TSTP Solution File: NUM565+3 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM565+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.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 13:10:33 EDT 2022
% Result : Theorem 0.19s 0.45s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM565+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n009.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Sep 2 11:45:20 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.19/0.45 % SZS status Theorem
% 0.19/0.45 % SZS output start Proof
% 0.19/0.45 tff(sdtlpdtrp0_type, type, (
% 0.19/0.45 sdtlpdtrp0: ( $i * $i ) > $i)).
% 0.19/0.45 tff(slbdtrb0_type, type, (
% 0.19/0.45 slbdtrb0: $i > $i)).
% 0.19/0.45 tff(sz00_type, type, (
% 0.19/0.45 sz00: $i)).
% 0.19/0.45 tff(xc_type, type, (
% 0.19/0.45 xc: $i)).
% 0.19/0.45 tff(tptp_fun_W0_29_type, type, (
% 0.19/0.45 tptp_fun_W0_29: $i)).
% 0.19/0.45 tff(sbrdtbr0_type, type, (
% 0.19/0.45 sbrdtbr0: $i > $i)).
% 0.19/0.45 tff(aSet0_type, type, (
% 0.19/0.45 aSet0: $i > $o)).
% 0.19/0.45 tff(aElementOf0_type, type, (
% 0.19/0.45 aElementOf0: ( $i * $i ) > $o)).
% 0.19/0.45 tff(szDzozmdt0_type, type, (
% 0.19/0.45 szDzozmdt0: $i > $i)).
% 0.19/0.45 tff(aSubsetOf0_type, type, (
% 0.19/0.45 aSubsetOf0: ( $i * $i ) > $o)).
% 0.19/0.45 tff(xS_type, type, (
% 0.19/0.45 xS: $i)).
% 0.19/0.45 tff(slbdtsldtrb0_type, type, (
% 0.19/0.45 slbdtsldtrb0: ( $i * $i ) > $i)).
% 0.19/0.45 tff(slcrc0_type, type, (
% 0.19/0.45 slcrc0: $i)).
% 0.19/0.45 tff(1,plain,
% 0.19/0.45 ((![W1: $i] : (~aElementOf0(W1, slbdtrb0(sz00))) & (~(sdtlpdtrp0(xc, W0!29) = sdtlpdtrp0(xc, slbdtrb0(sz00)))) & (aSet0(W0!29) & ![W1: $i] : ((~aElementOf0(W1, W0!29)) | aElementOf0(W1, xS)) & aSubsetOf0(W0!29, xS) & (sbrdtbr0(W0!29) = sz00) & aElementOf0(W0!29, szDzozmdt0(xc)))) <=> (![W1: $i] : (~aElementOf0(W1, slbdtrb0(sz00))) & (~(sdtlpdtrp0(xc, W0!29) = sdtlpdtrp0(xc, slbdtrb0(sz00)))) & aSet0(W0!29) & ![W1: $i] : ((~aElementOf0(W1, W0!29)) | aElementOf0(W1, xS)) & aSubsetOf0(W0!29, xS) & (sbrdtbr0(W0!29) = sz00) & aElementOf0(W0!29, szDzozmdt0(xc)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(2,plain,
% 0.19/0.45 ((aSet0(W0!29) & ![W1: $i] : ((~aElementOf0(W1, W0!29)) | aElementOf0(W1, xS)) & aSubsetOf0(W0!29, xS) & (sbrdtbr0(W0!29) = sz00) & aElementOf0(W0!29, szDzozmdt0(xc))) <=> (aSet0(W0!29) & ![W1: $i] : ((~aElementOf0(W1, W0!29)) | aElementOf0(W1, xS)) & aSubsetOf0(W0!29, xS) & (sbrdtbr0(W0!29) = sz00) & aElementOf0(W0!29, szDzozmdt0(xc)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(3,plain,
% 0.19/0.45 ((![W1: $i] : (~aElementOf0(W1, slbdtrb0(sz00))) & (~(sdtlpdtrp0(xc, W0!29) = sdtlpdtrp0(xc, slbdtrb0(sz00)))) & (aSet0(W0!29) & ![W1: $i] : ((~aElementOf0(W1, W0!29)) | aElementOf0(W1, xS)) & aSubsetOf0(W0!29, xS) & (sbrdtbr0(W0!29) = sz00) & aElementOf0(W0!29, szDzozmdt0(xc)))) <=> (![W1: $i] : (~aElementOf0(W1, slbdtrb0(sz00))) & (~(sdtlpdtrp0(xc, W0!29) = sdtlpdtrp0(xc, slbdtrb0(sz00)))) & (aSet0(W0!29) & ![W1: $i] : ((~aElementOf0(W1, W0!29)) | aElementOf0(W1, xS)) & aSubsetOf0(W0!29, xS) & (sbrdtbr0(W0!29) = sz00) & aElementOf0(W0!29, szDzozmdt0(xc))))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[2])).
% 0.19/0.45 tff(4,plain,
% 0.19/0.45 ((![W1: $i] : (~aElementOf0(W1, slbdtrb0(sz00))) & (~(sdtlpdtrp0(xc, W0!29) = sdtlpdtrp0(xc, slbdtrb0(sz00)))) & (aSet0(W0!29) & ![W1: $i] : ((~aElementOf0(W1, W0!29)) | aElementOf0(W1, xS)) & aSubsetOf0(W0!29, xS) & (sbrdtbr0(W0!29) = sz00) & aElementOf0(W0!29, szDzozmdt0(xc)))) <=> (![W1: $i] : (~aElementOf0(W1, slbdtrb0(sz00))) & (~(sdtlpdtrp0(xc, W0!29) = sdtlpdtrp0(xc, slbdtrb0(sz00)))) & aSet0(W0!29) & ![W1: $i] : ((~aElementOf0(W1, W0!29)) | aElementOf0(W1, xS)) & aSubsetOf0(W0!29, xS) & (sbrdtbr0(W0!29) = sz00) & aElementOf0(W0!29, szDzozmdt0(xc)))),
% 0.19/0.45 inference(transitivity,[status(thm)],[3, 1])).
% 0.19/0.45 tff(5,plain,
% 0.19/0.45 ((~![W0: $i] : (?[W1: $i] : aElementOf0(W1, slbdtrb0(sz00)) | (sdtlpdtrp0(xc, W0) = sdtlpdtrp0(xc, slbdtrb0(sz00))) | (~(aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)) & aSubsetOf0(W0, xS) & (sbrdtbr0(W0) = sz00) & aElementOf0(W0, szDzozmdt0(xc)))))) <=> (~![W0: $i] : (?[W1: $i] : aElementOf0(W1, slbdtrb0(sz00)) | (sdtlpdtrp0(xc, W0) = sdtlpdtrp0(xc, slbdtrb0(sz00))) | (~(aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)) & aSubsetOf0(W0, xS) & (sbrdtbr0(W0) = sz00) & aElementOf0(W0, szDzozmdt0(xc))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(6,plain,
% 0.19/0.45 ((~![W0: $i] : ((~(aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)) & aSubsetOf0(W0, xS) & (sbrdtbr0(W0) = sz00) & aElementOf0(W0, slbdtsldtrb0(xS, sz00)))) | ?[W1: $i] : aElementOf0(W1, slbdtrb0(sz00)) | (sdtlpdtrp0(xc, W0) = sdtlpdtrp0(xc, slbdtrb0(sz00))))) <=> (~![W0: $i] : (?[W1: $i] : aElementOf0(W1, slbdtrb0(sz00)) | (sdtlpdtrp0(xc, W0) = sdtlpdtrp0(xc, slbdtrb0(sz00))) | (~(aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)) & aSubsetOf0(W0, xS) & (sbrdtbr0(W0) = sz00) & aElementOf0(W0, szDzozmdt0(xc))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(7,plain,
% 0.19/0.45 ((~![W0: $i] : ((~(aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)) & aSubsetOf0(W0, xS) & (sbrdtbr0(W0) = sz00) & aElementOf0(W0, slbdtsldtrb0(xS, sz00)))) | ?[W1: $i] : aElementOf0(W1, slbdtrb0(sz00)) | (sdtlpdtrp0(xc, W0) = sdtlpdtrp0(xc, slbdtrb0(sz00))))) <=> (~![W0: $i] : ((~(aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)) & aSubsetOf0(W0, xS) & (sbrdtbr0(W0) = sz00) & aElementOf0(W0, slbdtsldtrb0(xS, sz00)))) | ?[W1: $i] : aElementOf0(W1, slbdtrb0(sz00)) | (sdtlpdtrp0(xc, W0) = sdtlpdtrp0(xc, slbdtrb0(sz00)))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(8,plain,
% 0.19/0.45 ((~![W0: $i] : (?[W1: $i] : aElementOf0(W1, slcrc0) | (sdtlpdtrp0(xc, W0) = sdtlpdtrp0(xc, slcrc0)) | (~(aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)) & aSubsetOf0(W0, xS) & (sbrdtbr0(W0) = sz00) & aElementOf0(W0, slbdtsldtrb0(xS, sz00)))))) <=> (~![W0: $i] : ((~(aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)) & aSubsetOf0(W0, xS) & (sbrdtbr0(W0) = sz00) & aElementOf0(W0, slbdtsldtrb0(xS, sz00)))) | ?[W1: $i] : aElementOf0(W1, slbdtrb0(sz00)) | (sdtlpdtrp0(xc, W0) = sdtlpdtrp0(xc, slbdtrb0(sz00)))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(9,plain,
% 0.19/0.45 ((~![W0: $i] : (?[W1: $i] : aElementOf0(W1, slcrc0) | (sdtlpdtrp0(xc, W0) = sdtlpdtrp0(xc, slcrc0)) | (~(aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)) & aSubsetOf0(W0, xS) & (sbrdtbr0(W0) = sz00) & aElementOf0(W0, slbdtsldtrb0(xS, sz00)))))) <=> (~![W0: $i] : (?[W1: $i] : aElementOf0(W1, slcrc0) | (sdtlpdtrp0(xc, W0) = sdtlpdtrp0(xc, slcrc0)) | (~(aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)) & aSubsetOf0(W0, xS) & (sbrdtbr0(W0) = sz00) & aElementOf0(W0, slbdtsldtrb0(xS, sz00))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(10,plain,
% 0.19/0.45 ((~![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] : (?[W1: $i] : aElementOf0(W1, slcrc0) | (sdtlpdtrp0(xc, W0) = sdtlpdtrp0(xc, slcrc0)) | (~(aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)) & aSubsetOf0(W0, xS) & (sbrdtbr0(W0) = sz00) & aElementOf0(W0, slbdtsldtrb0(xS, sz00))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(11,plain,
% 0.19/0.45 ((~![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))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(12,plain,
% 0.19/0.45 ((~![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))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(13,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/sandbox/benchmark/theBenchmark.p','m__')).
% 0.19/0.45 tff(14,plain,
% 0.19/0.45 (~![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)))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.19/0.45 tff(15,plain,
% 0.19/0.45 (~![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)))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[14, 11])).
% 0.19/0.45 tff(16,plain,
% 0.19/0.45 (~![W0: $i] : (?[W1: $i] : aElementOf0(W1, slcrc0) | (sdtlpdtrp0(xc, W0) = sdtlpdtrp0(xc, slcrc0)) | (~(aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)) & aSubsetOf0(W0, xS) & (sbrdtbr0(W0) = sz00) & aElementOf0(W0, slbdtsldtrb0(xS, sz00)))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[15, 10])).
% 0.19/0.45 tff(17,plain,
% 0.19/0.45 (~![W0: $i] : (?[W1: $i] : aElementOf0(W1, slcrc0) | (sdtlpdtrp0(xc, W0) = sdtlpdtrp0(xc, slcrc0)) | (~(aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)) & aSubsetOf0(W0, xS) & (sbrdtbr0(W0) = sz00) & aElementOf0(W0, slbdtsldtrb0(xS, sz00)))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[16, 9])).
% 0.19/0.45 tff(18,plain,
% 0.19/0.45 (~![W0: $i] : (?[W1: $i] : aElementOf0(W1, slcrc0) | (sdtlpdtrp0(xc, W0) = sdtlpdtrp0(xc, slcrc0)) | (~(aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)) & aSubsetOf0(W0, xS) & (sbrdtbr0(W0) = sz00) & aElementOf0(W0, slbdtsldtrb0(xS, sz00)))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[17, 9])).
% 0.19/0.45 tff(19,plain,
% 0.19/0.45 (~![W0: $i] : ((~(aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)) & aSubsetOf0(W0, xS) & (sbrdtbr0(W0) = sz00) & aElementOf0(W0, slbdtsldtrb0(xS, sz00)))) | ?[W1: $i] : aElementOf0(W1, slbdtrb0(sz00)) | (sdtlpdtrp0(xc, W0) = sdtlpdtrp0(xc, slbdtrb0(sz00))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[18, 8])).
% 0.19/0.45 tff(20,plain,
% 0.19/0.45 (~![W0: $i] : ((~(aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)) & aSubsetOf0(W0, xS) & (sbrdtbr0(W0) = sz00) & aElementOf0(W0, slbdtsldtrb0(xS, sz00)))) | ?[W1: $i] : aElementOf0(W1, slbdtrb0(sz00)) | (sdtlpdtrp0(xc, W0) = sdtlpdtrp0(xc, slbdtrb0(sz00))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[19, 7])).
% 0.19/0.45 tff(21,plain,
% 0.19/0.45 (~![W0: $i] : (?[W1: $i] : aElementOf0(W1, slbdtrb0(sz00)) | (sdtlpdtrp0(xc, W0) = sdtlpdtrp0(xc, slbdtrb0(sz00))) | (~(aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)) & aSubsetOf0(W0, xS) & (sbrdtbr0(W0) = sz00) & aElementOf0(W0, szDzozmdt0(xc)))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[20, 6])).
% 0.19/0.45 tff(22,plain,
% 0.19/0.45 (~![W0: $i] : (?[W1: $i] : aElementOf0(W1, slbdtrb0(sz00)) | (sdtlpdtrp0(xc, W0) = sdtlpdtrp0(xc, slbdtrb0(sz00))) | (~(aSet0(W0) & ![W1: $i] : ((~aElementOf0(W1, W0)) | aElementOf0(W1, xS)) & aSubsetOf0(W0, xS) & (sbrdtbr0(W0) = sz00) & aElementOf0(W0, szDzozmdt0(xc)))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[21, 5])).
% 0.19/0.45 tff(23,plain,
% 0.19/0.45 (![W1: $i] : (~aElementOf0(W1, slbdtrb0(sz00))) & (~(sdtlpdtrp0(xc, W0!29) = sdtlpdtrp0(xc, slbdtrb0(sz00)))) & aSet0(W0!29) & ![W1: $i] : ((~aElementOf0(W1, W0!29)) | aElementOf0(W1, xS)) & aSubsetOf0(W0!29, xS) & (sbrdtbr0(W0!29) = sz00) & aElementOf0(W0!29, szDzozmdt0(xc))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[22, 4])).
% 0.19/0.45 tff(24,plain,
% 0.19/0.45 (aSet0(W0!29)),
% 0.19/0.45 inference(and_elim,[status(thm)],[23])).
% 0.19/0.45 tff(25,plain,
% 0.19/0.45 (^[W0: $i] : refl(((~aSet0(W0)) | ((sbrdtbr0(W0) = sz00) <=> (W0 = slbdtrb0(sz00)))) <=> ((~aSet0(W0)) | ((sbrdtbr0(W0) = sz00) <=> (W0 = slbdtrb0(sz00)))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(26,plain,
% 0.19/0.45 (![W0: $i] : ((~aSet0(W0)) | ((sbrdtbr0(W0) = sz00) <=> (W0 = slbdtrb0(sz00)))) <=> ![W0: $i] : ((~aSet0(W0)) | ((sbrdtbr0(W0) = sz00) <=> (W0 = slbdtrb0(sz00))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[25])).
% 0.19/0.46 tff(27,plain,
% 0.19/0.46 (^[W0: $i] : rewrite(((~aSet0(W0)) | ((sbrdtbr0(W0) = sz00) <=> (W0 = slcrc0))) <=> ((~aSet0(W0)) | ((sbrdtbr0(W0) = sz00) <=> (W0 = slbdtrb0(sz00)))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(28,plain,
% 0.19/0.46 (![W0: $i] : ((~aSet0(W0)) | ((sbrdtbr0(W0) = sz00) <=> (W0 = slcrc0))) <=> ![W0: $i] : ((~aSet0(W0)) | ((sbrdtbr0(W0) = sz00) <=> (W0 = slbdtrb0(sz00))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[27])).
% 0.19/0.46 tff(29,plain,
% 0.19/0.46 (![W0: $i] : ((~aSet0(W0)) | ((sbrdtbr0(W0) = sz00) <=> (W0 = slcrc0))) <=> ![W0: $i] : ((~aSet0(W0)) | ((sbrdtbr0(W0) = sz00) <=> (W0 = slcrc0)))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(30,plain,
% 0.19/0.46 (^[W0: $i] : rewrite((aSet0(W0) => ((sbrdtbr0(W0) = sz00) <=> (W0 = slcrc0))) <=> ((~aSet0(W0)) | ((sbrdtbr0(W0) = sz00) <=> (W0 = slcrc0))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(31,plain,
% 0.19/0.46 (![W0: $i] : (aSet0(W0) => ((sbrdtbr0(W0) = sz00) <=> (W0 = slcrc0))) <=> ![W0: $i] : ((~aSet0(W0)) | ((sbrdtbr0(W0) = sz00) <=> (W0 = slcrc0)))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[30])).
% 0.19/0.46 tff(32,axiom,(![W0: $i] : (aSet0(W0) => ((sbrdtbr0(W0) = sz00) <=> (W0 = slcrc0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mCardEmpty')).
% 0.19/0.46 tff(33,plain,
% 0.19/0.46 (![W0: $i] : ((~aSet0(W0)) | ((sbrdtbr0(W0) = sz00) <=> (W0 = slcrc0)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.19/0.46 tff(34,plain,
% 0.19/0.46 (![W0: $i] : ((~aSet0(W0)) | ((sbrdtbr0(W0) = sz00) <=> (W0 = slcrc0)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[33, 29])).
% 0.19/0.46 tff(35,plain,
% 0.19/0.46 (![W0: $i] : ((~aSet0(W0)) | ((sbrdtbr0(W0) = sz00) <=> (W0 = slbdtrb0(sz00))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[34, 28])).
% 0.19/0.46 tff(36,plain,(
% 0.19/0.46 ![W0: $i] : ((~aSet0(W0)) | ((sbrdtbr0(W0) = sz00) <=> (W0 = slbdtrb0(sz00))))),
% 0.19/0.46 inference(skolemize,[status(sab)],[35])).
% 0.19/0.46 tff(37,plain,
% 0.19/0.46 (![W0: $i] : ((~aSet0(W0)) | ((sbrdtbr0(W0) = sz00) <=> (W0 = slbdtrb0(sz00))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[36, 26])).
% 0.19/0.46 tff(38,plain,
% 0.19/0.46 (((~![W0: $i] : ((~aSet0(W0)) | ((sbrdtbr0(W0) = sz00) <=> (W0 = slbdtrb0(sz00))))) | ((~aSet0(W0!29)) | ((sbrdtbr0(W0!29) = sz00) <=> (W0!29 = slbdtrb0(sz00))))) <=> ((~![W0: $i] : ((~aSet0(W0)) | ((sbrdtbr0(W0) = sz00) <=> (W0 = slbdtrb0(sz00))))) | (~aSet0(W0!29)) | ((sbrdtbr0(W0!29) = sz00) <=> (W0!29 = slbdtrb0(sz00))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(39,plain,
% 0.19/0.46 ((~![W0: $i] : ((~aSet0(W0)) | ((sbrdtbr0(W0) = sz00) <=> (W0 = slbdtrb0(sz00))))) | ((~aSet0(W0!29)) | ((sbrdtbr0(W0!29) = sz00) <=> (W0!29 = slbdtrb0(sz00))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(40,plain,
% 0.19/0.46 ((~![W0: $i] : ((~aSet0(W0)) | ((sbrdtbr0(W0) = sz00) <=> (W0 = slbdtrb0(sz00))))) | (~aSet0(W0!29)) | ((sbrdtbr0(W0!29) = sz00) <=> (W0!29 = slbdtrb0(sz00)))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.19/0.46 tff(41,plain,
% 0.19/0.46 ((sbrdtbr0(W0!29) = sz00) <=> (W0!29 = slbdtrb0(sz00))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[40, 37, 24])).
% 0.19/0.46 tff(42,plain,
% 0.19/0.46 (sbrdtbr0(W0!29) = sz00),
% 0.19/0.46 inference(and_elim,[status(thm)],[23])).
% 0.19/0.46 tff(43,plain,
% 0.19/0.46 ((~((sbrdtbr0(W0!29) = sz00) <=> (W0!29 = slbdtrb0(sz00)))) | (~(sbrdtbr0(W0!29) = sz00)) | (W0!29 = slbdtrb0(sz00))),
% 0.19/0.46 inference(tautology,[status(thm)],[])).
% 0.19/0.46 tff(44,plain,
% 0.19/0.46 ((~((sbrdtbr0(W0!29) = sz00) <=> (W0!29 = slbdtrb0(sz00)))) | (W0!29 = slbdtrb0(sz00))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.19/0.46 tff(45,plain,
% 0.19/0.46 (W0!29 = slbdtrb0(sz00)),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[44, 41])).
% 0.19/0.46 tff(46,plain,
% 0.19/0.46 (sdtlpdtrp0(xc, W0!29) = sdtlpdtrp0(xc, slbdtrb0(sz00))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[45])).
% 0.19/0.46 tff(47,plain,
% 0.19/0.46 (~(sdtlpdtrp0(xc, W0!29) = sdtlpdtrp0(xc, slbdtrb0(sz00)))),
% 0.19/0.46 inference(and_elim,[status(thm)],[23])).
% 0.19/0.46 tff(48,plain,
% 0.19/0.46 ($false),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.19/0.46 % SZS output end Proof
%------------------------------------------------------------------------------