%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM565+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:21:25 AM UTC 2025
% Result : Theorem 0.19s 0.42s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM565+3 : TPTP v9.0.0. Released v4.0.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n005.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 01:26:50 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.42 % SZS status Theorem
% 0.19/0.42 % SZS output start Proof
% 0.19/0.42 tff(sdtlpdtrp0_type, type, (
% 0.19/0.42 sdtlpdtrp0: ( $i * $i ) > $i)).
% 0.19/0.42 tff(slcrc0_type, type, (
% 0.19/0.42 slcrc0: $i)).
% 0.19/0.42 tff(xc_type, type, (
% 0.19/0.42 xc: $i)).
% 0.19/0.42 tff(tptp_fun_W0_29_type, type, (
% 0.19/0.42 tptp_fun_W0_29: $i)).
% 0.19/0.42 tff(sz00_type, type, (
% 0.19/0.42 sz00: $i)).
% 0.19/0.42 tff(sbrdtbr0_type, type, (
% 0.19/0.42 sbrdtbr0: $i > $i)).
% 0.19/0.42 tff(aSet0_type, type, (
% 0.19/0.42 aSet0: $i > $o)).
% 0.19/0.42 tff(aElementOf0_type, type, (
% 0.19/0.42 aElementOf0: ( $i * $i ) > $o)).
% 0.19/0.42 tff(slbdtsldtrb0_type, type, (
% 0.19/0.42 slbdtsldtrb0: ( $i * $i ) > $i)).
% 0.19/0.42 tff(xS_type, type, (
% 0.19/0.42 xS: $i)).
% 0.19/0.42 tff(aSubsetOf0_type, type, (
% 0.19/0.42 aSubsetOf0: ( $i * $i ) > $o)).
% 0.19/0.42 tff(1,plain,
% 0.19/0.42 (((~(sdtlpdtrp0(xc, W0!29) = sdtlpdtrp0(xc, slcrc0))) & (aSet0(slcrc0) & ![W1: $i] : (~aElementOf0(W1, slcrc0))) & (aSet0(W0!29) & ![W1: $i] : ((~aElementOf0(W1, W0!29)) | aElementOf0(W1, xS)) & aSubsetOf0(W0!29, xS) & (sbrdtbr0(W0!29) = sz00) & aElementOf0(W0!29, slbdtsldtrb0(xS, sz00)))) <=> ((~(sdtlpdtrp0(xc, W0!29) = sdtlpdtrp0(xc, slcrc0))) & aSet0(slcrc0) & ![W1: $i] : (~aElementOf0(W1, slcrc0)) & aSet0(W0!29) & ![W1: $i] : ((~aElementOf0(W1, W0!29)) | aElementOf0(W1, xS)) & aSubsetOf0(W0!29, xS) & (sbrdtbr0(W0!29) = sz00) & aElementOf0(W0!29, slbdtsldtrb0(xS, sz00)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(2,plain,
% 0.19/0.42 ((aSet0(W0!29) & ![W1: $i] : ((~aElementOf0(W1, W0!29)) | aElementOf0(W1, xS)) & aSubsetOf0(W0!29, xS) & (sbrdtbr0(W0!29) = sz00) & aElementOf0(W0!29, slbdtsldtrb0(xS, sz00))) <=> (aSet0(W0!29) & ![W1: $i] : ((~aElementOf0(W1, W0!29)) | aElementOf0(W1, xS)) & aSubsetOf0(W0!29, xS) & (sbrdtbr0(W0!29) = sz00) & aElementOf0(W0!29, slbdtsldtrb0(xS, sz00)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(3,plain,
% 0.19/0.42 ((aSet0(slcrc0) & ![W1: $i] : (~aElementOf0(W1, slcrc0))) <=> (aSet0(slcrc0) & ![W1: $i] : (~aElementOf0(W1, slcrc0)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(4,plain,
% 0.19/0.42 (((~(sdtlpdtrp0(xc, W0!29) = sdtlpdtrp0(xc, slcrc0))) & (aSet0(slcrc0) & ![W1: $i] : (~aElementOf0(W1, slcrc0))) & (aSet0(W0!29) & ![W1: $i] : ((~aElementOf0(W1, W0!29)) | aElementOf0(W1, xS)) & aSubsetOf0(W0!29, xS) & (sbrdtbr0(W0!29) = sz00) & aElementOf0(W0!29, slbdtsldtrb0(xS, sz00)))) <=> ((~(sdtlpdtrp0(xc, W0!29) = sdtlpdtrp0(xc, slcrc0))) & (aSet0(slcrc0) & ![W1: $i] : (~aElementOf0(W1, slcrc0))) & (aSet0(W0!29) & ![W1: $i] : ((~aElementOf0(W1, W0!29)) | aElementOf0(W1, xS)) & aSubsetOf0(W0!29, xS) & (sbrdtbr0(W0!29) = sz00) & aElementOf0(W0!29, slbdtsldtrb0(xS, sz00))))),
% 0.19/0.42 inference(monotonicity,[status(thm)],[3, 2])).
% 0.19/0.42 tff(5,plain,
% 0.19/0.42 (((~(sdtlpdtrp0(xc, W0!29) = sdtlpdtrp0(xc, slcrc0))) & (aSet0(slcrc0) & ![W1: $i] : (~aElementOf0(W1, slcrc0))) & (aSet0(W0!29) & ![W1: $i] : ((~aElementOf0(W1, W0!29)) | aElementOf0(W1, xS)) & aSubsetOf0(W0!29, xS) & (sbrdtbr0(W0!29) = sz00) & aElementOf0(W0!29, slbdtsldtrb0(xS, sz00)))) <=> ((~(sdtlpdtrp0(xc, W0!29) = sdtlpdtrp0(xc, slcrc0))) & aSet0(slcrc0) & ![W1: $i] : (~aElementOf0(W1, slcrc0)) & aSet0(W0!29) & ![W1: $i] : ((~aElementOf0(W1, W0!29)) | aElementOf0(W1, xS)) & aSubsetOf0(W0!29, xS) & (sbrdtbr0(W0!29) = sz00) & aElementOf0(W0!29, slbdtsldtrb0(xS, sz00)))),
% 0.19/0.42 inference(transitivity,[status(thm)],[4, 1])).
% 0.19/0.42 tff(6,plain,
% 0.19/0.42 ((~![W0: $i] : ((sdtlpdtrp0(xc, W0) = sdtlpdtrp0(xc, slcrc0)) | (~(aSet0(slcrc0) & (~?[W1: $i] : aElementOf0(W1, slcrc0)))) | (~(aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)) & aSubsetOf0(W0, xS) & (sbrdtbr0(W0) = sz00) & aElementOf0(W0, slbdtsldtrb0(xS, sz00)))))) <=> (~![W0: $i] : ((sdtlpdtrp0(xc, W0) = sdtlpdtrp0(xc, slcrc0)) | (~(aSet0(slcrc0) & (~?[W1: $i] : aElementOf0(W1, slcrc0)))) | (~(aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)) & aSubsetOf0(W0, xS) & (sbrdtbr0(W0) = sz00) & aElementOf0(W0, slbdtsldtrb0(xS, sz00))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(7,plain,
% 0.19/0.42 ((~![W0: $i] : (((((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xS))) & aSubsetOf0(W0, xS)) & (sbrdtbr0(W0) = sz00)) & aElementOf0(W0, slbdtsldtrb0(xS, sz00))) => ((aSet0(slcrc0) & (~?[W1: $i] : aElementOf0(W1, slcrc0))) => (sdtlpdtrp0(xc, W0) = sdtlpdtrp0(xc, slcrc0))))) <=> (~![W0: $i] : ((sdtlpdtrp0(xc, W0) = sdtlpdtrp0(xc, slcrc0)) | (~(aSet0(slcrc0) & (~?[W1: $i] : aElementOf0(W1, slcrc0)))) | (~(aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)) & aSubsetOf0(W0, xS) & (sbrdtbr0(W0) = sz00) & aElementOf0(W0, slbdtsldtrb0(xS, sz00))))))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(8,axiom,(~![W0: $i] : (((((aSet0(W0) & ![W1: $i] : (aElementOf0(W1, W0) => aElementOf0(W1, xS))) & aSubsetOf0(W0, xS)) & (sbrdtbr0(W0) = sz00)) & aElementOf0(W0, slbdtsldtrb0(xS, sz00))) => ((aSet0(slcrc0) & (~?[W1: $i] : aElementOf0(W1, slcrc0))) => (sdtlpdtrp0(xc, W0) = sdtlpdtrp0(xc, slcrc0))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__')).
% 0.19/0.42 tff(9,plain,
% 0.19/0.42 (~![W0: $i] : ((sdtlpdtrp0(xc, W0) = sdtlpdtrp0(xc, slcrc0)) | (~(aSet0(slcrc0) & (~?[W1: $i] : aElementOf0(W1, slcrc0)))) | (~(aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)) & aSubsetOf0(W0, xS) & (sbrdtbr0(W0) = sz00) & aElementOf0(W0, slbdtsldtrb0(xS, sz00)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.19/0.42 tff(10,plain,
% 0.19/0.42 (~![W0: $i] : ((sdtlpdtrp0(xc, W0) = sdtlpdtrp0(xc, slcrc0)) | (~(aSet0(slcrc0) & (~?[W1: $i] : aElementOf0(W1, slcrc0)))) | (~(aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)) & aSubsetOf0(W0, xS) & (sbrdtbr0(W0) = sz00) & aElementOf0(W0, slbdtsldtrb0(xS, sz00)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[9, 6])).
% 0.19/0.42 tff(11,plain,
% 0.19/0.42 (~![W0: $i] : ((sdtlpdtrp0(xc, W0) = sdtlpdtrp0(xc, slcrc0)) | (~(aSet0(slcrc0) & (~?[W1: $i] : aElementOf0(W1, slcrc0)))) | (~(aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)) & aSubsetOf0(W0, xS) & (sbrdtbr0(W0) = sz00) & aElementOf0(W0, slbdtsldtrb0(xS, sz00)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[10, 6])).
% 0.19/0.42 tff(12,plain,
% 0.19/0.42 (~![W0: $i] : ((sdtlpdtrp0(xc, W0) = sdtlpdtrp0(xc, slcrc0)) | (~(aSet0(slcrc0) & (~?[W1: $i] : aElementOf0(W1, slcrc0)))) | (~(aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)) & aSubsetOf0(W0, xS) & (sbrdtbr0(W0) = sz00) & aElementOf0(W0, slbdtsldtrb0(xS, sz00)))))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[11, 6])).
% 0.19/0.42 tff(13,plain,
% 0.19/0.42 ((~(sdtlpdtrp0(xc, W0!29) = sdtlpdtrp0(xc, slcrc0))) & aSet0(slcrc0) & ![W1: $i] : (~aElementOf0(W1, slcrc0)) & aSet0(W0!29) & ![W1: $i] : ((~aElementOf0(W1, W0!29)) | aElementOf0(W1, xS)) & aSubsetOf0(W0!29, xS) & (sbrdtbr0(W0!29) = sz00) & aElementOf0(W0!29, slbdtsldtrb0(xS, sz00))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[12, 5])).
% 0.19/0.42 tff(14,plain,
% 0.19/0.42 (aSet0(W0!29)),
% 0.19/0.42 inference(and_elim,[status(thm)],[13])).
% 0.19/0.42 tff(15,plain,
% 0.19/0.42 (^[W0: $i] : refl(((~aSet0(W0)) | ((sbrdtbr0(W0) = sz00) <=> (W0 = slcrc0))) <=> ((~aSet0(W0)) | ((sbrdtbr0(W0) = sz00) <=> (W0 = slcrc0))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(16,plain,
% 0.19/0.42 (![W0: $i] : ((~aSet0(W0)) | ((sbrdtbr0(W0) = sz00) <=> (W0 = slcrc0))) <=> ![W0: $i] : ((~aSet0(W0)) | ((sbrdtbr0(W0) = sz00) <=> (W0 = slcrc0)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[15])).
% 0.19/0.42 tff(17,plain,
% 0.19/0.42 (![W0: $i] : ((~aSet0(W0)) | ((sbrdtbr0(W0) = sz00) <=> (W0 = slcrc0))) <=> ![W0: $i] : ((~aSet0(W0)) | ((sbrdtbr0(W0) = sz00) <=> (W0 = slcrc0)))),
% 0.19/0.42 inference(rewrite,[status(thm)],[])).
% 0.19/0.42 tff(18,plain,
% 0.19/0.42 (^[W0: $i] : rewrite((aSet0(W0) => ((sbrdtbr0(W0) = sz00) <=> (W0 = slcrc0))) <=> ((~aSet0(W0)) | ((sbrdtbr0(W0) = sz00) <=> (W0 = slcrc0))))),
% 0.19/0.42 inference(bind,[status(th)],[])).
% 0.19/0.42 tff(19,plain,
% 0.19/0.42 (![W0: $i] : (aSet0(W0) => ((sbrdtbr0(W0) = sz00) <=> (W0 = slcrc0))) <=> ![W0: $i] : ((~aSet0(W0)) | ((sbrdtbr0(W0) = sz00) <=> (W0 = slcrc0)))),
% 0.19/0.42 inference(quant_intro,[status(thm)],[18])).
% 0.19/0.42 tff(20,axiom,(![W0: $i] : (aSet0(W0) => ((sbrdtbr0(W0) = sz00) <=> (W0 = slcrc0)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mCardEmpty')).
% 0.19/0.42 tff(21,plain,
% 0.19/0.42 (![W0: $i] : ((~aSet0(W0)) | ((sbrdtbr0(W0) = sz00) <=> (W0 = slcrc0)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.19/0.42 tff(22,plain,
% 0.19/0.42 (![W0: $i] : ((~aSet0(W0)) | ((sbrdtbr0(W0) = sz00) <=> (W0 = slcrc0)))),
% 0.19/0.42 inference(modus_ponens,[status(thm)],[21, 17])).
% 0.19/0.42 tff(23,plain,(
% 0.19/0.43 ![W0: $i] : ((~aSet0(W0)) | ((sbrdtbr0(W0) = sz00) <=> (W0 = slcrc0)))),
% 0.19/0.43 inference(skolemize,[status(sab)],[22])).
% 0.19/0.43 tff(24,plain,
% 0.19/0.43 (![W0: $i] : ((~aSet0(W0)) | ((sbrdtbr0(W0) = sz00) <=> (W0 = slcrc0)))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[23, 16])).
% 0.19/0.43 tff(25,plain,
% 0.19/0.43 (((~![W0: $i] : ((~aSet0(W0)) | ((sbrdtbr0(W0) = sz00) <=> (W0 = slcrc0)))) | ((~aSet0(W0!29)) | ((sbrdtbr0(W0!29) = sz00) <=> (W0!29 = slcrc0)))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ((sbrdtbr0(W0) = sz00) <=> (W0 = slcrc0)))) | (~aSet0(W0!29)) | ((sbrdtbr0(W0!29) = sz00) <=> (W0!29 = slcrc0)))),
% 0.19/0.43 inference(rewrite,[status(thm)],[])).
% 0.19/0.43 tff(26,plain,
% 0.19/0.43 ((~![W0: $i] : ((~aSet0(W0)) | ((sbrdtbr0(W0) = sz00) <=> (W0 = slcrc0)))) | ((~aSet0(W0!29)) | ((sbrdtbr0(W0!29) = sz00) <=> (W0!29 = slcrc0)))),
% 0.19/0.43 inference(quant_inst,[status(thm)],[])).
% 0.19/0.43 tff(27,plain,
% 0.19/0.43 ((~![W0: $i] : ((~aSet0(W0)) | ((sbrdtbr0(W0) = sz00) <=> (W0 = slcrc0)))) | (~aSet0(W0!29)) | ((sbrdtbr0(W0!29) = sz00) <=> (W0!29 = slcrc0))),
% 0.19/0.43 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.19/0.43 tff(28,plain,
% 0.19/0.43 ((sbrdtbr0(W0!29) = sz00) <=> (W0!29 = slcrc0)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[27, 24, 14])).
% 0.19/0.43 tff(29,plain,
% 0.19/0.43 (sbrdtbr0(W0!29) = sz00),
% 0.19/0.43 inference(and_elim,[status(thm)],[13])).
% 0.19/0.43 tff(30,plain,
% 0.19/0.43 ((~((sbrdtbr0(W0!29) = sz00) <=> (W0!29 = slcrc0))) | (~(sbrdtbr0(W0!29) = sz00)) | (W0!29 = slcrc0)),
% 0.19/0.43 inference(tautology,[status(thm)],[])).
% 0.19/0.43 tff(31,plain,
% 0.19/0.43 ((~((sbrdtbr0(W0!29) = sz00) <=> (W0!29 = slcrc0))) | (W0!29 = slcrc0)),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.19/0.43 tff(32,plain,
% 0.19/0.43 (W0!29 = slcrc0),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[31, 28])).
% 0.19/0.43 tff(33,plain,
% 0.19/0.43 (sdtlpdtrp0(xc, W0!29) = sdtlpdtrp0(xc, slcrc0)),
% 0.19/0.43 inference(monotonicity,[status(thm)],[32])).
% 0.19/0.43 tff(34,plain,
% 0.19/0.43 (~(sdtlpdtrp0(xc, W0!29) = sdtlpdtrp0(xc, slcrc0))),
% 0.19/0.43 inference(and_elim,[status(thm)],[13])).
% 0.19/0.43 tff(35,plain,
% 0.19/0.43 ($false),
% 0.19/0.43 inference(unit_resolution,[status(thm)],[34, 33])).
% 0.19/0.43 % SZS output end Proof
% 0.19/0.43 % E exiting
%------------------------------------------------------------------------------