TSTP Solution File: NUM606+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM606+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% 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 : Sun Sep 18 13:10:51 EDT 2022
% Result : Theorem 0.81s 0.81s
% Output : Proof 0.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : NUM606+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n005.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Sep 2 12:18:03 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36 Usage: tptp [options] [-file:]file
% 0.14/0.36 -h, -? prints this message.
% 0.14/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.36 -m, -model generate model.
% 0.14/0.36 -p, -proof generate proof.
% 0.14/0.36 -c, -core generate unsat core of named formulas.
% 0.14/0.36 -st, -statistics display statistics.
% 0.14/0.36 -t:timeout set timeout (in second).
% 0.14/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36 -<param>:<value> configuration parameter and value.
% 0.14/0.36 -o:<output-file> file to place output in.
% 0.81/0.81 % SZS status Theorem
% 0.81/0.81 % SZS output start Proof
% 0.81/0.81 tff(aElementOf0_type, type, (
% 0.81/0.81 aElementOf0: ( $i * $i ) > $o)).
% 0.81/0.81 tff(sdtlpdtrp0_type, type, (
% 0.81/0.81 sdtlpdtrp0: ( $i * $i ) > $i)).
% 0.81/0.81 tff(sz00_type, type, (
% 0.81/0.81 sz00: $i)).
% 0.81/0.81 tff(xN_type, type, (
% 0.81/0.81 xN: $i)).
% 0.81/0.81 tff(tptp_fun_W0_44_type, type, (
% 0.81/0.81 tptp_fun_W0_44: $i)).
% 0.81/0.81 tff(szDzozmdt0_type, type, (
% 0.81/0.81 szDzozmdt0: $i > $i)).
% 0.81/0.81 tff(xQ_type, type, (
% 0.81/0.81 xQ: $i)).
% 0.81/0.81 tff(szNzAzT0_type, type, (
% 0.81/0.81 szNzAzT0: $i)).
% 0.81/0.81 tff(aSubsetOf0_type, type, (
% 0.81/0.81 aSubsetOf0: ( $i * $i ) > $o)).
% 0.81/0.81 tff(xS_type, type, (
% 0.81/0.81 xS: $i)).
% 0.81/0.81 tff(aSet0_type, type, (
% 0.81/0.81 aSet0: $i > $o)).
% 0.81/0.81 tff(isCountable0_type, type, (
% 0.81/0.81 isCountable0: $i > $o)).
% 0.81/0.81 tff(sdtlcdtrc0_type, type, (
% 0.81/0.81 sdtlcdtrc0: ( $i * $i ) > $i)).
% 0.81/0.81 tff(sdtlbdtrb0_type, type, (
% 0.81/0.81 sdtlbdtrb0: ( $i * $i ) > $i)).
% 0.81/0.81 tff(szDzizrdt0_type, type, (
% 0.81/0.81 szDzizrdt0: $i > $i)).
% 0.81/0.81 tff(xd_type, type, (
% 0.81/0.81 xd: $i)).
% 0.81/0.81 tff(xe_type, type, (
% 0.81/0.81 xe: $i)).
% 0.81/0.81 tff(xO_type, type, (
% 0.81/0.81 xO: $i)).
% 0.81/0.81 tff(xK_type, type, (
% 0.81/0.81 xK: $i)).
% 0.81/0.81 tff(sbrdtbr0_type, type, (
% 0.81/0.81 sbrdtbr0: $i > $i)).
% 0.81/0.81 tff(slbdtsldtrb0_type, type, (
% 0.81/0.81 slbdtsldtrb0: ( $i * $i ) > $i)).
% 0.81/0.81 tff(1,plain,
% 0.81/0.81 ((~![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, szDzozmdt0(xN)))) <=> (~![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, szDzozmdt0(xN))))),
% 0.81/0.81 inference(rewrite,[status(thm)],[])).
% 0.81/0.81 tff(2,plain,
% 0.81/0.81 ((~![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, szNzAzT0))) <=> (~![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, szDzozmdt0(xN))))),
% 0.81/0.81 inference(rewrite,[status(thm)],[])).
% 0.81/0.81 tff(3,plain,
% 0.81/0.81 ((~![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, szNzAzT0))) <=> (~![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, szNzAzT0)))),
% 0.81/0.81 inference(rewrite,[status(thm)],[])).
% 0.81/0.81 tff(4,plain,
% 0.81/0.81 ((~![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, szNzAzT0))) <=> (~![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, szNzAzT0)))),
% 0.81/0.81 inference(rewrite,[status(thm)],[])).
% 0.81/0.81 tff(5,axiom,(~(![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, szNzAzT0)) | aSubsetOf0(xQ, szNzAzT0))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__')).
% 0.81/0.81 tff(6,plain,
% 0.81/0.81 (~![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, szNzAzT0))),
% 0.81/0.81 inference(or_elim,[status(thm)],[5])).
% 0.81/0.81 tff(7,plain,
% 0.81/0.81 (~![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, szNzAzT0))),
% 0.81/0.81 inference(modus_ponens,[status(thm)],[6, 4])).
% 0.81/0.81 tff(8,plain,
% 0.81/0.81 (~![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, szNzAzT0))),
% 0.81/0.81 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.81/0.81 tff(9,plain,
% 0.81/0.81 (~![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, szNzAzT0))),
% 0.81/0.81 inference(modus_ponens,[status(thm)],[8, 3])).
% 0.81/0.81 tff(10,plain,
% 0.81/0.81 (~![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, szNzAzT0))),
% 0.81/0.81 inference(modus_ponens,[status(thm)],[9, 3])).
% 0.81/0.81 tff(11,plain,
% 0.81/0.81 (~![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, szDzozmdt0(xN)))),
% 0.81/0.81 inference(modus_ponens,[status(thm)],[10, 2])).
% 0.81/0.81 tff(12,plain,
% 0.81/0.81 (~![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, szDzozmdt0(xN)))),
% 0.81/0.81 inference(modus_ponens,[status(thm)],[11, 1])).
% 0.81/0.81 tff(13,plain,
% 0.81/0.81 (~![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, szDzozmdt0(xN)))),
% 0.81/0.81 inference(modus_ponens,[status(thm)],[12, 1])).
% 0.81/0.81 tff(14,plain,
% 0.81/0.81 (~![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, szDzozmdt0(xN)))),
% 0.81/0.81 inference(modus_ponens,[status(thm)],[13, 1])).
% 0.81/0.81 tff(15,plain,(
% 0.81/0.81 ~((~aElementOf0(W0!44, xQ)) | aElementOf0(W0!44, szDzozmdt0(xN)))),
% 0.81/0.81 inference(skolemize,[status(sab)],[14])).
% 0.81/0.81 tff(16,plain,
% 0.81/0.81 (~aElementOf0(W0!44, szDzozmdt0(xN))),
% 0.81/0.81 inference(or_elim,[status(thm)],[15])).
% 0.81/0.81 tff(17,plain,
% 0.81/0.81 (^[W0: $i] : refl(((~aElementOf0(W0, sdtlpdtrp0(xN, sz00))) | aElementOf0(W0, szDzozmdt0(xN))) <=> ((~aElementOf0(W0, sdtlpdtrp0(xN, sz00))) | aElementOf0(W0, szDzozmdt0(xN))))),
% 0.81/0.81 inference(bind,[status(th)],[])).
% 0.81/0.81 tff(18,plain,
% 0.81/0.81 (![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, sz00))) | aElementOf0(W0, szDzozmdt0(xN))) <=> ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, sz00))) | aElementOf0(W0, szDzozmdt0(xN)))),
% 0.81/0.81 inference(quant_intro,[status(thm)],[17])).
% 0.81/0.81 tff(19,plain,
% 0.81/0.81 (^[W0: $i] : rewrite(((~aElementOf0(W0, xS)) | aElementOf0(W0, szNzAzT0)) <=> ((~aElementOf0(W0, sdtlpdtrp0(xN, sz00))) | aElementOf0(W0, szDzozmdt0(xN))))),
% 0.81/0.81 inference(bind,[status(th)],[])).
% 0.81/0.81 tff(20,plain,
% 0.81/0.81 (![W0: $i] : ((~aElementOf0(W0, xS)) | aElementOf0(W0, szNzAzT0)) <=> ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, sz00))) | aElementOf0(W0, szDzozmdt0(xN)))),
% 0.81/0.81 inference(quant_intro,[status(thm)],[19])).
% 0.81/0.81 tff(21,plain,
% 0.81/0.81 (![W0: $i] : ((~aElementOf0(W0, xS)) | aElementOf0(W0, szNzAzT0)) <=> ![W0: $i] : ((~aElementOf0(W0, xS)) | aElementOf0(W0, szNzAzT0))),
% 0.81/0.81 inference(rewrite,[status(thm)],[])).
% 0.81/0.81 tff(22,plain,
% 0.81/0.81 (^[W0: $i] : rewrite((aElementOf0(W0, xS) => aElementOf0(W0, szNzAzT0)) <=> ((~aElementOf0(W0, xS)) | aElementOf0(W0, szNzAzT0)))),
% 0.81/0.81 inference(bind,[status(th)],[])).
% 0.81/0.81 tff(23,plain,
% 0.81/0.81 (![W0: $i] : (aElementOf0(W0, xS) => aElementOf0(W0, szNzAzT0)) <=> ![W0: $i] : ((~aElementOf0(W0, xS)) | aElementOf0(W0, szNzAzT0))),
% 0.81/0.81 inference(quant_intro,[status(thm)],[22])).
% 0.81/0.81 tff(24,axiom,(((aSet0(xS) & ![W0: $i] : (aElementOf0(W0, xS) => aElementOf0(W0, szNzAzT0))) & aSubsetOf0(xS, szNzAzT0)) & isCountable0(xS)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__3435')).
% 0.81/0.81 tff(25,plain,
% 0.81/0.81 ((aSet0(xS) & ![W0: $i] : (aElementOf0(W0, xS) => aElementOf0(W0, szNzAzT0))) & aSubsetOf0(xS, szNzAzT0)),
% 0.81/0.81 inference(and_elim,[status(thm)],[24])).
% 0.81/0.81 tff(26,plain,
% 0.81/0.81 (aSet0(xS) & ![W0: $i] : (aElementOf0(W0, xS) => aElementOf0(W0, szNzAzT0))),
% 0.81/0.81 inference(and_elim,[status(thm)],[25])).
% 0.81/0.81 tff(27,plain,
% 0.81/0.81 (![W0: $i] : (aElementOf0(W0, xS) => aElementOf0(W0, szNzAzT0))),
% 0.81/0.81 inference(and_elim,[status(thm)],[26])).
% 0.81/0.81 tff(28,plain,
% 0.81/0.81 (![W0: $i] : ((~aElementOf0(W0, xS)) | aElementOf0(W0, szNzAzT0))),
% 0.81/0.81 inference(modus_ponens,[status(thm)],[27, 23])).
% 0.81/0.81 tff(29,plain,
% 0.81/0.81 (![W0: $i] : ((~aElementOf0(W0, xS)) | aElementOf0(W0, szNzAzT0))),
% 0.81/0.81 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.81/0.81 tff(30,plain,
% 0.81/0.81 (![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, sz00))) | aElementOf0(W0, szDzozmdt0(xN)))),
% 0.81/0.81 inference(modus_ponens,[status(thm)],[29, 20])).
% 0.81/0.81 tff(31,plain,(
% 0.81/0.81 ![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, sz00))) | aElementOf0(W0, szDzozmdt0(xN)))),
% 0.81/0.81 inference(skolemize,[status(sab)],[30])).
% 0.81/0.81 tff(32,plain,
% 0.81/0.81 (![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, sz00))) | aElementOf0(W0, szDzozmdt0(xN)))),
% 0.81/0.81 inference(modus_ponens,[status(thm)],[31, 18])).
% 0.81/0.81 tff(33,plain,
% 0.81/0.81 (((~![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, sz00))) | aElementOf0(W0, szDzozmdt0(xN)))) | ((~aElementOf0(W0!44, sdtlpdtrp0(xN, sz00))) | aElementOf0(W0!44, szDzozmdt0(xN)))) <=> ((~![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, sz00))) | aElementOf0(W0, szDzozmdt0(xN)))) | (~aElementOf0(W0!44, sdtlpdtrp0(xN, sz00))) | aElementOf0(W0!44, szDzozmdt0(xN)))),
% 0.81/0.81 inference(rewrite,[status(thm)],[])).
% 0.81/0.81 tff(34,plain,
% 0.81/0.81 ((~![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, sz00))) | aElementOf0(W0, szDzozmdt0(xN)))) | ((~aElementOf0(W0!44, sdtlpdtrp0(xN, sz00))) | aElementOf0(W0!44, szDzozmdt0(xN)))),
% 0.81/0.81 inference(quant_inst,[status(thm)],[])).
% 0.81/0.81 tff(35,plain,
% 0.81/0.81 ((~![W0: $i] : ((~aElementOf0(W0, sdtlpdtrp0(xN, sz00))) | aElementOf0(W0, szDzozmdt0(xN)))) | (~aElementOf0(W0!44, sdtlpdtrp0(xN, sz00))) | aElementOf0(W0!44, szDzozmdt0(xN))),
% 0.81/0.81 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.81/0.81 tff(36,plain,
% 0.81/0.81 (~aElementOf0(W0!44, sdtlpdtrp0(xN, sz00))),
% 0.81/0.81 inference(unit_resolution,[status(thm)],[35, 32, 16])).
% 0.81/0.81 tff(37,plain,
% 0.81/0.81 (aElementOf0(W0!44, xQ)),
% 0.81/0.81 inference(or_elim,[status(thm)],[15])).
% 0.81/0.81 tff(38,plain,
% 0.81/0.81 (^[W0: $i] : refl(((~aElementOf0(W0, xQ)) | aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) <=> ((~aElementOf0(W0, xQ)) | aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))))),
% 0.81/0.81 inference(bind,[status(th)],[])).
% 0.81/0.81 tff(39,plain,
% 0.81/0.81 (![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) <=> ![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))),
% 0.81/0.81 inference(quant_intro,[status(thm)],[38])).
% 0.81/0.81 tff(40,plain,
% 0.81/0.81 (^[W0: $i] : rewrite(((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO)) <=> ((~aElementOf0(W0, xQ)) | aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))))),
% 0.81/0.81 inference(bind,[status(th)],[])).
% 0.81/0.81 tff(41,plain,
% 0.81/0.81 (![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO)) <=> ![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))),
% 0.81/0.81 inference(quant_intro,[status(thm)],[40])).
% 0.81/0.81 tff(42,plain,
% 0.81/0.81 (![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO)) <=> ![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO))),
% 0.81/0.81 inference(rewrite,[status(thm)],[])).
% 0.81/0.81 tff(43,plain,
% 0.81/0.81 (^[W0: $i] : rewrite((aElementOf0(W0, xQ) => aElementOf0(W0, xO)) <=> ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO)))),
% 0.81/0.81 inference(bind,[status(th)],[])).
% 0.81/0.81 tff(44,plain,
% 0.81/0.81 (![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, xO)) <=> ![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO))),
% 0.81/0.81 inference(quant_intro,[status(thm)],[43])).
% 0.81/0.81 tff(45,axiom,((((aSet0(xQ) & ![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, xO))) & aSubsetOf0(xQ, xO)) & (sbrdtbr0(xQ) = xK)) & aElementOf0(xQ, slbdtsldtrb0(xO, xK))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__5078')).
% 0.81/0.81 tff(46,plain,
% 0.81/0.81 (((aSet0(xQ) & ![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, xO))) & aSubsetOf0(xQ, xO)) & (sbrdtbr0(xQ) = xK)),
% 0.81/0.81 inference(and_elim,[status(thm)],[45])).
% 0.81/0.81 tff(47,plain,
% 0.81/0.81 ((aSet0(xQ) & ![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, xO))) & aSubsetOf0(xQ, xO)),
% 0.81/0.81 inference(and_elim,[status(thm)],[46])).
% 0.81/0.81 tff(48,plain,
% 0.81/0.81 (aSet0(xQ) & ![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, xO))),
% 0.81/0.81 inference(and_elim,[status(thm)],[47])).
% 0.81/0.81 tff(49,plain,
% 0.81/0.81 (![W0: $i] : (aElementOf0(W0, xQ) => aElementOf0(W0, xO))),
% 0.81/0.81 inference(and_elim,[status(thm)],[48])).
% 0.81/0.81 tff(50,plain,
% 0.81/0.81 (![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO))),
% 0.81/0.81 inference(modus_ponens,[status(thm)],[49, 44])).
% 0.81/0.81 tff(51,plain,
% 0.81/0.81 (![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, xO))),
% 0.81/0.81 inference(modus_ponens,[status(thm)],[50, 42])).
% 0.81/0.81 tff(52,plain,
% 0.81/0.81 (![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))),
% 0.81/0.81 inference(modus_ponens,[status(thm)],[51, 41])).
% 0.81/0.81 tff(53,plain,(
% 0.81/0.81 ![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))),
% 0.81/0.81 inference(skolemize,[status(sab)],[52])).
% 0.81/0.81 tff(54,plain,
% 0.81/0.81 (![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))),
% 0.81/0.81 inference(modus_ponens,[status(thm)],[53, 39])).
% 0.81/0.81 tff(55,plain,
% 0.81/0.81 (((~![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))) | ((~aElementOf0(W0!44, xQ)) | aElementOf0(W0!44, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))) <=> ((~![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))) | (~aElementOf0(W0!44, xQ)) | aElementOf0(W0!44, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))),
% 0.81/0.81 inference(rewrite,[status(thm)],[])).
% 0.81/0.81 tff(56,plain,
% 0.81/0.81 ((~![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))) | ((~aElementOf0(W0!44, xQ)) | aElementOf0(W0!44, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))),
% 0.81/0.81 inference(quant_inst,[status(thm)],[])).
% 0.81/0.81 tff(57,plain,
% 0.81/0.81 ((~![W0: $i] : ((~aElementOf0(W0, xQ)) | aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd)))))) | (~aElementOf0(W0!44, xQ)) | aElementOf0(W0!44, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))),
% 0.81/0.81 inference(modus_ponens,[status(thm)],[56, 55])).
% 0.81/0.81 tff(58,plain,
% 0.81/0.81 (aElementOf0(W0!44, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))),
% 0.81/0.81 inference(unit_resolution,[status(thm)],[57, 54, 37])).
% 0.81/0.81 tff(59,plain,
% 0.81/0.81 (^[W0: $i] : refl(((~aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | aElementOf0(W0, sdtlpdtrp0(xN, sz00))) <=> ((~aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | aElementOf0(W0, sdtlpdtrp0(xN, sz00))))),
% 0.81/0.81 inference(bind,[status(th)],[])).
% 0.81/0.81 tff(60,plain,
% 0.81/0.83 (![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | aElementOf0(W0, sdtlpdtrp0(xN, sz00))) <=> ![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | aElementOf0(W0, sdtlpdtrp0(xN, sz00)))),
% 0.81/0.83 inference(quant_intro,[status(thm)],[59])).
% 0.81/0.83 tff(61,plain,
% 0.81/0.83 (^[W0: $i] : rewrite(((~aElementOf0(W0, xO)) | aElementOf0(W0, xS)) <=> ((~aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | aElementOf0(W0, sdtlpdtrp0(xN, sz00))))),
% 0.81/0.83 inference(bind,[status(th)],[])).
% 0.81/0.83 tff(62,plain,
% 0.81/0.83 (![W0: $i] : ((~aElementOf0(W0, xO)) | aElementOf0(W0, xS)) <=> ![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | aElementOf0(W0, sdtlpdtrp0(xN, sz00)))),
% 0.81/0.83 inference(quant_intro,[status(thm)],[61])).
% 0.81/0.83 tff(63,plain,
% 0.81/0.83 (![W0: $i] : ((~aElementOf0(W0, xO)) | aElementOf0(W0, xS)) <=> ![W0: $i] : ((~aElementOf0(W0, xO)) | aElementOf0(W0, xS))),
% 0.81/0.83 inference(rewrite,[status(thm)],[])).
% 0.81/0.83 tff(64,plain,
% 0.81/0.83 (^[W0: $i] : rewrite((aElementOf0(W0, xO) => aElementOf0(W0, xS)) <=> ((~aElementOf0(W0, xO)) | aElementOf0(W0, xS)))),
% 0.81/0.83 inference(bind,[status(th)],[])).
% 0.81/0.83 tff(65,plain,
% 0.81/0.83 (![W0: $i] : (aElementOf0(W0, xO) => aElementOf0(W0, xS)) <=> ![W0: $i] : ((~aElementOf0(W0, xO)) | aElementOf0(W0, xS))),
% 0.81/0.83 inference(quant_intro,[status(thm)],[64])).
% 0.81/0.83 tff(66,axiom,(![W0: $i] : (aElementOf0(W0, xO) => aElementOf0(W0, xS)) & aSubsetOf0(xO, xS)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__4998')).
% 0.81/0.83 tff(67,plain,
% 0.81/0.83 (![W0: $i] : (aElementOf0(W0, xO) => aElementOf0(W0, xS))),
% 0.81/0.83 inference(and_elim,[status(thm)],[66])).
% 0.81/0.83 tff(68,plain,
% 0.81/0.83 (![W0: $i] : ((~aElementOf0(W0, xO)) | aElementOf0(W0, xS))),
% 0.81/0.83 inference(modus_ponens,[status(thm)],[67, 65])).
% 0.81/0.83 tff(69,plain,
% 0.81/0.83 (![W0: $i] : ((~aElementOf0(W0, xO)) | aElementOf0(W0, xS))),
% 0.81/0.83 inference(modus_ponens,[status(thm)],[68, 63])).
% 0.81/0.83 tff(70,plain,
% 0.81/0.83 (![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | aElementOf0(W0, sdtlpdtrp0(xN, sz00)))),
% 0.81/0.83 inference(modus_ponens,[status(thm)],[69, 62])).
% 0.81/0.83 tff(71,plain,(
% 0.81/0.83 ![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | aElementOf0(W0, sdtlpdtrp0(xN, sz00)))),
% 0.81/0.83 inference(skolemize,[status(sab)],[70])).
% 0.81/0.83 tff(72,plain,
% 0.81/0.83 (![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | aElementOf0(W0, sdtlpdtrp0(xN, sz00)))),
% 0.81/0.83 inference(modus_ponens,[status(thm)],[71, 60])).
% 0.81/0.83 tff(73,plain,
% 0.81/0.83 (((~![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | aElementOf0(W0, sdtlpdtrp0(xN, sz00)))) | ((~aElementOf0(W0!44, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | aElementOf0(W0!44, sdtlpdtrp0(xN, sz00)))) <=> ((~![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | aElementOf0(W0, sdtlpdtrp0(xN, sz00)))) | (~aElementOf0(W0!44, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | aElementOf0(W0!44, sdtlpdtrp0(xN, sz00)))),
% 0.81/0.83 inference(rewrite,[status(thm)],[])).
% 0.81/0.83 tff(74,plain,
% 0.81/0.83 ((~![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | aElementOf0(W0, sdtlpdtrp0(xN, sz00)))) | ((~aElementOf0(W0!44, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | aElementOf0(W0!44, sdtlpdtrp0(xN, sz00)))),
% 0.81/0.83 inference(quant_inst,[status(thm)],[])).
% 0.81/0.83 tff(75,plain,
% 0.81/0.83 ((~![W0: $i] : ((~aElementOf0(W0, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | aElementOf0(W0, sdtlpdtrp0(xN, sz00)))) | (~aElementOf0(W0!44, sdtlcdtrc0(xe, sdtlbdtrb0(xd, szDzizrdt0(xd))))) | aElementOf0(W0!44, sdtlpdtrp0(xN, sz00))),
% 0.81/0.83 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.81/0.83 tff(76,plain,
% 0.81/0.83 ($false),
% 0.81/0.83 inference(unit_resolution,[status(thm)],[75, 72, 58, 36])).
% 0.81/0.83 % SZS output end Proof
%------------------------------------------------------------------------------