%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : RNG122+4 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 4.53s 4.75s
% Output : Proof 4.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : RNG122+4 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n001.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 03:29:49 EDT 2025
% 0.13/0.35 % CPUTime :
% 4.53/4.75 % SZS status Theorem
% 4.53/4.75 % SZS output start Proof
% 4.53/4.75 tff(sdtpldt0_type, type, (
% 4.53/4.75 sdtpldt0: ( $i * $i ) > $i)).
% 4.53/4.75 tff(xb_type, type, (
% 4.53/4.75 xb: $i)).
% 4.53/4.75 tff(smndt0_type, type, (
% 4.53/4.75 smndt0: $i > $i)).
% 4.53/4.75 tff(sdtasdt0_type, type, (
% 4.53/4.75 sdtasdt0: ( $i * $i ) > $i)).
% 4.53/4.75 tff(xu_type, type, (
% 4.53/4.75 xu: $i)).
% 4.53/4.75 tff(xq_type, type, (
% 4.53/4.75 xq: $i)).
% 4.53/4.75 tff(xr_type, type, (
% 4.53/4.75 xr: $i)).
% 4.53/4.75 tff(aElement0_type, type, (
% 4.53/4.75 aElement0: $i > $o)).
% 4.53/4.75 tff(iLess0_type, type, (
% 4.53/4.75 iLess0: ( $i * $i ) > $o)).
% 4.53/4.75 tff(sbrdtbr0_type, type, (
% 4.53/4.75 sbrdtbr0: $i > $i)).
% 4.53/4.75 tff(sz00_type, type, (
% 4.53/4.75 sz00: $i)).
% 4.53/4.75 tff(tptp_fun_W1_38_type, type, (
% 4.53/4.75 tptp_fun_W1_38: $i)).
% 4.53/4.75 tff(tptp_fun_W0_39_type, type, (
% 4.53/4.75 tptp_fun_W0_39: $i)).
% 4.53/4.75 tff(xa_type, type, (
% 4.53/4.75 xa: $i)).
% 4.53/4.75 tff(1,plain,
% 4.53/4.75 ((xb = sdtpldt0(sdtasdt0(xq, xu), xr)) <=> (xb = sdtpldt0(sdtasdt0(xq, xu), xr))),
% 4.53/4.75 inference(rewrite,[status(thm)],[])).
% 4.53/4.75 tff(2,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')).
% 4.53/4.75 tff(3,plain,
% 4.53/4.75 ((aElement0(xq) & aElement0(xr)) & (xb = sdtpldt0(sdtasdt0(xq, xu), xr))),
% 4.53/4.75 inference(and_elim,[status(thm)],[2])).
% 4.53/4.75 tff(4,plain,
% 4.53/4.75 (xb = sdtpldt0(sdtasdt0(xq, xu), xr)),
% 4.53/4.75 inference(and_elim,[status(thm)],[3])).
% 4.53/4.75 tff(5,plain,
% 4.53/4.75 (xb = sdtpldt0(sdtasdt0(xq, xu), xr)),
% 4.53/4.75 inference(modus_ponens,[status(thm)],[4, 1])).
% 4.53/4.75 tff(6,plain,
% 4.53/4.75 (sdtpldt0(smndt0(sdtasdt0(xq, xu)), xb) = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtpldt0(sdtasdt0(xq, xu), xr))),
% 4.53/4.75 inference(monotonicity,[status(thm)],[5])).
% 4.53/4.75 tff(7,plain,
% 4.53/4.75 (sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtpldt0(sdtasdt0(xq, xu), xr)) = sdtpldt0(smndt0(sdtasdt0(xq, xu)), xb)),
% 4.53/4.75 inference(symmetry,[status(thm)],[6])).
% 4.53/4.75 tff(8,plain,
% 4.53/4.75 (?[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))))),
% 4.53/4.75 inference(rewrite,[status(thm)],[])).
% 4.53/4.75 tff(9,plain,
% 4.53/4.75 (^[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)))))),
% 4.53/4.75 inference(bind,[status(th)],[])).
% 4.53/4.75 tff(10,plain,
% 4.53/4.75 (?[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))))),
% 4.53/4.75 inference(quant_intro,[status(thm)],[9])).
% 4.53/4.75 tff(11,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')).
% 4.53/4.75 tff(12,plain,
% 4.53/4.75 (?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))),
% 4.53/4.75 inference(modus_ponens,[status(thm)],[11, 10])).
% 4.53/4.75 tff(13,plain,
% 4.53/4.75 (?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))),
% 4.53/4.75 inference(modus_ponens,[status(thm)],[12, 8])).
% 4.53/4.75 tff(14,plain,(
% 4.53/4.75 aElement0(W0!39) & aElement0(W1!38) & (xu = sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(xb, W1!38)))),
% 4.53/4.75 inference(skolemize,[status(sab)],[13])).
% 4.53/4.75 tff(15,plain,
% 4.53/4.75 (xu = sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(xb, W1!38))),
% 4.53/4.75 inference(and_elim,[status(thm)],[14])).
% 4.53/4.75 tff(16,plain,
% 4.53/4.75 (sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(xb, W1!38)) = xu),
% 4.53/4.75 inference(symmetry,[status(thm)],[15])).
% 4.53/4.75 tff(17,plain,
% 4.53/4.75 (aElement0(sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(xb, W1!38))) <=> aElement0(xu)),
% 4.53/4.75 inference(monotonicity,[status(thm)],[16])).
% 4.53/4.75 tff(18,plain,
% 4.53/4.75 (aElement0(W0!39)),
% 4.53/4.75 inference(and_elim,[status(thm)],[14])).
% 4.53/4.75 tff(19,plain,
% 4.53/4.75 (aElement0(xa) <=> aElement0(xa)),
% 4.53/4.75 inference(rewrite,[status(thm)],[])).
% 4.53/4.75 tff(20,axiom,(aElement0(xa) & aElement0(xb)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__2091')).
% 4.53/4.75 tff(21,plain,
% 4.53/4.75 (aElement0(xa)),
% 4.53/4.75 inference(and_elim,[status(thm)],[20])).
% 4.53/4.75 tff(22,plain,
% 4.53/4.75 (aElement0(xa)),
% 4.53/4.75 inference(modus_ponens,[status(thm)],[21, 19])).
% 4.53/4.75 tff(23,plain,
% 4.53/4.75 (^[W0: $i, W1: $i] : refl((aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0))) <=> (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0))))),
% 4.53/4.75 inference(bind,[status(th)],[])).
% 4.53/4.75 tff(24,plain,
% 4.53/4.75 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0))) <=> ![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 4.53/4.75 inference(quant_intro,[status(thm)],[23])).
% 4.53/4.75 tff(25,plain,
% 4.53/4.75 (^[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)))))),
% 4.53/4.75 inference(bind,[status(th)],[])).
% 4.53/4.75 tff(26,plain,
% 4.53/4.75 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))) <=> ![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 4.53/4.75 inference(quant_intro,[status(thm)],[25])).
% 4.53/4.75 tff(27,plain,
% 4.53/4.75 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))) <=> ![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 4.53/4.75 inference(rewrite,[status(thm)],[])).
% 4.53/4.75 tff(28,plain,
% 4.53/4.75 (^[W0: $i, W1: $i] : rewrite(((aElement0(W0) & aElement0(W1)) => aElement0(sdtasdt0(W0, W1))) <=> (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))))),
% 4.53/4.75 inference(bind,[status(th)],[])).
% 4.53/4.75 tff(29,plain,
% 4.53/4.75 (![W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) => aElement0(sdtasdt0(W0, W1))) <=> ![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 4.53/4.75 inference(quant_intro,[status(thm)],[28])).
% 4.53/4.75 tff(30,axiom,(![W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) => aElement0(sdtasdt0(W0, W1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mSortsB_02')).
% 4.53/4.75 tff(31,plain,
% 4.53/4.75 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 4.53/4.75 inference(modus_ponens,[status(thm)],[30, 29])).
% 4.53/4.75 tff(32,plain,
% 4.53/4.75 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 4.53/4.75 inference(modus_ponens,[status(thm)],[31, 27])).
% 4.53/4.75 tff(33,plain,(
% 4.53/4.75 ![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 4.53/4.75 inference(skolemize,[status(sab)],[32])).
% 4.53/4.75 tff(34,plain,
% 4.53/4.75 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 4.53/4.75 inference(modus_ponens,[status(thm)],[33, 26])).
% 4.53/4.75 tff(35,plain,
% 4.53/4.75 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 4.53/4.75 inference(modus_ponens,[status(thm)],[34, 24])).
% 4.53/4.75 tff(36,plain,
% 4.53/4.75 (((~![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)))),
% 4.53/4.75 inference(rewrite,[status(thm)],[])).
% 4.53/4.75 tff(37,plain,
% 4.53/4.75 ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtasdt0(xa, W0!39)) | (~aElement0(W0!39)) | (~aElement0(xa)))),
% 4.53/4.75 inference(quant_inst,[status(thm)],[])).
% 4.53/4.75 tff(38,plain,
% 4.53/4.75 ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | aElement0(sdtasdt0(xa, W0!39)) | (~aElement0(W0!39)) | (~aElement0(xa))),
% 4.53/4.75 inference(modus_ponens,[status(thm)],[37, 36])).
% 4.53/4.75 tff(39,plain,
% 4.53/4.75 (aElement0(sdtasdt0(xa, W0!39))),
% 4.53/4.75 inference(unit_resolution,[status(thm)],[38, 35, 22, 18])).
% 4.53/4.75 tff(40,plain,
% 4.53/4.75 (aElement0(W1!38)),
% 4.53/4.75 inference(and_elim,[status(thm)],[14])).
% 4.53/4.75 tff(41,plain,
% 4.53/4.75 (aElement0(xb) <=> aElement0(xb)),
% 4.53/4.75 inference(rewrite,[status(thm)],[])).
% 4.53/4.75 tff(42,plain,
% 4.53/4.75 (aElement0(xb)),
% 4.53/4.75 inference(and_elim,[status(thm)],[20])).
% 4.53/4.75 tff(43,plain,
% 4.53/4.75 (aElement0(xb)),
% 4.53/4.75 inference(modus_ponens,[status(thm)],[42, 41])).
% 4.53/4.75 tff(44,plain,
% 4.53/4.75 (((~![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)))),
% 4.53/4.75 inference(rewrite,[status(thm)],[])).
% 4.53/4.75 tff(45,plain,
% 4.53/4.75 ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtasdt0(xb, W1!38)) | (~aElement0(W1!38)) | (~aElement0(xb)))),
% 4.53/4.75 inference(quant_inst,[status(thm)],[])).
% 4.53/4.75 tff(46,plain,
% 4.53/4.75 ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | aElement0(sdtasdt0(xb, W1!38)) | (~aElement0(W1!38)) | (~aElement0(xb))),
% 4.53/4.75 inference(modus_ponens,[status(thm)],[45, 44])).
% 4.53/4.75 tff(47,plain,
% 4.53/4.75 (aElement0(sdtasdt0(xb, W1!38))),
% 4.53/4.75 inference(unit_resolution,[status(thm)],[46, 35, 43, 40])).
% 4.53/4.75 tff(48,plain,
% 4.53/4.75 (^[W0: $i, W1: $i] : refl((aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0))) <=> (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0))))),
% 4.53/4.75 inference(bind,[status(th)],[])).
% 4.53/4.75 tff(49,plain,
% 4.53/4.75 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0))) <=> ![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 4.53/4.75 inference(quant_intro,[status(thm)],[48])).
% 4.53/4.75 tff(50,plain,
% 4.53/4.75 (^[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)))))),
% 4.53/4.75 inference(bind,[status(th)],[])).
% 4.53/4.75 tff(51,plain,
% 4.53/4.75 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))) <=> ![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 4.53/4.75 inference(quant_intro,[status(thm)],[50])).
% 4.53/4.75 tff(52,plain,
% 4.53/4.75 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))) <=> ![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 4.53/4.75 inference(rewrite,[status(thm)],[])).
% 4.53/4.75 tff(53,plain,
% 4.53/4.75 (^[W0: $i, W1: $i] : rewrite(((aElement0(W0) & aElement0(W1)) => aElement0(sdtpldt0(W0, W1))) <=> (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))))),
% 4.53/4.75 inference(bind,[status(th)],[])).
% 4.53/4.75 tff(54,plain,
% 4.53/4.75 (![W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) => aElement0(sdtpldt0(W0, W1))) <=> ![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 4.53/4.75 inference(quant_intro,[status(thm)],[53])).
% 4.53/4.75 tff(55,axiom,(![W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) => aElement0(sdtpldt0(W0, W1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mSortsB')).
% 4.53/4.75 tff(56,plain,
% 4.53/4.75 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 4.53/4.75 inference(modus_ponens,[status(thm)],[55, 54])).
% 4.53/4.75 tff(57,plain,
% 4.53/4.75 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 4.53/4.75 inference(modus_ponens,[status(thm)],[56, 52])).
% 4.53/4.75 tff(58,plain,(
% 4.53/4.75 ![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 4.53/4.75 inference(skolemize,[status(sab)],[57])).
% 4.53/4.75 tff(59,plain,
% 4.53/4.75 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 4.53/4.75 inference(modus_ponens,[status(thm)],[58, 51])).
% 4.53/4.75 tff(60,plain,
% 4.53/4.75 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 4.53/4.75 inference(modus_ponens,[status(thm)],[59, 49])).
% 4.53/4.75 tff(61,plain,
% 4.53/4.75 (((~![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))))),
% 4.53/4.75 inference(rewrite,[status(thm)],[])).
% 4.53/4.75 tff(62,plain,
% 4.53/4.75 ((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))))),
% 4.53/4.75 inference(rewrite,[status(thm)],[])).
% 4.53/4.75 tff(63,plain,
% 4.53/4.75 (((~![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)))))),
% 4.53/4.75 inference(monotonicity,[status(thm)],[62])).
% 4.53/4.75 tff(64,plain,
% 4.53/4.75 (((~![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))))),
% 4.53/4.75 inference(transitivity,[status(thm)],[63, 61])).
% 4.53/4.75 tff(65,plain,
% 4.53/4.75 ((~![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))))),
% 4.53/4.75 inference(quant_inst,[status(thm)],[])).
% 4.53/4.75 tff(66,plain,
% 4.53/4.75 ((~![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)))),
% 4.53/4.75 inference(modus_ponens,[status(thm)],[65, 64])).
% 4.53/4.75 tff(67,plain,
% 4.53/4.75 ((~aElement0(sdtasdt0(xb, W1!38))) | (~aElement0(sdtasdt0(xa, W0!39))) | aElement0(sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(xb, W1!38)))),
% 4.53/4.75 inference(unit_resolution,[status(thm)],[66, 60])).
% 4.53/4.75 tff(68,plain,
% 4.53/4.75 (aElement0(sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(xb, W1!38)))),
% 4.53/4.75 inference(unit_resolution,[status(thm)],[67, 47, 39])).
% 4.53/4.75 tff(69,plain,
% 4.53/4.75 (aElement0(xu)),
% 4.53/4.75 inference(modus_ponens,[status(thm)],[68, 17])).
% 4.53/4.75 tff(70,plain,
% 4.53/4.75 (aElement0(xq) <=> aElement0(xq)),
% 4.53/4.75 inference(rewrite,[status(thm)],[])).
% 4.53/4.75 tff(71,plain,
% 4.53/4.75 (aElement0(xq) & aElement0(xr)),
% 4.53/4.75 inference(and_elim,[status(thm)],[3])).
% 4.53/4.75 tff(72,plain,
% 4.53/4.75 (aElement0(xq)),
% 4.53/4.75 inference(and_elim,[status(thm)],[71])).
% 4.53/4.75 tff(73,plain,
% 4.53/4.75 (aElement0(xq)),
% 4.53/4.75 inference(modus_ponens,[status(thm)],[72, 70])).
% 4.53/4.75 tff(74,plain,
% 4.53/4.75 (((~![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)))),
% 4.53/4.75 inference(rewrite,[status(thm)],[])).
% 4.53/4.75 tff(75,plain,
% 4.53/4.75 ((aElement0(sdtasdt0(xq, xu)) | (~aElement0(xu)) | (~aElement0(xq))) <=> ((~aElement0(xu)) | aElement0(sdtasdt0(xq, xu)) | (~aElement0(xq)))),
% 4.53/4.75 inference(rewrite,[status(thm)],[])).
% 4.53/4.75 tff(76,plain,
% 4.53/4.75 (((~![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))))),
% 4.53/4.75 inference(monotonicity,[status(thm)],[75])).
% 4.53/4.75 tff(77,plain,
% 4.53/4.75 (((~![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)))),
% 4.53/4.75 inference(transitivity,[status(thm)],[76, 74])).
% 4.53/4.75 tff(78,plain,
% 4.53/4.75 ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtasdt0(xq, xu)) | (~aElement0(xu)) | (~aElement0(xq)))),
% 4.53/4.75 inference(quant_inst,[status(thm)],[])).
% 4.53/4.75 tff(79,plain,
% 4.53/4.75 ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(xu)) | aElement0(sdtasdt0(xq, xu)) | (~aElement0(xq))),
% 4.53/4.75 inference(modus_ponens,[status(thm)],[78, 77])).
% 4.53/4.75 tff(80,plain,
% 4.53/4.75 ((~aElement0(xu)) | aElement0(sdtasdt0(xq, xu))),
% 4.53/4.75 inference(unit_resolution,[status(thm)],[79, 35, 73])).
% 4.53/4.75 tff(81,plain,
% 4.53/4.75 (aElement0(sdtasdt0(xq, xu))),
% 4.53/4.75 inference(unit_resolution,[status(thm)],[80, 69])).
% 4.53/4.75 tff(82,plain,
% 4.53/4.75 (^[W0: $i] : refl((aElement0(smndt0(W0)) | (~aElement0(W0))) <=> (aElement0(smndt0(W0)) | (~aElement0(W0))))),
% 4.53/4.75 inference(bind,[status(th)],[])).
% 4.53/4.75 tff(83,plain,
% 4.53/4.75 (![W0: $i] : (aElement0(smndt0(W0)) | (~aElement0(W0))) <=> ![W0: $i] : (aElement0(smndt0(W0)) | (~aElement0(W0)))),
% 4.53/4.75 inference(quant_intro,[status(thm)],[82])).
% 4.53/4.75 tff(84,plain,
% 4.53/4.75 (![W0: $i] : (aElement0(smndt0(W0)) | (~aElement0(W0))) <=> ![W0: $i] : (aElement0(smndt0(W0)) | (~aElement0(W0)))),
% 4.53/4.75 inference(rewrite,[status(thm)],[])).
% 4.53/4.75 tff(85,plain,
% 4.53/4.75 (^[W0: $i] : rewrite((aElement0(W0) => aElement0(smndt0(W0))) <=> (aElement0(smndt0(W0)) | (~aElement0(W0))))),
% 4.53/4.75 inference(bind,[status(th)],[])).
% 4.53/4.75 tff(86,plain,
% 4.53/4.75 (![W0: $i] : (aElement0(W0) => aElement0(smndt0(W0))) <=> ![W0: $i] : (aElement0(smndt0(W0)) | (~aElement0(W0)))),
% 4.53/4.75 inference(quant_intro,[status(thm)],[85])).
% 4.53/4.75 tff(87,axiom,(![W0: $i] : (aElement0(W0) => aElement0(smndt0(W0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mSortsU')).
% 4.53/4.75 tff(88,plain,
% 4.53/4.75 (![W0: $i] : (aElement0(smndt0(W0)) | (~aElement0(W0)))),
% 4.53/4.75 inference(modus_ponens,[status(thm)],[87, 86])).
% 4.53/4.75 tff(89,plain,
% 4.53/4.75 (![W0: $i] : (aElement0(smndt0(W0)) | (~aElement0(W0)))),
% 4.53/4.75 inference(modus_ponens,[status(thm)],[88, 84])).
% 4.53/4.75 tff(90,plain,(
% 4.53/4.75 ![W0: $i] : (aElement0(smndt0(W0)) | (~aElement0(W0)))),
% 4.53/4.75 inference(skolemize,[status(sab)],[89])).
% 4.53/4.75 tff(91,plain,
% 4.53/4.75 (![W0: $i] : (aElement0(smndt0(W0)) | (~aElement0(W0)))),
% 4.53/4.75 inference(modus_ponens,[status(thm)],[90, 83])).
% 4.53/4.75 tff(92,plain,
% 4.53/4.75 (((~![W0: $i] : (aElement0(smndt0(W0)) | (~aElement0(W0)))) | (aElement0(smndt0(sdtasdt0(xq, xu))) | (~aElement0(sdtasdt0(xq, xu))))) <=> ((~![W0: $i] : (aElement0(smndt0(W0)) | (~aElement0(W0)))) | aElement0(smndt0(sdtasdt0(xq, xu))) | (~aElement0(sdtasdt0(xq, xu))))),
% 4.53/4.75 inference(rewrite,[status(thm)],[])).
% 4.53/4.75 tff(93,plain,
% 4.53/4.75 ((~![W0: $i] : (aElement0(smndt0(W0)) | (~aElement0(W0)))) | (aElement0(smndt0(sdtasdt0(xq, xu))) | (~aElement0(sdtasdt0(xq, xu))))),
% 4.53/4.75 inference(quant_inst,[status(thm)],[])).
% 4.53/4.75 tff(94,plain,
% 4.53/4.75 ((~![W0: $i] : (aElement0(smndt0(W0)) | (~aElement0(W0)))) | aElement0(smndt0(sdtasdt0(xq, xu))) | (~aElement0(sdtasdt0(xq, xu)))),
% 4.53/4.75 inference(modus_ponens,[status(thm)],[93, 92])).
% 4.53/4.75 tff(95,plain,
% 4.53/4.75 (aElement0(smndt0(sdtasdt0(xq, xu))) | (~aElement0(sdtasdt0(xq, xu)))),
% 4.53/4.75 inference(unit_resolution,[status(thm)],[94, 91])).
% 4.53/4.75 tff(96,plain,
% 4.53/4.75 (aElement0(smndt0(sdtasdt0(xq, xu)))),
% 4.53/4.75 inference(unit_resolution,[status(thm)],[95, 81])).
% 4.53/4.75 tff(97,plain,
% 4.53/4.75 (aElement0(xr) <=> aElement0(xr)),
% 4.53/4.75 inference(rewrite,[status(thm)],[])).
% 4.53/4.75 tff(98,plain,
% 4.53/4.75 (aElement0(xr)),
% 4.53/4.75 inference(and_elim,[status(thm)],[71])).
% 4.53/4.75 tff(99,plain,
% 4.53/4.75 (aElement0(xr)),
% 4.53/4.75 inference(modus_ponens,[status(thm)],[98, 97])).
% 4.53/4.75 tff(100,plain,
% 4.53/4.75 (^[W0: $i, W1: $i, W2: $i] : refl(((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0))) <=> ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0))))),
% 4.53/4.75 inference(bind,[status(th)],[])).
% 4.53/4.75 tff(101,plain,
% 4.53/4.75 (![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0))) <=> ![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 4.53/4.75 inference(quant_intro,[status(thm)],[100])).
% 4.53/4.75 tff(102,plain,
% 4.53/4.75 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(trans(monotonicity(rewrite((aElement0(W0) & aElement0(W1) & aElement0(W2)) <=> (~((~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0))))), ((~(aElement0(W0) & aElement0(W1) & aElement0(W2))) <=> (~(~((~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0))))))), rewrite((~(~((~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0))))) <=> ((~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))), ((~(aElement0(W0) & aElement0(W1) & aElement0(W2))) <=> ((~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0))))), (((~(aElement0(W0) & aElement0(W1) & aElement0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> (((~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))))), rewrite((((~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))), (((~(aElement0(W0) & aElement0(W1) & aElement0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))))),
% 4.53/4.75 inference(bind,[status(th)],[])).
% 4.53/4.75 tff(103,plain,
% 4.53/4.75 (![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aElement0(W1) & aElement0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> ![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 4.53/4.75 inference(quant_intro,[status(thm)],[102])).
% 4.53/4.75 tff(104,plain,
% 4.53/4.75 (![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aElement0(W1) & aElement0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> ![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aElement0(W1) & aElement0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))))),
% 4.53/4.75 inference(rewrite,[status(thm)],[])).
% 4.53/4.75 tff(105,plain,
% 4.53/4.75 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(rewrite(((aElement0(W0) & aElement0(W1)) & aElement0(W2)) <=> (aElement0(W0) & aElement0(W1) & aElement0(W2))), ((((aElement0(W0) & aElement0(W1)) & aElement0(W2)) => (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> ((aElement0(W0) & aElement0(W1) & aElement0(W2)) => (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))))), rewrite(((aElement0(W0) & aElement0(W1) & aElement0(W2)) => (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> ((~(aElement0(W0) & aElement0(W1) & aElement0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))))), ((((aElement0(W0) & aElement0(W1)) & aElement0(W2)) => (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> ((~(aElement0(W0) & aElement0(W1) & aElement0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))))))),
% 4.53/4.75 inference(bind,[status(th)],[])).
% 4.53/4.75 tff(106,plain,
% 4.53/4.75 (![W0: $i, W1: $i, W2: $i] : (((aElement0(W0) & aElement0(W1)) & aElement0(W2)) => (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2)))) <=> ![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aElement0(W1) & aElement0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))))),
% 4.53/4.75 inference(quant_intro,[status(thm)],[105])).
% 4.53/4.75 tff(107,axiom,(![W0: $i, W1: $i, W2: $i] : (((aElement0(W0) & aElement0(W1)) & aElement0(W2)) => (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mAddAsso')).
% 4.53/4.75 tff(108,plain,
% 4.53/4.75 (![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aElement0(W1) & aElement0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))))),
% 4.53/4.75 inference(modus_ponens,[status(thm)],[107, 106])).
% 4.53/4.75 tff(109,plain,
% 4.53/4.75 (![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aElement0(W1) & aElement0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))))),
% 4.53/4.75 inference(modus_ponens,[status(thm)],[108, 104])).
% 4.53/4.75 tff(110,plain,(
% 4.53/4.75 ![W0: $i, W1: $i, W2: $i] : ((~(aElement0(W0) & aElement0(W1) & aElement0(W2))) | (sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))))),
% 4.53/4.75 inference(skolemize,[status(sab)],[109])).
% 4.53/4.75 tff(111,plain,
% 4.53/4.75 (![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 4.53/4.75 inference(modus_ponens,[status(thm)],[110, 103])).
% 4.53/4.75 tff(112,plain,
% 4.53/4.75 (![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 4.53/4.75 inference(modus_ponens,[status(thm)],[111, 101])).
% 4.53/4.75 tff(113,plain,
% 4.53/4.75 (((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((~aElement0(xr)) | (~aElement0(sdtasdt0(xq, xu))) | (~aElement0(smndt0(sdtasdt0(xq, xu)))) | (sdtpldt0(sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)), xr) = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtpldt0(sdtasdt0(xq, xu), xr))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(xr)) | (~aElement0(sdtasdt0(xq, xu))) | (~aElement0(smndt0(sdtasdt0(xq, xu)))) | (sdtpldt0(sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)), xr) = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtpldt0(sdtasdt0(xq, xu), xr))))),
% 4.53/4.75 inference(rewrite,[status(thm)],[])).
% 4.53/4.75 tff(114,plain,
% 4.53/4.75 (((sdtpldt0(sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)), xr) = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtpldt0(sdtasdt0(xq, xu), xr))) | (~aElement0(xr)) | (~aElement0(sdtasdt0(xq, xu))) | (~aElement0(smndt0(sdtasdt0(xq, xu))))) <=> ((~aElement0(xr)) | (~aElement0(sdtasdt0(xq, xu))) | (~aElement0(smndt0(sdtasdt0(xq, xu)))) | (sdtpldt0(sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)), xr) = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtpldt0(sdtasdt0(xq, xu), xr))))),
% 4.53/4.75 inference(rewrite,[status(thm)],[])).
% 4.53/4.75 tff(115,plain,
% 4.53/4.75 (((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((sdtpldt0(sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)), xr) = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtpldt0(sdtasdt0(xq, xu), xr))) | (~aElement0(xr)) | (~aElement0(sdtasdt0(xq, xu))) | (~aElement0(smndt0(sdtasdt0(xq, xu)))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((~aElement0(xr)) | (~aElement0(sdtasdt0(xq, xu))) | (~aElement0(smndt0(sdtasdt0(xq, xu)))) | (sdtpldt0(sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)), xr) = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtpldt0(sdtasdt0(xq, xu), xr)))))),
% 4.53/4.75 inference(monotonicity,[status(thm)],[114])).
% 4.53/4.75 tff(116,plain,
% 4.53/4.75 (((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((sdtpldt0(sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)), xr) = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtpldt0(sdtasdt0(xq, xu), xr))) | (~aElement0(xr)) | (~aElement0(sdtasdt0(xq, xu))) | (~aElement0(smndt0(sdtasdt0(xq, xu)))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(xr)) | (~aElement0(sdtasdt0(xq, xu))) | (~aElement0(smndt0(sdtasdt0(xq, xu)))) | (sdtpldt0(sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)), xr) = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtpldt0(sdtasdt0(xq, xu), xr))))),
% 4.53/4.75 inference(transitivity,[status(thm)],[115, 113])).
% 4.53/4.75 tff(117,plain,
% 4.53/4.75 ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))) | ((sdtpldt0(sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)), xr) = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtpldt0(sdtasdt0(xq, xu), xr))) | (~aElement0(xr)) | (~aElement0(sdtasdt0(xq, xu))) | (~aElement0(smndt0(sdtasdt0(xq, xu)))))),
% 4.53/4.75 inference(quant_inst,[status(thm)],[])).
% 4.53/4.75 tff(118,plain,
% 4.53/4.75 ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(sdtpldt0(W0, W1), W2) = sdtpldt0(W0, sdtpldt0(W1, W2))) | (~aElement0(W2)) | (~aElement0(W1)) | (~aElement0(W0)))) | (~aElement0(xr)) | (~aElement0(sdtasdt0(xq, xu))) | (~aElement0(smndt0(sdtasdt0(xq, xu)))) | (sdtpldt0(sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)), xr) = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtpldt0(sdtasdt0(xq, xu), xr)))),
% 4.53/4.75 inference(modus_ponens,[status(thm)],[117, 116])).
% 4.53/4.75 tff(119,plain,
% 4.53/4.75 ((~aElement0(sdtasdt0(xq, xu))) | (~aElement0(smndt0(sdtasdt0(xq, xu)))) | (sdtpldt0(sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)), xr) = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtpldt0(sdtasdt0(xq, xu), xr)))),
% 4.53/4.75 inference(unit_resolution,[status(thm)],[118, 112, 99])).
% 4.53/4.75 tff(120,plain,
% 4.53/4.75 (sdtpldt0(sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)), xr) = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtpldt0(sdtasdt0(xq, xu), xr))),
% 4.53/4.75 inference(unit_resolution,[status(thm)],[119, 96, 81])).
% 4.53/4.75 tff(121,plain,
% 4.53/4.75 (^[W0: $i] : refl(((~aElement0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0)))))) <=> ((~aElement0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0)))))))),
% 4.53/4.75 inference(bind,[status(th)],[])).
% 4.53/4.75 tff(122,plain,
% 4.53/4.75 (![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0)))))) <=> ![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0))))))),
% 4.53/4.75 inference(quant_intro,[status(thm)],[121])).
% 4.53/4.75 tff(123,plain,
% 4.53/4.75 (^[W0: $i] : rewrite(((~aElement0(W0)) | ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0)))) <=> ((~aElement0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0)))))))),
% 4.53/4.75 inference(bind,[status(th)],[])).
% 4.53/4.75 tff(124,plain,
% 4.53/4.75 (![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0)))) <=> ![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0))))))),
% 4.53/4.75 inference(quant_intro,[status(thm)],[123])).
% 4.53/4.75 tff(125,plain,
% 4.53/4.75 (![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0)))) <=> ![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0))))),
% 4.53/4.76 inference(rewrite,[status(thm)],[])).
% 4.53/4.76 tff(126,plain,
% 4.53/4.76 (^[W0: $i] : rewrite((aElement0(W0) => ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0)))) <=> ((~aElement0(W0)) | ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0)))))),
% 4.53/4.76 inference(bind,[status(th)],[])).
% 4.53/4.76 tff(127,plain,
% 4.53/4.76 (![W0: $i] : (aElement0(W0) => ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0)))) <=> ![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0))))),
% 4.53/4.76 inference(quant_intro,[status(thm)],[126])).
% 4.53/4.76 tff(128,axiom,(![W0: $i] : (aElement0(W0) => ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mAddInvr')).
% 4.53/4.76 tff(129,plain,
% 4.53/4.76 (![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0))))),
% 4.53/4.76 inference(modus_ponens,[status(thm)],[128, 127])).
% 4.53/4.76 tff(130,plain,
% 4.53/4.76 (![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0))))),
% 4.53/4.76 inference(modus_ponens,[status(thm)],[129, 125])).
% 4.53/4.76 tff(131,plain,(
% 4.53/4.76 ![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0))))),
% 4.53/4.76 inference(skolemize,[status(sab)],[130])).
% 4.53/4.76 tff(132,plain,
% 4.53/4.76 (![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0))))))),
% 4.53/4.76 inference(modus_ponens,[status(thm)],[131, 124])).
% 4.53/4.76 tff(133,plain,
% 4.53/4.76 (![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0))))))),
% 4.53/4.76 inference(modus_ponens,[status(thm)],[132, 122])).
% 4.53/4.76 tff(134,plain,
% 4.53/4.76 (((~![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0))))))) | ((~aElement0(sdtasdt0(xq, xu))) | (~((~(sdtpldt0(sdtasdt0(xq, xu), smndt0(sdtasdt0(xq, xu))) = sz00)) | (~(sz00 = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)))))))) <=> ((~![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0))))))) | (~aElement0(sdtasdt0(xq, xu))) | (~((~(sdtpldt0(sdtasdt0(xq, xu), smndt0(sdtasdt0(xq, xu))) = sz00)) | (~(sz00 = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)))))))),
% 4.53/4.76 inference(rewrite,[status(thm)],[])).
% 4.53/4.76 tff(135,plain,
% 4.53/4.76 ((~![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0))))))) | ((~aElement0(sdtasdt0(xq, xu))) | (~((~(sdtpldt0(sdtasdt0(xq, xu), smndt0(sdtasdt0(xq, xu))) = sz00)) | (~(sz00 = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)))))))),
% 4.53/4.76 inference(quant_inst,[status(thm)],[])).
% 4.53/4.76 tff(136,plain,
% 4.53/4.76 ((~![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0))))))) | (~aElement0(sdtasdt0(xq, xu))) | (~((~(sdtpldt0(sdtasdt0(xq, xu), smndt0(sdtasdt0(xq, xu))) = sz00)) | (~(sz00 = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu))))))),
% 4.53/4.76 inference(modus_ponens,[status(thm)],[135, 134])).
% 4.53/4.76 tff(137,plain,
% 4.53/4.76 ((~aElement0(sdtasdt0(xq, xu))) | (~((~(sdtpldt0(sdtasdt0(xq, xu), smndt0(sdtasdt0(xq, xu))) = sz00)) | (~(sz00 = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu))))))),
% 4.53/4.76 inference(unit_resolution,[status(thm)],[136, 133])).
% 4.53/4.76 tff(138,plain,
% 4.53/4.76 (~((~(sdtpldt0(sdtasdt0(xq, xu), smndt0(sdtasdt0(xq, xu))) = sz00)) | (~(sz00 = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)))))),
% 4.53/4.76 inference(unit_resolution,[status(thm)],[137, 81])).
% 4.53/4.76 tff(139,plain,
% 4.53/4.76 (((~(sdtpldt0(sdtasdt0(xq, xu), smndt0(sdtasdt0(xq, xu))) = sz00)) | (~(sz00 = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu))))) | (sz00 = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)))),
% 4.53/4.76 inference(tautology,[status(thm)],[])).
% 4.53/4.76 tff(140,plain,
% 4.53/4.76 (sz00 = sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu))),
% 4.53/4.76 inference(unit_resolution,[status(thm)],[139, 138])).
% 4.53/4.76 tff(141,plain,
% 4.53/4.76 (sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)) = sz00),
% 4.53/4.76 inference(symmetry,[status(thm)],[140])).
% 4.53/4.76 tff(142,plain,
% 4.53/4.76 (sdtpldt0(sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)), xr) = sdtpldt0(sz00, xr)),
% 4.53/4.76 inference(monotonicity,[status(thm)],[141])).
% 4.53/4.76 tff(143,plain,
% 4.53/4.76 (sdtpldt0(sz00, xr) = sdtpldt0(sdtpldt0(smndt0(sdtasdt0(xq, xu)), sdtasdt0(xq, xu)), xr)),
% 4.53/4.76 inference(symmetry,[status(thm)],[142])).
% 4.53/4.76 tff(144,plain,
% 4.53/4.76 (^[W0: $i] : refl(((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0)))))) <=> ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0)))))))),
% 4.53/4.76 inference(bind,[status(th)],[])).
% 4.53/4.76 tff(145,plain,
% 4.53/4.76 (![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0)))))) <=> ![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))),
% 4.53/4.76 inference(quant_intro,[status(thm)],[144])).
% 4.53/4.76 tff(146,plain,
% 4.53/4.76 (^[W0: $i] : rewrite(((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))) <=> ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0)))))))),
% 4.53/4.76 inference(bind,[status(th)],[])).
% 4.53/4.76 tff(147,plain,
% 4.53/4.76 (![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))) <=> ![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))),
% 4.53/4.76 inference(quant_intro,[status(thm)],[146])).
% 4.53/4.76 tff(148,plain,
% 4.53/4.76 (![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))) <=> ![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))),
% 4.53/4.76 inference(rewrite,[status(thm)],[])).
% 4.53/4.76 tff(149,plain,
% 4.53/4.76 (^[W0: $i] : rewrite((aElement0(W0) => ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))) <=> ((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))))),
% 4.53/4.76 inference(bind,[status(th)],[])).
% 4.53/4.76 tff(150,plain,
% 4.53/4.76 (![W0: $i] : (aElement0(W0) => ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))) <=> ![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))),
% 4.53/4.76 inference(quant_intro,[status(thm)],[149])).
% 4.53/4.76 tff(151,axiom,(![W0: $i] : (aElement0(W0) => ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mAddZero')).
% 4.53/4.76 tff(152,plain,
% 4.53/4.76 (![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))),
% 4.53/4.76 inference(modus_ponens,[status(thm)],[151, 150])).
% 4.53/4.76 tff(153,plain,
% 4.53/4.76 (![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))),
% 4.53/4.76 inference(modus_ponens,[status(thm)],[152, 148])).
% 4.53/4.76 tff(154,plain,(
% 4.53/4.76 ![W0: $i] : ((~aElement0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))),
% 4.53/4.76 inference(skolemize,[status(sab)],[153])).
% 4.53/4.76 tff(155,plain,
% 4.53/4.76 (![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))),
% 4.53/4.76 inference(modus_ponens,[status(thm)],[154, 147])).
% 4.53/4.76 tff(156,plain,
% 4.53/4.76 (![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))),
% 4.53/4.76 inference(modus_ponens,[status(thm)],[155, 145])).
% 4.53/4.76 tff(157,plain,
% 4.53/4.76 (((~![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | ((~aElement0(xr)) | (~((~(sdtpldt0(xr, sz00) = xr)) | (~(xr = sdtpldt0(sz00, xr))))))) <=> ((~![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | (~aElement0(xr)) | (~((~(sdtpldt0(xr, sz00) = xr)) | (~(xr = sdtpldt0(sz00, xr))))))),
% 4.53/4.76 inference(rewrite,[status(thm)],[])).
% 4.53/4.76 tff(158,plain,
% 4.53/4.76 ((~![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | ((~aElement0(xr)) | (~((~(sdtpldt0(xr, sz00) = xr)) | (~(xr = sdtpldt0(sz00, xr))))))),
% 4.53/4.76 inference(quant_inst,[status(thm)],[])).
% 4.53/4.76 tff(159,plain,
% 4.53/4.76 ((~![W0: $i] : ((~aElement0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | (~aElement0(xr)) | (~((~(sdtpldt0(xr, sz00) = xr)) | (~(xr = sdtpldt0(sz00, xr)))))),
% 4.53/4.76 inference(modus_ponens,[status(thm)],[158, 157])).
% 4.53/4.76 tff(160,plain,
% 4.53/4.76 (~((~(sdtpldt0(xr, sz00) = xr)) | (~(xr = sdtpldt0(sz00, xr))))),
% 4.53/4.76 inference(unit_resolution,[status(thm)],[159, 156, 99])).
% 4.53/4.76 tff(161,plain,
% 4.53/4.76 (((~(sdtpldt0(xr, sz00) = xr)) | (~(xr = sdtpldt0(sz00, xr)))) | (xr = sdtpldt0(sz00, xr))),
% 4.53/4.76 inference(tautology,[status(thm)],[])).
% 4.53/4.76 tff(162,plain,
% 4.53/4.76 (xr = sdtpldt0(sz00, xr)),
% 4.53/4.76 inference(unit_resolution,[status(thm)],[161, 160])).
% 4.53/4.76 tff(163,plain,
% 4.53/4.76 (xr = sdtpldt0(smndt0(sdtasdt0(xq, xu)), xb)),
% 4.53/4.76 inference(transitivity,[status(thm)],[162, 143, 120, 7])).
% 4.53/4.76 tff(164,plain,
% 4.53/4.76 ((~(xr = sdtpldt0(smndt0(sdtasdt0(xq, xu)), xb))) <=> (~(xr = sdtpldt0(smndt0(sdtasdt0(xq, xu)), xb)))),
% 4.53/4.76 inference(rewrite,[status(thm)],[])).
% 4.53/4.76 tff(165,axiom,(~(xr = sdtpldt0(smndt0(sdtasdt0(xq, xu)), xb))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 4.53/4.76 tff(166,plain,
% 4.53/4.76 (~(xr = sdtpldt0(smndt0(sdtasdt0(xq, xu)), xb))),
% 4.53/4.76 inference(modus_ponens,[status(thm)],[165, 164])).
% 4.53/4.76 tff(167,plain,
% 4.53/4.76 ($false),
% 4.53/4.76 inference(unit_resolution,[status(thm)],[166, 163])).
% 4.53/4.76 % SZS output end Proof
% 4.53/4.78 % E exiting
%------------------------------------------------------------------------------