%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : RNG118+4 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 17.22s 17.41s
% Output : Proof 17.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : RNG118+4 : TPTP v9.0.0. Released v4.0.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n008.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 03:25:48 EDT 2025
% 0.13/0.35 % CPUTime :
% 17.22/17.41 % SZS status Theorem
% 17.22/17.41 % SZS output start Proof
% 17.22/17.41 tff(iLess0_type, type, (
% 17.22/17.41 iLess0: ( $i * $i ) > $o)).
% 17.22/17.41 tff(sbrdtbr0_type, type, (
% 17.22/17.41 sbrdtbr0: $i > $i)).
% 17.22/17.41 tff(xu_type, type, (
% 17.22/17.41 xu: $i)).
% 17.22/17.41 tff(tptp_fun_W3_13_type, type, (
% 17.22/17.41 tptp_fun_W3_13: ( $i * $i ) > $i)).
% 17.22/17.41 tff(xb_type, type, (
% 17.22/17.41 xb: $i)).
% 17.22/17.41 tff(sz00_type, type, (
% 17.22/17.41 sz00: $i)).
% 17.22/17.41 tff(sdtpldt0_type, type, (
% 17.22/17.41 sdtpldt0: ( $i * $i ) > $i)).
% 17.22/17.41 tff(sdtasdt0_type, type, (
% 17.22/17.41 sdtasdt0: ( $i * $i ) > $i)).
% 17.22/17.41 tff(tptp_fun_W2_14_type, type, (
% 17.22/17.41 tptp_fun_W2_14: ( $i * $i ) > $i)).
% 17.22/17.41 tff(aElement0_type, type, (
% 17.22/17.41 aElement0: $i > $o)).
% 17.22/17.41 tff(tptp_fun_W1_38_type, type, (
% 17.22/17.41 tptp_fun_W1_38: $i)).
% 17.22/17.41 tff(tptp_fun_W0_39_type, type, (
% 17.22/17.41 tptp_fun_W0_39: $i)).
% 17.22/17.41 tff(xa_type, type, (
% 17.22/17.41 xa: $i)).
% 17.22/17.41 tff(aElementOf0_type, type, (
% 17.22/17.41 aElementOf0: ( $i * $i ) > $o)).
% 17.22/17.41 tff(xI_type, type, (
% 17.22/17.41 xI: $i)).
% 17.22/17.41 tff(slsdtgt0_type, type, (
% 17.22/17.41 slsdtgt0: $i > $i)).
% 17.22/17.41 tff(1,plain,
% 17.22/17.41 (?[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))))),
% 17.22/17.41 inference(rewrite,[status(thm)],[])).
% 17.22/17.41 tff(2,plain,
% 17.22/17.41 (^[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)))))),
% 17.22/17.41 inference(bind,[status(th)],[])).
% 17.22/17.41 tff(3,plain,
% 17.22/17.41 (?[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))))),
% 17.22/17.41 inference(quant_intro,[status(thm)],[2])).
% 17.22/17.41 tff(4,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')).
% 17.22/17.41 tff(5,plain,
% 17.22/17.41 (?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))),
% 17.22/17.41 inference(modus_ponens,[status(thm)],[4, 3])).
% 17.22/17.41 tff(6,plain,
% 17.22/17.41 (?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xu = sdtpldt0(sdtasdt0(xa, W0), sdtasdt0(xb, W1))))),
% 17.22/17.41 inference(modus_ponens,[status(thm)],[5, 1])).
% 17.22/17.41 tff(7,plain,(
% 17.22/17.41 aElement0(W0!39) & aElement0(W1!38) & (xu = sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(xb, W1!38)))),
% 17.22/17.41 inference(skolemize,[status(sab)],[6])).
% 17.22/17.41 tff(8,plain,
% 17.22/17.41 (xu = sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(xb, W1!38))),
% 17.22/17.41 inference(and_elim,[status(thm)],[7])).
% 17.22/17.41 tff(9,plain,
% 17.22/17.41 (sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(xb, W1!38)) = xu),
% 17.22/17.41 inference(symmetry,[status(thm)],[8])).
% 17.22/17.41 tff(10,plain,
% 17.22/17.41 (aElement0(sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(xb, W1!38))) <=> aElement0(xu)),
% 17.22/17.41 inference(monotonicity,[status(thm)],[9])).
% 17.22/17.41 tff(11,plain,
% 17.22/17.41 (aElement0(W0!39)),
% 17.22/17.41 inference(and_elim,[status(thm)],[7])).
% 17.22/17.41 tff(12,plain,
% 17.22/17.41 (aElement0(xa) <=> aElement0(xa)),
% 17.22/17.41 inference(rewrite,[status(thm)],[])).
% 17.22/17.41 tff(13,axiom,(aElement0(xa) & aElement0(xb)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__2091')).
% 17.22/17.41 tff(14,plain,
% 17.22/17.41 (aElement0(xa)),
% 17.22/17.41 inference(and_elim,[status(thm)],[13])).
% 17.22/17.41 tff(15,plain,
% 17.22/17.41 (aElement0(xa)),
% 17.22/17.41 inference(modus_ponens,[status(thm)],[14, 12])).
% 17.22/17.41 tff(16,plain,
% 17.22/17.41 (^[W0: $i, W1: $i] : refl((aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0))) <=> (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0))))),
% 17.22/17.41 inference(bind,[status(th)],[])).
% 17.22/17.41 tff(17,plain,
% 17.22/17.41 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0))) <=> ![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 17.22/17.41 inference(quant_intro,[status(thm)],[16])).
% 17.22/17.41 tff(18,plain,
% 17.22/17.41 (^[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)))))),
% 17.22/17.41 inference(bind,[status(th)],[])).
% 17.22/17.41 tff(19,plain,
% 17.22/17.41 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))) <=> ![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 17.22/17.41 inference(quant_intro,[status(thm)],[18])).
% 17.22/17.41 tff(20,plain,
% 17.22/17.41 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))) <=> ![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 17.22/17.41 inference(rewrite,[status(thm)],[])).
% 17.22/17.41 tff(21,plain,
% 17.22/17.41 (^[W0: $i, W1: $i] : rewrite(((aElement0(W0) & aElement0(W1)) => aElement0(sdtasdt0(W0, W1))) <=> (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))))),
% 17.22/17.41 inference(bind,[status(th)],[])).
% 17.22/17.41 tff(22,plain,
% 17.22/17.41 (![W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) => aElement0(sdtasdt0(W0, W1))) <=> ![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 17.22/17.41 inference(quant_intro,[status(thm)],[21])).
% 17.22/17.41 tff(23,axiom,(![W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) => aElement0(sdtasdt0(W0, W1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mSortsB_02')).
% 17.22/17.41 tff(24,plain,
% 17.22/17.41 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 17.22/17.41 inference(modus_ponens,[status(thm)],[23, 22])).
% 17.22/17.41 tff(25,plain,
% 17.22/17.41 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 17.22/17.41 inference(modus_ponens,[status(thm)],[24, 20])).
% 17.22/17.41 tff(26,plain,(
% 17.22/17.41 ![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 17.22/17.41 inference(skolemize,[status(sab)],[25])).
% 17.22/17.41 tff(27,plain,
% 17.22/17.41 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 17.22/17.41 inference(modus_ponens,[status(thm)],[26, 19])).
% 17.22/17.41 tff(28,plain,
% 17.22/17.41 (![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 17.22/17.41 inference(modus_ponens,[status(thm)],[27, 17])).
% 17.22/17.41 tff(29,plain,
% 17.22/17.41 (((~![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)))),
% 17.22/17.41 inference(rewrite,[status(thm)],[])).
% 17.22/17.41 tff(30,plain,
% 17.22/17.41 ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtasdt0(xa, W0!39)) | (~aElement0(W0!39)) | (~aElement0(xa)))),
% 17.22/17.41 inference(quant_inst,[status(thm)],[])).
% 17.24/17.41 tff(31,plain,
% 17.24/17.41 ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | aElement0(sdtasdt0(xa, W0!39)) | (~aElement0(W0!39)) | (~aElement0(xa))),
% 17.24/17.41 inference(modus_ponens,[status(thm)],[30, 29])).
% 17.24/17.41 tff(32,plain,
% 17.24/17.41 (aElement0(sdtasdt0(xa, W0!39))),
% 17.24/17.41 inference(unit_resolution,[status(thm)],[31, 28, 15, 11])).
% 17.24/17.41 tff(33,plain,
% 17.24/17.41 (aElement0(W1!38)),
% 17.24/17.41 inference(and_elim,[status(thm)],[7])).
% 17.24/17.41 tff(34,plain,
% 17.24/17.41 (aElement0(xb) <=> aElement0(xb)),
% 17.24/17.41 inference(rewrite,[status(thm)],[])).
% 17.24/17.41 tff(35,plain,
% 17.24/17.41 (aElement0(xb)),
% 17.24/17.41 inference(and_elim,[status(thm)],[13])).
% 17.24/17.41 tff(36,plain,
% 17.24/17.41 (aElement0(xb)),
% 17.24/17.41 inference(modus_ponens,[status(thm)],[35, 34])).
% 17.24/17.41 tff(37,plain,
% 17.24/17.41 (((~![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)))),
% 17.24/17.41 inference(rewrite,[status(thm)],[])).
% 17.24/17.41 tff(38,plain,
% 17.24/17.41 ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | (aElement0(sdtasdt0(xb, W1!38)) | (~aElement0(W1!38)) | (~aElement0(xb)))),
% 17.24/17.41 inference(quant_inst,[status(thm)],[])).
% 17.24/17.41 tff(39,plain,
% 17.24/17.41 ((~![W0: $i, W1: $i] : (aElement0(sdtasdt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))) | aElement0(sdtasdt0(xb, W1!38)) | (~aElement0(W1!38)) | (~aElement0(xb))),
% 17.24/17.41 inference(modus_ponens,[status(thm)],[38, 37])).
% 17.24/17.41 tff(40,plain,
% 17.24/17.41 (aElement0(sdtasdt0(xb, W1!38))),
% 17.24/17.41 inference(unit_resolution,[status(thm)],[39, 28, 36, 33])).
% 17.24/17.41 tff(41,plain,
% 17.24/17.41 (^[W0: $i, W1: $i] : refl((aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0))) <=> (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0))))),
% 17.24/17.41 inference(bind,[status(th)],[])).
% 17.24/17.41 tff(42,plain,
% 17.24/17.41 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0))) <=> ![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 17.24/17.41 inference(quant_intro,[status(thm)],[41])).
% 17.24/17.41 tff(43,plain,
% 17.24/17.41 (^[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)))))),
% 17.24/17.41 inference(bind,[status(th)],[])).
% 17.24/17.41 tff(44,plain,
% 17.24/17.41 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))) <=> ![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 17.24/17.41 inference(quant_intro,[status(thm)],[43])).
% 17.24/17.41 tff(45,plain,
% 17.24/17.41 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))) <=> ![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 17.24/17.41 inference(rewrite,[status(thm)],[])).
% 17.24/17.41 tff(46,plain,
% 17.24/17.41 (^[W0: $i, W1: $i] : rewrite(((aElement0(W0) & aElement0(W1)) => aElement0(sdtpldt0(W0, W1))) <=> (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1)))))),
% 17.24/17.41 inference(bind,[status(th)],[])).
% 17.24/17.41 tff(47,plain,
% 17.24/17.41 (![W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) => aElement0(sdtpldt0(W0, W1))) <=> ![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 17.24/17.41 inference(quant_intro,[status(thm)],[46])).
% 17.24/17.41 tff(48,axiom,(![W0: $i, W1: $i] : ((aElement0(W0) & aElement0(W1)) => aElement0(sdtpldt0(W0, W1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mSortsB')).
% 17.24/17.41 tff(49,plain,
% 17.24/17.41 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 17.24/17.41 inference(modus_ponens,[status(thm)],[48, 47])).
% 17.24/17.41 tff(50,plain,
% 17.24/17.41 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 17.24/17.41 inference(modus_ponens,[status(thm)],[49, 45])).
% 17.24/17.41 tff(51,plain,(
% 17.24/17.41 ![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~(aElement0(W0) & aElement0(W1))))),
% 17.24/17.41 inference(skolemize,[status(sab)],[50])).
% 17.24/17.41 tff(52,plain,
% 17.24/17.41 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 17.24/17.41 inference(modus_ponens,[status(thm)],[51, 44])).
% 17.24/17.41 tff(53,plain,
% 17.24/17.41 (![W0: $i, W1: $i] : (aElement0(sdtpldt0(W0, W1)) | (~aElement0(W1)) | (~aElement0(W0)))),
% 17.24/17.41 inference(modus_ponens,[status(thm)],[52, 42])).
% 17.24/17.41 tff(54,plain,
% 17.24/17.41 (((~![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))))),
% 17.24/17.42 inference(rewrite,[status(thm)],[])).
% 17.24/17.42 tff(55,plain,
% 17.24/17.42 ((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))))),
% 17.24/17.42 inference(rewrite,[status(thm)],[])).
% 17.24/17.42 tff(56,plain,
% 17.24/17.42 (((~![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)))))),
% 17.24/17.42 inference(monotonicity,[status(thm)],[55])).
% 17.24/17.42 tff(57,plain,
% 17.24/17.42 (((~![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))))),
% 17.24/17.42 inference(transitivity,[status(thm)],[56, 54])).
% 17.24/17.42 tff(58,plain,
% 17.24/17.42 ((~![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))))),
% 17.24/17.42 inference(quant_inst,[status(thm)],[])).
% 17.24/17.42 tff(59,plain,
% 17.24/17.42 ((~![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)))),
% 17.24/17.42 inference(modus_ponens,[status(thm)],[58, 57])).
% 17.24/17.42 tff(60,plain,
% 17.24/17.42 ((~aElement0(sdtasdt0(xb, W1!38))) | (~aElement0(sdtasdt0(xa, W0!39))) | aElement0(sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(xb, W1!38)))),
% 17.24/17.42 inference(unit_resolution,[status(thm)],[59, 53])).
% 17.24/17.42 tff(61,plain,
% 17.24/17.42 (aElement0(sdtpldt0(sdtasdt0(xa, W0!39), sdtasdt0(xb, W1!38)))),
% 17.24/17.42 inference(unit_resolution,[status(thm)],[60, 40, 32])).
% 17.24/17.42 tff(62,plain,
% 17.24/17.42 (aElement0(xu)),
% 17.24/17.42 inference(modus_ponens,[status(thm)],[61, 10])).
% 17.24/17.42 tff(63,plain,
% 17.24/17.42 ((~(xu = sz00)) <=> (~(xu = sz00))),
% 17.24/17.42 inference(rewrite,[status(thm)],[])).
% 17.24/17.42 tff(64,axiom,(((?[W0: $i, W1: $i] : ((aElementOf0(W0, slsdtgt0(xa)) & aElementOf0(W1, slsdtgt0(xb))) & (sdtpldt0(W0, W1) = xu)) & aElementOf0(xu, xI)) & (~(xu = sz00))) & ![W0: $i] : (((?[W1: $i, W2: $i] : ((aElementOf0(W1, slsdtgt0(xa)) & aElementOf0(W2, slsdtgt0(xb))) & (sdtpldt0(W1, W2) = W0)) | aElementOf0(W0, xI)) & (~(W0 = sz00))) => (~iLess0(sbrdtbr0(W0), sbrdtbr0(xu))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__2273')).
% 17.24/17.42 tff(65,plain,
% 17.24/17.42 ((?[W0: $i, W1: $i] : ((aElementOf0(W0, slsdtgt0(xa)) & aElementOf0(W1, slsdtgt0(xb))) & (sdtpldt0(W0, W1) = xu)) & aElementOf0(xu, xI)) & (~(xu = sz00))),
% 17.24/17.42 inference(and_elim,[status(thm)],[64])).
% 17.24/17.42 tff(66,plain,
% 17.24/17.42 (~(xu = sz00)),
% 17.24/17.42 inference(and_elim,[status(thm)],[65])).
% 17.24/17.42 tff(67,plain,
% 17.24/17.42 (~(xu = sz00)),
% 17.24/17.42 inference(modus_ponens,[status(thm)],[66, 63])).
% 17.24/17.42 tff(68,plain,
% 17.24/17.42 (^[W0: $i, W1: $i] : refl(((W1 = sz00) | (~aElement0(W1)) | (~aElement0(W0)) | (~((~aElement0(tptp_fun_W2_14(W1, W0))) | (~aElement0(tptp_fun_W3_13(W1, W0))) | (~(W0 = sdtpldt0(sdtasdt0(tptp_fun_W2_14(W1, W0), W1), tptp_fun_W3_13(W1, W0)))) | (~((tptp_fun_W3_13(W1, W0) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(W1, W0)), sbrdtbr0(W1))))))) <=> ((W1 = sz00) | (~aElement0(W1)) | (~aElement0(W0)) | (~((~aElement0(tptp_fun_W2_14(W1, W0))) | (~aElement0(tptp_fun_W3_13(W1, W0))) | (~(W0 = sdtpldt0(sdtasdt0(tptp_fun_W2_14(W1, W0), W1), tptp_fun_W3_13(W1, W0)))) | (~((tptp_fun_W3_13(W1, W0) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(W1, W0)), sbrdtbr0(W1))))))))),
% 17.24/17.42 inference(bind,[status(th)],[])).
% 17.24/17.42 tff(69,plain,
% 17.24/17.42 (![W0: $i, W1: $i] : ((W1 = sz00) | (~aElement0(W1)) | (~aElement0(W0)) | (~((~aElement0(tptp_fun_W2_14(W1, W0))) | (~aElement0(tptp_fun_W3_13(W1, W0))) | (~(W0 = sdtpldt0(sdtasdt0(tptp_fun_W2_14(W1, W0), W1), tptp_fun_W3_13(W1, W0)))) | (~((tptp_fun_W3_13(W1, W0) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(W1, W0)), sbrdtbr0(W1))))))) <=> ![W0: $i, W1: $i] : ((W1 = sz00) | (~aElement0(W1)) | (~aElement0(W0)) | (~((~aElement0(tptp_fun_W2_14(W1, W0))) | (~aElement0(tptp_fun_W3_13(W1, W0))) | (~(W0 = sdtpldt0(sdtasdt0(tptp_fun_W2_14(W1, W0), W1), tptp_fun_W3_13(W1, W0)))) | (~((tptp_fun_W3_13(W1, W0) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(W1, W0)), sbrdtbr0(W1)))))))),
% 17.24/17.42 inference(quant_intro,[status(thm)],[68])).
% 17.24/17.42 tff(70,plain,
% 17.24/17.42 (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aElement0(W0) & aElement0(W1) & (~(W1 = sz00))) <=> (~((W1 = sz00) | (~aElement0(W1)) | (~aElement0(W0))))), ((~(aElement0(W0) & aElement0(W1) & (~(W1 = sz00)))) <=> (~(~((W1 = sz00) | (~aElement0(W1)) | (~aElement0(W0))))))), rewrite((~(~((W1 = sz00) | (~aElement0(W1)) | (~aElement0(W0))))) <=> ((W1 = sz00) | (~aElement0(W1)) | (~aElement0(W0)))), ((~(aElement0(W0) & aElement0(W1) & (~(W1 = sz00)))) <=> ((W1 = sz00) | (~aElement0(W1)) | (~aElement0(W0))))), rewrite((aElement0(tptp_fun_W2_14(W1, W0)) & aElement0(tptp_fun_W3_13(W1, W0)) & (W0 = sdtpldt0(sdtasdt0(tptp_fun_W2_14(W1, W0), W1), tptp_fun_W3_13(W1, W0))) & ((tptp_fun_W3_13(W1, W0) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(W1, W0)), sbrdtbr0(W1)))) <=> (~((~aElement0(tptp_fun_W2_14(W1, W0))) | (~aElement0(tptp_fun_W3_13(W1, W0))) | (~(W0 = sdtpldt0(sdtasdt0(tptp_fun_W2_14(W1, W0), W1), tptp_fun_W3_13(W1, W0)))) | (~((tptp_fun_W3_13(W1, W0) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(W1, W0)), sbrdtbr0(W1))))))), (((~(aElement0(W0) & aElement0(W1) & (~(W1 = sz00)))) | (aElement0(tptp_fun_W2_14(W1, W0)) & aElement0(tptp_fun_W3_13(W1, W0)) & (W0 = sdtpldt0(sdtasdt0(tptp_fun_W2_14(W1, W0), W1), tptp_fun_W3_13(W1, W0))) & ((tptp_fun_W3_13(W1, W0) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(W1, W0)), sbrdtbr0(W1))))) <=> (((W1 = sz00) | (~aElement0(W1)) | (~aElement0(W0))) | (~((~aElement0(tptp_fun_W2_14(W1, W0))) | (~aElement0(tptp_fun_W3_13(W1, W0))) | (~(W0 = sdtpldt0(sdtasdt0(tptp_fun_W2_14(W1, W0), W1), tptp_fun_W3_13(W1, W0)))) | (~((tptp_fun_W3_13(W1, W0) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(W1, W0)), sbrdtbr0(W1))))))))), rewrite((((W1 = sz00) | (~aElement0(W1)) | (~aElement0(W0))) | (~((~aElement0(tptp_fun_W2_14(W1, W0))) | (~aElement0(tptp_fun_W3_13(W1, W0))) | (~(W0 = sdtpldt0(sdtasdt0(tptp_fun_W2_14(W1, W0), W1), tptp_fun_W3_13(W1, W0)))) | (~((tptp_fun_W3_13(W1, W0) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(W1, W0)), sbrdtbr0(W1))))))) <=> ((W1 = sz00) | (~aElement0(W1)) | (~aElement0(W0)) | (~((~aElement0(tptp_fun_W2_14(W1, W0))) | (~aElement0(tptp_fun_W3_13(W1, W0))) | (~(W0 = sdtpldt0(sdtasdt0(tptp_fun_W2_14(W1, W0), W1), tptp_fun_W3_13(W1, W0)))) | (~((tptp_fun_W3_13(W1, W0) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(W1, W0)), sbrdtbr0(W1)))))))), (((~(aElement0(W0) & aElement0(W1) & (~(W1 = sz00)))) | (aElement0(tptp_fun_W2_14(W1, W0)) & aElement0(tptp_fun_W3_13(W1, W0)) & (W0 = sdtpldt0(sdtasdt0(tptp_fun_W2_14(W1, W0), W1), tptp_fun_W3_13(W1, W0))) & ((tptp_fun_W3_13(W1, W0) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(W1, W0)), sbrdtbr0(W1))))) <=> ((W1 = sz00) | (~aElement0(W1)) | (~aElement0(W0)) | (~((~aElement0(tptp_fun_W2_14(W1, W0))) | (~aElement0(tptp_fun_W3_13(W1, W0))) | (~(W0 = sdtpldt0(sdtasdt0(tptp_fun_W2_14(W1, W0), W1), tptp_fun_W3_13(W1, W0)))) | (~((tptp_fun_W3_13(W1, W0) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(W1, W0)), sbrdtbr0(W1)))))))))),
% 17.24/17.42 inference(bind,[status(th)],[])).
% 17.24/17.42 tff(71,plain,
% 17.24/17.42 (![W0: $i, W1: $i] : ((~(aElement0(W0) & aElement0(W1) & (~(W1 = sz00)))) | (aElement0(tptp_fun_W2_14(W1, W0)) & aElement0(tptp_fun_W3_13(W1, W0)) & (W0 = sdtpldt0(sdtasdt0(tptp_fun_W2_14(W1, W0), W1), tptp_fun_W3_13(W1, W0))) & ((tptp_fun_W3_13(W1, W0) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(W1, W0)), sbrdtbr0(W1))))) <=> ![W0: $i, W1: $i] : ((W1 = sz00) | (~aElement0(W1)) | (~aElement0(W0)) | (~((~aElement0(tptp_fun_W2_14(W1, W0))) | (~aElement0(tptp_fun_W3_13(W1, W0))) | (~(W0 = sdtpldt0(sdtasdt0(tptp_fun_W2_14(W1, W0), W1), tptp_fun_W3_13(W1, W0)))) | (~((tptp_fun_W3_13(W1, W0) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(W1, W0)), sbrdtbr0(W1)))))))),
% 17.24/17.42 inference(quant_intro,[status(thm)],[70])).
% 17.24/17.42 tff(72,plain,
% 17.24/17.42 (![W0: $i, W1: $i] : ((~(aElement0(W0) & aElement0(W1) & (~(W1 = sz00)))) | ?[W2: $i, W3: $i] : (aElement0(W2) & aElement0(W3) & (W0 = sdtpldt0(sdtasdt0(W2, W1), W3)) & ((W3 = sz00) | iLess0(sbrdtbr0(W3), sbrdtbr0(W1))))) <=> ![W0: $i, W1: $i] : ((~(aElement0(W0) & aElement0(W1) & (~(W1 = sz00)))) | ?[W2: $i, W3: $i] : (aElement0(W2) & aElement0(W3) & (W0 = sdtpldt0(sdtasdt0(W2, W1), W3)) & ((W3 = sz00) | iLess0(sbrdtbr0(W3), sbrdtbr0(W1)))))),
% 17.24/17.42 inference(rewrite,[status(thm)],[])).
% 17.24/17.42 tff(73,plain,
% 17.24/17.42 (^[W0: $i, W1: $i] : trans(monotonicity(rewrite(((aElement0(W0) & aElement0(W1)) & (~(W1 = sz00))) <=> (aElement0(W0) & aElement0(W1) & (~(W1 = sz00)))), quant_intro(proof_bind(^[W2: $i, W3: $i] : trans(monotonicity(rewrite(((aElement0(W2) & aElement0(W3)) & (W0 = sdtpldt0(sdtasdt0(W2, W1), W3))) <=> (aElement0(W2) & aElement0(W3) & (W0 = sdtpldt0(sdtasdt0(W2, W1), W3)))), rewrite(((~(W3 = sz00)) => iLess0(sbrdtbr0(W3), sbrdtbr0(W1))) <=> ((W3 = sz00) | iLess0(sbrdtbr0(W3), sbrdtbr0(W1)))), ((((aElement0(W2) & aElement0(W3)) & (W0 = sdtpldt0(sdtasdt0(W2, W1), W3))) & ((~(W3 = sz00)) => iLess0(sbrdtbr0(W3), sbrdtbr0(W1)))) <=> ((aElement0(W2) & aElement0(W3) & (W0 = sdtpldt0(sdtasdt0(W2, W1), W3))) & ((W3 = sz00) | iLess0(sbrdtbr0(W3), sbrdtbr0(W1)))))), rewrite(((aElement0(W2) & aElement0(W3) & (W0 = sdtpldt0(sdtasdt0(W2, W1), W3))) & ((W3 = sz00) | iLess0(sbrdtbr0(W3), sbrdtbr0(W1)))) <=> (aElement0(W2) & aElement0(W3) & (W0 = sdtpldt0(sdtasdt0(W2, W1), W3)) & ((W3 = sz00) | iLess0(sbrdtbr0(W3), sbrdtbr0(W1))))), ((((aElement0(W2) & aElement0(W3)) & (W0 = sdtpldt0(sdtasdt0(W2, W1), W3))) & ((~(W3 = sz00)) => iLess0(sbrdtbr0(W3), sbrdtbr0(W1)))) <=> (aElement0(W2) & aElement0(W3) & (W0 = sdtpldt0(sdtasdt0(W2, W1), W3)) & ((W3 = sz00) | iLess0(sbrdtbr0(W3), sbrdtbr0(W1))))))), (?[W2: $i, W3: $i] : (((aElement0(W2) & aElement0(W3)) & (W0 = sdtpldt0(sdtasdt0(W2, W1), W3))) & ((~(W3 = sz00)) => iLess0(sbrdtbr0(W3), sbrdtbr0(W1)))) <=> ?[W2: $i, W3: $i] : (aElement0(W2) & aElement0(W3) & (W0 = sdtpldt0(sdtasdt0(W2, W1), W3)) & ((W3 = sz00) | iLess0(sbrdtbr0(W3), sbrdtbr0(W1)))))), ((((aElement0(W0) & aElement0(W1)) & (~(W1 = sz00))) => ?[W2: $i, W3: $i] : (((aElement0(W2) & aElement0(W3)) & (W0 = sdtpldt0(sdtasdt0(W2, W1), W3))) & ((~(W3 = sz00)) => iLess0(sbrdtbr0(W3), sbrdtbr0(W1))))) <=> ((aElement0(W0) & aElement0(W1) & (~(W1 = sz00))) => ?[W2: $i, W3: $i] : (aElement0(W2) & aElement0(W3) & (W0 = sdtpldt0(sdtasdt0(W2, W1), W3)) & ((W3 = sz00) | iLess0(sbrdtbr0(W3), sbrdtbr0(W1))))))), rewrite(((aElement0(W0) & aElement0(W1) & (~(W1 = sz00))) => ?[W2: $i, W3: $i] : (aElement0(W2) & aElement0(W3) & (W0 = sdtpldt0(sdtasdt0(W2, W1), W3)) & ((W3 = sz00) | iLess0(sbrdtbr0(W3), sbrdtbr0(W1))))) <=> ((~(aElement0(W0) & aElement0(W1) & (~(W1 = sz00)))) | ?[W2: $i, W3: $i] : (aElement0(W2) & aElement0(W3) & (W0 = sdtpldt0(sdtasdt0(W2, W1), W3)) & ((W3 = sz00) | iLess0(sbrdtbr0(W3), sbrdtbr0(W1)))))), ((((aElement0(W0) & aElement0(W1)) & (~(W1 = sz00))) => ?[W2: $i, W3: $i] : (((aElement0(W2) & aElement0(W3)) & (W0 = sdtpldt0(sdtasdt0(W2, W1), W3))) & ((~(W3 = sz00)) => iLess0(sbrdtbr0(W3), sbrdtbr0(W1))))) <=> ((~(aElement0(W0) & aElement0(W1) & (~(W1 = sz00)))) | ?[W2: $i, W3: $i] : (aElement0(W2) & aElement0(W3) & (W0 = sdtpldt0(sdtasdt0(W2, W1), W3)) & ((W3 = sz00) | iLess0(sbrdtbr0(W3), sbrdtbr0(W1)))))))),
% 17.25/17.42 inference(bind,[status(th)],[])).
% 17.25/17.42 tff(74,plain,
% 17.25/17.42 (![W0: $i, W1: $i] : (((aElement0(W0) & aElement0(W1)) & (~(W1 = sz00))) => ?[W2: $i, W3: $i] : (((aElement0(W2) & aElement0(W3)) & (W0 = sdtpldt0(sdtasdt0(W2, W1), W3))) & ((~(W3 = sz00)) => iLess0(sbrdtbr0(W3), sbrdtbr0(W1))))) <=> ![W0: $i, W1: $i] : ((~(aElement0(W0) & aElement0(W1) & (~(W1 = sz00)))) | ?[W2: $i, W3: $i] : (aElement0(W2) & aElement0(W3) & (W0 = sdtpldt0(sdtasdt0(W2, W1), W3)) & ((W3 = sz00) | iLess0(sbrdtbr0(W3), sbrdtbr0(W1)))))),
% 17.25/17.42 inference(quant_intro,[status(thm)],[73])).
% 17.25/17.42 tff(75,axiom,(![W0: $i, W1: $i] : (((aElement0(W0) & aElement0(W1)) & (~(W1 = sz00))) => ?[W2: $i, W3: $i] : (((aElement0(W2) & aElement0(W3)) & (W0 = sdtpldt0(sdtasdt0(W2, W1), W3))) & ((~(W3 = sz00)) => iLess0(sbrdtbr0(W3), sbrdtbr0(W1)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mDivision')).
% 17.25/17.42 tff(76,plain,
% 17.25/17.42 (![W0: $i, W1: $i] : ((~(aElement0(W0) & aElement0(W1) & (~(W1 = sz00)))) | ?[W2: $i, W3: $i] : (aElement0(W2) & aElement0(W3) & (W0 = sdtpldt0(sdtasdt0(W2, W1), W3)) & ((W3 = sz00) | iLess0(sbrdtbr0(W3), sbrdtbr0(W1)))))),
% 17.25/17.42 inference(modus_ponens,[status(thm)],[75, 74])).
% 17.25/17.42 tff(77,plain,
% 17.25/17.42 (![W0: $i, W1: $i] : ((~(aElement0(W0) & aElement0(W1) & (~(W1 = sz00)))) | ?[W2: $i, W3: $i] : (aElement0(W2) & aElement0(W3) & (W0 = sdtpldt0(sdtasdt0(W2, W1), W3)) & ((W3 = sz00) | iLess0(sbrdtbr0(W3), sbrdtbr0(W1)))))),
% 17.25/17.42 inference(modus_ponens,[status(thm)],[76, 72])).
% 17.25/17.42 tff(78,plain,(
% 17.25/17.42 ![W0: $i, W1: $i] : ((~(aElement0(W0) & aElement0(W1) & (~(W1 = sz00)))) | (aElement0(tptp_fun_W2_14(W1, W0)) & aElement0(tptp_fun_W3_13(W1, W0)) & (W0 = sdtpldt0(sdtasdt0(tptp_fun_W2_14(W1, W0), W1), tptp_fun_W3_13(W1, W0))) & ((tptp_fun_W3_13(W1, W0) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(W1, W0)), sbrdtbr0(W1)))))),
% 17.25/17.42 inference(skolemize,[status(sab)],[77])).
% 17.25/17.42 tff(79,plain,
% 17.25/17.42 (![W0: $i, W1: $i] : ((W1 = sz00) | (~aElement0(W1)) | (~aElement0(W0)) | (~((~aElement0(tptp_fun_W2_14(W1, W0))) | (~aElement0(tptp_fun_W3_13(W1, W0))) | (~(W0 = sdtpldt0(sdtasdt0(tptp_fun_W2_14(W1, W0), W1), tptp_fun_W3_13(W1, W0)))) | (~((tptp_fun_W3_13(W1, W0) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(W1, W0)), sbrdtbr0(W1)))))))),
% 17.25/17.42 inference(modus_ponens,[status(thm)],[78, 71])).
% 17.25/17.42 tff(80,plain,
% 17.25/17.42 (![W0: $i, W1: $i] : ((W1 = sz00) | (~aElement0(W1)) | (~aElement0(W0)) | (~((~aElement0(tptp_fun_W2_14(W1, W0))) | (~aElement0(tptp_fun_W3_13(W1, W0))) | (~(W0 = sdtpldt0(sdtasdt0(tptp_fun_W2_14(W1, W0), W1), tptp_fun_W3_13(W1, W0)))) | (~((tptp_fun_W3_13(W1, W0) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(W1, W0)), sbrdtbr0(W1)))))))),
% 17.25/17.42 inference(modus_ponens,[status(thm)],[79, 69])).
% 17.25/17.42 tff(81,plain,
% 17.25/17.42 (((~![W0: $i, W1: $i] : ((W1 = sz00) | (~aElement0(W1)) | (~aElement0(W0)) | (~((~aElement0(tptp_fun_W2_14(W1, W0))) | (~aElement0(tptp_fun_W3_13(W1, W0))) | (~(W0 = sdtpldt0(sdtasdt0(tptp_fun_W2_14(W1, W0), W1), tptp_fun_W3_13(W1, W0)))) | (~((tptp_fun_W3_13(W1, W0) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(W1, W0)), sbrdtbr0(W1)))))))) | ((xu = sz00) | (~aElement0(xu)) | (~aElement0(xb)) | (~((~aElement0(tptp_fun_W2_14(xu, xb))) | (~aElement0(tptp_fun_W3_13(xu, xb))) | (~(xb = sdtpldt0(sdtasdt0(tptp_fun_W2_14(xu, xb), xu), tptp_fun_W3_13(xu, xb)))) | (~((tptp_fun_W3_13(xu, xb) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(xu, xb)), sbrdtbr0(xu)))))))) <=> ((~![W0: $i, W1: $i] : ((W1 = sz00) | (~aElement0(W1)) | (~aElement0(W0)) | (~((~aElement0(tptp_fun_W2_14(W1, W0))) | (~aElement0(tptp_fun_W3_13(W1, W0))) | (~(W0 = sdtpldt0(sdtasdt0(tptp_fun_W2_14(W1, W0), W1), tptp_fun_W3_13(W1, W0)))) | (~((tptp_fun_W3_13(W1, W0) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(W1, W0)), sbrdtbr0(W1)))))))) | (xu = sz00) | (~aElement0(xu)) | (~aElement0(xb)) | (~((~aElement0(tptp_fun_W2_14(xu, xb))) | (~aElement0(tptp_fun_W3_13(xu, xb))) | (~(xb = sdtpldt0(sdtasdt0(tptp_fun_W2_14(xu, xb), xu), tptp_fun_W3_13(xu, xb)))) | (~((tptp_fun_W3_13(xu, xb) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(xu, xb)), sbrdtbr0(xu)))))))),
% 17.25/17.42 inference(rewrite,[status(thm)],[])).
% 17.25/17.42 tff(82,plain,
% 17.25/17.42 ((~![W0: $i, W1: $i] : ((W1 = sz00) | (~aElement0(W1)) | (~aElement0(W0)) | (~((~aElement0(tptp_fun_W2_14(W1, W0))) | (~aElement0(tptp_fun_W3_13(W1, W0))) | (~(W0 = sdtpldt0(sdtasdt0(tptp_fun_W2_14(W1, W0), W1), tptp_fun_W3_13(W1, W0)))) | (~((tptp_fun_W3_13(W1, W0) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(W1, W0)), sbrdtbr0(W1)))))))) | ((xu = sz00) | (~aElement0(xu)) | (~aElement0(xb)) | (~((~aElement0(tptp_fun_W2_14(xu, xb))) | (~aElement0(tptp_fun_W3_13(xu, xb))) | (~(xb = sdtpldt0(sdtasdt0(tptp_fun_W2_14(xu, xb), xu), tptp_fun_W3_13(xu, xb)))) | (~((tptp_fun_W3_13(xu, xb) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(xu, xb)), sbrdtbr0(xu)))))))),
% 17.25/17.42 inference(quant_inst,[status(thm)],[])).
% 17.25/17.42 tff(83,plain,
% 17.25/17.42 ((~![W0: $i, W1: $i] : ((W1 = sz00) | (~aElement0(W1)) | (~aElement0(W0)) | (~((~aElement0(tptp_fun_W2_14(W1, W0))) | (~aElement0(tptp_fun_W3_13(W1, W0))) | (~(W0 = sdtpldt0(sdtasdt0(tptp_fun_W2_14(W1, W0), W1), tptp_fun_W3_13(W1, W0)))) | (~((tptp_fun_W3_13(W1, W0) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(W1, W0)), sbrdtbr0(W1)))))))) | (xu = sz00) | (~aElement0(xu)) | (~aElement0(xb)) | (~((~aElement0(tptp_fun_W2_14(xu, xb))) | (~aElement0(tptp_fun_W3_13(xu, xb))) | (~(xb = sdtpldt0(sdtasdt0(tptp_fun_W2_14(xu, xb), xu), tptp_fun_W3_13(xu, xb)))) | (~((tptp_fun_W3_13(xu, xb) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(xu, xb)), sbrdtbr0(xu))))))),
% 17.25/17.42 inference(modus_ponens,[status(thm)],[82, 81])).
% 17.25/17.42 tff(84,plain,
% 17.25/17.42 (~((~aElement0(tptp_fun_W2_14(xu, xb))) | (~aElement0(tptp_fun_W3_13(xu, xb))) | (~(xb = sdtpldt0(sdtasdt0(tptp_fun_W2_14(xu, xb), xu), tptp_fun_W3_13(xu, xb)))) | (~((tptp_fun_W3_13(xu, xb) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(xu, xb)), sbrdtbr0(xu)))))),
% 17.25/17.42 inference(unit_resolution,[status(thm)],[83, 80, 36, 67, 62])).
% 17.25/17.42 tff(85,plain,
% 17.25/17.42 (((~aElement0(tptp_fun_W2_14(xu, xb))) | (~aElement0(tptp_fun_W3_13(xu, xb))) | (~(xb = sdtpldt0(sdtasdt0(tptp_fun_W2_14(xu, xb), xu), tptp_fun_W3_13(xu, xb)))) | (~((tptp_fun_W3_13(xu, xb) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(xu, xb)), sbrdtbr0(xu))))) | ((tptp_fun_W3_13(xu, xb) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(xu, xb)), sbrdtbr0(xu)))),
% 17.25/17.42 inference(tautology,[status(thm)],[])).
% 17.25/17.42 tff(86,plain,
% 17.25/17.42 ((tptp_fun_W3_13(xu, xb) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(xu, xb)), sbrdtbr0(xu))),
% 17.25/17.42 inference(unit_resolution,[status(thm)],[85, 84])).
% 17.25/17.42 tff(87,plain,
% 17.25/17.42 (((~aElement0(tptp_fun_W2_14(xu, xb))) | (~aElement0(tptp_fun_W3_13(xu, xb))) | (~(xb = sdtpldt0(sdtasdt0(tptp_fun_W2_14(xu, xb), xu), tptp_fun_W3_13(xu, xb)))) | (~((tptp_fun_W3_13(xu, xb) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(xu, xb)), sbrdtbr0(xu))))) | (xb = sdtpldt0(sdtasdt0(tptp_fun_W2_14(xu, xb), xu), tptp_fun_W3_13(xu, xb)))),
% 17.25/17.42 inference(tautology,[status(thm)],[])).
% 17.25/17.42 tff(88,plain,
% 17.25/17.42 (xb = sdtpldt0(sdtasdt0(tptp_fun_W2_14(xu, xb), xu), tptp_fun_W3_13(xu, xb))),
% 17.25/17.42 inference(unit_resolution,[status(thm)],[87, 84])).
% 17.25/17.42 tff(89,plain,
% 17.25/17.42 (((~aElement0(tptp_fun_W2_14(xu, xb))) | (~aElement0(tptp_fun_W3_13(xu, xb))) | (~(xb = sdtpldt0(sdtasdt0(tptp_fun_W2_14(xu, xb), xu), tptp_fun_W3_13(xu, xb)))) | (~((tptp_fun_W3_13(xu, xb) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(xu, xb)), sbrdtbr0(xu))))) | aElement0(tptp_fun_W3_13(xu, xb))),
% 17.25/17.42 inference(tautology,[status(thm)],[])).
% 17.25/17.42 tff(90,plain,
% 17.25/17.42 (aElement0(tptp_fun_W3_13(xu, xb))),
% 17.25/17.42 inference(unit_resolution,[status(thm)],[89, 84])).
% 17.25/17.42 tff(91,plain,
% 17.25/17.42 (((~aElement0(tptp_fun_W2_14(xu, xb))) | (~aElement0(tptp_fun_W3_13(xu, xb))) | (~(xb = sdtpldt0(sdtasdt0(tptp_fun_W2_14(xu, xb), xu), tptp_fun_W3_13(xu, xb)))) | (~((tptp_fun_W3_13(xu, xb) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(xu, xb)), sbrdtbr0(xu))))) | aElement0(tptp_fun_W2_14(xu, xb))),
% 17.25/17.42 inference(tautology,[status(thm)],[])).
% 17.25/17.42 tff(92,plain,
% 17.25/17.42 (aElement0(tptp_fun_W2_14(xu, xb))),
% 17.25/17.42 inference(unit_resolution,[status(thm)],[91, 84])).
% 17.25/17.42 tff(93,plain,
% 17.25/17.42 (^[W0: $i, W1: $i] : refl(((~aElement0(W1)) | (~aElement0(W0)) | (~(xb = sdtpldt0(sdtasdt0(W0, xu), W1))) | (~((W1 = sz00) | iLess0(sbrdtbr0(W1), sbrdtbr0(xu))))) <=> ((~aElement0(W1)) | (~aElement0(W0)) | (~(xb = sdtpldt0(sdtasdt0(W0, xu), W1))) | (~((W1 = sz00) | iLess0(sbrdtbr0(W1), sbrdtbr0(xu))))))),
% 17.25/17.42 inference(bind,[status(th)],[])).
% 17.25/17.42 tff(94,plain,
% 17.25/17.42 (![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~(xb = sdtpldt0(sdtasdt0(W0, xu), W1))) | (~((W1 = sz00) | iLess0(sbrdtbr0(W1), sbrdtbr0(xu))))) <=> ![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~(xb = sdtpldt0(sdtasdt0(W0, xu), W1))) | (~((W1 = sz00) | iLess0(sbrdtbr0(W1), sbrdtbr0(xu)))))),
% 17.25/17.42 inference(quant_intro,[status(thm)],[93])).
% 17.25/17.42 tff(95,plain,
% 17.25/17.42 (^[W0: $i, W1: $i] : trans(monotonicity(rewrite((aElement0(W0) & aElement0(W1) & (xb = sdtpldt0(sdtasdt0(W0, xu), W1)) & ((W1 = sz00) | iLess0(sbrdtbr0(W1), sbrdtbr0(xu)))) <=> (~((~aElement0(W1)) | (~aElement0(W0)) | (~(xb = sdtpldt0(sdtasdt0(W0, xu), W1))) | (~((W1 = sz00) | iLess0(sbrdtbr0(W1), sbrdtbr0(xu))))))), ((~(aElement0(W0) & aElement0(W1) & (xb = sdtpldt0(sdtasdt0(W0, xu), W1)) & ((W1 = sz00) | iLess0(sbrdtbr0(W1), sbrdtbr0(xu))))) <=> (~(~((~aElement0(W1)) | (~aElement0(W0)) | (~(xb = sdtpldt0(sdtasdt0(W0, xu), W1))) | (~((W1 = sz00) | iLess0(sbrdtbr0(W1), sbrdtbr0(xu))))))))), rewrite((~(~((~aElement0(W1)) | (~aElement0(W0)) | (~(xb = sdtpldt0(sdtasdt0(W0, xu), W1))) | (~((W1 = sz00) | iLess0(sbrdtbr0(W1), sbrdtbr0(xu))))))) <=> ((~aElement0(W1)) | (~aElement0(W0)) | (~(xb = sdtpldt0(sdtasdt0(W0, xu), W1))) | (~((W1 = sz00) | iLess0(sbrdtbr0(W1), sbrdtbr0(xu)))))), ((~(aElement0(W0) & aElement0(W1) & (xb = sdtpldt0(sdtasdt0(W0, xu), W1)) & ((W1 = sz00) | iLess0(sbrdtbr0(W1), sbrdtbr0(xu))))) <=> ((~aElement0(W1)) | (~aElement0(W0)) | (~(xb = sdtpldt0(sdtasdt0(W0, xu), W1))) | (~((W1 = sz00) | iLess0(sbrdtbr0(W1), sbrdtbr0(xu)))))))),
% 17.25/17.42 inference(bind,[status(th)],[])).
% 17.25/17.42 tff(96,plain,
% 17.25/17.42 (![W0: $i, W1: $i] : (~(aElement0(W0) & aElement0(W1) & (xb = sdtpldt0(sdtasdt0(W0, xu), W1)) & ((W1 = sz00) | iLess0(sbrdtbr0(W1), sbrdtbr0(xu))))) <=> ![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~(xb = sdtpldt0(sdtasdt0(W0, xu), W1))) | (~((W1 = sz00) | iLess0(sbrdtbr0(W1), sbrdtbr0(xu)))))),
% 17.25/17.42 inference(quant_intro,[status(thm)],[95])).
% 17.25/17.42 tff(97,plain,
% 17.25/17.42 ((~?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xb = sdtpldt0(sdtasdt0(W0, xu), W1)) & ((W1 = sz00) | iLess0(sbrdtbr0(W1), sbrdtbr0(xu))))) <=> (~?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xb = sdtpldt0(sdtasdt0(W0, xu), W1)) & ((W1 = sz00) | iLess0(sbrdtbr0(W1), sbrdtbr0(xu)))))),
% 17.25/17.42 inference(rewrite,[status(thm)],[])).
% 17.25/17.42 tff(98,plain,
% 17.25/17.42 ((~?[W0: $i, W1: $i] : (((aElement0(W0) & aElement0(W1)) & (xb = sdtpldt0(sdtasdt0(W0, xu), W1))) & ((W1 = sz00) | iLess0(sbrdtbr0(W1), sbrdtbr0(xu))))) <=> (~?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xb = sdtpldt0(sdtasdt0(W0, xu), W1)) & ((W1 = sz00) | iLess0(sbrdtbr0(W1), sbrdtbr0(xu)))))),
% 17.25/17.42 inference(rewrite,[status(thm)],[])).
% 17.25/17.42 tff(99,axiom,(~?[W0: $i, W1: $i] : (((aElement0(W0) & aElement0(W1)) & (xb = sdtpldt0(sdtasdt0(W0, xu), W1))) & ((W1 = sz00) | iLess0(sbrdtbr0(W1), sbrdtbr0(xu))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 17.25/17.42 tff(100,plain,
% 17.25/17.42 (~?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xb = sdtpldt0(sdtasdt0(W0, xu), W1)) & ((W1 = sz00) | iLess0(sbrdtbr0(W1), sbrdtbr0(xu))))),
% 17.25/17.42 inference(modus_ponens,[status(thm)],[99, 98])).
% 17.25/17.42 tff(101,plain,
% 17.25/17.42 (~?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xb = sdtpldt0(sdtasdt0(W0, xu), W1)) & ((W1 = sz00) | iLess0(sbrdtbr0(W1), sbrdtbr0(xu))))),
% 17.25/17.42 inference(modus_ponens,[status(thm)],[100, 97])).
% 17.25/17.42 tff(102,plain,
% 17.25/17.42 (~?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xb = sdtpldt0(sdtasdt0(W0, xu), W1)) & ((W1 = sz00) | iLess0(sbrdtbr0(W1), sbrdtbr0(xu))))),
% 17.25/17.42 inference(modus_ponens,[status(thm)],[101, 97])).
% 17.25/17.42 tff(103,plain,
% 17.25/17.42 (~?[W0: $i, W1: $i] : (aElement0(W0) & aElement0(W1) & (xb = sdtpldt0(sdtasdt0(W0, xu), W1)) & ((W1 = sz00) | iLess0(sbrdtbr0(W1), sbrdtbr0(xu))))),
% 17.25/17.42 inference(modus_ponens,[status(thm)],[102, 97])).
% 17.25/17.42 tff(104,plain,
% 17.25/17.42 (^[W0: $i, W1: $i] : refl($oeq((~(aElement0(W0) & aElement0(W1) & (xb = sdtpldt0(sdtasdt0(W0, xu), W1)) & ((W1 = sz00) | iLess0(sbrdtbr0(W1), sbrdtbr0(xu))))), (~(aElement0(W0) & aElement0(W1) & (xb = sdtpldt0(sdtasdt0(W0, xu), W1)) & ((W1 = sz00) | iLess0(sbrdtbr0(W1), sbrdtbr0(xu)))))))),
% 17.25/17.42 inference(bind,[status(th)],[])).
% 17.25/17.42 tff(105,plain,(
% 17.25/17.42 ![W0: $i, W1: $i] : (~(aElement0(W0) & aElement0(W1) & (xb = sdtpldt0(sdtasdt0(W0, xu), W1)) & ((W1 = sz00) | iLess0(sbrdtbr0(W1), sbrdtbr0(xu)))))),
% 17.25/17.42 inference(nnf-neg,[status(sab)],[103, 104])).
% 17.25/17.42 tff(106,plain,
% 17.25/17.42 (![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~(xb = sdtpldt0(sdtasdt0(W0, xu), W1))) | (~((W1 = sz00) | iLess0(sbrdtbr0(W1), sbrdtbr0(xu)))))),
% 17.25/17.42 inference(modus_ponens,[status(thm)],[105, 96])).
% 17.25/17.42 tff(107,plain,
% 17.25/17.42 (![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~(xb = sdtpldt0(sdtasdt0(W0, xu), W1))) | (~((W1 = sz00) | iLess0(sbrdtbr0(W1), sbrdtbr0(xu)))))),
% 17.25/17.42 inference(modus_ponens,[status(thm)],[106, 94])).
% 17.25/17.42 tff(108,plain,
% 17.25/17.42 (((~![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~(xb = sdtpldt0(sdtasdt0(W0, xu), W1))) | (~((W1 = sz00) | iLess0(sbrdtbr0(W1), sbrdtbr0(xu)))))) | ((~aElement0(tptp_fun_W2_14(xu, xb))) | (~aElement0(tptp_fun_W3_13(xu, xb))) | (~(xb = sdtpldt0(sdtasdt0(tptp_fun_W2_14(xu, xb), xu), tptp_fun_W3_13(xu, xb)))) | (~((tptp_fun_W3_13(xu, xb) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(xu, xb)), sbrdtbr0(xu)))))) <=> ((~![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~(xb = sdtpldt0(sdtasdt0(W0, xu), W1))) | (~((W1 = sz00) | iLess0(sbrdtbr0(W1), sbrdtbr0(xu)))))) | (~aElement0(tptp_fun_W2_14(xu, xb))) | (~aElement0(tptp_fun_W3_13(xu, xb))) | (~(xb = sdtpldt0(sdtasdt0(tptp_fun_W2_14(xu, xb), xu), tptp_fun_W3_13(xu, xb)))) | (~((tptp_fun_W3_13(xu, xb) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(xu, xb)), sbrdtbr0(xu)))))),
% 17.25/17.42 inference(rewrite,[status(thm)],[])).
% 17.25/17.42 tff(109,plain,
% 17.25/17.42 (((~aElement0(tptp_fun_W3_13(xu, xb))) | (~aElement0(tptp_fun_W2_14(xu, xb))) | (~(xb = sdtpldt0(sdtasdt0(tptp_fun_W2_14(xu, xb), xu), tptp_fun_W3_13(xu, xb)))) | (~((tptp_fun_W3_13(xu, xb) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(xu, xb)), sbrdtbr0(xu))))) <=> ((~aElement0(tptp_fun_W2_14(xu, xb))) | (~aElement0(tptp_fun_W3_13(xu, xb))) | (~(xb = sdtpldt0(sdtasdt0(tptp_fun_W2_14(xu, xb), xu), tptp_fun_W3_13(xu, xb)))) | (~((tptp_fun_W3_13(xu, xb) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(xu, xb)), sbrdtbr0(xu)))))),
% 17.25/17.42 inference(rewrite,[status(thm)],[])).
% 17.25/17.42 tff(110,plain,
% 17.25/17.42 (((~![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~(xb = sdtpldt0(sdtasdt0(W0, xu), W1))) | (~((W1 = sz00) | iLess0(sbrdtbr0(W1), sbrdtbr0(xu)))))) | ((~aElement0(tptp_fun_W3_13(xu, xb))) | (~aElement0(tptp_fun_W2_14(xu, xb))) | (~(xb = sdtpldt0(sdtasdt0(tptp_fun_W2_14(xu, xb), xu), tptp_fun_W3_13(xu, xb)))) | (~((tptp_fun_W3_13(xu, xb) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(xu, xb)), sbrdtbr0(xu)))))) <=> ((~![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~(xb = sdtpldt0(sdtasdt0(W0, xu), W1))) | (~((W1 = sz00) | iLess0(sbrdtbr0(W1), sbrdtbr0(xu)))))) | ((~aElement0(tptp_fun_W2_14(xu, xb))) | (~aElement0(tptp_fun_W3_13(xu, xb))) | (~(xb = sdtpldt0(sdtasdt0(tptp_fun_W2_14(xu, xb), xu), tptp_fun_W3_13(xu, xb)))) | (~((tptp_fun_W3_13(xu, xb) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(xu, xb)), sbrdtbr0(xu))))))),
% 17.25/17.42 inference(monotonicity,[status(thm)],[109])).
% 17.25/17.42 tff(111,plain,
% 17.25/17.42 (((~![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~(xb = sdtpldt0(sdtasdt0(W0, xu), W1))) | (~((W1 = sz00) | iLess0(sbrdtbr0(W1), sbrdtbr0(xu)))))) | ((~aElement0(tptp_fun_W3_13(xu, xb))) | (~aElement0(tptp_fun_W2_14(xu, xb))) | (~(xb = sdtpldt0(sdtasdt0(tptp_fun_W2_14(xu, xb), xu), tptp_fun_W3_13(xu, xb)))) | (~((tptp_fun_W3_13(xu, xb) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(xu, xb)), sbrdtbr0(xu)))))) <=> ((~![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~(xb = sdtpldt0(sdtasdt0(W0, xu), W1))) | (~((W1 = sz00) | iLess0(sbrdtbr0(W1), sbrdtbr0(xu)))))) | (~aElement0(tptp_fun_W2_14(xu, xb))) | (~aElement0(tptp_fun_W3_13(xu, xb))) | (~(xb = sdtpldt0(sdtasdt0(tptp_fun_W2_14(xu, xb), xu), tptp_fun_W3_13(xu, xb)))) | (~((tptp_fun_W3_13(xu, xb) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(xu, xb)), sbrdtbr0(xu)))))),
% 17.25/17.46 inference(transitivity,[status(thm)],[110, 108])).
% 17.25/17.46 tff(112,plain,
% 17.25/17.46 ((~![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~(xb = sdtpldt0(sdtasdt0(W0, xu), W1))) | (~((W1 = sz00) | iLess0(sbrdtbr0(W1), sbrdtbr0(xu)))))) | ((~aElement0(tptp_fun_W3_13(xu, xb))) | (~aElement0(tptp_fun_W2_14(xu, xb))) | (~(xb = sdtpldt0(sdtasdt0(tptp_fun_W2_14(xu, xb), xu), tptp_fun_W3_13(xu, xb)))) | (~((tptp_fun_W3_13(xu, xb) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(xu, xb)), sbrdtbr0(xu)))))),
% 17.25/17.46 inference(quant_inst,[status(thm)],[])).
% 17.25/17.46 tff(113,plain,
% 17.25/17.46 ((~![W0: $i, W1: $i] : ((~aElement0(W1)) | (~aElement0(W0)) | (~(xb = sdtpldt0(sdtasdt0(W0, xu), W1))) | (~((W1 = sz00) | iLess0(sbrdtbr0(W1), sbrdtbr0(xu)))))) | (~aElement0(tptp_fun_W2_14(xu, xb))) | (~aElement0(tptp_fun_W3_13(xu, xb))) | (~(xb = sdtpldt0(sdtasdt0(tptp_fun_W2_14(xu, xb), xu), tptp_fun_W3_13(xu, xb)))) | (~((tptp_fun_W3_13(xu, xb) = sz00) | iLess0(sbrdtbr0(tptp_fun_W3_13(xu, xb)), sbrdtbr0(xu))))),
% 17.25/17.46 inference(modus_ponens,[status(thm)],[112, 111])).
% 17.25/17.46 tff(114,plain,
% 17.25/17.46 ($false),
% 17.25/17.46 inference(unit_resolution,[status(thm)],[113, 107, 92, 90, 88, 86])).
% 17.25/17.46 % SZS output end Proof
% 17.33/17.51 % E exiting
%------------------------------------------------------------------------------