%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM560+2 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:21:24 AM UTC 2025
% Result : Theorem 0.22s 0.43s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : NUM560+2 : TPTP v9.0.0. Released v4.0.0.
% 0.04/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n012.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 01:25:56 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.22/0.43 % SZS status Theorem
% 0.22/0.43 % SZS output start Proof
% 0.22/0.43 tff(aElementOf0_type, type, (
% 0.22/0.43 aElementOf0: ( $i * $i ) > $o)).
% 0.22/0.43 tff(sdtlbdtrb0_type, type, (
% 0.22/0.43 sdtlbdtrb0: ( $i * $i ) > $i)).
% 0.22/0.43 tff(xy_type, type, (
% 0.22/0.43 xy: $i)).
% 0.22/0.43 tff(xF_type, type, (
% 0.22/0.43 xF: $i)).
% 0.22/0.43 tff(tptp_fun_W0_13_type, type, (
% 0.22/0.43 tptp_fun_W0_13: $i)).
% 0.22/0.43 tff(sdtlpdtrp0_type, type, (
% 0.22/0.43 sdtlpdtrp0: ( $i * $i ) > $i)).
% 0.22/0.43 tff(szDzozmdt0_type, type, (
% 0.22/0.43 szDzozmdt0: $i > $i)).
% 0.22/0.43 tff(aSet0_type, type, (
% 0.22/0.43 aSet0: $i > $o)).
% 0.22/0.43 tff(aSubsetOf0_type, type, (
% 0.22/0.43 aSubsetOf0: ( $i * $i ) > $o)).
% 0.22/0.43 tff(1,plain,
% 0.22/0.43 ((~![W0: $i] : ((~aElementOf0(W0, sdtlbdtrb0(xF, xy))) | aElementOf0(W0, szDzozmdt0(xF)))) <=> (~![W0: $i] : ((~aElementOf0(W0, sdtlbdtrb0(xF, xy))) | aElementOf0(W0, szDzozmdt0(xF))))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(2,plain,
% 0.22/0.43 ((~((aSet0(sdtlbdtrb0(xF, xy)) & ![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xF, xy)) <=> (aElementOf0(W0, szDzozmdt0(xF)) & (sdtlpdtrp0(xF, W0) = xy)))) => (![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xF, xy)) => aElementOf0(W0, szDzozmdt0(xF))) | aSubsetOf0(sdtlbdtrb0(xF, xy), szDzozmdt0(xF))))) <=> (~(aSubsetOf0(sdtlbdtrb0(xF, xy), szDzozmdt0(xF)) | ![W0: $i] : ((~aElementOf0(W0, sdtlbdtrb0(xF, xy))) | aElementOf0(W0, szDzozmdt0(xF))) | (~(aSet0(sdtlbdtrb0(xF, xy)) & ![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xF, xy)) <=> (aElementOf0(W0, szDzozmdt0(xF)) & (sdtlpdtrp0(xF, W0) = xy)))))))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(3,axiom,(~((aSet0(sdtlbdtrb0(xF, xy)) & ![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xF, xy)) <=> (aElementOf0(W0, szDzozmdt0(xF)) & (sdtlpdtrp0(xF, W0) = xy)))) => (![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xF, xy)) => aElementOf0(W0, szDzozmdt0(xF))) | aSubsetOf0(sdtlbdtrb0(xF, xy), szDzozmdt0(xF))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__')).
% 0.22/0.43 tff(4,plain,
% 0.22/0.43 (~(aSubsetOf0(sdtlbdtrb0(xF, xy), szDzozmdt0(xF)) | ![W0: $i] : ((~aElementOf0(W0, sdtlbdtrb0(xF, xy))) | aElementOf0(W0, szDzozmdt0(xF))) | (~(aSet0(sdtlbdtrb0(xF, xy)) & ![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xF, xy)) <=> (aElementOf0(W0, szDzozmdt0(xF)) & (sdtlpdtrp0(xF, W0) = xy))))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.22/0.43 tff(5,plain,
% 0.22/0.43 (~![W0: $i] : ((~aElementOf0(W0, sdtlbdtrb0(xF, xy))) | aElementOf0(W0, szDzozmdt0(xF)))),
% 0.22/0.43 inference(or_elim,[status(thm)],[4])).
% 0.22/0.43 tff(6,plain,
% 0.22/0.43 (~![W0: $i] : ((~aElementOf0(W0, sdtlbdtrb0(xF, xy))) | aElementOf0(W0, szDzozmdt0(xF)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.22/0.43 tff(7,plain,
% 0.22/0.43 (~![W0: $i] : ((~aElementOf0(W0, sdtlbdtrb0(xF, xy))) | aElementOf0(W0, szDzozmdt0(xF)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.22/0.43 tff(8,plain,
% 0.22/0.43 (~![W0: $i] : ((~aElementOf0(W0, sdtlbdtrb0(xF, xy))) | aElementOf0(W0, szDzozmdt0(xF)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.22/0.43 tff(9,plain,(
% 0.22/0.43 ~((~aElementOf0(W0!13, sdtlbdtrb0(xF, xy))) | aElementOf0(W0!13, szDzozmdt0(xF)))),
% 0.22/0.43 inference(skolemize,[status(sab)],[8])).
% 0.22/0.43 tff(10,plain,
% 0.22/0.43 (~aElementOf0(W0!13, szDzozmdt0(xF))),
% 0.22/0.43 inference(or_elim,[status(thm)],[9])).
% 0.22/0.43 tff(11,plain,
% 0.22/0.43 (((~aElementOf0(W0!13, szDzozmdt0(xF))) | (~(sdtlpdtrp0(xF, W0!13) = xy))) | aElementOf0(W0!13, szDzozmdt0(xF))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(12,plain,
% 0.22/0.43 ((~aElementOf0(W0!13, szDzozmdt0(xF))) | (~(sdtlpdtrp0(xF, W0!13) = xy))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.22/0.43 tff(13,plain,
% 0.22/0.43 (aElementOf0(W0!13, sdtlbdtrb0(xF, xy))),
% 0.22/0.43 inference(or_elim,[status(thm)],[9])).
% 0.22/0.43 tff(14,plain,
% 0.22/0.43 ((((~aElementOf0(W0!13, szDzozmdt0(xF))) | (~(sdtlpdtrp0(xF, W0!13) = xy))) <=> aElementOf0(W0!13, sdtlbdtrb0(xF, xy))) | (~((~aElementOf0(W0!13, szDzozmdt0(xF))) | (~(sdtlpdtrp0(xF, W0!13) = xy)))) | (~aElementOf0(W0!13, sdtlbdtrb0(xF, xy)))),
% 0.22/0.43 inference(tautology,[status(thm)],[])).
% 0.22/0.43 tff(15,plain,
% 0.22/0.43 (((~aElementOf0(W0!13, szDzozmdt0(xF))) | (~(sdtlpdtrp0(xF, W0!13) = xy))) <=> aElementOf0(W0!13, sdtlbdtrb0(xF, xy))),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[14, 13, 12])).
% 0.22/0.43 tff(16,plain,
% 0.22/0.43 (^[W0: $i] : refl((~(((~aElementOf0(W0, szDzozmdt0(xF))) | (~(sdtlpdtrp0(xF, W0) = xy))) <=> aElementOf0(W0, sdtlbdtrb0(xF, xy)))) <=> (~(((~aElementOf0(W0, szDzozmdt0(xF))) | (~(sdtlpdtrp0(xF, W0) = xy))) <=> aElementOf0(W0, sdtlbdtrb0(xF, xy)))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(17,plain,
% 0.22/0.43 (![W0: $i] : (~(((~aElementOf0(W0, szDzozmdt0(xF))) | (~(sdtlpdtrp0(xF, W0) = xy))) <=> aElementOf0(W0, sdtlbdtrb0(xF, xy)))) <=> ![W0: $i] : (~(((~aElementOf0(W0, szDzozmdt0(xF))) | (~(sdtlpdtrp0(xF, W0) = xy))) <=> aElementOf0(W0, sdtlbdtrb0(xF, xy))))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[16])).
% 0.22/0.43 tff(18,plain,
% 0.22/0.43 (^[W0: $i] : trans(trans(monotonicity(rewrite((aElementOf0(W0, szDzozmdt0(xF)) & (sdtlpdtrp0(xF, W0) = xy)) <=> (~((~aElementOf0(W0, szDzozmdt0(xF))) | (~(sdtlpdtrp0(xF, W0) = xy))))), ((aElementOf0(W0, sdtlbdtrb0(xF, xy)) <=> (aElementOf0(W0, szDzozmdt0(xF)) & (sdtlpdtrp0(xF, W0) = xy))) <=> (aElementOf0(W0, sdtlbdtrb0(xF, xy)) <=> (~((~aElementOf0(W0, szDzozmdt0(xF))) | (~(sdtlpdtrp0(xF, W0) = xy))))))), rewrite((aElementOf0(W0, sdtlbdtrb0(xF, xy)) <=> (~((~aElementOf0(W0, szDzozmdt0(xF))) | (~(sdtlpdtrp0(xF, W0) = xy))))) <=> (~(((~aElementOf0(W0, szDzozmdt0(xF))) | (~(sdtlpdtrp0(xF, W0) = xy))) <=> aElementOf0(W0, sdtlbdtrb0(xF, xy))))), ((aElementOf0(W0, sdtlbdtrb0(xF, xy)) <=> (aElementOf0(W0, szDzozmdt0(xF)) & (sdtlpdtrp0(xF, W0) = xy))) <=> (~(((~aElementOf0(W0, szDzozmdt0(xF))) | (~(sdtlpdtrp0(xF, W0) = xy))) <=> aElementOf0(W0, sdtlbdtrb0(xF, xy)))))), rewrite((~(((~aElementOf0(W0, szDzozmdt0(xF))) | (~(sdtlpdtrp0(xF, W0) = xy))) <=> aElementOf0(W0, sdtlbdtrb0(xF, xy)))) <=> (~(((~aElementOf0(W0, szDzozmdt0(xF))) | (~(sdtlpdtrp0(xF, W0) = xy))) <=> aElementOf0(W0, sdtlbdtrb0(xF, xy))))), ((aElementOf0(W0, sdtlbdtrb0(xF, xy)) <=> (aElementOf0(W0, szDzozmdt0(xF)) & (sdtlpdtrp0(xF, W0) = xy))) <=> (~(((~aElementOf0(W0, szDzozmdt0(xF))) | (~(sdtlpdtrp0(xF, W0) = xy))) <=> aElementOf0(W0, sdtlbdtrb0(xF, xy))))))),
% 0.22/0.43 inference(bind,[status(th)],[])).
% 0.22/0.43 tff(19,plain,
% 0.22/0.43 (![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xF, xy)) <=> (aElementOf0(W0, szDzozmdt0(xF)) & (sdtlpdtrp0(xF, W0) = xy))) <=> ![W0: $i] : (~(((~aElementOf0(W0, szDzozmdt0(xF))) | (~(sdtlpdtrp0(xF, W0) = xy))) <=> aElementOf0(W0, sdtlbdtrb0(xF, xy))))),
% 0.22/0.43 inference(quant_intro,[status(thm)],[18])).
% 0.22/0.43 tff(20,plain,
% 0.22/0.43 (![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xF, xy)) <=> (aElementOf0(W0, szDzozmdt0(xF)) & (sdtlpdtrp0(xF, W0) = xy))) <=> ![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xF, xy)) <=> (aElementOf0(W0, szDzozmdt0(xF)) & (sdtlpdtrp0(xF, W0) = xy)))),
% 0.22/0.43 inference(rewrite,[status(thm)],[])).
% 0.22/0.43 tff(21,plain,
% 0.22/0.43 (aSet0(sdtlbdtrb0(xF, xy)) & ![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xF, xy)) <=> (aElementOf0(W0, szDzozmdt0(xF)) & (sdtlpdtrp0(xF, W0) = xy)))),
% 0.22/0.43 inference(or_elim,[status(thm)],[4])).
% 0.22/0.43 tff(22,plain,
% 0.22/0.43 (![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xF, xy)) <=> (aElementOf0(W0, szDzozmdt0(xF)) & (sdtlpdtrp0(xF, W0) = xy)))),
% 0.22/0.43 inference(and_elim,[status(thm)],[21])).
% 0.22/0.43 tff(23,plain,
% 0.22/0.43 (![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xF, xy)) <=> (aElementOf0(W0, szDzozmdt0(xF)) & (sdtlpdtrp0(xF, W0) = xy)))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[22, 20])).
% 0.22/0.43 tff(24,plain,(
% 0.22/0.43 ![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xF, xy)) <=> (aElementOf0(W0, szDzozmdt0(xF)) & (sdtlpdtrp0(xF, W0) = xy)))),
% 0.22/0.43 inference(skolemize,[status(sab)],[23])).
% 0.22/0.43 tff(25,plain,
% 0.22/0.43 (![W0: $i] : (~(((~aElementOf0(W0, szDzozmdt0(xF))) | (~(sdtlpdtrp0(xF, W0) = xy))) <=> aElementOf0(W0, sdtlbdtrb0(xF, xy))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[24, 19])).
% 0.22/0.43 tff(26,plain,
% 0.22/0.43 (![W0: $i] : (~(((~aElementOf0(W0, szDzozmdt0(xF))) | (~(sdtlpdtrp0(xF, W0) = xy))) <=> aElementOf0(W0, sdtlbdtrb0(xF, xy))))),
% 0.22/0.43 inference(modus_ponens,[status(thm)],[25, 17])).
% 0.22/0.43 tff(27,plain,
% 0.22/0.43 ((~![W0: $i] : (~(((~aElementOf0(W0, szDzozmdt0(xF))) | (~(sdtlpdtrp0(xF, W0) = xy))) <=> aElementOf0(W0, sdtlbdtrb0(xF, xy))))) | (~(((~aElementOf0(W0!13, szDzozmdt0(xF))) | (~(sdtlpdtrp0(xF, W0!13) = xy))) <=> aElementOf0(W0!13, sdtlbdtrb0(xF, xy))))),
% 0.22/0.43 inference(quant_inst,[status(thm)],[])).
% 0.22/0.43 tff(28,plain,
% 0.22/0.43 ($false),
% 0.22/0.43 inference(unit_resolution,[status(thm)],[27, 26, 15])).
% 0.22/0.43 % SZS output end Proof
% 0.22/0.44 % E exiting
%------------------------------------------------------------------------------