TSTP Solution File: NUM560+2 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM560+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n023.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 13:10:30 EDT 2022
% Result : Theorem 0.18s 0.42s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : NUM560+2 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n023.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 Sep 2 12:07:03 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -o:<output-file> file to place output in.
% 0.18/0.42 % SZS status Theorem
% 0.18/0.42 % SZS output start Proof
% 0.18/0.42 tff(xy_type, type, (
% 0.18/0.42 xy: $i)).
% 0.18/0.42 tff(sdtlpdtrp0_type, type, (
% 0.18/0.42 sdtlpdtrp0: ( $i * $i ) > $i)).
% 0.18/0.42 tff(tptp_fun_W0_13_type, type, (
% 0.18/0.42 tptp_fun_W0_13: $i)).
% 0.18/0.42 tff(xF_type, type, (
% 0.18/0.42 xF: $i)).
% 0.18/0.42 tff(aElementOf0_type, type, (
% 0.18/0.42 aElementOf0: ( $i * $i ) > $o)).
% 0.18/0.42 tff(szDzozmdt0_type, type, (
% 0.18/0.42 szDzozmdt0: $i > $i)).
% 0.18/0.42 tff(sdtlbdtrb0_type, type, (
% 0.18/0.42 sdtlbdtrb0: ( $i * $i ) > $i)).
% 0.18/0.42 tff(aSet0_type, type, (
% 0.18/0.42 aSet0: $i > $o)).
% 0.18/0.42 tff(aSubsetOf0_type, type, (
% 0.18/0.42 aSubsetOf0: ( $i * $i ) > $o)).
% 0.18/0.42 tff(1,plain,
% 0.18/0.42 ((~![W0: $i] : ((~aElementOf0(W0, sdtlbdtrb0(xF, xy))) | aElementOf0(W0, szDzozmdt0(xF)))) <=> (~![W0: $i] : ((~aElementOf0(W0, sdtlbdtrb0(xF, xy))) | aElementOf0(W0, szDzozmdt0(xF))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(2,plain,
% 0.18/0.42 ((~((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)))))))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 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/sandbox/benchmark/theBenchmark.p','m__')).
% 0.18/0.42 tff(4,plain,
% 0.18/0.42 (~(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))))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[3, 2])).
% 0.18/0.42 tff(5,plain,
% 0.18/0.42 (~![W0: $i] : ((~aElementOf0(W0, sdtlbdtrb0(xF, xy))) | aElementOf0(W0, szDzozmdt0(xF)))),
% 0.18/0.42 inference(or_elim,[status(thm)],[4])).
% 0.18/0.42 tff(6,plain,
% 0.18/0.42 (~![W0: $i] : ((~aElementOf0(W0, sdtlbdtrb0(xF, xy))) | aElementOf0(W0, szDzozmdt0(xF)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[5, 1])).
% 0.18/0.42 tff(7,plain,
% 0.18/0.42 (~![W0: $i] : ((~aElementOf0(W0, sdtlbdtrb0(xF, xy))) | aElementOf0(W0, szDzozmdt0(xF)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[6, 1])).
% 0.18/0.42 tff(8,plain,
% 0.18/0.42 (~![W0: $i] : ((~aElementOf0(W0, sdtlbdtrb0(xF, xy))) | aElementOf0(W0, szDzozmdt0(xF)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.18/0.42 tff(9,plain,
% 0.18/0.42 (~![W0: $i] : ((~aElementOf0(W0, sdtlbdtrb0(xF, xy))) | aElementOf0(W0, szDzozmdt0(xF)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[8, 1])).
% 0.18/0.42 tff(10,plain,
% 0.18/0.42 (~![W0: $i] : ((~aElementOf0(W0, sdtlbdtrb0(xF, xy))) | aElementOf0(W0, szDzozmdt0(xF)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[9, 1])).
% 0.18/0.42 tff(11,plain,
% 0.18/0.42 (~![W0: $i] : ((~aElementOf0(W0, sdtlbdtrb0(xF, xy))) | aElementOf0(W0, szDzozmdt0(xF)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[10, 1])).
% 0.18/0.42 tff(12,plain,
% 0.18/0.42 (~![W0: $i] : ((~aElementOf0(W0, sdtlbdtrb0(xF, xy))) | aElementOf0(W0, szDzozmdt0(xF)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[11, 1])).
% 0.18/0.42 tff(13,plain,(
% 0.18/0.42 ~((~aElementOf0(W0!13, sdtlbdtrb0(xF, xy))) | aElementOf0(W0!13, szDzozmdt0(xF)))),
% 0.18/0.42 inference(skolemize,[status(sab)],[12])).
% 0.18/0.42 tff(14,plain,
% 0.18/0.42 (~aElementOf0(W0!13, szDzozmdt0(xF))),
% 0.18/0.42 inference(or_elim,[status(thm)],[13])).
% 0.18/0.42 tff(15,plain,
% 0.18/0.42 (((~aElementOf0(W0!13, szDzozmdt0(xF))) | (~(sdtlpdtrp0(xF, W0!13) = xy))) | aElementOf0(W0!13, szDzozmdt0(xF))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(16,plain,
% 0.18/0.42 ((~aElementOf0(W0!13, szDzozmdt0(xF))) | (~(sdtlpdtrp0(xF, W0!13) = xy))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[15, 14])).
% 0.18/0.42 tff(17,plain,
% 0.18/0.42 (aElementOf0(W0!13, sdtlbdtrb0(xF, xy))),
% 0.18/0.42 inference(or_elim,[status(thm)],[13])).
% 0.18/0.42 tff(18,plain,
% 0.18/0.42 ((~(aElementOf0(W0!13, sdtlbdtrb0(xF, xy)) <=> (~((~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))))),
% 0.18/0.42 inference(tautology,[status(thm)],[])).
% 0.18/0.42 tff(19,plain,
% 0.18/0.42 (~(aElementOf0(W0!13, sdtlbdtrb0(xF, xy)) <=> (~((~aElementOf0(W0!13, szDzozmdt0(xF))) | (~(sdtlpdtrp0(xF, W0!13) = xy)))))),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[18, 17, 16])).
% 0.18/0.42 tff(20,plain,
% 0.18/0.42 (^[W0: $i] : refl((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))))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(21,plain,
% 0.18/0.42 (![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)))))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[20])).
% 0.18/0.42 tff(22,plain,
% 0.18/0.42 (^[W0: $i] : rewrite((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))))))),
% 0.18/0.42 inference(bind,[status(th)],[])).
% 0.18/0.42 tff(23,plain,
% 0.18/0.42 (![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)))))),
% 0.18/0.42 inference(quant_intro,[status(thm)],[22])).
% 0.18/0.42 tff(24,plain,
% 0.18/0.42 (![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)))),
% 0.18/0.42 inference(rewrite,[status(thm)],[])).
% 0.18/0.42 tff(25,plain,
% 0.18/0.42 (aSet0(sdtlbdtrb0(xF, xy)) & ![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xF, xy)) <=> (aElementOf0(W0, szDzozmdt0(xF)) & (sdtlpdtrp0(xF, W0) = xy)))),
% 0.18/0.42 inference(or_elim,[status(thm)],[4])).
% 0.18/0.42 tff(26,plain,
% 0.18/0.42 (![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xF, xy)) <=> (aElementOf0(W0, szDzozmdt0(xF)) & (sdtlpdtrp0(xF, W0) = xy)))),
% 0.18/0.42 inference(and_elim,[status(thm)],[25])).
% 0.18/0.42 tff(27,plain,
% 0.18/0.42 (![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xF, xy)) <=> (aElementOf0(W0, szDzozmdt0(xF)) & (sdtlpdtrp0(xF, W0) = xy)))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[26, 24])).
% 0.18/0.42 tff(28,plain,(
% 0.18/0.42 ![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xF, xy)) <=> (aElementOf0(W0, szDzozmdt0(xF)) & (sdtlpdtrp0(xF, W0) = xy)))),
% 0.18/0.42 inference(skolemize,[status(sab)],[27])).
% 0.18/0.42 tff(29,plain,
% 0.18/0.42 (![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xF, xy)) <=> (~((~aElementOf0(W0, szDzozmdt0(xF))) | (~(sdtlpdtrp0(xF, W0) = xy)))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[28, 23])).
% 0.18/0.42 tff(30,plain,
% 0.18/0.42 (![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xF, xy)) <=> (~((~aElementOf0(W0, szDzozmdt0(xF))) | (~(sdtlpdtrp0(xF, W0) = xy)))))),
% 0.18/0.42 inference(modus_ponens,[status(thm)],[29, 21])).
% 0.18/0.42 tff(31,plain,
% 0.18/0.42 ((~![W0: $i] : (aElementOf0(W0, sdtlbdtrb0(xF, xy)) <=> (~((~aElementOf0(W0, szDzozmdt0(xF))) | (~(sdtlpdtrp0(xF, W0) = xy)))))) | (aElementOf0(W0!13, sdtlbdtrb0(xF, xy)) <=> (~((~aElementOf0(W0!13, szDzozmdt0(xF))) | (~(sdtlpdtrp0(xF, W0!13) = xy)))))),
% 0.18/0.42 inference(quant_inst,[status(thm)],[])).
% 0.18/0.42 tff(32,plain,
% 0.18/0.42 ($false),
% 0.18/0.42 inference(unit_resolution,[status(thm)],[31, 30, 19])).
% 0.18/0.42 % SZS output end Proof
%------------------------------------------------------------------------------