%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : RNG111+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:24:13 AM UTC 2025
% Result : Theorem 6.14s 6.38s
% Output : Proof 6.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : RNG111+1 : TPTP v9.0.0. Released v4.0.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 03:24:05 EDT 2025
% 0.12/0.33 % CPUTime :
% 6.14/6.38 % SZS status Theorem
% 6.14/6.38 % SZS output start Proof
% 6.14/6.38 tff(aElementOf0_type, type, (
% 6.14/6.38 aElementOf0: ( $i * $i ) > $o)).
% 6.14/6.38 tff(xI_type, type, (
% 6.14/6.38 xI: $i)).
% 6.14/6.38 tff(tptp_fun_W2_22_type, type, (
% 6.14/6.38 tptp_fun_W2_22: $i > $i)).
% 6.14/6.38 tff(tptp_fun_W2_23_type, type, (
% 6.14/6.38 tptp_fun_W2_23: $i)).
% 6.14/6.38 tff(sz00_type, type, (
% 6.14/6.38 sz00: $i)).
% 6.14/6.38 tff(iLess0_type, type, (
% 6.14/6.38 iLess0: ( $i * $i ) > $o)).
% 6.14/6.38 tff(sbrdtbr0_type, type, (
% 6.14/6.38 sbrdtbr0: $i > $i)).
% 6.14/6.38 tff(tptp_fun_W0_21_type, type, (
% 6.14/6.38 tptp_fun_W0_21: $i)).
% 6.14/6.38 tff(1,plain,
% 6.14/6.38 (^[W1: $i] : refl(((W1 = sz00) | (~aElementOf0(W1, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W2_22(W1)), sbrdtbr0(W1))) | (tptp_fun_W2_22(W1) = sz00) | (~aElementOf0(tptp_fun_W2_22(W1), xI))))) <=> ((W1 = sz00) | (~aElementOf0(W1, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W2_22(W1)), sbrdtbr0(W1))) | (tptp_fun_W2_22(W1) = sz00) | (~aElementOf0(tptp_fun_W2_22(W1), xI))))))),
% 6.14/6.38 inference(bind,[status(th)],[])).
% 6.14/6.38 tff(2,plain,
% 6.14/6.38 (![W1: $i] : ((W1 = sz00) | (~aElementOf0(W1, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W2_22(W1)), sbrdtbr0(W1))) | (tptp_fun_W2_22(W1) = sz00) | (~aElementOf0(tptp_fun_W2_22(W1), xI))))) <=> ![W1: $i] : ((W1 = sz00) | (~aElementOf0(W1, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W2_22(W1)), sbrdtbr0(W1))) | (tptp_fun_W2_22(W1) = sz00) | (~aElementOf0(tptp_fun_W2_22(W1), xI)))))),
% 6.14/6.38 inference(quant_intro,[status(thm)],[1])).
% 6.14/6.38 tff(3,plain,
% 6.14/6.38 (^[W1: $i] : trans(monotonicity(rewrite((~((~iLess0(sbrdtbr0(tptp_fun_W2_22(W1)), sbrdtbr0(W1))) | (~(aElementOf0(tptp_fun_W2_22(W1), xI) & (~(tptp_fun_W2_22(W1) = sz00)))))) <=> (~((~iLess0(sbrdtbr0(tptp_fun_W2_22(W1)), sbrdtbr0(W1))) | (tptp_fun_W2_22(W1) = sz00) | (~aElementOf0(tptp_fun_W2_22(W1), xI))))), (((W1 = sz00) | (~aElementOf0(W1, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W2_22(W1)), sbrdtbr0(W1))) | (~(aElementOf0(tptp_fun_W2_22(W1), xI) & (~(tptp_fun_W2_22(W1) = sz00))))))) <=> ((W1 = sz00) | (~aElementOf0(W1, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W2_22(W1)), sbrdtbr0(W1))) | (tptp_fun_W2_22(W1) = sz00) | (~aElementOf0(tptp_fun_W2_22(W1), xI))))))), rewrite(((W1 = sz00) | (~aElementOf0(W1, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W2_22(W1)), sbrdtbr0(W1))) | (tptp_fun_W2_22(W1) = sz00) | (~aElementOf0(tptp_fun_W2_22(W1), xI))))) <=> ((W1 = sz00) | (~aElementOf0(W1, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W2_22(W1)), sbrdtbr0(W1))) | (tptp_fun_W2_22(W1) = sz00) | (~aElementOf0(tptp_fun_W2_22(W1), xI)))))), (((W1 = sz00) | (~aElementOf0(W1, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W2_22(W1)), sbrdtbr0(W1))) | (~(aElementOf0(tptp_fun_W2_22(W1), xI) & (~(tptp_fun_W2_22(W1) = sz00))))))) <=> ((W1 = sz00) | (~aElementOf0(W1, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W2_22(W1)), sbrdtbr0(W1))) | (tptp_fun_W2_22(W1) = sz00) | (~aElementOf0(tptp_fun_W2_22(W1), xI)))))))),
% 6.14/6.38 inference(bind,[status(th)],[])).
% 6.14/6.38 tff(4,plain,
% 6.14/6.38 (![W1: $i] : ((W1 = sz00) | (~aElementOf0(W1, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W2_22(W1)), sbrdtbr0(W1))) | (~(aElementOf0(tptp_fun_W2_22(W1), xI) & (~(tptp_fun_W2_22(W1) = sz00))))))) <=> ![W1: $i] : ((W1 = sz00) | (~aElementOf0(W1, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W2_22(W1)), sbrdtbr0(W1))) | (tptp_fun_W2_22(W1) = sz00) | (~aElementOf0(tptp_fun_W2_22(W1), xI)))))),
% 6.14/6.38 inference(quant_intro,[status(thm)],[3])).
% 6.14/6.38 tff(5,plain,
% 6.14/6.38 (((aElementOf0(W0!21, xI) & (~(W0!21 = sz00))) & ![W1: $i] : ((W1 = sz00) | (~aElementOf0(W1, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W2_22(W1)), sbrdtbr0(W1))) | (~(aElementOf0(tptp_fun_W2_22(W1), xI) & (~(tptp_fun_W2_22(W1) = sz00))))))) & ![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0!21))) | (~(aElementOf0(W1, xI) & (~(W1 = sz00)))) | (aElementOf0(W2!23, xI) & (~(W2!23 = sz00)) & ![W3: $i] : ((~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))) | (~(aElementOf0(W3, xI) & (~(W3 = sz00)))))))) <=> (aElementOf0(W0!21, xI) & (~(W0!21 = sz00)) & ![W1: $i] : ((W1 = sz00) | (~aElementOf0(W1, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W2_22(W1)), sbrdtbr0(W1))) | (~(aElementOf0(tptp_fun_W2_22(W1), xI) & (~(tptp_fun_W2_22(W1) = sz00))))))) & ![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0!21))) | (~(aElementOf0(W1, xI) & (~(W1 = sz00)))) | (aElementOf0(W2!23, xI) & (~(W2!23 = sz00)) & ![W3: $i] : ((~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))) | (~(aElementOf0(W3, xI) & (~(W3 = sz00))))))))),
% 6.14/6.38 inference(rewrite,[status(thm)],[])).
% 6.14/6.38 tff(6,plain,
% 6.14/6.38 (^[W1: $i] : rewrite(((~aElementOf0(W1, xI)) | (W1 = sz00) | (~((~iLess0(sbrdtbr0(tptp_fun_W2_22(W1)), sbrdtbr0(W1))) | (~(aElementOf0(tptp_fun_W2_22(W1), xI) & (~(tptp_fun_W2_22(W1) = sz00))))))) <=> ((W1 = sz00) | (~aElementOf0(W1, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W2_22(W1)), sbrdtbr0(W1))) | (~(aElementOf0(tptp_fun_W2_22(W1), xI) & (~(tptp_fun_W2_22(W1) = sz00))))))))),
% 6.14/6.38 inference(bind,[status(th)],[])).
% 6.14/6.38 tff(7,plain,
% 6.14/6.38 (![W1: $i] : ((~aElementOf0(W1, xI)) | (W1 = sz00) | (~((~iLess0(sbrdtbr0(tptp_fun_W2_22(W1)), sbrdtbr0(W1))) | (~(aElementOf0(tptp_fun_W2_22(W1), xI) & (~(tptp_fun_W2_22(W1) = sz00))))))) <=> ![W1: $i] : ((W1 = sz00) | (~aElementOf0(W1, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W2_22(W1)), sbrdtbr0(W1))) | (~(aElementOf0(tptp_fun_W2_22(W1), xI) & (~(tptp_fun_W2_22(W1) = sz00)))))))),
% 6.14/6.38 inference(quant_intro,[status(thm)],[6])).
% 6.14/6.38 tff(8,plain,
% 6.14/6.38 (((aElementOf0(W0!21, xI) & (~(W0!21 = sz00))) & ![W1: $i] : ((~aElementOf0(W1, xI)) | (W1 = sz00) | (~((~iLess0(sbrdtbr0(tptp_fun_W2_22(W1)), sbrdtbr0(W1))) | (~(aElementOf0(tptp_fun_W2_22(W1), xI) & (~(tptp_fun_W2_22(W1) = sz00))))))) & ![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0!21))) | (~(aElementOf0(W1, xI) & (~(W1 = sz00)))) | (aElementOf0(W2!23, xI) & (~(W2!23 = sz00)) & ![W3: $i] : ((~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))) | (~(aElementOf0(W3, xI) & (~(W3 = sz00)))))))) <=> ((aElementOf0(W0!21, xI) & (~(W0!21 = sz00))) & ![W1: $i] : ((W1 = sz00) | (~aElementOf0(W1, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W2_22(W1)), sbrdtbr0(W1))) | (~(aElementOf0(tptp_fun_W2_22(W1), xI) & (~(tptp_fun_W2_22(W1) = sz00))))))) & ![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0!21))) | (~(aElementOf0(W1, xI) & (~(W1 = sz00)))) | (aElementOf0(W2!23, xI) & (~(W2!23 = sz00)) & ![W3: $i] : ((~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))) | (~(aElementOf0(W3, xI) & (~(W3 = sz00))))))))),
% 6.14/6.38 inference(monotonicity,[status(thm)],[7])).
% 6.14/6.38 tff(9,plain,
% 6.14/6.38 (((aElementOf0(W0!21, xI) & (~(W0!21 = sz00))) & ![W1: $i] : ((~aElementOf0(W1, xI)) | (W1 = sz00) | (~((~iLess0(sbrdtbr0(tptp_fun_W2_22(W1)), sbrdtbr0(W1))) | (~(aElementOf0(tptp_fun_W2_22(W1), xI) & (~(tptp_fun_W2_22(W1) = sz00))))))) & ![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0!21))) | (~(aElementOf0(W1, xI) & (~(W1 = sz00)))) | (aElementOf0(W2!23, xI) & (~(W2!23 = sz00)) & ![W3: $i] : ((~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))) | (~(aElementOf0(W3, xI) & (~(W3 = sz00)))))))) <=> (aElementOf0(W0!21, xI) & (~(W0!21 = sz00)) & ![W1: $i] : ((W1 = sz00) | (~aElementOf0(W1, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W2_22(W1)), sbrdtbr0(W1))) | (~(aElementOf0(tptp_fun_W2_22(W1), xI) & (~(tptp_fun_W2_22(W1) = sz00))))))) & ![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0!21))) | (~(aElementOf0(W1, xI) & (~(W1 = sz00)))) | (aElementOf0(W2!23, xI) & (~(W2!23 = sz00)) & ![W3: $i] : ((~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))) | (~(aElementOf0(W3, xI) & (~(W3 = sz00))))))))),
% 6.14/6.38 inference(transitivity,[status(thm)],[8, 5])).
% 6.14/6.38 tff(10,plain,
% 6.14/6.38 ((~![W0: $i] : ((~(aElementOf0(W0, xI) & (~(W0 = sz00)))) | ?[W1: $i] : (aElementOf0(W1, xI) & (~(W1 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~(aElementOf0(W2, xI) & (~(W2 = sz00)))))) | (~![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0))) | (~(aElementOf0(W1, xI) & (~(W1 = sz00)))) | ?[W2: $i] : (aElementOf0(W2, xI) & (~(W2 = sz00)) & ![W3: $i] : ((~iLess0(sbrdtbr0(W3), sbrdtbr0(W2))) | (~(aElementOf0(W3, xI) & (~(W3 = sz00)))))))))) <=> (~![W0: $i] : ((~(aElementOf0(W0, xI) & (~(W0 = sz00)))) | ?[W1: $i] : (aElementOf0(W1, xI) & (~(W1 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~(aElementOf0(W2, xI) & (~(W2 = sz00)))))) | (~![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0))) | (~(aElementOf0(W1, xI) & (~(W1 = sz00)))) | ?[W2: $i] : (aElementOf0(W2, xI) & (~(W2 = sz00)) & ![W3: $i] : ((~iLess0(sbrdtbr0(W3), sbrdtbr0(W2))) | (~(aElementOf0(W3, xI) & (~(W3 = sz00))))))))))),
% 6.14/6.38 inference(rewrite,[status(thm)],[])).
% 6.14/6.38 tff(11,plain,
% 6.14/6.38 ((~![W0: $i] : ((aElementOf0(W0, xI) & (~(W0 = sz00))) => (![W1: $i] : ((aElementOf0(W1, xI) & (~(W1 = sz00))) => (iLess0(sbrdtbr0(W1), sbrdtbr0(W0)) => ?[W2: $i] : ((aElementOf0(W2, xI) & (~(W2 = sz00))) & ![W3: $i] : ((aElementOf0(W3, xI) & (~(W3 = sz00))) => (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2))))))) => ?[W1: $i] : ((aElementOf0(W1, xI) & (~(W1 = sz00))) & ![W2: $i] : ((aElementOf0(W2, xI) & (~(W2 = sz00))) => (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1)))))))) <=> (~![W0: $i] : ((~(aElementOf0(W0, xI) & (~(W0 = sz00)))) | ?[W1: $i] : (aElementOf0(W1, xI) & (~(W1 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~(aElementOf0(W2, xI) & (~(W2 = sz00)))))) | (~![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0))) | (~(aElementOf0(W1, xI) & (~(W1 = sz00)))) | ?[W2: $i] : (aElementOf0(W2, xI) & (~(W2 = sz00)) & ![W3: $i] : ((~iLess0(sbrdtbr0(W3), sbrdtbr0(W2))) | (~(aElementOf0(W3, xI) & (~(W3 = sz00))))))))))),
% 6.14/6.38 inference(rewrite,[status(thm)],[])).
% 6.14/6.38 tff(12,axiom,(~![W0: $i] : ((aElementOf0(W0, xI) & (~(W0 = sz00))) => (![W1: $i] : ((aElementOf0(W1, xI) & (~(W1 = sz00))) => (iLess0(sbrdtbr0(W1), sbrdtbr0(W0)) => ?[W2: $i] : ((aElementOf0(W2, xI) & (~(W2 = sz00))) & ![W3: $i] : ((aElementOf0(W3, xI) & (~(W3 = sz00))) => (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2))))))) => ?[W1: $i] : ((aElementOf0(W1, xI) & (~(W1 = sz00))) & ![W2: $i] : ((aElementOf0(W2, xI) & (~(W2 = sz00))) => (~iLess0(sbrdtbr0(W2), sbrdtbr0(W1)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__')).
% 6.14/6.38 tff(13,plain,
% 6.14/6.38 (~![W0: $i] : ((~(aElementOf0(W0, xI) & (~(W0 = sz00)))) | ?[W1: $i] : (aElementOf0(W1, xI) & (~(W1 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~(aElementOf0(W2, xI) & (~(W2 = sz00)))))) | (~![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0))) | (~(aElementOf0(W1, xI) & (~(W1 = sz00)))) | ?[W2: $i] : (aElementOf0(W2, xI) & (~(W2 = sz00)) & ![W3: $i] : ((~iLess0(sbrdtbr0(W3), sbrdtbr0(W2))) | (~(aElementOf0(W3, xI) & (~(W3 = sz00)))))))))),
% 6.14/6.38 inference(modus_ponens,[status(thm)],[12, 11])).
% 6.14/6.38 tff(14,plain,
% 6.14/6.38 (~![W0: $i] : ((~(aElementOf0(W0, xI) & (~(W0 = sz00)))) | ?[W1: $i] : (aElementOf0(W1, xI) & (~(W1 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~(aElementOf0(W2, xI) & (~(W2 = sz00)))))) | (~![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0))) | (~(aElementOf0(W1, xI) & (~(W1 = sz00)))) | ?[W2: $i] : (aElementOf0(W2, xI) & (~(W2 = sz00)) & ![W3: $i] : ((~iLess0(sbrdtbr0(W3), sbrdtbr0(W2))) | (~(aElementOf0(W3, xI) & (~(W3 = sz00)))))))))),
% 6.14/6.38 inference(modus_ponens,[status(thm)],[13, 10])).
% 6.14/6.38 tff(15,plain,
% 6.14/6.38 (~![W0: $i] : ((~(aElementOf0(W0, xI) & (~(W0 = sz00)))) | ?[W1: $i] : (aElementOf0(W1, xI) & (~(W1 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~(aElementOf0(W2, xI) & (~(W2 = sz00)))))) | (~![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0))) | (~(aElementOf0(W1, xI) & (~(W1 = sz00)))) | ?[W2: $i] : (aElementOf0(W2, xI) & (~(W2 = sz00)) & ![W3: $i] : ((~iLess0(sbrdtbr0(W3), sbrdtbr0(W2))) | (~(aElementOf0(W3, xI) & (~(W3 = sz00)))))))))),
% 6.14/6.38 inference(modus_ponens,[status(thm)],[14, 10])).
% 6.14/6.38 tff(16,plain,
% 6.14/6.38 (~![W0: $i] : ((~(aElementOf0(W0, xI) & (~(W0 = sz00)))) | ?[W1: $i] : (aElementOf0(W1, xI) & (~(W1 = sz00)) & ![W2: $i] : ((~iLess0(sbrdtbr0(W2), sbrdtbr0(W1))) | (~(aElementOf0(W2, xI) & (~(W2 = sz00)))))) | (~![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0))) | (~(aElementOf0(W1, xI) & (~(W1 = sz00)))) | ?[W2: $i] : (aElementOf0(W2, xI) & (~(W2 = sz00)) & ![W3: $i] : ((~iLess0(sbrdtbr0(W3), sbrdtbr0(W2))) | (~(aElementOf0(W3, xI) & (~(W3 = sz00)))))))))),
% 6.14/6.38 inference(modus_ponens,[status(thm)],[15, 10])).
% 6.14/6.38 tff(17,plain,
% 6.14/6.38 (aElementOf0(W0!21, xI) & (~(W0!21 = sz00)) & ![W1: $i] : ((W1 = sz00) | (~aElementOf0(W1, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W2_22(W1)), sbrdtbr0(W1))) | (~(aElementOf0(tptp_fun_W2_22(W1), xI) & (~(tptp_fun_W2_22(W1) = sz00))))))) & ![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0!21))) | (~(aElementOf0(W1, xI) & (~(W1 = sz00)))) | (aElementOf0(W2!23, xI) & (~(W2!23 = sz00)) & ![W3: $i] : ((~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))) | (~(aElementOf0(W3, xI) & (~(W3 = sz00)))))))),
% 6.14/6.38 inference(modus_ponens,[status(thm)],[16, 9])).
% 6.14/6.38 tff(18,plain,
% 6.14/6.38 (![W1: $i] : ((W1 = sz00) | (~aElementOf0(W1, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W2_22(W1)), sbrdtbr0(W1))) | (~(aElementOf0(tptp_fun_W2_22(W1), xI) & (~(tptp_fun_W2_22(W1) = sz00)))))))),
% 6.14/6.38 inference(and_elim,[status(thm)],[17])).
% 6.14/6.38 tff(19,plain,
% 6.14/6.38 (![W1: $i] : ((W1 = sz00) | (~aElementOf0(W1, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W2_22(W1)), sbrdtbr0(W1))) | (tptp_fun_W2_22(W1) = sz00) | (~aElementOf0(tptp_fun_W2_22(W1), xI)))))),
% 6.14/6.38 inference(modus_ponens,[status(thm)],[18, 4])).
% 6.14/6.38 tff(20,plain,
% 6.14/6.38 (![W1: $i] : ((W1 = sz00) | (~aElementOf0(W1, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W2_22(W1)), sbrdtbr0(W1))) | (tptp_fun_W2_22(W1) = sz00) | (~aElementOf0(tptp_fun_W2_22(W1), xI)))))),
% 6.14/6.38 inference(modus_ponens,[status(thm)],[19, 2])).
% 6.14/6.38 tff(21,plain,
% 6.14/6.38 (~(W0!21 = sz00)),
% 6.14/6.38 inference(and_elim,[status(thm)],[17])).
% 6.14/6.38 tff(22,plain,
% 6.14/6.38 (aElementOf0(W0!21, xI)),
% 6.14/6.38 inference(and_elim,[status(thm)],[17])).
% 6.14/6.38 tff(23,plain,
% 6.14/6.38 (((~![W1: $i] : ((W1 = sz00) | (~aElementOf0(W1, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W2_22(W1)), sbrdtbr0(W1))) | (tptp_fun_W2_22(W1) = sz00) | (~aElementOf0(tptp_fun_W2_22(W1), xI)))))) | ((W0!21 = sz00) | (~aElementOf0(W0!21, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W2_22(W0!21)), sbrdtbr0(W0!21))) | (tptp_fun_W2_22(W0!21) = sz00) | (~aElementOf0(tptp_fun_W2_22(W0!21), xI)))))) <=> ((~![W1: $i] : ((W1 = sz00) | (~aElementOf0(W1, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W2_22(W1)), sbrdtbr0(W1))) | (tptp_fun_W2_22(W1) = sz00) | (~aElementOf0(tptp_fun_W2_22(W1), xI)))))) | (W0!21 = sz00) | (~aElementOf0(W0!21, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W2_22(W0!21)), sbrdtbr0(W0!21))) | (tptp_fun_W2_22(W0!21) = sz00) | (~aElementOf0(tptp_fun_W2_22(W0!21), xI)))))),
% 6.14/6.38 inference(rewrite,[status(thm)],[])).
% 6.14/6.38 tff(24,plain,
% 6.14/6.38 ((~![W1: $i] : ((W1 = sz00) | (~aElementOf0(W1, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W2_22(W1)), sbrdtbr0(W1))) | (tptp_fun_W2_22(W1) = sz00) | (~aElementOf0(tptp_fun_W2_22(W1), xI)))))) | ((W0!21 = sz00) | (~aElementOf0(W0!21, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W2_22(W0!21)), sbrdtbr0(W0!21))) | (tptp_fun_W2_22(W0!21) = sz00) | (~aElementOf0(tptp_fun_W2_22(W0!21), xI)))))),
% 6.14/6.38 inference(quant_inst,[status(thm)],[])).
% 6.14/6.38 tff(25,plain,
% 6.14/6.38 ((~![W1: $i] : ((W1 = sz00) | (~aElementOf0(W1, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W2_22(W1)), sbrdtbr0(W1))) | (tptp_fun_W2_22(W1) = sz00) | (~aElementOf0(tptp_fun_W2_22(W1), xI)))))) | (W0!21 = sz00) | (~aElementOf0(W0!21, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W2_22(W0!21)), sbrdtbr0(W0!21))) | (tptp_fun_W2_22(W0!21) = sz00) | (~aElementOf0(tptp_fun_W2_22(W0!21), xI))))),
% 6.14/6.38 inference(modus_ponens,[status(thm)],[24, 23])).
% 6.14/6.38 tff(26,plain,
% 6.14/6.38 (~((~iLess0(sbrdtbr0(tptp_fun_W2_22(W0!21)), sbrdtbr0(W0!21))) | (tptp_fun_W2_22(W0!21) = sz00) | (~aElementOf0(tptp_fun_W2_22(W0!21), xI)))),
% 6.14/6.38 inference(unit_resolution,[status(thm)],[25, 22, 21, 20])).
% 6.14/6.38 tff(27,plain,
% 6.14/6.38 (((~iLess0(sbrdtbr0(tptp_fun_W2_22(W0!21)), sbrdtbr0(W0!21))) | (tptp_fun_W2_22(W0!21) = sz00) | (~aElementOf0(tptp_fun_W2_22(W0!21), xI))) | aElementOf0(tptp_fun_W2_22(W0!21), xI)),
% 6.14/6.38 inference(tautology,[status(thm)],[])).
% 6.14/6.38 tff(28,plain,
% 6.14/6.38 (aElementOf0(tptp_fun_W2_22(W0!21), xI)),
% 6.14/6.38 inference(unit_resolution,[status(thm)],[27, 26])).
% 6.14/6.38 tff(29,plain,
% 6.14/6.38 (((~iLess0(sbrdtbr0(tptp_fun_W2_22(W0!21)), sbrdtbr0(W0!21))) | (tptp_fun_W2_22(W0!21) = sz00) | (~aElementOf0(tptp_fun_W2_22(W0!21), xI))) | (~(tptp_fun_W2_22(W0!21) = sz00))),
% 6.14/6.38 inference(tautology,[status(thm)],[])).
% 6.14/6.38 tff(30,plain,
% 6.14/6.38 (~(tptp_fun_W2_22(W0!21) = sz00)),
% 6.14/6.38 inference(unit_resolution,[status(thm)],[29, 26])).
% 6.14/6.38 tff(31,plain,
% 6.14/6.38 (((~iLess0(sbrdtbr0(tptp_fun_W2_22(W0!21)), sbrdtbr0(W0!21))) | (tptp_fun_W2_22(W0!21) = sz00) | (~aElementOf0(tptp_fun_W2_22(W0!21), xI))) | iLess0(sbrdtbr0(tptp_fun_W2_22(W0!21)), sbrdtbr0(W0!21))),
% 6.14/6.38 inference(tautology,[status(thm)],[])).
% 6.14/6.38 tff(32,plain,
% 6.14/6.38 (iLess0(sbrdtbr0(tptp_fun_W2_22(W0!21)), sbrdtbr0(W0!21))),
% 6.14/6.38 inference(unit_resolution,[status(thm)],[31, 26])).
% 6.14/6.39 tff(33,plain,
% 6.14/6.39 (^[W1: $i] : refl(((W1 = sz00) | (~iLess0(sbrdtbr0(W1), sbrdtbr0(W0!21))) | (~aElementOf0(W1, xI)) | (~((W2!23 = sz00) | (~aElementOf0(W2!23, xI)) | (~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23)))))))) <=> ((W1 = sz00) | (~iLess0(sbrdtbr0(W1), sbrdtbr0(W0!21))) | (~aElementOf0(W1, xI)) | (~((W2!23 = sz00) | (~aElementOf0(W2!23, xI)) | (~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23)))))))))),
% 6.14/6.39 inference(bind,[status(th)],[])).
% 6.14/6.39 tff(34,plain,
% 6.14/6.39 (![W1: $i] : ((W1 = sz00) | (~iLess0(sbrdtbr0(W1), sbrdtbr0(W0!21))) | (~aElementOf0(W1, xI)) | (~((W2!23 = sz00) | (~aElementOf0(W2!23, xI)) | (~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23)))))))) <=> ![W1: $i] : ((W1 = sz00) | (~iLess0(sbrdtbr0(W1), sbrdtbr0(W0!21))) | (~aElementOf0(W1, xI)) | (~((W2!23 = sz00) | (~aElementOf0(W2!23, xI)) | (~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))))))))),
% 6.14/6.39 inference(quant_intro,[status(thm)],[33])).
% 6.14/6.39 tff(35,plain,
% 6.14/6.39 (^[W1: $i] : rewrite(((W1 = sz00) | (~iLess0(sbrdtbr0(W1), sbrdtbr0(W0!21))) | (~aElementOf0(W1, xI)) | (~((W2!23 = sz00) | (~aElementOf0(W2!23, xI)) | (~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23)))))))) <=> ((W1 = sz00) | (~iLess0(sbrdtbr0(W1), sbrdtbr0(W0!21))) | (~aElementOf0(W1, xI)) | (~((W2!23 = sz00) | (~aElementOf0(W2!23, xI)) | (~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23)))))))))),
% 6.14/6.39 inference(bind,[status(th)],[])).
% 6.14/6.39 tff(36,plain,
% 6.14/6.39 (![W1: $i] : ((W1 = sz00) | (~iLess0(sbrdtbr0(W1), sbrdtbr0(W0!21))) | (~aElementOf0(W1, xI)) | (~((W2!23 = sz00) | (~aElementOf0(W2!23, xI)) | (~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23)))))))) <=> ![W1: $i] : ((W1 = sz00) | (~iLess0(sbrdtbr0(W1), sbrdtbr0(W0!21))) | (~aElementOf0(W1, xI)) | (~((W2!23 = sz00) | (~aElementOf0(W2!23, xI)) | (~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))))))))),
% 6.14/6.39 inference(quant_intro,[status(thm)],[35])).
% 6.14/6.39 tff(37,plain,
% 6.14/6.39 (![W1: $i] : ((W1 = sz00) | (~iLess0(sbrdtbr0(W1), sbrdtbr0(W0!21))) | (~aElementOf0(W1, xI)) | (~((W2!23 = sz00) | (~aElementOf0(W2!23, xI)) | (~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23)))))))) <=> ![W1: $i] : ((W1 = sz00) | (~iLess0(sbrdtbr0(W1), sbrdtbr0(W0!21))) | (~aElementOf0(W1, xI)) | (~((W2!23 = sz00) | (~aElementOf0(W2!23, xI)) | (~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))))))))),
% 6.14/6.39 inference(transitivity,[status(thm)],[36, 34])).
% 6.14/6.39 tff(38,plain,
% 6.14/6.39 (^[W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aElementOf0(W1, xI) & (~(W1 = sz00))) <=> (~((~aElementOf0(W1, xI)) | (W1 = sz00)))), ((~(aElementOf0(W1, xI) & (~(W1 = sz00)))) <=> (~(~((~aElementOf0(W1, xI)) | (W1 = sz00)))))), rewrite((~(~((~aElementOf0(W1, xI)) | (W1 = sz00)))) <=> ((~aElementOf0(W1, xI)) | (W1 = sz00))), ((~(aElementOf0(W1, xI) & (~(W1 = sz00)))) <=> ((~aElementOf0(W1, xI)) | (W1 = sz00)))), trans(monotonicity(quant_intro(proof_bind(^[W3: $i] : trans(monotonicity(trans(monotonicity(rewrite((aElementOf0(W3, xI) & (~(W3 = sz00))) <=> (~((~aElementOf0(W3, xI)) | (W3 = sz00)))), ((~(aElementOf0(W3, xI) & (~(W3 = sz00)))) <=> (~(~((~aElementOf0(W3, xI)) | (W3 = sz00)))))), rewrite((~(~((~aElementOf0(W3, xI)) | (W3 = sz00)))) <=> ((~aElementOf0(W3, xI)) | (W3 = sz00))), ((~(aElementOf0(W3, xI) & (~(W3 = sz00)))) <=> ((~aElementOf0(W3, xI)) | (W3 = sz00)))), (((~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))) | (~(aElementOf0(W3, xI) & (~(W3 = sz00))))) <=> ((~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))) | ((~aElementOf0(W3, xI)) | (W3 = sz00))))), rewrite(((~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))) | ((~aElementOf0(W3, xI)) | (W3 = sz00))) <=> ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))))), (((~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))) | (~(aElementOf0(W3, xI) & (~(W3 = sz00))))) <=> ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))))))), (![W3: $i] : ((~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))) | (~(aElementOf0(W3, xI) & (~(W3 = sz00))))) <=> ![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23)))))), ((aElementOf0(W2!23, xI) & (~(W2!23 = sz00)) & ![W3: $i] : ((~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))) | (~(aElementOf0(W3, xI) & (~(W3 = sz00)))))) <=> (aElementOf0(W2!23, xI) & (~(W2!23 = sz00)) & ![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))))))), rewrite((aElementOf0(W2!23, xI) & (~(W2!23 = sz00)) & ![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))))) <=> (~((W2!23 = sz00) | (~aElementOf0(W2!23, xI)) | (~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23)))))))), ((aElementOf0(W2!23, xI) & (~(W2!23 = sz00)) & ![W3: $i] : ((~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))) | (~(aElementOf0(W3, xI) & (~(W3 = sz00)))))) <=> (~((W2!23 = sz00) | (~aElementOf0(W2!23, xI)) | (~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))))))))), (((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0!21))) | (~(aElementOf0(W1, xI) & (~(W1 = sz00)))) | (aElementOf0(W2!23, xI) & (~(W2!23 = sz00)) & ![W3: $i] : ((~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))) | (~(aElementOf0(W3, xI) & (~(W3 = sz00))))))) <=> ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0!21))) | ((~aElementOf0(W1, xI)) | (W1 = sz00)) | (~((W2!23 = sz00) | (~aElementOf0(W2!23, xI)) | (~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23)))))))))), rewrite(((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0!21))) | ((~aElementOf0(W1, xI)) | (W1 = sz00)) | (~((W2!23 = sz00) | (~aElementOf0(W2!23, xI)) | (~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23)))))))) <=> ((W1 = sz00) | (~iLess0(sbrdtbr0(W1), sbrdtbr0(W0!21))) | (~aElementOf0(W1, xI)) | (~((W2!23 = sz00) | (~aElementOf0(W2!23, xI)) | (~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))))))))), (((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0!21))) | (~(aElementOf0(W1, xI) & (~(W1 = sz00)))) | (aElementOf0(W2!23, xI) & (~(W2!23 = sz00)) & ![W3: $i] : ((~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))) | (~(aElementOf0(W3, xI) & (~(W3 = sz00))))))) <=> ((W1 = sz00) | (~iLess0(sbrdtbr0(W1), sbrdtbr0(W0!21))) | (~aElementOf0(W1, xI)) | (~((W2!23 = sz00) | (~aElementOf0(W2!23, xI)) | (~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))))))))))),
% 6.14/6.39 inference(bind,[status(th)],[])).
% 6.14/6.39 tff(39,plain,
% 6.14/6.39 (![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0!21))) | (~(aElementOf0(W1, xI) & (~(W1 = sz00)))) | (aElementOf0(W2!23, xI) & (~(W2!23 = sz00)) & ![W3: $i] : ((~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))) | (~(aElementOf0(W3, xI) & (~(W3 = sz00))))))) <=> ![W1: $i] : ((W1 = sz00) | (~iLess0(sbrdtbr0(W1), sbrdtbr0(W0!21))) | (~aElementOf0(W1, xI)) | (~((W2!23 = sz00) | (~aElementOf0(W2!23, xI)) | (~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))))))))),
% 6.14/6.39 inference(quant_intro,[status(thm)],[38])).
% 6.14/6.39 tff(40,plain,
% 6.14/6.39 (![W1: $i] : ((~iLess0(sbrdtbr0(W1), sbrdtbr0(W0!21))) | (~(aElementOf0(W1, xI) & (~(W1 = sz00)))) | (aElementOf0(W2!23, xI) & (~(W2!23 = sz00)) & ![W3: $i] : ((~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))) | (~(aElementOf0(W3, xI) & (~(W3 = sz00)))))))),
% 6.14/6.39 inference(and_elim,[status(thm)],[17])).
% 6.14/6.39 tff(41,plain,
% 6.14/6.39 (![W1: $i] : ((W1 = sz00) | (~iLess0(sbrdtbr0(W1), sbrdtbr0(W0!21))) | (~aElementOf0(W1, xI)) | (~((W2!23 = sz00) | (~aElementOf0(W2!23, xI)) | (~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))))))))),
% 6.14/6.39 inference(modus_ponens,[status(thm)],[40, 39])).
% 6.14/6.39 tff(42,plain,
% 6.14/6.39 (![W1: $i] : ((W1 = sz00) | (~iLess0(sbrdtbr0(W1), sbrdtbr0(W0!21))) | (~aElementOf0(W1, xI)) | (~((W2!23 = sz00) | (~aElementOf0(W2!23, xI)) | (~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))))))))),
% 6.14/6.39 inference(modus_ponens,[status(thm)],[41, 37])).
% 6.14/6.39 tff(43,plain,
% 6.14/6.39 (((~![W1: $i] : ((W1 = sz00) | (~iLess0(sbrdtbr0(W1), sbrdtbr0(W0!21))) | (~aElementOf0(W1, xI)) | (~((W2!23 = sz00) | (~aElementOf0(W2!23, xI)) | (~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))))))))) | ((~((W2!23 = sz00) | (~aElementOf0(W2!23, xI)) | (~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))))))) | (~iLess0(sbrdtbr0(tptp_fun_W2_22(W0!21)), sbrdtbr0(W0!21))) | (tptp_fun_W2_22(W0!21) = sz00) | (~aElementOf0(tptp_fun_W2_22(W0!21), xI)))) <=> ((~![W1: $i] : ((W1 = sz00) | (~iLess0(sbrdtbr0(W1), sbrdtbr0(W0!21))) | (~aElementOf0(W1, xI)) | (~((W2!23 = sz00) | (~aElementOf0(W2!23, xI)) | (~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))))))))) | (~((W2!23 = sz00) | (~aElementOf0(W2!23, xI)) | (~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))))))) | (~iLess0(sbrdtbr0(tptp_fun_W2_22(W0!21)), sbrdtbr0(W0!21))) | (tptp_fun_W2_22(W0!21) = sz00) | (~aElementOf0(tptp_fun_W2_22(W0!21), xI)))),
% 6.14/6.39 inference(rewrite,[status(thm)],[])).
% 6.14/6.39 tff(44,plain,
% 6.14/6.39 (((tptp_fun_W2_22(W0!21) = sz00) | (~iLess0(sbrdtbr0(tptp_fun_W2_22(W0!21)), sbrdtbr0(W0!21))) | (~aElementOf0(tptp_fun_W2_22(W0!21), xI)) | (~((W2!23 = sz00) | (~aElementOf0(W2!23, xI)) | (~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23)))))))) <=> ((~((W2!23 = sz00) | (~aElementOf0(W2!23, xI)) | (~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))))))) | (~iLess0(sbrdtbr0(tptp_fun_W2_22(W0!21)), sbrdtbr0(W0!21))) | (tptp_fun_W2_22(W0!21) = sz00) | (~aElementOf0(tptp_fun_W2_22(W0!21), xI)))),
% 6.14/6.39 inference(rewrite,[status(thm)],[])).
% 6.14/6.39 tff(45,plain,
% 6.14/6.39 ((~((W2!23 = sz00) | (~aElementOf0(W2!23, xI)) | (~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))))))) <=> (~((W2!23 = sz00) | (~aElementOf0(W2!23, xI)) | (~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23)))))))),
% 6.14/6.39 inference(rewrite,[status(thm)],[])).
% 6.14/6.39 tff(46,plain,
% 6.14/6.39 (((tptp_fun_W2_22(W0!21) = sz00) | (~iLess0(sbrdtbr0(tptp_fun_W2_22(W0!21)), sbrdtbr0(W0!21))) | (~aElementOf0(tptp_fun_W2_22(W0!21), xI)) | (~((W2!23 = sz00) | (~aElementOf0(W2!23, xI)) | (~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23)))))))) <=> ((tptp_fun_W2_22(W0!21) = sz00) | (~iLess0(sbrdtbr0(tptp_fun_W2_22(W0!21)), sbrdtbr0(W0!21))) | (~aElementOf0(tptp_fun_W2_22(W0!21), xI)) | (~((W2!23 = sz00) | (~aElementOf0(W2!23, xI)) | (~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))))))))),
% 6.14/6.39 inference(monotonicity,[status(thm)],[45])).
% 6.14/6.39 tff(47,plain,
% 6.14/6.39 (((tptp_fun_W2_22(W0!21) = sz00) | (~iLess0(sbrdtbr0(tptp_fun_W2_22(W0!21)), sbrdtbr0(W0!21))) | (~aElementOf0(tptp_fun_W2_22(W0!21), xI)) | (~((W2!23 = sz00) | (~aElementOf0(W2!23, xI)) | (~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23)))))))) <=> ((~((W2!23 = sz00) | (~aElementOf0(W2!23, xI)) | (~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))))))) | (~iLess0(sbrdtbr0(tptp_fun_W2_22(W0!21)), sbrdtbr0(W0!21))) | (tptp_fun_W2_22(W0!21) = sz00) | (~aElementOf0(tptp_fun_W2_22(W0!21), xI)))),
% 6.14/6.39 inference(transitivity,[status(thm)],[46, 44])).
% 6.14/6.39 tff(48,plain,
% 6.14/6.39 (((~![W1: $i] : ((W1 = sz00) | (~iLess0(sbrdtbr0(W1), sbrdtbr0(W0!21))) | (~aElementOf0(W1, xI)) | (~((W2!23 = sz00) | (~aElementOf0(W2!23, xI)) | (~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))))))))) | ((tptp_fun_W2_22(W0!21) = sz00) | (~iLess0(sbrdtbr0(tptp_fun_W2_22(W0!21)), sbrdtbr0(W0!21))) | (~aElementOf0(tptp_fun_W2_22(W0!21), xI)) | (~((W2!23 = sz00) | (~aElementOf0(W2!23, xI)) | (~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))))))))) <=> ((~![W1: $i] : ((W1 = sz00) | (~iLess0(sbrdtbr0(W1), sbrdtbr0(W0!21))) | (~aElementOf0(W1, xI)) | (~((W2!23 = sz00) | (~aElementOf0(W2!23, xI)) | (~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))))))))) | ((~((W2!23 = sz00) | (~aElementOf0(W2!23, xI)) | (~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))))))) | (~iLess0(sbrdtbr0(tptp_fun_W2_22(W0!21)), sbrdtbr0(W0!21))) | (tptp_fun_W2_22(W0!21) = sz00) | (~aElementOf0(tptp_fun_W2_22(W0!21), xI))))),
% 6.14/6.39 inference(monotonicity,[status(thm)],[47])).
% 6.14/6.39 tff(49,plain,
% 6.14/6.39 (((~![W1: $i] : ((W1 = sz00) | (~iLess0(sbrdtbr0(W1), sbrdtbr0(W0!21))) | (~aElementOf0(W1, xI)) | (~((W2!23 = sz00) | (~aElementOf0(W2!23, xI)) | (~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))))))))) | ((tptp_fun_W2_22(W0!21) = sz00) | (~iLess0(sbrdtbr0(tptp_fun_W2_22(W0!21)), sbrdtbr0(W0!21))) | (~aElementOf0(tptp_fun_W2_22(W0!21), xI)) | (~((W2!23 = sz00) | (~aElementOf0(W2!23, xI)) | (~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))))))))) <=> ((~![W1: $i] : ((W1 = sz00) | (~iLess0(sbrdtbr0(W1), sbrdtbr0(W0!21))) | (~aElementOf0(W1, xI)) | (~((W2!23 = sz00) | (~aElementOf0(W2!23, xI)) | (~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))))))))) | (~((W2!23 = sz00) | (~aElementOf0(W2!23, xI)) | (~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))))))) | (~iLess0(sbrdtbr0(tptp_fun_W2_22(W0!21)), sbrdtbr0(W0!21))) | (tptp_fun_W2_22(W0!21) = sz00) | (~aElementOf0(tptp_fun_W2_22(W0!21), xI)))),
% 6.14/6.39 inference(transitivity,[status(thm)],[48, 43])).
% 6.14/6.39 tff(50,plain,
% 6.14/6.39 ((~![W1: $i] : ((W1 = sz00) | (~iLess0(sbrdtbr0(W1), sbrdtbr0(W0!21))) | (~aElementOf0(W1, xI)) | (~((W2!23 = sz00) | (~aElementOf0(W2!23, xI)) | (~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))))))))) | ((tptp_fun_W2_22(W0!21) = sz00) | (~iLess0(sbrdtbr0(tptp_fun_W2_22(W0!21)), sbrdtbr0(W0!21))) | (~aElementOf0(tptp_fun_W2_22(W0!21), xI)) | (~((W2!23 = sz00) | (~aElementOf0(W2!23, xI)) | (~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))))))))),
% 6.14/6.39 inference(quant_inst,[status(thm)],[])).
% 6.14/6.39 tff(51,plain,
% 6.14/6.39 ((~![W1: $i] : ((W1 = sz00) | (~iLess0(sbrdtbr0(W1), sbrdtbr0(W0!21))) | (~aElementOf0(W1, xI)) | (~((W2!23 = sz00) | (~aElementOf0(W2!23, xI)) | (~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))))))))) | (~((W2!23 = sz00) | (~aElementOf0(W2!23, xI)) | (~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))))))) | (~iLess0(sbrdtbr0(tptp_fun_W2_22(W0!21)), sbrdtbr0(W0!21))) | (tptp_fun_W2_22(W0!21) = sz00) | (~aElementOf0(tptp_fun_W2_22(W0!21), xI))),
% 6.14/6.39 inference(modus_ponens,[status(thm)],[50, 49])).
% 6.14/6.39 tff(52,plain,
% 6.14/6.39 (~((W2!23 = sz00) | (~aElementOf0(W2!23, xI)) | (~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))))))),
% 6.14/6.39 inference(unit_resolution,[status(thm)],[51, 42, 32, 30, 28])).
% 6.14/6.39 tff(53,plain,
% 6.14/6.39 (((W2!23 = sz00) | (~aElementOf0(W2!23, xI)) | (~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23)))))) | aElementOf0(W2!23, xI)),
% 6.14/6.39 inference(tautology,[status(thm)],[])).
% 6.14/6.39 tff(54,plain,
% 6.14/6.39 (aElementOf0(W2!23, xI)),
% 6.14/6.39 inference(unit_resolution,[status(thm)],[53, 52])).
% 6.14/6.39 tff(55,plain,
% 6.14/6.39 (((W2!23 = sz00) | (~aElementOf0(W2!23, xI)) | (~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23)))))) | (~(W2!23 = sz00))),
% 6.14/6.39 inference(tautology,[status(thm)],[])).
% 6.14/6.39 tff(56,plain,
% 6.14/6.39 (~(W2!23 = sz00)),
% 6.14/6.39 inference(unit_resolution,[status(thm)],[55, 52])).
% 6.14/6.39 tff(57,plain,
% 6.14/6.39 (((~![W1: $i] : ((W1 = sz00) | (~aElementOf0(W1, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W2_22(W1)), sbrdtbr0(W1))) | (tptp_fun_W2_22(W1) = sz00) | (~aElementOf0(tptp_fun_W2_22(W1), xI)))))) | ((W2!23 = sz00) | (~aElementOf0(W2!23, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W2_22(W2!23)), sbrdtbr0(W2!23))) | (tptp_fun_W2_22(W2!23) = sz00) | (~aElementOf0(tptp_fun_W2_22(W2!23), xI)))))) <=> ((~![W1: $i] : ((W1 = sz00) | (~aElementOf0(W1, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W2_22(W1)), sbrdtbr0(W1))) | (tptp_fun_W2_22(W1) = sz00) | (~aElementOf0(tptp_fun_W2_22(W1), xI)))))) | (W2!23 = sz00) | (~aElementOf0(W2!23, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W2_22(W2!23)), sbrdtbr0(W2!23))) | (tptp_fun_W2_22(W2!23) = sz00) | (~aElementOf0(tptp_fun_W2_22(W2!23), xI)))))),
% 6.14/6.39 inference(rewrite,[status(thm)],[])).
% 6.14/6.39 tff(58,plain,
% 6.14/6.39 ((~![W1: $i] : ((W1 = sz00) | (~aElementOf0(W1, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W2_22(W1)), sbrdtbr0(W1))) | (tptp_fun_W2_22(W1) = sz00) | (~aElementOf0(tptp_fun_W2_22(W1), xI)))))) | ((W2!23 = sz00) | (~aElementOf0(W2!23, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W2_22(W2!23)), sbrdtbr0(W2!23))) | (tptp_fun_W2_22(W2!23) = sz00) | (~aElementOf0(tptp_fun_W2_22(W2!23), xI)))))),
% 6.14/6.39 inference(quant_inst,[status(thm)],[])).
% 6.14/6.39 tff(59,plain,
% 6.14/6.39 ((~![W1: $i] : ((W1 = sz00) | (~aElementOf0(W1, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W2_22(W1)), sbrdtbr0(W1))) | (tptp_fun_W2_22(W1) = sz00) | (~aElementOf0(tptp_fun_W2_22(W1), xI)))))) | (W2!23 = sz00) | (~aElementOf0(W2!23, xI)) | (~((~iLess0(sbrdtbr0(tptp_fun_W2_22(W2!23)), sbrdtbr0(W2!23))) | (tptp_fun_W2_22(W2!23) = sz00) | (~aElementOf0(tptp_fun_W2_22(W2!23), xI))))),
% 6.14/6.39 inference(modus_ponens,[status(thm)],[58, 57])).
% 6.14/6.39 tff(60,plain,
% 6.14/6.39 (~((~iLess0(sbrdtbr0(tptp_fun_W2_22(W2!23)), sbrdtbr0(W2!23))) | (tptp_fun_W2_22(W2!23) = sz00) | (~aElementOf0(tptp_fun_W2_22(W2!23), xI)))),
% 6.14/6.39 inference(unit_resolution,[status(thm)],[59, 20, 56, 54])).
% 6.14/6.39 tff(61,plain,
% 6.14/6.39 (((~iLess0(sbrdtbr0(tptp_fun_W2_22(W2!23)), sbrdtbr0(W2!23))) | (tptp_fun_W2_22(W2!23) = sz00) | (~aElementOf0(tptp_fun_W2_22(W2!23), xI))) | aElementOf0(tptp_fun_W2_22(W2!23), xI)),
% 6.14/6.39 inference(tautology,[status(thm)],[])).
% 6.14/6.39 tff(62,plain,
% 6.14/6.39 (aElementOf0(tptp_fun_W2_22(W2!23), xI)),
% 6.14/6.39 inference(unit_resolution,[status(thm)],[61, 60])).
% 6.14/6.39 tff(63,plain,
% 6.14/6.39 (((~iLess0(sbrdtbr0(tptp_fun_W2_22(W2!23)), sbrdtbr0(W2!23))) | (tptp_fun_W2_22(W2!23) = sz00) | (~aElementOf0(tptp_fun_W2_22(W2!23), xI))) | (~(tptp_fun_W2_22(W2!23) = sz00))),
% 6.14/6.39 inference(tautology,[status(thm)],[])).
% 6.14/6.39 tff(64,plain,
% 6.14/6.39 (~(tptp_fun_W2_22(W2!23) = sz00)),
% 6.14/6.39 inference(unit_resolution,[status(thm)],[63, 60])).
% 6.14/6.39 tff(65,plain,
% 6.14/6.39 (((~iLess0(sbrdtbr0(tptp_fun_W2_22(W2!23)), sbrdtbr0(W2!23))) | (tptp_fun_W2_22(W2!23) = sz00) | (~aElementOf0(tptp_fun_W2_22(W2!23), xI))) | iLess0(sbrdtbr0(tptp_fun_W2_22(W2!23)), sbrdtbr0(W2!23))),
% 6.14/6.39 inference(tautology,[status(thm)],[])).
% 6.14/6.39 tff(66,plain,
% 6.14/6.39 (iLess0(sbrdtbr0(tptp_fun_W2_22(W2!23)), sbrdtbr0(W2!23))),
% 6.14/6.39 inference(unit_resolution,[status(thm)],[65, 60])).
% 6.14/6.39 tff(67,plain,
% 6.14/6.39 (((W2!23 = sz00) | (~aElementOf0(W2!23, xI)) | (~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23)))))) | ![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))))),
% 6.14/6.39 inference(tautology,[status(thm)],[])).
% 6.14/6.39 tff(68,plain,
% 6.14/6.39 (![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))))),
% 6.14/6.39 inference(unit_resolution,[status(thm)],[67, 52])).
% 6.14/6.39 tff(69,plain,
% 6.14/6.39 (((~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))))) | ((~iLess0(sbrdtbr0(tptp_fun_W2_22(W2!23)), sbrdtbr0(W2!23))) | (tptp_fun_W2_22(W2!23) = sz00) | (~aElementOf0(tptp_fun_W2_22(W2!23), xI)))) <=> ((~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))))) | (~iLess0(sbrdtbr0(tptp_fun_W2_22(W2!23)), sbrdtbr0(W2!23))) | (tptp_fun_W2_22(W2!23) = sz00) | (~aElementOf0(tptp_fun_W2_22(W2!23), xI)))),
% 6.14/6.39 inference(rewrite,[status(thm)],[])).
% 6.14/6.39 tff(70,plain,
% 6.14/6.39 (((tptp_fun_W2_22(W2!23) = sz00) | (~aElementOf0(tptp_fun_W2_22(W2!23), xI)) | (~iLess0(sbrdtbr0(tptp_fun_W2_22(W2!23)), sbrdtbr0(W2!23)))) <=> ((~iLess0(sbrdtbr0(tptp_fun_W2_22(W2!23)), sbrdtbr0(W2!23))) | (tptp_fun_W2_22(W2!23) = sz00) | (~aElementOf0(tptp_fun_W2_22(W2!23), xI)))),
% 6.25/6.40 inference(rewrite,[status(thm)],[])).
% 6.25/6.40 tff(71,plain,
% 6.25/6.40 (((~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))))) | ((tptp_fun_W2_22(W2!23) = sz00) | (~aElementOf0(tptp_fun_W2_22(W2!23), xI)) | (~iLess0(sbrdtbr0(tptp_fun_W2_22(W2!23)), sbrdtbr0(W2!23))))) <=> ((~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))))) | ((~iLess0(sbrdtbr0(tptp_fun_W2_22(W2!23)), sbrdtbr0(W2!23))) | (tptp_fun_W2_22(W2!23) = sz00) | (~aElementOf0(tptp_fun_W2_22(W2!23), xI))))),
% 6.25/6.40 inference(monotonicity,[status(thm)],[70])).
% 6.25/6.40 tff(72,plain,
% 6.25/6.40 (((~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))))) | ((tptp_fun_W2_22(W2!23) = sz00) | (~aElementOf0(tptp_fun_W2_22(W2!23), xI)) | (~iLess0(sbrdtbr0(tptp_fun_W2_22(W2!23)), sbrdtbr0(W2!23))))) <=> ((~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))))) | (~iLess0(sbrdtbr0(tptp_fun_W2_22(W2!23)), sbrdtbr0(W2!23))) | (tptp_fun_W2_22(W2!23) = sz00) | (~aElementOf0(tptp_fun_W2_22(W2!23), xI)))),
% 6.25/6.40 inference(transitivity,[status(thm)],[71, 69])).
% 6.25/6.40 tff(73,plain,
% 6.25/6.40 ((~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))))) | ((tptp_fun_W2_22(W2!23) = sz00) | (~aElementOf0(tptp_fun_W2_22(W2!23), xI)) | (~iLess0(sbrdtbr0(tptp_fun_W2_22(W2!23)), sbrdtbr0(W2!23))))),
% 6.25/6.40 inference(quant_inst,[status(thm)],[])).
% 6.25/6.40 tff(74,plain,
% 6.25/6.40 ((~![W3: $i] : ((W3 = sz00) | (~aElementOf0(W3, xI)) | (~iLess0(sbrdtbr0(W3), sbrdtbr0(W2!23))))) | (~iLess0(sbrdtbr0(tptp_fun_W2_22(W2!23)), sbrdtbr0(W2!23))) | (tptp_fun_W2_22(W2!23) = sz00) | (~aElementOf0(tptp_fun_W2_22(W2!23), xI))),
% 6.25/6.40 inference(modus_ponens,[status(thm)],[73, 72])).
% 6.25/6.40 tff(75,plain,
% 6.25/6.40 ($false),
% 6.25/6.40 inference(unit_resolution,[status(thm)],[74, 68, 66, 64, 62])).
% 6.25/6.40 % SZS output end Proof
% 6.25/6.43 % E exiting
%------------------------------------------------------------------------------