%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM615+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:21:36 AM UTC 2025
% Result : Theorem 0.19s 0.47s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM615+3 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n007.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 01:37:05 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.47 % SZS status Theorem
% 0.19/0.47 % SZS output start Proof
% 0.19/0.47 tff(aElementOf0_type, type, (
% 0.19/0.47 aElementOf0: ( $i * $i ) > $o)).
% 0.19/0.47 tff(sdtlbdtrb0_type, type, (
% 0.19/0.47 sdtlbdtrb0: ( $i * $i ) > $i)).
% 0.19/0.47 tff(szDzizrdt0_type, type, (
% 0.19/0.47 szDzizrdt0: $i > $i)).
% 0.19/0.47 tff(xd_type, type, (
% 0.19/0.47 xd: $i)).
% 0.19/0.47 tff(tptp_fun_W0_44_type, type, (
% 0.19/0.47 tptp_fun_W0_44: $i)).
% 0.19/0.47 tff(szDzozmdt0_type, type, (
% 0.19/0.47 szDzozmdt0: $i > $i)).
% 0.19/0.47 tff(sdtlpdtrp0_type, type, (
% 0.19/0.47 sdtlpdtrp0: ( $i * $i ) > $i)).
% 0.19/0.47 tff(xp_type, type, (
% 0.19/0.47 xp: $i)).
% 0.19/0.47 tff(xe_type, type, (
% 0.19/0.47 xe: $i)).
% 0.19/0.47 tff(1,plain,
% 0.19/0.47 (?[W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W0) = xp)) <=> ?[W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W0) = xp))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(2,axiom,(?[W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W0) = xp))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__5182')).
% 0.19/0.47 tff(3,plain,
% 0.19/0.47 (?[W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W0) = xp))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.19/0.47 tff(4,plain,(
% 0.19/0.47 aElementOf0(W0!44, sdtlbdtrb0(xd, szDzizrdt0(xd))) & (sdtlpdtrp0(xe, W0!44) = xp)),
% 0.19/0.47 inference(skolemize,[status(sab)],[3])).
% 0.19/0.47 tff(5,plain,
% 0.19/0.47 (aElementOf0(W0!44, sdtlbdtrb0(xd, szDzizrdt0(xd)))),
% 0.19/0.47 inference(and_elim,[status(thm)],[4])).
% 0.19/0.47 tff(6,plain,
% 0.19/0.47 (((~((~(sdtlpdtrp0(xd, W0!44) = szDzizrdt0(xd))) | (~aElementOf0(W0!44, szDzozmdt0(xd))))) | aElementOf0(W0!44, sdtlbdtrb0(xd, szDzizrdt0(xd)))) | (~aElementOf0(W0!44, sdtlbdtrb0(xd, szDzizrdt0(xd))))),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(7,plain,
% 0.19/0.47 ((~((~(sdtlpdtrp0(xd, W0!44) = szDzizrdt0(xd))) | (~aElementOf0(W0!44, szDzozmdt0(xd))))) | aElementOf0(W0!44, sdtlbdtrb0(xd, szDzizrdt0(xd)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[6, 5])).
% 0.19/0.47 tff(8,plain,
% 0.19/0.47 (^[W0: $i] : refl(((~((~((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd))))) | aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~(sdtlpdtrp0(xe, W0) = xp))) <=> ((~((~((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd))))) | aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~(sdtlpdtrp0(xe, W0) = xp))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(9,plain,
% 0.19/0.47 (![W0: $i] : ((~((~((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd))))) | aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~(sdtlpdtrp0(xe, W0) = xp))) <=> ![W0: $i] : ((~((~((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd))))) | aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~(sdtlpdtrp0(xe, W0) = xp)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[8])).
% 0.19/0.47 tff(10,plain,
% 0.19/0.47 (^[W0: $i] : trans(monotonicity(trans(monotonicity(rewrite(((aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | aElementOf0(W0, sdtlbdtrb0(xd, 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(xe, W0) = xp)) <=> (((~((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd))))) | aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W0) = xp)))), rewrite((((~((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd))))) | aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W0) = xp)) <=> (~((~((~((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd))))) | aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~(sdtlpdtrp0(xe, W0) = xp))))), ((((aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W0) = xp)) <=> (~((~((~((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd))))) | aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~(sdtlpdtrp0(xe, W0) = xp)))))), ((~(((aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W0) = xp))) <=> (~(~((~((~((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd))))) | aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~(sdtlpdtrp0(xe, W0) = xp))))))), rewrite((~(~((~((~((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd))))) | aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~(sdtlpdtrp0(xe, W0) = xp))))) <=> ((~((~((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd))))) | aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~(sdtlpdtrp0(xe, W0) = xp)))), ((~(((aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W0) = xp))) <=> ((~((~((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd))))) | aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~(sdtlpdtrp0(xe, W0) = xp)))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(11,plain,
% 0.19/0.47 (![W0: $i] : (~(((aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W0) = xp))) <=> ![W0: $i] : ((~((~((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd))))) | aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~(sdtlpdtrp0(xe, W0) = xp)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[10])).
% 0.19/0.47 tff(12,plain,
% 0.19/0.47 ((~?[W0: $i] : (((aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W0) = xp))) <=> (~?[W0: $i] : (((aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W0) = xp)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(13,axiom,(~?[W0: $i] : (((aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W0) = xp))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 0.19/0.47 tff(14,plain,
% 0.19/0.47 (~?[W0: $i] : (((aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W0) = xp))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.19/0.47 tff(15,plain,
% 0.19/0.47 (~?[W0: $i] : (((aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W0) = xp))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[14, 12])).
% 0.19/0.47 tff(16,plain,
% 0.19/0.47 (~?[W0: $i] : (((aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W0) = xp))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.19/0.47 tff(17,plain,
% 0.19/0.47 (~?[W0: $i] : (((aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W0) = xp))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.19/0.47 tff(18,plain,
% 0.19/0.47 (^[W0: $i] : refl($oeq((~(((aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W0) = xp))), (~(((aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W0) = xp)))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(19,plain,(
% 0.19/0.47 ![W0: $i] : (~(((aElementOf0(W0, szDzozmdt0(xd)) & (sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd)))) & (sdtlpdtrp0(xe, W0) = xp)))),
% 0.19/0.47 inference(nnf-neg,[status(sab)],[17, 18])).
% 0.19/0.47 tff(20,plain,
% 0.19/0.47 (![W0: $i] : ((~((~((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd))))) | aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~(sdtlpdtrp0(xe, W0) = xp)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[19, 11])).
% 0.19/0.47 tff(21,plain,
% 0.19/0.47 (![W0: $i] : ((~((~((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd))))) | aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~(sdtlpdtrp0(xe, W0) = xp)))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[20, 9])).
% 0.19/0.48 tff(22,plain,
% 0.19/0.48 (sdtlpdtrp0(xe, W0!44) = xp),
% 0.19/0.48 inference(and_elim,[status(thm)],[4])).
% 0.19/0.48 tff(23,plain,
% 0.19/0.48 (((~![W0: $i] : ((~((~((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd))))) | aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~(sdtlpdtrp0(xe, W0) = xp)))) | ((~((~((~(sdtlpdtrp0(xd, W0!44) = szDzizrdt0(xd))) | (~aElementOf0(W0!44, szDzozmdt0(xd))))) | aElementOf0(W0!44, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~(sdtlpdtrp0(xe, W0!44) = xp)))) <=> ((~![W0: $i] : ((~((~((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd))))) | aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~(sdtlpdtrp0(xe, W0) = xp)))) | (~((~((~(sdtlpdtrp0(xd, W0!44) = szDzizrdt0(xd))) | (~aElementOf0(W0!44, szDzozmdt0(xd))))) | aElementOf0(W0!44, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~(sdtlpdtrp0(xe, W0!44) = xp)))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(24,plain,
% 0.19/0.48 ((~![W0: $i] : ((~((~((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd))))) | aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~(sdtlpdtrp0(xe, W0) = xp)))) | ((~((~((~(sdtlpdtrp0(xd, W0!44) = szDzizrdt0(xd))) | (~aElementOf0(W0!44, szDzozmdt0(xd))))) | aElementOf0(W0!44, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~(sdtlpdtrp0(xe, W0!44) = xp)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(25,plain,
% 0.19/0.48 ((~![W0: $i] : ((~((~((~(sdtlpdtrp0(xd, W0) = szDzizrdt0(xd))) | (~aElementOf0(W0, szDzozmdt0(xd))))) | aElementOf0(W0, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~(sdtlpdtrp0(xe, W0) = xp)))) | (~((~((~(sdtlpdtrp0(xd, W0!44) = szDzizrdt0(xd))) | (~aElementOf0(W0!44, szDzozmdt0(xd))))) | aElementOf0(W0!44, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | (~(sdtlpdtrp0(xe, W0!44) = xp))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.19/0.48 tff(26,plain,
% 0.19/0.48 ($false),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[25, 22, 21, 7])).
% 0.19/0.48 % SZS output end Proof
% 0.19/0.48 % E exiting
%------------------------------------------------------------------------------