%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : RNG119+4 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:24:15 AM UTC 2025
% Result : Theorem 1.84s 2.07s
% Output : Proof 1.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : RNG119+4 : TPTP v9.0.0. Released v4.0.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n013.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 03:25:38 EDT 2025
% 0.14/0.36 % CPUTime :
% 1.84/2.07 % SZS status Theorem
% 1.84/2.07 % SZS output start Proof
% 1.84/2.07 tff(xb_type, type, (
% 1.84/2.07 xb: $i)).
% 1.84/2.07 tff(sdtasdt0_type, type, (
% 1.84/2.07 sdtasdt0: ( $i * $i ) > $i)).
% 1.84/2.07 tff(xq_type, type, (
% 1.84/2.07 xq: $i)).
% 1.84/2.07 tff(xu_type, type, (
% 1.84/2.07 xu: $i)).
% 1.84/2.07 tff(sdtpldt0_type, type, (
% 1.84/2.07 sdtpldt0: ( $i * $i ) > $i)).
% 1.84/2.07 tff(sz00_type, type, (
% 1.84/2.07 sz00: $i)).
% 1.84/2.07 tff(xr_type, type, (
% 1.84/2.07 xr: $i)).
% 1.84/2.07 tff(aElement0_type, type, (
% 1.84/2.07 aElement0: $i > $o)).
% 1.84/2.07 tff(iLess0_type, type, (
% 1.84/2.07 iLess0: ( $i * $i ) > $o)).
% 1.84/2.07 tff(sbrdtbr0_type, type, (
% 1.84/2.07 sbrdtbr0: $i > $i)).
% 1.84/2.07 tff(tptp_fun_W1_38_type, type, (
% 1.84/2.07 tptp_fun_W1_38: $i)).
% 1.84/2.07 tff(tptp_fun_W0_39_type, type, (
% 1.84/2.07 tptp_fun_W0_39: $i)).
% 1.84/2.07 tff(xa_type, type, (
% 1.84/2.07 xa: $i)).
% 1.84/2.07 tff(doDivides0_type, type, (
% 1.84/2.07 doDivides0: ( $i * $i ) > $o)).
% 1.84/2.07 tff(1,plain,
% 1.84/2.07 ((sdtasdt0(xq, xu) = sdtpldt0(sdtasdt0(xq, xu), sz00)) <=> (sdtpldt0(sdtasdt0(xq, xu), sz00) = sdtasdt0(xq, xu))),
% 1.84/2.07 inference(commutativity,[status(thm)],[])).
% 1.84/2.07 tff(2,plain,
% 1.84/2.07 ((xr = sz00) <=> (xr = sz00)),
% 1.84/2.07 inference(rewrite,[status(thm)],[])).
% 1.84/2.07 tff(3,plain,
% 1.84/2.07 ((~(~(xr = sz00))) <=> (xr = sz00)),
% 1.84/2.07 inference(rewrite,[status(thm)],[])).
% 1.84/2.07 tff(4,axiom,(~(~(xr = sz00))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 1.84/2.07 tff(5,plain,
% 1.84/2.07 (xr = sz00),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[4, 3])).
% 1.84/2.07 tff(6,plain,
% 1.84/2.07 (xr = sz00),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[5, 2])).
% 1.84/2.07 tff(7,plain,
% 1.84/2.07 (sz00 = xr),
% 1.84/2.07 inference(symmetry,[status(thm)],[6])).
% 1.84/2.07 tff(8,plain,
% 1.84/2.07 (sdtpldt0(sdtasdt0(xq, xu), sz00) = sdtpldt0(sdtasdt0(xq, xu), xr)),
% 1.84/2.07 inference(monotonicity,[status(thm)],[7])).
% 1.84/2.07 tff(9,plain,
% 1.84/2.07 (sdtpldt0(sdtasdt0(xq, xu), xr) = sdtpldt0(sdtasdt0(xq, xu), sz00)),
% 1.84/2.07 inference(symmetry,[status(thm)],[8])).
% 1.84/2.07 tff(10,plain,
% 1.84/2.07 ((xb = sdtpldt0(sdtasdt0(xq, xu), xr)) <=> (xb = sdtpldt0(sdtasdt0(xq, xu), xr))),
% 1.84/2.07 inference(rewrite,[status(thm)],[])).
% 1.84/2.07 tff(11,axiom,(((aElement0(xq) & aElement0(xr)) & (xb = sdtpldt0(sdtasdt0(xq, xu), xr))) & ((xr = sz00) | iLess0(sbrdtbr0(xr), sbrdtbr0(xu)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__2666')).
% 1.84/2.07 tff(12,plain,
% 1.84/2.07 ((aElement0(xq) & aElement0(xr)) & (xb = sdtpldt0(sdtasdt0(xq, xu), xr))),
% 1.84/2.07 inference(and_elim,[status(thm)],[11])).
% 1.84/2.07 tff(13,plain,
% 1.84/2.07 (xb = sdtpldt0(sdtasdt0(xq, xu), xr)),
% 1.84/2.07 inference(and_elim,[status(thm)],[12])).
% 1.84/2.07 tff(14,plain,
% 1.84/2.07 (xb = sdtpldt0(sdtasdt0(xq, xu), xr)),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[13, 10])).
% 1.84/2.07 tff(15,plain,
% 1.84/2.07 (xb = sdtpldt0(sdtasdt0(xq, xu), sz00)),
% 1.84/2.07 inference(transitivity,[status(thm)],[14, 9])).
% 1.84/2.07 tff(16,plain,
% 1.84/2.07 (?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))) <=> ?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))),
% 1.84/2.07 inference(rewrite,[status(thm)],[])).
% 1.84/2.07 tff(17,plain,
% 1.84/2.07 (^[W0: $i, W1: $i] : rewrite(((aElement0(W0) & aElement0(W1)) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))) <=> (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))))),
% 1.84/2.07 inference(bind,[status(th)],[])).
% 1.84/2.07 tff(18,plain,
% 1.84/2.07 (?[W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1)))) <=> ?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))),
% 1.84/2.07 inference(quant_intro,[status(thm)],[17])).
% 1.84/2.07 tff(19,axiom,(?[W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__2416')).
% 1.84/2.07 tff(20,plain,
% 1.84/2.07 (?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[19, 18])).
% 1.84/2.07 tff(21,plain,
% 1.84/2.07 (?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[20, 16])).
% 1.84/2.07 tff(22,plain,(
% 1.84/2.07 aElement0(W0!39) & aElement0(W1!38) & (xu = sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(xb, W1!38)))),
% 1.84/2.07 inference(skolemize,[status(sab)],[21])).
% 1.84/2.07 tff(23,plain,
% 1.84/2.07 (xu = sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(xb, W1!38))),
% 1.84/2.07 inference(and_elim,[status(thm)],[22])).
% 1.84/2.07 tff(24,plain,
% 1.84/2.07 (sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(xb, W1!38)) = xu),
% 1.84/2.07 inference(symmetry,[status(thm)],[23])).
% 1.84/2.07 tff(25,plain,
% 1.84/2.07 (aElement0(sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(xb, W1!38))) <=> aElement0(xu)),
% 1.84/2.07 inference(monotonicity,[status(thm)],[24])).
% 1.84/2.07 tff(26,plain,
% 1.84/2.07 (aElement0(W0!39)),
% 1.84/2.07 inference(and_elim,[status(thm)],[22])).
% 1.84/2.07 tff(27,plain,
% 1.84/2.07 (aElement0(xa) <=> aElement0(xa)),
% 1.84/2.07 inference(rewrite,[status(thm)],[])).
% 1.84/2.07 tff(28,axiom,(aElement0(xa) & aElement0(xb)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__2091')).
% 1.84/2.07 tff(29,plain,
% 1.84/2.07 (aElement0(xa)),
% 1.84/2.07 inference(and_elim,[status(thm)],[28])).
% 1.84/2.07 tff(30,plain,
% 1.84/2.07 (aElement0(xa)),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[29, 27])).
% 1.84/2.07 tff(31,plain,
% 1.84/2.07 (^[W0: $i, W1: $i] : refl((aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0))) <=> (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0))))),
% 1.84/2.07 inference(bind,[status(th)],[])).
% 1.84/2.07 tff(32,plain,
% 1.84/2.07 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0))) <=> ![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 1.84/2.07 inference(quant_intro,[status(thm)],[31])).
% 1.84/2.07 tff(33,plain,
% 1.84/2.07 (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aElement0(W0) & aElement0(W1)) <=> (~((~aElement0(W1)) | (~aElement0(W0))))), ((~(aElement0(W0) & aElement0(W1))) <=> (~(~((~aElement0(W1)) | (~aElement0(W0))))))), rewrite((~(~((~aElement0(W1)) | (~aElement0(W0))))) <=> ((~aElement0(W1)) | (~aElement0(W0)))), ((~(aElement0(W0) & aElement0(W1))) <=> ((~aElement0(W1)) | (~aElement0(W0))))), ((aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))) <=> (aElement0(sdtasdt0(W0, W1)) | ((~aElement0(W1)) | (~aElement0(W0)))))), rewrite((aElement0(sdtasdt0(W0, W1)) | ((~aElement0(W1)) | (~aElement0(W0)))) <=> (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))), ((aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))) <=> (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))))),
% 1.84/2.07 inference(bind,[status(th)],[])).
% 1.84/2.07 tff(34,plain,
% 1.84/2.07 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))) <=> ![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 1.84/2.07 inference(quant_intro,[status(thm)],[33])).
% 1.84/2.07 tff(35,plain,
% 1.84/2.07 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))) <=> ![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 1.84/2.07 inference(rewrite,[status(thm)],[])).
% 1.84/2.07 tff(36,plain,
% 1.84/2.07 (^[W0: $i, W1: $i] : rewrite(((aElement0(W0) & aElement0(W1)) => aElement0(sdtasdt0(W0, W1))) <=> (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))))),
% 1.84/2.07 inference(bind,[status(th)],[])).
% 1.84/2.07 tff(37,plain,
% 1.84/2.07 (![W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) => aElement0(sdtasdt0(W0, W1))) <=> ![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 1.84/2.07 inference(quant_intro,[status(thm)],[36])).
% 1.84/2.07 tff(38,axiom,(![W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) => aElement0(sdtasdt0(W0, W1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mSortsB_02')).
% 1.84/2.07 tff(39,plain,
% 1.84/2.07 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[38, 37])).
% 1.84/2.07 tff(40,plain,
% 1.84/2.07 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[39, 35])).
% 1.84/2.07 tff(41,plain,(
% 1.84/2.07 ![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 1.84/2.07 inference(skolemize,[status(sab)],[40])).
% 1.84/2.07 tff(42,plain,
% 1.84/2.07 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[41, 34])).
% 1.84/2.07 tff(43,plain,
% 1.84/2.07 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[42, 32])).
% 1.84/2.07 tff(44,plain,
% 1.84/2.07 (((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtasdt0(xa, W0!39)) | (~aElement0(W0!39)) | (~aElement0(xa)))) <=> ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | aElement0(sdtasdt0(xa, W0!39)) | (~aElement0(W0!39)) | (~aElement0(xa)))),
% 1.84/2.07 inference(rewrite,[status(thm)],[])).
% 1.84/2.07 tff(45,plain,
% 1.84/2.07 ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtasdt0(xa, W0!39)) | (~aElement0(W0!39)) | (~aElement0(xa)))),
% 1.84/2.07 inference(quant_inst,[status(thm)],[])).
% 1.84/2.07 tff(46,plain,
% 1.84/2.07 ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | aElement0(sdtasdt0(xa, W0!39)) | (~aElement0(W0!39)) | (~aElement0(xa))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[45, 44])).
% 1.84/2.07 tff(47,plain,
% 1.84/2.07 (aElement0(sdtasdt0(xa, W0!39))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[46, 43, 30, 26])).
% 1.84/2.07 tff(48,plain,
% 1.84/2.07 (aElement0(W1!38)),
% 1.84/2.07 inference(and_elim,[status(thm)],[22])).
% 1.84/2.07 tff(49,plain,
% 1.84/2.07 (aElement0(xb) <=> aElement0(xb)),
% 1.84/2.07 inference(rewrite,[status(thm)],[])).
% 1.84/2.07 tff(50,plain,
% 1.84/2.07 (aElement0(xb)),
% 1.84/2.07 inference(and_elim,[status(thm)],[28])).
% 1.84/2.07 tff(51,plain,
% 1.84/2.07 (aElement0(xb)),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[50, 49])).
% 1.84/2.07 tff(52,plain,
% 1.84/2.07 (((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtasdt0(xb, W1!38)) | (~aElement0(W1!38)) | (~aElement0(xb)))) <=> ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | aElement0(sdtasdt0(xb, W1!38)) | (~aElement0(W1!38)) | (~aElement0(xb)))),
% 1.84/2.07 inference(rewrite,[status(thm)],[])).
% 1.84/2.07 tff(53,plain,
% 1.84/2.07 ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtasdt0(xb, W1!38)) | (~aElement0(W1!38)) | (~aElement0(xb)))),
% 1.84/2.07 inference(quant_inst,[status(thm)],[])).
% 1.84/2.07 tff(54,plain,
% 1.84/2.07 ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | aElement0(sdtasdt0(xb, W1!38)) | (~aElement0(W1!38)) | (~aElement0(xb))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[53, 52])).
% 1.84/2.07 tff(55,plain,
% 1.84/2.07 (aElement0(sdtasdt0(xb, W1!38))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[54, 43, 51, 48])).
% 1.84/2.07 tff(56,plain,
% 1.84/2.07 (^[W0: $i, W1: $i] : refl((aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0))) <=> (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0))))),
% 1.84/2.07 inference(bind,[status(th)],[])).
% 1.84/2.07 tff(57,plain,
% 1.84/2.07 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0))) <=> ![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 1.84/2.07 inference(quant_intro,[status(thm)],[56])).
% 1.84/2.07 tff(58,plain,
% 1.84/2.07 (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aElement0(W0) & aElement0(W1)) <=> (~((~aElement0(W1)) | (~aElement0(W0))))), ((~(aElement0(W0) & aElement0(W1))) <=> (~(~((~aElement0(W1)) | (~aElement0(W0))))))), rewrite((~(~((~aElement0(W1)) | (~aElement0(W0))))) <=> ((~aElement0(W1)) | (~aElement0(W0)))), ((~(aElement0(W0) & aElement0(W1))) <=> ((~aElement0(W1)) | (~aElement0(W0))))), ((aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))) <=> (aElement0(sdtpldt0(W0, W1)) | ((~aElement0(W1)) | (~aElement0(W0)))))), rewrite((aElement0(sdtpldt0(W0, W1)) | ((~aElement0(W1)) | (~aElement0(W0)))) <=> (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))), ((aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))) <=> (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))))),
% 1.84/2.07 inference(bind,[status(th)],[])).
% 1.84/2.07 tff(59,plain,
% 1.84/2.07 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))) <=> ![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 1.84/2.07 inference(quant_intro,[status(thm)],[58])).
% 1.84/2.07 tff(60,plain,
% 1.84/2.07 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))) <=> ![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 1.84/2.07 inference(rewrite,[status(thm)],[])).
% 1.84/2.07 tff(61,plain,
% 1.84/2.07 (^[W0: $i, W1: $i] : rewrite(((aElement0(W0) & aElement0(W1)) => aElement0(sdtpldt0(W0, W1))) <=> (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))))),
% 1.84/2.07 inference(bind,[status(th)],[])).
% 1.84/2.07 tff(62,plain,
% 1.84/2.07 (![W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) => aElement0(sdtpldt0(W0, W1))) <=> ![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 1.84/2.07 inference(quant_intro,[status(thm)],[61])).
% 1.84/2.07 tff(63,axiom,(![W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) => aElement0(sdtpldt0(W0, W1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mSortsB')).
% 1.84/2.07 tff(64,plain,
% 1.84/2.07 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[63, 62])).
% 1.84/2.07 tff(65,plain,
% 1.84/2.07 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[64, 60])).
% 1.84/2.07 tff(66,plain,(
% 1.84/2.07 ![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 1.84/2.07 inference(skolemize,[status(sab)],[65])).
% 1.84/2.07 tff(67,plain,
% 1.84/2.07 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[66, 59])).
% 1.84/2.07 tff(68,plain,
% 1.84/2.07 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[67, 57])).
% 1.84/2.07 tff(69,plain,
% 1.84/2.07 (((~![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((~aElement0(sdtasdt0(xb, W1!38))) | (~aElement0(sdtasdt0(xa, W0!39))) | aElement0(sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(xb, W1!38))))) <=> ((~![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(sdtasdt0(xb, W1!38))) | (~aElement0(sdtasdt0(xa, W0!39))) | aElement0(sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(xb, W1!38))))),
% 1.84/2.07 inference(rewrite,[status(thm)],[])).
% 1.84/2.07 tff(70,plain,
% 1.84/2.07 ((aElement0(sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(xb, W1!38))) | (~aElement0(sdtasdt0(xb, W1!38))) | (~aElement0(sdtasdt0(xa, W0!39)))) <=> ((~aElement0(sdtasdt0(xb, W1!38))) | (~aElement0(sdtasdt0(xa, W0!39))) | aElement0(sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(xb, W1!38))))),
% 1.84/2.07 inference(rewrite,[status(thm)],[])).
% 1.84/2.07 tff(71,plain,
% 1.84/2.07 (((~![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(xb, W1!38))) | (~aElement0(sdtasdt0(xb, W1!38))) | (~aElement0(sdtasdt0(xa, W0!39))))) <=> ((~![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((~aElement0(sdtasdt0(xb, W1!38))) | (~aElement0(sdtasdt0(xa, W0!39))) | aElement0(sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(xb, W1!38)))))),
% 1.84/2.07 inference(monotonicity,[status(thm)],[70])).
% 1.84/2.07 tff(72,plain,
% 1.84/2.07 (((~![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(xb, W1!38))) | (~aElement0(sdtasdt0(xb, W1!38))) | (~aElement0(sdtasdt0(xa, W0!39))))) <=> ((~![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(sdtasdt0(xb, W1!38))) | (~aElement0(sdtasdt0(xa, W0!39))) | aElement0(sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(xb, W1!38))))),
% 1.84/2.07 inference(transitivity,[status(thm)],[71, 69])).
% 1.84/2.07 tff(73,plain,
% 1.84/2.07 ((~![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(xb, W1!38))) | (~aElement0(sdtasdt0(xb, W1!38))) | (~aElement0(sdtasdt0(xa, W0!39))))),
% 1.84/2.07 inference(quant_inst,[status(thm)],[])).
% 1.84/2.07 tff(74,plain,
% 1.84/2.07 ((~![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(sdtasdt0(xb, W1!38))) | (~aElement0(sdtasdt0(xa, W0!39))) | aElement0(sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(xb, W1!38)))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[73, 72])).
% 1.84/2.07 tff(75,plain,
% 1.84/2.07 ((~aElement0(sdtasdt0(xb, W1!38))) | (~aElement0(sdtasdt0(xa, W0!39))) | aElement0(sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(xb, W1!38)))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[74, 68])).
% 1.84/2.07 tff(76,plain,
% 1.84/2.07 (aElement0(sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(xb, W1!38)))),
% 1.84/2.07 inference(unit_resolution,[status(thm)],[75, 55, 47])).
% 1.84/2.07 tff(77,plain,
% 1.84/2.07 (aElement0(xu)),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[76, 25])).
% 1.84/2.07 tff(78,plain,
% 1.84/2.07 (aElement0(xq) <=> aElement0(xq)),
% 1.84/2.07 inference(rewrite,[status(thm)],[])).
% 1.84/2.07 tff(79,plain,
% 1.84/2.07 (aElement0(xq) & aElement0(xr)),
% 1.84/2.07 inference(and_elim,[status(thm)],[12])).
% 1.84/2.07 tff(80,plain,
% 1.84/2.07 (aElement0(xq)),
% 1.84/2.07 inference(and_elim,[status(thm)],[79])).
% 1.84/2.07 tff(81,plain,
% 1.84/2.07 (aElement0(xq)),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[80, 78])).
% 1.84/2.07 tff(82,plain,
% 1.84/2.07 (^[W0: $i, W1: $i] : refl(((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0))) <=> ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0))))),
% 1.84/2.07 inference(bind,[status(th)],[])).
% 1.84/2.07 tff(83,plain,
% 1.84/2.07 (![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0))) <=> ![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 1.84/2.07 inference(quant_intro,[status(thm)],[82])).
% 1.84/2.07 tff(84,plain,
% 1.84/2.07 (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aElement0(W0) & aElement0(W1)) <=> (~((~aElement0(W1)) | (~aElement0(W0))))), ((~(aElement0(W0) & aElement0(W1))) <=> (~(~((~aElement0(W1)) | (~aElement0(W0))))))), rewrite((~(~((~aElement0(W1)) | (~aElement0(W0))))) <=> ((~aElement0(W1)) | (~aElement0(W0)))), ((~(aElement0(W0) & aElement0(W1))) <=> ((~aElement0(W1)) | (~aElement0(W0))))), (((~(aElement0(W0) & aElement0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> (((~aElement0(W1)) | (~aElement0(W0))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))))), rewrite((((~aElement0(W1)) | (~aElement0(W0))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))), (((~(aElement0(W0) & aElement0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))))),
% 1.84/2.07 inference(bind,[status(th)],[])).
% 1.84/2.07 tff(85,plain,
% 1.84/2.07 (![W0: $i, W1: $i] : ((~(aElement0(W0) & aElement0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 1.84/2.07 inference(quant_intro,[status(thm)],[84])).
% 1.84/2.07 tff(86,plain,
% 1.84/2.07 (![W0: $i, W1: $i] : ((~(aElement0(W0) & aElement0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ![W0: $i, W1: $i] : ((~(aElement0(W0) & aElement0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 1.84/2.07 inference(rewrite,[status(thm)],[])).
% 1.84/2.07 tff(87,plain,
% 1.84/2.07 (^[W0: $i, W1: $i] : rewrite(((aElement0(W0) & aElement0(W1)) => (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ((~(aElement0(W0) & aElement0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))))),
% 1.84/2.07 inference(bind,[status(th)],[])).
% 1.84/2.07 tff(88,plain,
% 1.84/2.07 (![W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) => (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ![W0: $i, W1: $i] : ((~(aElement0(W0) & aElement0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 1.84/2.07 inference(quant_intro,[status(thm)],[87])).
% 1.84/2.07 tff(89,axiom,(![W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) => (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mMulComm')).
% 1.84/2.07 tff(90,plain,
% 1.84/2.07 (![W0: $i, W1: $i] : ((~(aElement0(W0) & aElement0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[89, 88])).
% 1.84/2.07 tff(91,plain,
% 1.84/2.07 (![W0: $i, W1: $i] : ((~(aElement0(W0) & aElement0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 1.84/2.07 inference(modus_ponens,[status(thm)],[90, 86])).
% 1.84/2.07 tff(92,plain,(
% 1.84/2.07 ![W0: $i, W1: $i] : ((~(aElement0(W0) & aElement0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 1.84/2.07 inference(skolemize,[status(sab)],[91])).
% 1.84/2.07 tff(93,plain,
% 1.84/2.07 (![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 1.92/2.08 inference(modus_ponens,[status(thm)],[92, 85])).
% 1.92/2.08 tff(94,plain,
% 1.92/2.08 (![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 1.92/2.08 inference(modus_ponens,[status(thm)],[93, 83])).
% 1.92/2.08 tff(95,plain,
% 1.92/2.08 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((~aElement0(xu)) | (~aElement0(xq)) | (sdtasdt0(xu, xq) = sdtasdt0(xq, xu)))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(xu)) | (~aElement0(xq)) | (sdtasdt0(xu, xq) = sdtasdt0(xq, xu)))),
% 1.92/2.08 inference(rewrite,[status(thm)],[])).
% 1.92/2.08 tff(96,plain,
% 1.92/2.08 (((sdtasdt0(xu, xq) = sdtasdt0(xq, xu)) | (~aElement0(xq)) | (~aElement0(xu))) <=> ((~aElement0(xu)) | (~aElement0(xq)) | (sdtasdt0(xu, xq) = sdtasdt0(xq, xu)))),
% 1.92/2.08 inference(rewrite,[status(thm)],[])).
% 1.92/2.08 tff(97,plain,
% 1.92/2.08 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((sdtasdt0(xu, xq) = sdtasdt0(xq, xu)) | (~aElement0(xq)) | (~aElement0(xu)))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((~aElement0(xu)) | (~aElement0(xq)) | (sdtasdt0(xu, xq) = sdtasdt0(xq, xu))))),
% 1.92/2.08 inference(monotonicity,[status(thm)],[96])).
% 1.92/2.08 tff(98,plain,
% 1.92/2.08 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((sdtasdt0(xu, xq) = sdtasdt0(xq, xu)) | (~aElement0(xq)) | (~aElement0(xu)))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(xu)) | (~aElement0(xq)) | (sdtasdt0(xu, xq) = sdtasdt0(xq, xu)))),
% 1.92/2.08 inference(transitivity,[status(thm)],[97, 95])).
% 1.92/2.08 tff(99,plain,
% 1.92/2.08 ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((sdtasdt0(xu, xq) = sdtasdt0(xq, xu)) | (~aElement0(xq)) | (~aElement0(xu)))),
% 1.92/2.08 inference(quant_inst,[status(thm)],[])).
% 1.92/2.08 tff(100,plain,
% 1.92/2.08 ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(xu)) | (~aElement0(xq)) | (sdtasdt0(xu, xq) = sdtasdt0(xq, xu))),
% 1.92/2.08 inference(modus_ponens,[status(thm)],[99, 98])).
% 1.92/2.08 tff(101,plain,
% 1.92/2.08 ((~aElement0(xu)) | (sdtasdt0(xu, xq) = sdtasdt0(xq, xu))),
% 1.92/2.08 inference(unit_resolution,[status(thm)],[100, 94, 81])).
% 1.92/2.08 tff(102,plain,
% 1.92/2.08 (sdtasdt0(xu, xq) = sdtasdt0(xq, xu)),
% 1.92/2.08 inference(unit_resolution,[status(thm)],[101, 77])).
% 1.92/2.08 tff(103,plain,
% 1.92/2.08 ((sdtasdt0(xu, xq) = xb) <=> (sdtasdt0(xq, xu) = sdtpldt0(sdtasdt0(xq, xu), sz00))),
% 1.92/2.08 inference(monotonicity,[status(thm)],[102, 15])).
% 1.92/2.08 tff(104,plain,
% 1.92/2.08 ((sdtasdt0(xu, xq) = xb) <=> (sdtpldt0(sdtasdt0(xq, xu), sz00) = sdtasdt0(xq, xu))),
% 1.92/2.08 inference(transitivity,[status(thm)],[103, 1])).
% 1.92/2.08 tff(105,plain,
% 1.92/2.08 ((sdtpldt0(sdtasdt0(xq, xu), sz00) = sdtasdt0(xq, xu)) <=> (sdtasdt0(xu, xq) = xb)),
% 1.92/2.08 inference(symmetry,[status(thm)],[104])).
% 1.92/2.08 tff(106,plain,
% 1.92/2.08 (((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((~aElement0(xu)) | aElement0(sdtasdt0(xq, xu)) | (~aElement0(xq)))) <=> ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(xu)) | aElement0(sdtasdt0(xq, xu)) | (~aElement0(xq)))),
% 1.92/2.08 inference(rewrite,[status(thm)],[])).
% 1.92/2.08 tff(107,plain,
% 1.92/2.08 ((aElement0(sdtasdt0(xq, xu)) | (~aElement0(xu)) | (~aElement0(xq))) <=> ((~aElement0(xu)) | aElement0(sdtasdt0(xq, xu)) | (~aElement0(xq)))),
% 1.92/2.08 inference(rewrite,[status(thm)],[])).
% 1.92/2.08 tff(108,plain,
% 1.92/2.08 (((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtasdt0(xq, xu)) | (~aElement0(xu)) | (~aElement0(xq)))) <=> ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((~aElement0(xu)) | aElement0(sdtasdt0(xq, xu)) | (~aElement0(xq))))),
% 1.92/2.08 inference(monotonicity,[status(thm)],[107])).
% 1.92/2.08 tff(109,plain,
% 1.92/2.08 (((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtasdt0(xq, xu)) | (~aElement0(xu)) | (~aElement0(xq)))) <=> ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(xu)) | aElement0(sdtasdt0(xq, xu)) | (~aElement0(xq)))),
% 1.92/2.08 inference(transitivity,[status(thm)],[108, 106])).
% 1.92/2.08 tff(110,plain,
% 1.92/2.08 ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtasdt0(xq, xu)) | (~aElement0(xu)) | (~aElement0(xq)))),
% 1.92/2.08 inference(quant_inst,[status(thm)],[])).
% 1.92/2.08 tff(111,plain,
% 1.92/2.08 ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(xu)) | aElement0(sdtasdt0(xq, xu)) | (~aElement0(xq))),
% 1.92/2.08 inference(modus_ponens,[status(thm)],[110, 109])).
% 1.92/2.08 tff(112,plain,
% 1.92/2.08 ((~aElement0(xu)) | aElement0(sdtasdt0(xq, xu))),
% 1.92/2.08 inference(unit_resolution,[status(thm)],[111, 43, 81])).
% 1.92/2.08 tff(113,plain,
% 1.92/2.08 (aElement0(sdtasdt0(xq, xu))),
% 1.92/2.08 inference(unit_resolution,[status(thm)],[112, 77])).
% 1.92/2.08 tff(114,plain,
% 1.92/2.08 (^[W0: $i] : refl(((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0)))))) <=> ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0)))))))),
% 1.92/2.08 inference(bind,[status(th)],[])).
% 1.92/2.08 tff(115,plain,
% 1.92/2.08 (![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0)))))) <=> ![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))),
% 1.92/2.08 inference(quant_intro,[status(thm)],[114])).
% 1.92/2.08 tff(116,plain,
% 1.92/2.08 (^[W0: $i] : rewrite(((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))) <=> ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0)))))))),
% 1.92/2.08 inference(bind,[status(th)],[])).
% 1.92/2.08 tff(117,plain,
% 1.92/2.08 (![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))) <=> ![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))),
% 1.92/2.08 inference(quant_intro,[status(thm)],[116])).
% 1.92/2.08 tff(118,plain,
% 1.92/2.08 (![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))) <=> ![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))),
% 1.92/2.08 inference(rewrite,[status(thm)],[])).
% 1.92/2.08 tff(119,plain,
% 1.92/2.08 (^[W0: $i] : rewrite((aElement0(W0) => ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))) <=> ((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))))),
% 1.92/2.08 inference(bind,[status(th)],[])).
% 1.92/2.08 tff(120,plain,
% 1.92/2.08 (![W0: $i] : (aElement0(W0) => ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))) <=> ![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))),
% 1.92/2.08 inference(quant_intro,[status(thm)],[119])).
% 1.92/2.08 tff(121,axiom,(![W0: $i] : (aElement0(W0) => ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mAddZero')).
% 1.92/2.08 tff(122,plain,
% 1.92/2.08 (![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))),
% 1.92/2.08 inference(modus_ponens,[status(thm)],[121, 120])).
% 1.92/2.08 tff(123,plain,
% 1.92/2.08 (![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))),
% 1.92/2.08 inference(modus_ponens,[status(thm)],[122, 118])).
% 1.92/2.08 tff(124,plain,(
% 1.92/2.08 ![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))),
% 1.92/2.08 inference(skolemize,[status(sab)],[123])).
% 1.92/2.08 tff(125,plain,
% 1.92/2.08 (![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))),
% 1.92/2.08 inference(modus_ponens,[status(thm)],[124, 117])).
% 1.92/2.08 tff(126,plain,
% 1.92/2.08 (![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))),
% 1.92/2.08 inference(modus_ponens,[status(thm)],[125, 115])).
% 1.92/2.08 tff(127,plain,
% 1.92/2.08 (((~![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | ((~aElement0(sdtasdt0(xq, xu))) | (~((~(sdtpldt0(sdtasdt0(xq, xu), sz00) = sdtasdt0(xq, xu))) | (~(sdtasdt0(xq, xu) = sdtpldt0(sz00, sdtasdt0(xq, xu)))))))) <=> ((~![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | (~aElement0(sdtasdt0(xq, xu))) | (~((~(sdtpldt0(sdtasdt0(xq, xu), sz00) = sdtasdt0(xq, xu))) | (~(sdtasdt0(xq, xu) = sdtpldt0(sz00, sdtasdt0(xq, xu)))))))),
% 1.92/2.08 inference(rewrite,[status(thm)],[])).
% 1.92/2.08 tff(128,plain,
% 1.92/2.08 ((~![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | ((~aElement0(sdtasdt0(xq, xu))) | (~((~(sdtpldt0(sdtasdt0(xq, xu), sz00) = sdtasdt0(xq, xu))) | (~(sdtasdt0(xq, xu) = sdtpldt0(sz00, sdtasdt0(xq, xu)))))))),
% 1.92/2.08 inference(quant_inst,[status(thm)],[])).
% 1.92/2.08 tff(129,plain,
% 1.92/2.08 ((~![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | (~aElement0(sdtasdt0(xq, xu))) | (~((~(sdtpldt0(sdtasdt0(xq, xu), sz00) = sdtasdt0(xq, xu))) | (~(sdtasdt0(xq, xu) = sdtpldt0(sz00, sdtasdt0(xq, xu))))))),
% 1.92/2.08 inference(modus_ponens,[status(thm)],[128, 127])).
% 1.92/2.08 tff(130,plain,
% 1.92/2.08 ((~aElement0(sdtasdt0(xq, xu))) | (~((~(sdtpldt0(sdtasdt0(xq, xu), sz00) = sdtasdt0(xq, xu))) | (~(sdtasdt0(xq, xu) = sdtpldt0(sz00, sdtasdt0(xq, xu))))))),
% 1.92/2.08 inference(unit_resolution,[status(thm)],[129, 126])).
% 1.92/2.08 tff(131,plain,
% 1.92/2.08 (~((~(sdtpldt0(sdtasdt0(xq, xu), sz00) = sdtasdt0(xq, xu))) | (~(sdtasdt0(xq, xu) = sdtpldt0(sz00, sdtasdt0(xq, xu)))))),
% 1.92/2.08 inference(unit_resolution,[status(thm)],[130, 113])).
% 1.92/2.08 tff(132,plain,
% 1.92/2.08 (((~(sdtpldt0(sdtasdt0(xq, xu), sz00) = sdtasdt0(xq, xu))) | (~(sdtasdt0(xq, xu) = sdtpldt0(sz00, sdtasdt0(xq, xu))))) | (sdtpldt0(sdtasdt0(xq, xu), sz00) = sdtasdt0(xq, xu))),
% 1.92/2.08 inference(tautology,[status(thm)],[])).
% 1.92/2.08 tff(133,plain,
% 1.92/2.08 (sdtpldt0(sdtasdt0(xq, xu), sz00) = sdtasdt0(xq, xu)),
% 1.92/2.08 inference(unit_resolution,[status(thm)],[132, 131])).
% 1.92/2.08 tff(134,plain,
% 1.92/2.08 (sdtasdt0(xu, xq) = xb),
% 1.92/2.08 inference(modus_ponens,[status(thm)],[133, 105])).
% 1.92/2.08 tff(135,plain,
% 1.92/2.08 (^[W0: $i] : refl(((~aElement0(W0)) | (~(sdtasdt0(xu, W0) = xb))) <=> ((~aElement0(W0)) | (~(sdtasdt0(xu, W0) = xb))))),
% 1.92/2.08 inference(bind,[status(th)],[])).
% 1.92/2.08 tff(136,plain,
% 1.92/2.08 (![W0: $i] : ((~aElement0(W0)) | (~(sdtasdt0(xu, W0) = xb))) <=> ![W0: $i] : ((~aElement0(W0)) | (~(sdtasdt0(xu, W0) = xb)))),
% 1.92/2.08 inference(quant_intro,[status(thm)],[135])).
% 1.92/2.08 tff(137,plain,
% 1.92/2.08 (^[W0: $i] : trans(monotonicity(rewrite((aElement0(W0) & (sdtasdt0(xu, W0) = xb)) <=> (~((~aElement0(W0)) | (~(sdtasdt0(xu, W0) = xb))))), ((~(aElement0(W0) & (sdtasdt0(xu, W0) = xb))) <=> (~(~((~aElement0(W0)) | (~(sdtasdt0(xu, W0) = xb))))))), rewrite((~(~((~aElement0(W0)) | (~(sdtasdt0(xu, W0) = xb))))) <=> ((~aElement0(W0)) | (~(sdtasdt0(xu, W0) = xb)))), ((~(aElement0(W0) & (sdtasdt0(xu, W0) = xb))) <=> ((~aElement0(W0)) | (~(sdtasdt0(xu, W0) = xb)))))),
% 1.92/2.08 inference(bind,[status(th)],[])).
% 1.92/2.08 tff(138,plain,
% 1.92/2.08 (![W0: $i] : (~(aElement0(W0) & (sdtasdt0(xu, W0) = xb))) <=> ![W0: $i] : ((~aElement0(W0)) | (~(sdtasdt0(xu, W0) = xb)))),
% 1.92/2.08 inference(quant_intro,[status(thm)],[137])).
% 1.92/2.08 tff(139,plain,
% 1.92/2.08 ((~?[W0: $i] : (aElement0(W0) & (sdtasdt0(xu, W0) = xb))) <=> (~?[W0: $i] : (aElement0(W0) & (sdtasdt0(xu, W0) = xb)))),
% 1.92/2.08 inference(rewrite,[status(thm)],[])).
% 1.92/2.08 tff(140,axiom,(~(?[W0: $i] : (aElement0(W0) & (sdtasdt0(xu, W0) = xb)) | doDivides0(xu, xb))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__2612')).
% 1.92/2.08 tff(141,plain,
% 1.92/2.08 (~?[W0: $i] : (aElement0(W0) & (sdtasdt0(xu, W0) = xb))),
% 1.92/2.08 inference(or_elim,[status(thm)],[140])).
% 1.92/2.08 tff(142,plain,
% 1.92/2.08 (~?[W0: $i] : (aElement0(W0) & (sdtasdt0(xu, W0) = xb))),
% 1.92/2.08 inference(modus_ponens,[status(thm)],[141, 139])).
% 1.92/2.08 tff(143,plain,
% 1.92/2.08 (^[W0: $i] : refl($oeq((~(aElement0(W0) & (sdtasdt0(xu, W0) = xb))), (~(aElement0(W0) & (sdtasdt0(xu, W0) = xb)))))),
% 1.92/2.08 inference(bind,[status(th)],[])).
% 1.92/2.08 tff(144,plain,(
% 1.92/2.08 ![W0: $i] : (~(aElement0(W0) & (sdtasdt0(xu, W0) = xb)))),
% 1.92/2.08 inference(nnf-neg,[status(sab)],[142, 143])).
% 1.92/2.08 tff(145,plain,
% 1.92/2.08 (![W0: $i] : ((~aElement0(W0)) | (~(sdtasdt0(xu, W0) = xb)))),
% 1.92/2.08 inference(modus_ponens,[status(thm)],[144, 138])).
% 1.92/2.08 tff(146,plain,
% 1.92/2.08 (![W0: $i] : ((~aElement0(W0)) | (~(sdtasdt0(xu, W0) = xb)))),
% 1.92/2.08 inference(modus_ponens,[status(thm)],[145, 136])).
% 1.92/2.09 tff(147,plain,
% 1.92/2.09 (((~![W0: $i] : ((~aElement0(W0)) | (~(sdtasdt0(xu, W0) = xb)))) | ((~aElement0(xq)) | (~(sdtasdt0(xu, xq) = xb)))) <=> ((~![W0: $i] : ((~aElement0(W0)) | (~(sdtasdt0(xu, W0) = xb)))) | (~aElement0(xq)) | (~(sdtasdt0(xu, xq) = xb)))),
% 1.92/2.09 inference(rewrite,[status(thm)],[])).
% 1.92/2.09 tff(148,plain,
% 1.92/2.09 ((~![W0: $i] : ((~aElement0(W0)) | (~(sdtasdt0(xu, W0) = xb)))) | ((~aElement0(xq)) | (~(sdtasdt0(xu, xq) = xb)))),
% 1.92/2.09 inference(quant_inst,[status(thm)],[])).
% 1.92/2.09 tff(149,plain,
% 1.92/2.09 ((~![W0: $i] : ((~aElement0(W0)) | (~(sdtasdt0(xu, W0) = xb)))) | (~aElement0(xq)) | (~(sdtasdt0(xu, xq) = xb))),
% 1.92/2.09 inference(modus_ponens,[status(thm)],[148, 147])).
% 1.92/2.09 tff(150,plain,
% 1.92/2.09 (~(sdtasdt0(xu, xq) = xb)),
% 1.92/2.09 inference(unit_resolution,[status(thm)],[149, 146, 81])).
% 1.92/2.09 tff(151,plain,
% 1.92/2.09 ($false),
% 1.92/2.09 inference(unit_resolution,[status(thm)],[150, 134])).
% 1.92/2.09 % SZS output end Proof
% 1.92/2.09 % E exiting
%------------------------------------------------------------------------------