TSTP Solution File: NUM537+2 by leanCoP---2.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : leanCoP---2.2
% Problem : NUM537+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : leancop_casc.sh %s %d
% Computer : n029.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 : 600s
% DateTime : Mon Jul 18 11:41:48 EDT 2022
% Result : Theorem 3.03s 3.47s
% Output : Proof 3.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM537+2 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : leancop_casc.sh %s %d
% 0.12/0.34 % Computer : n029.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jul 6 00:30:28 EDT 2022
% 0.12/0.34 % CPUTime :
% 3.03/3.47 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.07/3.47 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.07/3.48
% 3.07/3.48 %-----------------------------------------------------
% 3.07/3.48 fof(m__, conjecture, (aSet0(sdtpldt0(xS, xx)) & ! [_60686] : (aElementOf0(_60686, sdtpldt0(xS, xx)) <=> aElement0(_60686) & (aElementOf0(_60686, xS) | _60686 = xx)) => aSet0(sdtmndt0(sdtpldt0(xS, xx), xx)) & ! [_60686] : (aElementOf0(_60686, sdtmndt0(sdtpldt0(xS, xx), xx)) <=> aElement0(_60686) & aElementOf0(_60686, sdtpldt0(xS, xx)) & (! _60686) = xx) => ! [_60686] : (aElementOf0(_60686, xS) => aElementOf0(_60686, sdtmndt0(sdtpldt0(xS, xx), xx))) | aSubsetOf0(xS, sdtmndt0(sdtpldt0(xS, xx), xx))) & (aSet0(sdtpldt0(xS, xx)) & ! [_60686] : (aElementOf0(_60686, sdtpldt0(xS, xx)) <=> aElement0(_60686) & (aElementOf0(_60686, xS) | _60686 = xx)) => aSet0(sdtmndt0(sdtpldt0(xS, xx), xx)) & ! [_60686] : (aElementOf0(_60686, sdtmndt0(sdtpldt0(xS, xx), xx)) <=> aElement0(_60686) & aElementOf0(_60686, sdtpldt0(xS, xx)) & (! _60686) = xx) => ! [_60686] : (aElementOf0(_60686, sdtmndt0(sdtpldt0(xS, xx), xx)) => aElementOf0(_60686, xS)) | aSubsetOf0(sdtmndt0(sdtpldt0(xS, xx), xx), xS)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', m__)).
% 3.07/3.48 fof(mEOfElem, axiom, ! [_62103] : (aSet0(_62103) => ! [_62118] : (aElementOf0(_62118, _62103) => aElement0(_62118))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', mEOfElem)).
% 3.07/3.48 fof(mDefCons, definition, ! [_62298, _62301] : (aSet0(_62298) & aElement0(_62301) => ! [_62323] : (_62323 = sdtpldt0(_62298, _62301) <=> aSet0(_62323) & ! [_62351] : (aElementOf0(_62351, _62323) <=> aElement0(_62351) & (aElementOf0(_62351, _62298) | _62351 = _62301)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', mDefCons)).
% 3.07/3.48 fof(m__679, hypothesis, aElement0(xx) & aSet0(xS), file('/export/starexec/sandbox/benchmark/theBenchmark.p', m__679)).
% 3.07/3.48 fof(m__679_02, hypothesis, ~ aElementOf0(xx, xS), file('/export/starexec/sandbox/benchmark/theBenchmark.p', m__679_02)).
% 3.07/3.48 fof(mDefDiff, definition, ! [_62782, _62785] : (aSet0(_62782) & aElement0(_62785) => ! [_62807] : (_62807 = sdtmndt0(_62782, _62785) <=> aSet0(_62807) & ! [_62835] : (aElementOf0(_62835, _62807) <=> aElement0(_62835) & aElementOf0(_62835, _62782) & (! _62835) = _62785))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', mDefDiff)).
% 3.07/3.48
% 3.07/3.48 cnf(1, plain, [-(12 ^ [_28410]), _28410 = xx], clausify(m__)).
% 3.07/3.48 cnf(2, plain, [-(12 ^ [_28410]), -(aElementOf0(_28410, sdtpldt0(xS, xx)))], clausify(m__)).
% 3.07/3.48 cnf(3, plain, [-(10 ^ [_27928]), -(aElementOf0(_27928, xS)), -(_27928 = xx)], clausify(m__)).
% 3.07/3.48 cnf(4, plain, [-(14 ^ []), aElementOf0(_27928, sdtpldt0(xS, xx)), 10 ^ [_27928]], clausify(m__)).
% 3.07/3.48 cnf(5, plain, [-(14 ^ []), aElementOf0(_28410, sdtmndt0(sdtpldt0(xS, xx), xx)), 12 ^ [_28410]], clausify(m__)).
% 3.07/3.48 cnf(6, plain, [-(14 ^ []), aElementOf0(13 ^ [], xS)], clausify(m__)).
% 3.07/3.48 cnf(7, plain, [-(14 ^ []), -(aElementOf0(13 ^ [], sdtmndt0(sdtpldt0(xS, xx), xx)))], clausify(m__)).
% 3.07/3.48 cnf(8, plain, [-(6 ^ [_26487]), aElementOf0(_26487, xS)], clausify(m__)).
% 3.07/3.48 cnf(9, plain, [-(9 ^ []), -(aElementOf0(_26487, sdtpldt0(xS, xx))), aElement0(_26487), 6 ^ [_26487]], clausify(m__)).
% 3.07/3.48 cnf(10, plain, [-(9 ^ []), -(aSet0(sdtpldt0(xS, xx)))], clausify(m__)).
% 3.07/3.48 cnf(11, plain, [-(9 ^ []), aElementOf0(8 ^ [], sdtmndt0(sdtpldt0(xS, xx), xx))], clausify(m__)).
% 3.07/3.48 cnf(12, plain, [-(9 ^ []), -(aElementOf0(8 ^ [], xS))], clausify(m__)).
% 3.07/3.48 cnf(13, plain, [9 ^ [], 14 ^ []], clausify(m__)).
% 3.07/3.48 cnf(14, plain, [-(_13716 = _13716)], theory(equality)).
% 3.07/3.48 cnf(15, plain, [-(aElementOf0(_15020, _15151)), aElementOf0(_14953, _15086), _14953 = _15020, _15086 = _15151], theory(equality)).
% 3.07/3.48 cnf(16, plain, [aSet0(_19015), aElementOf0(_19102, _19015), -(aElement0(_19102))], clausify(mEOfElem)).
% 3.07/3.48 cnf(17, plain, [aElement0(_23521), aSet0(_23431), _23701 = sdtpldt0(_23431, _23521), aElementOf0(_23913, _23701), -(aElementOf0(_23913, _23431)), -(_23913 = _23521)], clausify(mDefCons)).
% 3.07/3.48 cnf(18, plain, [-(aElement0(xx))], clausify(m__679)).
% 3.07/3.48 cnf(19, plain, [-(aSet0(xS))], clausify(m__679)).
% 3.07/3.48 cnf(20, plain, [aElementOf0(xx, xS)], clausify(m__679_02)).
% 3.07/3.48 cnf(21, plain, [aElement0(_24475), aSet0(_24383), -(_24657 = sdtmndt0(_24383, _24475)), aSet0(_24657), -(aElementOf0(4 ^ [_24657, _24475, _24383], _24657)), -(aElement0(4 ^ [_24657, _24475, _24383]))], clausify(mDefDiff)).
% 3.07/3.48 cnf(22, plain, [aElement0(_24475), aSet0(_24383), -(_24657 = sdtmndt0(_24383, _24475)), aSet0(_24657), -(aElementOf0(4 ^ [_24657, _24475, _24383], _24657)), -(aElementOf0(4 ^ [_24657, _24475, _24383], _24383))], clausify(mDefDiff)).
% 3.07/3.48 cnf(23, plain, [aElement0(_24475), aSet0(_24383), -(_24657 = sdtmndt0(_24383, _24475)), aSet0(_24657), -(aElementOf0(4 ^ [_24657, _24475, _24383], _24657)), 4 ^ [_24657, _24475, _24383] = _24475], clausify(mDefDiff)).
% 3.07/3.48 cnf(24, plain, [aElement0(_24475), aSet0(_24383), -(_24657 = sdtmndt0(_24383, _24475)), aSet0(_24657), aElementOf0(4 ^ [_24657, _24475, _24383], _24657), aElement0(4 ^ [_24657, _24475, _24383]), aElementOf0(4 ^ [_24657, _24475, _24383], _24383), -(4 ^ [_24657, _24475, _24383] = _24475)], clausify(mDefDiff)).
% 3.07/3.48
% 3.07/3.48 cnf('1',plain,[9 ^ [], 14 ^ []],start(13)).
% 3.07/3.48 cnf('1.1',plain,[-(9 ^ []), -(aSet0(sdtpldt0(xS, xx)))],extension(10)).
% 3.07/3.48 cnf('1.1.1',plain,[aSet0(sdtpldt0(xS, xx)), aElement0(xx), -(xS = sdtmndt0(sdtpldt0(xS, xx), xx)), aSet0(xS), aElementOf0(4 ^ [xS, xx, sdtpldt0(xS, xx)], xS), aElement0(4 ^ [xS, xx, sdtpldt0(xS, xx)]), aElementOf0(4 ^ [xS, xx, sdtpldt0(xS, xx)], sdtpldt0(xS, xx)), -(4 ^ [xS, xx, sdtpldt0(xS, xx)] = xx)],extension(24,bind([[_24657, _24383, _24475], [xS, sdtpldt0(xS, xx), xx]]))).
% 3.07/3.48 cnf('1.1.1.1',plain,[-(aElement0(xx))],extension(18)).
% 3.07/3.48 cnf('1.1.1.2',plain,[xS = sdtmndt0(sdtpldt0(xS, xx), xx), -(aElementOf0(8 ^ [], sdtmndt0(sdtpldt0(xS, xx), xx))), aElementOf0(8 ^ [], xS), 8 ^ [] = 8 ^ []],extension(15,bind([[_15151, _15086, _14953, _15020], [sdtmndt0(sdtpldt0(xS, xx), xx), xS, 8 ^ [], 8 ^ []]]))).
% 3.07/3.48 cnf('1.1.1.2.1',plain,[aElementOf0(8 ^ [], sdtmndt0(sdtpldt0(xS, xx), xx)), -(9 ^ [])],extension(11)).
% 3.07/3.48 cnf('1.1.1.2.1.1',plain,[9 ^ []],reduction('1')).
% 3.07/3.48 cnf('1.1.1.2.2',plain,[-(aElementOf0(8 ^ [], xS)), -(9 ^ [])],extension(12)).
% 3.07/3.48 cnf('1.1.1.2.2.1',plain,[9 ^ []],reduction('1')).
% 3.07/3.48 cnf('1.1.1.2.3',plain,[-(8 ^ [] = 8 ^ [])],extension(14,bind([[_13716], [8 ^ []]]))).
% 3.07/3.48 cnf('1.1.1.3',plain,[-(aSet0(xS))],extension(19)).
% 3.07/3.48 cnf('1.1.1.4',plain,[-(aElementOf0(4 ^ [xS, xx, sdtpldt0(xS, xx)], xS)), aElement0(xx), aSet0(xS), sdtpldt0(xS, xx) = sdtpldt0(xS, xx), aElementOf0(4 ^ [xS, xx, sdtpldt0(xS, xx)], sdtpldt0(xS, xx)), -(4 ^ [xS, xx, sdtpldt0(xS, xx)] = xx)],extension(17,bind([[_23431, _23701, _23913, _23521], [xS, sdtpldt0(xS, xx), 4 ^ [xS, xx, sdtpldt0(xS, xx)], xx]]))).
% 3.07/3.48 cnf('1.1.1.4.1',plain,[-(aElement0(xx))],extension(18)).
% 3.07/3.48 cnf('1.1.1.4.2',plain,[-(aSet0(xS))],extension(19)).
% 3.07/3.48 cnf('1.1.1.4.3',plain,[-(sdtpldt0(xS, xx) = sdtpldt0(xS, xx))],extension(14,bind([[_13716], [sdtpldt0(xS, xx)]]))).
% 3.07/3.48 cnf('1.1.1.4.4',plain,[-(aElementOf0(4 ^ [xS, xx, sdtpldt0(xS, xx)], sdtpldt0(xS, xx))), aElement0(xx), aSet0(sdtpldt0(xS, xx)), -(xS = sdtmndt0(sdtpldt0(xS, xx), xx)), aSet0(xS), -(aElementOf0(4 ^ [xS, xx, sdtpldt0(xS, xx)], xS))],extension(22,bind([[_24475, _24383, _24657], [xx, sdtpldt0(xS, xx), xS]]))).
% 3.07/3.48 cnf('1.1.1.4.4.1',plain,[-(aElement0(xx))],extension(18)).
% 3.07/3.48 cnf('1.1.1.4.4.2',plain,[-(aSet0(sdtpldt0(xS, xx)))],reduction('1.1')).
% 3.07/3.48 cnf('1.1.1.4.4.3',plain,[xS = sdtmndt0(sdtpldt0(xS, xx), xx)],lemmata('1.1.1')).
% 3.07/3.48 cnf('1.1.1.4.4.4',plain,[-(aSet0(xS))],extension(19)).
% 3.07/3.48 cnf('1.1.1.4.4.5',plain,[aElementOf0(4 ^ [xS, xx, sdtpldt0(xS, xx)], xS)],reduction('1.1.1')).
% 3.07/3.48 cnf('1.1.1.4.5',plain,[4 ^ [xS, xx, sdtpldt0(xS, xx)] = xx, aElement0(xx), aSet0(sdtpldt0(xS, xx)), -(xS = sdtmndt0(sdtpldt0(xS, xx), xx)), aSet0(xS), -(aElementOf0(4 ^ [xS, xx, sdtpldt0(xS, xx)], xS))],extension(23,bind([[_24475, _24383, _24657], [xx, sdtpldt0(xS, xx), xS]]))).
% 3.07/3.48 cnf('1.1.1.4.5.1',plain,[-(aElement0(xx))],extension(18)).
% 3.07/3.48 cnf('1.1.1.4.5.2',plain,[-(aSet0(sdtpldt0(xS, xx)))],reduction('1.1')).
% 3.07/3.48 cnf('1.1.1.4.5.3',plain,[xS = sdtmndt0(sdtpldt0(xS, xx), xx)],lemmata('1.1.1')).
% 3.07/3.48 cnf('1.1.1.4.5.4',plain,[-(aSet0(xS))],extension(19)).
% 3.07/3.48 cnf('1.1.1.4.5.5',plain,[aElementOf0(4 ^ [xS, xx, sdtpldt0(xS, xx)], xS)],reduction('1.1.1')).
% 3.07/3.48 cnf('1.1.1.5',plain,[-(aElement0(4 ^ [xS, xx, sdtpldt0(xS, xx)])), aElement0(xx), aSet0(sdtpldt0(xS, xx)), -(xS = sdtmndt0(sdtpldt0(xS, xx), xx)), aSet0(xS), -(aElementOf0(4 ^ [xS, xx, sdtpldt0(xS, xx)], xS))],extension(21,bind([[_24475, _24383, _24657], [xx, sdtpldt0(xS, xx), xS]]))).
% 3.07/3.48 cnf('1.1.1.5.1',plain,[-(aElement0(xx))],extension(18)).
% 3.07/3.48 cnf('1.1.1.5.2',plain,[-(aSet0(sdtpldt0(xS, xx)))],reduction('1.1')).
% 3.07/3.48 cnf('1.1.1.5.3',plain,[xS = sdtmndt0(sdtpldt0(xS, xx), xx)],lemmata('1.1.1')).
% 3.07/3.48 cnf('1.1.1.5.4',plain,[-(aSet0(xS))],extension(19)).
% 3.07/3.48 cnf('1.1.1.5.5',plain,[aElementOf0(4 ^ [xS, xx, sdtpldt0(xS, xx)], xS), aSet0(xS), -(aElement0(4 ^ [xS, xx, sdtpldt0(xS, xx)]))],extension(16,bind([[_19015, _19102], [xS, 4 ^ [xS, xx, sdtpldt0(xS, xx)]]]))).
% 3.07/3.48 cnf('1.1.1.5.5.1',plain,[-(aSet0(xS))],extension(19)).
% 3.07/3.48 cnf('1.1.1.5.5.2',plain,[aElement0(4 ^ [xS, xx, sdtpldt0(xS, xx)])],reduction('1.1.1')).
% 3.07/3.48 cnf('1.1.1.6',plain,[-(aElementOf0(4 ^ [xS, xx, sdtpldt0(xS, xx)], sdtpldt0(xS, xx))), -(9 ^ []), aElement0(4 ^ [xS, xx, sdtpldt0(xS, xx)]), 6 ^ [4 ^ [xS, xx, sdtpldt0(xS, xx)]]],extension(9,bind([[_26487], [4 ^ [xS, xx, sdtpldt0(xS, xx)]]]))).
% 3.07/3.48 cnf('1.1.1.6.1',plain,[9 ^ []],reduction('1')).
% 3.07/3.48 cnf('1.1.1.6.2',plain,[-(aElement0(4 ^ [xS, xx, sdtpldt0(xS, xx)]))],lemmata('1.1.1')).
% 3.07/3.48 cnf('1.1.1.6.3',plain,[-(6 ^ [4 ^ [xS, xx, sdtpldt0(xS, xx)]]), aElementOf0(4 ^ [xS, xx, sdtpldt0(xS, xx)], xS)],extension(8,bind([[_26487], [4 ^ [xS, xx, sdtpldt0(xS, xx)]]]))).
% 3.07/3.48 cnf('1.1.1.6.3.1',plain,[-(aElementOf0(4 ^ [xS, xx, sdtpldt0(xS, xx)], xS))],lemmata('1.1.1')).
% 3.07/3.48 cnf('1.1.1.7',plain,[4 ^ [xS, xx, sdtpldt0(xS, xx)] = xx, -(aElementOf0(xx, xS)), aElementOf0(4 ^ [xS, xx, sdtpldt0(xS, xx)], xS), xS = xS],extension(15,bind([[_15020, _14953, _15086, _15151], [xx, 4 ^ [xS, xx, sdtpldt0(xS, xx)], xS, xS]]))).
% 3.07/3.48 cnf('1.1.1.7.1',plain,[aElementOf0(xx, xS)],extension(20)).
% 3.07/3.48 cnf('1.1.1.7.2',plain,[-(aElementOf0(4 ^ [xS, xx, sdtpldt0(xS, xx)], xS)), aElement0(xx), aSet0(sdtpldt0(xS, xx)), -(xS = sdtmndt0(sdtpldt0(xS, xx), xx)), aSet0(xS), 4 ^ [xS, xx, sdtpldt0(xS, xx)] = xx],extension(23,bind([[_24657, _24383, _24475], [xS, sdtpldt0(xS, xx), xx]]))).
% 3.07/3.48 cnf('1.1.1.7.2.1',plain,[-(aElement0(xx))],extension(18)).
% 3.07/3.48 cnf('1.1.1.7.2.2',plain,[-(aSet0(sdtpldt0(xS, xx)))],reduction('1.1')).
% 3.07/3.48 cnf('1.1.1.7.2.3',plain,[xS = sdtmndt0(sdtpldt0(xS, xx), xx)],lemmata('1.1.1')).
% 3.07/3.48 cnf('1.1.1.7.2.4',plain,[-(aSet0(xS))],extension(19)).
% 3.07/3.48 cnf('1.1.1.7.2.5',plain,[-(4 ^ [xS, xx, sdtpldt0(xS, xx)] = xx)],reduction('1.1.1')).
% 3.07/3.48 cnf('1.1.1.7.3',plain,[-(xS = xS)],extension(14,bind([[_13716], [xS]]))).
% 3.07/3.48 cnf('1.2',plain,[-(14 ^ []), aElementOf0(13 ^ [], sdtpldt0(xS, xx)), 10 ^ [13 ^ []]],extension(4,bind([[_27928], [13 ^ []]]))).
% 3.07/3.48 cnf('1.2.1',plain,[-(aElementOf0(13 ^ [], sdtpldt0(xS, xx))), -(12 ^ [13 ^ []])],extension(2,bind([[_28410], [13 ^ []]]))).
% 3.07/3.48 cnf('1.2.1.1',plain,[12 ^ [13 ^ []], -(14 ^ []), aElementOf0(13 ^ [], sdtmndt0(sdtpldt0(xS, xx), xx))],extension(5,bind([[_28410], [13 ^ []]]))).
% 3.07/3.48 cnf('1.2.1.1.1',plain,[14 ^ []],reduction('1')).
% 3.07/3.48 cnf('1.2.1.1.2',plain,[-(aElementOf0(13 ^ [], sdtmndt0(sdtpldt0(xS, xx), xx))), -(14 ^ [])],extension(7)).
% 3.07/3.48 cnf('1.2.1.1.2.1',plain,[14 ^ []],lemmata('1.2.1.1')).
% 3.07/3.48 cnf('1.2.2',plain,[-(10 ^ [13 ^ []]), -(aElementOf0(13 ^ [], xS)), -(13 ^ [] = xx)],extension(3,bind([[_27928], [13 ^ []]]))).
% 3.07/3.48 cnf('1.2.2.1',plain,[aElementOf0(13 ^ [], xS), -(14 ^ [])],extension(6)).
% 3.07/3.48 cnf('1.2.2.1.1',plain,[14 ^ []],reduction('1')).
% 3.07/3.48 cnf('1.2.2.2',plain,[13 ^ [] = xx, -(12 ^ [13 ^ []])],extension(1,bind([[_28410], [13 ^ []]]))).
% 3.07/3.48 cnf('1.2.2.2.1',plain,[12 ^ [13 ^ []], -(14 ^ []), aElementOf0(13 ^ [], sdtmndt0(sdtpldt0(xS, xx), xx))],extension(5,bind([[_28410], [13 ^ []]]))).
% 3.07/3.48 cnf('1.2.2.2.1.1',plain,[14 ^ []],reduction('1')).
% 3.07/3.48 cnf('1.2.2.2.1.2',plain,[-(aElementOf0(13 ^ [], sdtmndt0(sdtpldt0(xS, xx), xx))), -(14 ^ [])],extension(7)).
% 3.07/3.48 cnf('1.2.2.2.1.2.1',plain,[14 ^ []],lemmata('1.2.2.2.1')).
% 3.07/3.48 %-----------------------------------------------------
% 3.07/3.48
% 3.07/3.48 % SZS output end Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------