sdtasdt0: ( $i * $i ) > $i)).
% 18.50/24.99 tff(aInteger0_type, type, (
% 18.50/24.99 aInteger0: $i > $o)).
% 18.50/24.99 tff(tptp_fun_W4_14_type, type, (
% 18.50/24.99 tptp_fun_W4_14: ( $i * $i * $i ) > $i)).
% 18.50/24.99 tff(sz00_type, type, (
% 18.50/24.99 sz00: $i)).
% 18.50/24.99 tff(cS1395_type, type, (
% 18.50/24.99 cS1395: $i)).
% 18.50/24.99 tff(isOpen0_type, type, (
% 18.50/24.99 isOpen0: $i > $o)).
% 18.50/24.99 tff(xS_type, type, (
% 18.50/24.99 xS: $i)).
% 18.50/24.99 tff(sbsmnsldt0_type, type, (
% 18.50/24.99 sbsmnsldt0: $i > $i)).
% 18.50/24.99 tff(tptp_fun_W3_16_type, type, (
% 18.50/24.99 tptp_fun_W3_16: ( $i * $i ) > $i)).
% 18.50/24.99 tff(1,plain,
% 18.50/24.99 (^[W0: $i] : refl((~((~((~aElementOf0(W0, sbsmnsldt0(xS))) | (~((~aInteger0(W0)) | (~aElementOf0(tptp_fun_W1_18(W0), xS)) | (~aElementOf0(W0, tptp_fun_W1_18(W0))))))) | (~((~aInteger0(W0)) | aElementOf0(W0, sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(W0, W1))))))) <=> (~((~((~aElementOf0(W0, sbsmnsldt0(xS))) | (~((~aInteger0(W0)) | (~aElementOf0(tptp_fun_W1_18(W0), xS)) | (~aElementOf0(W0, tptp_fun_W1_18(W0))))))) | (~((~aInteger0(W0)) | aElementOf0(W0, sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(W0, W1))))))))),
% 18.50/24.99 inference(bind,[status(th)],[])).
% 18.50/24.99 tff(2,plain,
% 18.50/24.99 (![W0: $i] : (~((~((~aElementOf0(W0, sbsmnsldt0(xS))) | (~((~aInteger0(W0)) | (~aElementOf0(tptp_fun_W1_18(W0), xS)) | (~aElementOf0(W0, tptp_fun_W1_18(W0))))))) | (~((~aInteger0(W0)) | aElementOf0(W0, sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(W0, W1))))))) <=> ![W0: $i] : (~((~((~aElementOf0(W0, sbsmnsldt0(xS))) | (~((~aInteger0(W0)) | (~aElementOf0(tptp_fun_W1_18(W0), xS)) | (~aElementOf0(W0, tptp_fun_W1_18(W0))))))) | (~((~aInteger0(W0)) | aElementOf0(W0, sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(W0, W1)))))))),
% 18.50/24.99 inference(quant_intro,[status(thm)],[1])).
% 18.50/24.99 tff(3,plain,
% 18.50/24.99 (^[W0: $i] : rewrite((~((~((~aElementOf0(W0, sbsmnsldt0(xS))) | (~((~aInteger0(W0)) | (~aElementOf0(tptp_fun_W1_18(W0), xS)) | (~aElementOf0(W0, tptp_fun_W1_18(W0))))))) | (~((~aInteger0(W0)) | aElementOf0(W0, sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(W0, W1))))))) <=> (~((~((~aElementOf0(W0, sbsmnsldt0(xS))) | (~((~aInteger0(W0)) | (~aElementOf0(tptp_fun_W1_18(W0), xS)) | (~aElementOf0(W0, tptp_fun_W1_18(W0))))))) | (~((~aInteger0(W0)) | aElementOf0(W0, sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(W0, W1))))))))),
% 18.50/24.99 inference(bind,[status(th)],[])).
% 18.50/24.99 tff(4,plain,
% 18.50/24.99 (![W0: $i] : (~((~((~aElementOf0(W0, sbsmnsldt0(xS))) | (~((~aInteger0(W0)) | (~aElementOf0(tptp_fun_W1_18(W0), xS)) | (~aElementOf0(W0, tptp_fun_W1_18(W0))))))) | (~((~aInteger0(W0)) | aElementOf0(W0, sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(W0, W1))))))) <=> ![W0: $i] : (~((~((~aElementOf0(W0, sbsmnsldt0(xS))) | (~((~aInteger0(W0)) | (~aElementOf0(tptp_fun_W1_18(W0), xS)) | (~aElementOf0(W0, tptp_fun_W1_18(W0))))))) | (~((~aInteger0(W0)) | aElementOf0(W0, sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(W0, W1)))))))),
% 18.50/24.99 inference(quant_intro,[status(thm)],[3])).
% 18.50/24.99 tff(5,plain,
% 18.50/24.99 (![W0: $i] : (~((~((~aElementOf0(W0, sbsmnsldt0(xS))) | (~((~aInteger0(W0)) | (~aElementOf0(tptp_fun_W1_18(W0), xS)) | (~aElementOf0(W0, tptp_fun_W1_18(W0))))))) | (~((~aInteger0(W0)) | aElementOf0(W0, sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(W0, W1))))))) <=> ![W0: $i] : (~((~((~aElementOf0(W0, sbsmnsldt0(xS))) | (~((~aInteger0(W0)) | (~aElementOf0(tptp_fun_W1_18(W0), xS)) | (~aElementOf0(W0, tptp_fun_W1_18(W0))))))) | (~((~aInteger0(W0)) | aElementOf0(W0, sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(W0, W1)))))))),
% 18.50/24.99 inference(transitivity,[status(thm)],[4, 2])).
% 18.50/24.99 tff(6,plain,
% 18.50/24.99 (^[W0: $i] : trans(monotonicity(rewrite(((~aElementOf0(W0, sbsmnsldt0(xS))) | (aInteger0(W0) & aElementOf0(tptp_fun_W1_18(W0), xS) & aElementOf0(W0, tptp_fun_W1_18(W0)))) <=> ((~aElementOf0(W0, sbsmnsldt0(xS))) | (~((~aInteger0(W0)) | (~aElementOf0(tptp_fun_W1_18(W0), xS)) | (~aElementOf0(W0, tptp_fun_W1_18(W0))))))), rewrite(((~aInteger0(W0)) | aElementOf0(W0, sbsmnsldt0(xS)) | ![W1: $i] : (~(aElementOf0(W1, xS) & aElementOf0(W0, W1)))) <=> ((~aInteger0(W0)) | aElementOf0(W0, sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(W0, W1))))), ((((~aElementOf0(W0, sbsmnsldt0(xS))) | (aInteger0(W0) & aElementOf0(tptp_fun_W1_18(W0), xS) & aElementOf0(W0, tptp_fun_W1_18(W0)))) & ((~aInteger0(W0)) | aElementOf0(W0, sbsmnsldt0(xS)) | ![W1: $i] : (~(aElementOf0(W1, xS) & aElementOf0(W0, W1))))) <=> (((~aElementOf0(W0, sbsmnsldt0(xS))) | (~((~aInteger0(W0)) | (~aElementOf0(tptp_fun_W1_18(W0), xS)) | (~aElementOf0(W0, tptp_fun_W1_18(W0)))))) & ((~aInteger0(W0)) | aElementOf0(W0, sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(W0, W1))))))), rewrite((((~aElementOf0(W0, sbsmnsldt0(xS))) | (~((~aInteger0(W0)) | (~aElementOf0(tptp_fun_W1_18(W0), xS)) | (~aElementOf0(W0, tptp_fun_W1_18(W0)))))) & ((~aInteger0(W0)) | aElementOf0(W0, sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(W0, W1))))) <=> (~((~((~aElementOf0(W0, sbsmnsldt0(xS))) | (~((~aInteger0(W0)) | (~aElementOf0(tptp_fun_W1_18(W0), xS)) | (~aElementOf0(W0, tptp_fun_W1_18(W0))))))) | (~((~aInteger0(W0)) | aElementOf0(W0, sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(W0, W1)))))))), ((((~aElementOf0(W0, sbsmnsldt0(xS))) | (aInteger0(W0) & aElementOf0(tptp_fun_W1_18(W0), xS) & aElementOf0(W0, tptp_fun_W1_18(W0)))) & ((~aInteger0(W0)) | aElementOf0(W0, sbsmnsldt0(xS)) | ![W1: $i] : (~(aElementOf0(W1, xS) & aElementOf0(W0, W1))))) <=> (~((~((~aElementOf0(W0, sbsmnsldt0(xS))) | (~((~aInteger0(W0)) | (~aElementOf0(tptp_fun_W1_18(W0), xS)) | (~aElementOf0(W0, tptp_fun_W1_18(W0))))))) | (~((~aInteger0(W0)) | aElementOf0(W0, sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(W0, W1)))))))))),
% 18.50/24.99 inference(bind,[status(th)],[])).
% 18.50/24.99 tff(7,plain,
% 18.50/24.99 (![W0: $i] : (((~aElementOf0(W0, sbsmnsldt0(xS))) | (aInteger0(W0) & aElementOf0(tptp_fun_W1_18(W0), xS) & aElementOf0(W0, tptp_fun_W1_18(W0)))) & ((~aInteger0(W0)) | aElementOf0(W0, sbsmnsldt0(xS)) | ![W1: $i] : (~(aElementOf0(W1, xS) & aElementOf0(W0, W1))))) <=> ![W0: $i] : (~((~((~aElementOf0(W0, sbsmnsldt0(xS))) | (~((~aInteger0(W0)) | (~aElementOf0(tptp_fun_W1_18(W0), xS)) | (~aElementOf0(W0, tptp_fun_W1_18(W0))))))) | (~((~aInteger0(W0)) | aElementOf0(W0, sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(W0, W1)))))))),
% 18.50/24.99 inference(quant_intro,[status(thm)],[6])).
% 18.50/24.99 tff(8,plain,
% 18.50/24.99 (^[W0: $i] : rewrite((((~aElementOf0(W0, sbsmnsldt0(xS))) | (aInteger0(W0) & (aElementOf0(tptp_fun_W1_18(W0), xS) & aElementOf0(W0, tptp_fun_W1_18(W0))))) & (aElementOf0(W0, sbsmnsldt0(xS)) | ((~aInteger0(W0)) | ![W1: $i] : (~(aElementOf0(W1, xS) & aElementOf0(W0, W1)))))) <=> (((~aElementOf0(W0, sbsmnsldt0(xS))) | (aInteger0(W0) & aElementOf0(tptp_fun_W1_18(W0), xS) & aElementOf0(W0, tptp_fun_W1_18(W0)))) & ((~aInteger0(W0)) | aElementOf0(W0, sbsmnsldt0(xS)) | ![W1: $i] : (~(aElementOf0(W1, xS) & aElementOf0(W0, W1))))))),
% 18.50/24.99 inference(bind,[status(th)],[])).
% 18.50/24.99 tff(9,plain,
% 18.50/24.99 (![W0: $i] : (((~aElementOf0(W0, sbsmnsldt0(xS))) | (aInteger0(W0) & (aElementOf0(tptp_fun_W1_18(W0), xS) & aElementOf0(W0, tptp_fun_W1_18(W0))))) & (aElementOf0(W0, sbsmnsldt0(xS)) | ((~aInteger0(W0)) | ![W1: $i] : (~(aElementOf0(W1, xS) & aElementOf0(W0, W1)))))) <=> ![W0: $i] : (((~aElementOf0(W0, sbsmnsldt0(xS))) | (aInteger0(W0) & aElementOf0(tptp_fun_W1_18(W0), xS) & aElementOf0(W0, tptp_fun_W1_18(W0)))) & ((~aInteger0(W0)) | aElementOf0(W0, sbsmnsldt0(xS)) | ![W1: $i] : (~(aElementOf0(W1, xS) & aElementOf0(W0, W1)))))),
% 18.50/24.99 inference(quant_intro,[status(thm)],[8])).
% 18.50/24.99 tff(10,plain,
% 18.50/24.99 (![W0: $i] : (aElementOf0(W0, sbsmnsldt0(xS)) <=> (aInteger0(W0) & ?[W1: $i] : (aElementOf0(W1, xS) & aElementOf0(W0, W1)))) <=> ![W0: $i] : (aElementOf0(W0, sbsmnsldt0(xS)) <=> (aInteger0(W0) & ?[W1: $i] : (aElementOf0(W1, xS) & aElementOf0(W0, W1))))),
% 18.50/24.99 inference(rewrite,[status(thm)],[])).
% 18.50/24.99 tff(11,plain,
% 18.50/24.99 ((~((aSet0(sbsmnsldt0(xS)) & ![W0: $i] : (aElementOf0(W0, sbsmnsldt0(xS)) <=> (aInteger0(W0) & ?[W1: $i] : (aElementOf0(W1, xS) & aElementOf0(W0, W1))))) => (![W0: $i] : (aElementOf0(W0, sbsmnsldt0(xS)) => ?[W1: $i] : ((aInteger0(W1) & (~(W1 = sz00))) & ((aSet0(szAzrzSzezqlpdtcmdtrp0(W0, W1)) & ![W2: $i] : ((aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0, W1)) => (((aInteger0(W2) & ?[W3: $i] : (aInteger0(W3) & (sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0))))) & aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0)))) & sdteqdtlpzmzozddtrp0(W2, W0, W1))) & ((aInteger0(W2) & ((?[W3: $i] : (aInteger0(W3) & (sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0)))) | aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0)))) | sdteqdtlpzmzozddtrp0(W2, W0, W1))) => aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0, W1))))) => (![W2: $i] : (aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0, W1)) => aElementOf0(W2, sbsmnsldt0(xS))) | aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0, W1), sbsmnsldt0(xS)))))) | isOpen0(sbsmnsldt0(xS))))) <=> (~(isOpen0(sbsmnsldt0(xS)) | ![W0: $i] : ((~aElementOf0(W0, sbsmnsldt0(xS))) | ?[W1: $i] : (aInteger0(W1) & (~(W1 = sz00)) & (aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0, W1), sbsmnsldt0(xS)) | (~(aSet0(szAzrzSzezqlpdtcmdtrp0(W0, W1)) & ![W2: $i] : (((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0, W1))) | (aInteger0(W2) & ?[W3: $i] : (aInteger0(W3) & (sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0)))) & aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0))) & sdteqdtlpzmzozddtrp0(W2, W0, W1))) & ((~(aInteger0(W2) & (sdteqdtlpzmzozddtrp0(W2, W0, W1) | aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0))) | ?[W3: $i] : (aInteger0(W3) & (sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0))))))) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0, W1)))))) | ![W2: $i] : ((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0, W1))) | aElementOf0(W2, sbsmnsldt0(xS)))))) | (~(aSet0(sbsmnsldt0(xS)) & ![W0: $i] : (aElementOf0(W0, sbsmnsldt0(xS)) <=> (aInteger0(W0) & ?[W1: $i] : (aElementOf0(W1, xS) & aElementOf0(W0, W1))))))))),
% 18.50/24.99 inference(rewrite,[status(thm)],[])).
% 18.50/24.99 tff(12,axiom,(~((aSet0(sbsmnsldt0(xS)) & ![W0: $i] : (aElementOf0(W0, sbsmnsldt0(xS)) <=> (aInteger0(W0) & ?[W1: $i] : (aElementOf0(W1, xS) & aElementOf0(W0, W1))))) => (![W0: $i] : (aElementOf0(W0, sbsmnsldt0(xS)) => ?[W1: $i] : ((aInteger0(W1) & (~(W1 = sz00))) & ((aSet0(szAzrzSzezqlpdtcmdtrp0(W0, W1)) & ![W2: $i] : ((aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0, W1)) => (((aInteger0(W2) & ?[W3: $i] : (aInteger0(W3) & (sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0))))) & aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0)))) & sdteqdtlpzmzozddtrp0(W2, W0, W1))) & ((aInteger0(W2) & ((?[W3: $i] : (aInteger0(W3) & (sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0)))) | aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0)))) | sdteqdtlpzmzozddtrp0(W2, W0, W1))) => aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0, W1))))) => (![W2: $i] : (aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0, W1)) => aElementOf0(W2, sbsmnsldt0(xS))) | aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0, W1), sbsmnsldt0(xS)))))) | isOpen0(sbsmnsldt0(xS))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 18.50/24.99 tff(13,plain,
% 18.50/24.99 (~(isOpen0(sbsmnsldt0(xS)) | ![W0: $i] : ((~aElementOf0(W0, sbsmnsldt0(xS))) | ?[W1: $i] : (aInteger0(W1) & (~(W1 = sz00)) & (aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0, W1), sbsmnsldt0(xS)) | (~(aSet0(szAzrzSzezqlpdtcmdtrp0(W0, W1)) & ![W2: $i] : (((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0, W1))) | (aInteger0(W2) & ?[W3: $i] : (aInteger0(W3) & (sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0)))) & aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0))) & sdteqdtlpzmzozddtrp0(W2, W0, W1))) & ((~(aInteger0(W2) & (sdteqdtlpzmzozddtrp0(W2, W0, W1) | aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0))) | ?[W3: $i] : (aInteger0(W3) & (sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0))))))) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0, W1)))))) | ![W2: $i] : ((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0, W1))) | aElementOf0(W2, sbsmnsldt0(xS)))))) | (~(aSet0(sbsmnsldt0(xS)) & ![W0: $i] : (aElementOf0(W0, sbsmnsldt0(xS)) <=> (aInteger0(W0) & ?[W1: $i] : (aElementOf0(W1, xS) & aElementOf0(W0, W1)))))))),
% 18.50/24.99 inference(modus_ponens,[status(thm)],[12, 11])).
% 18.50/24.99 tff(14,plain,
% 18.50/24.99 (aSet0(sbsmnsldt0(xS)) & ![W0: $i] : (aElementOf0(W0, sbsmnsldt0(xS)) <=> (aInteger0(W0) & ?[W1: $i] : (aElementOf0(W1, xS) & aElementOf0(W0, W1))))),
% 18.50/24.99 inference(or_elim,[status(thm)],[13])).
% 18.50/24.99 tff(15,plain,
% 18.50/24.99 (![W0: $i] : (aElementOf0(W0, sbsmnsldt0(xS)) <=> (aInteger0(W0) & ?[W1: $i] : (aElementOf0(W1, xS) & aElementOf0(W0, W1))))),
% 18.50/24.99 inference(and_elim,[status(thm)],[14])).
% 18.50/24.99 tff(16,plain,
% 18.50/24.99 (![W0: $i] : (aElementOf0(W0, sbsmnsldt0(xS)) <=> (aInteger0(W0) & ?[W1: $i] : (aElementOf0(W1, xS) & aElementOf0(W0, W1))))),
% 18.50/24.99 inference(modus_ponens,[status(thm)],[15, 10])).
% 18.50/24.99 tff(17,plain,(
% 18.50/24.99 ![W0: $i] : (((~aElementOf0(W0, sbsmnsldt0(xS))) | (aInteger0(W0) & (aElementOf0(tptp_fun_W1_18(W0), xS) & aElementOf0(W0, tptp_fun_W1_18(W0))))) & (aElementOf0(W0, sbsmnsldt0(xS)) | ((~aInteger0(W0)) | ![W1: $i] : (~(aElementOf0(W1, xS) & aElementOf0(W0, W1))))))),
% 18.50/24.99 inference(skolemize,[status(sab)],[16])).
% 18.50/24.99 tff(18,plain,
% 18.50/24.99 (![W0: $i] : (((~aElementOf0(W0, sbsmnsldt0(xS))) | (aInteger0(W0) & aElementOf0(tptp_fun_W1_18(W0), xS) & aElementOf0(W0, tptp_fun_W1_18(W0)))) & ((~aInteger0(W0)) | aElementOf0(W0, sbsmnsldt0(xS)) | ![W1: $i] : (~(aElementOf0(W1, xS) & aElementOf0(W0, W1)))))),
% 18.50/24.99 inference(modus_ponens,[status(thm)],[17, 9])).
% 18.50/24.99 tff(19,plain,
% 18.50/24.99 (![W0: $i] : (~((~((~aElementOf0(W0, sbsmnsldt0(xS))) | (~((~aInteger0(W0)) | (~aElementOf0(tptp_fun_W1_18(W0), xS)) | (~aElementOf0(W0, tptp_fun_W1_18(W0))))))) | (~((~aInteger0(W0)) | aElementOf0(W0, sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(W0, W1)))))))),
% 18.50/24.99 inference(modus_ponens,[status(thm)],[18, 7])).
% 18.50/24.99 tff(20,plain,
% 18.50/24.99 (![W0: $i] : (~((~((~aElementOf0(W0, sbsmnsldt0(xS))) | (~((~aInteger0(W0)) | (~aElementOf0(tptp_fun_W1_18(W0), xS)) | (~aElementOf0(W0, tptp_fun_W1_18(W0))))))) | (~((~aInteger0(W0)) | aElementOf0(W0, sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(W0, W1)))))))),
% 18.50/24.99 inference(modus_ponens,[status(thm)],[19, 5])).
% 18.50/24.99 tff(21,plain,
% 18.50/24.99 (((~![W0: $i] : (~((~((~aElementOf0(W0, sbsmnsldt0(xS))) | (~((~aInteger0(W0)) | (~aElementOf0(tptp_fun_W1_18(W0), xS)) | (~aElementOf0(W0, tptp_fun_W1_18(W0))))))) | (~((~aInteger0(W0)) | aElementOf0(W0, sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(W0, W1)))))))) | (~((~((~aInteger0(W0!15)) | aElementOf0(W0!15, sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(W0!15, W1))))) | (~((~aElementOf0(W0!15, sbsmnsldt0(xS))) | (~((~aInteger0(W0!15)) | (~aElementOf0(W0!15, tptp_fun_W1_18(W0!15))) | (~aElementOf0(tptp_fun_W1_18(W0!15), xS))))))))) <=> ((~![W0: $i] : (~((~((~aElementOf0(W0, sbsmnsldt0(xS))) | (~((~aInteger0(W0)) | (~aElementOf0(tptp_fun_W1_18(W0), xS)) | (~aElementOf0(W0, tptp_fun_W1_18(W0))))))) | (~((~aInteger0(W0)) | aElementOf0(W0, sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(W0, W1)))))))) | (~((~((~aInteger0(W0!15)) | aElementOf0(W0!15, sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(W0!15, W1))))) | (~((~aElementOf0(W0!15, sbsmnsldt0(xS))) | (~((~aInteger0(W0!15)) | (~aElementOf0(W0!15, tptp_fun_W1_18(W0!15))) | (~aElementOf0(tptp_fun_W1_18(W0!15), xS)))))))))),
% 18.50/24.99 inference(rewrite,[status(thm)],[])).
% 18.50/24.99 tff(22,plain,
% 18.50/24.99 ((~((~((~aElementOf0(W0!15, sbsmnsldt0(xS))) | (~((~aInteger0(W0!15)) | (~aElementOf0(tptp_fun_W1_18(W0!15), xS)) | (~aElementOf0(W0!15, tptp_fun_W1_18(W0!15))))))) | (~((~aInteger0(W0!15)) | aElementOf0(W0!15, sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(W0!15, W1))))))) <=> (~((~((~aInteger0(W0!15)) | aElementOf0(W0!15, sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(W0!15, W1))))) | (~((~aElementOf0(W0!15, sbsmnsldt0(xS))) | (~((~aInteger0(W0!15)) | (~aElementOf0(W0!15, tptp_fun_W1_18(W0!15))) | (~aElementOf0(tptp_fun_W1_18(W0!15), xS))))))))),
% 18.50/25.00 inference(rewrite,[status(thm)],[])).
% 18.50/25.00 tff(23,plain,
% 18.50/25.00 (((~![W0: $i] : (~((~((~aElementOf0(W0, sbsmnsldt0(xS))) | (~((~aInteger0(W0)) | (~aElementOf0(tptp_fun_W1_18(W0), xS)) | (~aElementOf0(W0, tptp_fun_W1_18(W0))))))) | (~((~aInteger0(W0)) | aElementOf0(W0, sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(W0, W1)))))))) | (~((~((~aElementOf0(W0!15, sbsmnsldt0(xS))) | (~((~aInteger0(W0!15)) | (~aElementOf0(tptp_fun_W1_18(W0!15), xS)) | (~aElementOf0(W0!15, tptp_fun_W1_18(W0!15))))))) | (~((~aInteger0(W0!15)) | aElementOf0(W0!15, sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(W0!15, W1)))))))) <=> ((~![W0: $i] : (~((~((~aElementOf0(W0, sbsmnsldt0(xS))) | (~((~aInteger0(W0)) | (~aElementOf0(tptp_fun_W1_18(W0), xS)) | (~aElementOf0(W0, tptp_fun_W1_18(W0))))))) | (~((~aInteger0(W0)) | aElementOf0(W0, sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(W0, W1)))))))) | (~((~((~aInteger0(W0!15)) | aElementOf0(W0!15, sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(W0!15, W1))))) | (~((~aElementOf0(W0!15, sbsmnsldt0(xS))) | (~((~aInteger0(W0!15)) | (~aElementOf0(W0!15, tptp_fun_W1_18(W0!15))) | (~aElementOf0(tptp_fun_W1_18(W0!15), xS)))))))))),
% 18.50/25.00 inference(monotonicity,[status(thm)],[22])).
% 18.50/25.00 tff(24,plain,
% 18.50/25.00 (((~![W0: $i] : (~((~((~aElementOf0(W0, sbsmnsldt0(xS))) | (~((~aInteger0(W0)) | (~aElementOf0(tptp_fun_W1_18(W0), xS)) | (~aElementOf0(W0, tptp_fun_W1_18(W0))))))) | (~((~aInteger0(W0)) | aElementOf0(W0, sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(W0, W1)))))))) | (~((~((~aElementOf0(W0!15, sbsmnsldt0(xS))) | (~((~aInteger0(W0!15)) | (~aElementOf0(tptp_fun_W1_18(W0!15), xS)) | (~aElementOf0(W0!15, tptp_fun_W1_18(W0!15))))))) | (~((~aInteger0(W0!15)) | aElementOf0(W0!15, sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(W0!15, W1)))))))) <=> ((~![W0: $i] : (~((~((~aElementOf0(W0, sbsmnsldt0(xS))) | (~((~aInteger0(W0)) | (~aElementOf0(tptp_fun_W1_18(W0), xS)) | (~aElementOf0(W0, tptp_fun_W1_18(W0))))))) | (~((~aInteger0(W0)) | aElementOf0(W0, sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(W0, W1)))))))) | (~((~((~aInteger0(W0!15)) | aElementOf0(W0!15, sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(W0!15, W1))))) | (~((~aElementOf0(W0!15, sbsmnsldt0(xS))) | (~((~aInteger0(W0!15)) | (~aElementOf0(W0!15, tptp_fun_W1_18(W0!15))) | (~aElementOf0(tptp_fun_W1_18(W0!15), xS)))))))))),
% 18.50/25.00 inference(transitivity,[status(thm)],[23, 21])).
% 18.50/25.00 tff(25,plain,
% 18.50/25.00 ((~![W0: $i] : (~((~((~aElementOf0(W0, sbsmnsldt0(xS))) | (~((~aInteger0(W0)) | (~aElementOf0(tptp_fun_W1_18(W0), xS)) | (~aElementOf0(W0, tptp_fun_W1_18(W0))))))) | (~((~aInteger0(W0)) | aElementOf0(W0, sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(W0, W1)))))))) | (~((~((~aElementOf0(W0!15, sbsmnsldt0(xS))) | (~((~aInteger0(W0!15)) | (~aElementOf0(tptp_fun_W1_18(W0!15), xS)) | (~aElementOf0(W0!15, tptp_fun_W1_18(W0!15))))))) | (~((~aInteger0(W0!15)) | aElementOf0(W0!15, sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(W0!15, W1)))))))),
% 18.50/25.00 inference(quant_inst,[status(thm)],[])).
% 18.50/25.00 tff(26,plain,
% 18.50/25.00 ((~![W0: $i] : (~((~((~aElementOf0(W0, sbsmnsldt0(xS))) | (~((~aInteger0(W0)) | (~aElementOf0(tptp_fun_W1_18(W0), xS)) | (~aElementOf0(W0, tptp_fun_W1_18(W0))))))) | (~((~aInteger0(W0)) | aElementOf0(W0, sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(W0, W1)))))))) | (~((~((~aInteger0(W0!15)) | aElementOf0(W0!15, sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(W0!15, W1))))) | (~((~aElementOf0(W0!15, sbsmnsldt0(xS))) | (~((~aInteger0(W0!15)) | (~aElementOf0(W0!15, tptp_fun_W1_18(W0!15))) | (~aElementOf0(tptp_fun_W1_18(W0!15), xS))))))))),
% 18.50/25.00 inference(modus_ponens,[status(thm)],[25, 24])).
% 18.50/25.00 tff(27,plain,
% 18.50/25.00 (~((~((~aInteger0(W0!15)) | aElementOf0(W0!15, sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(W0!15, W1))))) | (~((~aElementOf0(W0!15, sbsmnsldt0(xS))) | (~((~aInteger0(W0!15)) | (~aElementOf0(W0!15, tptp_fun_W1_18(W0!15))) | (~aElementOf0(tptp_fun_W1_18(W0!15), xS)))))))),
% 18.50/25.00 inference(unit_resolution,[status(thm)],[26, 20])).
% 18.50/25.00 tff(28,plain,
% 18.50/25.00 (((~((~aInteger0(W0!15)) | aElementOf0(W0!15, sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(W0!15, W1))))) | (~((~aElementOf0(W0!15, sbsmnsldt0(xS))) | (~((~aInteger0(W0!15)) | (~aElementOf0(W0!15, tptp_fun_W1_18(W0!15))) | (~aElementOf0(tptp_fun_W1_18(W0!15), xS))))))) | ((~aElementOf0(W0!15, sbsmnsldt0(xS))) | (~((~aInteger0(W0!15)) | (~aElementOf0(W0!15, tptp_fun_W1_18(W0!15))) | (~aElementOf0(tptp_fun_W1_18(W0!15), xS)))))),
% 18.50/25.00 inference(tautology,[status(thm)],[])).
% 18.50/25.00 tff(29,plain,
% 18.50/25.00 ((~aElementOf0(W0!15, sbsmnsldt0(xS))) | (~((~aInteger0(W0!15)) | (~aElementOf0(W0!15, tptp_fun_W1_18(W0!15))) | (~aElementOf0(tptp_fun_W1_18(W0!15), xS))))),
% 18.50/25.00 inference(unit_resolution,[status(thm)],[28, 27])).
% 18.50/25.00 tff(30,plain,
% 18.50/25.00 ((aElementOf0(W0!15, sbsmnsldt0(xS)) & ![W1: $i] : ((~aInteger0(W1)) | (W1 = sz00) | ((~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1), sbsmnsldt0(xS))) & (aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) & ![W2: $i] : (((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (aInteger0(W2) & (aInteger0(tptp_fun_W3_16(W2, W1)) & (sdtasdt0(W1, tptp_fun_W3_16(W2, W1)) = sdtpldt0(W2, smndt0(W0!15)))) & aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15))) & sdteqdtlpzmzozddtrp0(W2, W0!15, W1))) & (((~aInteger0(W2)) | ((~sdteqdtlpzmzozddtrp0(W2, W0!15, W1)) & (~aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15)))) & ![W3: $i] : (~(aInteger0(W3) & (sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15))))))) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1))))) & (~((~aElementOf0(tptp_fun_W2_17(W1), szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | aElementOf0(tptp_fun_W2_17(W1), sbsmnsldt0(xS))))))) <=> (aElementOf0(W0!15, sbsmnsldt0(xS)) & ![W1: $i] : ((~aInteger0(W1)) | (W1 = sz00) | ((~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1), sbsmnsldt0(xS))) & aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) & ![W2: $i] : (((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (aInteger0(W2) & aInteger0(tptp_fun_W3_16(W2, W1)) & (sdtasdt0(W1, tptp_fun_W3_16(W2, W1)) = sdtpldt0(W2, smndt0(W0!15))) & aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15))) & sdteqdtlpzmzozddtrp0(W2, W0!15, W1))) & ((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) | ((~sdteqdtlpzmzozddtrp0(W2, W0!15, W1)) & (~aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15)))) & ![W3: $i] : (~(aInteger0(W3) & (sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15)))))))) & (~((~aElementOf0(tptp_fun_W2_17(W1), szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | aElementOf0(tptp_fun_W2_17(W1), sbsmnsldt0(xS)))))))),
% 18.50/25.00 inference(rewrite,[status(thm)],[])).
% 18.50/25.00 tff(31,plain,
% 18.50/25.00 ((~![W0: $i] : ((~aElementOf0(W0, sbsmnsldt0(xS))) | ?[W1: $i] : (aInteger0(W1) & (~(W1 = sz00)) & (aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0, W1), sbsmnsldt0(xS)) | (~(aSet0(szAzrzSzezqlpdtcmdtrp0(W0, W1)) & ![W2: $i] : (((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0, W1))) | (aInteger0(W2) & ?[W3: $i] : (aInteger0(W3) & (sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0)))) & aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0))) & sdteqdtlpzmzozddtrp0(W2, W0, W1))) & ((~(aInteger0(W2) & (sdteqdtlpzmzozddtrp0(W2, W0, W1) | aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0))) | ?[W3: $i] : (aInteger0(W3) & (sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0))))))) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0, W1)))))) | ![W2: $i] : ((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0, W1))) | aElementOf0(W2, sbsmnsldt0(xS))))))) <=> (~![W0: $i] : ((~aElementOf0(W0, sbsmnsldt0(xS))) | ?[W1: $i] : (aInteger0(W1) & (~(W1 = sz00)) & (aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0, W1), sbsmnsldt0(xS)) | (~(aSet0(szAzrzSzezqlpdtcmdtrp0(W0, W1)) & ![W2: $i] : (((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0, W1))) | (aInteger0(W2) & ?[W3: $i] : (aInteger0(W3) & (sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0)))) & aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0))) & sdteqdtlpzmzozddtrp0(W2, W0, W1))) & ((~(aInteger0(W2) & (sdteqdtlpzmzozddtrp0(W2, W0, W1) | aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0))) | ?[W3: $i] : (aInteger0(W3) & (sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0))))))) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0, W1)))))) | ![W2: $i] : ((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0, W1))) | aElementOf0(W2, sbsmnsldt0(xS)))))))),
% 18.50/25.00 inference(rewrite,[status(thm)],[])).
% 18.50/25.00 tff(32,plain,
% 18.50/25.00 (~![W0: $i] : ((~aElementOf0(W0, sbsmnsldt0(xS))) | ?[W1: $i] : (aInteger0(W1) & (~(W1 = sz00)) & (aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0, W1), sbsmnsldt0(xS)) | (~(aSet0(szAzrzSzezqlpdtcmdtrp0(W0, W1)) & ![W2: $i] : (((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0, W1))) | (aInteger0(W2) & ?[W3: $i] : (aInteger0(W3) & (sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0)))) & aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0))) & sdteqdtlpzmzozddtrp0(W2, W0, W1))) & ((~(aInteger0(W2) & (sdteqdtlpzmzozddtrp0(W2, W0, W1) | aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0))) | ?[W3: $i] : (aInteger0(W3) & (sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0))))))) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0, W1)))))) | ![W2: $i] : ((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0, W1))) | aElementOf0(W2, sbsmnsldt0(xS))))))),
% 18.50/25.00 inference(or_elim,[status(thm)],[13])).
% 18.50/25.00 tff(33,plain,
% 18.50/25.00 (~![W0: $i] : ((~aElementOf0(W0, sbsmnsldt0(xS))) | ?[W1: $i] : (aInteger0(W1) & (~(W1 = sz00)) & (aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0, W1), sbsmnsldt0(xS)) | (~(aSet0(szAzrzSzezqlpdtcmdtrp0(W0, W1)) & ![W2: $i] : (((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0, W1))) | (aInteger0(W2) & ?[W3: $i] : (aInteger0(W3) & (sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0)))) & aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0))) & sdteqdtlpzmzozddtrp0(W2, W0, W1))) & ((~(aInteger0(W2) & (sdteqdtlpzmzozddtrp0(W2, W0, W1) | aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0))) | ?[W3: $i] : (aInteger0(W3) & (sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0))))))) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0, W1)))))) | ![W2: $i] : ((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0, W1))) | aElementOf0(W2, sbsmnsldt0(xS))))))),
% 18.50/25.00 inference(modus_ponens,[status(thm)],[32, 31])).
% 18.50/25.00 tff(34,plain,
% 18.50/25.00 (~![W0: $i] : ((~aElementOf0(W0, sbsmnsldt0(xS))) | ?[W1: $i] : (aInteger0(W1) & (~(W1 = sz00)) & (aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0, W1), sbsmnsldt0(xS)) | (~(aSet0(szAzrzSzezqlpdtcmdtrp0(W0, W1)) & ![W2: $i] : (((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0, W1))) | (aInteger0(W2) & ?[W3: $i] : (aInteger0(W3) & (sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0)))) & aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0))) & sdteqdtlpzmzozddtrp0(W2, W0, W1))) & ((~(aInteger0(W2) & (sdteqdtlpzmzozddtrp0(W2, W0, W1) | aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0))) | ?[W3: $i] : (aInteger0(W3) & (sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0))))))) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0, W1)))))) | ![W2: $i] : ((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0, W1))) | aElementOf0(W2, sbsmnsldt0(xS))))))),
% 18.50/25.00 inference(modus_ponens,[status(thm)],[33, 31])).
% 18.50/25.00 tff(35,plain,
% 18.50/25.00 (~![W0: $i] : ((~aElementOf0(W0, sbsmnsldt0(xS))) | ?[W1: $i] : (aInteger0(W1) & (~(W1 = sz00)) & (aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0, W1), sbsmnsldt0(xS)) | (~(aSet0(szAzrzSzezqlpdtcmdtrp0(W0, W1)) & ![W2: $i] : (((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0, W1))) | (aInteger0(W2) & ?[W3: $i] : (aInteger0(W3) & (sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0)))) & aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0))) & sdteqdtlpzmzozddtrp0(W2, W0, W1))) & ((~(aInteger0(W2) & (sdteqdtlpzmzozddtrp0(W2, W0, W1) | aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0))) | ?[W3: $i] : (aInteger0(W3) & (sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0))))))) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0, W1)))))) | ![W2: $i] : ((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0, W1))) | aElementOf0(W2, sbsmnsldt0(xS))))))),
% 18.50/25.00 inference(modus_ponens,[status(thm)],[34, 31])).
% 18.50/25.00 tff(36,plain,
% 18.50/25.00 (aElementOf0(W0!15, sbsmnsldt0(xS)) & ![W1: $i] : ((~aInteger0(W1)) | (W1 = sz00) | ((~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1), sbsmnsldt0(xS))) & aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) & ![W2: $i] : (((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (aInteger0(W2) & aInteger0(tptp_fun_W3_16(W2, W1)) & (sdtasdt0(W1, tptp_fun_W3_16(W2, W1)) = sdtpldt0(W2, smndt0(W0!15))) & aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15))) & sdteqdtlpzmzozddtrp0(W2, W0!15, W1))) & ((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) | ((~sdteqdtlpzmzozddtrp0(W2, W0!15, W1)) & (~aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15)))) & ![W3: $i] : (~(aInteger0(W3) & (sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15)))))))) & (~((~aElementOf0(tptp_fun_W2_17(W1), szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | aElementOf0(tptp_fun_W2_17(W1), sbsmnsldt0(xS))))))),
% 18.50/25.00 inference(modus_ponens,[status(thm)],[35, 30])).
% 18.50/25.00 tff(37,plain,
% 18.50/25.00 (aElementOf0(W0!15, sbsmnsldt0(xS))),
% 18.50/25.00 inference(and_elim,[status(thm)],[36])).
% 18.50/25.00 tff(38,plain,
% 18.50/25.00 ((~((~aElementOf0(W0!15, sbsmnsldt0(xS))) | (~((~aInteger0(W0!15)) | (~aElementOf0(W0!15, tptp_fun_W1_18(W0!15))) | (~aElementOf0(tptp_fun_W1_18(W0!15), xS)))))) | (~aElementOf0(W0!15, sbsmnsldt0(xS))) | (~((~aInteger0(W0!15)) | (~aElementOf0(W0!15, tptp_fun_W1_18(W0!15))) | (~aElementOf0(tptp_fun_W1_18(W0!15), xS))))),
% 18.50/25.00 inference(tautology,[status(thm)],[])).
% 18.50/25.00 tff(39,plain,
% 18.50/25.00 ((~((~aElementOf0(W0!15, sbsmnsldt0(xS))) | (~((~aInteger0(W0!15)) | (~aElementOf0(W0!15, tptp_fun_W1_18(W0!15))) | (~aElementOf0(tptp_fun_W1_18(W0!15), xS)))))) | (~((~aInteger0(W0!15)) | (~aElementOf0(W0!15, tptp_fun_W1_18(W0!15))) | (~aElementOf0(tptp_fun_W1_18(W0!15), xS))))),
% 18.50/25.00 inference(unit_resolution,[status(thm)],[38, 37])).
% 18.50/25.00 tff(40,plain,
% 18.50/25.00 (~((~aInteger0(W0!15)) | (~aElementOf0(W0!15, tptp_fun_W1_18(W0!15))) | (~aElementOf0(tptp_fun_W1_18(W0!15), xS)))),
% 18.50/25.00 inference(unit_resolution,[status(thm)],[39, 29])).
% 18.50/25.00 tff(41,plain,
% 18.50/25.00 (((~aInteger0(W0!15)) | (~aElementOf0(W0!15, tptp_fun_W1_18(W0!15))) | (~aElementOf0(tptp_fun_W1_18(W0!15), xS))) | aElementOf0(tptp_fun_W1_18(W0!15), xS)),
% 18.50/25.00 inference(tautology,[status(thm)],[])).
% 18.50/25.00 tff(42,plain,
% 18.50/25.00 (aElementOf0(tptp_fun_W1_18(W0!15), xS)),
% 18.50/25.00 inference(unit_resolution,[status(thm)],[41, 40])).
% 18.50/25.00 tff(43,plain,
% 18.50/25.00 (^[W0: $i] : rewrite(((~aElementOf0(W0, xS)) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, cS1395)) | (~isOpen0(W0)) | (~aSet0(cS1395)) | (~![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | (~((tptp_fun_W2_13(W1, W0) = sz00) | (~aInteger0(tptp_fun_W2_13(W1, W0))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~((~aInteger0(W3)) | (~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0))) | (~aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1)))) | (~aInteger0(tptp_fun_W4_14(W3, W1, W0))) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), tptp_fun_W4_14(W3, W1, W0)) = sdtpldt0(W3, smndt0(W1)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0))) | (~(aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1))) | sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0)) | (~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), W4) = sdtpldt0(W3, smndt0(W1))))))))))))) | (~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | aElementOf0(W3, W0))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)), W0))))))))) <=> ((~aElementOf0(W0, xS)) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, cS1395)) | (~isOpen0(W0)) | (~aSet0(cS1395)) | (~![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | (~((tptp_fun_W2_13(W1, W0) = sz00) | (~aInteger0(tptp_fun_W2_13(W1, W0))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)), W0)) | (~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | aElementOf0(W3, W0))) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~((~aInteger0(W3)) | (~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0))) | (~aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1)))) | (~aInteger0(tptp_fun_W4_14(W3, W1, W0))) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), tptp_fun_W4_14(W3, W1, W0)) = sdtpldt0(W3, smndt0(W1)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0))) | (~(aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1))) | sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0)) | (~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), W4) = sdtpldt0(W3, smndt0(W1)))))))))))))))))))))),
% 18.50/25.00 inference(bind,[status(th)],[])).
% 18.50/25.00 tff(44,plain,
% 18.50/25.00 (![W0: $i] : ((~aElementOf0(W0, xS)) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, cS1395)) | (~isOpen0(W0)) | (~aSet0(cS1395)) | (~![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | (~((tptp_fun_W2_13(W1, W0) = sz00) | (~aInteger0(tptp_fun_W2_13(W1, W0))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~((~aInteger0(W3)) | (~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0))) | (~aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1)))) | (~aInteger0(tptp_fun_W4_14(W3, W1, W0))) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), tptp_fun_W4_14(W3, W1, W0)) = sdtpldt0(W3, smndt0(W1)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0))) | (~(aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1))) | sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0)) | (~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), W4) = sdtpldt0(W3, smndt0(W1))))))))))))) | (~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | aElementOf0(W3, W0))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)), W0))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, xS)) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, cS1395)) | (~isOpen0(W0)) | (~aSet0(cS1395)) | (~![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | (~((tptp_fun_W2_13(W1, W0) = sz00) | (~aInteger0(tptp_fun_W2_13(W1, W0))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)), W0)) | (~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | aElementOf0(W3, W0))) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~((~aInteger0(W3)) | (~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0))) | (~aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1)))) | (~aInteger0(tptp_fun_W4_14(W3, W1, W0))) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), tptp_fun_W4_14(W3, W1, W0)) = sdtpldt0(W3, smndt0(W1)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0))) | (~(aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1))) | sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0)) | (~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), W4) = sdtpldt0(W3, smndt0(W1))))))))))))))))))))),
% 18.50/25.00 inference(quant_intro,[status(thm)],[43])).
% 18.50/25.00 tff(45,plain,
% 18.50/25.00 (^[W0: $i] : refl(((~aElementOf0(W0, xS)) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, cS1395)) | (~isOpen0(W0)) | (~aSet0(cS1395)) | (~![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | (~((tptp_fun_W2_13(W1, W0) = sz00) | (~aInteger0(tptp_fun_W2_13(W1, W0))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~((~aInteger0(W3)) | (~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0))) | (~aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1)))) | (~aInteger0(tptp_fun_W4_14(W3, W1, W0))) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), tptp_fun_W4_14(W3, W1, W0)) = sdtpldt0(W3, smndt0(W1)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0))) | (~(aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1))) | sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0)) | (~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), W4) = sdtpldt0(W3, smndt0(W1))))))))))))) | (~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | aElementOf0(W3, W0))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)), W0))))))))) <=> ((~aElementOf0(W0, xS)) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, cS1395)) | (~isOpen0(W0)) | (~aSet0(cS1395)) | (~![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | (~((tptp_fun_W2_13(W1, W0) = sz00) | (~aInteger0(tptp_fun_W2_13(W1, W0))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~((~aInteger0(W3)) | (~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0))) | (~aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1)))) | (~aInteger0(tptp_fun_W4_14(W3, W1, W0))) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), tptp_fun_W4_14(W3, W1, W0)) = sdtpldt0(W3, smndt0(W1)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0))) | (~(aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1))) | sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0)) | (~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), W4) = sdtpldt0(W3, smndt0(W1))))))))))))) | (~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | aElementOf0(W3, W0))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)), W0))))))))))),
% 18.50/25.00 inference(bind,[status(th)],[])).
% 18.50/25.00 tff(46,plain,
% 18.50/25.00 (![W0: $i] : ((~aElementOf0(W0, xS)) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, cS1395)) | (~isOpen0(W0)) | (~aSet0(cS1395)) | (~![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | (~((tptp_fun_W2_13(W1, W0) = sz00) | (~aInteger0(tptp_fun_W2_13(W1, W0))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~((~aInteger0(W3)) | (~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0))) | (~aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1)))) | (~aInteger0(tptp_fun_W4_14(W3, W1, W0))) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), tptp_fun_W4_14(W3, W1, W0)) = sdtpldt0(W3, smndt0(W1)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0))) | (~(aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1))) | sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0)) | (~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), W4) = sdtpldt0(W3, smndt0(W1))))))))))))) | (~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | aElementOf0(W3, W0))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)), W0))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, xS)) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, cS1395)) | (~isOpen0(W0)) | (~aSet0(cS1395)) | (~![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | (~((tptp_fun_W2_13(W1, W0) = sz00) | (~aInteger0(tptp_fun_W2_13(W1, W0))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~((~aInteger0(W3)) | (~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0))) | (~aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1)))) | (~aInteger0(tptp_fun_W4_14(W3, W1, W0))) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), tptp_fun_W4_14(W3, W1, W0)) = sdtpldt0(W3, smndt0(W1)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0))) | (~(aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1))) | sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0)) | (~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), W4) = sdtpldt0(W3, smndt0(W1))))))))))))) | (~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | aElementOf0(W3, W0))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)), W0)))))))))),
% 18.50/25.00 inference(quant_intro,[status(thm)],[45])).
% 18.50/25.00 tff(47,plain,
% 18.50/25.00 (^[W0: $i] : rewrite(((~aElementOf0(W0, xS)) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, cS1395)) | (~isOpen0(W0)) | (~aSet0(cS1395)) | (~![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | (~((tptp_fun_W2_13(W1, W0) = sz00) | (~aInteger0(tptp_fun_W2_13(W1, W0))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~((~aInteger0(W3)) | (~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0))) | (~aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1)))) | (~aInteger0(tptp_fun_W4_14(W3, W1, W0))) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), tptp_fun_W4_14(W3, W1, W0)) = sdtpldt0(W3, smndt0(W1)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0))) | (~(aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1))) | sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0)) | (~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), W4) = sdtpldt0(W3, smndt0(W1))))))))))))) | (~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | aElementOf0(W3, W0))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)), W0))))))))) <=> ((~aElementOf0(W0, xS)) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, cS1395)) | (~isOpen0(W0)) | (~aSet0(cS1395)) | (~![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | (~((tptp_fun_W2_13(W1, W0) = sz00) | (~aInteger0(tptp_fun_W2_13(W1, W0))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~((~aInteger0(W3)) | (~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0))) | (~aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1)))) | (~aInteger0(tptp_fun_W4_14(W3, W1, W0))) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), tptp_fun_W4_14(W3, W1, W0)) = sdtpldt0(W3, smndt0(W1)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0))) | (~(aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1))) | sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0)) | (~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), W4) = sdtpldt0(W3, smndt0(W1))))))))))))) | (~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | aElementOf0(W3, W0))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)), W0))))))))))),
% 18.50/25.00 inference(bind,[status(th)],[])).
% 18.50/25.00 tff(48,plain,
% 18.50/25.00 (![W0: $i] : ((~aElementOf0(W0, xS)) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, cS1395)) | (~isOpen0(W0)) | (~aSet0(cS1395)) | (~![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | (~((tptp_fun_W2_13(W1, W0) = sz00) | (~aInteger0(tptp_fun_W2_13(W1, W0))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~((~aInteger0(W3)) | (~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0))) | (~aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1)))) | (~aInteger0(tptp_fun_W4_14(W3, W1, W0))) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), tptp_fun_W4_14(W3, W1, W0)) = sdtpldt0(W3, smndt0(W1)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0))) | (~(aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1))) | sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0)) | (~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), W4) = sdtpldt0(W3, smndt0(W1))))))))))))) | (~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | aElementOf0(W3, W0))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)), W0))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, xS)) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, cS1395)) | (~isOpen0(W0)) | (~aSet0(cS1395)) | (~![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | (~((tptp_fun_W2_13(W1, W0) = sz00) | (~aInteger0(tptp_fun_W2_13(W1, W0))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~((~aInteger0(W3)) | (~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0))) | (~aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1)))) | (~aInteger0(tptp_fun_W4_14(W3, W1, W0))) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), tptp_fun_W4_14(W3, W1, W0)) = sdtpldt0(W3, smndt0(W1)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0))) | (~(aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1))) | sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0)) | (~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), W4) = sdtpldt0(W3, smndt0(W1))))))))))))) | (~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | aElementOf0(W3, W0))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)), W0)))))))))),
% 18.50/25.00 inference(quant_intro,[status(thm)],[47])).
% 18.50/25.00 tff(49,plain,
% 18.50/25.00 (![W0: $i] : ((~aElementOf0(W0, xS)) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, cS1395)) | (~isOpen0(W0)) | (~aSet0(cS1395)) | (~![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | (~((tptp_fun_W2_13(W1, W0) = sz00) | (~aInteger0(tptp_fun_W2_13(W1, W0))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~((~aInteger0(W3)) | (~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0))) | (~aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1)))) | (~aInteger0(tptp_fun_W4_14(W3, W1, W0))) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), tptp_fun_W4_14(W3, W1, W0)) = sdtpldt0(W3, smndt0(W1)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0))) | (~(aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1))) | sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0)) | (~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), W4) = sdtpldt0(W3, smndt0(W1))))))))))))) | (~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | aElementOf0(W3, W0))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)), W0))))))))) <=> ![W0: $i] : ((~aElementOf0(W0, xS)) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, cS1395)) | (~isOpen0(W0)) | (~aSet0(cS1395)) | (~![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | (~((tptp_fun_W2_13(W1, W0) = sz00) | (~aInteger0(tptp_fun_W2_13(W1, W0))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~((~aInteger0(W3)) | (~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0))) | (~aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1)))) | (~aInteger0(tptp_fun_W4_14(W3, W1, W0))) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), tptp_fun_W4_14(W3, W1, W0)) = sdtpldt0(W3, smndt0(W1)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0))) | (~(aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1))) | sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0)) | (~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), W4) = sdtpldt0(W3, smndt0(W1))))))))))))) | (~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | aElementOf0(W3, W0))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)), W0)))))))))),
% 18.50/25.00 inference(transitivity,[status(thm)],[48, 46])).
% 18.50/25.00 tff(50,plain,
% 18.50/25.00 (^[W0: $i] : rewrite(((~aElementOf0(W0, xS)) | (aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1)) & aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395)) & aSubsetOf0(W0, cS1395) & ![W1: $i] : ((~aElementOf0(W1, W0)) | (aInteger0(tptp_fun_W2_13(W1, W0)) & (~(tptp_fun_W2_13(W1, W0) = sz00)) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0))) & ![W3: $i] : (((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (aInteger0(W3) & aInteger0(tptp_fun_W4_14(W3, W1, W0)) & (sdtasdt0(tptp_fun_W2_13(W1, W0), tptp_fun_W4_14(W3, W1, W0)) = sdtpldt0(W3, smndt0(W1))) & aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1))) & sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0)))) & ((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0))) | ((~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0))) & (~aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1)))) & ![W4: $i] : (~(aInteger0(W4) & (sdtasdt0(tptp_fun_W2_13(W1, W0), W4) = sdtpldt0(W3, smndt0(W1)))))))) & ![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | aElementOf0(W3, W0)) & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)), W0))) & isOpen0(W0))) <=> ((~aElementOf0(W0, xS)) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, cS1395)) | (~isOpen0(W0)) | (~aSet0(cS1395)) | (~![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | (~((tptp_fun_W2_13(W1, W0) = sz00) | (~aInteger0(tptp_fun_W2_13(W1, W0))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~((~aInteger0(W3)) | (~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0))) | (~aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1)))) | (~aInteger0(tptp_fun_W4_14(W3, W1, W0))) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), tptp_fun_W4_14(W3, W1, W0)) = sdtpldt0(W3, smndt0(W1)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0))) | (~(aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1))) | sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0)) | (~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), W4) = sdtpldt0(W3, smndt0(W1))))))))))))) | (~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | aElementOf0(W3, W0))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)), W0))))))))))),
% 18.50/25.00 inference(bind,[status(th)],[])).
% 18.50/25.00 tff(51,plain,
% 18.50/25.00 (![W0: $i] : ((~aElementOf0(W0, xS)) | (aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1)) & aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395)) & aSubsetOf0(W0, cS1395) & ![W1: $i] : ((~aElementOf0(W1, W0)) | (aInteger0(tptp_fun_W2_13(W1, W0)) & (~(tptp_fun_W2_13(W1, W0) = sz00)) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0))) & ![W3: $i] : (((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (aInteger0(W3) & aInteger0(tptp_fun_W4_14(W3, W1, W0)) & (sdtasdt0(tptp_fun_W2_13(W1, W0), tptp_fun_W4_14(W3, W1, W0)) = sdtpldt0(W3, smndt0(W1))) & aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1))) & sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0)))) & ((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0))) | ((~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0))) & (~aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1)))) & ![W4: $i] : (~(aInteger0(W4) & (sdtasdt0(tptp_fun_W2_13(W1, W0), W4) = sdtpldt0(W3, smndt0(W1)))))))) & ![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | aElementOf0(W3, W0)) & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)), W0))) & isOpen0(W0))) <=> ![W0: $i] : ((~aElementOf0(W0, xS)) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, cS1395)) | (~isOpen0(W0)) | (~aSet0(cS1395)) | (~![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | (~((tptp_fun_W2_13(W1, W0) = sz00) | (~aInteger0(tptp_fun_W2_13(W1, W0))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~((~aInteger0(W3)) | (~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0))) | (~aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1)))) | (~aInteger0(tptp_fun_W4_14(W3, W1, W0))) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), tptp_fun_W4_14(W3, W1, W0)) = sdtpldt0(W3, smndt0(W1)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0))) | (~(aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1))) | sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0)) | (~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), W4) = sdtpldt0(W3, smndt0(W1))))))))))))) | (~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | aElementOf0(W3, W0))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)), W0)))))))))),
% 18.50/25.00 inference(quant_intro,[status(thm)],[50])).
% 18.50/25.00 tff(52,plain,
% 18.50/25.00 (^[W0: $i] : rewrite(((~aElementOf0(W0, xS)) | (aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1)) & aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395)) & aSubsetOf0(W0, cS1395) & ![W1: $i] : ((~aElementOf0(W1, W0)) | (aInteger0(tptp_fun_W2_13(W1, W0)) & (~(tptp_fun_W2_13(W1, W0) = sz00)) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0))) & ![W3: $i] : (((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (aInteger0(W3) & (aInteger0(tptp_fun_W4_14(W3, W1, W0)) & (sdtasdt0(tptp_fun_W2_13(W1, W0), tptp_fun_W4_14(W3, W1, W0)) = sdtpldt0(W3, smndt0(W1)))) & aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1))) & sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0)))) & (((~aInteger0(W3)) | ((~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0))) & (~aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1)))) & ![W4: $i] : (~(aInteger0(W4) & (sdtasdt0(tptp_fun_W2_13(W1, W0), W4) = sdtpldt0(W3, smndt0(W1))))))) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0))))) & ![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | aElementOf0(W3, W0)) & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)), W0))) & isOpen0(W0))) <=> ((~aElementOf0(W0, xS)) | (aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1)) & aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395)) & aSubsetOf0(W0, cS1395) & ![W1: $i] : ((~aElementOf0(W1, W0)) | (aInteger0(tptp_fun_W2_13(W1, W0)) & (~(tptp_fun_W2_13(W1, W0) = sz00)) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0))) & ![W3: $i] : (((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (aInteger0(W3) & aInteger0(tptp_fun_W4_14(W3, W1, W0)) & (sdtasdt0(tptp_fun_W2_13(W1, W0), tptp_fun_W4_14(W3, W1, W0)) = sdtpldt0(W3, smndt0(W1))) & aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1))) & sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0)))) & ((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0))) | ((~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0))) & (~aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1)))) & ![W4: $i] : (~(aInteger0(W4) & (sdtasdt0(tptp_fun_W2_13(W1, W0), W4) = sdtpldt0(W3, smndt0(W1)))))))) & ![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | aElementOf0(W3, W0)) & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)), W0))) & isOpen0(W0))))),
% 18.50/25.00 inference(bind,[status(th)],[])).
% 18.50/25.00 tff(53,plain,
% 18.50/25.00 (![W0: $i] : ((~aElementOf0(W0, xS)) | (aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1)) & aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395)) & aSubsetOf0(W0, cS1395) & ![W1: $i] : ((~aElementOf0(W1, W0)) | (aInteger0(tptp_fun_W2_13(W1, W0)) & (~(tptp_fun_W2_13(W1, W0) = sz00)) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0))) & ![W3: $i] : (((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (aInteger0(W3) & (aInteger0(tptp_fun_W4_14(W3, W1, W0)) & (sdtasdt0(tptp_fun_W2_13(W1, W0), tptp_fun_W4_14(W3, W1, W0)) = sdtpldt0(W3, smndt0(W1)))) & aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1))) & sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0)))) & (((~aInteger0(W3)) | ((~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0))) & (~aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1)))) & ![W4: $i] : (~(aInteger0(W4) & (sdtasdt0(tptp_fun_W2_13(W1, W0), W4) = sdtpldt0(W3, smndt0(W1))))))) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0))))) & ![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | aElementOf0(W3, W0)) & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)), W0))) & isOpen0(W0))) <=> ![W0: $i] : ((~aElementOf0(W0, xS)) | (aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1)) & aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395)) & aSubsetOf0(W0, cS1395) & ![W1: $i] : ((~aElementOf0(W1, W0)) | (aInteger0(tptp_fun_W2_13(W1, W0)) & (~(tptp_fun_W2_13(W1, W0) = sz00)) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0))) & ![W3: $i] : (((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (aInteger0(W3) & aInteger0(tptp_fun_W4_14(W3, W1, W0)) & (sdtasdt0(tptp_fun_W2_13(W1, W0), tptp_fun_W4_14(W3, W1, W0)) = sdtpldt0(W3, smndt0(W1))) & aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1))) & sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0)))) & ((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0))) | ((~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0))) & (~aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1)))) & ![W4: $i] : (~(aInteger0(W4) & (sdtasdt0(tptp_fun_W2_13(W1, W0), W4) = sdtpldt0(W3, smndt0(W1)))))))) & ![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | aElementOf0(W3, W0)) & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)), W0))) & isOpen0(W0)))),
% 18.50/25.00 inference(quant_intro,[status(thm)],[52])).
% 18.50/25.00 tff(54,plain,
% 18.50/25.00 (![W0: $i] : ((~aElementOf0(W0, xS)) | (aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1)) & aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395)) & aSubsetOf0(W0, cS1395) & ![W1: $i] : ((~aElementOf0(W1, W0)) | ?[W2: $i] : (aInteger0(W2) & (~(W2 = sz00)) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2)) & ![W3: $i] : (((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | (aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((~(aInteger0(W3) & (sdteqdtlpzmzozddtrp0(W3, W1, W2) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) | ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))))) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)))) & ![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | aElementOf0(W3, W0)) & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, W2), W0))) & isOpen0(W0))) <=> ![W0: $i] : ((~aElementOf0(W0, xS)) | (aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1)) & aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395)) & aSubsetOf0(W0, cS1395) & ![W1: $i] : ((~aElementOf0(W1, W0)) | ?[W2: $i] : (aInteger0(W2) & (~(W2 = sz00)) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2)) & ![W3: $i] : (((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | (aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((~(aInteger0(W3) & (sdteqdtlpzmzozddtrp0(W3, W1, W2) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) | ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))))) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)))) & ![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | aElementOf0(W3, W0)) & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, W2), W0))) & isOpen0(W0)))),
% 18.50/25.01 inference(rewrite,[status(thm)],[])).
% 18.50/25.01 tff(55,plain,
% 18.50/25.01 (^[W0: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) <=> (aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1)))), (((aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) & aSet0(W0)) <=> ((aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) & aSet0(W0)))), rewrite(((aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) & aSet0(W0)) <=> (aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1)) & aSet0(W0))), (((aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) & aSet0(W0)) <=> (aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1)) & aSet0(W0)))), quant_intro(proof_bind(^[W1: $i] : rewrite((aElementOf0(W1, W0) => aElementOf0(W1, cS1395)) <=> ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395)))), (![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, cS1395)) <=> ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395)))), ((((aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) & aSet0(W0)) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, cS1395))) <=> ((aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1)) & aSet0(W0)) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395))))), rewrite(((aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1)) & aSet0(W0)) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395))) <=> (aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1)) & aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395)))), ((((aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) & aSet0(W0)) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, cS1395))) <=> (aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1)) & aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395))))), (((((aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) & aSet0(W0)) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, cS1395))) & aSubsetOf0(W0, cS1395)) <=> ((aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1)) & aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395))) & aSubsetOf0(W0, cS1395)))), rewrite(((aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1)) & aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395))) & aSubsetOf0(W0, cS1395)) <=> (aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1)) & aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395)) & aSubsetOf0(W0, cS1395))), (((((aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) & aSet0(W0)) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, cS1395))) & aSubsetOf0(W0, cS1395)) <=> (aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1)) & aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395)) & aSubsetOf0(W0, cS1395)))), quant_intro(proof_bind(^[W1: $i] : trans(monotonicity(quant_intro(proof_bind(^[W2: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((aInteger0(W2) & (~(W2 = sz00))) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2))) <=> (aInteger0(W2) & (~(W2 = sz00)) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2)))), quant_intro(proof_bind(^[W3: $i] : rewrite(((aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)) => (((aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1)))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((aInteger0(W3) & ((?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1)))) | sdteqdtlpzmzozddtrp0(W3, W1, W2))) => aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)))) <=> (((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | (aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((~(aInteger0(W3) & (sdteqdtlpzmzozddtrp0(W3, W1, W2) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) | ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))))) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)))))), (![W3: $i] : ((aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)) => (((aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1)))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((aInteger0(W3) & ((?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1)))) | sdteqdtlpzmzozddtrp0(W3, W1, W2))) => aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)))) <=> ![W3: $i] : (((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | (aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((~(aInteger0(W3) & (sdteqdtlpzmzozddtrp0(W3, W1, W2) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) | ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))))) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)))))), ((((aInteger0(W2) & (~(W2 = sz00))) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2))) & ![W3: $i] : ((aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)) => (((aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1)))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((aInteger0(W3) & ((?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1)))) | sdteqdtlpzmzozddtrp0(W3, W1, W2))) => aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))))) <=> ((aInteger0(W2) & (~(W2 = sz00)) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2))) & ![W3: $i] : (((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | (aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((~(aInteger0(W3) & (sdteqdtlpzmzozddtrp0(W3, W1, W2) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) | ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))))) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))))))), rewrite(((aInteger0(W2) & (~(W2 = sz00)) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2))) & ![W3: $i] : (((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | (aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((~(aInteger0(W3) & (sdteqdtlpzmzozddtrp0(W3, W1, W2) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) | ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))))) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))))) <=> (aInteger0(W2) & (~(W2 = sz00)) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2)) & ![W3: $i] : (((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | (aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((~(aInteger0(W3) & (sdteqdtlpzmzozddtrp0(W3, W1, W2) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) | ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))))) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)))))), ((((aInteger0(W2) & (~(W2 = sz00))) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2))) & ![W3: $i] : ((aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)) => (((aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1)))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((aInteger0(W3) & ((?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1)))) | sdteqdtlpzmzozddtrp0(W3, W1, W2))) => aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))))) <=> (aInteger0(W2) & (~(W2 = sz00)) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2)) & ![W3: $i] : (((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | (aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((~(aInteger0(W3) & (sdteqdtlpzmzozddtrp0(W3, W1, W2) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) | ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))))) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))))))), quant_intro(proof_bind(^[W3: $i] : rewrite((aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)) => aElementOf0(W3, W0)) <=> ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | aElementOf0(W3, W0)))), (![W3: $i] : (aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)) => aElementOf0(W3, W0)) <=> ![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | aElementOf0(W3, W0)))), (((((aInteger0(W2) & (~(W2 = sz00))) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2))) & ![W3: $i] : ((aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)) => (((aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1)))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((aInteger0(W3) & ((?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1)))) | sdteqdtlpzmzozddtrp0(W3, W1, W2))) => aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))))) & ![W3: $i] : (aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)) => aElementOf0(W3, W0))) <=> ((aInteger0(W2) & (~(W2 = sz00)) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2)) & ![W3: $i] : (((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | (aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((~(aInteger0(W3) & (sdteqdtlpzmzozddtrp0(W3, W1, W2) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) | ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))))) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))))) & ![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | aElementOf0(W3, W0))))), rewrite(((aInteger0(W2) & (~(W2 = sz00)) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2)) & ![W3: $i] : (((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | (aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((~(aInteger0(W3) & (sdteqdtlpzmzozddtrp0(W3, W1, W2) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) | ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))))) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))))) & ![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | aElementOf0(W3, W0))) <=> (aInteger0(W2) & (~(W2 = sz00)) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2)) & ![W3: $i] : (((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | (aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((~(aInteger0(W3) & (sdteqdtlpzmzozddtrp0(W3, W1, W2) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) | ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))))) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)))) & ![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | aElementOf0(W3, W0)))), (((((aInteger0(W2) & (~(W2 = sz00))) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2))) & ![W3: $i] : ((aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)) => (((aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1)))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((aInteger0(W3) & ((?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1)))) | sdteqdtlpzmzozddtrp0(W3, W1, W2))) => aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))))) & ![W3: $i] : (aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)) => aElementOf0(W3, W0))) <=> (aInteger0(W2) & (~(W2 = sz00)) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2)) & ![W3: $i] : (((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | (aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((~(aInteger0(W3) & (sdteqdtlpzmzozddtrp0(W3, W1, W2) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) | ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))))) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)))) & ![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | aElementOf0(W3, W0))))), ((((((aInteger0(W2) & (~(W2 = sz00))) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2))) & ![W3: $i] : ((aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)) => (((aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1)))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((aInteger0(W3) & ((?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1)))) | sdteqdtlpzmzozddtrp0(W3, W1, W2))) => aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))))) & ![W3: $i] : (aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)) => aElementOf0(W3, W0))) & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, W2), W0)) <=> ((aInteger0(W2) & (~(W2 = sz00)) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2)) & ![W3: $i] : (((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | (aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((~(aInteger0(W3) & (sdteqdtlpzmzozddtrp0(W3, W1, W2) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) | ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))))) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)))) & ![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | aElementOf0(W3, W0))) & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, W2), W0)))), rewrite(((aInteger0(W2) & (~(W2 = sz00)) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2)) & ![W3: $i] : (((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | (aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((~(aInteger0(W3) & (sdteqdtlpzmzozddtrp0(W3, W1, W2) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) | ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))))) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)))) & ![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | aElementOf0(W3, W0))) & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, W2), W0)) <=> (aInteger0(W2) & (~(W2 = sz00)) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2)) & ![W3: $i] : (((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | (aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((~(aInteger0(W3) & (sdteqdtlpzmzozddtrp0(W3, W1, W2) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) | ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))))) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)))) & ![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | aElementOf0(W3, W0)) & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, W2), W0))), ((((((aInteger0(W2) & (~(W2 = sz00))) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2))) & ![W3: $i] : ((aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)) => (((aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1)))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((aInteger0(W3) & ((?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1)))) | sdteqdtlpzmzozddtrp0(W3, W1, W2))) => aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))))) & ![W3: $i] : (aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)) => aElementOf0(W3, W0))) & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, W2), W0)) <=> (aInteger0(W2) & (~(W2 = sz00)) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2)) & ![W3: $i] : (((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | (aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((~(aInteger0(W3) & (sdteqdtlpzmzozddtrp0(W3, W1, W2) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) | ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))))) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)))) & ![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | aElementOf0(W3, W0)) & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, W2), W0))))), (?[W2: $i] : (((((aInteger0(W2) & (~(W2 = sz00))) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2))) & ![W3: $i] : ((aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)) => (((aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1)))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((aInteger0(W3) & ((?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1)))) | sdteqdtlpzmzozddtrp0(W3, W1, W2))) => aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))))) & ![W3: $i] : (aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)) => aElementOf0(W3, W0))) & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, W2), W0)) <=> ?[W2: $i] : (aInteger0(W2) & (~(W2 = sz00)) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2)) & ![W3: $i] : (((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | (aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((~(aInteger0(W3) & (sdteqdtlpzmzozddtrp0(W3, W1, W2) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) | ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))))) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)))) & ![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | aElementOf0(W3, W0)) & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, W2), W0)))), ((aElementOf0(W1, W0) => ?[W2: $i] : (((((aInteger0(W2) & (~(W2 = sz00))) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2))) & ![W3: $i] : ((aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)) => (((aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1)))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((aInteger0(W3) & ((?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1)))) | sdteqdtlpzmzozddtrp0(W3, W1, W2))) => aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))))) & ![W3: $i] : (aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)) => aElementOf0(W3, W0))) & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, W2), W0))) <=> (aElementOf0(W1, W0) => ?[W2: $i] : (aInteger0(W2) & (~(W2 = sz00)) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2)) & ![W3: $i] : (((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | (aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((~(aInteger0(W3) & (sdteqdtlpzmzozddtrp0(W3, W1, W2) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) | ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))))) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)))) & ![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | aElementOf0(W3, W0)) & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, W2), W0))))), rewrite((aElementOf0(W1, W0) => ?[W2: $i] : (aInteger0(W2) & (~(W2 = sz00)) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2)) & ![W3: $i] : (((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | (aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((~(aInteger0(W3) & (sdteqdtlpzmzozddtrp0(W3, W1, W2) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) | ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))))) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)))) & ![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | aElementOf0(W3, W0)) & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, W2), W0))) <=> ((~aElementOf0(W1, W0)) | ?[W2: $i] : (aInteger0(W2) & (~(W2 = sz00)) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2)) & ![W3: $i] : (((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | (aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((~(aInteger0(W3) & (sdteqdtlpzmzozddtrp0(W3, W1, W2) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) | ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))))) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)))) & ![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | aElementOf0(W3, W0)) & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, W2), W0)))), ((aElementOf0(W1, W0) => ?[W2: $i] : (((((aInteger0(W2) & (~(W2 = sz00))) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2))) & ![W3: $i] : ((aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)) => (((aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1)))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((aInteger0(W3) & ((?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1)))) | sdteqdtlpzmzozddtrp0(W3, W1, W2))) => aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))))) & ![W3: $i] : (aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)) => aElementOf0(W3, W0))) & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, W2), W0))) <=> ((~aElementOf0(W1, W0)) | ?[W2: $i] : (aInteger0(W2) & (~(W2 = sz00)) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2)) & ![W3: $i] : (((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | (aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((~(aInteger0(W3) & (sdteqdtlpzmzozddtrp0(W3, W1, W2) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) | ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))))) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)))) & ![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | aElementOf0(W3, W0)) & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, W2), W0)))))), (![W1: $i] : (aElementOf0(W1, W0) => ?[W2: $i] : (((((aInteger0(W2) & (~(W2 = sz00))) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2))) & ![W3: $i] : ((aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)) => (((aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1)))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((aInteger0(W3) & ((?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1)))) | sdteqdtlpzmzozddtrp0(W3, W1, W2))) => aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))))) & ![W3: $i] : (aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)) => aElementOf0(W3, W0))) & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, W2), W0))) <=> ![W1: $i] : ((~aElementOf0(W1, W0)) | ?[W2: $i] : (aInteger0(W2) & (~(W2 = sz00)) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2)) & ![W3: $i] : (((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | (aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((~(aInteger0(W3) & (sdteqdtlpzmzozddtrp0(W3, W1, W2) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) | ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))))) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)))) & ![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | aElementOf0(W3, W0)) & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, W2), W0))))), ((((((aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) & aSet0(W0)) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, cS1395))) & aSubsetOf0(W0, cS1395)) & ![W1: $i] : (aElementOf0(W1, W0) => ?[W2: $i] : (((((aInteger0(W2) & (~(W2 = sz00))) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2))) & ![W3: $i] : ((aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)) => (((aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1)))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((aInteger0(W3) & ((?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1)))) | sdteqdtlpzmzozddtrp0(W3, W1, W2))) => aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))))) & ![W3: $i] : (aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)) => aElementOf0(W3, W0))) & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, W2), W0)))) <=> ((aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1)) & aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395)) & aSubsetOf0(W0, cS1395)) & ![W1: $i] : ((~aElementOf0(W1, W0)) | ?[W2: $i] : (aInteger0(W2) & (~(W2 = sz00)) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2)) & ![W3: $i] : (((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | (aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((~(aInteger0(W3) & (sdteqdtlpzmzozddtrp0(W3, W1, W2) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) | ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))))) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)))) & ![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | aElementOf0(W3, W0)) & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, W2), W0)))))), rewrite(((aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1)) & aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395)) & aSubsetOf0(W0, cS1395)) & ![W1: $i] : ((~aElementOf0(W1, W0)) | ?[W2: $i] : (aInteger0(W2) & (~(W2 = sz00)) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2)) & ![W3: $i] : (((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | (aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((~(aInteger0(W3) & (sdteqdtlpzmzozddtrp0(W3, W1, W2) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) | ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))))) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)))) & ![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | aElementOf0(W3, W0)) & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, W2), W0)))) <=> (aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1)) & aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395)) & aSubsetOf0(W0, cS1395) & ![W1: $i] : ((~aElementOf0(W1, W0)) | ?[W2: $i] : (aInteger0(W2) & (~(W2 = sz00)) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2)) & ![W3: $i] : (((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | (aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((~(aInteger0(W3) & (sdteqdtlpzmzozddtrp0(W3, W1, W2) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) | ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))))) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)))) & ![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | aElementOf0(W3, W0)) & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, W2), W0))))), ((((((aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) & aSet0(W0)) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, cS1395))) & aSubsetOf0(W0, cS1395)) & ![W1: $i] : (aElementOf0(W1, W0) => ?[W2: $i] : (((((aInteger0(W2) & (~(W2 = sz00))) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2))) & ![W3: $i] : ((aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)) => (((aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1)))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((aInteger0(W3) & ((?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1)))) | sdteqdtlpzmzozddtrp0(W3, W1, W2))) => aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))))) & ![W3: $i] : (aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)) => aElementOf0(W3, W0))) & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, W2), W0)))) <=> (aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1)) & aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395)) & aSubsetOf0(W0, cS1395) & ![W1: $i] : ((~aElementOf0(W1, W0)) | ?[W2: $i] : (aInteger0(W2) & (~(W2 = sz00)) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2)) & ![W3: $i] : (((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | (aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((~(aInteger0(W3) & (sdteqdtlpzmzozddtrp0(W3, W1, W2) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) | ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))))) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)))) & ![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | aElementOf0(W3, W0)) & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, W2), W0)))))), (((((((aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) & aSet0(W0)) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, cS1395))) & aSubsetOf0(W0, cS1395)) & ![W1: $i] : (aElementOf0(W1, W0) => ?[W2: $i] : (((((aInteger0(W2) & (~(W2 = sz00))) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2))) & ![W3: $i] : ((aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)) => (((aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1)))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((aInteger0(W3) & ((?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1)))) | sdteqdtlpzmzozddtrp0(W3, W1, W2))) => aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))))) & ![W3: $i] : (aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)) => aElementOf0(W3, W0))) & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, W2), W0)))) & isOpen0(W0)) <=> ((aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1)) & aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395)) & aSubsetOf0(W0, cS1395) & ![W1: $i] : ((~aElementOf0(W1, W0)) | ?[W2: $i] : (aInteger0(W2) & (~(W2 = sz00)) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2)) & ![W3: $i] : (((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | (aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((~(aInteger0(W3) & (sdteqdtlpzmzozddtrp0(W3, W1, W2) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) | ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))))) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)))) & ![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | aElementOf0(W3, W0)) & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, W2), W0)))) & isOpen0(W0)))), rewrite(((aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1)) & aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395)) & aSubsetOf0(W0, cS1395) & ![W1: $i] : ((~aElementOf0(W1, W0)) | ?[W2: $i] : (aInteger0(W2) & (~(W2 = sz00)) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2)) & ![W3: $i] : (((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | (aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((~(aInteger0(W3) & (sdteqdtlpzmzozddtrp0(W3, W1, W2) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) | ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))))) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)))) & ![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | aElementOf0(W3, W0)) & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, W2), W0)))) & isOpen0(W0)) <=> (aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1)) & aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395)) & aSubsetOf0(W0, cS1395) & ![W1: $i] : ((~aElementOf0(W1, W0)) | ?[W2: $i] : (aInteger0(W2) & (~(W2 = sz00)) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2)) & ![W3: $i] : (((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | (aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((~(aInteger0(W3) & (sdteqdtlpzmzozddtrp0(W3, W1, W2) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) | ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))))) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)))) & ![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | aElementOf0(W3, W0)) & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, W2), W0))) & isOpen0(W0))), (((((((aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) & aSet0(W0)) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, cS1395))) & aSubsetOf0(W0, cS1395)) & ![W1: $i] : (aElementOf0(W1, W0) => ?[W2: $i] : (((((aInteger0(W2) & (~(W2 = sz00))) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2))) & ![W3: $i] : ((aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)) => (((aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1)))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((aInteger0(W3) & ((?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1)))) | sdteqdtlpzmzozddtrp0(W3, W1, W2))) => aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))))) & ![W3: $i] : (aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)) => aElementOf0(W3, W0))) & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, W2), W0)))) & isOpen0(W0)) <=> (aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1)) & aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395)) & aSubsetOf0(W0, cS1395) & ![W1: $i] : ((~aElementOf0(W1, W0)) | ?[W2: $i] : (aInteger0(W2) & (~(W2 = sz00)) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2)) & ![W3: $i] : (((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | (aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((~(aInteger0(W3) & (sdteqdtlpzmzozddtrp0(W3, W1, W2) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) | ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))))) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)))) & ![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | aElementOf0(W3, W0)) & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, W2), W0))) & isOpen0(W0)))), ((aElementOf0(W0, xS) => ((((((aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) & aSet0(W0)) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, cS1395))) & aSubsetOf0(W0, cS1395)) & ![W1: $i] : (aElementOf0(W1, W0) => ?[W2: $i] : (((((aInteger0(W2) & (~(W2 = sz00))) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2))) & ![W3: $i] : ((aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)) => (((aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1)))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((aInteger0(W3) & ((?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1)))) | sdteqdtlpzmzozddtrp0(W3, W1, W2))) => aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))))) & ![W3: $i] : (aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)) => aElementOf0(W3, W0))) & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, W2), W0)))) & isOpen0(W0))) <=> (aElementOf0(W0, xS) => (aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1)) & aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395)) & aSubsetOf0(W0, cS1395) & ![W1: $i] : ((~aElementOf0(W1, W0)) | ?[W2: $i] : (aInteger0(W2) & (~(W2 = sz00)) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2)) & ![W3: $i] : (((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | (aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((~(aInteger0(W3) & (sdteqdtlpzmzozddtrp0(W3, W1, W2) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) | ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))))) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)))) & ![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | aElementOf0(W3, W0)) & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, W2), W0))) & isOpen0(W0))))), rewrite((aElementOf0(W0, xS) => (aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1)) & aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395)) & aSubsetOf0(W0, cS1395) & ![W1: $i] : ((~aElementOf0(W1, W0)) | ?[W2: $i] : (aInteger0(W2) & (~(W2 = sz00)) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2)) & ![W3: $i] : (((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | (aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((~(aInteger0(W3) & (sdteqdtlpzmzozddtrp0(W3, W1, W2) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) | ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))))) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)))) & ![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | aElementOf0(W3, W0)) & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, W2), W0))) & isOpen0(W0))) <=> ((~aElementOf0(W0, xS)) | (aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1)) & aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395)) & aSubsetOf0(W0, cS1395) & ![W1: $i] : ((~aElementOf0(W1, W0)) | ?[W2: $i] : (aInteger0(W2) & (~(W2 = sz00)) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2)) & ![W3: $i] : (((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | (aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((~(aInteger0(W3) & (sdteqdtlpzmzozddtrp0(W3, W1, W2) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) | ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))))) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)))) & ![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | aElementOf0(W3, W0)) & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, W2), W0))) & isOpen0(W0)))), ((aElementOf0(W0, xS) => ((((((aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) & aSet0(W0)) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, cS1395))) & aSubsetOf0(W0, cS1395)) & ![W1: $i] : (aElementOf0(W1, W0) => ?[W2: $i] : (((((aInteger0(W2) & (~(W2 = sz00))) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2))) & ![W3: $i] : ((aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)) => (((aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1)))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((aInteger0(W3) & ((?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1)))) | sdteqdtlpzmzozddtrp0(W3, W1, W2))) => aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))))) & ![W3: $i] : (aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)) => aElementOf0(W3, W0))) & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, W2), W0)))) & isOpen0(W0))) <=> ((~aElementOf0(W0, xS)) | (aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1)) & aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395)) & aSubsetOf0(W0, cS1395) & ![W1: $i] : ((~aElementOf0(W1, W0)) | ?[W2: $i] : (aInteger0(W2) & (~(W2 = sz00)) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2)) & ![W3: $i] : (((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | (aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((~(aInteger0(W3) & (sdteqdtlpzmzozddtrp0(W3, W1, W2) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) | ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))))) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)))) & ![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | aElementOf0(W3, W0)) & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, W2), W0))) & isOpen0(W0)))))),
% 18.50/25.01 inference(bind,[status(th)],[])).
% 18.50/25.01 tff(56,plain,
% 18.50/25.01 (![W0: $i] : (aElementOf0(W0, xS) => ((((((aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) & aSet0(W0)) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, cS1395))) & aSubsetOf0(W0, cS1395)) & ![W1: $i] : (aElementOf0(W1, W0) => ?[W2: $i] : (((((aInteger0(W2) & (~(W2 = sz00))) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2))) & ![W3: $i] : ((aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)) => (((aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1)))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((aInteger0(W3) & ((?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1)))) | sdteqdtlpzmzozddtrp0(W3, W1, W2))) => aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))))) & ![W3: $i] : (aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)) => aElementOf0(W3, W0))) & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, W2), W0)))) & isOpen0(W0))) <=> ![W0: $i] : ((~aElementOf0(W0, xS)) | (aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1)) & aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395)) & aSubsetOf0(W0, cS1395) & ![W1: $i] : ((~aElementOf0(W1, W0)) | ?[W2: $i] : (aInteger0(W2) & (~(W2 = sz00)) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2)) & ![W3: $i] : (((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | (aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((~(aInteger0(W3) & (sdteqdtlpzmzozddtrp0(W3, W1, W2) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) | ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))))) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)))) & ![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | aElementOf0(W3, W0)) & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, W2), W0))) & isOpen0(W0)))),
% 18.50/25.01 inference(quant_intro,[status(thm)],[55])).
% 18.50/25.01 tff(57,axiom,(aSet0(xS) & ![W0: $i] : (aElementOf0(W0, xS) => ((((((aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) & aSet0(W0)) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, cS1395))) & aSubsetOf0(W0, cS1395)) & ![W1: $i] : (aElementOf0(W1, W0) => ?[W2: $i] : (((((aInteger0(W2) & (~(W2 = sz00))) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2))) & ![W3: $i] : ((aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)) => (((aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1)))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((aInteger0(W3) & ((?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1)))) | sdteqdtlpzmzozddtrp0(W3, W1, W2))) => aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))))) & ![W3: $i] : (aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)) => aElementOf0(W3, W0))) & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, W2), W0)))) & isOpen0(W0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__1750')).
% 18.50/25.01 tff(58,plain,
% 18.50/25.01 (![W0: $i] : (aElementOf0(W0, xS) => ((((((aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) & aSet0(W0)) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, cS1395))) & aSubsetOf0(W0, cS1395)) & ![W1: $i] : (aElementOf0(W1, W0) => ?[W2: $i] : (((((aInteger0(W2) & (~(W2 = sz00))) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2))) & ![W3: $i] : ((aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)) => (((aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1)))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((aInteger0(W3) & ((?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1)))) | sdteqdtlpzmzozddtrp0(W3, W1, W2))) => aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))))) & ![W3: $i] : (aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)) => aElementOf0(W3, W0))) & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, W2), W0)))) & isOpen0(W0)))),
% 18.50/25.01 inference(and_elim,[status(thm)],[57])).
% 18.50/25.01 tff(59,plain,
% 18.50/25.01 (![W0: $i] : ((~aElementOf0(W0, xS)) | (aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1)) & aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395)) & aSubsetOf0(W0, cS1395) & ![W1: $i] : ((~aElementOf0(W1, W0)) | ?[W2: $i] : (aInteger0(W2) & (~(W2 = sz00)) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2)) & ![W3: $i] : (((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | (aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((~(aInteger0(W3) & (sdteqdtlpzmzozddtrp0(W3, W1, W2) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) | ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))))) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)))) & ![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | aElementOf0(W3, W0)) & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, W2), W0))) & isOpen0(W0)))),
% 18.50/25.01 inference(modus_ponens,[status(thm)],[58, 56])).
% 18.50/25.01 tff(60,plain,
% 18.50/25.01 (![W0: $i] : ((~aElementOf0(W0, xS)) | (aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1)) & aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395)) & aSubsetOf0(W0, cS1395) & ![W1: $i] : ((~aElementOf0(W1, W0)) | ?[W2: $i] : (aInteger0(W2) & (~(W2 = sz00)) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, W2)) & ![W3: $i] : (((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | (aInteger0(W3) & ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1)))) & aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) & sdteqdtlpzmzozddtrp0(W3, W1, W2))) & ((~(aInteger0(W3) & (sdteqdtlpzmzozddtrp0(W3, W1, W2) | aDivisorOf0(W2, sdtpldt0(W3, smndt0(W1))) | ?[W4: $i] : (aInteger0(W4) & (sdtasdt0(W2, W4) = sdtpldt0(W3, smndt0(W1))))))) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2)))) & ![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, W2))) | aElementOf0(W3, W0)) & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, W2), W0))) & isOpen0(W0)))),
% 18.50/25.01 inference(modus_ponens,[status(thm)],[59, 54])).
% 18.50/25.01 tff(61,plain,(
% 18.50/25.01 ![W0: $i] : ((~aElementOf0(W0, xS)) | (aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1)) & aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395)) & aSubsetOf0(W0, cS1395) & ![W1: $i] : ((~aElementOf0(W1, W0)) | (aInteger0(tptp_fun_W2_13(W1, W0)) & (~(tptp_fun_W2_13(W1, W0) = sz00)) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0))) & ![W3: $i] : (((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (aInteger0(W3) & (aInteger0(tptp_fun_W4_14(W3, W1, W0)) & (sdtasdt0(tptp_fun_W2_13(W1, W0), tptp_fun_W4_14(W3, W1, W0)) = sdtpldt0(W3, smndt0(W1)))) & aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1))) & sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0)))) & (((~aInteger0(W3)) | ((~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0))) & (~aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1)))) & ![W4: $i] : (~(aInteger0(W4) & (sdtasdt0(tptp_fun_W2_13(W1, W0), W4) = sdtpldt0(W3, smndt0(W1))))))) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0))))) & ![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | aElementOf0(W3, W0)) & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)), W0))) & isOpen0(W0)))),
% 18.50/25.01 inference(skolemize,[status(sab)],[60])).
% 18.50/25.01 tff(62,plain,
% 18.50/25.01 (![W0: $i] : ((~aElementOf0(W0, xS)) | (aSet0(cS1395) & ![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1)) & aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395)) & aSubsetOf0(W0, cS1395) & ![W1: $i] : ((~aElementOf0(W1, W0)) | (aInteger0(tptp_fun_W2_13(W1, W0)) & (~(tptp_fun_W2_13(W1, W0) = sz00)) & aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0))) & ![W3: $i] : (((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (aInteger0(W3) & aInteger0(tptp_fun_W4_14(W3, W1, W0)) & (sdtasdt0(tptp_fun_W2_13(W1, W0), tptp_fun_W4_14(W3, W1, W0)) = sdtpldt0(W3, smndt0(W1))) & aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1))) & sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0)))) & ((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0))) | ((~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0))) & (~aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1)))) & ![W4: $i] : (~(aInteger0(W4) & (sdtasdt0(tptp_fun_W2_13(W1, W0), W4) = sdtpldt0(W3, smndt0(W1)))))))) & ![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | aElementOf0(W3, W0)) & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)), W0))) & isOpen0(W0)))),
% 18.50/25.01 inference(modus_ponens,[status(thm)],[61, 53])).
% 18.50/25.01 tff(63,plain,
% 18.50/25.01 (![W0: $i] : ((~aElementOf0(W0, xS)) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, cS1395)) | (~isOpen0(W0)) | (~aSet0(cS1395)) | (~![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | (~((tptp_fun_W2_13(W1, W0) = sz00) | (~aInteger0(tptp_fun_W2_13(W1, W0))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~((~aInteger0(W3)) | (~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0))) | (~aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1)))) | (~aInteger0(tptp_fun_W4_14(W3, W1, W0))) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), tptp_fun_W4_14(W3, W1, W0)) = sdtpldt0(W3, smndt0(W1)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0))) | (~(aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1))) | sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0)) | (~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), W4) = sdtpldt0(W3, smndt0(W1))))))))))))) | (~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | aElementOf0(W3, W0))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)), W0)))))))))),
% 18.50/25.01 inference(modus_ponens,[status(thm)],[62, 51])).
% 18.50/25.01 tff(64,plain,
% 18.50/25.01 (![W0: $i] : ((~aElementOf0(W0, xS)) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, cS1395)) | (~isOpen0(W0)) | (~aSet0(cS1395)) | (~![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | (~((tptp_fun_W2_13(W1, W0) = sz00) | (~aInteger0(tptp_fun_W2_13(W1, W0))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~((~aInteger0(W3)) | (~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0))) | (~aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1)))) | (~aInteger0(tptp_fun_W4_14(W3, W1, W0))) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), tptp_fun_W4_14(W3, W1, W0)) = sdtpldt0(W3, smndt0(W1)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0))) | (~(aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1))) | sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0)) | (~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), W4) = sdtpldt0(W3, smndt0(W1))))))))))))) | (~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | aElementOf0(W3, W0))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)), W0)))))))))),
% 18.50/25.01 inference(modus_ponens,[status(thm)],[63, 49])).
% 18.50/25.01 tff(65,plain,
% 18.50/25.01 (![W0: $i] : ((~aElementOf0(W0, xS)) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, cS1395)) | (~isOpen0(W0)) | (~aSet0(cS1395)) | (~![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | (~((tptp_fun_W2_13(W1, W0) = sz00) | (~aInteger0(tptp_fun_W2_13(W1, W0))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)), W0)) | (~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | aElementOf0(W3, W0))) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~((~aInteger0(W3)) | (~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0))) | (~aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1)))) | (~aInteger0(tptp_fun_W4_14(W3, W1, W0))) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), tptp_fun_W4_14(W3, W1, W0)) = sdtpldt0(W3, smndt0(W1)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0))) | (~(aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1))) | sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0)) | (~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), W4) = sdtpldt0(W3, smndt0(W1))))))))))))))))))))),
% 18.50/25.01 inference(modus_ponens,[status(thm)],[64, 44])).
% 18.50/25.01 tff(66,plain,
% 18.50/25.01 (((~![W0: $i] : ((~aElementOf0(W0, xS)) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, cS1395)) | (~isOpen0(W0)) | (~aSet0(cS1395)) | (~![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | (~((tptp_fun_W2_13(W1, W0) = sz00) | (~aInteger0(tptp_fun_W2_13(W1, W0))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)), W0)) | (~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | aElementOf0(W3, W0))) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~((~aInteger0(W3)) | (~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0))) | (~aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1)))) | (~aInteger0(tptp_fun_W4_14(W3, W1, W0))) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), tptp_fun_W4_14(W3, W1, W0)) = sdtpldt0(W3, smndt0(W1)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0))) | (~(aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1))) | sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0)) | (~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), W4) = sdtpldt0(W3, smndt0(W1))))))))))))))))))))) | ((~aElementOf0(tptp_fun_W1_18(W0!15), xS)) | (~((~aSet0(cS1395)) | (~![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) | (~![W1: $i] : ((~aElementOf0(W1, tptp_fun_W1_18(W0!15))) | aElementOf0(W1, cS1395))) | (~isOpen0(tptp_fun_W1_18(W0!15))) | (~aSubsetOf0(tptp_fun_W1_18(W0!15), cS1395)) | (~aSet0(tptp_fun_W1_18(W0!15))) | (~![W1: $i] : ((~aElementOf0(W1, tptp_fun_W1_18(W0!15))) | (~((~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | aElementOf0(W3, tptp_fun_W1_18(W0!15)))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | (~aInteger0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))) | (tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)) = sz00) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), tptp_fun_W4_14(W3, W1, tptp_fun_W1_18(W0!15))) = sdtpldt0(W3, smndt0(W1)))) | (~aInteger0(tptp_fun_W4_14(W3, W1, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W1)))) | (~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))) | (~((~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), W4) = sdtpldt0(W3, smndt0(W1)))))) | sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W1)))))))))))))))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, xS)) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, cS1395)) | (~isOpen0(W0)) | (~aSet0(cS1395)) | (~![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | (~((tptp_fun_W2_13(W1, W0) = sz00) | (~aInteger0(tptp_fun_W2_13(W1, W0))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)), W0)) | (~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | aElementOf0(W3, W0))) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~((~aInteger0(W3)) | (~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0))) | (~aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1)))) | (~aInteger0(tptp_fun_W4_14(W3, W1, W0))) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), tptp_fun_W4_14(W3, W1, W0)) = sdtpldt0(W3, smndt0(W1)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0))) | (~(aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1))) | sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0)) | (~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), W4) = sdtpldt0(W3, smndt0(W1))))))))))))))))))))) | (~aElementOf0(tptp_fun_W1_18(W0!15), xS)) | (~((~aSet0(cS1395)) | (~![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) | (~![W1: $i] : ((~aElementOf0(W1, tptp_fun_W1_18(W0!15))) | aElementOf0(W1, cS1395))) | (~isOpen0(tptp_fun_W1_18(W0!15))) | (~aSubsetOf0(tptp_fun_W1_18(W0!15), cS1395)) | (~aSet0(tptp_fun_W1_18(W0!15))) | (~![W1: $i] : ((~aElementOf0(W1, tptp_fun_W1_18(W0!15))) | (~((~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | aElementOf0(W3, tptp_fun_W1_18(W0!15)))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | (~aInteger0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))) | (tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)) = sz00) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), tptp_fun_W4_14(W3, W1, tptp_fun_W1_18(W0!15))) = sdtpldt0(W3, smndt0(W1)))) | (~aInteger0(tptp_fun_W4_14(W3, W1, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W1)))) | (~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))) | (~((~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), W4) = sdtpldt0(W3, smndt0(W1)))))) | sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W1)))))))))))))))))),
% 18.50/25.02 inference(rewrite,[status(thm)],[])).
% 18.50/25.02 tff(67,plain,
% 18.50/25.02 (((~aElementOf0(tptp_fun_W1_18(W0!15), xS)) | (~((~aSet0(tptp_fun_W1_18(W0!15))) | (~aSubsetOf0(tptp_fun_W1_18(W0!15), cS1395)) | (~isOpen0(tptp_fun_W1_18(W0!15))) | (~aSet0(cS1395)) | (~![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) | (~![W1: $i] : ((~aElementOf0(W1, tptp_fun_W1_18(W0!15))) | aElementOf0(W1, cS1395))) | (~![W1: $i] : ((~aElementOf0(W1, tptp_fun_W1_18(W0!15))) | (~((tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)) = sz00) | (~aInteger0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15))) | (~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | aElementOf0(W3, tptp_fun_W1_18(W0!15)))) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W3)) | (~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W1)))) | (~aInteger0(tptp_fun_W4_14(W3, W1, tptp_fun_W1_18(W0!15)))) | (~(sdtasdt0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), tptp_fun_W4_14(W3, W1, tptp_fun_W1_18(W0!15))) = sdtpldt0(W3, smndt0(W1)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))) | (~(aDivisorOf0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W1))) | sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))) | (~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), W4) = sdtpldt0(W3, smndt0(W1)))))))))))))))))))) <=> ((~aElementOf0(tptp_fun_W1_18(W0!15), xS)) | (~((~aSet0(cS1395)) | (~![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) | (~![W1: $i] : ((~aElementOf0(W1, tptp_fun_W1_18(W0!15))) | aElementOf0(W1, cS1395))) | (~isOpen0(tptp_fun_W1_18(W0!15))) | (~aSubsetOf0(tptp_fun_W1_18(W0!15), cS1395)) | (~aSet0(tptp_fun_W1_18(W0!15))) | (~![W1: $i] : ((~aElementOf0(W1, tptp_fun_W1_18(W0!15))) | (~((~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | aElementOf0(W3, tptp_fun_W1_18(W0!15)))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | (~aInteger0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))) | (tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)) = sz00) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), tptp_fun_W4_14(W3, W1, tptp_fun_W1_18(W0!15))) = sdtpldt0(W3, smndt0(W1)))) | (~aInteger0(tptp_fun_W4_14(W3, W1, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W1)))) | (~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))) | (~((~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), W4) = sdtpldt0(W3, smndt0(W1)))))) | sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W1)))))))))))))))))),
% 18.50/25.02 inference(rewrite,[status(thm)],[])).
% 18.50/25.02 tff(68,plain,
% 18.50/25.02 (((~![W0: $i] : ((~aElementOf0(W0, xS)) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, cS1395)) | (~isOpen0(W0)) | (~aSet0(cS1395)) | (~![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | (~((tptp_fun_W2_13(W1, W0) = sz00) | (~aInteger0(tptp_fun_W2_13(W1, W0))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)), W0)) | (~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | aElementOf0(W3, W0))) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~((~aInteger0(W3)) | (~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0))) | (~aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1)))) | (~aInteger0(tptp_fun_W4_14(W3, W1, W0))) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), tptp_fun_W4_14(W3, W1, W0)) = sdtpldt0(W3, smndt0(W1)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0))) | (~(aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1))) | sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0)) | (~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), W4) = sdtpldt0(W3, smndt0(W1))))))))))))))))))))) | ((~aElementOf0(tptp_fun_W1_18(W0!15), xS)) | (~((~aSet0(tptp_fun_W1_18(W0!15))) | (~aSubsetOf0(tptp_fun_W1_18(W0!15), cS1395)) | (~isOpen0(tptp_fun_W1_18(W0!15))) | (~aSet0(cS1395)) | (~![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) | (~![W1: $i] : ((~aElementOf0(W1, tptp_fun_W1_18(W0!15))) | aElementOf0(W1, cS1395))) | (~![W1: $i] : ((~aElementOf0(W1, tptp_fun_W1_18(W0!15))) | (~((tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)) = sz00) | (~aInteger0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15))) | (~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | aElementOf0(W3, tptp_fun_W1_18(W0!15)))) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W3)) | (~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W1)))) | (~aInteger0(tptp_fun_W4_14(W3, W1, tptp_fun_W1_18(W0!15)))) | (~(sdtasdt0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), tptp_fun_W4_14(W3, W1, tptp_fun_W1_18(W0!15))) = sdtpldt0(W3, smndt0(W1)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))) | (~(aDivisorOf0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W1))) | sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))) | (~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), W4) = sdtpldt0(W3, smndt0(W1))))))))))))))))))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, xS)) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, cS1395)) | (~isOpen0(W0)) | (~aSet0(cS1395)) | (~![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | (~((tptp_fun_W2_13(W1, W0) = sz00) | (~aInteger0(tptp_fun_W2_13(W1, W0))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)), W0)) | (~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | aElementOf0(W3, W0))) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~((~aInteger0(W3)) | (~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0))) | (~aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1)))) | (~aInteger0(tptp_fun_W4_14(W3, W1, W0))) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), tptp_fun_W4_14(W3, W1, W0)) = sdtpldt0(W3, smndt0(W1)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0))) | (~(aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1))) | sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0)) | (~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), W4) = sdtpldt0(W3, smndt0(W1))))))))))))))))))))) | ((~aElementOf0(tptp_fun_W1_18(W0!15), xS)) | (~((~aSet0(cS1395)) | (~![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) | (~![W1: $i] : ((~aElementOf0(W1, tptp_fun_W1_18(W0!15))) | aElementOf0(W1, cS1395))) | (~isOpen0(tptp_fun_W1_18(W0!15))) | (~aSubsetOf0(tptp_fun_W1_18(W0!15), cS1395)) | (~aSet0(tptp_fun_W1_18(W0!15))) | (~![W1: $i] : ((~aElementOf0(W1, tptp_fun_W1_18(W0!15))) | (~((~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | aElementOf0(W3, tptp_fun_W1_18(W0!15)))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | (~aInteger0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))) | (tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)) = sz00) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), tptp_fun_W4_14(W3, W1, tptp_fun_W1_18(W0!15))) = sdtpldt0(W3, smndt0(W1)))) | (~aInteger0(tptp_fun_W4_14(W3, W1, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W1)))) | (~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))) | (~((~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), W4) = sdtpldt0(W3, smndt0(W1)))))) | sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W1))))))))))))))))))),
% 18.50/25.02 inference(monotonicity,[status(thm)],[67])).
% 18.50/25.02 tff(69,plain,
% 18.50/25.02 (((~![W0: $i] : ((~aElementOf0(W0, xS)) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, cS1395)) | (~isOpen0(W0)) | (~aSet0(cS1395)) | (~![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | (~((tptp_fun_W2_13(W1, W0) = sz00) | (~aInteger0(tptp_fun_W2_13(W1, W0))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)), W0)) | (~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | aElementOf0(W3, W0))) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~((~aInteger0(W3)) | (~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0))) | (~aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1)))) | (~aInteger0(tptp_fun_W4_14(W3, W1, W0))) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), tptp_fun_W4_14(W3, W1, W0)) = sdtpldt0(W3, smndt0(W1)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0))) | (~(aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1))) | sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0)) | (~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), W4) = sdtpldt0(W3, smndt0(W1))))))))))))))))))))) | ((~aElementOf0(tptp_fun_W1_18(W0!15), xS)) | (~((~aSet0(tptp_fun_W1_18(W0!15))) | (~aSubsetOf0(tptp_fun_W1_18(W0!15), cS1395)) | (~isOpen0(tptp_fun_W1_18(W0!15))) | (~aSet0(cS1395)) | (~![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) | (~![W1: $i] : ((~aElementOf0(W1, tptp_fun_W1_18(W0!15))) | aElementOf0(W1, cS1395))) | (~![W1: $i] : ((~aElementOf0(W1, tptp_fun_W1_18(W0!15))) | (~((tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)) = sz00) | (~aInteger0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15))) | (~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | aElementOf0(W3, tptp_fun_W1_18(W0!15)))) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W3)) | (~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W1)))) | (~aInteger0(tptp_fun_W4_14(W3, W1, tptp_fun_W1_18(W0!15)))) | (~(sdtasdt0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), tptp_fun_W4_14(W3, W1, tptp_fun_W1_18(W0!15))) = sdtpldt0(W3, smndt0(W1)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))) | (~(aDivisorOf0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W1))) | sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))) | (~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), W4) = sdtpldt0(W3, smndt0(W1))))))))))))))))))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, xS)) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, cS1395)) | (~isOpen0(W0)) | (~aSet0(cS1395)) | (~![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | (~((tptp_fun_W2_13(W1, W0) = sz00) | (~aInteger0(tptp_fun_W2_13(W1, W0))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)), W0)) | (~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | aElementOf0(W3, W0))) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~((~aInteger0(W3)) | (~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0))) | (~aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1)))) | (~aInteger0(tptp_fun_W4_14(W3, W1, W0))) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), tptp_fun_W4_14(W3, W1, W0)) = sdtpldt0(W3, smndt0(W1)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0))) | (~(aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1))) | sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0)) | (~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), W4) = sdtpldt0(W3, smndt0(W1))))))))))))))))))))) | (~aElementOf0(tptp_fun_W1_18(W0!15), xS)) | (~((~aSet0(cS1395)) | (~![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) | (~![W1: $i] : ((~aElementOf0(W1, tptp_fun_W1_18(W0!15))) | aElementOf0(W1, cS1395))) | (~isOpen0(tptp_fun_W1_18(W0!15))) | (~aSubsetOf0(tptp_fun_W1_18(W0!15), cS1395)) | (~aSet0(tptp_fun_W1_18(W0!15))) | (~![W1: $i] : ((~aElementOf0(W1, tptp_fun_W1_18(W0!15))) | (~((~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | aElementOf0(W3, tptp_fun_W1_18(W0!15)))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | (~aInteger0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))) | (tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)) = sz00) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), tptp_fun_W4_14(W3, W1, tptp_fun_W1_18(W0!15))) = sdtpldt0(W3, smndt0(W1)))) | (~aInteger0(tptp_fun_W4_14(W3, W1, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W1)))) | (~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))) | (~((~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), W4) = sdtpldt0(W3, smndt0(W1)))))) | sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W1)))))))))))))))))),
% 18.50/25.02 inference(transitivity,[status(thm)],[68, 66])).
% 18.50/25.02 tff(70,plain,
% 18.50/25.02 ((~![W0: $i] : ((~aElementOf0(W0, xS)) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, cS1395)) | (~isOpen0(W0)) | (~aSet0(cS1395)) | (~![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | (~((tptp_fun_W2_13(W1, W0) = sz00) | (~aInteger0(tptp_fun_W2_13(W1, W0))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)), W0)) | (~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | aElementOf0(W3, W0))) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~((~aInteger0(W3)) | (~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0))) | (~aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1)))) | (~aInteger0(tptp_fun_W4_14(W3, W1, W0))) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), tptp_fun_W4_14(W3, W1, W0)) = sdtpldt0(W3, smndt0(W1)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0))) | (~(aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1))) | sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0)) | (~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), W4) = sdtpldt0(W3, smndt0(W1))))))))))))))))))))) | ((~aElementOf0(tptp_fun_W1_18(W0!15), xS)) | (~((~aSet0(tptp_fun_W1_18(W0!15))) | (~aSubsetOf0(tptp_fun_W1_18(W0!15), cS1395)) | (~isOpen0(tptp_fun_W1_18(W0!15))) | (~aSet0(cS1395)) | (~![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) | (~![W1: $i] : ((~aElementOf0(W1, tptp_fun_W1_18(W0!15))) | aElementOf0(W1, cS1395))) | (~![W1: $i] : ((~aElementOf0(W1, tptp_fun_W1_18(W0!15))) | (~((tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)) = sz00) | (~aInteger0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15))) | (~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | aElementOf0(W3, tptp_fun_W1_18(W0!15)))) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W3)) | (~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W1)))) | (~aInteger0(tptp_fun_W4_14(W3, W1, tptp_fun_W1_18(W0!15)))) | (~(sdtasdt0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), tptp_fun_W4_14(W3, W1, tptp_fun_W1_18(W0!15))) = sdtpldt0(W3, smndt0(W1)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))) | (~(aDivisorOf0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W1))) | sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))) | (~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), W4) = sdtpldt0(W3, smndt0(W1))))))))))))))))))))),
% 18.50/25.02 inference(quant_inst,[status(thm)],[])).
% 18.50/25.02 tff(71,plain,
% 18.50/25.02 ((~![W0: $i] : ((~aElementOf0(W0, xS)) | (~((~aSet0(W0)) | (~aSubsetOf0(W0, cS1395)) | (~isOpen0(W0)) | (~aSet0(cS1395)) | (~![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, cS1395))) | (~![W1: $i] : ((~aElementOf0(W1, W0)) | (~((tptp_fun_W2_13(W1, W0) = sz00) | (~aInteger0(tptp_fun_W2_13(W1, W0))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)), W0)) | (~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | aElementOf0(W3, W0))) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0)))) | (~((~aInteger0(W3)) | (~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0))) | (~aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1)))) | (~aInteger0(tptp_fun_W4_14(W3, W1, W0))) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), tptp_fun_W4_14(W3, W1, W0)) = sdtpldt0(W3, smndt0(W1)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, W0))) | (~(aDivisorOf0(tptp_fun_W2_13(W1, W0), sdtpldt0(W3, smndt0(W1))) | sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, W0)) | (~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W1, W0), W4) = sdtpldt0(W3, smndt0(W1))))))))))))))))))))) | (~aElementOf0(tptp_fun_W1_18(W0!15), xS)) | (~((~aSet0(cS1395)) | (~![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) | (~![W1: $i] : ((~aElementOf0(W1, tptp_fun_W1_18(W0!15))) | aElementOf0(W1, cS1395))) | (~isOpen0(tptp_fun_W1_18(W0!15))) | (~aSubsetOf0(tptp_fun_W1_18(W0!15), cS1395)) | (~aSet0(tptp_fun_W1_18(W0!15))) | (~![W1: $i] : ((~aElementOf0(W1, tptp_fun_W1_18(W0!15))) | (~((~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | aElementOf0(W3, tptp_fun_W1_18(W0!15)))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | (~aInteger0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))) | (tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)) = sz00) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), tptp_fun_W4_14(W3, W1, tptp_fun_W1_18(W0!15))) = sdtpldt0(W3, smndt0(W1)))) | (~aInteger0(tptp_fun_W4_14(W3, W1, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W1)))) | (~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))) | (~((~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), W4) = sdtpldt0(W3, smndt0(W1)))))) | sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W1))))))))))))))))),
% 18.50/25.02 inference(modus_ponens,[status(thm)],[70, 69])).
% 18.50/25.02 tff(72,plain,
% 18.50/25.02 (~((~aSet0(cS1395)) | (~![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) | (~![W1: $i] : ((~aElementOf0(W1, tptp_fun_W1_18(W0!15))) | aElementOf0(W1, cS1395))) | (~isOpen0(tptp_fun_W1_18(W0!15))) | (~aSubsetOf0(tptp_fun_W1_18(W0!15), cS1395)) | (~aSet0(tptp_fun_W1_18(W0!15))) | (~![W1: $i] : ((~aElementOf0(W1, tptp_fun_W1_18(W0!15))) | (~((~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | aElementOf0(W3, tptp_fun_W1_18(W0!15)))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | (~aInteger0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))) | (tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)) = sz00) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), tptp_fun_W4_14(W3, W1, tptp_fun_W1_18(W0!15))) = sdtpldt0(W3, smndt0(W1)))) | (~aInteger0(tptp_fun_W4_14(W3, W1, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W1)))) | (~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))) | (~((~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), W4) = sdtpldt0(W3, smndt0(W1)))))) | sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W1)))))))))))))))),
% 18.50/25.02 inference(unit_resolution,[status(thm)],[71, 65, 42])).
% 18.50/25.02 tff(73,plain,
% 18.50/25.02 (((~aSet0(cS1395)) | (~![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) | (~![W1: $i] : ((~aElementOf0(W1, tptp_fun_W1_18(W0!15))) | aElementOf0(W1, cS1395))) | (~isOpen0(tptp_fun_W1_18(W0!15))) | (~aSubsetOf0(tptp_fun_W1_18(W0!15), cS1395)) | (~aSet0(tptp_fun_W1_18(W0!15))) | (~![W1: $i] : ((~aElementOf0(W1, tptp_fun_W1_18(W0!15))) | (~((~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | aElementOf0(W3, tptp_fun_W1_18(W0!15)))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | (~aInteger0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))) | (tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)) = sz00) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), tptp_fun_W4_14(W3, W1, tptp_fun_W1_18(W0!15))) = sdtpldt0(W3, smndt0(W1)))) | (~aInteger0(tptp_fun_W4_14(W3, W1, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W1)))) | (~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))) | (~((~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), W4) = sdtpldt0(W3, smndt0(W1)))))) | sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W1))))))))))))))) | aSet0(tptp_fun_W1_18(W0!15))),
% 18.50/25.02 inference(tautology,[status(thm)],[])).
% 18.50/25.02 tff(74,plain,
% 18.50/25.02 (aSet0(tptp_fun_W1_18(W0!15))),
% 18.50/25.02 inference(unit_resolution,[status(thm)],[73, 72])).
% 18.50/25.02 tff(75,plain,
% 18.50/25.02 (^[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_2(W1, W0), W1)) | aElementOf0(tptp_fun_W2_2(W1, W0), W0)))))))) <=> ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_2(W1, W0), W1)) | aElementOf0(tptp_fun_W2_2(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))))))))),
% 18.50/25.02 inference(bind,[status(th)],[])).
% 18.50/25.02 tff(76,plain,
% 18.50/25.02 (![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_2(W1, W0), W1)) | aElementOf0(tptp_fun_W2_2(W1, W0), W0)))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_2(W1, W0), W1)) | aElementOf0(tptp_fun_W2_2(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))),
% 18.50/25.02 inference(quant_intro,[status(thm)],[75])).
% 18.50/25.02 tff(77,plain,
% 18.50/25.02 (^[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_2(W1, W0), W1)) | aElementOf0(tptp_fun_W2_2(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_2(W1, W0), W1)) | aElementOf0(tptp_fun_W2_2(W1, W0), W0)))))))))),
% 18.50/25.02 inference(bind,[status(th)],[])).
% 18.50/25.02 tff(78,plain,
% 18.50/25.02 (![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_2(W1, W0), W1)) | aElementOf0(tptp_fun_W2_2(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_2(W1, W0), W1)) | aElementOf0(tptp_fun_W2_2(W1, W0), W0))))))))),
% 18.50/25.02 inference(quant_intro,[status(thm)],[77])).
% 18.50/25.02 tff(79,plain,
% 18.50/25.02 (^[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_2(W1, W0), W1)) | aElementOf0(tptp_fun_W2_2(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_2(W1, W0), W1)) | aElementOf0(tptp_fun_W2_2(W1, W0), W0)))))))))),
% 18.50/25.02 inference(bind,[status(th)],[])).
% 18.50/25.02 tff(80,plain,
% 18.50/25.02 (![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_2(W1, W0), W1)) | aElementOf0(tptp_fun_W2_2(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_2(W1, W0), W1)) | aElementOf0(tptp_fun_W2_2(W1, W0), W0))))))))),
% 18.50/25.02 inference(quant_intro,[status(thm)],[79])).
% 18.50/25.02 tff(81,plain,
% 18.50/25.02 (![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_2(W1, W0), W1)) | aElementOf0(tptp_fun_W2_2(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_2(W1, W0), W1)) | aElementOf0(tptp_fun_W2_2(W1, W0), W0))))))))),
% 18.50/25.02 inference(transitivity,[status(thm)],[80, 78])).
% 18.50/25.02 tff(82,plain,
% 18.50/25.02 (^[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_2(W1, W0), W1)) | aElementOf0(tptp_fun_W2_2(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_2(W1, W0), W1)) | aElementOf0(tptp_fun_W2_2(W1, W0), W0)))))))))),
% 18.50/25.02 inference(bind,[status(th)],[])).
% 18.50/25.02 tff(83,plain,
% 18.50/25.02 (![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_2(W1, W0), W1)) | aElementOf0(tptp_fun_W2_2(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_2(W1, W0), W1)) | aElementOf0(tptp_fun_W2_2(W1, W0), W0))))))))),
% 18.50/25.02 inference(quant_intro,[status(thm)],[82])).
% 18.50/25.02 tff(84,plain,
% 18.50/25.02 (^[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_2(W1, W0), W1)) | aElementOf0(tptp_fun_W2_2(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_2(W1, W0), W1)) | aElementOf0(tptp_fun_W2_2(W1, W0), W0)))))))),
% 18.50/25.02 inference(bind,[status(th)],[])).
% 18.50/25.02 tff(85,plain,
% 18.50/25.02 (![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_2(W1, W0), W1)) | aElementOf0(tptp_fun_W2_2(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_2(W1, W0), W1)) | aElementOf0(tptp_fun_W2_2(W1, W0), W0))))))),
% 18.50/25.02 inference(quant_intro,[status(thm)],[84])).
% 18.50/25.02 tff(86,plain,
% 18.50/25.02 (![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)))))),
% 18.50/25.02 inference(rewrite,[status(thm)],[])).
% 18.50/25.02 tff(87,plain,
% 18.50/25.02 (^[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)))))))),
% 18.50/25.02 inference(bind,[status(th)],[])).
% 18.50/25.02 tff(88,plain,
% 18.50/25.02 (![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)))))),
% 18.50/25.02 inference(quant_intro,[status(thm)],[87])).
% 18.50/25.02 tff(89,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','mSubset')).
% 18.50/25.02 tff(90,plain,
% 18.50/25.02 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))),
% 18.50/25.02 inference(modus_ponens,[status(thm)],[89, 88])).
% 18.50/25.02 tff(91,plain,
% 18.50/25.02 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))),
% 18.50/25.02 inference(modus_ponens,[status(thm)],[90, 86])).
% 18.50/25.02 tff(92,plain,(
% 18.50/25.02 ![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_2(W1, W0), W1)) | aElementOf0(tptp_fun_W2_2(W1, W0), W0)))))))),
% 18.50/25.02 inference(skolemize,[status(sab)],[91])).
% 18.50/25.02 tff(93,plain,
% 18.50/25.02 (![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_2(W1, W0), W1)) | aElementOf0(tptp_fun_W2_2(W1, W0), W0))))))),
% 18.50/25.02 inference(modus_ponens,[status(thm)],[92, 85])).
% 18.50/25.02 tff(94,plain,
% 18.50/25.02 (![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_2(W1, W0), W1)) | aElementOf0(tptp_fun_W2_2(W1, W0), W0))))))))),
% 18.50/25.02 inference(modus_ponens,[status(thm)],[93, 83])).
% 18.50/25.02 tff(95,plain,
% 18.50/25.02 (![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_2(W1, W0), W1)) | aElementOf0(tptp_fun_W2_2(W1, W0), W0))))))))),
% 18.50/25.02 inference(modus_ponens,[status(thm)],[94, 81])).
% 18.50/25.02 tff(96,plain,
% 18.50/25.02 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_2(W1, W0), W1)) | aElementOf0(tptp_fun_W2_2(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))),
% 18.50/25.02 inference(modus_ponens,[status(thm)],[95, 76])).
% 18.50/25.02 tff(97,plain,
% 18.50/25.02 (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_2(W1, W0), W1)) | aElementOf0(tptp_fun_W2_2(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(tptp_fun_W1_18(W0!15))) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, tptp_fun_W1_18(W0!15)) | (~((~aElementOf0(tptp_fun_W2_2(W1, tptp_fun_W1_18(W0!15)), W1)) | aElementOf0(tptp_fun_W2_2(W1, tptp_fun_W1_18(W0!15)), tptp_fun_W1_18(W0!15)))))) | (~((~aSubsetOf0(W1, tptp_fun_W1_18(W0!15))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, tptp_fun_W1_18(W0!15)))))))))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_2(W1, W0), W1)) | aElementOf0(tptp_fun_W2_2(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | (~aSet0(tptp_fun_W1_18(W0!15))) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, tptp_fun_W1_18(W0!15)) | (~((~aElementOf0(tptp_fun_W2_2(W1, tptp_fun_W1_18(W0!15)), W1)) | aElementOf0(tptp_fun_W2_2(W1, tptp_fun_W1_18(W0!15)), tptp_fun_W1_18(W0!15)))))) | (~((~aSubsetOf0(W1, tptp_fun_W1_18(W0!15))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, tptp_fun_W1_18(W0!15)))))))))))),
% 18.50/25.02 inference(rewrite,[status(thm)],[])).
% 18.50/25.02 tff(98,plain,
% 18.50/25.02 (((~aSet0(tptp_fun_W1_18(W0!15))) | ![W1: $i] : (~((~(aSubsetOf0(W1, tptp_fun_W1_18(W0!15)) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_2(W1, tptp_fun_W1_18(W0!15)), W1)) | aElementOf0(tptp_fun_W2_2(W1, tptp_fun_W1_18(W0!15)), tptp_fun_W1_18(W0!15)))))) | (~((~aSubsetOf0(W1, tptp_fun_W1_18(W0!15))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, tptp_fun_W1_18(W0!15))))))))))) <=> ((~aSet0(tptp_fun_W1_18(W0!15))) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, tptp_fun_W1_18(W0!15)) | (~((~aElementOf0(tptp_fun_W2_2(W1, tptp_fun_W1_18(W0!15)), W1)) | aElementOf0(tptp_fun_W2_2(W1, tptp_fun_W1_18(W0!15)), tptp_fun_W1_18(W0!15)))))) | (~((~aSubsetOf0(W1, tptp_fun_W1_18(W0!15))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, tptp_fun_W1_18(W0!15)))))))))))),
% 18.50/25.02 inference(rewrite,[status(thm)],[])).
% 18.50/25.02 tff(99,plain,
% 18.50/25.02 (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_2(W1, W0), W1)) | aElementOf0(tptp_fun_W2_2(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(tptp_fun_W1_18(W0!15))) | ![W1: $i] : (~((~(aSubsetOf0(W1, tptp_fun_W1_18(W0!15)) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_2(W1, tptp_fun_W1_18(W0!15)), W1)) | aElementOf0(tptp_fun_W2_2(W1, tptp_fun_W1_18(W0!15)), tptp_fun_W1_18(W0!15)))))) | (~((~aSubsetOf0(W1, tptp_fun_W1_18(W0!15))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, tptp_fun_W1_18(W0!15)))))))))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_2(W1, W0), W1)) | aElementOf0(tptp_fun_W2_2(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(tptp_fun_W1_18(W0!15))) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, tptp_fun_W1_18(W0!15)) | (~((~aElementOf0(tptp_fun_W2_2(W1, tptp_fun_W1_18(W0!15)), W1)) | aElementOf0(tptp_fun_W2_2(W1, tptp_fun_W1_18(W0!15)), tptp_fun_W1_18(W0!15)))))) | (~((~aSubsetOf0(W1, tptp_fun_W1_18(W0!15))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, tptp_fun_W1_18(W0!15))))))))))))),
% 18.50/25.03 inference(monotonicity,[status(thm)],[98])).
% 18.50/25.03 tff(100,plain,
% 18.50/25.03 (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_2(W1, W0), W1)) | aElementOf0(tptp_fun_W2_2(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(tptp_fun_W1_18(W0!15))) | ![W1: $i] : (~((~(aSubsetOf0(W1, tptp_fun_W1_18(W0!15)) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_2(W1, tptp_fun_W1_18(W0!15)), W1)) | aElementOf0(tptp_fun_W2_2(W1, tptp_fun_W1_18(W0!15)), tptp_fun_W1_18(W0!15)))))) | (~((~aSubsetOf0(W1, tptp_fun_W1_18(W0!15))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, tptp_fun_W1_18(W0!15)))))))))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_2(W1, W0), W1)) | aElementOf0(tptp_fun_W2_2(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | (~aSet0(tptp_fun_W1_18(W0!15))) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, tptp_fun_W1_18(W0!15)) | (~((~aElementOf0(tptp_fun_W2_2(W1, tptp_fun_W1_18(W0!15)), W1)) | aElementOf0(tptp_fun_W2_2(W1, tptp_fun_W1_18(W0!15)), tptp_fun_W1_18(W0!15)))))) | (~((~aSubsetOf0(W1, tptp_fun_W1_18(W0!15))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, tptp_fun_W1_18(W0!15)))))))))))),
% 18.50/25.03 inference(transitivity,[status(thm)],[99, 97])).
% 18.50/25.03 tff(101,plain,
% 18.50/25.03 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_2(W1, W0), W1)) | aElementOf0(tptp_fun_W2_2(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(tptp_fun_W1_18(W0!15))) | ![W1: $i] : (~((~(aSubsetOf0(W1, tptp_fun_W1_18(W0!15)) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_2(W1, tptp_fun_W1_18(W0!15)), W1)) | aElementOf0(tptp_fun_W2_2(W1, tptp_fun_W1_18(W0!15)), tptp_fun_W1_18(W0!15)))))) | (~((~aSubsetOf0(W1, tptp_fun_W1_18(W0!15))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, tptp_fun_W1_18(W0!15)))))))))))),
% 18.50/25.03 inference(quant_inst,[status(thm)],[])).
% 18.50/25.03 tff(102,plain,
% 18.50/25.03 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_2(W1, W0), W1)) | aElementOf0(tptp_fun_W2_2(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | (~aSet0(tptp_fun_W1_18(W0!15))) | ![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, tptp_fun_W1_18(W0!15)) | (~((~aElementOf0(tptp_fun_W2_2(W1, tptp_fun_W1_18(W0!15)), W1)) | aElementOf0(tptp_fun_W2_2(W1, tptp_fun_W1_18(W0!15)), tptp_fun_W1_18(W0!15)))))) | (~((~aSubsetOf0(W1, tptp_fun_W1_18(W0!15))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, tptp_fun_W1_18(W0!15))))))))))),
% 18.50/25.03 inference(modus_ponens,[status(thm)],[101, 100])).
% 18.50/25.03 tff(103,plain,
% 18.50/25.03 (![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, tptp_fun_W1_18(W0!15)) | (~((~aElementOf0(tptp_fun_W2_2(W1, tptp_fun_W1_18(W0!15)), W1)) | aElementOf0(tptp_fun_W2_2(W1, tptp_fun_W1_18(W0!15)), tptp_fun_W1_18(W0!15)))))) | (~((~aSubsetOf0(W1, tptp_fun_W1_18(W0!15))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, tptp_fun_W1_18(W0!15))))))))))),
% 18.50/25.03 inference(unit_resolution,[status(thm)],[102, 96, 74])).
% 18.50/25.03 tff(104,plain,
% 18.50/25.03 ((~![W1: $i] : (~((~((~aSet0(W1)) | aSubsetOf0(W1, tptp_fun_W1_18(W0!15)) | (~((~aElementOf0(tptp_fun_W2_2(W1, tptp_fun_W1_18(W0!15)), W1)) | aElementOf0(tptp_fun_W2_2(W1, tptp_fun_W1_18(W0!15)), tptp_fun_W1_18(W0!15)))))) | (~((~aSubsetOf0(W1, tptp_fun_W1_18(W0!15))) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, tptp_fun_W1_18(W0!15))))))))))) | (~((~((~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15)) | (~((~aElementOf0(tptp_fun_W2_2(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15)), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(tptp_fun_W2_2(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15)), tptp_fun_W1_18(W0!15)))))) | (~((~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15))) | (~((~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~![W2: $i] : ((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(W2, tptp_fun_W1_18(W0!15))))))))))),
% 18.50/25.03 inference(quant_inst,[status(thm)],[])).
% 18.50/25.03 tff(105,plain,
% 18.50/25.03 (~((~((~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15)) | (~((~aElementOf0(tptp_fun_W2_2(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15)), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(tptp_fun_W2_2(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15)), tptp_fun_W1_18(W0!15)))))) | (~((~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15))) | (~((~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~![W2: $i] : ((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(W2, tptp_fun_W1_18(W0!15)))))))))),
% 18.50/25.03 inference(unit_resolution,[status(thm)],[104, 103])).
% 18.50/25.03 tff(106,plain,
% 18.50/25.03 (((~((~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15)) | (~((~aElementOf0(tptp_fun_W2_2(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15)), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(tptp_fun_W2_2(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15)), tptp_fun_W1_18(W0!15)))))) | (~((~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15))) | (~((~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~![W2: $i] : ((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(W2, tptp_fun_W1_18(W0!15))))))))) | ((~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15))) | (~((~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~![W2: $i] : ((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(W2, tptp_fun_W1_18(W0!15)))))))),
% 18.50/25.03 inference(tautology,[status(thm)],[])).
% 18.50/25.03 tff(107,plain,
% 18.50/25.03 ((~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15))) | (~((~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~![W2: $i] : ((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(W2, tptp_fun_W1_18(W0!15))))))),
% 18.50/25.03 inference(unit_resolution,[status(thm)],[106, 105])).
% 18.50/25.03 tff(108,plain,
% 18.50/25.03 (((~aSet0(cS1395)) | (~![W1: $i] : (aElementOf0(W1, cS1395) <=> aInteger0(W1))) | (~![W1: $i] : ((~aElementOf0(W1, tptp_fun_W1_18(W0!15))) | aElementOf0(W1, cS1395))) | (~isOpen0(tptp_fun_W1_18(W0!15))) | (~aSubsetOf0(tptp_fun_W1_18(W0!15), cS1395)) | (~aSet0(tptp_fun_W1_18(W0!15))) | (~![W1: $i] : ((~aElementOf0(W1, tptp_fun_W1_18(W0!15))) | (~((~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | aElementOf0(W3, tptp_fun_W1_18(W0!15)))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | (~aInteger0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))) | (tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)) = sz00) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), tptp_fun_W4_14(W3, W1, tptp_fun_W1_18(W0!15))) = sdtpldt0(W3, smndt0(W1)))) | (~aInteger0(tptp_fun_W4_14(W3, W1, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W1)))) | (~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))) | (~((~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), W4) = sdtpldt0(W3, smndt0(W1)))))) | sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W1))))))))))))))) | ![W1: $i] : ((~aElementOf0(W1, tptp_fun_W1_18(W0!15))) | (~((~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | aElementOf0(W3, tptp_fun_W1_18(W0!15)))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | (~aInteger0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))) | (tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)) = sz00) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), tptp_fun_W4_14(W3, W1, tptp_fun_W1_18(W0!15))) = sdtpldt0(W3, smndt0(W1)))) | (~aInteger0(tptp_fun_W4_14(W3, W1, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W1)))) | (~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))) | (~((~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), W4) = sdtpldt0(W3, smndt0(W1)))))) | sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W1)))))))))))))),
% 18.50/25.03 inference(tautology,[status(thm)],[])).
% 18.50/25.03 tff(109,plain,
% 18.50/25.03 (![W1: $i] : ((~aElementOf0(W1, tptp_fun_W1_18(W0!15))) | (~((~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | aElementOf0(W3, tptp_fun_W1_18(W0!15)))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | (~aInteger0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))) | (tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)) = sz00) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), tptp_fun_W4_14(W3, W1, tptp_fun_W1_18(W0!15))) = sdtpldt0(W3, smndt0(W1)))) | (~aInteger0(tptp_fun_W4_14(W3, W1, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W1)))) | (~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))) | (~((~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), W4) = sdtpldt0(W3, smndt0(W1)))))) | sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W1)))))))))))))),
% 18.50/25.03 inference(unit_resolution,[status(thm)],[108, 72])).
% 18.50/25.03 tff(110,plain,
% 18.50/25.03 (((~aInteger0(W0!15)) | (~aElementOf0(W0!15, tptp_fun_W1_18(W0!15))) | (~aElementOf0(tptp_fun_W1_18(W0!15), xS))) | aElementOf0(W0!15, tptp_fun_W1_18(W0!15))),
% 18.50/25.03 inference(tautology,[status(thm)],[])).
% 18.50/25.03 tff(111,plain,
% 18.50/25.03 (aElementOf0(W0!15, tptp_fun_W1_18(W0!15))),
% 18.50/25.03 inference(unit_resolution,[status(thm)],[110, 40])).
% 18.50/25.03 tff(112,plain,
% 18.50/25.03 (((~![W1: $i] : ((~aElementOf0(W1, tptp_fun_W1_18(W0!15))) | (~((~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | aElementOf0(W3, tptp_fun_W1_18(W0!15)))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | (~aInteger0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))) | (tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)) = sz00) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), tptp_fun_W4_14(W3, W1, tptp_fun_W1_18(W0!15))) = sdtpldt0(W3, smndt0(W1)))) | (~aInteger0(tptp_fun_W4_14(W3, W1, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W1)))) | (~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))) | (~((~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), W4) = sdtpldt0(W3, smndt0(W1)))))) | sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W1)))))))))))))) | ((~aElementOf0(W0!15, tptp_fun_W1_18(W0!15))) | (~((~aInteger0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)) = sz00) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15))) | (~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(W3, tptp_fun_W1_18(W0!15)))) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W3)) | (~sdteqdtlpzmzozddtrp0(W3, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W4_14(W3, W0!15, tptp_fun_W1_18(W0!15)))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W4_14(W3, W0!15, tptp_fun_W1_18(W0!15))) = sdtpldt0(W3, smndt0(W0!15)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~(sdteqdtlpzmzozddtrp0(W3, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W0!15))) | (~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W4) = sdtpldt0(W3, smndt0(W0!15))))))))))))))))) <=> ((~![W1: $i] : ((~aElementOf0(W1, tptp_fun_W1_18(W0!15))) | (~((~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | aElementOf0(W3, tptp_fun_W1_18(W0!15)))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | (~aInteger0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))) | (tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)) = sz00) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), tptp_fun_W4_14(W3, W1, tptp_fun_W1_18(W0!15))) = sdtpldt0(W3, smndt0(W1)))) | (~aInteger0(tptp_fun_W4_14(W3, W1, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W1)))) | (~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))) | (~((~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), W4) = sdtpldt0(W3, smndt0(W1)))))) | sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W1)))))))))))))) | (~aElementOf0(W0!15, tptp_fun_W1_18(W0!15))) | (~((~aInteger0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)) = sz00) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15))) | (~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(W3, tptp_fun_W1_18(W0!15)))) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W3)) | (~sdteqdtlpzmzozddtrp0(W3, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W4_14(W3, W0!15, tptp_fun_W1_18(W0!15)))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W4_14(W3, W0!15, tptp_fun_W1_18(W0!15))) = sdtpldt0(W3, smndt0(W0!15)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~(sdteqdtlpzmzozddtrp0(W3, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W0!15))) | (~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W4) = sdtpldt0(W3, smndt0(W0!15))))))))))))))))),
% 18.50/25.03 inference(rewrite,[status(thm)],[])).
% 18.50/25.03 tff(113,plain,
% 18.50/25.03 (((~aElementOf0(W0!15, tptp_fun_W1_18(W0!15))) | (~((~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(W3, tptp_fun_W1_18(W0!15)))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~aInteger0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)) = sz00) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W4_14(W3, W0!15, tptp_fun_W1_18(W0!15))) = sdtpldt0(W3, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W4_14(W3, W0!15, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W0!15)))) | (~sdteqdtlpzmzozddtrp0(W3, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~((~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W4) = sdtpldt0(W3, smndt0(W0!15)))))) | sdteqdtlpzmzozddtrp0(W3, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W0!15))))))))))))) <=> ((~aElementOf0(W0!15, tptp_fun_W1_18(W0!15))) | (~((~aInteger0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)) = sz00) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15))) | (~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(W3, tptp_fun_W1_18(W0!15)))) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W3)) | (~sdteqdtlpzmzozddtrp0(W3, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W4_14(W3, W0!15, tptp_fun_W1_18(W0!15)))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W4_14(W3, W0!15, tptp_fun_W1_18(W0!15))) = sdtpldt0(W3, smndt0(W0!15)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~(sdteqdtlpzmzozddtrp0(W3, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W0!15))) | (~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W4) = sdtpldt0(W3, smndt0(W0!15))))))))))))))))),
% 18.50/25.03 inference(rewrite,[status(thm)],[])).
% 18.50/25.03 tff(114,plain,
% 18.50/25.03 (((~![W1: $i] : ((~aElementOf0(W1, tptp_fun_W1_18(W0!15))) | (~((~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | aElementOf0(W3, tptp_fun_W1_18(W0!15)))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | (~aInteger0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))) | (tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)) = sz00) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), tptp_fun_W4_14(W3, W1, tptp_fun_W1_18(W0!15))) = sdtpldt0(W3, smndt0(W1)))) | (~aInteger0(tptp_fun_W4_14(W3, W1, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W1)))) | (~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))) | (~((~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), W4) = sdtpldt0(W3, smndt0(W1)))))) | sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W1)))))))))))))) | ((~aElementOf0(W0!15, tptp_fun_W1_18(W0!15))) | (~((~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(W3, tptp_fun_W1_18(W0!15)))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~aInteger0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)) = sz00) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W4_14(W3, W0!15, tptp_fun_W1_18(W0!15))) = sdtpldt0(W3, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W4_14(W3, W0!15, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W0!15)))) | (~sdteqdtlpzmzozddtrp0(W3, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~((~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W4) = sdtpldt0(W3, smndt0(W0!15)))))) | sdteqdtlpzmzozddtrp0(W3, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W0!15)))))))))))))) <=> ((~![W1: $i] : ((~aElementOf0(W1, tptp_fun_W1_18(W0!15))) | (~((~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | aElementOf0(W3, tptp_fun_W1_18(W0!15)))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | (~aInteger0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))) | (tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)) = sz00) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), tptp_fun_W4_14(W3, W1, tptp_fun_W1_18(W0!15))) = sdtpldt0(W3, smndt0(W1)))) | (~aInteger0(tptp_fun_W4_14(W3, W1, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W1)))) | (~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))) | (~((~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), W4) = sdtpldt0(W3, smndt0(W1)))))) | sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W1)))))))))))))) | ((~aElementOf0(W0!15, tptp_fun_W1_18(W0!15))) | (~((~aInteger0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)) = sz00) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15))) | (~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(W3, tptp_fun_W1_18(W0!15)))) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W3)) | (~sdteqdtlpzmzozddtrp0(W3, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W4_14(W3, W0!15, tptp_fun_W1_18(W0!15)))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W4_14(W3, W0!15, tptp_fun_W1_18(W0!15))) = sdtpldt0(W3, smndt0(W0!15)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~(sdteqdtlpzmzozddtrp0(W3, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W0!15))) | (~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W4) = sdtpldt0(W3, smndt0(W0!15)))))))))))))))))),
% 18.50/25.03 inference(monotonicity,[status(thm)],[113])).
% 18.50/25.03 tff(115,plain,
% 18.50/25.03 (((~![W1: $i] : ((~aElementOf0(W1, tptp_fun_W1_18(W0!15))) | (~((~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | aElementOf0(W3, tptp_fun_W1_18(W0!15)))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | (~aInteger0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))) | (tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)) = sz00) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), tptp_fun_W4_14(W3, W1, tptp_fun_W1_18(W0!15))) = sdtpldt0(W3, smndt0(W1)))) | (~aInteger0(tptp_fun_W4_14(W3, W1, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W1)))) | (~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))) | (~((~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), W4) = sdtpldt0(W3, smndt0(W1)))))) | sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W1)))))))))))))) | ((~aElementOf0(W0!15, tptp_fun_W1_18(W0!15))) | (~((~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(W3, tptp_fun_W1_18(W0!15)))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~aInteger0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)) = sz00) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W4_14(W3, W0!15, tptp_fun_W1_18(W0!15))) = sdtpldt0(W3, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W4_14(W3, W0!15, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W0!15)))) | (~sdteqdtlpzmzozddtrp0(W3, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~((~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W4) = sdtpldt0(W3, smndt0(W0!15)))))) | sdteqdtlpzmzozddtrp0(W3, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W0!15)))))))))))))) <=> ((~![W1: $i] : ((~aElementOf0(W1, tptp_fun_W1_18(W0!15))) | (~((~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | aElementOf0(W3, tptp_fun_W1_18(W0!15)))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | (~aInteger0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))) | (tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)) = sz00) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), tptp_fun_W4_14(W3, W1, tptp_fun_W1_18(W0!15))) = sdtpldt0(W3, smndt0(W1)))) | (~aInteger0(tptp_fun_W4_14(W3, W1, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W1)))) | (~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))) | (~((~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), W4) = sdtpldt0(W3, smndt0(W1)))))) | sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W1)))))))))))))) | (~aElementOf0(W0!15, tptp_fun_W1_18(W0!15))) | (~((~aInteger0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)) = sz00) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15))) | (~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(W3, tptp_fun_W1_18(W0!15)))) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W3)) | (~sdteqdtlpzmzozddtrp0(W3, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W4_14(W3, W0!15, tptp_fun_W1_18(W0!15)))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W4_14(W3, W0!15, tptp_fun_W1_18(W0!15))) = sdtpldt0(W3, smndt0(W0!15)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~(sdteqdtlpzmzozddtrp0(W3, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W0!15))) | (~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W4) = sdtpldt0(W3, smndt0(W0!15))))))))))))))))),
% 18.50/25.03 inference(transitivity,[status(thm)],[114, 112])).
% 18.50/25.03 tff(116,plain,
% 18.50/25.03 ((~![W1: $i] : ((~aElementOf0(W1, tptp_fun_W1_18(W0!15))) | (~((~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | aElementOf0(W3, tptp_fun_W1_18(W0!15)))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | (~aInteger0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))) | (tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)) = sz00) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), tptp_fun_W4_14(W3, W1, tptp_fun_W1_18(W0!15))) = sdtpldt0(W3, smndt0(W1)))) | (~aInteger0(tptp_fun_W4_14(W3, W1, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W1)))) | (~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))) | (~((~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), W4) = sdtpldt0(W3, smndt0(W1)))))) | sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W1)))))))))))))) | ((~aElementOf0(W0!15, tptp_fun_W1_18(W0!15))) | (~((~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(W3, tptp_fun_W1_18(W0!15)))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~aInteger0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)) = sz00) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W4_14(W3, W0!15, tptp_fun_W1_18(W0!15))) = sdtpldt0(W3, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W4_14(W3, W0!15, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W0!15)))) | (~sdteqdtlpzmzozddtrp0(W3, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~((~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W4) = sdtpldt0(W3, smndt0(W0!15)))))) | sdteqdtlpzmzozddtrp0(W3, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W0!15)))))))))))))),
% 18.50/25.03 inference(quant_inst,[status(thm)],[])).
% 18.50/25.03 tff(117,plain,
% 18.50/25.03 ((~![W1: $i] : ((~aElementOf0(W1, tptp_fun_W1_18(W0!15))) | (~((~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | aElementOf0(W3, tptp_fun_W1_18(W0!15)))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15))) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | (~aInteger0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))) | (tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)) = sz00) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), tptp_fun_W4_14(W3, W1, tptp_fun_W1_18(W0!15))) = sdtpldt0(W3, smndt0(W1)))) | (~aInteger0(tptp_fun_W4_14(W3, W1, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W1)))) | (~sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)))) | (~((~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), W4) = sdtpldt0(W3, smndt0(W1)))))) | sdteqdtlpzmzozddtrp0(W3, W1, tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W1, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W1)))))))))))))) | (~aElementOf0(W0!15, tptp_fun_W1_18(W0!15))) | (~((~aInteger0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)) = sz00) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15))) | (~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(W3, tptp_fun_W1_18(W0!15)))) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W3)) | (~sdteqdtlpzmzozddtrp0(W3, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W4_14(W3, W0!15, tptp_fun_W1_18(W0!15)))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W4_14(W3, W0!15, tptp_fun_W1_18(W0!15))) = sdtpldt0(W3, smndt0(W0!15)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~(sdteqdtlpzmzozddtrp0(W3, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W0!15))) | (~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W4) = sdtpldt0(W3, smndt0(W0!15)))))))))))))))),
% 18.50/25.03 inference(modus_ponens,[status(thm)],[116, 115])).
% 18.50/25.03 tff(118,plain,
% 18.50/25.03 (~((~aInteger0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)) = sz00) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15))) | (~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(W3, tptp_fun_W1_18(W0!15)))) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W3)) | (~sdteqdtlpzmzozddtrp0(W3, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W4_14(W3, W0!15, tptp_fun_W1_18(W0!15)))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W4_14(W3, W0!15, tptp_fun_W1_18(W0!15))) = sdtpldt0(W3, smndt0(W0!15)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~(sdteqdtlpzmzozddtrp0(W3, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W0!15))) | (~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W4) = sdtpldt0(W3, smndt0(W0!15))))))))))))))),
% 18.50/25.04 inference(unit_resolution,[status(thm)],[117, 111, 109])).
% 18.50/25.04 tff(119,plain,
% 18.50/25.04 (((~aInteger0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)) = sz00) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15))) | (~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(W3, tptp_fun_W1_18(W0!15)))) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W3)) | (~sdteqdtlpzmzozddtrp0(W3, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W4_14(W3, W0!15, tptp_fun_W1_18(W0!15)))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W4_14(W3, W0!15, tptp_fun_W1_18(W0!15))) = sdtpldt0(W3, smndt0(W0!15)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~(sdteqdtlpzmzozddtrp0(W3, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W0!15))) | (~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W4) = sdtpldt0(W3, smndt0(W0!15)))))))))))))) | aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15))),
% 18.50/25.04 inference(tautology,[status(thm)],[])).
% 18.50/25.04 tff(120,plain,
% 18.50/25.04 (aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15))),
% 18.50/25.04 inference(unit_resolution,[status(thm)],[119, 118])).
% 18.50/25.04 tff(121,plain,
% 18.50/25.04 ((~((~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15))) | (~((~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~![W2: $i] : ((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(W2, tptp_fun_W1_18(W0!15)))))))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15))) | (~((~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~![W2: $i] : ((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(W2, tptp_fun_W1_18(W0!15))))))),
% 18.50/25.04 inference(tautology,[status(thm)],[])).
% 18.50/25.04 tff(122,plain,
% 18.50/25.04 ((~((~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15))) | (~((~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~![W2: $i] : ((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(W2, tptp_fun_W1_18(W0!15)))))))) | (~((~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~![W2: $i] : ((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(W2, tptp_fun_W1_18(W0!15))))))),
% 18.50/25.04 inference(unit_resolution,[status(thm)],[121, 120])).
% 18.50/25.04 tff(123,plain,
% 18.50/25.04 (~((~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~![W2: $i] : ((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(W2, tptp_fun_W1_18(W0!15)))))),
% 18.50/25.04 inference(unit_resolution,[status(thm)],[122, 107])).
% 18.50/25.04 tff(124,plain,
% 18.50/25.04 (((~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~![W2: $i] : ((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(W2, tptp_fun_W1_18(W0!15))))) | ![W2: $i] : ((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(W2, tptp_fun_W1_18(W0!15)))),
% 18.50/25.04 inference(tautology,[status(thm)],[])).
% 18.50/25.04 tff(125,plain,
% 18.50/25.04 (![W2: $i] : ((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(W2, tptp_fun_W1_18(W0!15)))),
% 18.50/25.04 inference(unit_resolution,[status(thm)],[124, 123])).
% 18.50/25.04 tff(126,plain,
% 18.50/25.04 (((~aInteger0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)) = sz00) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15))) | (~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(W3, tptp_fun_W1_18(W0!15)))) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W3)) | (~sdteqdtlpzmzozddtrp0(W3, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W4_14(W3, W0!15, tptp_fun_W1_18(W0!15)))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W4_14(W3, W0!15, tptp_fun_W1_18(W0!15))) = sdtpldt0(W3, smndt0(W0!15)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~(sdteqdtlpzmzozddtrp0(W3, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W0!15))) | (~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W4) = sdtpldt0(W3, smndt0(W0!15)))))))))))))) | (~(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)) = sz00))),
% 18.50/25.04 inference(tautology,[status(thm)],[])).
% 18.50/25.04 tff(127,plain,
% 18.50/25.04 (~(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)) = sz00)),
% 18.50/25.04 inference(unit_resolution,[status(thm)],[126, 118])).
% 18.50/25.04 tff(128,plain,
% 18.50/25.04 (((~aInteger0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)) = sz00) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15))) | (~![W3: $i] : ((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(W3, tptp_fun_W1_18(W0!15)))) | (~![W3: $i] : (~((~((~aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W3)) | (~sdteqdtlpzmzozddtrp0(W3, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W4_14(W3, W0!15, tptp_fun_W1_18(W0!15)))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W4_14(W3, W0!15, tptp_fun_W1_18(W0!15))) = sdtpldt0(W3, smndt0(W0!15)))))))) | (~((~aInteger0(W3)) | aElementOf0(W3, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~(sdteqdtlpzmzozddtrp0(W3, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W3, smndt0(W0!15))) | (~![W4: $i] : ((~aInteger0(W4)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W4) = sdtpldt0(W3, smndt0(W0!15)))))))))))))) | aInteger0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))),
% 18.50/25.04 inference(tautology,[status(thm)],[])).
% 18.50/25.04 tff(129,plain,
% 18.50/25.04 (aInteger0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))),
% 18.50/25.04 inference(unit_resolution,[status(thm)],[128, 118])).
% 18.50/25.04 tff(130,plain,
% 18.50/25.04 (^[W1: $i] : refl(((W1 = sz00) | (~aInteger0(W1)) | (~(aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1), sbsmnsldt0(xS)) | (~aElementOf0(tptp_fun_W2_17(W1), szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | aElementOf0(tptp_fun_W2_17(W1), sbsmnsldt0(xS)) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, W1)) | (~aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, W1))) | (~(sdtasdt0(W1, tptp_fun_W3_16(W2, W1)) = sdtpldt0(W2, smndt0(W0!15)))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) | (~(aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(W2, W0!15, W1) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15)))))))))))))))) <=> ((W1 = sz00) | (~aInteger0(W1)) | (~(aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1), sbsmnsldt0(xS)) | (~aElementOf0(tptp_fun_W2_17(W1), szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | aElementOf0(tptp_fun_W2_17(W1), sbsmnsldt0(xS)) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, W1)) | (~aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, W1))) | (~(sdtasdt0(W1, tptp_fun_W3_16(W2, W1)) = sdtpldt0(W2, smndt0(W0!15)))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) | (~(aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(W2, W0!15, W1) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15)))))))))))))))))),
% 18.50/25.04 inference(bind,[status(th)],[])).
% 18.50/25.04 tff(131,plain,
% 18.50/25.04 (![W1: $i] : ((W1 = sz00) | (~aInteger0(W1)) | (~(aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1), sbsmnsldt0(xS)) | (~aElementOf0(tptp_fun_W2_17(W1), szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | aElementOf0(tptp_fun_W2_17(W1), sbsmnsldt0(xS)) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, W1)) | (~aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, W1))) | (~(sdtasdt0(W1, tptp_fun_W3_16(W2, W1)) = sdtpldt0(W2, smndt0(W0!15)))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) | (~(aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(W2, W0!15, W1) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15)))))))))))))))) <=> ![W1: $i] : ((W1 = sz00) | (~aInteger0(W1)) | (~(aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1), sbsmnsldt0(xS)) | (~aElementOf0(tptp_fun_W2_17(W1), szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | aElementOf0(tptp_fun_W2_17(W1), sbsmnsldt0(xS)) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, W1)) | (~aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, W1))) | (~(sdtasdt0(W1, tptp_fun_W3_16(W2, W1)) = sdtpldt0(W2, smndt0(W0!15)))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) | (~(aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(W2, W0!15, W1) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15))))))))))))))))),
% 18.50/25.04 inference(quant_intro,[status(thm)],[130])).
% 18.50/25.04 tff(132,plain,
% 18.50/25.04 (^[W1: $i] : rewrite(((W1 = sz00) | (~aInteger0(W1)) | (~(aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1), sbsmnsldt0(xS)) | (~aElementOf0(tptp_fun_W2_17(W1), szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | aElementOf0(tptp_fun_W2_17(W1), sbsmnsldt0(xS)) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, W1)) | (~aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, W1))) | (~(sdtasdt0(W1, tptp_fun_W3_16(W2, W1)) = sdtpldt0(W2, smndt0(W0!15)))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) | (~(aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(W2, W0!15, W1) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15)))))))))))))))) <=> ((W1 = sz00) | (~aInteger0(W1)) | (~(aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1), sbsmnsldt0(xS)) | (~aElementOf0(tptp_fun_W2_17(W1), szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | aElementOf0(tptp_fun_W2_17(W1), sbsmnsldt0(xS)) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, W1)) | (~aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, W1))) | (~(sdtasdt0(W1, tptp_fun_W3_16(W2, W1)) = sdtpldt0(W2, smndt0(W0!15)))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) | (~(aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(W2, W0!15, W1) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15)))))))))))))))))),
% 18.50/25.04 inference(bind,[status(th)],[])).
% 18.50/25.04 tff(133,plain,
% 18.50/25.04 (![W1: $i] : ((W1 = sz00) | (~aInteger0(W1)) | (~(aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1), sbsmnsldt0(xS)) | (~aElementOf0(tptp_fun_W2_17(W1), szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | aElementOf0(tptp_fun_W2_17(W1), sbsmnsldt0(xS)) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, W1)) | (~aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, W1))) | (~(sdtasdt0(W1, tptp_fun_W3_16(W2, W1)) = sdtpldt0(W2, smndt0(W0!15)))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) | (~(aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(W2, W0!15, W1) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15)))))))))))))))) <=> ![W1: $i] : ((W1 = sz00) | (~aInteger0(W1)) | (~(aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1), sbsmnsldt0(xS)) | (~aElementOf0(tptp_fun_W2_17(W1), szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | aElementOf0(tptp_fun_W2_17(W1), sbsmnsldt0(xS)) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, W1)) | (~aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, W1))) | (~(sdtasdt0(W1, tptp_fun_W3_16(W2, W1)) = sdtpldt0(W2, smndt0(W0!15)))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) | (~(aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(W2, W0!15, W1) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15))))))))))))))))),
% 18.50/25.04 inference(quant_intro,[status(thm)],[132])).
% 18.50/25.04 tff(134,plain,
% 18.50/25.04 (![W1: $i] : ((W1 = sz00) | (~aInteger0(W1)) | (~(aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1), sbsmnsldt0(xS)) | (~aElementOf0(tptp_fun_W2_17(W1), szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | aElementOf0(tptp_fun_W2_17(W1), sbsmnsldt0(xS)) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, W1)) | (~aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, W1))) | (~(sdtasdt0(W1, tptp_fun_W3_16(W2, W1)) = sdtpldt0(W2, smndt0(W0!15)))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) | (~(aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(W2, W0!15, W1) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15)))))))))))))))) <=> ![W1: $i] : ((W1 = sz00) | (~aInteger0(W1)) | (~(aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1), sbsmnsldt0(xS)) | (~aElementOf0(tptp_fun_W2_17(W1), szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | aElementOf0(tptp_fun_W2_17(W1), sbsmnsldt0(xS)) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, W1)) | (~aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, W1))) | (~(sdtasdt0(W1, tptp_fun_W3_16(W2, W1)) = sdtpldt0(W2, smndt0(W0!15)))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) | (~(aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(W2, W0!15, W1) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15))))))))))))))))),
% 18.50/25.04 inference(transitivity,[status(thm)],[133, 131])).
% 18.50/25.04 tff(135,plain,
% 18.50/25.04 (^[W1: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[W2: $i] : trans(monotonicity(rewrite(((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (aInteger0(W2) & aInteger0(tptp_fun_W3_16(W2, W1)) & (sdtasdt0(W1, tptp_fun_W3_16(W2, W1)) = sdtpldt0(W2, smndt0(W0!15))) & aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15))) & sdteqdtlpzmzozddtrp0(W2, W0!15, W1))) <=> ((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, W1)) | (~aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, W1))) | (~(sdtasdt0(W1, tptp_fun_W3_16(W2, W1)) = sdtpldt0(W2, smndt0(W0!15)))))))), trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[W3: $i] : trans(monotonicity(rewrite((aInteger0(W3) & (sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15)))) <=> (~((~aInteger0(W3)) | (~(sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15))))))), ((~(aInteger0(W3) & (sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15))))) <=> (~(~((~aInteger0(W3)) | (~(sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15))))))))), rewrite((~(~((~aInteger0(W3)) | (~(sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15))))))) <=> ((~aInteger0(W3)) | (~(sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15)))))), ((~(aInteger0(W3) & (sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15))))) <=> ((~aInteger0(W3)) | (~(sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15)))))))), (![W3: $i] : (~(aInteger0(W3) & (sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15))))) <=> ![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15))))))), (((~sdteqdtlpzmzozddtrp0(W2, W0!15, W1)) & (~aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15)))) & ![W3: $i] : (~(aInteger0(W3) & (sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15)))))) <=> ((~sdteqdtlpzmzozddtrp0(W2, W0!15, W1)) & (~aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15)))) & ![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15)))))))), rewrite(((~sdteqdtlpzmzozddtrp0(W2, W0!15, W1)) & (~aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15)))) & ![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15)))))) <=> (~(aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(W2, W0!15, W1) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15))))))))), (((~sdteqdtlpzmzozddtrp0(W2, W0!15, W1)) & (~aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15)))) & ![W3: $i] : (~(aInteger0(W3) & (sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15)))))) <=> (~(aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(W2, W0!15, W1) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15)))))))))), (((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) | ((~sdteqdtlpzmzozddtrp0(W2, W0!15, W1)) & (~aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15)))) & ![W3: $i] : (~(aInteger0(W3) & (sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15))))))) <=> ((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) | (~(aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(W2, W0!15, W1) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15))))))))))), rewrite(((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) | (~(aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(W2, W0!15, W1) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15))))))))) <=> ((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) | (~(aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(W2, W0!15, W1) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15)))))))))), (((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) | ((~sdteqdtlpzmzozddtrp0(W2, W0!15, W1)) & (~aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15)))) & ![W3: $i] : (~(aInteger0(W3) & (sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15))))))) <=> ((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) | (~(aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(W2, W0!15, W1) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15))))))))))), ((((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (aInteger0(W2) & aInteger0(tptp_fun_W3_16(W2, W1)) & (sdtasdt0(W1, tptp_fun_W3_16(W2, W1)) = sdtpldt0(W2, smndt0(W0!15))) & aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15))) & sdteqdtlpzmzozddtrp0(W2, W0!15, W1))) & ((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) | ((~sdteqdtlpzmzozddtrp0(W2, W0!15, W1)) & (~aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15)))) & ![W3: $i] : (~(aInteger0(W3) & (sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15)))))))) <=> (((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, W1)) | (~aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, W1))) | (~(sdtasdt0(W1, tptp_fun_W3_16(W2, W1)) = sdtpldt0(W2, smndt0(W0!15))))))) & ((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) | (~(aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(W2, W0!15, W1) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15)))))))))))), rewrite((((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, W1)) | (~aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, W1))) | (~(sdtasdt0(W1, tptp_fun_W3_16(W2, W1)) = sdtpldt0(W2, smndt0(W0!15))))))) & ((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) | (~(aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(W2, W0!15, W1) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15)))))))))) <=> (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, W1)) | (~aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, W1))) | (~(sdtasdt0(W1, tptp_fun_W3_16(W2, W1)) = sdtpldt0(W2, smndt0(W0!15)))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) | (~(aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(W2, W0!15, W1) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15))))))))))))), ((((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (aInteger0(W2) & aInteger0(tptp_fun_W3_16(W2, W1)) & (sdtasdt0(W1, tptp_fun_W3_16(W2, W1)) = sdtpldt0(W2, smndt0(W0!15))) & aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15))) & sdteqdtlpzmzozddtrp0(W2, W0!15, W1))) & ((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) | ((~sdteqdtlpzmzozddtrp0(W2, W0!15, W1)) & (~aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15)))) & ![W3: $i] : (~(aInteger0(W3) & (sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15)))))))) <=> (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, W1)) | (~aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, W1))) | (~(sdtasdt0(W1, tptp_fun_W3_16(W2, W1)) = sdtpldt0(W2, smndt0(W0!15)))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) | (~(aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(W2, W0!15, W1) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15))))))))))))))), (![W2: $i] : (((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (aInteger0(W2) & aInteger0(tptp_fun_W3_16(W2, W1)) & (sdtasdt0(W1, tptp_fun_W3_16(W2, W1)) = sdtpldt0(W2, smndt0(W0!15))) & aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15))) & sdteqdtlpzmzozddtrp0(W2, W0!15, W1))) & ((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) | ((~sdteqdtlpzmzozddtrp0(W2, W0!15, W1)) & (~aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15)))) & ![W3: $i] : (~(aInteger0(W3) & (sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15)))))))) <=> ![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, W1)) | (~aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, W1))) | (~(sdtasdt0(W1, tptp_fun_W3_16(W2, W1)) = sdtpldt0(W2, smndt0(W0!15)))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) | (~(aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(W2, W0!15, W1) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15)))))))))))))), (((~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1), sbsmnsldt0(xS))) & aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) & ![W2: $i] : (((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (aInteger0(W2) & aInteger0(tptp_fun_W3_16(W2, W1)) & (sdtasdt0(W1, tptp_fun_W3_16(W2, W1)) = sdtpldt0(W2, smndt0(W0!15))) & aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15))) & sdteqdtlpzmzozddtrp0(W2, W0!15, W1))) & ((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) | ((~sdteqdtlpzmzozddtrp0(W2, W0!15, W1)) & (~aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15)))) & ![W3: $i] : (~(aInteger0(W3) & (sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15)))))))) & (~((~aElementOf0(tptp_fun_W2_17(W1), szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | aElementOf0(tptp_fun_W2_17(W1), sbsmnsldt0(xS))))) <=> ((~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1), sbsmnsldt0(xS))) & aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) & ![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, W1)) | (~aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, W1))) | (~(sdtasdt0(W1, tptp_fun_W3_16(W2, W1)) = sdtpldt0(W2, smndt0(W0!15)))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) | (~(aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(W2, W0!15, W1) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15)))))))))))) & (~((~aElementOf0(tptp_fun_W2_17(W1), szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | aElementOf0(tptp_fun_W2_17(W1), sbsmnsldt0(xS))))))), rewrite(((~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1), sbsmnsldt0(xS))) & aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) & ![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, W1)) | (~aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, W1))) | (~(sdtasdt0(W1, tptp_fun_W3_16(W2, W1)) = sdtpldt0(W2, smndt0(W0!15)))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) | (~(aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(W2, W0!15, W1) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15)))))))))))) & (~((~aElementOf0(tptp_fun_W2_17(W1), szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | aElementOf0(tptp_fun_W2_17(W1), sbsmnsldt0(xS))))) <=> (~(aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1), sbsmnsldt0(xS)) | (~aElementOf0(tptp_fun_W2_17(W1), szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | aElementOf0(tptp_fun_W2_17(W1), sbsmnsldt0(xS)) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, W1)) | (~aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, W1))) | (~(sdtasdt0(W1, tptp_fun_W3_16(W2, W1)) = sdtpldt0(W2, smndt0(W0!15)))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) | (~(aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(W2, W0!15, W1) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15)))))))))))))))), (((~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1), sbsmnsldt0(xS))) & aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) & ![W2: $i] : (((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (aInteger0(W2) & aInteger0(tptp_fun_W3_16(W2, W1)) & (sdtasdt0(W1, tptp_fun_W3_16(W2, W1)) = sdtpldt0(W2, smndt0(W0!15))) & aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15))) & sdteqdtlpzmzozddtrp0(W2, W0!15, W1))) & ((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) | ((~sdteqdtlpzmzozddtrp0(W2, W0!15, W1)) & (~aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15)))) & ![W3: $i] : (~(aInteger0(W3) & (sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15)))))))) & (~((~aElementOf0(tptp_fun_W2_17(W1), szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | aElementOf0(tptp_fun_W2_17(W1), sbsmnsldt0(xS))))) <=> (~(aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1), sbsmnsldt0(xS)) | (~aElementOf0(tptp_fun_W2_17(W1), szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | aElementOf0(tptp_fun_W2_17(W1), sbsmnsldt0(xS)) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, W1)) | (~aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, W1))) | (~(sdtasdt0(W1, tptp_fun_W3_16(W2, W1)) = sdtpldt0(W2, smndt0(W0!15)))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) | (~(aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(W2, W0!15, W1) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15))))))))))))))))), (((~aInteger0(W1)) | (W1 = sz00) | ((~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1), sbsmnsldt0(xS))) & aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) & ![W2: $i] : (((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (aInteger0(W2) & aInteger0(tptp_fun_W3_16(W2, W1)) & (sdtasdt0(W1, tptp_fun_W3_16(W2, W1)) = sdtpldt0(W2, smndt0(W0!15))) & aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15))) & sdteqdtlpzmzozddtrp0(W2, W0!15, W1))) & ((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) | ((~sdteqdtlpzmzozddtrp0(W2, W0!15, W1)) & (~aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15)))) & ![W3: $i] : (~(aInteger0(W3) & (sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15)))))))) & (~((~aElementOf0(tptp_fun_W2_17(W1), szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | aElementOf0(tptp_fun_W2_17(W1), sbsmnsldt0(xS)))))) <=> ((~aInteger0(W1)) | (W1 = sz00) | (~(aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1), sbsmnsldt0(xS)) | (~aElementOf0(tptp_fun_W2_17(W1), szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | aElementOf0(tptp_fun_W2_17(W1), sbsmnsldt0(xS)) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, W1)) | (~aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, W1))) | (~(sdtasdt0(W1, tptp_fun_W3_16(W2, W1)) = sdtpldt0(W2, smndt0(W0!15)))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) | (~(aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(W2, W0!15, W1) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15)))))))))))))))))), rewrite(((~aInteger0(W1)) | (W1 = sz00) | (~(aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1), sbsmnsldt0(xS)) | (~aElementOf0(tptp_fun_W2_17(W1), szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | aElementOf0(tptp_fun_W2_17(W1), sbsmnsldt0(xS)) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, W1)) | (~aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, W1))) | (~(sdtasdt0(W1, tptp_fun_W3_16(W2, W1)) = sdtpldt0(W2, smndt0(W0!15)))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) | (~(aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(W2, W0!15, W1) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15)))))))))))))))) <=> ((W1 = sz00) | (~aInteger0(W1)) | (~(aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1), sbsmnsldt0(xS)) | (~aElementOf0(tptp_fun_W2_17(W1), szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | aElementOf0(tptp_fun_W2_17(W1), sbsmnsldt0(xS)) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, W1)) | (~aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, W1))) | (~(sdtasdt0(W1, tptp_fun_W3_16(W2, W1)) = sdtpldt0(W2, smndt0(W0!15)))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) | (~(aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(W2, W0!15, W1) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15))))))))))))))))), (((~aInteger0(W1)) | (W1 = sz00) | ((~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1), sbsmnsldt0(xS))) & aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) & ![W2: $i] : (((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (aInteger0(W2) & aInteger0(tptp_fun_W3_16(W2, W1)) & (sdtasdt0(W1, tptp_fun_W3_16(W2, W1)) = sdtpldt0(W2, smndt0(W0!15))) & aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15))) & sdteqdtlpzmzozddtrp0(W2, W0!15, W1))) & ((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) | ((~sdteqdtlpzmzozddtrp0(W2, W0!15, W1)) & (~aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15)))) & ![W3: $i] : (~(aInteger0(W3) & (sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15)))))))) & (~((~aElementOf0(tptp_fun_W2_17(W1), szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | aElementOf0(tptp_fun_W2_17(W1), sbsmnsldt0(xS)))))) <=> ((W1 = sz00) | (~aInteger0(W1)) | (~(aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1), sbsmnsldt0(xS)) | (~aElementOf0(tptp_fun_W2_17(W1), szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | aElementOf0(tptp_fun_W2_17(W1), sbsmnsldt0(xS)) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, W1)) | (~aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, W1))) | (~(sdtasdt0(W1, tptp_fun_W3_16(W2, W1)) = sdtpldt0(W2, smndt0(W0!15)))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) | (~(aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(W2, W0!15, W1) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15))))))))))))))))))),
% 18.50/25.04 inference(bind,[status(th)],[])).
% 18.50/25.04 tff(136,plain,
% 18.50/25.04 (![W1: $i] : ((~aInteger0(W1)) | (W1 = sz00) | ((~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1), sbsmnsldt0(xS))) & aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) & ![W2: $i] : (((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (aInteger0(W2) & aInteger0(tptp_fun_W3_16(W2, W1)) & (sdtasdt0(W1, tptp_fun_W3_16(W2, W1)) = sdtpldt0(W2, smndt0(W0!15))) & aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15))) & sdteqdtlpzmzozddtrp0(W2, W0!15, W1))) & ((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) | ((~sdteqdtlpzmzozddtrp0(W2, W0!15, W1)) & (~aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15)))) & ![W3: $i] : (~(aInteger0(W3) & (sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15)))))))) & (~((~aElementOf0(tptp_fun_W2_17(W1), szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | aElementOf0(tptp_fun_W2_17(W1), sbsmnsldt0(xS)))))) <=> ![W1: $i] : ((W1 = sz00) | (~aInteger0(W1)) | (~(aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1), sbsmnsldt0(xS)) | (~aElementOf0(tptp_fun_W2_17(W1), szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | aElementOf0(tptp_fun_W2_17(W1), sbsmnsldt0(xS)) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, W1)) | (~aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, W1))) | (~(sdtasdt0(W1, tptp_fun_W3_16(W2, W1)) = sdtpldt0(W2, smndt0(W0!15)))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) | (~(aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(W2, W0!15, W1) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15))))))))))))))))),
% 18.50/25.04 inference(quant_intro,[status(thm)],[135])).
% 18.50/25.04 tff(137,plain,
% 18.50/25.04 (![W1: $i] : ((~aInteger0(W1)) | (W1 = sz00) | ((~aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1), sbsmnsldt0(xS))) & aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) & ![W2: $i] : (((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (aInteger0(W2) & aInteger0(tptp_fun_W3_16(W2, W1)) & (sdtasdt0(W1, tptp_fun_W3_16(W2, W1)) = sdtpldt0(W2, smndt0(W0!15))) & aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15))) & sdteqdtlpzmzozddtrp0(W2, W0!15, W1))) & ((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) | ((~sdteqdtlpzmzozddtrp0(W2, W0!15, W1)) & (~aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15)))) & ![W3: $i] : (~(aInteger0(W3) & (sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15)))))))) & (~((~aElementOf0(tptp_fun_W2_17(W1), szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | aElementOf0(tptp_fun_W2_17(W1), sbsmnsldt0(xS))))))),
% 18.50/25.04 inference(and_elim,[status(thm)],[36])).
% 18.50/25.04 tff(138,plain,
% 18.50/25.04 (![W1: $i] : ((W1 = sz00) | (~aInteger0(W1)) | (~(aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1), sbsmnsldt0(xS)) | (~aElementOf0(tptp_fun_W2_17(W1), szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | aElementOf0(tptp_fun_W2_17(W1), sbsmnsldt0(xS)) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, W1)) | (~aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, W1))) | (~(sdtasdt0(W1, tptp_fun_W3_16(W2, W1)) = sdtpldt0(W2, smndt0(W0!15)))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) | (~(aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(W2, W0!15, W1) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15))))))))))))))))),
% 18.50/25.04 inference(modus_ponens,[status(thm)],[137, 136])).
% 18.50/25.04 tff(139,plain,
% 18.50/25.04 (![W1: $i] : ((W1 = sz00) | (~aInteger0(W1)) | (~(aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1), sbsmnsldt0(xS)) | (~aElementOf0(tptp_fun_W2_17(W1), szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | aElementOf0(tptp_fun_W2_17(W1), sbsmnsldt0(xS)) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, W1)) | (~aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, W1))) | (~(sdtasdt0(W1, tptp_fun_W3_16(W2, W1)) = sdtpldt0(W2, smndt0(W0!15)))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) | (~(aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(W2, W0!15, W1) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15))))))))))))))))),
% 18.50/25.04 inference(modus_ponens,[status(thm)],[138, 134])).
% 18.50/25.04 tff(140,plain,
% 18.50/25.04 (((~![W1: $i] : ((W1 = sz00) | (~aInteger0(W1)) | (~(aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1), sbsmnsldt0(xS)) | (~aElementOf0(tptp_fun_W2_17(W1), szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | aElementOf0(tptp_fun_W2_17(W1), sbsmnsldt0(xS)) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, W1)) | (~aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, W1))) | (~(sdtasdt0(W1, tptp_fun_W3_16(W2, W1)) = sdtpldt0(W2, smndt0(W0!15)))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) | (~(aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(W2, W0!15, W1) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15))))))))))))))))) | ((~aInteger0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)) = sz00) | (~((~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | (~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15)))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) = sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~(sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15))) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W3) = sdtpldt0(W2, smndt0(W0!15))))))))))))))))) <=> ((~![W1: $i] : ((W1 = sz00) | (~aInteger0(W1)) | (~(aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1), sbsmnsldt0(xS)) | (~aElementOf0(tptp_fun_W2_17(W1), szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | aElementOf0(tptp_fun_W2_17(W1), sbsmnsldt0(xS)) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, W1)) | (~aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, W1))) | (~(sdtasdt0(W1, tptp_fun_W3_16(W2, W1)) = sdtpldt0(W2, smndt0(W0!15)))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) | (~(aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(W2, W0!15, W1) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15))))))))))))))))) | (~aInteger0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)) = sz00) | (~((~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | (~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15)))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) = sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~(sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15))) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W3) = sdtpldt0(W2, smndt0(W0!15))))))))))))))))),
% 18.50/25.05 inference(rewrite,[status(thm)],[])).
% 18.50/25.05 tff(141,plain,
% 18.50/25.05 (((tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)) = sz00) | (~aInteger0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~((~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | (~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15)))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) = sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~(sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15))) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W3) = sdtpldt0(W2, smndt0(W0!15)))))))))))))))) <=> ((~aInteger0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)) = sz00) | (~((~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | (~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15)))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) = sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~(sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15))) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W3) = sdtpldt0(W2, smndt0(W0!15))))))))))))))))),
% 18.50/25.05 inference(rewrite,[status(thm)],[])).
% 18.50/25.05 tff(142,plain,
% 18.50/25.05 ((~(aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) = sdtpldt0(W2, smndt0(W0!15)))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~(aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W3) = sdtpldt0(W2, smndt0(W0!15))))))))))))))) <=> (~((~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | (~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15)))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) = sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~(sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15))) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W3) = sdtpldt0(W2, smndt0(W0!15)))))))))))))))),
% 18.50/25.05 inference(rewrite,[status(thm)],[])).
% 18.50/25.05 tff(143,plain,
% 18.50/25.05 (((tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)) = sz00) | (~aInteger0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~(aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) = sdtpldt0(W2, smndt0(W0!15)))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~(aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W3) = sdtpldt0(W2, smndt0(W0!15)))))))))))))))) <=> ((tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)) = sz00) | (~aInteger0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~((~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | (~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15)))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) = sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~(sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15))) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W3) = sdtpldt0(W2, smndt0(W0!15))))))))))))))))),
% 18.50/25.05 inference(monotonicity,[status(thm)],[142])).
% 18.50/25.05 tff(144,plain,
% 18.50/25.05 (((tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)) = sz00) | (~aInteger0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~(aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) = sdtpldt0(W2, smndt0(W0!15)))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~(aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W3) = sdtpldt0(W2, smndt0(W0!15)))))))))))))))) <=> ((~aInteger0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)) = sz00) | (~((~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | (~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15)))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) = sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~(sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15))) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W3) = sdtpldt0(W2, smndt0(W0!15))))))))))))))))),
% 18.50/25.05 inference(transitivity,[status(thm)],[143, 141])).
% 18.50/25.05 tff(145,plain,
% 18.50/25.05 (((~![W1: $i] : ((W1 = sz00) | (~aInteger0(W1)) | (~(aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1), sbsmnsldt0(xS)) | (~aElementOf0(tptp_fun_W2_17(W1), szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | aElementOf0(tptp_fun_W2_17(W1), sbsmnsldt0(xS)) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, W1)) | (~aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, W1))) | (~(sdtasdt0(W1, tptp_fun_W3_16(W2, W1)) = sdtpldt0(W2, smndt0(W0!15)))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) | (~(aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(W2, W0!15, W1) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15))))))))))))))))) | ((tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)) = sz00) | (~aInteger0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~(aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) = sdtpldt0(W2, smndt0(W0!15)))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~(aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W3) = sdtpldt0(W2, smndt0(W0!15))))))))))))))))) <=> ((~![W1: $i] : ((W1 = sz00) | (~aInteger0(W1)) | (~(aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1), sbsmnsldt0(xS)) | (~aElementOf0(tptp_fun_W2_17(W1), szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | aElementOf0(tptp_fun_W2_17(W1), sbsmnsldt0(xS)) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, W1)) | (~aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, W1))) | (~(sdtasdt0(W1, tptp_fun_W3_16(W2, W1)) = sdtpldt0(W2, smndt0(W0!15)))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) | (~(aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(W2, W0!15, W1) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15))))))))))))))))) | ((~aInteger0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)) = sz00) | (~((~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | (~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15)))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) = sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~(sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15))) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W3) = sdtpldt0(W2, smndt0(W0!15)))))))))))))))))),
% 18.50/25.05 inference(monotonicity,[status(thm)],[144])).
% 18.50/25.05 tff(146,plain,
% 18.50/25.05 (((~![W1: $i] : ((W1 = sz00) | (~aInteger0(W1)) | (~(aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1), sbsmnsldt0(xS)) | (~aElementOf0(tptp_fun_W2_17(W1), szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | aElementOf0(tptp_fun_W2_17(W1), sbsmnsldt0(xS)) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, W1)) | (~aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, W1))) | (~(sdtasdt0(W1, tptp_fun_W3_16(W2, W1)) = sdtpldt0(W2, smndt0(W0!15)))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) | (~(aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(W2, W0!15, W1) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15))))))))))))))))) | ((tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)) = sz00) | (~aInteger0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~(aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) = sdtpldt0(W2, smndt0(W0!15)))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~(aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W3) = sdtpldt0(W2, smndt0(W0!15))))))))))))))))) <=> ((~![W1: $i] : ((W1 = sz00) | (~aInteger0(W1)) | (~(aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1), sbsmnsldt0(xS)) | (~aElementOf0(tptp_fun_W2_17(W1), szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | aElementOf0(tptp_fun_W2_17(W1), sbsmnsldt0(xS)) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, W1)) | (~aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, W1))) | (~(sdtasdt0(W1, tptp_fun_W3_16(W2, W1)) = sdtpldt0(W2, smndt0(W0!15)))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) | (~(aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(W2, W0!15, W1) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15))))))))))))))))) | (~aInteger0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)) = sz00) | (~((~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | (~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15)))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) = sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~(sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15))) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W3) = sdtpldt0(W2, smndt0(W0!15))))))))))))))))),
% 18.50/25.05 inference(transitivity,[status(thm)],[145, 140])).
% 18.50/25.05 tff(147,plain,
% 18.50/25.05 ((~![W1: $i] : ((W1 = sz00) | (~aInteger0(W1)) | (~(aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1), sbsmnsldt0(xS)) | (~aElementOf0(tptp_fun_W2_17(W1), szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | aElementOf0(tptp_fun_W2_17(W1), sbsmnsldt0(xS)) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, W1)) | (~aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, W1))) | (~(sdtasdt0(W1, tptp_fun_W3_16(W2, W1)) = sdtpldt0(W2, smndt0(W0!15)))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) | (~(aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(W2, W0!15, W1) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15))))))))))))))))) | ((tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)) = sz00) | (~aInteger0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~(aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) = sdtpldt0(W2, smndt0(W0!15)))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~(aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W3) = sdtpldt0(W2, smndt0(W0!15))))))))))))))))),
% 18.50/25.05 inference(quant_inst,[status(thm)],[])).
% 18.50/25.05 tff(148,plain,
% 18.50/25.05 ((~![W1: $i] : ((W1 = sz00) | (~aInteger0(W1)) | (~(aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1), sbsmnsldt0(xS)) | (~aElementOf0(tptp_fun_W2_17(W1), szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | aElementOf0(tptp_fun_W2_17(W1), sbsmnsldt0(xS)) | (~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, W1)) | (~aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, W1))) | (~(sdtasdt0(W1, tptp_fun_W3_16(W2, W1)) = sdtpldt0(W2, smndt0(W0!15)))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, W1)) | (~(aDivisorOf0(W1, sdtpldt0(W2, smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(W2, W0!15, W1) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(W1, W3) = sdtpldt0(W2, smndt0(W0!15))))))))))))))))) | (~aInteger0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)) = sz00) | (~((~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | (~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15)))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) = sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~(sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15))) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W3) = sdtpldt0(W2, smndt0(W0!15)))))))))))))))),
% 18.50/25.05 inference(modus_ponens,[status(thm)],[147, 146])).
% 18.50/25.05 tff(149,plain,
% 18.50/25.05 (~((~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | (~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15)))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) = sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~(sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15))) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W3) = sdtpldt0(W2, smndt0(W0!15))))))))))))))),
% 18.50/25.05 inference(unit_resolution,[status(thm)],[148, 139, 129, 127])).
% 18.50/25.05 tff(150,plain,
% 18.50/25.05 (((~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | (~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15)))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) = sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~(sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15))) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W3) = sdtpldt0(W2, smndt0(W0!15)))))))))))))) | aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))),
% 18.50/25.06 inference(tautology,[status(thm)],[])).
% 18.50/25.06 tff(151,plain,
% 18.50/25.06 (aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))),
% 18.50/25.06 inference(unit_resolution,[status(thm)],[150, 149])).
% 18.50/25.06 tff(152,plain,
% 18.50/25.06 (((~![W2: $i] : ((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(W2, tptp_fun_W1_18(W0!15)))) | ((~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15)))) <=> ((~![W2: $i] : ((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(W2, tptp_fun_W1_18(W0!15)))) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15)))),
% 18.50/25.06 inference(rewrite,[status(thm)],[])).
% 18.50/25.06 tff(153,plain,
% 18.50/25.06 ((~![W2: $i] : ((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(W2, tptp_fun_W1_18(W0!15)))) | ((~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15)))),
% 18.50/25.06 inference(quant_inst,[status(thm)],[])).
% 18.50/25.06 tff(154,plain,
% 18.50/25.06 ((~![W2: $i] : ((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(W2, tptp_fun_W1_18(W0!15)))) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15))),
% 18.50/25.06 inference(modus_ponens,[status(thm)],[153, 152])).
% 18.50/25.06 tff(155,plain,
% 18.50/25.06 (aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15))),
% 18.50/25.06 inference(unit_resolution,[status(thm)],[154, 151, 125])).
% 18.50/25.06 tff(156,plain,
% 18.50/25.06 (((~![W0: $i] : (~((~((~aElementOf0(W0, sbsmnsldt0(xS))) | (~((~aInteger0(W0)) | (~aElementOf0(tptp_fun_W1_18(W0), xS)) | (~aElementOf0(W0, tptp_fun_W1_18(W0))))))) | (~((~aInteger0(W0)) | aElementOf0(W0, sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(W0, W1)))))))) | (~((~((~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W1))))) | (~((~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS))) | (~((~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))))) | (~aElementOf0(tptp_fun_W1_18(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))), xS))))))))) <=> ((~![W0: $i] : (~((~((~aElementOf0(W0, sbsmnsldt0(xS))) | (~((~aInteger0(W0)) | (~aElementOf0(tptp_fun_W1_18(W0), xS)) | (~aElementOf0(W0, tptp_fun_W1_18(W0))))))) | (~((~aInteger0(W0)) | aElementOf0(W0, sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(W0, W1)))))))) | (~((~((~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W1))))) | (~((~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS))) | (~((~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))))) | (~aElementOf0(tptp_fun_W1_18(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))), xS)))))))))),
% 18.50/25.06 inference(rewrite,[status(thm)],[])).
% 18.50/25.06 tff(157,plain,
% 18.50/25.06 ((~((~((~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS))) | (~((~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~aElementOf0(tptp_fun_W1_18(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))), xS)) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))))))))) | (~((~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W1))))))) <=> (~((~((~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W1))))) | (~((~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS))) | (~((~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))))) | (~aElementOf0(tptp_fun_W1_18(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))), xS))))))))),
% 18.50/25.06 inference(rewrite,[status(thm)],[])).
% 18.50/25.06 tff(158,plain,
% 18.50/25.06 (((~![W0: $i] : (~((~((~aElementOf0(W0, sbsmnsldt0(xS))) | (~((~aInteger0(W0)) | (~aElementOf0(tptp_fun_W1_18(W0), xS)) | (~aElementOf0(W0, tptp_fun_W1_18(W0))))))) | (~((~aInteger0(W0)) | aElementOf0(W0, sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(W0, W1)))))))) | (~((~((~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS))) | (~((~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~aElementOf0(tptp_fun_W1_18(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))), xS)) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))))))))) | (~((~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W1)))))))) <=> ((~![W0: $i] : (~((~((~aElementOf0(W0, sbsmnsldt0(xS))) | (~((~aInteger0(W0)) | (~aElementOf0(tptp_fun_W1_18(W0), xS)) | (~aElementOf0(W0, tptp_fun_W1_18(W0))))))) | (~((~aInteger0(W0)) | aElementOf0(W0, sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(W0, W1)))))))) | (~((~((~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W1))))) | (~((~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS))) | (~((~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))))) | (~aElementOf0(tptp_fun_W1_18(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))), xS)))))))))),
% 18.50/25.06 inference(monotonicity,[status(thm)],[157])).
% 18.50/25.06 tff(159,plain,
% 18.50/25.06 (((~![W0: $i] : (~((~((~aElementOf0(W0, sbsmnsldt0(xS))) | (~((~aInteger0(W0)) | (~aElementOf0(tptp_fun_W1_18(W0), xS)) | (~aElementOf0(W0, tptp_fun_W1_18(W0))))))) | (~((~aInteger0(W0)) | aElementOf0(W0, sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(W0, W1)))))))) | (~((~((~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS))) | (~((~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~aElementOf0(tptp_fun_W1_18(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))), xS)) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))))))))) | (~((~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W1)))))))) <=> ((~![W0: $i] : (~((~((~aElementOf0(W0, sbsmnsldt0(xS))) | (~((~aInteger0(W0)) | (~aElementOf0(tptp_fun_W1_18(W0), xS)) | (~aElementOf0(W0, tptp_fun_W1_18(W0))))))) | (~((~aInteger0(W0)) | aElementOf0(W0, sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(W0, W1)))))))) | (~((~((~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W1))))) | (~((~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS))) | (~((~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))))) | (~aElementOf0(tptp_fun_W1_18(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))), xS)))))))))),
% 18.50/25.06 inference(transitivity,[status(thm)],[158, 156])).
% 18.50/25.06 tff(160,plain,
% 18.50/25.06 ((~![W0: $i] : (~((~((~aElementOf0(W0, sbsmnsldt0(xS))) | (~((~aInteger0(W0)) | (~aElementOf0(tptp_fun_W1_18(W0), xS)) | (~aElementOf0(W0, tptp_fun_W1_18(W0))))))) | (~((~aInteger0(W0)) | aElementOf0(W0, sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(W0, W1)))))))) | (~((~((~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS))) | (~((~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~aElementOf0(tptp_fun_W1_18(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))), xS)) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))))))))) | (~((~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W1)))))))),
% 18.50/25.06 inference(quant_inst,[status(thm)],[])).
% 18.50/25.06 tff(161,plain,
% 18.50/25.06 ((~![W0: $i] : (~((~((~aElementOf0(W0, sbsmnsldt0(xS))) | (~((~aInteger0(W0)) | (~aElementOf0(tptp_fun_W1_18(W0), xS)) | (~aElementOf0(W0, tptp_fun_W1_18(W0))))))) | (~((~aInteger0(W0)) | aElementOf0(W0, sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(W0, W1)))))))) | (~((~((~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W1))))) | (~((~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS))) | (~((~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))))) | (~aElementOf0(tptp_fun_W1_18(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))), xS))))))))),
% 18.50/25.06 inference(modus_ponens,[status(thm)],[160, 159])).
% 18.50/25.06 tff(162,plain,
% 18.50/25.06 (~((~((~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W1))))) | (~((~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS))) | (~((~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))))) | (~aElementOf0(tptp_fun_W1_18(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))), xS)))))))),
% 18.50/25.06 inference(unit_resolution,[status(thm)],[161, 20])).
% 18.50/25.06 tff(163,plain,
% 18.50/25.06 (((~((~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W1))))) | (~((~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS))) | (~((~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))))) | (~aElementOf0(tptp_fun_W1_18(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))), xS))))))) | ((~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W1))))),
% 18.50/25.06 inference(tautology,[status(thm)],[])).
% 18.50/25.06 tff(164,plain,
% 18.50/25.06 ((~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W1)))),
% 18.50/25.06 inference(unit_resolution,[status(thm)],[163, 162])).
% 18.50/25.06 tff(165,plain,
% 18.50/25.06 (((~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | (~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15)))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) = sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~(sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15))) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W3) = sdtpldt0(W2, smndt0(W0!15)))))))))))))) | ![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15)))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) = sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~(sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15))) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W3) = sdtpldt0(W2, smndt0(W0!15))))))))))))),
% 18.50/25.06 inference(tautology,[status(thm)],[])).
% 18.50/25.06 tff(166,plain,
% 18.50/25.06 (![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15)))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) = sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~(sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15))) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W3) = sdtpldt0(W2, smndt0(W0!15))))))))))))),
% 18.50/25.06 inference(unit_resolution,[status(thm)],[165, 149])).
% 18.50/25.06 tff(167,plain,
% 18.50/25.06 (((~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15)))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) = sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~(sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15))) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W3) = sdtpldt0(W2, smndt0(W0!15))))))))))))) | (~((~((~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~aInteger0(tptp_fun_W3_16(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W3_16(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) = sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15)))) | (~sdteqdtlpzmzozddtrp0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))))))) | (~(aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W3) = sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15)))))) | aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))))))))) <=> ((~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15)))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) = sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~(sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15))) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W3) = sdtpldt0(W2, smndt0(W0!15))))))))))))) | (~((~((~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~aInteger0(tptp_fun_W3_16(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W3_16(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) = sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15)))) | (~sdteqdtlpzmzozddtrp0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))))))) | (~(aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W3) = sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15)))))) | aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))))))))),
% 18.50/25.06 inference(rewrite,[status(thm)],[])).
% 18.50/25.06 tff(168,plain,
% 18.50/25.06 ((~((~((~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~sdteqdtlpzmzozddtrp0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15)))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W3_16(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) = sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))))))) | (~((~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~(sdteqdtlpzmzozddtrp0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15))) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W3) = sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15)))))))))))) <=> (~((~((~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~aInteger0(tptp_fun_W3_16(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W3_16(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) = sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15)))) | (~sdteqdtlpzmzozddtrp0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))))))) | (~(aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W3) = sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15)))))) | aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))))))))),
% 18.50/25.06 inference(rewrite,[status(thm)],[])).
% 18.50/25.06 tff(169,plain,
% 18.50/25.06 (((~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15)))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) = sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~(sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15))) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W3) = sdtpldt0(W2, smndt0(W0!15))))))))))))) | (~((~((~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~sdteqdtlpzmzozddtrp0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15)))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W3_16(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) = sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))))))) | (~((~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~(sdteqdtlpzmzozddtrp0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15))) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W3) = sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15))))))))))))) <=> ((~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15)))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) = sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~(sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15))) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W3) = sdtpldt0(W2, smndt0(W0!15))))))))))))) | (~((~((~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~aInteger0(tptp_fun_W3_16(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W3_16(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) = sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15)))) | (~sdteqdtlpzmzozddtrp0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))))))) | (~(aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W3) = sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15)))))) | aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))))))))),
% 18.50/25.07 inference(monotonicity,[status(thm)],[168])).
% 18.50/25.07 tff(170,plain,
% 18.50/25.07 (((~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15)))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) = sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~(sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15))) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W3) = sdtpldt0(W2, smndt0(W0!15))))))))))))) | (~((~((~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~sdteqdtlpzmzozddtrp0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15)))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W3_16(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) = sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))))))) | (~((~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~(sdteqdtlpzmzozddtrp0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15))) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W3) = sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15))))))))))))) <=> ((~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15)))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) = sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~(sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15))) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W3) = sdtpldt0(W2, smndt0(W0!15))))))))))))) | (~((~((~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~aInteger0(tptp_fun_W3_16(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W3_16(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) = sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15)))) | (~sdteqdtlpzmzozddtrp0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))))))) | (~(aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W3) = sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15)))))) | aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))))))))),
% 18.50/25.07 inference(transitivity,[status(thm)],[169, 167])).
% 18.50/25.07 tff(171,plain,
% 18.50/25.07 ((~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15)))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) = sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~(sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15))) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W3) = sdtpldt0(W2, smndt0(W0!15))))))))))))) | (~((~((~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~sdteqdtlpzmzozddtrp0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15)))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W3_16(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) = sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))))))) | (~((~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~(sdteqdtlpzmzozddtrp0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15))) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W3) = sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15))))))))))))),
% 18.50/25.07 inference(quant_inst,[status(thm)],[])).
% 18.50/25.07 tff(172,plain,
% 18.50/25.07 ((~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15)))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) = sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~(sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15))) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W3) = sdtpldt0(W2, smndt0(W0!15))))))))))))) | (~((~((~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~aInteger0(tptp_fun_W3_16(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W3_16(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) = sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15)))) | (~sdteqdtlpzmzozddtrp0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))))))) | (~(aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W3) = sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15)))))) | aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))))))))),
% 18.50/25.07 inference(modus_ponens,[status(thm)],[171, 170])).
% 18.50/25.07 tff(173,plain,
% 18.50/25.07 (~((~((~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~aInteger0(tptp_fun_W3_16(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W3_16(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) = sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15)))) | (~sdteqdtlpzmzozddtrp0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))))))) | (~(aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W3) = sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15)))))) | aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))))))),
% 18.50/25.07 inference(unit_resolution,[status(thm)],[172, 166])).
% 18.50/25.07 tff(174,plain,
% 18.50/25.07 (((~((~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~aInteger0(tptp_fun_W3_16(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W3_16(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) = sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15)))) | (~sdteqdtlpzmzozddtrp0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))))))) | (~(aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W3) = sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15)))))) | aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15))) | sdteqdtlpzmzozddtrp0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))))))) | ((~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~aInteger0(tptp_fun_W3_16(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W3_16(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) = sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15)))) | (~sdteqdtlpzmzozddtrp0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))))))),
% 18.50/25.07 inference(tautology,[status(thm)],[])).
% 18.50/25.07 tff(175,plain,
% 18.50/25.07 ((~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~aInteger0(tptp_fun_W3_16(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W3_16(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) = sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15)))) | (~sdteqdtlpzmzozddtrp0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))))),
% 18.50/25.07 inference(unit_resolution,[status(thm)],[174, 173])).
% 18.50/25.07 tff(176,plain,
% 18.50/25.07 ((~((~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~aInteger0(tptp_fun_W3_16(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W3_16(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) = sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15)))) | (~sdteqdtlpzmzozddtrp0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))))))) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~aInteger0(tptp_fun_W3_16(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W3_16(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) = sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15)))) | (~sdteqdtlpzmzozddtrp0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))))),
% 18.50/25.07 inference(tautology,[status(thm)],[])).
% 18.50/25.07 tff(177,plain,
% 18.50/25.07 ((~((~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~aInteger0(tptp_fun_W3_16(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W3_16(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) = sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15)))) | (~sdteqdtlpzmzozddtrp0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))))))) | (~((~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~aInteger0(tptp_fun_W3_16(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W3_16(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) = sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15)))) | (~sdteqdtlpzmzozddtrp0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))))),
% 18.50/25.07 inference(unit_resolution,[status(thm)],[176, 151])).
% 18.50/25.07 tff(178,plain,
% 18.50/25.07 (~((~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~aInteger0(tptp_fun_W3_16(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W3_16(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) = sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15)))) | (~sdteqdtlpzmzozddtrp0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))))),
% 18.50/25.07 inference(unit_resolution,[status(thm)],[177, 175])).
% 18.50/25.07 tff(179,plain,
% 18.50/25.07 (((~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~aInteger0(tptp_fun_W3_16(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W3_16(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) = sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), smndt0(W0!15)))) | (~sdteqdtlpzmzozddtrp0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))),
% 18.50/25.07 inference(tautology,[status(thm)],[])).
% 18.50/25.07 tff(180,plain,
% 18.50/25.07 (aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))),
% 18.50/25.07 inference(unit_resolution,[status(thm)],[179, 178])).
% 18.50/25.07 tff(181,plain,
% 18.50/25.07 (((~aSet0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | (~![W2: $i] : (~((~((~aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | (~((~aInteger0(W2)) | (~sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15)))) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) = sdtpldt0(W2, smndt0(W0!15)))) | (~aInteger0(tptp_fun_W3_16(W2, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))))))) | (~((~aInteger0(W2)) | aElementOf0(W2, szAzrzSzezqlpdtcmdtrp0(W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)))) | (~(sdteqdtlpzmzozddtrp0(W2, W0!15, tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))) | aDivisorOf0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), sdtpldt0(W2, smndt0(W0!15))) | (~![W3: $i] : ((~aInteger0(W3)) | (~(sdtasdt0(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15)), W3) = sdtpldt0(W2, smndt0(W0!15)))))))))))))) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)))),
% 18.61/25.13 inference(tautology,[status(thm)],[])).
% 18.61/25.13 tff(182,plain,
% 18.61/25.13 (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS))),
% 18.61/25.13 inference(unit_resolution,[status(thm)],[181, 149])).
% 18.61/25.13 tff(183,plain,
% 18.61/25.13 ((~((~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W1))))) | (~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W1)))),
% 18.61/25.13 inference(tautology,[status(thm)],[])).
% 18.61/25.13 tff(184,plain,
% 18.61/25.13 ((~((~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), sbsmnsldt0(xS)) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W1))))) | (~aInteger0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))))) | ![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W1)))),
% 18.61/25.13 inference(unit_resolution,[status(thm)],[183, 182])).
% 18.61/25.13 tff(185,plain,
% 18.61/25.13 (![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W1)))),
% 18.61/25.13 inference(unit_resolution,[status(thm)],[184, 180, 164])).
% 18.61/25.13 tff(186,plain,
% 18.61/25.13 (((~![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W1)))) | ((~aElementOf0(tptp_fun_W1_18(W0!15), xS)) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15))))) <=> ((~![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W1)))) | (~aElementOf0(tptp_fun_W1_18(W0!15), xS)) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15))))),
% 18.61/25.13 inference(rewrite,[status(thm)],[])).
% 18.61/25.13 tff(187,plain,
% 18.61/25.13 ((~![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W1)))) | ((~aElementOf0(tptp_fun_W1_18(W0!15), xS)) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15))))),
% 18.61/25.13 inference(quant_inst,[status(thm)],[])).
% 18.61/25.13 tff(188,plain,
% 18.61/25.13 ((~![W1: $i] : ((~aElementOf0(W1, xS)) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), W1)))) | (~aElementOf0(tptp_fun_W1_18(W0!15), xS)) | (~aElementOf0(tptp_fun_W2_17(tptp_fun_W2_13(W0!15, tptp_fun_W1_18(W0!15))), tptp_fun_W1_18(W0!15)))),
% 18.61/25.13 inference(modus_ponens,[status(thm)],[187, 186])).
% 18.61/25.13 tff(189,plain,
% 18.61/25.13 ($false),
% 18.61/25.13 inference(unit_resolution,[status(thm)],[188, 42, 185, 155])).
% 18.61/25.13 % SZS output end Proof
% 18.66/25.14 % E exiting
%------------------------------------------------------------------------------