%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM539+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:21:20 AM UTC 2025
% Result : Theorem 1.57s 1.74s
% Output : Proof 1.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM539+1 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n014.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 01:24:24 EDT 2025
% 0.12/0.34 % CPUTime :
% 1.57/1.74 % SZS status Theorem
% 1.57/1.74 % SZS output start Proof
% 1.57/1.74 tff(sdtlseqdt0_type, type, (
% 1.57/1.74 sdtlseqdt0: ( $i * $i ) > $o)).
% 1.57/1.74 tff(tptp_fun_W1_4_type, type, (
% 1.57/1.74 tptp_fun_W1_4: $i > $i)).
% 1.57/1.74 tff(szszuzczcdt0_type, type, (
% 1.57/1.74 szszuzczcdt0: $i > $i)).
% 1.57/1.74 tff(szmzizndt0_type, type, (
% 1.57/1.74 szmzizndt0: $i > $i)).
% 1.57/1.74 tff(xT_type, type, (
% 1.57/1.74 xT: $i)).
% 1.57/1.74 tff(aElementOf0_type, type, (
% 1.57/1.74 aElementOf0: ( $i * $i ) > $o)).
% 1.57/1.74 tff(tptp_fun_W2_6_type, type, (
% 1.57/1.74 tptp_fun_W2_6: ( $i * $i ) > $i)).
% 1.57/1.74 tff(slcrc0_type, type, (
% 1.57/1.74 slcrc0: $i)).
% 1.57/1.74 tff(xS_type, type, (
% 1.57/1.74 xS: $i)).
% 1.57/1.74 tff(aSubsetOf0_type, type, (
% 1.57/1.74 aSubsetOf0: ( $i * $i ) > $o)).
% 1.57/1.74 tff(szNzAzT0_type, type, (
% 1.57/1.74 szNzAzT0: $i)).
% 1.57/1.74 tff(sz00_type, type, (
% 1.57/1.74 sz00: $i)).
% 1.57/1.74 tff(aSet0_type, type, (
% 1.57/1.74 aSet0: $i > $o)).
% 1.57/1.74 tff(tptp_fun_W2_1_type, type, (
% 1.57/1.74 tptp_fun_W2_1: ( $i * $i ) > $i)).
% 1.57/1.74 tff(isCountable0_type, type, (
% 1.57/1.74 isCountable0: $i > $o)).
% 1.57/1.74 tff(1,plain,
% 1.57/1.74 ((~(xT = slcrc0)) <=> (~(xT = slcrc0))),
% 1.57/1.74 inference(rewrite,[status(thm)],[])).
% 1.57/1.74 tff(2,axiom,(((aSubsetOf0(xS, szNzAzT0) & aSubsetOf0(xT, szNzAzT0)) & (~(xS = slcrc0))) & (~(xT = slcrc0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__1779')).
% 1.57/1.74 tff(3,plain,
% 1.57/1.74 (~(xT = slcrc0)),
% 1.57/1.74 inference(and_elim,[status(thm)],[2])).
% 1.57/1.74 tff(4,plain,
% 1.57/1.74 (~(xT = slcrc0)),
% 1.57/1.74 inference(modus_ponens,[status(thm)],[3, 1])).
% 1.57/1.74 tff(5,plain,
% 1.57/1.74 (aSubsetOf0(xT, szNzAzT0) <=> aSubsetOf0(xT, szNzAzT0)),
% 1.57/1.74 inference(rewrite,[status(thm)],[])).
% 1.57/1.74 tff(6,plain,
% 1.57/1.74 ((aSubsetOf0(xS, szNzAzT0) & aSubsetOf0(xT, szNzAzT0)) & (~(xS = slcrc0))),
% 1.57/1.74 inference(and_elim,[status(thm)],[2])).
% 1.57/1.74 tff(7,plain,
% 1.57/1.74 (aSubsetOf0(xS, szNzAzT0) & aSubsetOf0(xT, szNzAzT0)),
% 1.57/1.74 inference(and_elim,[status(thm)],[6])).
% 1.57/1.74 tff(8,plain,
% 1.57/1.74 (aSubsetOf0(xT, szNzAzT0)),
% 1.57/1.74 inference(and_elim,[status(thm)],[7])).
% 1.57/1.74 tff(9,plain,
% 1.57/1.74 (aSubsetOf0(xT, szNzAzT0)),
% 1.57/1.74 inference(modus_ponens,[status(thm)],[8, 5])).
% 1.57/1.74 tff(10,plain,
% 1.57/1.74 (^[W0: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: $i] : rewrite((~((~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))))) <=> (~((~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))) | (~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))))))), (![W1: $i] : (~((~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))))) <=> ![W1: $i] : (~((~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))) | (~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))))))), (((W0 = slcrc0) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0))))))))) <=> ((W0 = slcrc0) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))) | (~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)))))))))))), rewrite(((W0 = slcrc0) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))) | (~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)))))))))) <=> ((W0 = slcrc0) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))) | (~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))))))), (((W0 = slcrc0) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0))))))))) <=> ((W0 = slcrc0) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))) | (~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))))))))),
% 1.57/1.75 inference(bind,[status(th)],[])).
% 1.57/1.75 tff(11,plain,
% 1.57/1.75 (![W0: $i] : ((W0 = slcrc0) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0))))))))) <=> ![W0: $i] : ((W0 = slcrc0) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))) | (~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))))))),
% 1.57/1.75 inference(quant_intro,[status(thm)],[10])).
% 1.57/1.75 tff(12,plain,
% 1.57/1.75 (^[W0: $i] : refl(((W0 = slcrc0) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0))))))))) <=> ((W0 = slcrc0) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0))))))))))),
% 1.57/1.75 inference(bind,[status(th)],[])).
% 1.57/1.75 tff(13,plain,
% 1.57/1.75 (![W0: $i] : ((W0 = slcrc0) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0))))))))) <=> ![W0: $i] : ((W0 = slcrc0) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))))))),
% 1.57/1.75 inference(quant_intro,[status(thm)],[12])).
% 1.57/1.75 tff(14,plain,
% 1.57/1.75 (^[W0: $i] : rewrite(((W0 = slcrc0) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0))))))))) <=> ((W0 = slcrc0) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0))))))))))),
% 1.57/1.75 inference(bind,[status(th)],[])).
% 1.57/1.75 tff(15,plain,
% 1.57/1.75 (![W0: $i] : ((W0 = slcrc0) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0))))))))) <=> ![W0: $i] : ((W0 = slcrc0) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))))))),
% 1.57/1.75 inference(quant_intro,[status(thm)],[14])).
% 1.57/1.75 tff(16,plain,
% 1.57/1.75 (![W0: $i] : ((W0 = slcrc0) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0))))))))) <=> ![W0: $i] : ((W0 = slcrc0) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))))))),
% 1.57/1.75 inference(transitivity,[status(thm)],[15, 13])).
% 1.57/1.75 tff(17,plain,
% 1.57/1.75 (^[W0: $i] : trans(monotonicity(trans(monotonicity(rewrite((aSubsetOf0(W0, szNzAzT0) & (~(W0 = slcrc0))) <=> (~((~aSubsetOf0(W0, szNzAzT0)) | (W0 = slcrc0)))), ((~(aSubsetOf0(W0, szNzAzT0) & (~(W0 = slcrc0)))) <=> (~(~((~aSubsetOf0(W0, szNzAzT0)) | (W0 = slcrc0)))))), rewrite((~(~((~aSubsetOf0(W0, szNzAzT0)) | (W0 = slcrc0)))) <=> ((~aSubsetOf0(W0, szNzAzT0)) | (W0 = slcrc0))), ((~(aSubsetOf0(W0, szNzAzT0) & (~(W0 = slcrc0)))) <=> ((~aSubsetOf0(W0, szNzAzT0)) | (W0 = slcrc0)))), quant_intro(proof_bind(^[W1: $i] : trans(monotonicity(rewrite(((~(W1 = szmzizndt0(W0))) | (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)))) <=> ((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))), rewrite(((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0))))) <=> ((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))), ((((~(W1 = szmzizndt0(W0))) | (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)))) & ((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))) <=> (((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)))))) & ((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))))), rewrite((((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)))))) & ((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))) <=> (~((~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0))))))))), ((((~(W1 = szmzizndt0(W0))) | (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)))) & ((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))) <=> (~((~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0))))))))))), (![W1: $i] : (((~(W1 = szmzizndt0(W0))) | (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)))) & ((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))) <=> ![W1: $i] : (~((~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))))))), (((~(aSubsetOf0(W0, szNzAzT0) & (~(W0 = slcrc0)))) | ![W1: $i] : (((~(W1 = szmzizndt0(W0))) | (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)))) & ((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0))))))) <=> (((~aSubsetOf0(W0, szNzAzT0)) | (W0 = slcrc0)) | ![W1: $i] : (~((~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0))))))))))), rewrite((((~aSubsetOf0(W0, szNzAzT0)) | (W0 = slcrc0)) | ![W1: $i] : (~((~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0))))))))) <=> ((W0 = slcrc0) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))))))), (((~(aSubsetOf0(W0, szNzAzT0) & (~(W0 = slcrc0)))) | ![W1: $i] : (((~(W1 = szmzizndt0(W0))) | (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)))) & ((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0))))))) <=> ((W0 = slcrc0) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))))))))),
% 1.57/1.75 inference(bind,[status(th)],[])).
% 1.57/1.75 tff(18,plain,
% 1.57/1.75 (![W0: $i] : ((~(aSubsetOf0(W0, szNzAzT0) & (~(W0 = slcrc0)))) | ![W1: $i] : (((~(W1 = szmzizndt0(W0))) | (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)))) & ((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0))))))) <=> ![W0: $i] : ((W0 = slcrc0) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))))))),
% 1.57/1.75 inference(quant_intro,[status(thm)],[17])).
% 1.57/1.75 tff(19,plain,
% 1.57/1.75 (^[W0: $i] : rewrite(((~(aSubsetOf0(W0, szNzAzT0) & (~(W0 = slcrc0)))) | ![W1: $i] : (((~(W1 = szmzizndt0(W0))) | (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)))) & ((W1 = szmzizndt0(W0)) | ((~aElementOf0(W1, W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))))) <=> ((~(aSubsetOf0(W0, szNzAzT0) & (~(W0 = slcrc0)))) | ![W1: $i] : (((~(W1 = szmzizndt0(W0))) | (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)))) & ((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0))))))))),
% 1.57/1.75 inference(bind,[status(th)],[])).
% 1.57/1.75 tff(20,plain,
% 1.57/1.75 (![W0: $i] : ((~(aSubsetOf0(W0, szNzAzT0) & (~(W0 = slcrc0)))) | ![W1: $i] : (((~(W1 = szmzizndt0(W0))) | (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)))) & ((W1 = szmzizndt0(W0)) | ((~aElementOf0(W1, W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))))) <=> ![W0: $i] : ((~(aSubsetOf0(W0, szNzAzT0) & (~(W0 = slcrc0)))) | ![W1: $i] : (((~(W1 = szmzizndt0(W0))) | (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)))) & ((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))))),
% 1.57/1.75 inference(quant_intro,[status(thm)],[19])).
% 1.57/1.75 tff(21,plain,
% 1.57/1.75 (![W0: $i] : ((~(aSubsetOf0(W0, szNzAzT0) & (~(W0 = slcrc0)))) | ![W1: $i] : ((W1 = szmzizndt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))) <=> ![W0: $i] : ((~(aSubsetOf0(W0, szNzAzT0) & (~(W0 = slcrc0)))) | ![W1: $i] : ((W1 = szmzizndt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)))))),
% 1.57/1.75 inference(rewrite,[status(thm)],[])).
% 1.57/1.75 tff(22,plain,
% 1.57/1.75 (^[W0: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: $i] : rewrite(((W1 = szmzizndt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : (aElementOf0(W2, W0) => sdtlseqdt0(W1, W2)))) <=> ((W1 = szmzizndt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)))))), (![W1: $i] : ((W1 = szmzizndt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : (aElementOf0(W2, W0) => sdtlseqdt0(W1, W2)))) <=> ![W1: $i] : ((W1 = szmzizndt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)))))), (((aSubsetOf0(W0, szNzAzT0) & (~(W0 = slcrc0))) => ![W1: $i] : ((W1 = szmzizndt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : (aElementOf0(W2, W0) => sdtlseqdt0(W1, W2))))) <=> ((aSubsetOf0(W0, szNzAzT0) & (~(W0 = slcrc0))) => ![W1: $i] : ((W1 = szmzizndt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))), rewrite(((aSubsetOf0(W0, szNzAzT0) & (~(W0 = slcrc0))) => ![W1: $i] : ((W1 = szmzizndt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))) <=> ((~(aSubsetOf0(W0, szNzAzT0) & (~(W0 = slcrc0)))) | ![W1: $i] : ((W1 = szmzizndt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)))))), (((aSubsetOf0(W0, szNzAzT0) & (~(W0 = slcrc0))) => ![W1: $i] : ((W1 = szmzizndt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : (aElementOf0(W2, W0) => sdtlseqdt0(W1, W2))))) <=> ((~(aSubsetOf0(W0, szNzAzT0) & (~(W0 = slcrc0)))) | ![W1: $i] : ((W1 = szmzizndt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)))))))),
% 1.57/1.75 inference(bind,[status(th)],[])).
% 1.57/1.75 tff(23,plain,
% 1.57/1.75 (![W0: $i] : ((aSubsetOf0(W0, szNzAzT0) & (~(W0 = slcrc0))) => ![W1: $i] : ((W1 = szmzizndt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : (aElementOf0(W2, W0) => sdtlseqdt0(W1, W2))))) <=> ![W0: $i] : ((~(aSubsetOf0(W0, szNzAzT0) & (~(W0 = slcrc0)))) | ![W1: $i] : ((W1 = szmzizndt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)))))),
% 1.57/1.75 inference(quant_intro,[status(thm)],[22])).
% 1.57/1.75 tff(24,axiom,(![W0: $i] : ((aSubsetOf0(W0, szNzAzT0) & (~(W0 = slcrc0))) => ![W1: $i] : ((W1 = szmzizndt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : (aElementOf0(W2, W0) => sdtlseqdt0(W1, W2)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mDefMin')).
% 1.57/1.75 tff(25,plain,
% 1.57/1.75 (![W0: $i] : ((~(aSubsetOf0(W0, szNzAzT0) & (~(W0 = slcrc0)))) | ![W1: $i] : ((W1 = szmzizndt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)))))),
% 1.57/1.75 inference(modus_ponens,[status(thm)],[24, 23])).
% 1.57/1.75 tff(26,plain,
% 1.57/1.75 (![W0: $i] : ((~(aSubsetOf0(W0, szNzAzT0) & (~(W0 = slcrc0)))) | ![W1: $i] : ((W1 = szmzizndt0(W0)) <=> (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)))))),
% 1.57/1.75 inference(modus_ponens,[status(thm)],[25, 21])).
% 1.57/1.75 tff(27,plain,(
% 1.57/1.75 ![W0: $i] : ((~(aSubsetOf0(W0, szNzAzT0) & (~(W0 = slcrc0)))) | ![W1: $i] : (((~(W1 = szmzizndt0(W0))) | (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)))) & ((W1 = szmzizndt0(W0)) | ((~aElementOf0(W1, W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0))))))))),
% 1.57/1.75 inference(skolemize,[status(sab)],[26])).
% 1.57/1.75 tff(28,plain,
% 1.57/1.75 (![W0: $i] : ((~(aSubsetOf0(W0, szNzAzT0) & (~(W0 = slcrc0)))) | ![W1: $i] : (((~(W1 = szmzizndt0(W0))) | (aElementOf0(W1, W0) & ![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2)))) & ((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))))),
% 1.57/1.75 inference(modus_ponens,[status(thm)],[27, 20])).
% 1.57/1.75 tff(29,plain,
% 1.57/1.75 (![W0: $i] : ((W0 = slcrc0) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))))))),
% 1.57/1.75 inference(modus_ponens,[status(thm)],[28, 18])).
% 1.57/1.75 tff(30,plain,
% 1.57/1.75 (![W0: $i] : ((W0 = slcrc0) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))) | (~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))))))),
% 1.57/1.75 inference(modus_ponens,[status(thm)],[29, 16])).
% 1.57/1.75 tff(31,plain,
% 1.57/1.75 (![W0: $i] : ((W0 = slcrc0) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))) | (~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))))))),
% 1.57/1.75 inference(modus_ponens,[status(thm)],[30, 11])).
% 1.57/1.75 tff(32,plain,
% 1.57/1.75 (((~![W0: $i] : ((W0 = slcrc0) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))) | (~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))))))) | ((xT = slcrc0) | ![W1: $i] : (~((~((~aElementOf0(W1, xT)) | (W1 = szmzizndt0(xT)) | (~((~aElementOf0(tptp_fun_W2_6(W1, xT), xT)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, xT)))))) | (~((~(W1 = szmzizndt0(xT))) | (~((~aElementOf0(W1, xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | sdtlseqdt0(W1, W2))))))))) | (~aSubsetOf0(xT, szNzAzT0)))) <=> ((~![W0: $i] : ((W0 = slcrc0) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))) | (~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))))))) | (xT = slcrc0) | ![W1: $i] : (~((~((~aElementOf0(W1, xT)) | (W1 = szmzizndt0(xT)) | (~((~aElementOf0(tptp_fun_W2_6(W1, xT), xT)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, xT)))))) | (~((~(W1 = szmzizndt0(xT))) | (~((~aElementOf0(W1, xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | sdtlseqdt0(W1, W2))))))))) | (~aSubsetOf0(xT, szNzAzT0)))),
% 1.57/1.75 inference(rewrite,[status(thm)],[])).
% 1.57/1.75 tff(33,plain,
% 1.57/1.75 (((xT = slcrc0) | (~aSubsetOf0(xT, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, xT)) | (W1 = szmzizndt0(xT)) | (~((~aElementOf0(tptp_fun_W2_6(W1, xT), xT)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, xT)))))) | (~((~(W1 = szmzizndt0(xT))) | (~((~aElementOf0(W1, xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | sdtlseqdt0(W1, W2)))))))))) <=> ((xT = slcrc0) | ![W1: $i] : (~((~((~aElementOf0(W1, xT)) | (W1 = szmzizndt0(xT)) | (~((~aElementOf0(tptp_fun_W2_6(W1, xT), xT)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, xT)))))) | (~((~(W1 = szmzizndt0(xT))) | (~((~aElementOf0(W1, xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | sdtlseqdt0(W1, W2))))))))) | (~aSubsetOf0(xT, szNzAzT0)))),
% 1.57/1.75 inference(rewrite,[status(thm)],[])).
% 1.57/1.75 tff(34,plain,
% 1.57/1.75 (((~![W0: $i] : ((W0 = slcrc0) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))) | (~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))))))) | ((xT = slcrc0) | (~aSubsetOf0(xT, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, xT)) | (W1 = szmzizndt0(xT)) | (~((~aElementOf0(tptp_fun_W2_6(W1, xT), xT)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, xT)))))) | (~((~(W1 = szmzizndt0(xT))) | (~((~aElementOf0(W1, xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | sdtlseqdt0(W1, W2))))))))))) <=> ((~![W0: $i] : ((W0 = slcrc0) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))) | (~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))))))) | ((xT = slcrc0) | ![W1: $i] : (~((~((~aElementOf0(W1, xT)) | (W1 = szmzizndt0(xT)) | (~((~aElementOf0(tptp_fun_W2_6(W1, xT), xT)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, xT)))))) | (~((~(W1 = szmzizndt0(xT))) | (~((~aElementOf0(W1, xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | sdtlseqdt0(W1, W2))))))))) | (~aSubsetOf0(xT, szNzAzT0))))),
% 1.57/1.75 inference(monotonicity,[status(thm)],[33])).
% 1.57/1.75 tff(35,plain,
% 1.57/1.75 (((~![W0: $i] : ((W0 = slcrc0) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))) | (~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))))))) | ((xT = slcrc0) | (~aSubsetOf0(xT, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, xT)) | (W1 = szmzizndt0(xT)) | (~((~aElementOf0(tptp_fun_W2_6(W1, xT), xT)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, xT)))))) | (~((~(W1 = szmzizndt0(xT))) | (~((~aElementOf0(W1, xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | sdtlseqdt0(W1, W2))))))))))) <=> ((~![W0: $i] : ((W0 = slcrc0) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))) | (~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))))))) | (xT = slcrc0) | ![W1: $i] : (~((~((~aElementOf0(W1, xT)) | (W1 = szmzizndt0(xT)) | (~((~aElementOf0(tptp_fun_W2_6(W1, xT), xT)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, xT)))))) | (~((~(W1 = szmzizndt0(xT))) | (~((~aElementOf0(W1, xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | sdtlseqdt0(W1, W2))))))))) | (~aSubsetOf0(xT, szNzAzT0)))),
% 1.57/1.75 inference(transitivity,[status(thm)],[34, 32])).
% 1.57/1.75 tff(36,plain,
% 1.57/1.75 ((~![W0: $i] : ((W0 = slcrc0) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))) | (~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))))))) | ((xT = slcrc0) | (~aSubsetOf0(xT, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, xT)) | (W1 = szmzizndt0(xT)) | (~((~aElementOf0(tptp_fun_W2_6(W1, xT), xT)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, xT)))))) | (~((~(W1 = szmzizndt0(xT))) | (~((~aElementOf0(W1, xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | sdtlseqdt0(W1, W2))))))))))),
% 1.57/1.75 inference(quant_inst,[status(thm)],[])).
% 1.57/1.75 tff(37,plain,
% 1.57/1.75 ((~![W0: $i] : ((W0 = slcrc0) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))) | (~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))))))) | (xT = slcrc0) | ![W1: $i] : (~((~((~aElementOf0(W1, xT)) | (W1 = szmzizndt0(xT)) | (~((~aElementOf0(tptp_fun_W2_6(W1, xT), xT)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, xT)))))) | (~((~(W1 = szmzizndt0(xT))) | (~((~aElementOf0(W1, xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | sdtlseqdt0(W1, W2))))))))) | (~aSubsetOf0(xT, szNzAzT0))),
% 1.59/1.75 inference(modus_ponens,[status(thm)],[36, 35])).
% 1.59/1.75 tff(38,plain,
% 1.59/1.75 (![W1: $i] : (~((~((~aElementOf0(W1, xT)) | (W1 = szmzizndt0(xT)) | (~((~aElementOf0(tptp_fun_W2_6(W1, xT), xT)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, xT)))))) | (~((~(W1 = szmzizndt0(xT))) | (~((~aElementOf0(W1, xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | sdtlseqdt0(W1, W2)))))))))),
% 1.59/1.75 inference(unit_resolution,[status(thm)],[37, 31, 9, 4])).
% 1.59/1.75 tff(39,plain,
% 1.59/1.75 (((~![W1: $i] : (~((~((~aElementOf0(W1, xT)) | (W1 = szmzizndt0(xT)) | (~((~aElementOf0(tptp_fun_W2_6(W1, xT), xT)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, xT)))))) | (~((~(W1 = szmzizndt0(xT))) | (~((~aElementOf0(W1, xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | sdtlseqdt0(W1, W2)))))))))) | (~((~((tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))) = szmzizndt0(xT)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT)) | (~((~aElementOf0(tptp_fun_W2_6(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT), xT)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), tptp_fun_W2_6(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT)))))) | (~((~(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))) = szmzizndt0(xT))) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), W2)))))))))) <=> ((~![W1: $i] : (~((~((~aElementOf0(W1, xT)) | (W1 = szmzizndt0(xT)) | (~((~aElementOf0(tptp_fun_W2_6(W1, xT), xT)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, xT)))))) | (~((~(W1 = szmzizndt0(xT))) | (~((~aElementOf0(W1, xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | sdtlseqdt0(W1, W2)))))))))) | (~((~((tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))) = szmzizndt0(xT)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT)) | (~((~aElementOf0(tptp_fun_W2_6(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT), xT)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), tptp_fun_W2_6(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT)))))) | (~((~(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))) = szmzizndt0(xT))) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), W2))))))))))),
% 1.59/1.75 inference(rewrite,[status(thm)],[])).
% 1.59/1.75 tff(40,plain,
% 1.59/1.75 ((~((~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT)) | (tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))) = szmzizndt0(xT)) | (~((~aElementOf0(tptp_fun_W2_6(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT), xT)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), tptp_fun_W2_6(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT)))))) | (~((~(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))) = szmzizndt0(xT))) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), W2))))))))) <=> (~((~((tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))) = szmzizndt0(xT)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT)) | (~((~aElementOf0(tptp_fun_W2_6(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT), xT)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), tptp_fun_W2_6(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT)))))) | (~((~(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))) = szmzizndt0(xT))) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), W2)))))))))),
% 1.59/1.75 inference(rewrite,[status(thm)],[])).
% 1.59/1.75 tff(41,plain,
% 1.59/1.75 (((~![W1: $i] : (~((~((~aElementOf0(W1, xT)) | (W1 = szmzizndt0(xT)) | (~((~aElementOf0(tptp_fun_W2_6(W1, xT), xT)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, xT)))))) | (~((~(W1 = szmzizndt0(xT))) | (~((~aElementOf0(W1, xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | sdtlseqdt0(W1, W2)))))))))) | (~((~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT)) | (tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))) = szmzizndt0(xT)) | (~((~aElementOf0(tptp_fun_W2_6(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT), xT)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), tptp_fun_W2_6(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT)))))) | (~((~(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))) = szmzizndt0(xT))) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), W2)))))))))) <=> ((~![W1: $i] : (~((~((~aElementOf0(W1, xT)) | (W1 = szmzizndt0(xT)) | (~((~aElementOf0(tptp_fun_W2_6(W1, xT), xT)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, xT)))))) | (~((~(W1 = szmzizndt0(xT))) | (~((~aElementOf0(W1, xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | sdtlseqdt0(W1, W2)))))))))) | (~((~((tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))) = szmzizndt0(xT)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT)) | (~((~aElementOf0(tptp_fun_W2_6(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT), xT)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), tptp_fun_W2_6(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT)))))) | (~((~(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))) = szmzizndt0(xT))) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), W2))))))))))),
% 1.59/1.75 inference(monotonicity,[status(thm)],[40])).
% 1.59/1.75 tff(42,plain,
% 1.59/1.75 (((~![W1: $i] : (~((~((~aElementOf0(W1, xT)) | (W1 = szmzizndt0(xT)) | (~((~aElementOf0(tptp_fun_W2_6(W1, xT), xT)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, xT)))))) | (~((~(W1 = szmzizndt0(xT))) | (~((~aElementOf0(W1, xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | sdtlseqdt0(W1, W2)))))))))) | (~((~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT)) | (tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))) = szmzizndt0(xT)) | (~((~aElementOf0(tptp_fun_W2_6(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT), xT)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), tptp_fun_W2_6(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT)))))) | (~((~(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))) = szmzizndt0(xT))) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), W2)))))))))) <=> ((~![W1: $i] : (~((~((~aElementOf0(W1, xT)) | (W1 = szmzizndt0(xT)) | (~((~aElementOf0(tptp_fun_W2_6(W1, xT), xT)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, xT)))))) | (~((~(W1 = szmzizndt0(xT))) | (~((~aElementOf0(W1, xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | sdtlseqdt0(W1, W2)))))))))) | (~((~((tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))) = szmzizndt0(xT)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT)) | (~((~aElementOf0(tptp_fun_W2_6(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT), xT)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), tptp_fun_W2_6(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT)))))) | (~((~(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))) = szmzizndt0(xT))) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), W2))))))))))),
% 1.59/1.75 inference(transitivity,[status(thm)],[41, 39])).
% 1.59/1.75 tff(43,plain,
% 1.59/1.75 ((~![W1: $i] : (~((~((~aElementOf0(W1, xT)) | (W1 = szmzizndt0(xT)) | (~((~aElementOf0(tptp_fun_W2_6(W1, xT), xT)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, xT)))))) | (~((~(W1 = szmzizndt0(xT))) | (~((~aElementOf0(W1, xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | sdtlseqdt0(W1, W2)))))))))) | (~((~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT)) | (tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))) = szmzizndt0(xT)) | (~((~aElementOf0(tptp_fun_W2_6(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT), xT)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), tptp_fun_W2_6(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT)))))) | (~((~(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))) = szmzizndt0(xT))) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), W2)))))))))),
% 1.59/1.75 inference(quant_inst,[status(thm)],[])).
% 1.59/1.75 tff(44,plain,
% 1.59/1.75 ((~![W1: $i] : (~((~((~aElementOf0(W1, xT)) | (W1 = szmzizndt0(xT)) | (~((~aElementOf0(tptp_fun_W2_6(W1, xT), xT)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, xT)))))) | (~((~(W1 = szmzizndt0(xT))) | (~((~aElementOf0(W1, xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | sdtlseqdt0(W1, W2)))))))))) | (~((~((tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))) = szmzizndt0(xT)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT)) | (~((~aElementOf0(tptp_fun_W2_6(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT), xT)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), tptp_fun_W2_6(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT)))))) | (~((~(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))) = szmzizndt0(xT))) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), W2)))))))))),
% 1.59/1.75 inference(modus_ponens,[status(thm)],[43, 42])).
% 1.59/1.75 tff(45,plain,
% 1.59/1.75 (~((~((tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))) = szmzizndt0(xT)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT)) | (~((~aElementOf0(tptp_fun_W2_6(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT), xT)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), tptp_fun_W2_6(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT)))))) | (~((~(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))) = szmzizndt0(xT))) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), W2))))))))),
% 1.59/1.75 inference(unit_resolution,[status(thm)],[44, 38])).
% 1.59/1.75 tff(46,plain,
% 1.59/1.75 (((~((tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))) = szmzizndt0(xT)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT)) | (~((~aElementOf0(tptp_fun_W2_6(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT), xT)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), tptp_fun_W2_6(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT)))))) | (~((~(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))) = szmzizndt0(xT))) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), W2)))))))) | ((~(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))) = szmzizndt0(xT))) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), W2))))))),
% 1.59/1.75 inference(tautology,[status(thm)],[])).
% 1.59/1.75 tff(47,plain,
% 1.59/1.75 ((~(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))) = szmzizndt0(xT))) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), W2)))))),
% 1.59/1.75 inference(unit_resolution,[status(thm)],[46, 45])).
% 1.59/1.75 tff(48,plain,
% 1.59/1.75 (aSet0(szNzAzT0) <=> aSet0(szNzAzT0)),
% 1.59/1.75 inference(rewrite,[status(thm)],[])).
% 1.59/1.75 tff(49,axiom,(aSet0(szNzAzT0) & isCountable0(szNzAzT0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mNATSet')).
% 1.59/1.75 tff(50,plain,
% 1.59/1.75 (aSet0(szNzAzT0)),
% 1.59/1.75 inference(and_elim,[status(thm)],[49])).
% 1.59/1.75 tff(51,plain,
% 1.59/1.75 (aSet0(szNzAzT0)),
% 1.59/1.75 inference(modus_ponens,[status(thm)],[50, 48])).
% 1.59/1.75 tff(52,plain,
% 1.59/1.75 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))))))))),
% 1.59/1.75 inference(bind,[status(th)],[])).
% 1.59/1.75 tff(53,plain,
% 1.59/1.75 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))),
% 1.59/1.75 inference(quant_intro,[status(thm)],[52])).
% 1.59/1.75 tff(54,plain,
% 1.59/1.75 (^[W0: $i] : refl(((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))))),
% 1.59/1.75 inference(bind,[status(th)],[])).
% 1.59/1.75 tff(55,plain,
% 1.59/1.75 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 1.59/1.75 inference(quant_intro,[status(thm)],[54])).
% 1.59/1.75 tff(56,plain,
% 1.59/1.75 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))))),
% 1.59/1.75 inference(bind,[status(th)],[])).
% 1.59/1.75 tff(57,plain,
% 1.59/1.75 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 1.59/1.75 inference(quant_intro,[status(thm)],[56])).
% 1.59/1.75 tff(58,plain,
% 1.59/1.75 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 1.59/1.75 inference(transitivity,[status(thm)],[57, 55])).
% 1.59/1.75 tff(59,plain,
% 1.59/1.75 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))) <=> ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))))),
% 1.59/1.76 inference(bind,[status(th)],[])).
% 1.59/1.76 tff(60,plain,
% 1.59/1.76 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 1.59/1.76 inference(quant_intro,[status(thm)],[59])).
% 1.59/1.76 tff(61,plain,
% 1.59/1.76 (^[W0: $i] : rewrite(((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))) <=> ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))),
% 1.59/1.76 inference(bind,[status(th)],[])).
% 1.59/1.76 tff(62,plain,
% 1.59/1.76 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))) <=> ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))),
% 1.59/1.76 inference(quant_intro,[status(thm)],[61])).
% 1.59/1.76 tff(63,plain,
% 1.59/1.76 (![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)))))),
% 1.59/1.76 inference(rewrite,[status(thm)],[])).
% 1.59/1.76 tff(64,plain,
% 1.59/1.76 (^[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)))))))),
% 1.59/1.76 inference(bind,[status(th)],[])).
% 1.59/1.76 tff(65,plain,
% 1.59/1.76 (![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)))))),
% 1.59/1.76 inference(quant_intro,[status(thm)],[64])).
% 1.59/1.76 tff(66,axiom,(![W0: $i] : (aSet0(W0) => ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, W0)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mDefSub')).
% 1.59/1.76 tff(67,plain,
% 1.59/1.76 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))),
% 1.59/1.76 inference(modus_ponens,[status(thm)],[66, 65])).
% 1.59/1.76 tff(68,plain,
% 1.59/1.76 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (aSubsetOf0(W1, W0) <=> (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))))),
% 1.59/1.76 inference(modus_ponens,[status(thm)],[67, 63])).
% 1.59/1.76 tff(69,plain,(
% 1.59/1.76 ![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | ((~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0)))))))),
% 1.59/1.76 inference(skolemize,[status(sab)],[68])).
% 1.59/1.76 tff(70,plain,
% 1.59/1.76 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (((~aSubsetOf0(W1, W0)) | (aSet0(W1) & ![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0)))) & (aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))),
% 1.59/1.76 inference(modus_ponens,[status(thm)],[69, 62])).
% 1.59/1.76 tff(71,plain,
% 1.59/1.76 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 1.59/1.76 inference(modus_ponens,[status(thm)],[70, 60])).
% 1.59/1.76 tff(72,plain,
% 1.59/1.76 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))) | (~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))))))),
% 1.59/1.76 inference(modus_ponens,[status(thm)],[71, 58])).
% 1.59/1.76 tff(73,plain,
% 1.59/1.76 (![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))),
% 1.59/1.76 inference(modus_ponens,[status(thm)],[72, 53])).
% 1.59/1.76 tff(74,plain,
% 1.59/1.76 (((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(szNzAzT0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, szNzAzT0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, szNzAzT0), W1)) | aElementOf0(tptp_fun_W2_1(W1, szNzAzT0), szNzAzT0))))) | (~((~aSubsetOf0(W1, szNzAzT0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, szNzAzT0))))))))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | (~aSet0(szNzAzT0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, szNzAzT0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, szNzAzT0), W1)) | aElementOf0(tptp_fun_W2_1(W1, szNzAzT0), szNzAzT0))))) | (~((~aSubsetOf0(W1, szNzAzT0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, szNzAzT0))))))))))),
% 1.59/1.76 inference(rewrite,[status(thm)],[])).
% 1.59/1.76 tff(75,plain,
% 1.59/1.76 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | ((~aSet0(szNzAzT0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, szNzAzT0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, szNzAzT0), W1)) | aElementOf0(tptp_fun_W2_1(W1, szNzAzT0), szNzAzT0))))) | (~((~aSubsetOf0(W1, szNzAzT0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, szNzAzT0))))))))))),
% 1.59/1.76 inference(quant_inst,[status(thm)],[])).
% 1.59/1.76 tff(76,plain,
% 1.59/1.76 ((~![W0: $i] : ((~aSet0(W0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, W0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, W0), W1)) | aElementOf0(tptp_fun_W2_1(W1, W0), W0))))) | (~((~aSubsetOf0(W1, W0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, W0))))))))))) | (~aSet0(szNzAzT0)) | ![W1: $i] : (~((~(aSubsetOf0(W1, szNzAzT0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, szNzAzT0), W1)) | aElementOf0(tptp_fun_W2_1(W1, szNzAzT0), szNzAzT0))))) | (~((~aSubsetOf0(W1, szNzAzT0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, szNzAzT0)))))))))),
% 1.59/1.76 inference(modus_ponens,[status(thm)],[75, 74])).
% 1.59/1.76 tff(77,plain,
% 1.59/1.76 (![W1: $i] : (~((~(aSubsetOf0(W1, szNzAzT0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, szNzAzT0), W1)) | aElementOf0(tptp_fun_W2_1(W1, szNzAzT0), szNzAzT0))))) | (~((~aSubsetOf0(W1, szNzAzT0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, szNzAzT0)))))))))),
% 1.59/1.76 inference(unit_resolution,[status(thm)],[76, 73, 51])).
% 1.59/1.76 tff(78,plain,
% 1.59/1.76 ((~![W1: $i] : (~((~(aSubsetOf0(W1, szNzAzT0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, szNzAzT0), W1)) | aElementOf0(tptp_fun_W2_1(W1, szNzAzT0), szNzAzT0))))) | (~((~aSubsetOf0(W1, szNzAzT0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, szNzAzT0)))))))))) | (~((~(aSubsetOf0(xS, szNzAzT0) | (~aSet0(xS)) | (~((~aElementOf0(tptp_fun_W2_1(xS, szNzAzT0), xS)) | aElementOf0(tptp_fun_W2_1(xS, szNzAzT0), szNzAzT0))))) | (~((~aSubsetOf0(xS, szNzAzT0)) | (~((~aSet0(xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | aElementOf0(W2, szNzAzT0)))))))))),
% 1.59/1.76 inference(quant_inst,[status(thm)],[])).
% 1.59/1.76 tff(79,plain,
% 1.59/1.76 (~((~(aSubsetOf0(xS, szNzAzT0) | (~aSet0(xS)) | (~((~aElementOf0(tptp_fun_W2_1(xS, szNzAzT0), xS)) | aElementOf0(tptp_fun_W2_1(xS, szNzAzT0), szNzAzT0))))) | (~((~aSubsetOf0(xS, szNzAzT0)) | (~((~aSet0(xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | aElementOf0(W2, szNzAzT0))))))))),
% 1.59/1.76 inference(unit_resolution,[status(thm)],[78, 77])).
% 1.59/1.76 tff(80,plain,
% 1.59/1.76 (((~(aSubsetOf0(xS, szNzAzT0) | (~aSet0(xS)) | (~((~aElementOf0(tptp_fun_W2_1(xS, szNzAzT0), xS)) | aElementOf0(tptp_fun_W2_1(xS, szNzAzT0), szNzAzT0))))) | (~((~aSubsetOf0(xS, szNzAzT0)) | (~((~aSet0(xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | aElementOf0(W2, szNzAzT0)))))))) | ((~aSubsetOf0(xS, szNzAzT0)) | (~((~aSet0(xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | aElementOf0(W2, szNzAzT0))))))),
% 1.59/1.76 inference(tautology,[status(thm)],[])).
% 1.59/1.76 tff(81,plain,
% 1.59/1.76 ((~aSubsetOf0(xS, szNzAzT0)) | (~((~aSet0(xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | aElementOf0(W2, szNzAzT0)))))),
% 1.59/1.76 inference(unit_resolution,[status(thm)],[80, 79])).
% 1.59/1.76 tff(82,plain,
% 1.59/1.76 (aSubsetOf0(xS, szNzAzT0) <=> aSubsetOf0(xS, szNzAzT0)),
% 1.59/1.76 inference(rewrite,[status(thm)],[])).
% 1.59/1.76 tff(83,plain,
% 1.59/1.76 (aSubsetOf0(xS, szNzAzT0)),
% 1.59/1.76 inference(and_elim,[status(thm)],[7])).
% 1.59/1.76 tff(84,plain,
% 1.59/1.76 (aSubsetOf0(xS, szNzAzT0)),
% 1.59/1.76 inference(modus_ponens,[status(thm)],[83, 82])).
% 1.59/1.76 tff(85,plain,
% 1.59/1.76 ((~((~aSubsetOf0(xS, szNzAzT0)) | (~((~aSet0(xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | aElementOf0(W2, szNzAzT0))))))) | (~aSubsetOf0(xS, szNzAzT0)) | (~((~aSet0(xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | aElementOf0(W2, szNzAzT0)))))),
% 1.59/1.76 inference(tautology,[status(thm)],[])).
% 1.59/1.76 tff(86,plain,
% 1.59/1.76 ((~((~aSubsetOf0(xS, szNzAzT0)) | (~((~aSet0(xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | aElementOf0(W2, szNzAzT0))))))) | (~((~aSet0(xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | aElementOf0(W2, szNzAzT0)))))),
% 1.59/1.76 inference(unit_resolution,[status(thm)],[85, 84])).
% 1.59/1.76 tff(87,plain,
% 1.59/1.76 (~((~aSet0(xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | aElementOf0(W2, szNzAzT0))))),
% 1.59/1.76 inference(unit_resolution,[status(thm)],[86, 81])).
% 1.59/1.76 tff(88,plain,
% 1.59/1.76 (((~aSet0(xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | aElementOf0(W2, szNzAzT0)))) | ![W2: $i] : ((~aElementOf0(W2, xS)) | aElementOf0(W2, szNzAzT0))),
% 1.59/1.76 inference(tautology,[status(thm)],[])).
% 1.59/1.76 tff(89,plain,
% 1.59/1.76 (![W2: $i] : ((~aElementOf0(W2, xS)) | aElementOf0(W2, szNzAzT0))),
% 1.59/1.76 inference(unit_resolution,[status(thm)],[88, 87])).
% 1.59/1.76 tff(90,plain,
% 1.59/1.76 (aElementOf0(szmzizndt0(xT), xS) <=> aElementOf0(szmzizndt0(xT), xS)),
% 1.59/1.76 inference(rewrite,[status(thm)],[])).
% 1.59/1.76 tff(91,axiom,(aElementOf0(szmzizndt0(xS), xT) & aElementOf0(szmzizndt0(xT), xS)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__1802')).
% 1.59/1.76 tff(92,plain,
% 1.59/1.76 (aElementOf0(szmzizndt0(xT), xS)),
% 1.59/1.76 inference(and_elim,[status(thm)],[91])).
% 1.59/1.76 tff(93,plain,
% 1.59/1.76 (aElementOf0(szmzizndt0(xT), xS)),
% 1.59/1.76 inference(modus_ponens,[status(thm)],[92, 90])).
% 1.59/1.76 tff(94,plain,
% 1.59/1.76 (((~![W2: $i] : ((~aElementOf0(W2, xS)) | aElementOf0(W2, szNzAzT0))) | ((~aElementOf0(szmzizndt0(xT), xS)) | aElementOf0(szmzizndt0(xT), szNzAzT0))) <=> ((~![W2: $i] : ((~aElementOf0(W2, xS)) | aElementOf0(W2, szNzAzT0))) | (~aElementOf0(szmzizndt0(xT), xS)) | aElementOf0(szmzizndt0(xT), szNzAzT0))),
% 1.59/1.76 inference(rewrite,[status(thm)],[])).
% 1.59/1.76 tff(95,plain,
% 1.59/1.76 ((~![W2: $i] : ((~aElementOf0(W2, xS)) | aElementOf0(W2, szNzAzT0))) | ((~aElementOf0(szmzizndt0(xT), xS)) | aElementOf0(szmzizndt0(xT), szNzAzT0))),
% 1.59/1.76 inference(quant_inst,[status(thm)],[])).
% 1.59/1.76 tff(96,plain,
% 1.59/1.76 ((~![W2: $i] : ((~aElementOf0(W2, xS)) | aElementOf0(W2, szNzAzT0))) | (~aElementOf0(szmzizndt0(xT), xS)) | aElementOf0(szmzizndt0(xT), szNzAzT0)),
% 1.59/1.76 inference(modus_ponens,[status(thm)],[95, 94])).
% 1.59/1.76 tff(97,plain,
% 1.59/1.76 (aElementOf0(szmzizndt0(xT), szNzAzT0)),
% 1.59/1.76 inference(unit_resolution,[status(thm)],[96, 93, 89])).
% 1.59/1.76 tff(98,plain,
% 1.59/1.76 (^[W0: $i] : refl(((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00)))) <=> ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00)))))),
% 1.59/1.76 inference(bind,[status(th)],[])).
% 1.59/1.76 tff(99,plain,
% 1.59/1.76 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00)))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00))))),
% 1.59/1.76 inference(quant_intro,[status(thm)],[98])).
% 1.59/1.76 tff(100,plain,
% 1.59/1.76 (^[W0: $i] : rewrite(((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(szszuzczcdt0(W0), szNzAzT0) & (~(szszuzczcdt0(W0) = sz00)))) <=> ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00)))))),
% 1.59/1.76 inference(bind,[status(th)],[])).
% 1.59/1.76 tff(101,plain,
% 1.59/1.76 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(szszuzczcdt0(W0), szNzAzT0) & (~(szszuzczcdt0(W0) = sz00)))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00))))),
% 1.59/1.76 inference(quant_intro,[status(thm)],[100])).
% 1.59/1.76 tff(102,plain,
% 1.59/1.76 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(szszuzczcdt0(W0), szNzAzT0) & (~(szszuzczcdt0(W0) = sz00)))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(szszuzczcdt0(W0), szNzAzT0) & (~(szszuzczcdt0(W0) = sz00))))),
% 1.59/1.76 inference(rewrite,[status(thm)],[])).
% 1.59/1.76 tff(103,plain,
% 1.59/1.76 (^[W0: $i] : rewrite((aElementOf0(W0, szNzAzT0) => (aElementOf0(szszuzczcdt0(W0), szNzAzT0) & (~(szszuzczcdt0(W0) = sz00)))) <=> ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(szszuzczcdt0(W0), szNzAzT0) & (~(szszuzczcdt0(W0) = sz00)))))),
% 1.59/1.76 inference(bind,[status(th)],[])).
% 1.59/1.76 tff(104,plain,
% 1.59/1.76 (![W0: $i] : (aElementOf0(W0, szNzAzT0) => (aElementOf0(szszuzczcdt0(W0), szNzAzT0) & (~(szszuzczcdt0(W0) = sz00)))) <=> ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(szszuzczcdt0(W0), szNzAzT0) & (~(szszuzczcdt0(W0) = sz00))))),
% 1.59/1.76 inference(quant_intro,[status(thm)],[103])).
% 1.59/1.76 tff(105,axiom,(![W0: $i] : (aElementOf0(W0, szNzAzT0) => (aElementOf0(szszuzczcdt0(W0), szNzAzT0) & (~(szszuzczcdt0(W0) = sz00))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mSuccNum')).
% 1.59/1.76 tff(106,plain,
% 1.59/1.76 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(szszuzczcdt0(W0), szNzAzT0) & (~(szszuzczcdt0(W0) = sz00))))),
% 1.59/1.76 inference(modus_ponens,[status(thm)],[105, 104])).
% 1.59/1.76 tff(107,plain,
% 1.59/1.76 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(szszuzczcdt0(W0), szNzAzT0) & (~(szszuzczcdt0(W0) = sz00))))),
% 1.59/1.76 inference(modus_ponens,[status(thm)],[106, 102])).
% 1.59/1.76 tff(108,plain,(
% 1.59/1.76 ![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (aElementOf0(szszuzczcdt0(W0), szNzAzT0) & (~(szszuzczcdt0(W0) = sz00))))),
% 1.59/1.76 inference(skolemize,[status(sab)],[107])).
% 1.59/1.76 tff(109,plain,
% 1.59/1.76 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00))))),
% 1.59/1.76 inference(modus_ponens,[status(thm)],[108, 101])).
% 1.59/1.76 tff(110,plain,
% 1.59/1.76 (![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00))))),
% 1.59/1.76 inference(modus_ponens,[status(thm)],[109, 99])).
% 1.59/1.76 tff(111,plain,
% 1.59/1.76 (((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00))))) | ((~aElementOf0(szmzizndt0(xT), szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(szmzizndt0(xT)), szNzAzT0)) | (szszuzczcdt0(szmzizndt0(xT)) = sz00))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00))))) | (~aElementOf0(szmzizndt0(xT), szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(szmzizndt0(xT)), szNzAzT0)) | (szszuzczcdt0(szmzizndt0(xT)) = sz00))))),
% 1.59/1.76 inference(rewrite,[status(thm)],[])).
% 1.59/1.76 tff(112,plain,
% 1.59/1.76 ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00))))) | ((~aElementOf0(szmzizndt0(xT), szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(szmzizndt0(xT)), szNzAzT0)) | (szszuzczcdt0(szmzizndt0(xT)) = sz00))))),
% 1.59/1.76 inference(quant_inst,[status(thm)],[])).
% 1.59/1.76 tff(113,plain,
% 1.59/1.76 ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00))))) | (~aElementOf0(szmzizndt0(xT), szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(szmzizndt0(xT)), szNzAzT0)) | (szszuzczcdt0(szmzizndt0(xT)) = sz00)))),
% 1.59/1.76 inference(modus_ponens,[status(thm)],[112, 111])).
% 1.59/1.76 tff(114,plain,
% 1.59/1.76 (~((~aElementOf0(szszuzczcdt0(szmzizndt0(xT)), szNzAzT0)) | (szszuzczcdt0(szmzizndt0(xT)) = sz00))),
% 1.59/1.76 inference(unit_resolution,[status(thm)],[113, 110, 97])).
% 1.59/1.76 tff(115,plain,
% 1.59/1.76 (((~aElementOf0(szszuzczcdt0(szmzizndt0(xT)), szNzAzT0)) | (szszuzczcdt0(szmzizndt0(xT)) = sz00)) | (~(szszuzczcdt0(szmzizndt0(xT)) = sz00))),
% 1.59/1.76 inference(tautology,[status(thm)],[])).
% 1.59/1.76 tff(116,plain,
% 1.59/1.76 (~(szszuzczcdt0(szmzizndt0(xT)) = sz00)),
% 1.59/1.76 inference(unit_resolution,[status(thm)],[115, 114])).
% 1.59/1.76 tff(117,plain,
% 1.59/1.76 (((~aElementOf0(szszuzczcdt0(szmzizndt0(xT)), szNzAzT0)) | (szszuzczcdt0(szmzizndt0(xT)) = sz00)) | aElementOf0(szszuzczcdt0(szmzizndt0(xT)), szNzAzT0)),
% 1.59/1.76 inference(tautology,[status(thm)],[])).
% 1.59/1.76 tff(118,plain,
% 1.59/1.76 (aElementOf0(szszuzczcdt0(szmzizndt0(xT)), szNzAzT0)),
% 1.59/1.76 inference(unit_resolution,[status(thm)],[117, 114])).
% 1.59/1.76 tff(119,plain,
% 1.59/1.76 (^[W0: $i] : refl(((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0))))))) <=> ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0))))))))),
% 1.59/1.76 inference(bind,[status(th)],[])).
% 1.59/1.76 tff(120,plain,
% 1.59/1.76 (![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0))))))) <=> ![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))))),
% 1.59/1.76 inference(quant_intro,[status(thm)],[119])).
% 1.59/1.76 tff(121,plain,
% 1.59/1.76 (^[W0: $i] : trans(monotonicity(rewrite((aElementOf0(tptp_fun_W1_4(W0), szNzAzT0) & (W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))) <=> (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0))))))), (((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (aElementOf0(tptp_fun_W1_4(W0), szNzAzT0) & (W0 = szszuzczcdt0(tptp_fun_W1_4(W0))))) <=> ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0))))))))), rewrite(((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0))))))) <=> ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))))), (((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (aElementOf0(tptp_fun_W1_4(W0), szNzAzT0) & (W0 = szszuzczcdt0(tptp_fun_W1_4(W0))))) <=> ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))))))),
% 1.59/1.76 inference(bind,[status(th)],[])).
% 1.59/1.76 tff(122,plain,
% 1.59/1.76 (![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (aElementOf0(tptp_fun_W1_4(W0), szNzAzT0) & (W0 = szszuzczcdt0(tptp_fun_W1_4(W0))))) <=> ![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))))),
% 1.59/1.76 inference(quant_intro,[status(thm)],[121])).
% 1.59/1.76 tff(123,plain,
% 1.59/1.76 (^[W0: $i] : rewrite(((aElementOf0(tptp_fun_W1_4(W0), szNzAzT0) & (W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))) | (W0 = sz00) | (~aElementOf0(W0, szNzAzT0))) <=> ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (aElementOf0(tptp_fun_W1_4(W0), szNzAzT0) & (W0 = szszuzczcdt0(tptp_fun_W1_4(W0))))))),
% 1.59/1.76 inference(bind,[status(th)],[])).
% 1.59/1.76 tff(124,plain,
% 1.59/1.76 (![W0: $i] : ((aElementOf0(tptp_fun_W1_4(W0), szNzAzT0) & (W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))) | (W0 = sz00) | (~aElementOf0(W0, szNzAzT0))) <=> ![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (aElementOf0(tptp_fun_W1_4(W0), szNzAzT0) & (W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))),
% 1.59/1.76 inference(quant_intro,[status(thm)],[123])).
% 1.59/1.76 tff(125,plain,
% 1.59/1.76 (![W0: $i] : (?[W1: $i] : (aElementOf0(W1, szNzAzT0) & (W0 = szszuzczcdt0(W1))) | (W0 = sz00) | (~aElementOf0(W0, szNzAzT0))) <=> ![W0: $i] : (?[W1: $i] : (aElementOf0(W1, szNzAzT0) & (W0 = szszuzczcdt0(W1))) | (W0 = sz00) | (~aElementOf0(W0, szNzAzT0)))),
% 1.59/1.76 inference(rewrite,[status(thm)],[])).
% 1.59/1.76 tff(126,plain,
% 1.59/1.76 (^[W0: $i] : trans(monotonicity(rewrite(((W0 = sz00) | ?[W1: $i] : (aElementOf0(W1, szNzAzT0) & (W0 = szszuzczcdt0(W1)))) <=> ((W0 = sz00) | ?[W1: $i] : (aElementOf0(W1, szNzAzT0) & (W0 = szszuzczcdt0(W1))))), ((aElementOf0(W0, szNzAzT0) => ((W0 = sz00) | ?[W1: $i] : (aElementOf0(W1, szNzAzT0) & (W0 = szszuzczcdt0(W1))))) <=> (aElementOf0(W0, szNzAzT0) => ((W0 = sz00) | ?[W1: $i] : (aElementOf0(W1, szNzAzT0) & (W0 = szszuzczcdt0(W1))))))), rewrite((aElementOf0(W0, szNzAzT0) => ((W0 = sz00) | ?[W1: $i] : (aElementOf0(W1, szNzAzT0) & (W0 = szszuzczcdt0(W1))))) <=> (?[W1: $i] : (aElementOf0(W1, szNzAzT0) & (W0 = szszuzczcdt0(W1))) | (W0 = sz00) | (~aElementOf0(W0, szNzAzT0)))), ((aElementOf0(W0, szNzAzT0) => ((W0 = sz00) | ?[W1: $i] : (aElementOf0(W1, szNzAzT0) & (W0 = szszuzczcdt0(W1))))) <=> (?[W1: $i] : (aElementOf0(W1, szNzAzT0) & (W0 = szszuzczcdt0(W1))) | (W0 = sz00) | (~aElementOf0(W0, szNzAzT0)))))),
% 1.59/1.76 inference(bind,[status(th)],[])).
% 1.59/1.76 tff(127,plain,
% 1.59/1.76 (![W0: $i] : (aElementOf0(W0, szNzAzT0) => ((W0 = sz00) | ?[W1: $i] : (aElementOf0(W1, szNzAzT0) & (W0 = szszuzczcdt0(W1))))) <=> ![W0: $i] : (?[W1: $i] : (aElementOf0(W1, szNzAzT0) & (W0 = szszuzczcdt0(W1))) | (W0 = sz00) | (~aElementOf0(W0, szNzAzT0)))),
% 1.59/1.76 inference(quant_intro,[status(thm)],[126])).
% 1.59/1.76 tff(128,axiom,(![W0: $i] : (aElementOf0(W0, szNzAzT0) => ((W0 = sz00) | ?[W1: $i] : (aElementOf0(W1, szNzAzT0) & (W0 = szszuzczcdt0(W1)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mNatExtra')).
% 1.59/1.76 tff(129,plain,
% 1.59/1.76 (![W0: $i] : (?[W1: $i] : (aElementOf0(W1, szNzAzT0) & (W0 = szszuzczcdt0(W1))) | (W0 = sz00) | (~aElementOf0(W0, szNzAzT0)))),
% 1.59/1.76 inference(modus_ponens,[status(thm)],[128, 127])).
% 1.59/1.76 tff(130,plain,
% 1.59/1.76 (![W0: $i] : (?[W1: $i] : (aElementOf0(W1, szNzAzT0) & (W0 = szszuzczcdt0(W1))) | (W0 = sz00) | (~aElementOf0(W0, szNzAzT0)))),
% 1.59/1.76 inference(modus_ponens,[status(thm)],[129, 125])).
% 1.59/1.76 tff(131,plain,(
% 1.59/1.76 ![W0: $i] : ((aElementOf0(tptp_fun_W1_4(W0), szNzAzT0) & (W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))) | (W0 = sz00) | (~aElementOf0(W0, szNzAzT0)))),
% 1.59/1.76 inference(skolemize,[status(sab)],[130])).
% 1.59/1.76 tff(132,plain,
% 1.59/1.76 (![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (aElementOf0(tptp_fun_W1_4(W0), szNzAzT0) & (W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))),
% 1.59/1.76 inference(modus_ponens,[status(thm)],[131, 124])).
% 1.59/1.76 tff(133,plain,
% 1.59/1.76 (![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))))),
% 1.59/1.76 inference(modus_ponens,[status(thm)],[132, 122])).
% 1.59/1.76 tff(134,plain,
% 1.59/1.76 (![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))))),
% 1.59/1.76 inference(modus_ponens,[status(thm)],[133, 120])).
% 1.59/1.76 tff(135,plain,
% 1.59/1.76 (((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))))) | ((~aElementOf0(szszuzczcdt0(szmzizndt0(xT)), szNzAzT0)) | (szszuzczcdt0(szmzizndt0(xT)) = sz00) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), szNzAzT0)) | (~(szszuzczcdt0(szmzizndt0(xT)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT)))))))))) <=> ((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))))) | (~aElementOf0(szszuzczcdt0(szmzizndt0(xT)), szNzAzT0)) | (szszuzczcdt0(szmzizndt0(xT)) = sz00) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), szNzAzT0)) | (~(szszuzczcdt0(szmzizndt0(xT)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT)))))))))),
% 1.59/1.76 inference(rewrite,[status(thm)],[])).
% 1.59/1.76 tff(136,plain,
% 1.59/1.76 (((szszuzczcdt0(szmzizndt0(xT)) = sz00) | (~aElementOf0(szszuzczcdt0(szmzizndt0(xT)), szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), szNzAzT0)) | (~(szszuzczcdt0(szmzizndt0(xT)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))))))))) <=> ((~aElementOf0(szszuzczcdt0(szmzizndt0(xT)), szNzAzT0)) | (szszuzczcdt0(szmzizndt0(xT)) = sz00) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), szNzAzT0)) | (~(szszuzczcdt0(szmzizndt0(xT)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT)))))))))),
% 1.59/1.76 inference(rewrite,[status(thm)],[])).
% 1.59/1.76 tff(137,plain,
% 1.59/1.76 (((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))))) | ((szszuzczcdt0(szmzizndt0(xT)) = sz00) | (~aElementOf0(szszuzczcdt0(szmzizndt0(xT)), szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), szNzAzT0)) | (~(szszuzczcdt0(szmzizndt0(xT)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT)))))))))) <=> ((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))))) | ((~aElementOf0(szszuzczcdt0(szmzizndt0(xT)), szNzAzT0)) | (szszuzczcdt0(szmzizndt0(xT)) = sz00) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), szNzAzT0)) | (~(szszuzczcdt0(szmzizndt0(xT)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))))))))))),
% 1.59/1.76 inference(monotonicity,[status(thm)],[136])).
% 1.59/1.76 tff(138,plain,
% 1.59/1.76 (((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))))) | ((szszuzczcdt0(szmzizndt0(xT)) = sz00) | (~aElementOf0(szszuzczcdt0(szmzizndt0(xT)), szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), szNzAzT0)) | (~(szszuzczcdt0(szmzizndt0(xT)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT)))))))))) <=> ((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))))) | (~aElementOf0(szszuzczcdt0(szmzizndt0(xT)), szNzAzT0)) | (szszuzczcdt0(szmzizndt0(xT)) = sz00) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), szNzAzT0)) | (~(szszuzczcdt0(szmzizndt0(xT)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT)))))))))),
% 1.59/1.76 inference(transitivity,[status(thm)],[137, 135])).
% 1.59/1.76 tff(139,plain,
% 1.59/1.76 ((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))))) | ((szszuzczcdt0(szmzizndt0(xT)) = sz00) | (~aElementOf0(szszuzczcdt0(szmzizndt0(xT)), szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), szNzAzT0)) | (~(szszuzczcdt0(szmzizndt0(xT)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT)))))))))),
% 1.59/1.76 inference(quant_inst,[status(thm)],[])).
% 1.59/1.76 tff(140,plain,
% 1.59/1.76 ((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))))) | (~aElementOf0(szszuzczcdt0(szmzizndt0(xT)), szNzAzT0)) | (szszuzczcdt0(szmzizndt0(xT)) = sz00) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), szNzAzT0)) | (~(szszuzczcdt0(szmzizndt0(xT)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))))))))),
% 1.59/1.76 inference(modus_ponens,[status(thm)],[139, 138])).
% 1.59/1.76 tff(141,plain,
% 1.59/1.76 (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), szNzAzT0)) | (~(szszuzczcdt0(szmzizndt0(xT)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT)))))))),
% 1.59/1.76 inference(unit_resolution,[status(thm)],[140, 134, 118, 116])).
% 1.59/1.76 tff(142,plain,
% 1.59/1.76 (((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), szNzAzT0)) | (~(szszuzczcdt0(szmzizndt0(xT)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))))))) | (szszuzczcdt0(szmzizndt0(xT)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT)))))),
% 1.59/1.76 inference(tautology,[status(thm)],[])).
% 1.59/1.76 tff(143,plain,
% 1.59/1.76 (szszuzczcdt0(szmzizndt0(xT)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))))),
% 1.59/1.76 inference(unit_resolution,[status(thm)],[142, 141])).
% 1.59/1.76 tff(144,plain,
% 1.59/1.76 (szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT)))) = szszuzczcdt0(szmzizndt0(xT))),
% 1.59/1.76 inference(symmetry,[status(thm)],[143])).
% 1.59/1.76 tff(145,plain,
% 1.59/1.76 (((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), szNzAzT0)) | (~(szszuzczcdt0(szmzizndt0(xT)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))))))) | aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), szNzAzT0)),
% 1.59/1.76 inference(tautology,[status(thm)],[])).
% 1.59/1.76 tff(146,plain,
% 1.59/1.76 (aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), szNzAzT0)),
% 1.59/1.76 inference(unit_resolution,[status(thm)],[145, 141])).
% 1.59/1.76 tff(147,plain,
% 1.59/1.76 (^[W0: $i, W1: $i] : refl(((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0))) <=> ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0))))),
% 1.59/1.76 inference(bind,[status(th)],[])).
% 1.59/1.76 tff(148,plain,
% 1.59/1.76 (![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0))) <=> ![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))),
% 1.59/1.76 inference(quant_intro,[status(thm)],[147])).
% 1.59/1.76 tff(149,plain,
% 1.59/1.76 (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) <=> (~((~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0))))), ((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) <=> (~(~((~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0))))))), rewrite((~(~((~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0))))) <=> ((~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)))), ((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))) <=> ((~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0))))), (((W0 = W1) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)))) <=> ((W0 = W1) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | ((~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)))))), rewrite(((W0 = W1) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | ((~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)))) <=> ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))), (((W0 = W1) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)))) <=> ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))))),
% 1.59/1.76 inference(bind,[status(th)],[])).
% 1.59/1.76 tff(150,plain,
% 1.59/1.76 (![W0: $i, W1: $i] : ((W0 = W1) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)))) <=> ![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))),
% 1.59/1.76 inference(quant_intro,[status(thm)],[149])).
% 1.59/1.76 tff(151,plain,
% 1.59/1.76 (![W0: $i, W1: $i] : ((W0 = W1) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)))) <=> ![W0: $i, W1: $i] : ((W0 = W1) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))))),
% 1.59/1.76 inference(rewrite,[status(thm)],[])).
% 1.59/1.76 tff(152,plain,
% 1.59/1.76 (^[W0: $i, W1: $i] : trans(monotonicity(rewrite(((szszuzczcdt0(W0) = szszuzczcdt0(W1)) => (W0 = W1)) <=> ((~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (W0 = W1))), (((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) => ((szszuzczcdt0(W0) = szszuzczcdt0(W1)) => (W0 = W1))) <=> ((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) => ((~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (W0 = W1))))), rewrite(((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) => ((~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (W0 = W1))) <=> ((W0 = W1) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))))), (((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) => ((szszuzczcdt0(W0) = szszuzczcdt0(W1)) => (W0 = W1))) <=> ((W0 = W1) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))))))),
% 1.59/1.76 inference(bind,[status(th)],[])).
% 1.59/1.76 tff(153,plain,
% 1.59/1.76 (![W0: $i, W1: $i] : ((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) => ((szszuzczcdt0(W0) = szszuzczcdt0(W1)) => (W0 = W1))) <=> ![W0: $i, W1: $i] : ((W0 = W1) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))))),
% 1.59/1.76 inference(quant_intro,[status(thm)],[152])).
% 1.59/1.76 tff(154,axiom,(![W0: $i, W1: $i] : ((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) => ((szszuzczcdt0(W0) = szszuzczcdt0(W1)) => (W0 = W1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mSuccEquSucc')).
% 1.59/1.76 tff(155,plain,
% 1.59/1.76 (![W0: $i, W1: $i] : ((W0 = W1) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))))),
% 1.59/1.76 inference(modus_ponens,[status(thm)],[154, 153])).
% 1.59/1.76 tff(156,plain,
% 1.59/1.76 (![W0: $i, W1: $i] : ((W0 = W1) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))))),
% 1.59/1.76 inference(modus_ponens,[status(thm)],[155, 151])).
% 1.59/1.76 tff(157,plain,(
% 1.59/1.76 ![W0: $i, W1: $i] : ((W0 = W1) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0))))),
% 1.59/1.76 inference(skolemize,[status(sab)],[156])).
% 1.59/1.76 tff(158,plain,
% 1.59/1.76 (![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))),
% 1.59/1.76 inference(modus_ponens,[status(thm)],[157, 150])).
% 1.59/1.76 tff(159,plain,
% 1.59/1.76 (![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))),
% 1.59/1.76 inference(modus_ponens,[status(thm)],[158, 148])).
% 1.59/1.76 tff(160,plain,
% 1.59/1.76 (((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | ((~aElementOf0(szmzizndt0(xT), szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), szNzAzT0)) | (tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))) = szmzizndt0(xT)) | (~(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT)))) = szszuzczcdt0(szmzizndt0(xT)))))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | (~aElementOf0(szmzizndt0(xT), szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), szNzAzT0)) | (tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))) = szmzizndt0(xT)) | (~(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT)))) = szszuzczcdt0(szmzizndt0(xT)))))),
% 1.59/1.76 inference(rewrite,[status(thm)],[])).
% 1.59/1.76 tff(161,plain,
% 1.59/1.76 (((tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))) = szmzizndt0(xT)) | (~aElementOf0(szmzizndt0(xT), szNzAzT0)) | (~(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT)))) = szszuzczcdt0(szmzizndt0(xT)))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), szNzAzT0))) <=> ((~aElementOf0(szmzizndt0(xT), szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), szNzAzT0)) | (tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))) = szmzizndt0(xT)) | (~(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT)))) = szszuzczcdt0(szmzizndt0(xT)))))),
% 1.59/1.76 inference(rewrite,[status(thm)],[])).
% 1.59/1.76 tff(162,plain,
% 1.59/1.76 (((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | ((tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))) = szmzizndt0(xT)) | (~aElementOf0(szmzizndt0(xT), szNzAzT0)) | (~(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT)))) = szszuzczcdt0(szmzizndt0(xT)))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), szNzAzT0)))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | ((~aElementOf0(szmzizndt0(xT), szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), szNzAzT0)) | (tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))) = szmzizndt0(xT)) | (~(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT)))) = szszuzczcdt0(szmzizndt0(xT))))))),
% 1.59/1.76 inference(monotonicity,[status(thm)],[161])).
% 1.59/1.76 tff(163,plain,
% 1.59/1.76 (((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | ((tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))) = szmzizndt0(xT)) | (~aElementOf0(szmzizndt0(xT), szNzAzT0)) | (~(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT)))) = szszuzczcdt0(szmzizndt0(xT)))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), szNzAzT0)))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | (~aElementOf0(szmzizndt0(xT), szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), szNzAzT0)) | (tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))) = szmzizndt0(xT)) | (~(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT)))) = szszuzczcdt0(szmzizndt0(xT)))))),
% 1.59/1.76 inference(transitivity,[status(thm)],[162, 160])).
% 1.59/1.76 tff(164,plain,
% 1.59/1.76 ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | ((tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))) = szmzizndt0(xT)) | (~aElementOf0(szmzizndt0(xT), szNzAzT0)) | (~(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT)))) = szszuzczcdt0(szmzizndt0(xT)))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), szNzAzT0)))),
% 1.59/1.76 inference(quant_inst,[status(thm)],[])).
% 1.59/1.76 tff(165,plain,
% 1.59/1.76 ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | (~aElementOf0(szmzizndt0(xT), szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), szNzAzT0)) | (tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))) = szmzizndt0(xT)) | (~(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT)))) = szszuzczcdt0(szmzizndt0(xT))))),
% 1.59/1.77 inference(modus_ponens,[status(thm)],[164, 163])).
% 1.59/1.77 tff(166,plain,
% 1.59/1.77 (tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))) = szmzizndt0(xT)),
% 1.59/1.77 inference(unit_resolution,[status(thm)],[165, 159, 97, 146, 144])).
% 1.59/1.77 tff(167,plain,
% 1.59/1.77 ((~((~(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))) = szmzizndt0(xT))) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), W2))))))) | (~(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))) = szmzizndt0(xT))) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), W2)))))),
% 1.59/1.77 inference(tautology,[status(thm)],[])).
% 1.59/1.77 tff(168,plain,
% 1.59/1.77 ((~((~(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))) = szmzizndt0(xT))) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), W2))))))) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), W2)))))),
% 1.59/1.77 inference(unit_resolution,[status(thm)],[167, 166])).
% 1.59/1.77 tff(169,plain,
% 1.59/1.77 (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), W2))))),
% 1.59/1.77 inference(unit_resolution,[status(thm)],[168, 47])).
% 1.59/1.77 tff(170,plain,
% 1.59/1.77 (((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), W2)))) | ![W2: $i] : ((~aElementOf0(W2, xT)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), W2))),
% 1.59/1.77 inference(tautology,[status(thm)],[])).
% 1.59/1.77 tff(171,plain,
% 1.59/1.77 (![W2: $i] : ((~aElementOf0(W2, xT)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), W2))),
% 1.59/1.77 inference(unit_resolution,[status(thm)],[170, 169])).
% 1.59/1.77 tff(172,plain,
% 1.59/1.77 ((~![W1: $i] : (~((~(aSubsetOf0(W1, szNzAzT0) | (~aSet0(W1)) | (~((~aElementOf0(tptp_fun_W2_1(W1, szNzAzT0), W1)) | aElementOf0(tptp_fun_W2_1(W1, szNzAzT0), szNzAzT0))))) | (~((~aSubsetOf0(W1, szNzAzT0)) | (~((~aSet0(W1)) | (~![W2: $i] : ((~aElementOf0(W2, W1)) | aElementOf0(W2, szNzAzT0)))))))))) | (~((~(aSubsetOf0(xT, szNzAzT0) | (~aSet0(xT)) | (~((~aElementOf0(tptp_fun_W2_1(xT, szNzAzT0), xT)) | aElementOf0(tptp_fun_W2_1(xT, szNzAzT0), szNzAzT0))))) | (~((~aSubsetOf0(xT, szNzAzT0)) | (~((~aSet0(xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | aElementOf0(W2, szNzAzT0)))))))))),
% 1.59/1.77 inference(quant_inst,[status(thm)],[])).
% 1.59/1.77 tff(173,plain,
% 1.59/1.77 (~((~(aSubsetOf0(xT, szNzAzT0) | (~aSet0(xT)) | (~((~aElementOf0(tptp_fun_W2_1(xT, szNzAzT0), xT)) | aElementOf0(tptp_fun_W2_1(xT, szNzAzT0), szNzAzT0))))) | (~((~aSubsetOf0(xT, szNzAzT0)) | (~((~aSet0(xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | aElementOf0(W2, szNzAzT0))))))))),
% 1.59/1.77 inference(unit_resolution,[status(thm)],[172, 77])).
% 1.59/1.77 tff(174,plain,
% 1.59/1.77 (((~(aSubsetOf0(xT, szNzAzT0) | (~aSet0(xT)) | (~((~aElementOf0(tptp_fun_W2_1(xT, szNzAzT0), xT)) | aElementOf0(tptp_fun_W2_1(xT, szNzAzT0), szNzAzT0))))) | (~((~aSubsetOf0(xT, szNzAzT0)) | (~((~aSet0(xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | aElementOf0(W2, szNzAzT0)))))))) | ((~aSubsetOf0(xT, szNzAzT0)) | (~((~aSet0(xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | aElementOf0(W2, szNzAzT0))))))),
% 1.59/1.77 inference(tautology,[status(thm)],[])).
% 1.59/1.77 tff(175,plain,
% 1.59/1.77 ((~aSubsetOf0(xT, szNzAzT0)) | (~((~aSet0(xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | aElementOf0(W2, szNzAzT0)))))),
% 1.59/1.77 inference(unit_resolution,[status(thm)],[174, 173])).
% 1.59/1.77 tff(176,plain,
% 1.59/1.77 ((~((~aSubsetOf0(xT, szNzAzT0)) | (~((~aSet0(xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | aElementOf0(W2, szNzAzT0))))))) | (~aSubsetOf0(xT, szNzAzT0)) | (~((~aSet0(xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | aElementOf0(W2, szNzAzT0)))))),
% 1.59/1.77 inference(tautology,[status(thm)],[])).
% 1.59/1.77 tff(177,plain,
% 1.59/1.77 ((~((~aSubsetOf0(xT, szNzAzT0)) | (~((~aSet0(xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | aElementOf0(W2, szNzAzT0))))))) | (~((~aSet0(xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | aElementOf0(W2, szNzAzT0)))))),
% 1.59/1.77 inference(unit_resolution,[status(thm)],[176, 9])).
% 1.59/1.77 tff(178,plain,
% 1.59/1.77 (~((~aSet0(xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | aElementOf0(W2, szNzAzT0))))),
% 1.59/1.77 inference(unit_resolution,[status(thm)],[177, 175])).
% 1.59/1.77 tff(179,plain,
% 1.59/1.77 (((~aSet0(xT)) | (~![W2: $i] : ((~aElementOf0(W2, xT)) | aElementOf0(W2, szNzAzT0)))) | ![W2: $i] : ((~aElementOf0(W2, xT)) | aElementOf0(W2, szNzAzT0))),
% 1.59/1.77 inference(tautology,[status(thm)],[])).
% 1.59/1.77 tff(180,plain,
% 1.59/1.77 (![W2: $i] : ((~aElementOf0(W2, xT)) | aElementOf0(W2, szNzAzT0))),
% 1.59/1.77 inference(unit_resolution,[status(thm)],[179, 178])).
% 1.59/1.77 tff(181,plain,
% 1.59/1.77 (aElementOf0(szmzizndt0(xS), xT) <=> aElementOf0(szmzizndt0(xS), xT)),
% 1.59/1.77 inference(rewrite,[status(thm)],[])).
% 1.59/1.77 tff(182,plain,
% 1.59/1.77 (aElementOf0(szmzizndt0(xS), xT)),
% 1.59/1.77 inference(and_elim,[status(thm)],[91])).
% 1.59/1.77 tff(183,plain,
% 1.59/1.77 (aElementOf0(szmzizndt0(xS), xT)),
% 1.59/1.77 inference(modus_ponens,[status(thm)],[182, 181])).
% 1.59/1.77 tff(184,plain,
% 1.59/1.77 (((~![W2: $i] : ((~aElementOf0(W2, xT)) | aElementOf0(W2, szNzAzT0))) | ((~aElementOf0(szmzizndt0(xS), xT)) | aElementOf0(szmzizndt0(xS), szNzAzT0))) <=> ((~![W2: $i] : ((~aElementOf0(W2, xT)) | aElementOf0(W2, szNzAzT0))) | (~aElementOf0(szmzizndt0(xS), xT)) | aElementOf0(szmzizndt0(xS), szNzAzT0))),
% 1.59/1.77 inference(rewrite,[status(thm)],[])).
% 1.59/1.77 tff(185,plain,
% 1.59/1.77 ((~![W2: $i] : ((~aElementOf0(W2, xT)) | aElementOf0(W2, szNzAzT0))) | ((~aElementOf0(szmzizndt0(xS), xT)) | aElementOf0(szmzizndt0(xS), szNzAzT0))),
% 1.59/1.77 inference(quant_inst,[status(thm)],[])).
% 1.59/1.77 tff(186,plain,
% 1.59/1.77 ((~![W2: $i] : ((~aElementOf0(W2, xT)) | aElementOf0(W2, szNzAzT0))) | (~aElementOf0(szmzizndt0(xS), xT)) | aElementOf0(szmzizndt0(xS), szNzAzT0)),
% 1.59/1.77 inference(modus_ponens,[status(thm)],[185, 184])).
% 1.59/1.77 tff(187,plain,
% 1.59/1.77 (aElementOf0(szmzizndt0(xS), szNzAzT0)),
% 1.59/1.77 inference(unit_resolution,[status(thm)],[186, 183, 180])).
% 1.59/1.77 tff(188,plain,
% 1.59/1.77 (((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00))))) | ((~aElementOf0(szmzizndt0(xS), szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(szmzizndt0(xS)), szNzAzT0)) | (szszuzczcdt0(szmzizndt0(xS)) = sz00))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00))))) | (~aElementOf0(szmzizndt0(xS), szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(szmzizndt0(xS)), szNzAzT0)) | (szszuzczcdt0(szmzizndt0(xS)) = sz00))))),
% 1.59/1.77 inference(rewrite,[status(thm)],[])).
% 1.59/1.77 tff(189,plain,
% 1.59/1.77 ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00))))) | ((~aElementOf0(szmzizndt0(xS), szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(szmzizndt0(xS)), szNzAzT0)) | (szszuzczcdt0(szmzizndt0(xS)) = sz00))))),
% 1.59/1.77 inference(quant_inst,[status(thm)],[])).
% 1.59/1.77 tff(190,plain,
% 1.59/1.77 ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00))))) | (~aElementOf0(szmzizndt0(xS), szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(szmzizndt0(xS)), szNzAzT0)) | (szszuzczcdt0(szmzizndt0(xS)) = sz00)))),
% 1.59/1.77 inference(modus_ponens,[status(thm)],[189, 188])).
% 1.59/1.77 tff(191,plain,
% 1.59/1.77 (~((~aElementOf0(szszuzczcdt0(szmzizndt0(xS)), szNzAzT0)) | (szszuzczcdt0(szmzizndt0(xS)) = sz00))),
% 1.59/1.77 inference(unit_resolution,[status(thm)],[190, 110, 187])).
% 1.59/1.77 tff(192,plain,
% 1.59/1.77 (((~aElementOf0(szszuzczcdt0(szmzizndt0(xS)), szNzAzT0)) | (szszuzczcdt0(szmzizndt0(xS)) = sz00)) | (~(szszuzczcdt0(szmzizndt0(xS)) = sz00))),
% 1.59/1.77 inference(tautology,[status(thm)],[])).
% 1.59/1.77 tff(193,plain,
% 1.59/1.77 (~(szszuzczcdt0(szmzizndt0(xS)) = sz00)),
% 1.59/1.77 inference(unit_resolution,[status(thm)],[192, 191])).
% 1.59/1.77 tff(194,plain,
% 1.59/1.77 (((~aElementOf0(szszuzczcdt0(szmzizndt0(xS)), szNzAzT0)) | (szszuzczcdt0(szmzizndt0(xS)) = sz00)) | aElementOf0(szszuzczcdt0(szmzizndt0(xS)), szNzAzT0)),
% 1.59/1.77 inference(tautology,[status(thm)],[])).
% 1.59/1.77 tff(195,plain,
% 1.59/1.77 (aElementOf0(szszuzczcdt0(szmzizndt0(xS)), szNzAzT0)),
% 1.59/1.77 inference(unit_resolution,[status(thm)],[194, 191])).
% 1.59/1.77 tff(196,plain,
% 1.59/1.77 (((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))))) | ((~aElementOf0(szszuzczcdt0(szmzizndt0(xS)), szNzAzT0)) | (szszuzczcdt0(szmzizndt0(xS)) = sz00) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), szNzAzT0)) | (~(szszuzczcdt0(szmzizndt0(xS)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS)))))))))) <=> ((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))))) | (~aElementOf0(szszuzczcdt0(szmzizndt0(xS)), szNzAzT0)) | (szszuzczcdt0(szmzizndt0(xS)) = sz00) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), szNzAzT0)) | (~(szszuzczcdt0(szmzizndt0(xS)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS)))))))))),
% 1.59/1.77 inference(rewrite,[status(thm)],[])).
% 1.59/1.77 tff(197,plain,
% 1.59/1.77 (((szszuzczcdt0(szmzizndt0(xS)) = sz00) | (~aElementOf0(szszuzczcdt0(szmzizndt0(xS)), szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), szNzAzT0)) | (~(szszuzczcdt0(szmzizndt0(xS)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))))))))) <=> ((~aElementOf0(szszuzczcdt0(szmzizndt0(xS)), szNzAzT0)) | (szszuzczcdt0(szmzizndt0(xS)) = sz00) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), szNzAzT0)) | (~(szszuzczcdt0(szmzizndt0(xS)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS)))))))))),
% 1.59/1.77 inference(rewrite,[status(thm)],[])).
% 1.59/1.77 tff(198,plain,
% 1.59/1.77 (((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))))) | ((szszuzczcdt0(szmzizndt0(xS)) = sz00) | (~aElementOf0(szszuzczcdt0(szmzizndt0(xS)), szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), szNzAzT0)) | (~(szszuzczcdt0(szmzizndt0(xS)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS)))))))))) <=> ((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))))) | ((~aElementOf0(szszuzczcdt0(szmzizndt0(xS)), szNzAzT0)) | (szszuzczcdt0(szmzizndt0(xS)) = sz00) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), szNzAzT0)) | (~(szszuzczcdt0(szmzizndt0(xS)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))))))))))),
% 1.59/1.77 inference(monotonicity,[status(thm)],[197])).
% 1.59/1.77 tff(199,plain,
% 1.59/1.77 (((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))))) | ((szszuzczcdt0(szmzizndt0(xS)) = sz00) | (~aElementOf0(szszuzczcdt0(szmzizndt0(xS)), szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), szNzAzT0)) | (~(szszuzczcdt0(szmzizndt0(xS)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS)))))))))) <=> ((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))))) | (~aElementOf0(szszuzczcdt0(szmzizndt0(xS)), szNzAzT0)) | (szszuzczcdt0(szmzizndt0(xS)) = sz00) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), szNzAzT0)) | (~(szszuzczcdt0(szmzizndt0(xS)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS)))))))))),
% 1.59/1.77 inference(transitivity,[status(thm)],[198, 196])).
% 1.59/1.77 tff(200,plain,
% 1.59/1.77 ((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))))) | ((szszuzczcdt0(szmzizndt0(xS)) = sz00) | (~aElementOf0(szszuzczcdt0(szmzizndt0(xS)), szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), szNzAzT0)) | (~(szszuzczcdt0(szmzizndt0(xS)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS)))))))))),
% 1.59/1.77 inference(quant_inst,[status(thm)],[])).
% 1.59/1.77 tff(201,plain,
% 1.59/1.77 ((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))))) | (~aElementOf0(szszuzczcdt0(szmzizndt0(xS)), szNzAzT0)) | (szszuzczcdt0(szmzizndt0(xS)) = sz00) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), szNzAzT0)) | (~(szszuzczcdt0(szmzizndt0(xS)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))))))))),
% 1.59/1.77 inference(modus_ponens,[status(thm)],[200, 199])).
% 1.59/1.77 tff(202,plain,
% 1.59/1.77 (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), szNzAzT0)) | (~(szszuzczcdt0(szmzizndt0(xS)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS)))))))),
% 1.59/1.77 inference(unit_resolution,[status(thm)],[201, 134, 195, 193])).
% 1.59/1.77 tff(203,plain,
% 1.59/1.77 (((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), szNzAzT0)) | (~(szszuzczcdt0(szmzizndt0(xS)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))))))) | (szszuzczcdt0(szmzizndt0(xS)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS)))))),
% 1.59/1.77 inference(tautology,[status(thm)],[])).
% 1.59/1.77 tff(204,plain,
% 1.59/1.77 (szszuzczcdt0(szmzizndt0(xS)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))))),
% 1.59/1.77 inference(unit_resolution,[status(thm)],[203, 202])).
% 1.59/1.77 tff(205,plain,
% 1.59/1.77 (((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), szNzAzT0)) | (~(szszuzczcdt0(szmzizndt0(xS)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))))))) | aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), szNzAzT0)),
% 1.59/1.77 inference(tautology,[status(thm)],[])).
% 1.59/1.77 tff(206,plain,
% 1.59/1.77 (aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), szNzAzT0)),
% 1.59/1.77 inference(unit_resolution,[status(thm)],[205, 202])).
% 1.59/1.77 tff(207,plain,
% 1.59/1.77 (((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | ((~aElementOf0(szmzizndt0(xS), szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), szNzAzT0)) | (~(szszuzczcdt0(szmzizndt0(xS)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS)))))) | (szmzizndt0(xS) = tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS)))))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | (~aElementOf0(szmzizndt0(xS), szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), szNzAzT0)) | (~(szszuzczcdt0(szmzizndt0(xS)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS)))))) | (szmzizndt0(xS) = tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS)))))),
% 1.59/1.77 inference(rewrite,[status(thm)],[])).
% 1.59/1.77 tff(208,plain,
% 1.59/1.77 (((szmzizndt0(xS) = tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS)))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), szNzAzT0)) | (~(szszuzczcdt0(szmzizndt0(xS)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS)))))) | (~aElementOf0(szmzizndt0(xS), szNzAzT0))) <=> ((~aElementOf0(szmzizndt0(xS), szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), szNzAzT0)) | (~(szszuzczcdt0(szmzizndt0(xS)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS)))))) | (szmzizndt0(xS) = tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS)))))),
% 1.59/1.77 inference(rewrite,[status(thm)],[])).
% 1.59/1.77 tff(209,plain,
% 1.59/1.77 (((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | ((szmzizndt0(xS) = tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS)))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), szNzAzT0)) | (~(szszuzczcdt0(szmzizndt0(xS)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS)))))) | (~aElementOf0(szmzizndt0(xS), szNzAzT0)))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | ((~aElementOf0(szmzizndt0(xS), szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), szNzAzT0)) | (~(szszuzczcdt0(szmzizndt0(xS)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS)))))) | (szmzizndt0(xS) = tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))))))),
% 1.59/1.77 inference(monotonicity,[status(thm)],[208])).
% 1.59/1.77 tff(210,plain,
% 1.59/1.77 (((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | ((szmzizndt0(xS) = tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS)))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), szNzAzT0)) | (~(szszuzczcdt0(szmzizndt0(xS)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS)))))) | (~aElementOf0(szmzizndt0(xS), szNzAzT0)))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | (~aElementOf0(szmzizndt0(xS), szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), szNzAzT0)) | (~(szszuzczcdt0(szmzizndt0(xS)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS)))))) | (szmzizndt0(xS) = tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS)))))),
% 1.59/1.77 inference(transitivity,[status(thm)],[209, 207])).
% 1.59/1.77 tff(211,plain,
% 1.59/1.77 ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | ((szmzizndt0(xS) = tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS)))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), szNzAzT0)) | (~(szszuzczcdt0(szmzizndt0(xS)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS)))))) | (~aElementOf0(szmzizndt0(xS), szNzAzT0)))),
% 1.59/1.77 inference(quant_inst,[status(thm)],[])).
% 1.59/1.77 tff(212,plain,
% 1.59/1.77 ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | (~aElementOf0(szmzizndt0(xS), szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), szNzAzT0)) | (~(szszuzczcdt0(szmzizndt0(xS)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS)))))) | (szmzizndt0(xS) = tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))))),
% 1.59/1.77 inference(modus_ponens,[status(thm)],[211, 210])).
% 1.59/1.77 tff(213,plain,
% 1.59/1.77 (szmzizndt0(xS) = tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS)))),
% 1.59/1.77 inference(unit_resolution,[status(thm)],[212, 159, 187, 206, 204])).
% 1.59/1.77 tff(214,plain,
% 1.59/1.77 (tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))) = szmzizndt0(xS)),
% 1.59/1.77 inference(symmetry,[status(thm)],[213])).
% 1.59/1.77 tff(215,plain,
% 1.59/1.77 (aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xT) <=> aElementOf0(szmzizndt0(xS), xT)),
% 1.59/1.77 inference(monotonicity,[status(thm)],[214])).
% 1.59/1.77 tff(216,plain,
% 1.59/1.77 (aElementOf0(szmzizndt0(xS), xT) <=> aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xT)),
% 1.59/1.77 inference(symmetry,[status(thm)],[215])).
% 1.59/1.77 tff(217,plain,
% 1.59/1.77 (aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xT)),
% 1.59/1.77 inference(modus_ponens,[status(thm)],[183, 216])).
% 1.59/1.77 tff(218,plain,
% 1.59/1.77 ((~(xS = slcrc0)) <=> (~(xS = slcrc0))),
% 1.59/1.77 inference(rewrite,[status(thm)],[])).
% 1.59/1.77 tff(219,plain,
% 1.59/1.77 (~(xS = slcrc0)),
% 1.59/1.77 inference(and_elim,[status(thm)],[6])).
% 1.59/1.77 tff(220,plain,
% 1.59/1.77 (~(xS = slcrc0)),
% 1.59/1.77 inference(modus_ponens,[status(thm)],[219, 218])).
% 1.59/1.77 tff(221,plain,
% 1.59/1.77 (((~![W0: $i] : ((W0 = slcrc0) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))) | (~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))))))) | ((xS = slcrc0) | ![W1: $i] : (~((~((~aElementOf0(W1, xS)) | (W1 = szmzizndt0(xS)) | (~((~aElementOf0(tptp_fun_W2_6(W1, xS), xS)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, xS)))))) | (~((~(W1 = szmzizndt0(xS))) | (~((~aElementOf0(W1, xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(W1, W2))))))))) | (~aSubsetOf0(xS, szNzAzT0)))) <=> ((~![W0: $i] : ((W0 = slcrc0) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))) | (~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))))))) | (xS = slcrc0) | ![W1: $i] : (~((~((~aElementOf0(W1, xS)) | (W1 = szmzizndt0(xS)) | (~((~aElementOf0(tptp_fun_W2_6(W1, xS), xS)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, xS)))))) | (~((~(W1 = szmzizndt0(xS))) | (~((~aElementOf0(W1, xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(W1, W2))))))))) | (~aSubsetOf0(xS, szNzAzT0)))),
% 1.59/1.77 inference(rewrite,[status(thm)],[])).
% 1.59/1.77 tff(222,plain,
% 1.59/1.77 (((xS = slcrc0) | (~aSubsetOf0(xS, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, xS)) | (W1 = szmzizndt0(xS)) | (~((~aElementOf0(tptp_fun_W2_6(W1, xS), xS)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, xS)))))) | (~((~(W1 = szmzizndt0(xS))) | (~((~aElementOf0(W1, xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(W1, W2)))))))))) <=> ((xS = slcrc0) | ![W1: $i] : (~((~((~aElementOf0(W1, xS)) | (W1 = szmzizndt0(xS)) | (~((~aElementOf0(tptp_fun_W2_6(W1, xS), xS)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, xS)))))) | (~((~(W1 = szmzizndt0(xS))) | (~((~aElementOf0(W1, xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(W1, W2))))))))) | (~aSubsetOf0(xS, szNzAzT0)))),
% 1.59/1.77 inference(rewrite,[status(thm)],[])).
% 1.59/1.77 tff(223,plain,
% 1.59/1.77 (((~![W0: $i] : ((W0 = slcrc0) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))) | (~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))))))) | ((xS = slcrc0) | (~aSubsetOf0(xS, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, xS)) | (W1 = szmzizndt0(xS)) | (~((~aElementOf0(tptp_fun_W2_6(W1, xS), xS)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, xS)))))) | (~((~(W1 = szmzizndt0(xS))) | (~((~aElementOf0(W1, xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(W1, W2))))))))))) <=> ((~![W0: $i] : ((W0 = slcrc0) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))) | (~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))))))) | ((xS = slcrc0) | ![W1: $i] : (~((~((~aElementOf0(W1, xS)) | (W1 = szmzizndt0(xS)) | (~((~aElementOf0(tptp_fun_W2_6(W1, xS), xS)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, xS)))))) | (~((~(W1 = szmzizndt0(xS))) | (~((~aElementOf0(W1, xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(W1, W2))))))))) | (~aSubsetOf0(xS, szNzAzT0))))),
% 1.59/1.77 inference(monotonicity,[status(thm)],[222])).
% 1.59/1.77 tff(224,plain,
% 1.59/1.77 (((~![W0: $i] : ((W0 = slcrc0) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))) | (~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))))))) | ((xS = slcrc0) | (~aSubsetOf0(xS, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, xS)) | (W1 = szmzizndt0(xS)) | (~((~aElementOf0(tptp_fun_W2_6(W1, xS), xS)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, xS)))))) | (~((~(W1 = szmzizndt0(xS))) | (~((~aElementOf0(W1, xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(W1, W2))))))))))) <=> ((~![W0: $i] : ((W0 = slcrc0) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))) | (~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))))))) | (xS = slcrc0) | ![W1: $i] : (~((~((~aElementOf0(W1, xS)) | (W1 = szmzizndt0(xS)) | (~((~aElementOf0(tptp_fun_W2_6(W1, xS), xS)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, xS)))))) | (~((~(W1 = szmzizndt0(xS))) | (~((~aElementOf0(W1, xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(W1, W2))))))))) | (~aSubsetOf0(xS, szNzAzT0)))),
% 1.59/1.77 inference(transitivity,[status(thm)],[223, 221])).
% 1.59/1.77 tff(225,plain,
% 1.59/1.77 ((~![W0: $i] : ((W0 = slcrc0) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))) | (~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))))))) | ((xS = slcrc0) | (~aSubsetOf0(xS, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, xS)) | (W1 = szmzizndt0(xS)) | (~((~aElementOf0(tptp_fun_W2_6(W1, xS), xS)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, xS)))))) | (~((~(W1 = szmzizndt0(xS))) | (~((~aElementOf0(W1, xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(W1, W2))))))))))),
% 1.59/1.77 inference(quant_inst,[status(thm)],[])).
% 1.59/1.77 tff(226,plain,
% 1.59/1.77 ((~![W0: $i] : ((W0 = slcrc0) | (~aSubsetOf0(W0, szNzAzT0)) | ![W1: $i] : (~((~((~aElementOf0(W1, W0)) | (W1 = szmzizndt0(W0)) | (~((~aElementOf0(tptp_fun_W2_6(W1, W0), W0)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, W0)))))) | (~((~(W1 = szmzizndt0(W0))) | (~((~aElementOf0(W1, W0)) | (~![W2: $i] : ((~aElementOf0(W2, W0)) | sdtlseqdt0(W1, W2))))))))))) | (xS = slcrc0) | ![W1: $i] : (~((~((~aElementOf0(W1, xS)) | (W1 = szmzizndt0(xS)) | (~((~aElementOf0(tptp_fun_W2_6(W1, xS), xS)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, xS)))))) | (~((~(W1 = szmzizndt0(xS))) | (~((~aElementOf0(W1, xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(W1, W2))))))))) | (~aSubsetOf0(xS, szNzAzT0))),
% 1.59/1.77 inference(modus_ponens,[status(thm)],[225, 224])).
% 1.59/1.77 tff(227,plain,
% 1.59/1.77 (![W1: $i] : (~((~((~aElementOf0(W1, xS)) | (W1 = szmzizndt0(xS)) | (~((~aElementOf0(tptp_fun_W2_6(W1, xS), xS)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, xS)))))) | (~((~(W1 = szmzizndt0(xS))) | (~((~aElementOf0(W1, xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(W1, W2)))))))))),
% 1.59/1.77 inference(unit_resolution,[status(thm)],[226, 31, 84, 220])).
% 1.59/1.77 tff(228,plain,
% 1.59/1.77 ((~![W1: $i] : (~((~((~aElementOf0(W1, xS)) | (W1 = szmzizndt0(xS)) | (~((~aElementOf0(tptp_fun_W2_6(W1, xS), xS)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, xS)))))) | (~((~(W1 = szmzizndt0(xS))) | (~((~aElementOf0(W1, xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(W1, W2)))))))))) | (~((~((~aElementOf0(szmzizndt0(xT), xS)) | (szmzizndt0(xT) = szmzizndt0(xS)) | (~((~aElementOf0(tptp_fun_W2_6(szmzizndt0(xT), xS), xS)) | sdtlseqdt0(szmzizndt0(xT), tptp_fun_W2_6(szmzizndt0(xT), xS)))))) | (~((~(szmzizndt0(xT) = szmzizndt0(xS))) | (~((~aElementOf0(szmzizndt0(xT), xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(szmzizndt0(xT), W2)))))))))),
% 1.59/1.77 inference(quant_inst,[status(thm)],[])).
% 1.59/1.77 tff(229,plain,
% 1.59/1.77 (~((~((~aElementOf0(szmzizndt0(xT), xS)) | (szmzizndt0(xT) = szmzizndt0(xS)) | (~((~aElementOf0(tptp_fun_W2_6(szmzizndt0(xT), xS), xS)) | sdtlseqdt0(szmzizndt0(xT), tptp_fun_W2_6(szmzizndt0(xT), xS)))))) | (~((~(szmzizndt0(xT) = szmzizndt0(xS))) | (~((~aElementOf0(szmzizndt0(xT), xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(szmzizndt0(xT), W2))))))))),
% 1.59/1.77 inference(unit_resolution,[status(thm)],[228, 227])).
% 1.59/1.77 tff(230,plain,
% 1.59/1.77 (((~((~aElementOf0(szmzizndt0(xT), xS)) | (szmzizndt0(xT) = szmzizndt0(xS)) | (~((~aElementOf0(tptp_fun_W2_6(szmzizndt0(xT), xS), xS)) | sdtlseqdt0(szmzizndt0(xT), tptp_fun_W2_6(szmzizndt0(xT), xS)))))) | (~((~(szmzizndt0(xT) = szmzizndt0(xS))) | (~((~aElementOf0(szmzizndt0(xT), xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(szmzizndt0(xT), W2)))))))) | ((~aElementOf0(szmzizndt0(xT), xS)) | (szmzizndt0(xT) = szmzizndt0(xS)) | (~((~aElementOf0(tptp_fun_W2_6(szmzizndt0(xT), xS), xS)) | sdtlseqdt0(szmzizndt0(xT), tptp_fun_W2_6(szmzizndt0(xT), xS)))))),
% 1.59/1.77 inference(tautology,[status(thm)],[])).
% 1.59/1.77 tff(231,plain,
% 1.59/1.77 ((~aElementOf0(szmzizndt0(xT), xS)) | (szmzizndt0(xT) = szmzizndt0(xS)) | (~((~aElementOf0(tptp_fun_W2_6(szmzizndt0(xT), xS), xS)) | sdtlseqdt0(szmzizndt0(xT), tptp_fun_W2_6(szmzizndt0(xT), xS))))),
% 1.59/1.77 inference(unit_resolution,[status(thm)],[230, 229])).
% 1.59/1.77 tff(232,plain,
% 1.59/1.77 ((szmzizndt0(xT) = szmzizndt0(xS)) <=> (szmzizndt0(xS) = szmzizndt0(xT))),
% 1.59/1.77 inference(commutativity,[status(thm)],[])).
% 1.59/1.77 tff(233,plain,
% 1.59/1.77 ((szmzizndt0(xS) = szmzizndt0(xT)) <=> (szmzizndt0(xT) = szmzizndt0(xS))),
% 1.59/1.77 inference(symmetry,[status(thm)],[232])).
% 1.59/1.77 tff(234,plain,
% 1.59/1.77 ((~(szmzizndt0(xS) = szmzizndt0(xT))) <=> (~(szmzizndt0(xT) = szmzizndt0(xS)))),
% 1.59/1.77 inference(monotonicity,[status(thm)],[233])).
% 1.59/1.77 tff(235,plain,
% 1.59/1.77 ((~(szmzizndt0(xS) = szmzizndt0(xT))) <=> (~(szmzizndt0(xS) = szmzizndt0(xT)))),
% 1.59/1.77 inference(rewrite,[status(thm)],[])).
% 1.59/1.77 tff(236,axiom,(~(szmzizndt0(xS) = szmzizndt0(xT))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__')).
% 1.59/1.77 tff(237,plain,
% 1.59/1.77 (~(szmzizndt0(xS) = szmzizndt0(xT))),
% 1.59/1.77 inference(modus_ponens,[status(thm)],[236, 235])).
% 1.59/1.77 tff(238,plain,
% 1.59/1.77 (~(szmzizndt0(xT) = szmzizndt0(xS))),
% 1.59/1.77 inference(modus_ponens,[status(thm)],[237, 234])).
% 1.59/1.77 tff(239,plain,
% 1.59/1.77 ((~((~aElementOf0(szmzizndt0(xT), xS)) | (szmzizndt0(xT) = szmzizndt0(xS)) | (~((~aElementOf0(tptp_fun_W2_6(szmzizndt0(xT), xS), xS)) | sdtlseqdt0(szmzizndt0(xT), tptp_fun_W2_6(szmzizndt0(xT), xS)))))) | (~aElementOf0(szmzizndt0(xT), xS)) | (szmzizndt0(xT) = szmzizndt0(xS)) | (~((~aElementOf0(tptp_fun_W2_6(szmzizndt0(xT), xS), xS)) | sdtlseqdt0(szmzizndt0(xT), tptp_fun_W2_6(szmzizndt0(xT), xS))))),
% 1.59/1.77 inference(tautology,[status(thm)],[])).
% 1.59/1.77 tff(240,plain,
% 1.59/1.77 ((~((~aElementOf0(szmzizndt0(xT), xS)) | (szmzizndt0(xT) = szmzizndt0(xS)) | (~((~aElementOf0(tptp_fun_W2_6(szmzizndt0(xT), xS), xS)) | sdtlseqdt0(szmzizndt0(xT), tptp_fun_W2_6(szmzizndt0(xT), xS)))))) | (szmzizndt0(xT) = szmzizndt0(xS)) | (~((~aElementOf0(tptp_fun_W2_6(szmzizndt0(xT), xS), xS)) | sdtlseqdt0(szmzizndt0(xT), tptp_fun_W2_6(szmzizndt0(xT), xS))))),
% 1.59/1.77 inference(unit_resolution,[status(thm)],[239, 93])).
% 1.59/1.77 tff(241,plain,
% 1.59/1.77 (~((~aElementOf0(tptp_fun_W2_6(szmzizndt0(xT), xS), xS)) | sdtlseqdt0(szmzizndt0(xT), tptp_fun_W2_6(szmzizndt0(xT), xS)))),
% 1.59/1.77 inference(unit_resolution,[status(thm)],[240, 238, 231])).
% 1.59/1.77 tff(242,plain,
% 1.59/1.77 (((~aElementOf0(tptp_fun_W2_6(szmzizndt0(xT), xS), xS)) | sdtlseqdt0(szmzizndt0(xT), tptp_fun_W2_6(szmzizndt0(xT), xS))) | aElementOf0(tptp_fun_W2_6(szmzizndt0(xT), xS), xS)),
% 1.59/1.77 inference(tautology,[status(thm)],[])).
% 1.59/1.77 tff(243,plain,
% 1.59/1.77 (aElementOf0(tptp_fun_W2_6(szmzizndt0(xT), xS), xS)),
% 1.59/1.77 inference(unit_resolution,[status(thm)],[242, 241])).
% 1.59/1.77 tff(244,plain,
% 1.59/1.77 (((~![W2: $i] : ((~aElementOf0(W2, xS)) | aElementOf0(W2, szNzAzT0))) | ((~aElementOf0(tptp_fun_W2_6(szmzizndt0(xT), xS), xS)) | aElementOf0(tptp_fun_W2_6(szmzizndt0(xT), xS), szNzAzT0))) <=> ((~![W2: $i] : ((~aElementOf0(W2, xS)) | aElementOf0(W2, szNzAzT0))) | (~aElementOf0(tptp_fun_W2_6(szmzizndt0(xT), xS), xS)) | aElementOf0(tptp_fun_W2_6(szmzizndt0(xT), xS), szNzAzT0))),
% 1.59/1.77 inference(rewrite,[status(thm)],[])).
% 1.59/1.77 tff(245,plain,
% 1.59/1.77 ((~![W2: $i] : ((~aElementOf0(W2, xS)) | aElementOf0(W2, szNzAzT0))) | ((~aElementOf0(tptp_fun_W2_6(szmzizndt0(xT), xS), xS)) | aElementOf0(tptp_fun_W2_6(szmzizndt0(xT), xS), szNzAzT0))),
% 1.59/1.77 inference(quant_inst,[status(thm)],[])).
% 1.59/1.77 tff(246,plain,
% 1.59/1.77 ((~![W2: $i] : ((~aElementOf0(W2, xS)) | aElementOf0(W2, szNzAzT0))) | (~aElementOf0(tptp_fun_W2_6(szmzizndt0(xT), xS), xS)) | aElementOf0(tptp_fun_W2_6(szmzizndt0(xT), xS), szNzAzT0)),
% 1.59/1.77 inference(modus_ponens,[status(thm)],[245, 244])).
% 1.59/1.77 tff(247,plain,
% 1.59/1.77 (aElementOf0(tptp_fun_W2_6(szmzizndt0(xT), xS), szNzAzT0)),
% 1.59/1.77 inference(unit_resolution,[status(thm)],[246, 89, 243])).
% 1.59/1.77 tff(248,plain,
% 1.59/1.77 (((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00))))) | ((~aElementOf0(tptp_fun_W2_6(szmzizndt0(xT), xS), szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)), szNzAzT0)) | (szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)) = sz00))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00))))) | (~aElementOf0(tptp_fun_W2_6(szmzizndt0(xT), xS), szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)), szNzAzT0)) | (szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)) = sz00))))),
% 1.59/1.77 inference(rewrite,[status(thm)],[])).
% 1.59/1.77 tff(249,plain,
% 1.59/1.77 ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00))))) | ((~aElementOf0(tptp_fun_W2_6(szmzizndt0(xT), xS), szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)), szNzAzT0)) | (szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)) = sz00))))),
% 1.59/1.78 inference(quant_inst,[status(thm)],[])).
% 1.59/1.78 tff(250,plain,
% 1.59/1.78 ((~![W0: $i] : ((~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(W0), szNzAzT0)) | (szszuzczcdt0(W0) = sz00))))) | (~aElementOf0(tptp_fun_W2_6(szmzizndt0(xT), xS), szNzAzT0)) | (~((~aElementOf0(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)), szNzAzT0)) | (szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)) = sz00)))),
% 1.59/1.78 inference(modus_ponens,[status(thm)],[249, 248])).
% 1.59/1.78 tff(251,plain,
% 1.59/1.78 (~((~aElementOf0(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)), szNzAzT0)) | (szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)) = sz00))),
% 1.59/1.78 inference(unit_resolution,[status(thm)],[250, 110, 247])).
% 1.59/1.78 tff(252,plain,
% 1.59/1.78 (((~aElementOf0(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)), szNzAzT0)) | (szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)) = sz00)) | (~(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)) = sz00))),
% 1.59/1.78 inference(tautology,[status(thm)],[])).
% 1.59/1.78 tff(253,plain,
% 1.59/1.78 (~(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)) = sz00)),
% 1.59/1.78 inference(unit_resolution,[status(thm)],[252, 251])).
% 1.59/1.78 tff(254,plain,
% 1.59/1.78 (((~aElementOf0(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)), szNzAzT0)) | (szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)) = sz00)) | aElementOf0(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)), szNzAzT0)),
% 1.59/1.78 inference(tautology,[status(thm)],[])).
% 1.59/1.78 tff(255,plain,
% 1.59/1.78 (aElementOf0(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)), szNzAzT0)),
% 1.59/1.78 inference(unit_resolution,[status(thm)],[254, 251])).
% 1.59/1.78 tff(256,plain,
% 1.59/1.78 (((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))))) | ((~aElementOf0(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)), szNzAzT0)) | (szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)) = sz00) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))), szNzAzT0)) | (~(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)))))))))) <=> ((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))))) | (~aElementOf0(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)), szNzAzT0)) | (szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)) = sz00) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))), szNzAzT0)) | (~(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)))))))))),
% 1.59/1.78 inference(rewrite,[status(thm)],[])).
% 1.59/1.78 tff(257,plain,
% 1.59/1.78 (((szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)) = sz00) | (~aElementOf0(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)), szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))), szNzAzT0)) | (~(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))))))))) <=> ((~aElementOf0(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)), szNzAzT0)) | (szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)) = sz00) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))), szNzAzT0)) | (~(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)))))))))),
% 1.59/1.78 inference(rewrite,[status(thm)],[])).
% 1.59/1.78 tff(258,plain,
% 1.59/1.78 (((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))))) | ((szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)) = sz00) | (~aElementOf0(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)), szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))), szNzAzT0)) | (~(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)))))))))) <=> ((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))))) | ((~aElementOf0(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)), szNzAzT0)) | (szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)) = sz00) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))), szNzAzT0)) | (~(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))))))))))),
% 1.59/1.78 inference(monotonicity,[status(thm)],[257])).
% 1.59/1.78 tff(259,plain,
% 1.59/1.78 (((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))))) | ((szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)) = sz00) | (~aElementOf0(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)), szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))), szNzAzT0)) | (~(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)))))))))) <=> ((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))))) | (~aElementOf0(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)), szNzAzT0)) | (szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)) = sz00) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))), szNzAzT0)) | (~(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)))))))))),
% 1.59/1.78 inference(transitivity,[status(thm)],[258, 256])).
% 1.59/1.78 tff(260,plain,
% 1.59/1.78 ((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))))) | ((szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)) = sz00) | (~aElementOf0(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)), szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))), szNzAzT0)) | (~(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)))))))))),
% 1.59/1.78 inference(quant_inst,[status(thm)],[])).
% 1.59/1.78 tff(261,plain,
% 1.59/1.78 ((~![W0: $i] : ((W0 = sz00) | (~aElementOf0(W0, szNzAzT0)) | (~((~aElementOf0(tptp_fun_W1_4(W0), szNzAzT0)) | (~(W0 = szszuzczcdt0(tptp_fun_W1_4(W0)))))))) | (~aElementOf0(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)), szNzAzT0)) | (szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)) = sz00) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))), szNzAzT0)) | (~(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))))))))),
% 1.59/1.78 inference(modus_ponens,[status(thm)],[260, 259])).
% 1.59/1.78 tff(262,plain,
% 1.59/1.78 (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))), szNzAzT0)) | (~(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)))))))),
% 1.59/1.78 inference(unit_resolution,[status(thm)],[261, 134, 255, 253])).
% 1.59/1.78 tff(263,plain,
% 1.59/1.78 (((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))), szNzAzT0)) | (~(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))))))) | (szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)))))),
% 1.59/1.78 inference(tautology,[status(thm)],[])).
% 1.59/1.78 tff(264,plain,
% 1.59/1.78 (szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))))),
% 1.59/1.78 inference(unit_resolution,[status(thm)],[263, 262])).
% 1.59/1.78 tff(265,plain,
% 1.59/1.78 (((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))), szNzAzT0)) | (~(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))))))) | aElementOf0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))), szNzAzT0)),
% 1.59/1.78 inference(tautology,[status(thm)],[])).
% 1.59/1.78 tff(266,plain,
% 1.59/1.78 (aElementOf0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))), szNzAzT0)),
% 1.59/1.78 inference(unit_resolution,[status(thm)],[265, 262])).
% 1.59/1.78 tff(267,plain,
% 1.59/1.78 (((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | ((~aElementOf0(tptp_fun_W2_6(szmzizndt0(xT), xS), szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))), szNzAzT0)) | (~(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)))))) | (tptp_fun_W2_6(szmzizndt0(xT), xS) = tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)))))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | (~aElementOf0(tptp_fun_W2_6(szmzizndt0(xT), xS), szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))), szNzAzT0)) | (~(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)))))) | (tptp_fun_W2_6(szmzizndt0(xT), xS) = tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)))))),
% 1.59/1.78 inference(rewrite,[status(thm)],[])).
% 1.59/1.78 tff(268,plain,
% 1.59/1.78 (((tptp_fun_W2_6(szmzizndt0(xT), xS) = tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))), szNzAzT0)) | (~(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)))))) | (~aElementOf0(tptp_fun_W2_6(szmzizndt0(xT), xS), szNzAzT0))) <=> ((~aElementOf0(tptp_fun_W2_6(szmzizndt0(xT), xS), szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))), szNzAzT0)) | (~(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)))))) | (tptp_fun_W2_6(szmzizndt0(xT), xS) = tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)))))),
% 1.59/1.78 inference(rewrite,[status(thm)],[])).
% 1.59/1.78 tff(269,plain,
% 1.59/1.78 (((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | ((tptp_fun_W2_6(szmzizndt0(xT), xS) = tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))), szNzAzT0)) | (~(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)))))) | (~aElementOf0(tptp_fun_W2_6(szmzizndt0(xT), xS), szNzAzT0)))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | ((~aElementOf0(tptp_fun_W2_6(szmzizndt0(xT), xS), szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))), szNzAzT0)) | (~(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)))))) | (tptp_fun_W2_6(szmzizndt0(xT), xS) = tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))))))),
% 1.59/1.78 inference(monotonicity,[status(thm)],[268])).
% 1.59/1.78 tff(270,plain,
% 1.59/1.78 (((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | ((tptp_fun_W2_6(szmzizndt0(xT), xS) = tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))), szNzAzT0)) | (~(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)))))) | (~aElementOf0(tptp_fun_W2_6(szmzizndt0(xT), xS), szNzAzT0)))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | (~aElementOf0(tptp_fun_W2_6(szmzizndt0(xT), xS), szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))), szNzAzT0)) | (~(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)))))) | (tptp_fun_W2_6(szmzizndt0(xT), xS) = tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)))))),
% 1.59/1.78 inference(transitivity,[status(thm)],[269, 267])).
% 1.59/1.78 tff(271,plain,
% 1.59/1.78 ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | ((tptp_fun_W2_6(szmzizndt0(xT), xS) = tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))), szNzAzT0)) | (~(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)))))) | (~aElementOf0(tptp_fun_W2_6(szmzizndt0(xT), xS), szNzAzT0)))),
% 1.59/1.78 inference(quant_inst,[status(thm)],[])).
% 1.59/1.78 tff(272,plain,
% 1.59/1.78 ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | (~aElementOf0(tptp_fun_W2_6(szmzizndt0(xT), xS), szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))), szNzAzT0)) | (~(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)))))) | (tptp_fun_W2_6(szmzizndt0(xT), xS) = tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))))),
% 1.59/1.78 inference(modus_ponens,[status(thm)],[271, 270])).
% 1.59/1.78 tff(273,plain,
% 1.59/1.78 (tptp_fun_W2_6(szmzizndt0(xT), xS) = tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)))),
% 1.59/1.78 inference(unit_resolution,[status(thm)],[272, 159, 247, 266, 264])).
% 1.59/1.78 tff(274,plain,
% 1.59/1.78 (tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))) = tptp_fun_W2_6(szmzizndt0(xT), xS)),
% 1.59/1.78 inference(symmetry,[status(thm)],[273])).
% 1.59/1.78 tff(275,plain,
% 1.59/1.78 (aElementOf0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))), xS) <=> aElementOf0(tptp_fun_W2_6(szmzizndt0(xT), xS), xS)),
% 1.59/1.78 inference(monotonicity,[status(thm)],[274])).
% 1.59/1.78 tff(276,plain,
% 1.59/1.78 (aElementOf0(tptp_fun_W2_6(szmzizndt0(xT), xS), xS) <=> aElementOf0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))), xS)),
% 1.59/1.78 inference(symmetry,[status(thm)],[275])).
% 1.59/1.78 tff(277,plain,
% 1.59/1.78 (aElementOf0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))), xS)),
% 1.59/1.78 inference(modus_ponens,[status(thm)],[243, 276])).
% 1.59/1.78 tff(278,assumption,(~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))), xS)), introduced(assumption)).
% 1.59/1.78 tff(279,plain,
% 1.59/1.78 ($false),
% 1.59/1.78 inference(unit_resolution,[status(thm)],[278, 277])).
% 1.59/1.78 tff(280,plain,(aElementOf0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))), xS)), inference(lemma,lemma(discharge,[]))).
% 1.59/1.78 tff(281,plain,
% 1.59/1.78 (((~![W1: $i] : (~((~((~aElementOf0(W1, xS)) | (W1 = szmzizndt0(xS)) | (~((~aElementOf0(tptp_fun_W2_6(W1, xS), xS)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, xS)))))) | (~((~(W1 = szmzizndt0(xS))) | (~((~aElementOf0(W1, xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(W1, W2)))))))))) | (~((~((tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))) = szmzizndt0(xS)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS)) | (~((~aElementOf0(tptp_fun_W2_6(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS), xS)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), tptp_fun_W2_6(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS)))))) | (~((~(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))) = szmzizndt0(xS))) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), W2)))))))))) <=> ((~![W1: $i] : (~((~((~aElementOf0(W1, xS)) | (W1 = szmzizndt0(xS)) | (~((~aElementOf0(tptp_fun_W2_6(W1, xS), xS)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, xS)))))) | (~((~(W1 = szmzizndt0(xS))) | (~((~aElementOf0(W1, xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(W1, W2)))))))))) | (~((~((tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))) = szmzizndt0(xS)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS)) | (~((~aElementOf0(tptp_fun_W2_6(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS), xS)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), tptp_fun_W2_6(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS)))))) | (~((~(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))) = szmzizndt0(xS))) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), W2))))))))))),
% 1.59/1.78 inference(rewrite,[status(thm)],[])).
% 1.59/1.78 tff(282,plain,
% 1.59/1.78 ((~((~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS)) | (tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))) = szmzizndt0(xS)) | (~((~aElementOf0(tptp_fun_W2_6(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS), xS)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), tptp_fun_W2_6(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS)))))) | (~((~(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))) = szmzizndt0(xS))) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), W2))))))))) <=> (~((~((tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))) = szmzizndt0(xS)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS)) | (~((~aElementOf0(tptp_fun_W2_6(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS), xS)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), tptp_fun_W2_6(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS)))))) | (~((~(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))) = szmzizndt0(xS))) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), W2)))))))))),
% 1.59/1.78 inference(rewrite,[status(thm)],[])).
% 1.59/1.78 tff(283,plain,
% 1.59/1.78 (((~![W1: $i] : (~((~((~aElementOf0(W1, xS)) | (W1 = szmzizndt0(xS)) | (~((~aElementOf0(tptp_fun_W2_6(W1, xS), xS)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, xS)))))) | (~((~(W1 = szmzizndt0(xS))) | (~((~aElementOf0(W1, xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(W1, W2)))))))))) | (~((~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS)) | (tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))) = szmzizndt0(xS)) | (~((~aElementOf0(tptp_fun_W2_6(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS), xS)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), tptp_fun_W2_6(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS)))))) | (~((~(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))) = szmzizndt0(xS))) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), W2)))))))))) <=> ((~![W1: $i] : (~((~((~aElementOf0(W1, xS)) | (W1 = szmzizndt0(xS)) | (~((~aElementOf0(tptp_fun_W2_6(W1, xS), xS)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, xS)))))) | (~((~(W1 = szmzizndt0(xS))) | (~((~aElementOf0(W1, xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(W1, W2)))))))))) | (~((~((tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))) = szmzizndt0(xS)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS)) | (~((~aElementOf0(tptp_fun_W2_6(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS), xS)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), tptp_fun_W2_6(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS)))))) | (~((~(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))) = szmzizndt0(xS))) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), W2))))))))))),
% 1.59/1.78 inference(monotonicity,[status(thm)],[282])).
% 1.59/1.78 tff(284,plain,
% 1.59/1.78 (((~![W1: $i] : (~((~((~aElementOf0(W1, xS)) | (W1 = szmzizndt0(xS)) | (~((~aElementOf0(tptp_fun_W2_6(W1, xS), xS)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, xS)))))) | (~((~(W1 = szmzizndt0(xS))) | (~((~aElementOf0(W1, xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(W1, W2)))))))))) | (~((~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS)) | (tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))) = szmzizndt0(xS)) | (~((~aElementOf0(tptp_fun_W2_6(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS), xS)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), tptp_fun_W2_6(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS)))))) | (~((~(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))) = szmzizndt0(xS))) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), W2)))))))))) <=> ((~![W1: $i] : (~((~((~aElementOf0(W1, xS)) | (W1 = szmzizndt0(xS)) | (~((~aElementOf0(tptp_fun_W2_6(W1, xS), xS)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, xS)))))) | (~((~(W1 = szmzizndt0(xS))) | (~((~aElementOf0(W1, xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(W1, W2)))))))))) | (~((~((tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))) = szmzizndt0(xS)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS)) | (~((~aElementOf0(tptp_fun_W2_6(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS), xS)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), tptp_fun_W2_6(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS)))))) | (~((~(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))) = szmzizndt0(xS))) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), W2))))))))))),
% 1.59/1.78 inference(transitivity,[status(thm)],[283, 281])).
% 1.59/1.78 tff(285,plain,
% 1.59/1.78 ((~![W1: $i] : (~((~((~aElementOf0(W1, xS)) | (W1 = szmzizndt0(xS)) | (~((~aElementOf0(tptp_fun_W2_6(W1, xS), xS)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, xS)))))) | (~((~(W1 = szmzizndt0(xS))) | (~((~aElementOf0(W1, xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(W1, W2)))))))))) | (~((~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS)) | (tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))) = szmzizndt0(xS)) | (~((~aElementOf0(tptp_fun_W2_6(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS), xS)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), tptp_fun_W2_6(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS)))))) | (~((~(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))) = szmzizndt0(xS))) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), W2)))))))))),
% 1.59/1.78 inference(quant_inst,[status(thm)],[])).
% 1.59/1.78 tff(286,plain,
% 1.59/1.78 ((~![W1: $i] : (~((~((~aElementOf0(W1, xS)) | (W1 = szmzizndt0(xS)) | (~((~aElementOf0(tptp_fun_W2_6(W1, xS), xS)) | sdtlseqdt0(W1, tptp_fun_W2_6(W1, xS)))))) | (~((~(W1 = szmzizndt0(xS))) | (~((~aElementOf0(W1, xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(W1, W2)))))))))) | (~((~((tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))) = szmzizndt0(xS)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS)) | (~((~aElementOf0(tptp_fun_W2_6(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS), xS)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), tptp_fun_W2_6(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS)))))) | (~((~(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))) = szmzizndt0(xS))) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), W2)))))))))),
% 1.59/1.78 inference(modus_ponens,[status(thm)],[285, 284])).
% 1.59/1.78 tff(287,plain,
% 1.59/1.78 (~((~((tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))) = szmzizndt0(xS)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS)) | (~((~aElementOf0(tptp_fun_W2_6(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS), xS)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), tptp_fun_W2_6(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS)))))) | (~((~(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))) = szmzizndt0(xS))) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), W2))))))))),
% 1.59/1.78 inference(unit_resolution,[status(thm)],[286, 227])).
% 1.59/1.78 tff(288,plain,
% 1.59/1.78 (((~((tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))) = szmzizndt0(xS)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS)) | (~((~aElementOf0(tptp_fun_W2_6(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS), xS)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), tptp_fun_W2_6(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS)))))) | (~((~(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))) = szmzizndt0(xS))) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), W2)))))))) | ((~(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))) = szmzizndt0(xS))) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), W2))))))),
% 1.59/1.78 inference(tautology,[status(thm)],[])).
% 1.59/1.78 tff(289,plain,
% 1.59/1.78 ((~(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))) = szmzizndt0(xS))) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), W2)))))),
% 1.59/1.78 inference(unit_resolution,[status(thm)],[288, 287])).
% 1.59/1.78 tff(290,plain,
% 1.59/1.78 (szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS)))) = szszuzczcdt0(szmzizndt0(xS))),
% 1.59/1.78 inference(symmetry,[status(thm)],[204])).
% 1.59/1.78 tff(291,plain,
% 1.59/1.78 (((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | ((~aElementOf0(szmzizndt0(xS), szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), szNzAzT0)) | (tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))) = szmzizndt0(xS)) | (~(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS)))) = szszuzczcdt0(szmzizndt0(xS)))))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | (~aElementOf0(szmzizndt0(xS), szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), szNzAzT0)) | (tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))) = szmzizndt0(xS)) | (~(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS)))) = szszuzczcdt0(szmzizndt0(xS)))))),
% 1.59/1.78 inference(rewrite,[status(thm)],[])).
% 1.59/1.78 tff(292,plain,
% 1.59/1.78 (((tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))) = szmzizndt0(xS)) | (~aElementOf0(szmzizndt0(xS), szNzAzT0)) | (~(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS)))) = szszuzczcdt0(szmzizndt0(xS)))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), szNzAzT0))) <=> ((~aElementOf0(szmzizndt0(xS), szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), szNzAzT0)) | (tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))) = szmzizndt0(xS)) | (~(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS)))) = szszuzczcdt0(szmzizndt0(xS)))))),
% 1.59/1.78 inference(rewrite,[status(thm)],[])).
% 1.59/1.78 tff(293,plain,
% 1.59/1.78 (((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | ((tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))) = szmzizndt0(xS)) | (~aElementOf0(szmzizndt0(xS), szNzAzT0)) | (~(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS)))) = szszuzczcdt0(szmzizndt0(xS)))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), szNzAzT0)))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | ((~aElementOf0(szmzizndt0(xS), szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), szNzAzT0)) | (tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))) = szmzizndt0(xS)) | (~(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS)))) = szszuzczcdt0(szmzizndt0(xS))))))),
% 1.59/1.78 inference(monotonicity,[status(thm)],[292])).
% 1.59/1.78 tff(294,plain,
% 1.59/1.78 (((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | ((tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))) = szmzizndt0(xS)) | (~aElementOf0(szmzizndt0(xS), szNzAzT0)) | (~(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS)))) = szszuzczcdt0(szmzizndt0(xS)))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), szNzAzT0)))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | (~aElementOf0(szmzizndt0(xS), szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), szNzAzT0)) | (tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))) = szmzizndt0(xS)) | (~(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS)))) = szszuzczcdt0(szmzizndt0(xS)))))),
% 1.59/1.78 inference(transitivity,[status(thm)],[293, 291])).
% 1.59/1.78 tff(295,plain,
% 1.59/1.78 ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | ((tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))) = szmzizndt0(xS)) | (~aElementOf0(szmzizndt0(xS), szNzAzT0)) | (~(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS)))) = szszuzczcdt0(szmzizndt0(xS)))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), szNzAzT0)))),
% 1.59/1.78 inference(quant_inst,[status(thm)],[])).
% 1.59/1.78 tff(296,plain,
% 1.59/1.78 ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | (~aElementOf0(szmzizndt0(xS), szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), szNzAzT0)) | (tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))) = szmzizndt0(xS)) | (~(szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS)))) = szszuzczcdt0(szmzizndt0(xS))))),
% 1.59/1.78 inference(modus_ponens,[status(thm)],[295, 294])).
% 1.59/1.78 tff(297,plain,
% 1.59/1.78 (tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))) = szmzizndt0(xS)),
% 1.59/1.78 inference(unit_resolution,[status(thm)],[296, 159, 187, 206, 290])).
% 1.59/1.78 tff(298,plain,
% 1.59/1.78 ((~((~(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))) = szmzizndt0(xS))) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), W2))))))) | (~(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))) = szmzizndt0(xS))) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), W2)))))),
% 1.59/1.78 inference(tautology,[status(thm)],[])).
% 1.59/1.78 tff(299,plain,
% 1.59/1.78 ((~((~(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))) = szmzizndt0(xS))) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), W2))))))) | (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), W2)))))),
% 1.59/1.78 inference(unit_resolution,[status(thm)],[298, 297])).
% 1.59/1.78 tff(300,plain,
% 1.59/1.78 (~((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), W2))))),
% 1.59/1.78 inference(unit_resolution,[status(thm)],[299, 289])).
% 1.59/1.78 tff(301,plain,
% 1.59/1.78 (((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xS)) | (~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), W2)))) | ![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), W2))),
% 1.59/1.78 inference(tautology,[status(thm)],[])).
% 1.59/1.78 tff(302,plain,
% 1.59/1.78 (![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), W2))),
% 1.59/1.78 inference(unit_resolution,[status(thm)],[301, 300])).
% 1.59/1.78 tff(303,assumption,(aElementOf0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))), xS)), introduced(assumption)).
% 1.59/1.78 tff(304,assumption,(~sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))))), introduced(assumption)).
% 1.59/1.78 tff(305,plain,
% 1.59/1.78 (((~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), W2))) | ((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))), xS)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)))))) <=> ((~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), W2))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))), xS)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)))))),
% 1.59/1.78 inference(rewrite,[status(thm)],[])).
% 1.59/1.78 tff(306,plain,
% 1.59/1.78 ((~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), W2))) | ((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))), xS)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)))))),
% 1.59/1.78 inference(quant_inst,[status(thm)],[])).
% 1.59/1.78 tff(307,plain,
% 1.59/1.78 ((~![W2: $i] : ((~aElementOf0(W2, xS)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), W2))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))), xS)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))))),
% 1.59/1.78 inference(modus_ponens,[status(thm)],[306, 305])).
% 1.59/1.78 tff(308,plain,
% 1.59/1.78 ($false),
% 1.59/1.78 inference(unit_resolution,[status(thm)],[307, 304, 303, 302])).
% 1.59/1.78 tff(309,plain,((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))), xS)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))))), inference(lemma,lemma(discharge,[]))).
% 1.59/1.78 tff(310,plain,
% 1.59/1.78 (sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))))),
% 1.59/1.78 inference(unit_resolution,[status(thm)],[309, 280])).
% 1.59/1.78 tff(311,plain,
% 1.59/1.78 (sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)))) <=> sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), tptp_fun_W2_6(szmzizndt0(xT), xS))),
% 1.59/1.78 inference(monotonicity,[status(thm)],[274])).
% 1.59/1.78 tff(312,plain,
% 1.59/1.78 (sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), tptp_fun_W2_6(szmzizndt0(xT), xS)) <=> sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))))),
% 1.59/1.78 inference(symmetry,[status(thm)],[311])).
% 1.59/1.78 tff(313,plain,
% 1.59/1.78 ((~sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), tptp_fun_W2_6(szmzizndt0(xT), xS))) <=> (~sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)))))),
% 1.59/1.78 inference(monotonicity,[status(thm)],[312])).
% 1.59/1.78 tff(314,plain,
% 1.59/1.78 (((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | ((~aElementOf0(szmzizndt0(xT), szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), szNzAzT0)) | (~(szszuzczcdt0(szmzizndt0(xT)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT)))))) | (szmzizndt0(xT) = tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT)))))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | (~aElementOf0(szmzizndt0(xT), szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), szNzAzT0)) | (~(szszuzczcdt0(szmzizndt0(xT)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT)))))) | (szmzizndt0(xT) = tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT)))))),
% 1.59/1.78 inference(rewrite,[status(thm)],[])).
% 1.59/1.78 tff(315,plain,
% 1.59/1.78 (((szmzizndt0(xT) = tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT)))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), szNzAzT0)) | (~(szszuzczcdt0(szmzizndt0(xT)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT)))))) | (~aElementOf0(szmzizndt0(xT), szNzAzT0))) <=> ((~aElementOf0(szmzizndt0(xT), szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), szNzAzT0)) | (~(szszuzczcdt0(szmzizndt0(xT)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT)))))) | (szmzizndt0(xT) = tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT)))))),
% 1.59/1.79 inference(rewrite,[status(thm)],[])).
% 1.59/1.79 tff(316,plain,
% 1.59/1.79 (((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | ((szmzizndt0(xT) = tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT)))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), szNzAzT0)) | (~(szszuzczcdt0(szmzizndt0(xT)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT)))))) | (~aElementOf0(szmzizndt0(xT), szNzAzT0)))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | ((~aElementOf0(szmzizndt0(xT), szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), szNzAzT0)) | (~(szszuzczcdt0(szmzizndt0(xT)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT)))))) | (szmzizndt0(xT) = tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))))))),
% 1.59/1.79 inference(monotonicity,[status(thm)],[315])).
% 1.59/1.79 tff(317,plain,
% 1.59/1.79 (((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | ((szmzizndt0(xT) = tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT)))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), szNzAzT0)) | (~(szszuzczcdt0(szmzizndt0(xT)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT)))))) | (~aElementOf0(szmzizndt0(xT), szNzAzT0)))) <=> ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | (~aElementOf0(szmzizndt0(xT), szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), szNzAzT0)) | (~(szszuzczcdt0(szmzizndt0(xT)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT)))))) | (szmzizndt0(xT) = tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT)))))),
% 1.59/1.79 inference(transitivity,[status(thm)],[316, 314])).
% 1.59/1.79 tff(318,plain,
% 1.59/1.79 ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | ((szmzizndt0(xT) = tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT)))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), szNzAzT0)) | (~(szszuzczcdt0(szmzizndt0(xT)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT)))))) | (~aElementOf0(szmzizndt0(xT), szNzAzT0)))),
% 1.59/1.79 inference(quant_inst,[status(thm)],[])).
% 1.59/1.79 tff(319,plain,
% 1.59/1.79 ((~![W0: $i, W1: $i] : ((W0 = W1) | (~aElementOf0(W1, szNzAzT0)) | (~(szszuzczcdt0(W0) = szszuzczcdt0(W1))) | (~aElementOf0(W0, szNzAzT0)))) | (~aElementOf0(szmzizndt0(xT), szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), szNzAzT0)) | (~(szszuzczcdt0(szmzizndt0(xT)) = szszuzczcdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT)))))) | (szmzizndt0(xT) = tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))))),
% 1.59/1.79 inference(modus_ponens,[status(thm)],[318, 317])).
% 1.59/1.79 tff(320,plain,
% 1.59/1.79 (szmzizndt0(xT) = tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT)))),
% 1.59/1.79 inference(unit_resolution,[status(thm)],[319, 159, 97, 146, 143])).
% 1.59/1.79 tff(321,plain,
% 1.59/1.79 (sdtlseqdt0(szmzizndt0(xT), tptp_fun_W2_6(szmzizndt0(xT), xS)) <=> sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), tptp_fun_W2_6(szmzizndt0(xT), xS))),
% 1.59/1.79 inference(monotonicity,[status(thm)],[320])).
% 1.59/1.79 tff(322,plain,
% 1.59/1.79 ((~sdtlseqdt0(szmzizndt0(xT), tptp_fun_W2_6(szmzizndt0(xT), xS))) <=> (~sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), tptp_fun_W2_6(szmzizndt0(xT), xS)))),
% 1.59/1.79 inference(monotonicity,[status(thm)],[321])).
% 1.59/1.79 tff(323,plain,
% 1.59/1.79 (((~aElementOf0(tptp_fun_W2_6(szmzizndt0(xT), xS), xS)) | sdtlseqdt0(szmzizndt0(xT), tptp_fun_W2_6(szmzizndt0(xT), xS))) | (~sdtlseqdt0(szmzizndt0(xT), tptp_fun_W2_6(szmzizndt0(xT), xS)))),
% 1.59/1.79 inference(tautology,[status(thm)],[])).
% 1.59/1.79 tff(324,plain,
% 1.59/1.79 (~sdtlseqdt0(szmzizndt0(xT), tptp_fun_W2_6(szmzizndt0(xT), xS))),
% 1.59/1.79 inference(unit_resolution,[status(thm)],[323, 241])).
% 1.59/1.79 tff(325,plain,
% 1.59/1.79 (~sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), tptp_fun_W2_6(szmzizndt0(xT), xS))),
% 1.59/1.79 inference(modus_ponens,[status(thm)],[324, 322])).
% 1.59/1.79 tff(326,plain,
% 1.59/1.79 (~sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))))),
% 1.59/1.79 inference(modus_ponens,[status(thm)],[325, 313])).
% 1.59/1.79 tff(327,plain,
% 1.59/1.79 (^[W0: $i, W1: $i, W2: $i] : refl((sdtlseqdt0(W0, W2) | (~aElementOf0(W2, szNzAzT0)) | (~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W2)) | (~sdtlseqdt0(W0, W1)) | (~aElementOf0(W0, szNzAzT0))) <=> (sdtlseqdt0(W0, W2) | (~aElementOf0(W2, szNzAzT0)) | (~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W2)) | (~sdtlseqdt0(W0, W1)) | (~aElementOf0(W0, szNzAzT0))))),
% 1.59/1.79 inference(bind,[status(th)],[])).
% 1.59/1.79 tff(328,plain,
% 1.59/1.79 (![W0: $i, W1: $i, W2: $i] : (sdtlseqdt0(W0, W2) | (~aElementOf0(W2, szNzAzT0)) | (~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W2)) | (~sdtlseqdt0(W0, W1)) | (~aElementOf0(W0, szNzAzT0))) <=> ![W0: $i, W1: $i, W2: $i] : (sdtlseqdt0(W0, W2) | (~aElementOf0(W2, szNzAzT0)) | (~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W2)) | (~sdtlseqdt0(W0, W1)) | (~aElementOf0(W0, szNzAzT0)))),
% 1.59/1.79 inference(quant_intro,[status(thm)],[327])).
% 1.59/1.79 tff(329,plain,
% 1.59/1.79 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(trans(monotonicity(rewrite((sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W2)) <=> (~((~sdtlseqdt0(W1, W2)) | (~sdtlseqdt0(W0, W1))))), ((~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W2))) <=> (~(~((~sdtlseqdt0(W1, W2)) | (~sdtlseqdt0(W0, W1))))))), rewrite((~(~((~sdtlseqdt0(W1, W2)) | (~sdtlseqdt0(W0, W1))))) <=> ((~sdtlseqdt0(W1, W2)) | (~sdtlseqdt0(W0, W1)))), ((~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W2))) <=> ((~sdtlseqdt0(W1, W2)) | (~sdtlseqdt0(W0, W1))))), trans(monotonicity(rewrite((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0) & aElementOf0(W2, szNzAzT0)) <=> (~((~aElementOf0(W2, szNzAzT0)) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0))))), ((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0) & aElementOf0(W2, szNzAzT0))) <=> (~(~((~aElementOf0(W2, szNzAzT0)) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0))))))), rewrite((~(~((~aElementOf0(W2, szNzAzT0)) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0))))) <=> ((~aElementOf0(W2, szNzAzT0)) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)))), ((~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0) & aElementOf0(W2, szNzAzT0))) <=> ((~aElementOf0(W2, szNzAzT0)) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0))))), ((sdtlseqdt0(W0, W2) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W2))) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0) & aElementOf0(W2, szNzAzT0)))) <=> (sdtlseqdt0(W0, W2) | ((~sdtlseqdt0(W1, W2)) | (~sdtlseqdt0(W0, W1))) | ((~aElementOf0(W2, szNzAzT0)) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)))))), rewrite((sdtlseqdt0(W0, W2) | ((~sdtlseqdt0(W1, W2)) | (~sdtlseqdt0(W0, W1))) | ((~aElementOf0(W2, szNzAzT0)) | (~aElementOf0(W1, szNzAzT0)) | (~aElementOf0(W0, szNzAzT0)))) <=> (sdtlseqdt0(W0, W2) | (~aElementOf0(W2, szNzAzT0)) | (~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W2)) | (~sdtlseqdt0(W0, W1)) | (~aElementOf0(W0, szNzAzT0)))), ((sdtlseqdt0(W0, W2) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W2))) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0) & aElementOf0(W2, szNzAzT0)))) <=> (sdtlseqdt0(W0, W2) | (~aElementOf0(W2, szNzAzT0)) | (~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W2)) | (~sdtlseqdt0(W0, W1)) | (~aElementOf0(W0, szNzAzT0)))))),
% 1.59/1.79 inference(bind,[status(th)],[])).
% 1.59/1.79 tff(330,plain,
% 1.59/1.79 (![W0: $i, W1: $i, W2: $i] : (sdtlseqdt0(W0, W2) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W2))) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0) & aElementOf0(W2, szNzAzT0)))) <=> ![W0: $i, W1: $i, W2: $i] : (sdtlseqdt0(W0, W2) | (~aElementOf0(W2, szNzAzT0)) | (~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W2)) | (~sdtlseqdt0(W0, W1)) | (~aElementOf0(W0, szNzAzT0)))),
% 1.59/1.79 inference(quant_intro,[status(thm)],[329])).
% 1.59/1.79 tff(331,plain,
% 1.59/1.79 (![W0: $i, W1: $i, W2: $i] : (sdtlseqdt0(W0, W2) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W2))) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0) & aElementOf0(W2, szNzAzT0)))) <=> ![W0: $i, W1: $i, W2: $i] : (sdtlseqdt0(W0, W2) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W2))) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0) & aElementOf0(W2, szNzAzT0))))),
% 1.59/1.79 inference(rewrite,[status(thm)],[])).
% 1.59/1.79 tff(332,plain,
% 1.59/1.79 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(rewrite(((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) & aElementOf0(W2, szNzAzT0)) <=> (aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0) & aElementOf0(W2, szNzAzT0))), rewrite(((sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W2)) => sdtlseqdt0(W0, W2)) <=> ((~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W2))) | sdtlseqdt0(W0, W2))), ((((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) & aElementOf0(W2, szNzAzT0)) => ((sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W2)) => sdtlseqdt0(W0, W2))) <=> ((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0) & aElementOf0(W2, szNzAzT0)) => ((~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W2))) | sdtlseqdt0(W0, W2))))), rewrite(((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0) & aElementOf0(W2, szNzAzT0)) => ((~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W2))) | sdtlseqdt0(W0, W2))) <=> (sdtlseqdt0(W0, W2) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W2))) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0) & aElementOf0(W2, szNzAzT0))))), ((((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) & aElementOf0(W2, szNzAzT0)) => ((sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W2)) => sdtlseqdt0(W0, W2))) <=> (sdtlseqdt0(W0, W2) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W2))) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0) & aElementOf0(W2, szNzAzT0))))))),
% 1.59/1.79 inference(bind,[status(th)],[])).
% 1.59/1.79 tff(333,plain,
% 1.59/1.79 (![W0: $i, W1: $i, W2: $i] : (((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) & aElementOf0(W2, szNzAzT0)) => ((sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W2)) => sdtlseqdt0(W0, W2))) <=> ![W0: $i, W1: $i, W2: $i] : (sdtlseqdt0(W0, W2) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W2))) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0) & aElementOf0(W2, szNzAzT0))))),
% 1.59/1.79 inference(quant_intro,[status(thm)],[332])).
% 1.59/1.79 tff(334,axiom,(![W0: $i, W1: $i, W2: $i] : (((aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0)) & aElementOf0(W2, szNzAzT0)) => ((sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W2)) => sdtlseqdt0(W0, W2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mLessTrans')).
% 1.59/1.79 tff(335,plain,
% 1.59/1.79 (![W0: $i, W1: $i, W2: $i] : (sdtlseqdt0(W0, W2) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W2))) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0) & aElementOf0(W2, szNzAzT0))))),
% 1.59/1.79 inference(modus_ponens,[status(thm)],[334, 333])).
% 1.59/1.79 tff(336,plain,
% 1.59/1.79 (![W0: $i, W1: $i, W2: $i] : (sdtlseqdt0(W0, W2) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W2))) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0) & aElementOf0(W2, szNzAzT0))))),
% 1.59/1.79 inference(modus_ponens,[status(thm)],[335, 331])).
% 1.59/1.79 tff(337,plain,(
% 1.59/1.79 ![W0: $i, W1: $i, W2: $i] : (sdtlseqdt0(W0, W2) | (~(sdtlseqdt0(W0, W1) & sdtlseqdt0(W1, W2))) | (~(aElementOf0(W0, szNzAzT0) & aElementOf0(W1, szNzAzT0) & aElementOf0(W2, szNzAzT0))))),
% 1.59/1.79 inference(skolemize,[status(sab)],[336])).
% 1.59/1.79 tff(338,plain,
% 1.59/1.79 (![W0: $i, W1: $i, W2: $i] : (sdtlseqdt0(W0, W2) | (~aElementOf0(W2, szNzAzT0)) | (~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W2)) | (~sdtlseqdt0(W0, W1)) | (~aElementOf0(W0, szNzAzT0)))),
% 1.59/1.79 inference(modus_ponens,[status(thm)],[337, 330])).
% 1.59/1.79 tff(339,plain,
% 1.59/1.79 (![W0: $i, W1: $i, W2: $i] : (sdtlseqdt0(W0, W2) | (~aElementOf0(W2, szNzAzT0)) | (~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W2)) | (~sdtlseqdt0(W0, W1)) | (~aElementOf0(W0, szNzAzT0)))),
% 1.59/1.79 inference(modus_ponens,[status(thm)],[338, 328])).
% 1.59/1.79 tff(340,plain,
% 1.59/1.79 (((~![W0: $i, W1: $i, W2: $i] : (sdtlseqdt0(W0, W2) | (~aElementOf0(W2, szNzAzT0)) | (~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W2)) | (~sdtlseqdt0(W0, W1)) | (~aElementOf0(W0, szNzAzT0)))) | ((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), szNzAzT0)) | (~sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))), szNzAzT0)) | (~sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))))) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)))))) <=> ((~![W0: $i, W1: $i, W2: $i] : (sdtlseqdt0(W0, W2) | (~aElementOf0(W2, szNzAzT0)) | (~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W2)) | (~sdtlseqdt0(W0, W1)) | (~aElementOf0(W0, szNzAzT0)))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), szNzAzT0)) | (~sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))), szNzAzT0)) | (~sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))))) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)))))),
% 1.59/1.79 inference(rewrite,[status(thm)],[])).
% 1.59/1.79 tff(341,plain,
% 1.59/1.79 ((sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))), szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), szNzAzT0)) | (~sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))))) | (~sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), szNzAzT0))) <=> ((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), szNzAzT0)) | (~sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))), szNzAzT0)) | (~sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))))) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)))))),
% 1.59/1.79 inference(rewrite,[status(thm)],[])).
% 1.59/1.79 tff(342,plain,
% 1.59/1.79 (((~![W0: $i, W1: $i, W2: $i] : (sdtlseqdt0(W0, W2) | (~aElementOf0(W2, szNzAzT0)) | (~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W2)) | (~sdtlseqdt0(W0, W1)) | (~aElementOf0(W0, szNzAzT0)))) | (sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))), szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), szNzAzT0)) | (~sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))))) | (~sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), szNzAzT0)))) <=> ((~![W0: $i, W1: $i, W2: $i] : (sdtlseqdt0(W0, W2) | (~aElementOf0(W2, szNzAzT0)) | (~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W2)) | (~sdtlseqdt0(W0, W1)) | (~aElementOf0(W0, szNzAzT0)))) | ((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), szNzAzT0)) | (~sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))), szNzAzT0)) | (~sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))))) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))))))),
% 1.59/1.79 inference(monotonicity,[status(thm)],[341])).
% 1.59/1.79 tff(343,plain,
% 1.59/1.79 (((~![W0: $i, W1: $i, W2: $i] : (sdtlseqdt0(W0, W2) | (~aElementOf0(W2, szNzAzT0)) | (~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W2)) | (~sdtlseqdt0(W0, W1)) | (~aElementOf0(W0, szNzAzT0)))) | (sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))), szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), szNzAzT0)) | (~sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))))) | (~sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), szNzAzT0)))) <=> ((~![W0: $i, W1: $i, W2: $i] : (sdtlseqdt0(W0, W2) | (~aElementOf0(W2, szNzAzT0)) | (~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W2)) | (~sdtlseqdt0(W0, W1)) | (~aElementOf0(W0, szNzAzT0)))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), szNzAzT0)) | (~sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))), szNzAzT0)) | (~sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))))) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)))))),
% 1.59/1.79 inference(transitivity,[status(thm)],[342, 340])).
% 1.59/1.79 tff(344,plain,
% 1.59/1.79 ((~![W0: $i, W1: $i, W2: $i] : (sdtlseqdt0(W0, W2) | (~aElementOf0(W2, szNzAzT0)) | (~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W2)) | (~sdtlseqdt0(W0, W1)) | (~aElementOf0(W0, szNzAzT0)))) | (sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))), szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), szNzAzT0)) | (~sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))))) | (~sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), szNzAzT0)))),
% 1.59/1.79 inference(quant_inst,[status(thm)],[])).
% 1.59/1.79 tff(345,plain,
% 1.59/1.79 ((~![W0: $i, W1: $i, W2: $i] : (sdtlseqdt0(W0, W2) | (~aElementOf0(W2, szNzAzT0)) | (~aElementOf0(W1, szNzAzT0)) | (~sdtlseqdt0(W1, W2)) | (~sdtlseqdt0(W0, W1)) | (~aElementOf0(W0, szNzAzT0)))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), szNzAzT0)) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), szNzAzT0)) | (~sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))), szNzAzT0)) | (~sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))))) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS))))),
% 1.59/1.79 inference(modus_ponens,[status(thm)],[344, 343])).
% 1.59/1.79 tff(346,plain,
% 1.59/1.79 ((~sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))))) | (~sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), tptp_fun_W1_4(szszuzczcdt0(tptp_fun_W2_6(szmzizndt0(xT), xS)))))),
% 1.59/1.79 inference(unit_resolution,[status(thm)],[345, 339, 206, 146, 266, 326])).
% 1.59/1.79 tff(347,plain,
% 1.59/1.79 (~sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))))),
% 1.59/1.79 inference(unit_resolution,[status(thm)],[346, 310])).
% 1.59/1.80 tff(348,plain,
% 1.59/1.80 (((~![W2: $i] : ((~aElementOf0(W2, xT)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), W2))) | ((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xT)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS)))))) <=> ((~![W2: $i] : ((~aElementOf0(W2, xT)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), W2))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xT)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS)))))),
% 1.59/1.80 inference(rewrite,[status(thm)],[])).
% 1.59/1.80 tff(349,plain,
% 1.59/1.80 ((~![W2: $i] : ((~aElementOf0(W2, xT)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), W2))) | ((~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xT)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS)))))),
% 1.59/1.80 inference(quant_inst,[status(thm)],[])).
% 1.59/1.80 tff(350,plain,
% 1.59/1.80 ((~![W2: $i] : ((~aElementOf0(W2, xT)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), W2))) | (~aElementOf0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))), xT)) | sdtlseqdt0(tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xT))), tptp_fun_W1_4(szszuzczcdt0(szmzizndt0(xS))))),
% 1.59/1.80 inference(modus_ponens,[status(thm)],[349, 348])).
% 1.59/1.80 tff(351,plain,
% 1.59/1.80 ($false),
% 1.59/1.80 inference(unit_resolution,[status(thm)],[350, 347, 217, 171])).
% 1.59/1.80 % SZS output end Proof
% 1.59/1.80 % E exiting
%------------------------------------------------------------------------------