%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM597+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 0.47s 0.66s
% Output : Proof 0.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM597+3 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 01:33:03 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.47/0.66 % SZS status Theorem
% 0.47/0.66 % SZS output start Proof
% 0.47/0.66 tff(aElementOf0_type, type, (
% 0.47/0.66 aElementOf0: ( $i * $i ) > $o)).
% 0.47/0.66 tff(sdtlcdtrc0_type, type, (
% 0.47/0.66 sdtlcdtrc0: ( $i * $i ) > $i)).
% 0.47/0.66 tff(szDzozmdt0_type, type, (
% 0.47/0.66 szDzozmdt0: $i > $i)).
% 0.47/0.66 tff(xd_type, type, (
% 0.47/0.66 xd: $i)).
% 0.47/0.66 tff(sdtlpdtrp0_type, type, (
% 0.47/0.66 sdtlpdtrp0: ( $i * $i ) > $i)).
% 0.47/0.66 tff(tptp_fun_W0_41_type, type, (
% 0.47/0.66 tptp_fun_W0_41: $i)).
% 0.47/0.66 tff(szDzizrdt0_type, type, (
% 0.47/0.66 szDzizrdt0: $i > $i)).
% 0.47/0.66 tff(sdtlbdtrb0_type, type, (
% 0.47/0.66 sdtlbdtrb0: ( $i * $i ) > $i)).
% 0.47/0.66 tff(aSet0_type, type, (
% 0.47/0.66 aSet0: $i > $o)).
% 0.47/0.66 tff(xT_type, type, (
% 0.47/0.66 xT: $i)).
% 0.47/0.66 tff(aSubsetOf0_type, type, (
% 0.47/0.66 aSubsetOf0: ( $i * $i ) > $o)).
% 0.47/0.66 tff(aFunction0_type, type, (
% 0.47/0.66 aFunction0: $i > $o)).
% 0.47/0.66 tff(szNzAzT0_type, type, (
% 0.47/0.66 szNzAzT0: $i)).
% 0.47/0.66 tff(xC_type, type, (
% 0.47/0.66 xC: $i)).
% 0.47/0.66 tff(slbdtsldtrb0_type, type, (
% 0.47/0.66 slbdtsldtrb0: ( $i * $i ) > $i)).
% 0.47/0.66 tff(xk_type, type, (
% 0.47/0.66 xk: $i)).
% 0.47/0.66 tff(szszuzczcdt0_type, type, (
% 0.47/0.66 szszuzczcdt0: $i > $i)).
% 0.47/0.66 tff(xN_type, type, (
% 0.47/0.66 xN: $i)).
% 0.47/0.66 tff(sbrdtbr0_type, type, (
% 0.47/0.66 sbrdtbr0: $i > $i)).
% 0.47/0.66 tff(1,plain,
% 0.47/0.66 (^[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))))))),
% 0.47/0.66 inference(bind,[status(th)],[])).
% 0.47/0.66 tff(2,plain,
% 0.47/0.66 (![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)))))),
% 0.47/0.66 inference(quant_intro,[status(thm)],[1])).
% 0.47/0.66 tff(3,plain,
% 0.47/0.66 (^[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)))))))),
% 0.47/0.66 inference(bind,[status(th)],[])).
% 0.47/0.66 tff(4,plain,
% 0.47/0.66 (![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)))))),
% 0.47/0.66 inference(quant_intro,[status(thm)],[3])).
% 0.47/0.66 tff(5,plain,
% 0.47/0.66 (![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))))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(6,plain,
% 0.47/0.67 ((~((aSet0(sdtlbdtrb0(xd, szDzizrdt0(xd))) & ![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)))))) <=> (~((~?[W0: $i] : aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(aSet0(sdtlbdtrb0(xd, szDzizrdt0(xd))) & ![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))))))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(7,axiom,(~((aSet0(sdtlbdtrb0(xd, szDzizrdt0(xd))) & ![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)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__4868')).
% 0.47/0.67 tff(8,plain,
% 0.47/0.67 (~((~?[W0: $i] : aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~(aSet0(sdtlbdtrb0(xd, szDzizrdt0(xd))) & ![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd)))))))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.47/0.67 tff(9,plain,
% 0.47/0.67 (aSet0(sdtlbdtrb0(xd, szDzizrdt0(xd))) & ![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))),
% 0.47/0.67 inference(or_elim,[status(thm)],[8])).
% 0.47/0.67 tff(10,plain,
% 0.47/0.67 (![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))),
% 0.47/0.67 inference(and_elim,[status(thm)],[9])).
% 0.47/0.67 tff(11,plain,
% 0.47/0.67 (![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[10, 5])).
% 0.47/0.67 tff(12,plain,(
% 0.47/0.67 ![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> (aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))))),
% 0.47/0.67 inference(skolemize,[status(sab)],[11])).
% 0.47/0.67 tff(13,plain,
% 0.47/0.67 (![W0: $i] : (~(((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd)))) <=> aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[12, 4])).
% 0.47/0.67 tff(14,plain,
% 0.47/0.67 (![W0: $i] : (~(((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd)))) <=> aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[13, 2])).
% 0.47/0.67 tff(15,plain,
% 0.47/0.67 ((~![W0: $i] : (~(((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd)))) <=> aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))))) | (~(((~(sdtlpdtrp0(xd, W0!41) = szDzizrdt0(xd))) | (~aElementOf0(W0!41, szDzozmdt0(xd)))) <=> aElementOf0(W0!41, sdtlbdtrb0(xd, szDzizrdt0(xd)))))),
% 0.47/0.67 inference(quant_inst,[status(thm)],[])).
% 0.47/0.67 tff(16,plain,
% 0.47/0.67 (~(((~(sdtlpdtrp0(xd, W0!41) = szDzizrdt0(xd))) | (~aElementOf0(W0!41, szDzozmdt0(xd)))) <=> aElementOf0(W0!41, sdtlbdtrb0(xd, szDzizrdt0(xd))))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[15, 14])).
% 0.47/0.67 tff(17,plain,
% 0.47/0.67 (?[W0: $i] : aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) <=> ?[W0: $i] : aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(18,plain,
% 0.47/0.67 (?[W0: $i] : aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))),
% 0.47/0.67 inference(or_elim,[status(thm)],[8])).
% 0.47/0.67 tff(19,plain,
% 0.47/0.67 (?[W0: $i] : aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.47/0.67 tff(20,plain,(
% 0.47/0.67 aElementOf0(W0!41, sdtlbdtrb0(xd, szDzizrdt0(xd)))),
% 0.47/0.67 inference(skolemize,[status(sab)],[19])).
% 0.47/0.67 tff(21,plain,
% 0.47/0.67 ((((~(sdtlpdtrp0(xd, W0!41) = szDzizrdt0(xd))) | (~aElementOf0(W0!41, szDzozmdt0(xd)))) <=> aElementOf0(W0!41, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~((~(sdtlpdtrp0(xd, W0!41) = szDzizrdt0(xd))) | (~aElementOf0(W0!41, szDzozmdt0(xd))))) | (~aElementOf0(W0!41, sdtlbdtrb0(xd, szDzizrdt0(xd))))),
% 0.47/0.67 inference(tautology,[status(thm)],[])).
% 0.47/0.67 tff(22,plain,
% 0.47/0.67 ((((~(sdtlpdtrp0(xd, W0!41) = szDzizrdt0(xd))) | (~aElementOf0(W0!41, szDzozmdt0(xd)))) <=> aElementOf0(W0!41, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~((~(sdtlpdtrp0(xd, W0!41) = szDzizrdt0(xd))) | (~aElementOf0(W0!41, szDzozmdt0(xd)))))),
% 0.50/0.67 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.50/0.67 tff(23,plain,
% 0.50/0.67 (~((~(sdtlpdtrp0(xd, W0!41) = szDzizrdt0(xd))) | (~aElementOf0(W0!41, szDzozmdt0(xd))))),
% 0.50/0.67 inference(unit_resolution,[status(thm)],[22, 16])).
% 0.50/0.67 tff(24,plain,
% 0.50/0.67 (((~(sdtlpdtrp0(xd, W0!41) = szDzizrdt0(xd))) | (~aElementOf0(W0!41, szDzozmdt0(xd)))) | (sdtlpdtrp0(xd, W0!41) = szDzizrdt0(xd))),
% 0.50/0.67 inference(tautology,[status(thm)],[])).
% 0.50/0.67 tff(25,plain,
% 0.50/0.67 (sdtlpdtrp0(xd, W0!41) = szDzizrdt0(xd)),
% 0.50/0.67 inference(unit_resolution,[status(thm)],[24, 23])).
% 0.50/0.67 tff(26,plain,
% 0.50/0.67 (aElementOf0(sdtlpdtrp0(xd, W0!41), sdtlcdtrc0(xd, szDzozmdt0(xd))) <=> aElementOf0(szDzizrdt0(xd), sdtlcdtrc0(xd, szDzozmdt0(xd)))),
% 0.50/0.67 inference(monotonicity,[status(thm)],[25])).
% 0.50/0.67 tff(27,plain,
% 0.50/0.67 (aElementOf0(szDzizrdt0(xd), sdtlcdtrc0(xd, szDzozmdt0(xd))) <=> aElementOf0(sdtlpdtrp0(xd, W0!41), sdtlcdtrc0(xd, szDzozmdt0(xd)))),
% 0.50/0.67 inference(symmetry,[status(thm)],[26])).
% 0.50/0.67 tff(28,plain,
% 0.50/0.67 ((~aElementOf0(szDzizrdt0(xd), sdtlcdtrc0(xd, szDzozmdt0(xd)))) <=> (~aElementOf0(sdtlpdtrp0(xd, W0!41), sdtlcdtrc0(xd, szDzozmdt0(xd))))),
% 0.50/0.67 inference(monotonicity,[status(thm)],[27])).
% 0.50/0.67 tff(29,plain,
% 0.50/0.67 ((~aElementOf0(szDzizrdt0(xd), xT)) <=> (~aElementOf0(szDzizrdt0(xd), xT))),
% 0.50/0.67 inference(rewrite,[status(thm)],[])).
% 0.50/0.67 tff(30,axiom,(~aElementOf0(szDzizrdt0(xd), xT)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 0.50/0.67 tff(31,plain,
% 0.50/0.67 (~aElementOf0(szDzizrdt0(xd), xT)),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.50/0.67 tff(32,plain,
% 0.50/0.67 (^[W0: $i] : refl(((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xd)))) | aElementOf0(W0, xT)) <=> ((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xd)))) | aElementOf0(W0, xT)))),
% 0.50/0.67 inference(bind,[status(th)],[])).
% 0.50/0.67 tff(33,plain,
% 0.50/0.67 (![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xd)))) | aElementOf0(W0, xT)) <=> ![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xd)))) | aElementOf0(W0, xT))),
% 0.50/0.67 inference(quant_intro,[status(thm)],[32])).
% 0.50/0.67 tff(34,plain,
% 0.50/0.67 (![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xd)))) | aElementOf0(W0, xT)) <=> ![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xd)))) | aElementOf0(W0, xT))),
% 0.50/0.67 inference(rewrite,[status(thm)],[])).
% 0.50/0.67 tff(35,plain,
% 0.50/0.67 (^[W0: $i] : rewrite((aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xd))) => aElementOf0(W0, xT)) <=> ((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xd)))) | aElementOf0(W0, xT)))),
% 0.50/0.67 inference(bind,[status(th)],[])).
% 0.50/0.67 tff(36,plain,
% 0.50/0.67 (![W0: $i] : (aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xd))) => aElementOf0(W0, xT)) <=> ![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xd)))) | aElementOf0(W0, xT))),
% 0.50/0.67 inference(quant_intro,[status(thm)],[35])).
% 0.50/0.67 tff(37,axiom,(((aSet0(sdtlcdtrc0(xd, szDzozmdt0(xd))) & ![W0: $i] : (aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xd))) <=> ?[W1: $i] : (aElementOf0(W1, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W1) = W0)))) & ![W0: $i] : (aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xd))) => aElementOf0(W0, xT))) & aSubsetOf0(sdtlcdtrc0(xd, szDzozmdt0(xd)), xT)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__4758')).
% 0.50/0.67 tff(38,plain,
% 0.50/0.67 ((aSet0(sdtlcdtrc0(xd, szDzozmdt0(xd))) & ![W0: $i] : (aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xd))) <=> ?[W1: $i] : (aElementOf0(W1, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W1) = W0)))) & ![W0: $i] : (aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xd))) => aElementOf0(W0, xT))),
% 0.50/0.67 inference(and_elim,[status(thm)],[37])).
% 0.50/0.67 tff(39,plain,
% 0.50/0.67 (![W0: $i] : (aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xd))) => aElementOf0(W0, xT))),
% 0.50/0.67 inference(and_elim,[status(thm)],[38])).
% 0.50/0.67 tff(40,plain,
% 0.50/0.67 (![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xd)))) | aElementOf0(W0, xT))),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[39, 36])).
% 0.50/0.67 tff(41,plain,
% 0.50/0.67 (![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xd)))) | aElementOf0(W0, xT))),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[40, 34])).
% 0.50/0.67 tff(42,plain,(
% 0.50/0.67 ![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xd)))) | aElementOf0(W0, xT))),
% 0.50/0.67 inference(skolemize,[status(sab)],[41])).
% 0.50/0.67 tff(43,plain,
% 0.50/0.67 (![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xd)))) | aElementOf0(W0, xT))),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[42, 33])).
% 0.50/0.67 tff(44,plain,
% 0.50/0.67 (((~![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xd)))) | aElementOf0(W0, xT))) | ((~aElementOf0(szDzizrdt0(xd), sdtlcdtrc0(xd, szDzozmdt0(xd)))) | aElementOf0(szDzizrdt0(xd), xT))) <=> ((~![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xd)))) | aElementOf0(W0, xT))) | (~aElementOf0(szDzizrdt0(xd), sdtlcdtrc0(xd, szDzozmdt0(xd)))) | aElementOf0(szDzizrdt0(xd), xT))),
% 0.50/0.67 inference(rewrite,[status(thm)],[])).
% 0.50/0.67 tff(45,plain,
% 0.50/0.67 ((~![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xd)))) | aElementOf0(W0, xT))) | ((~aElementOf0(szDzizrdt0(xd), sdtlcdtrc0(xd, szDzozmdt0(xd)))) | aElementOf0(szDzizrdt0(xd), xT))),
% 0.50/0.67 inference(quant_inst,[status(thm)],[])).
% 0.50/0.67 tff(46,plain,
% 0.50/0.67 ((~![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xd, szDzozmdt0(xd)))) | aElementOf0(W0, xT))) | (~aElementOf0(szDzizrdt0(xd), sdtlcdtrc0(xd, szDzozmdt0(xd)))) | aElementOf0(szDzizrdt0(xd), xT)),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[45, 44])).
% 0.50/0.67 tff(47,plain,
% 0.50/0.67 (~aElementOf0(szDzizrdt0(xd), sdtlcdtrc0(xd, szDzozmdt0(xd)))),
% 0.50/0.67 inference(unit_resolution,[status(thm)],[46, 43, 31])).
% 0.50/0.67 tff(48,plain,
% 0.50/0.67 (~aElementOf0(sdtlpdtrp0(xd, W0!41), sdtlcdtrc0(xd, szDzozmdt0(xd)))),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[47, 28])).
% 0.50/0.67 tff(49,plain,
% 0.50/0.67 (aFunction0(xd) <=> aFunction0(xd)),
% 0.50/0.67 inference(rewrite,[status(thm)],[])).
% 0.50/0.67 tff(50,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')).
% 0.50/0.67 tff(51,plain,
% 0.50/0.67 (aFunction0(xd) & (szDzozmdt0(xd) = szNzAzT0)),
% 0.50/0.67 inference(and_elim,[status(thm)],[50])).
% 0.50/0.67 tff(52,plain,
% 0.50/0.67 (aFunction0(xd)),
% 0.50/0.67 inference(and_elim,[status(thm)],[51])).
% 0.50/0.67 tff(53,plain,
% 0.50/0.67 (aFunction0(xd)),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[52, 49])).
% 0.50/0.67 tff(54,plain,
% 0.50/0.67 (^[W0: $i] : refl(((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0))))) <=> ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0))))))),
% 0.50/0.67 inference(bind,[status(th)],[])).
% 0.50/0.67 tff(55,plain,
% 0.50/0.67 (![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0))))) <=> ![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0)))))),
% 0.50/0.67 inference(quant_intro,[status(thm)],[54])).
% 0.50/0.67 tff(56,plain,
% 0.50/0.67 (^[W0: $i] : rewrite(((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0))))) <=> ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0))))))),
% 0.50/0.67 inference(bind,[status(th)],[])).
% 0.50/0.67 tff(57,plain,
% 0.50/0.67 (![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0))))) <=> ![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0)))))),
% 0.50/0.67 inference(quant_intro,[status(thm)],[56])).
% 0.50/0.67 tff(58,plain,
% 0.50/0.67 (![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0))))) <=> ![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0)))))),
% 0.50/0.67 inference(transitivity,[status(thm)],[57, 55])).
% 0.50/0.67 tff(59,plain,
% 0.50/0.67 (![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0))))) <=> ![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0)))))),
% 0.50/0.67 inference(rewrite,[status(thm)],[])).
% 0.50/0.67 tff(60,plain,
% 0.50/0.67 (^[W0: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: $i] : rewrite((aElementOf0(W1, szDzozmdt0(W0)) => aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0)))) <=> ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0)))))), (![W1: $i] : (aElementOf0(W1, szDzozmdt0(W0)) => aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0)))) <=> ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0)))))), ((aFunction0(W0) => ![W1: $i] : (aElementOf0(W1, szDzozmdt0(W0)) => aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0))))) <=> (aFunction0(W0) => ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0))))))), rewrite((aFunction0(W0) => ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0))))) <=> ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0)))))), ((aFunction0(W0) => ![W1: $i] : (aElementOf0(W1, szDzozmdt0(W0)) => aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0))))) <=> ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0)))))))),
% 0.50/0.67 inference(bind,[status(th)],[])).
% 0.50/0.67 tff(61,plain,
% 0.50/0.67 (![W0: $i] : (aFunction0(W0) => ![W1: $i] : (aElementOf0(W1, szDzozmdt0(W0)) => aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0))))) <=> ![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0)))))),
% 0.50/0.67 inference(quant_intro,[status(thm)],[60])).
% 0.50/0.67 tff(62,axiom,(![W0: $i] : (aFunction0(W0) => ![W1: $i] : (aElementOf0(W1, szDzozmdt0(W0)) => aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mImgRng')).
% 0.50/0.67 tff(63,plain,
% 0.50/0.67 (![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0)))))),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[62, 61])).
% 0.50/0.67 tff(64,plain,
% 0.50/0.67 (![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0)))))),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[63, 59])).
% 0.50/0.67 tff(65,plain,(
% 0.50/0.67 ![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0)))))),
% 0.50/0.67 inference(skolemize,[status(sab)],[64])).
% 0.50/0.67 tff(66,plain,
% 0.50/0.67 (![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0)))))),
% 0.50/0.67 inference(modus_ponens,[status(thm)],[65, 58])).
% 0.50/0.67 tff(67,plain,
% 0.50/0.67 (((~![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0)))))) | ((~aFunction0(xd)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xd))) | aElementOf0(sdtlpdtrp0(xd, W1), sdtlcdtrc0(xd, szDzozmdt0(xd)))))) <=> ((~![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0)))))) | (~aFunction0(xd)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xd))) | aElementOf0(sdtlpdtrp0(xd, W1), sdtlcdtrc0(xd, szDzozmdt0(xd)))))),
% 0.50/0.68 inference(rewrite,[status(thm)],[])).
% 0.50/0.68 tff(68,plain,
% 0.50/0.68 ((~![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0)))))) | ((~aFunction0(xd)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xd))) | aElementOf0(sdtlpdtrp0(xd, W1), sdtlcdtrc0(xd, szDzozmdt0(xd)))))),
% 0.50/0.68 inference(quant_inst,[status(thm)],[])).
% 0.50/0.68 tff(69,plain,
% 0.50/0.68 ((~![W0: $i] : ((~aFunction0(W0)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(W0))) | aElementOf0(sdtlpdtrp0(W0, W1), sdtlcdtrc0(W0, szDzozmdt0(W0)))))) | (~aFunction0(xd)) | ![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xd))) | aElementOf0(sdtlpdtrp0(xd, W1), sdtlcdtrc0(xd, szDzozmdt0(xd))))),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.50/0.68 tff(70,plain,
% 0.50/0.68 (![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xd))) | aElementOf0(sdtlpdtrp0(xd, W1), sdtlcdtrc0(xd, szDzozmdt0(xd))))),
% 0.50/0.68 inference(unit_resolution,[status(thm)],[69, 66, 53])).
% 0.50/0.68 tff(71,plain,
% 0.50/0.68 (((~(sdtlpdtrp0(xd, W0!41) = szDzizrdt0(xd))) | (~aElementOf0(W0!41, szDzozmdt0(xd)))) | aElementOf0(W0!41, szDzozmdt0(xd))),
% 0.50/0.68 inference(tautology,[status(thm)],[])).
% 0.50/0.68 tff(72,plain,
% 0.50/0.68 (aElementOf0(W0!41, szDzozmdt0(xd))),
% 0.50/0.68 inference(unit_resolution,[status(thm)],[71, 23])).
% 0.50/0.68 tff(73,plain,
% 0.50/0.68 (((~![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xd))) | aElementOf0(sdtlpdtrp0(xd, W1), sdtlcdtrc0(xd, szDzozmdt0(xd))))) | ((~aElementOf0(W0!41, szDzozmdt0(xd))) | aElementOf0(sdtlpdtrp0(xd, W0!41), sdtlcdtrc0(xd, szDzozmdt0(xd))))) <=> ((~![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xd))) | aElementOf0(sdtlpdtrp0(xd, W1), sdtlcdtrc0(xd, szDzozmdt0(xd))))) | (~aElementOf0(W0!41, szDzozmdt0(xd))) | aElementOf0(sdtlpdtrp0(xd, W0!41), sdtlcdtrc0(xd, szDzozmdt0(xd))))),
% 0.50/0.68 inference(rewrite,[status(thm)],[])).
% 0.50/0.68 tff(74,plain,
% 0.50/0.68 ((~![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xd))) | aElementOf0(sdtlpdtrp0(xd, W1), sdtlcdtrc0(xd, szDzozmdt0(xd))))) | ((~aElementOf0(W0!41, szDzozmdt0(xd))) | aElementOf0(sdtlpdtrp0(xd, W0!41), sdtlcdtrc0(xd, szDzozmdt0(xd))))),
% 0.50/0.68 inference(quant_inst,[status(thm)],[])).
% 0.50/0.68 tff(75,plain,
% 0.50/0.68 ((~![W1: $i] : ((~aElementOf0(W1, szDzozmdt0(xd))) | aElementOf0(sdtlpdtrp0(xd, W1), sdtlcdtrc0(xd, szDzozmdt0(xd))))) | (~aElementOf0(W0!41, szDzozmdt0(xd))) | aElementOf0(sdtlpdtrp0(xd, W0!41), sdtlcdtrc0(xd, szDzozmdt0(xd)))),
% 0.50/0.68 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.50/0.68 tff(76,plain,
% 0.50/0.68 (aElementOf0(sdtlpdtrp0(xd, W0!41), sdtlcdtrc0(xd, szDzozmdt0(xd)))),
% 0.50/0.68 inference(unit_resolution,[status(thm)],[75, 72, 70])).
% 0.50/0.68 tff(77,plain,
% 0.50/0.68 ($false),
% 0.50/0.68 inference(unit_resolution,[status(thm)],[76, 48])).
% 0.50/0.68 % SZS output end Proof
% 0.50/0.68 % E exiting
%------------------------------------------------------------------------------