%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM600+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:21:32 AM UTC 2025
% Result : Theorem 0.21s 0.47s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM600+3 : TPTP v9.0.0. Released v4.0.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n004.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Jun 20 01:33:23 EDT 2025
% 0.19/0.33 % CPUTime :
% 0.21/0.47 % SZS status Theorem
% 0.21/0.47 % SZS output start Proof
% 0.21/0.47 tff(aElementOf0_type, type, (
% 0.21/0.47 aElementOf0: ( $i * $i ) > $o)).
% 0.21/0.47 tff(szNzAzT0_type, type, (
% 0.21/0.47 szNzAzT0: $i)).
% 0.21/0.47 tff(tptp_fun_W1_43_type, type, (
% 0.21/0.47 tptp_fun_W1_43: $i)).
% 0.21/0.47 tff(szDzozmdt0_type, type, (
% 0.21/0.47 szDzozmdt0: $i > $i)).
% 0.21/0.47 tff(xd_type, type, (
% 0.21/0.47 xd: $i)).
% 0.21/0.47 tff(aFunction0_type, type, (
% 0.21/0.47 aFunction0: $i > $o)).
% 0.21/0.47 tff(sdtlpdtrp0_type, type, (
% 0.21/0.47 sdtlpdtrp0: ( $i * $i ) > $i)).
% 0.21/0.47 tff(xC_type, type, (
% 0.21/0.47 xC: $i)).
% 0.21/0.47 tff(slbdtsldtrb0_type, type, (
% 0.21/0.47 slbdtsldtrb0: ( $i * $i ) > $i)).
% 0.21/0.47 tff(xk_type, type, (
% 0.21/0.47 xk: $i)).
% 0.21/0.47 tff(szszuzczcdt0_type, type, (
% 0.21/0.47 szszuzczcdt0: $i > $i)).
% 0.21/0.47 tff(xN_type, type, (
% 0.21/0.47 xN: $i)).
% 0.21/0.47 tff(sbrdtbr0_type, type, (
% 0.21/0.47 sbrdtbr0: $i > $i)).
% 0.21/0.47 tff(aSubsetOf0_type, type, (
% 0.21/0.47 aSubsetOf0: ( $i * $i ) > $o)).
% 0.21/0.47 tff(aSet0_type, type, (
% 0.21/0.47 aSet0: $i > $o)).
% 0.21/0.47 tff(szDzizrdt0_type, type, (
% 0.21/0.47 szDzizrdt0: $i > $i)).
% 0.21/0.47 tff(sdtlbdtrb0_type, type, (
% 0.21/0.47 sdtlbdtrb0: ( $i * $i ) > $i)).
% 0.21/0.47 tff(xT_type, type, (
% 0.21/0.47 xT: $i)).
% 0.21/0.47 tff(tptp_fun_W0_42_type, type, (
% 0.21/0.47 tptp_fun_W0_42: $i)).
% 0.21/0.47 tff(xe_type, type, (
% 0.21/0.47 xe: $i)).
% 0.21/0.47 tff(xO_type, type, (
% 0.21/0.47 xO: $i)).
% 0.21/0.47 tff(1,plain,
% 0.21/0.47 ((szDzozmdt0(xd) = szNzAzT0) <=> (szDzozmdt0(xd) = szNzAzT0)),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(2,axiom,((aFunction0(xd) & (szDzozmdt0(xd) = szNzAzT0)) & ![W0: $i] : (aElementOf0(W0, szNzAzT0) => ![W1: $i] : ((aSet0(W1) & (((![W2: $i] : (aElementOf0(W2, W1) => aElementOf0(W2, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) | aSubsetOf0(W1, sdtlpdtrp0(xN, szszuzczcdt0(W0)))) & (sbrdtbr0(W1) = xk)) | aElementOf0(W1, slbdtsldtrb0(sdtlpdtrp0(xN, szszuzczcdt0(W0)), xk)))) => (sdtlpdtrp0(xd, W0) = sdtlpdtrp0(sdtlpdtrp0(xC, W0), W1))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__4730')).
% 0.21/0.47 tff(3,plain,
% 0.21/0.47 (aFunction0(xd) & (szDzozmdt0(xd) = szNzAzT0)),
% 0.21/0.47 inference(and_elim,[status(thm)],[2])).
% 0.21/0.47 tff(4,plain,
% 0.21/0.47 (szDzozmdt0(xd) = szNzAzT0),
% 0.21/0.47 inference(and_elim,[status(thm)],[3])).
% 0.21/0.47 tff(5,plain,
% 0.21/0.47 (szDzozmdt0(xd) = szNzAzT0),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[4, 1])).
% 0.21/0.47 tff(6,plain,
% 0.21/0.47 (szNzAzT0 = szDzozmdt0(xd)),
% 0.21/0.47 inference(symmetry,[status(thm)],[5])).
% 0.21/0.47 tff(7,plain,
% 0.21/0.47 (aElementOf0(W1!43, szNzAzT0) <=> aElementOf0(W1!43, szDzozmdt0(xd))),
% 0.21/0.47 inference(monotonicity,[status(thm)],[6])).
% 0.21/0.47 tff(8,plain,
% 0.21/0.47 (aElementOf0(W1!43, szDzozmdt0(xd)) <=> aElementOf0(W1!43, szNzAzT0)),
% 0.21/0.47 inference(symmetry,[status(thm)],[7])).
% 0.21/0.47 tff(9,plain,
% 0.21/0.47 (^[W0: $i] : refl((~(((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd)))) <=> aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))))) <=> (~(((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd)))) <=> aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(10,plain,
% 0.21/0.47 (![W0: $i] : (~(((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd)))) <=> aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))))) <=> ![W0: $i] : (~(((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd)))) <=> aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[9])).
% 0.21/0.47 tff(11,plain,
% 0.21/0.47 (^[W0: $i] : trans(trans(monotonicity(rewrite((aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) <=> (~((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd)))))), ((aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd)))) <=> (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (~((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd)))))))), rewrite((aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (~((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd)))))) <=> (~(((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd)))) <=> aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))))), ((aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd)))) <=> (~(((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd)))) <=> aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))))))), rewrite((~(((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd)))) <=> aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))))) <=> (~(((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd)))) <=> aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))))), ((aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd)))) <=> (~(((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd)))) <=> aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))))))),
% 0.21/0.47 inference(bind,[status(th)],[])).
% 0.21/0.47 tff(12,plain,
% 0.21/0.47 (![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd)))) <=> ![W0: $i] : (~(((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd)))) <=> aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))))),
% 0.21/0.47 inference(quant_intro,[status(thm)],[11])).
% 0.21/0.47 tff(13,plain,
% 0.21/0.47 (![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd)))) <=> ![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(14,axiom,((aElementOf0(szDzizrdt0(xd), xT) & aSet0(sdtlbdtrb0(xd, szDzizrdt0(xd)))) & ![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__4854')).
% 0.21/0.47 tff(15,plain,
% 0.21/0.47 (![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))),
% 0.21/0.47 inference(and_elim,[status(thm)],[14])).
% 0.21/0.47 tff(16,plain,
% 0.21/0.47 (![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[15, 13])).
% 0.21/0.47 tff(17,plain,(
% 0.21/0.47 ![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))),
% 0.21/0.47 inference(skolemize,[status(sab)],[16])).
% 0.21/0.47 tff(18,plain,
% 0.21/0.47 (![W0: $i] : (~(((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd)))) <=> aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[17, 12])).
% 0.21/0.47 tff(19,plain,
% 0.21/0.47 (![W0: $i] : (~(((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd)))) <=> aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[18, 10])).
% 0.21/0.47 tff(20,plain,
% 0.21/0.47 ((~![W0: $i] : (~(((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd)))) <=> aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))))) | (~(((~(sdtlpdtrp0(xd, W1!43) = szDzizrdt0(xd))) | (~aElementOf0(W1!43, szDzozmdt0(xd)))) <=> aElementOf0(W1!43, sdtlbdtrb0(xd, szDzizrdt0(xd)))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(21,plain,
% 0.21/0.47 (~(((~(sdtlpdtrp0(xd, W1!43) = szDzizrdt0(xd))) | (~aElementOf0(W1!43, szDzozmdt0(xd)))) <=> aElementOf0(W1!43, sdtlbdtrb0(xd, szDzizrdt0(xd))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[20, 19])).
% 0.21/0.47 tff(22,plain,
% 0.21/0.47 (((aElementOf0(W1!43, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1!43) = W0!42) & aElementOf0(W0!42, xO)) & ![W1: $i] : (~(aElementOf0(W1, szNzAzT0) & ((sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) | aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W1) = W0!42)))) <=> (aElementOf0(W1!43, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1!43) = W0!42) & aElementOf0(W0!42, xO) & ![W1: $i] : (~(aElementOf0(W1, szNzAzT0) & ((sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) | aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W1) = W0!42))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(23,plain,
% 0.21/0.47 (((aElementOf0(W1!43, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1!43) = W0!42)) & aElementOf0(W0!42, xO)) <=> (aElementOf0(W1!43, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1!43) = W0!42) & aElementOf0(W0!42, xO))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(24,plain,
% 0.21/0.48 ((((aElementOf0(W1!43, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1!43) = W0!42)) & aElementOf0(W0!42, xO)) & ![W1: $i] : (~(aElementOf0(W1, szNzAzT0) & ((sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) | aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W1) = W0!42)))) <=> ((aElementOf0(W1!43, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1!43) = W0!42) & aElementOf0(W0!42, xO)) & ![W1: $i] : (~(aElementOf0(W1, szNzAzT0) & ((sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) | aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W1) = W0!42))))),
% 0.21/0.48 inference(monotonicity,[status(thm)],[23])).
% 0.21/0.48 tff(25,plain,
% 0.21/0.48 ((((aElementOf0(W1!43, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1!43) = W0!42)) & aElementOf0(W0!42, xO)) & ![W1: $i] : (~(aElementOf0(W1, szNzAzT0) & ((sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) | aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W1) = W0!42)))) <=> (aElementOf0(W1!43, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1!43) = W0!42) & aElementOf0(W0!42, xO) & ![W1: $i] : (~(aElementOf0(W1, szNzAzT0) & ((sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) | aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W1) = W0!42))))),
% 0.21/0.48 inference(transitivity,[status(thm)],[24, 22])).
% 0.21/0.48 tff(26,plain,
% 0.21/0.48 ((~![W0: $i] : ((~(?[W1: $i] : (aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)) & aElementOf0(W0, xO))) | ?[W1: $i] : (aElementOf0(W1, szNzAzT0) & ((sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) | aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W1) = W0)))) <=> (~![W0: $i] : ((~(?[W1: $i] : (aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)) & aElementOf0(W0, xO))) | ?[W1: $i] : (aElementOf0(W1, szNzAzT0) & ((sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) | aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W1) = W0))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(27,plain,
% 0.21/0.48 ((~![W0: $i] : ((?[W1: $i] : (aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)) & aElementOf0(W0, xO)) => ?[W1: $i] : ((aElementOf0(W1, szNzAzT0) & ((sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) | aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))))) & (sdtlpdtrp0(xe, W1) = W0)))) <=> (~![W0: $i] : ((~(?[W1: $i] : (aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)) & aElementOf0(W0, xO))) | ?[W1: $i] : (aElementOf0(W1, szNzAzT0) & ((sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) | aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W1) = W0))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(28,axiom,(~![W0: $i] : ((?[W1: $i] : (aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)) & aElementOf0(W0, xO)) => ?[W1: $i] : ((aElementOf0(W1, szNzAzT0) & ((sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) | aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))))) & (sdtlpdtrp0(xe, W1) = W0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 0.21/0.48 tff(29,plain,
% 0.21/0.48 (~![W0: $i] : ((~(?[W1: $i] : (aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)) & aElementOf0(W0, xO))) | ?[W1: $i] : (aElementOf0(W1, szNzAzT0) & ((sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) | aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W1) = W0)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.21/0.48 tff(30,plain,
% 0.21/0.48 (~![W0: $i] : ((~(?[W1: $i] : (aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)) & aElementOf0(W0, xO))) | ?[W1: $i] : (aElementOf0(W1, szNzAzT0) & ((sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) | aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W1) = W0)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[29, 26])).
% 0.21/0.48 tff(31,plain,
% 0.21/0.48 (~![W0: $i] : ((~(?[W1: $i] : (aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)) & aElementOf0(W0, xO))) | ?[W1: $i] : (aElementOf0(W1, szNzAzT0) & ((sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) | aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W1) = W0)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.21/0.48 tff(32,plain,
% 0.21/0.48 (~![W0: $i] : ((~(?[W1: $i] : (aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1) = W0)) & aElementOf0(W0, xO))) | ?[W1: $i] : (aElementOf0(W1, szNzAzT0) & ((sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) | aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W1) = W0)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[31, 26])).
% 0.21/0.48 tff(33,plain,
% 0.21/0.48 (aElementOf0(W1!43, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W1!43) = W0!42) & aElementOf0(W0!42, xO) & ![W1: $i] : (~(aElementOf0(W1, szNzAzT0) & ((sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) | aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W1) = W0!42)))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[32, 25])).
% 0.21/0.48 tff(34,plain,
% 0.21/0.48 (aElementOf0(W1!43, sdtlbdtrb0(xd, szDzizrdt0(xd)))),
% 0.21/0.48 inference(and_elim,[status(thm)],[33])).
% 0.21/0.48 tff(35,plain,
% 0.21/0.48 ((((~(sdtlpdtrp0(xd, W1!43) = szDzizrdt0(xd))) | (~aElementOf0(W1!43, szDzozmdt0(xd)))) <=> aElementOf0(W1!43, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~((~(sdtlpdtrp0(xd, W1!43) = szDzizrdt0(xd))) | (~aElementOf0(W1!43, szDzozmdt0(xd))))) | (~aElementOf0(W1!43, sdtlbdtrb0(xd, szDzizrdt0(xd))))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(36,plain,
% 0.21/0.48 ((((~(sdtlpdtrp0(xd, W1!43) = szDzizrdt0(xd))) | (~aElementOf0(W1!43, szDzozmdt0(xd)))) <=> aElementOf0(W1!43, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~((~(sdtlpdtrp0(xd, W1!43) = szDzizrdt0(xd))) | (~aElementOf0(W1!43, szDzozmdt0(xd)))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.21/0.48 tff(37,plain,
% 0.21/0.48 (~((~(sdtlpdtrp0(xd, W1!43) = szDzizrdt0(xd))) | (~aElementOf0(W1!43, szDzozmdt0(xd))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[36, 21])).
% 0.21/0.48 tff(38,plain,
% 0.21/0.48 (((~(sdtlpdtrp0(xd, W1!43) = szDzizrdt0(xd))) | (~aElementOf0(W1!43, szDzozmdt0(xd)))) | aElementOf0(W1!43, szDzozmdt0(xd))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(39,plain,
% 0.21/0.48 (aElementOf0(W1!43, szDzozmdt0(xd))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.21/0.48 tff(40,plain,
% 0.21/0.48 (aElementOf0(W1!43, szNzAzT0)),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[39, 8])).
% 0.21/0.48 tff(41,plain,
% 0.21/0.48 (((sdtlpdtrp0(xd, W1!43) = szDzizrdt0(xd)) | aElementOf0(W1!43, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~aElementOf0(W1!43, sdtlbdtrb0(xd, szDzizrdt0(xd))))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(42,plain,
% 0.21/0.48 ((sdtlpdtrp0(xd, W1!43) = szDzizrdt0(xd)) | aElementOf0(W1!43, sdtlbdtrb0(xd, szDzizrdt0(xd)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[41, 34])).
% 0.21/0.48 tff(43,plain,
% 0.21/0.48 (^[W1: $i] : refl(((~aElementOf0(W1, szNzAzT0)) | (~((sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) | aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~(sdtlpdtrp0(xe, W1) = W0!42))) <=> ((~aElementOf0(W1, szNzAzT0)) | (~((sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) | aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~(sdtlpdtrp0(xe, W1) = W0!42))))),
% 0.21/0.48 inference(bind,[status(th)],[])).
% 0.21/0.48 tff(44,plain,
% 0.21/0.48 (![W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~((sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) | aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~(sdtlpdtrp0(xe, W1) = W0!42))) <=> ![W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~((sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) | aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~(sdtlpdtrp0(xe, W1) = W0!42)))),
% 0.21/0.48 inference(quant_intro,[status(thm)],[43])).
% 0.21/0.48 tff(45,plain,
% 0.21/0.48 (^[W1: $i] : trans(monotonicity(rewrite((aElementOf0(W1, szNzAzT0) & ((sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) | aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W1) = W0!42)) <=> (~((~aElementOf0(W1, szNzAzT0)) | (~((sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) | aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~(sdtlpdtrp0(xe, W1) = W0!42))))), ((~(aElementOf0(W1, szNzAzT0) & ((sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) | aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W1) = W0!42))) <=> (~(~((~aElementOf0(W1, szNzAzT0)) | (~((sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) | aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~(sdtlpdtrp0(xe, W1) = W0!42))))))), rewrite((~(~((~aElementOf0(W1, szNzAzT0)) | (~((sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) | aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~(sdtlpdtrp0(xe, W1) = W0!42))))) <=> ((~aElementOf0(W1, szNzAzT0)) | (~((sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) | aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~(sdtlpdtrp0(xe, W1) = W0!42)))), ((~(aElementOf0(W1, szNzAzT0) & ((sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) | aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W1) = W0!42))) <=> ((~aElementOf0(W1, szNzAzT0)) | (~((sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) | aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~(sdtlpdtrp0(xe, W1) = W0!42)))))),
% 0.21/0.49 inference(bind,[status(th)],[])).
% 0.21/0.49 tff(46,plain,
% 0.21/0.49 (![W1: $i] : (~(aElementOf0(W1, szNzAzT0) & ((sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) | aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W1) = W0!42))) <=> ![W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~((sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) | aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~(sdtlpdtrp0(xe, W1) = W0!42)))),
% 0.21/0.49 inference(quant_intro,[status(thm)],[45])).
% 0.21/0.49 tff(47,plain,
% 0.21/0.49 (![W1: $i] : (~(aElementOf0(W1, szNzAzT0) & ((sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) | aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W1) = W0!42)))),
% 0.21/0.49 inference(and_elim,[status(thm)],[33])).
% 0.21/0.49 tff(48,plain,
% 0.21/0.49 (![W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~((sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) | aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~(sdtlpdtrp0(xe, W1) = W0!42)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.21/0.49 tff(49,plain,
% 0.21/0.49 (![W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~((sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) | aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~(sdtlpdtrp0(xe, W1) = W0!42)))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.21/0.49 tff(50,plain,
% 0.21/0.49 (sdtlpdtrp0(xe, W1!43) = W0!42),
% 0.21/0.49 inference(and_elim,[status(thm)],[33])).
% 0.21/0.49 tff(51,plain,
% 0.21/0.49 (((~![W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~((sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) | aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~(sdtlpdtrp0(xe, W1) = W0!42)))) | ((~aElementOf0(W1!43, szNzAzT0)) | (~((sdtlpdtrp0(xd, W1!43) = szDzizrdt0(xd)) | aElementOf0(W1!43, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~(sdtlpdtrp0(xe, W1!43) = W0!42)))) <=> ((~![W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~((sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) | aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~(sdtlpdtrp0(xe, W1) = W0!42)))) | (~aElementOf0(W1!43, szNzAzT0)) | (~((sdtlpdtrp0(xd, W1!43) = szDzizrdt0(xd)) | aElementOf0(W1!43, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~(sdtlpdtrp0(xe, W1!43) = W0!42)))),
% 0.21/0.49 inference(rewrite,[status(thm)],[])).
% 0.21/0.49 tff(52,plain,
% 0.21/0.49 ((~![W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~((sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) | aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~(sdtlpdtrp0(xe, W1) = W0!42)))) | ((~aElementOf0(W1!43, szNzAzT0)) | (~((sdtlpdtrp0(xd, W1!43) = szDzizrdt0(xd)) | aElementOf0(W1!43, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~(sdtlpdtrp0(xe, W1!43) = W0!42)))),
% 0.21/0.49 inference(quant_inst,[status(thm)],[])).
% 0.21/0.49 tff(53,plain,
% 0.21/0.49 ((~![W1: $i] : ((~aElementOf0(W1, szNzAzT0)) | (~((sdtlpdtrp0(xd, W1) = szDzizrdt0(xd)) | aElementOf0(W1, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~(sdtlpdtrp0(xe, W1) = W0!42)))) | (~aElementOf0(W1!43, szNzAzT0)) | (~((sdtlpdtrp0(xd, W1!43) = szDzizrdt0(xd)) | aElementOf0(W1!43, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~(sdtlpdtrp0(xe, W1!43) = W0!42))),
% 0.21/0.49 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.21/0.49 tff(54,plain,
% 0.21/0.49 (~aElementOf0(W1!43, szNzAzT0)),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[53, 50, 49, 42])).
% 0.21/0.49 tff(55,plain,
% 0.21/0.49 ($false),
% 0.21/0.49 inference(unit_resolution,[status(thm)],[54, 40])).
% 0.21/0.49 % SZS output end Proof
% 0.21/0.49 % E exiting
%------------------------------------------------------------------------------