%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM475+2 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:21:06 AM UTC 2025
% Result : Theorem 5.31s 5.47s
% Output : Proof 5.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : NUM475+2 : TPTP v9.0.0. Released v4.0.0.
% 0.08/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 01:15:05 EDT 2025
% 0.12/0.34 % CPUTime :
% 5.31/5.47 % SZS status Theorem
% 5.31/5.47 % SZS output start Proof
% 5.31/5.47 tff(sdtpldt0_type, type, (
% 5.31/5.47 sdtpldt0: ( $i * $i ) > $i)).
% 5.31/5.47 tff(sdtasdt0_type, type, (
% 5.31/5.47 sdtasdt0: ( $i * $i ) > $i)).
% 5.31/5.47 tff(xr_type, type, (
% 5.31/5.47 xr: $i)).
% 5.31/5.47 tff(xl_type, type, (
% 5.31/5.47 xl: $i)).
% 5.31/5.47 tff(tptp_fun_W0_2_type, type, (
% 5.31/5.47 tptp_fun_W0_2: $i)).
% 5.31/5.47 tff(xn_type, type, (
% 5.31/5.47 xn: $i)).
% 5.31/5.47 tff(aNaturalNumber0_type, type, (
% 5.31/5.47 aNaturalNumber0: $i > $o)).
% 5.31/5.47 tff(xm_type, type, (
% 5.31/5.47 xm: $i)).
% 5.31/5.47 tff(doDivides0_type, type, (
% 5.31/5.47 doDivides0: ( $i * $i ) > $o)).
% 5.31/5.47 tff(sdtmndt0_type, type, (
% 5.31/5.47 sdtmndt0: ( $i * $i ) > $i)).
% 5.31/5.47 tff(xp_type, type, (
% 5.31/5.47 xp: $i)).
% 5.31/5.47 tff(xq_type, type, (
% 5.31/5.47 xq: $i)).
% 5.31/5.47 tff(sdtsldt0_type, type, (
% 5.31/5.47 sdtsldt0: ( $i * $i ) > $i)).
% 5.31/5.47 tff(1,plain,
% 5.31/5.47 (?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xl, W0))) <=> ?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xl, W0)))),
% 5.31/5.47 inference(rewrite,[status(thm)],[])).
% 5.31/5.47 tff(2,axiom,(((?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xl, W0))) & doDivides0(xl, xm)) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, xn) = sdtasdt0(xl, W0)))) & doDivides0(xl, sdtpldt0(xm, xn))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__1324_04')).
% 5.31/5.47 tff(3,plain,
% 5.31/5.47 ((?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xl, W0))) & doDivides0(xl, xm)) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, xn) = sdtasdt0(xl, W0)))),
% 5.31/5.47 inference(and_elim,[status(thm)],[2])).
% 5.31/5.47 tff(4,plain,
% 5.31/5.47 (?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xl, W0))) & doDivides0(xl, xm)),
% 5.31/5.47 inference(and_elim,[status(thm)],[3])).
% 5.31/5.47 tff(5,plain,
% 5.31/5.47 (?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xl, W0)))),
% 5.31/5.47 inference(and_elim,[status(thm)],[4])).
% 5.31/5.47 tff(6,plain,
% 5.31/5.47 (?[W0: $i] : (aNaturalNumber0(W0) & (xm = sdtasdt0(xl, W0)))),
% 5.31/5.47 inference(modus_ponens,[status(thm)],[5, 1])).
% 5.31/5.47 tff(7,plain,(
% 5.31/5.47 aNaturalNumber0(W0!2) & (xm = sdtasdt0(xl, W0!2))),
% 5.31/5.47 inference(skolemize,[status(sab)],[6])).
% 5.31/5.47 tff(8,plain,
% 5.31/5.47 (xm = sdtasdt0(xl, W0!2)),
% 5.31/5.47 inference(and_elim,[status(thm)],[7])).
% 5.31/5.47 tff(9,plain,
% 5.31/5.47 (sdtasdt0(xl, W0!2) = xm),
% 5.31/5.47 inference(symmetry,[status(thm)],[8])).
% 5.31/5.47 tff(10,plain,
% 5.31/5.47 (aNaturalNumber0(sdtasdt0(xl, W0!2)) <=> aNaturalNumber0(xm)),
% 5.31/5.47 inference(monotonicity,[status(thm)],[9])).
% 5.31/5.47 tff(11,plain,
% 5.31/5.47 (aNaturalNumber0(xm) <=> aNaturalNumber0(sdtasdt0(xl, W0!2))),
% 5.31/5.47 inference(symmetry,[status(thm)],[10])).
% 5.31/5.47 tff(12,plain,
% 5.31/5.47 (aNaturalNumber0(xm) <=> aNaturalNumber0(xm)),
% 5.31/5.47 inference(rewrite,[status(thm)],[])).
% 5.31/5.47 tff(13,axiom,((aNaturalNumber0(xl) & aNaturalNumber0(xm)) & aNaturalNumber0(xn)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__1324')).
% 5.31/5.47 tff(14,plain,
% 5.31/5.47 (aNaturalNumber0(xl) & aNaturalNumber0(xm)),
% 5.31/5.47 inference(and_elim,[status(thm)],[13])).
% 5.31/5.47 tff(15,plain,
% 5.31/5.47 (aNaturalNumber0(xm)),
% 5.31/5.47 inference(and_elim,[status(thm)],[14])).
% 5.31/5.47 tff(16,plain,
% 5.31/5.47 (aNaturalNumber0(xm)),
% 5.31/5.47 inference(modus_ponens,[status(thm)],[15, 12])).
% 5.31/5.47 tff(17,plain,
% 5.31/5.47 (aNaturalNumber0(sdtasdt0(xl, W0!2))),
% 5.31/5.47 inference(modus_ponens,[status(thm)],[16, 11])).
% 5.31/5.47 tff(18,plain,
% 5.31/5.47 ((xr = sdtmndt0(xq, xp)) <=> (xr = sdtmndt0(xq, xp))),
% 5.31/5.47 inference(rewrite,[status(thm)],[])).
% 5.31/5.47 tff(19,axiom,((aNaturalNumber0(xr) & (sdtpldt0(xp, xr) = xq)) & (xr = sdtmndt0(xq, xp))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__1422')).
% 5.31/5.47 tff(20,plain,
% 5.31/5.47 (xr = sdtmndt0(xq, xp)),
% 5.31/5.47 inference(and_elim,[status(thm)],[19])).
% 5.31/5.47 tff(21,plain,
% 5.31/5.47 (xr = sdtmndt0(xq, xp)),
% 5.31/5.47 inference(modus_ponens,[status(thm)],[20, 18])).
% 5.31/5.47 tff(22,plain,
% 5.31/5.47 (sdtmndt0(xq, xp) = xr),
% 5.31/5.47 inference(symmetry,[status(thm)],[21])).
% 5.31/5.47 tff(23,plain,
% 5.31/5.47 (sdtasdt0(xl, sdtmndt0(xq, xp)) = sdtasdt0(xl, xr)),
% 5.31/5.47 inference(monotonicity,[status(thm)],[22])).
% 5.31/5.47 tff(24,plain,
% 5.31/5.47 (aNaturalNumber0(sdtasdt0(xl, sdtmndt0(xq, xp))) <=> aNaturalNumber0(sdtasdt0(xl, xr))),
% 5.31/5.47 inference(monotonicity,[status(thm)],[23])).
% 5.31/5.47 tff(25,plain,
% 5.31/5.47 (aNaturalNumber0(sdtmndt0(xq, xp)) <=> aNaturalNumber0(xr)),
% 5.31/5.47 inference(monotonicity,[status(thm)],[22])).
% 5.31/5.47 tff(26,plain,
% 5.31/5.47 (aNaturalNumber0(xr) <=> aNaturalNumber0(sdtmndt0(xq, xp))),
% 5.31/5.47 inference(symmetry,[status(thm)],[25])).
% 5.31/5.47 tff(27,plain,
% 5.31/5.47 (aNaturalNumber0(xr) <=> aNaturalNumber0(xr)),
% 5.31/5.47 inference(rewrite,[status(thm)],[])).
% 5.31/5.47 tff(28,plain,
% 5.31/5.47 (aNaturalNumber0(xr) & (sdtpldt0(xp, xr) = xq)),
% 5.31/5.47 inference(and_elim,[status(thm)],[19])).
% 5.31/5.47 tff(29,plain,
% 5.31/5.47 (aNaturalNumber0(xr)),
% 5.31/5.47 inference(and_elim,[status(thm)],[28])).
% 5.31/5.47 tff(30,plain,
% 5.31/5.47 (aNaturalNumber0(xr)),
% 5.31/5.47 inference(modus_ponens,[status(thm)],[29, 27])).
% 5.31/5.47 tff(31,plain,
% 5.31/5.47 (aNaturalNumber0(sdtmndt0(xq, xp))),
% 5.31/5.47 inference(modus_ponens,[status(thm)],[30, 26])).
% 5.31/5.47 tff(32,plain,
% 5.31/5.47 (aNaturalNumber0(xl) <=> aNaturalNumber0(xl)),
% 5.31/5.47 inference(rewrite,[status(thm)],[])).
% 5.31/5.47 tff(33,plain,
% 5.31/5.47 (aNaturalNumber0(xl)),
% 5.31/5.47 inference(and_elim,[status(thm)],[14])).
% 5.31/5.47 tff(34,plain,
% 5.31/5.47 (aNaturalNumber0(xl)),
% 5.31/5.47 inference(modus_ponens,[status(thm)],[33, 32])).
% 5.31/5.47 tff(35,plain,
% 5.31/5.47 (^[W0: $i, W1: $i] : refl((aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))),
% 5.31/5.47 inference(bind,[status(th)],[])).
% 5.31/5.47 tff(36,plain,
% 5.31/5.47 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 5.31/5.47 inference(quant_intro,[status(thm)],[35])).
% 5.31/5.47 tff(37,plain,
% 5.31/5.47 (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aNaturalNumber0(W0) & aNaturalNumber0(W1)) <=> (~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))), ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) <=> (~(~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))))), rewrite((~(~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))) <=> ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) <=> ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))), ((aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> (aNaturalNumber0(sdtasdt0(W0, W1)) | ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))))), rewrite((aNaturalNumber0(sdtasdt0(W0, W1)) | ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) <=> (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), ((aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))))),
% 5.31/5.47 inference(bind,[status(th)],[])).
% 5.31/5.47 tff(38,plain,
% 5.31/5.47 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 5.31/5.47 inference(quant_intro,[status(thm)],[37])).
% 5.31/5.47 tff(39,plain,
% 5.31/5.47 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 5.31/5.47 inference(rewrite,[status(thm)],[])).
% 5.31/5.47 tff(40,plain,
% 5.31/5.47 (^[W0: $i, W1: $i] : rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtasdt0(W0, W1))) <=> (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))))),
% 5.31/5.47 inference(bind,[status(th)],[])).
% 5.31/5.47 tff(41,plain,
% 5.31/5.47 (![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtasdt0(W0, W1))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 5.31/5.47 inference(quant_intro,[status(thm)],[40])).
% 5.31/5.47 tff(42,axiom,(![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtasdt0(W0, W1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mSortsB_02')).
% 5.31/5.47 tff(43,plain,
% 5.31/5.47 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 5.31/5.47 inference(modus_ponens,[status(thm)],[42, 41])).
% 5.31/5.47 tff(44,plain,
% 5.31/5.47 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 5.31/5.47 inference(modus_ponens,[status(thm)],[43, 39])).
% 5.31/5.47 tff(45,plain,(
% 5.31/5.47 ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 5.31/5.47 inference(skolemize,[status(sab)],[44])).
% 5.31/5.47 tff(46,plain,
% 5.31/5.47 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 5.31/5.47 inference(modus_ponens,[status(thm)],[45, 38])).
% 5.31/5.47 tff(47,plain,
% 5.31/5.47 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 5.31/5.47 inference(modus_ponens,[status(thm)],[46, 36])).
% 5.31/5.47 tff(48,plain,
% 5.31/5.47 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(sdtmndt0(xq, xp))) | (~aNaturalNumber0(xl)) | aNaturalNumber0(sdtasdt0(xl, sdtmndt0(xq, xp))))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(sdtmndt0(xq, xp))) | (~aNaturalNumber0(xl)) | aNaturalNumber0(sdtasdt0(xl, sdtmndt0(xq, xp))))),
% 5.31/5.47 inference(rewrite,[status(thm)],[])).
% 5.31/5.47 tff(49,plain,
% 5.31/5.47 ((aNaturalNumber0(sdtasdt0(xl, sdtmndt0(xq, xp))) | (~aNaturalNumber0(sdtmndt0(xq, xp))) | (~aNaturalNumber0(xl))) <=> ((~aNaturalNumber0(sdtmndt0(xq, xp))) | (~aNaturalNumber0(xl)) | aNaturalNumber0(sdtasdt0(xl, sdtmndt0(xq, xp))))),
% 5.31/5.47 inference(rewrite,[status(thm)],[])).
% 5.31/5.47 tff(50,plain,
% 5.31/5.47 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(xl, sdtmndt0(xq, xp))) | (~aNaturalNumber0(sdtmndt0(xq, xp))) | (~aNaturalNumber0(xl)))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(sdtmndt0(xq, xp))) | (~aNaturalNumber0(xl)) | aNaturalNumber0(sdtasdt0(xl, sdtmndt0(xq, xp)))))),
% 5.31/5.47 inference(monotonicity,[status(thm)],[49])).
% 5.31/5.47 tff(51,plain,
% 5.31/5.47 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(xl, sdtmndt0(xq, xp))) | (~aNaturalNumber0(sdtmndt0(xq, xp))) | (~aNaturalNumber0(xl)))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(sdtmndt0(xq, xp))) | (~aNaturalNumber0(xl)) | aNaturalNumber0(sdtasdt0(xl, sdtmndt0(xq, xp))))),
% 5.31/5.47 inference(transitivity,[status(thm)],[50, 48])).
% 5.31/5.47 tff(52,plain,
% 5.31/5.47 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(xl, sdtmndt0(xq, xp))) | (~aNaturalNumber0(sdtmndt0(xq, xp))) | (~aNaturalNumber0(xl)))),
% 5.31/5.47 inference(quant_inst,[status(thm)],[])).
% 5.31/5.47 tff(53,plain,
% 5.31/5.47 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(sdtmndt0(xq, xp))) | (~aNaturalNumber0(xl)) | aNaturalNumber0(sdtasdt0(xl, sdtmndt0(xq, xp)))),
% 5.31/5.47 inference(modus_ponens,[status(thm)],[52, 51])).
% 5.31/5.47 tff(54,plain,
% 5.31/5.47 ((~aNaturalNumber0(sdtmndt0(xq, xp))) | aNaturalNumber0(sdtasdt0(xl, sdtmndt0(xq, xp)))),
% 5.31/5.47 inference(unit_resolution,[status(thm)],[53, 47, 34])).
% 5.31/5.47 tff(55,plain,
% 5.31/5.47 (aNaturalNumber0(sdtasdt0(xl, sdtmndt0(xq, xp)))),
% 5.31/5.47 inference(unit_resolution,[status(thm)],[54, 31])).
% 5.31/5.47 tff(56,plain,
% 5.31/5.47 (aNaturalNumber0(sdtasdt0(xl, xr))),
% 5.31/5.47 inference(modus_ponens,[status(thm)],[55, 24])).
% 5.31/5.47 tff(57,plain,
% 5.31/5.47 (^[W0: $i, W1: $i] : refl(((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))),
% 5.31/5.47 inference(bind,[status(th)],[])).
% 5.31/5.47 tff(58,plain,
% 5.31/5.47 (![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 5.31/5.47 inference(quant_intro,[status(thm)],[57])).
% 5.31/5.47 tff(59,plain,
% 5.31/5.47 (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aNaturalNumber0(W0) & aNaturalNumber0(W1)) <=> (~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))), ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) <=> (~(~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))))), rewrite((~(~((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))) <=> ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) <=> ((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))), (((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))) <=> (((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))))), rewrite((((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))) <=> ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), (((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))) <=> ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))))),
% 5.31/5.48 inference(bind,[status(th)],[])).
% 5.31/5.48 tff(60,plain,
% 5.31/5.48 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))) <=> ![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 5.31/5.48 inference(quant_intro,[status(thm)],[59])).
% 5.31/5.48 tff(61,plain,
% 5.31/5.48 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))) <=> ![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0)))),
% 5.31/5.48 inference(rewrite,[status(thm)],[])).
% 5.31/5.48 tff(62,plain,
% 5.31/5.48 (^[W0: $i, W1: $i] : rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))) <=> ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))))),
% 5.31/5.48 inference(bind,[status(th)],[])).
% 5.31/5.48 tff(63,plain,
% 5.31/5.48 (![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtpldt0(W0, W1) = sdtpldt0(W1, W0))) <=> ![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0)))),
% 5.31/5.48 inference(quant_intro,[status(thm)],[62])).
% 5.31/5.48 tff(64,axiom,(![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtpldt0(W0, W1) = sdtpldt0(W1, W0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mAddComm')).
% 5.31/5.48 tff(65,plain,
% 5.31/5.48 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0)))),
% 5.31/5.48 inference(modus_ponens,[status(thm)],[64, 63])).
% 5.31/5.48 tff(66,plain,
% 5.31/5.48 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0)))),
% 5.31/5.48 inference(modus_ponens,[status(thm)],[65, 61])).
% 5.31/5.48 tff(67,plain,(
% 5.31/5.48 ![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtpldt0(W0, W1) = sdtpldt0(W1, W0)))),
% 5.31/5.48 inference(skolemize,[status(sab)],[66])).
% 5.31/5.48 tff(68,plain,
% 5.31/5.48 (![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 5.31/5.48 inference(modus_ponens,[status(thm)],[67, 60])).
% 5.31/5.48 tff(69,plain,
% 5.31/5.48 (![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 5.31/5.48 inference(modus_ponens,[status(thm)],[68, 58])).
% 5.31/5.48 tff(70,plain,
% 5.31/5.48 (((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (~aNaturalNumber0(sdtasdt0(xl, xr))) | (sdtpldt0(sdtasdt0(xl, xr), sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, xr))))) <=> ((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (~aNaturalNumber0(sdtasdt0(xl, xr))) | (sdtpldt0(sdtasdt0(xl, xr), sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, xr))))),
% 5.31/5.48 inference(rewrite,[status(thm)],[])).
% 5.31/5.48 tff(71,plain,
% 5.31/5.48 (((sdtpldt0(sdtasdt0(xl, xr), sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, xr))) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (~aNaturalNumber0(sdtasdt0(xl, xr)))) <=> ((~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (~aNaturalNumber0(sdtasdt0(xl, xr))) | (sdtpldt0(sdtasdt0(xl, xr), sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, xr))))),
% 5.31/5.48 inference(rewrite,[status(thm)],[])).
% 5.31/5.48 tff(72,plain,
% 5.31/5.48 (((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtpldt0(sdtasdt0(xl, xr), sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, xr))) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (~aNaturalNumber0(sdtasdt0(xl, xr))))) <=> ((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (~aNaturalNumber0(sdtasdt0(xl, xr))) | (sdtpldt0(sdtasdt0(xl, xr), sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, xr)))))),
% 5.31/5.48 inference(monotonicity,[status(thm)],[71])).
% 5.31/5.48 tff(73,plain,
% 5.31/5.48 (((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtpldt0(sdtasdt0(xl, xr), sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, xr))) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (~aNaturalNumber0(sdtasdt0(xl, xr))))) <=> ((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (~aNaturalNumber0(sdtasdt0(xl, xr))) | (sdtpldt0(sdtasdt0(xl, xr), sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, xr))))),
% 5.31/5.48 inference(transitivity,[status(thm)],[72, 70])).
% 5.31/5.48 tff(74,plain,
% 5.31/5.48 ((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtpldt0(sdtasdt0(xl, xr), sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, xr))) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (~aNaturalNumber0(sdtasdt0(xl, xr))))),
% 5.31/5.48 inference(quant_inst,[status(thm)],[])).
% 5.31/5.48 tff(75,plain,
% 5.31/5.48 ((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (~aNaturalNumber0(sdtasdt0(xl, xr))) | (sdtpldt0(sdtasdt0(xl, xr), sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, xr)))),
% 5.31/5.48 inference(modus_ponens,[status(thm)],[74, 73])).
% 5.31/5.48 tff(76,plain,
% 5.31/5.48 ((~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (~aNaturalNumber0(sdtasdt0(xl, xr))) | (sdtpldt0(sdtasdt0(xl, xr), sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, xr)))),
% 5.31/5.48 inference(unit_resolution,[status(thm)],[75, 69])).
% 5.31/5.48 tff(77,plain,
% 5.31/5.48 (sdtpldt0(sdtasdt0(xl, xr), sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, xr))),
% 5.31/5.48 inference(unit_resolution,[status(thm)],[76, 56, 17])).
% 5.31/5.48 tff(78,plain,
% 5.31/5.48 (sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, xr)) = sdtpldt0(sdtasdt0(xl, xr), sdtasdt0(xl, W0!2))),
% 5.31/5.48 inference(symmetry,[status(thm)],[77])).
% 5.31/5.48 tff(79,plain,
% 5.31/5.48 ((xm = sdtasdt0(xl, xp)) <=> (xm = sdtasdt0(xl, xp))),
% 5.31/5.48 inference(rewrite,[status(thm)],[])).
% 5.31/5.48 tff(80,axiom,((aNaturalNumber0(xp) & (xm = sdtasdt0(xl, xp))) & (xp = sdtsldt0(xm, xl))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__1360')).
% 5.31/5.48 tff(81,plain,
% 5.31/5.48 (aNaturalNumber0(xp) & (xm = sdtasdt0(xl, xp))),
% 5.31/5.48 inference(and_elim,[status(thm)],[80])).
% 5.31/5.48 tff(82,plain,
% 5.31/5.48 (xm = sdtasdt0(xl, xp)),
% 5.31/5.48 inference(and_elim,[status(thm)],[81])).
% 5.31/5.48 tff(83,plain,
% 5.31/5.48 (xm = sdtasdt0(xl, xp)),
% 5.31/5.48 inference(modus_ponens,[status(thm)],[82, 79])).
% 5.31/5.48 tff(84,plain,
% 5.31/5.48 (sdtasdt0(xl, W0!2) = sdtasdt0(xl, xp)),
% 5.31/5.48 inference(transitivity,[status(thm)],[9, 83])).
% 5.31/5.48 tff(85,plain,
% 5.31/5.48 (sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, xr)) = sdtpldt0(sdtasdt0(xl, xp), sdtasdt0(xl, xr))),
% 5.31/5.48 inference(monotonicity,[status(thm)],[84])).
% 5.31/5.48 tff(86,plain,
% 5.31/5.48 (sdtpldt0(sdtasdt0(xl, xp), sdtasdt0(xl, xr)) = sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, xr))),
% 5.31/5.48 inference(symmetry,[status(thm)],[85])).
% 5.31/5.48 tff(87,plain,
% 5.31/5.48 ((sdtpldt0(sdtasdt0(xl, xp), sdtasdt0(xl, xr)) = sdtpldt0(sdtasdt0(xl, xp), xn)) <=> (sdtpldt0(sdtasdt0(xl, xp), sdtasdt0(xl, xr)) = sdtpldt0(sdtasdt0(xl, xp), xn))),
% 5.31/5.48 inference(rewrite,[status(thm)],[])).
% 5.31/5.48 tff(88,axiom,(sdtpldt0(sdtasdt0(xl, xp), sdtasdt0(xl, xr)) = sdtpldt0(sdtasdt0(xl, xp), xn)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__1459')).
% 5.31/5.48 tff(89,plain,
% 5.31/5.48 (sdtpldt0(sdtasdt0(xl, xp), sdtasdt0(xl, xr)) = sdtpldt0(sdtasdt0(xl, xp), xn)),
% 5.31/5.48 inference(modus_ponens,[status(thm)],[88, 87])).
% 5.31/5.48 tff(90,plain,
% 5.31/5.48 (sdtpldt0(sdtasdt0(xl, xp), xn) = sdtpldt0(sdtasdt0(xl, xp), sdtasdt0(xl, xr))),
% 5.31/5.48 inference(symmetry,[status(thm)],[89])).
% 5.31/5.48 tff(91,plain,
% 5.31/5.48 (sdtasdt0(xl, xp) = xm),
% 5.31/5.48 inference(symmetry,[status(thm)],[83])).
% 5.31/5.48 tff(92,plain,
% 5.31/5.48 (sdtpldt0(sdtasdt0(xl, xp), xn) = sdtpldt0(xm, xn)),
% 5.31/5.48 inference(monotonicity,[status(thm)],[91])).
% 5.31/5.48 tff(93,plain,
% 5.31/5.48 (sdtpldt0(xm, xn) = sdtpldt0(sdtasdt0(xl, xp), xn)),
% 5.31/5.48 inference(symmetry,[status(thm)],[92])).
% 5.31/5.48 tff(94,plain,
% 5.31/5.48 (sdtpldt0(sdtasdt0(xl, W0!2), xn) = sdtpldt0(xm, xn)),
% 5.31/5.48 inference(monotonicity,[status(thm)],[9])).
% 5.31/5.48 tff(95,plain,
% 5.31/5.48 (aNaturalNumber0(xn) <=> aNaturalNumber0(xn)),
% 5.31/5.48 inference(rewrite,[status(thm)],[])).
% 5.31/5.48 tff(96,plain,
% 5.31/5.48 (aNaturalNumber0(xn)),
% 5.31/5.48 inference(and_elim,[status(thm)],[13])).
% 5.31/5.48 tff(97,plain,
% 5.31/5.48 (aNaturalNumber0(xn)),
% 5.31/5.48 inference(modus_ponens,[status(thm)],[96, 95])).
% 5.31/5.48 tff(98,plain,
% 5.31/5.48 (((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xn)) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (sdtpldt0(xn, sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, W0!2), xn)))) <=> ((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (sdtpldt0(xn, sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, W0!2), xn)))),
% 5.31/5.48 inference(rewrite,[status(thm)],[])).
% 5.31/5.48 tff(99,plain,
% 5.31/5.48 (((sdtpldt0(xn, sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, W0!2), xn)) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (~aNaturalNumber0(xn))) <=> ((~aNaturalNumber0(xn)) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (sdtpldt0(xn, sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, W0!2), xn)))),
% 5.31/5.48 inference(rewrite,[status(thm)],[])).
% 5.31/5.48 tff(100,plain,
% 5.31/5.48 (((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtpldt0(xn, sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, W0!2), xn)) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (~aNaturalNumber0(xn)))) <=> ((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xn)) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (sdtpldt0(xn, sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, W0!2), xn))))),
% 5.31/5.48 inference(monotonicity,[status(thm)],[99])).
% 5.31/5.48 tff(101,plain,
% 5.31/5.48 (((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtpldt0(xn, sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, W0!2), xn)) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (~aNaturalNumber0(xn)))) <=> ((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (sdtpldt0(xn, sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, W0!2), xn)))),
% 5.31/5.48 inference(transitivity,[status(thm)],[100, 98])).
% 5.31/5.48 tff(102,plain,
% 5.31/5.48 ((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtpldt0(xn, sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, W0!2), xn)) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (~aNaturalNumber0(xn)))),
% 5.31/5.48 inference(quant_inst,[status(thm)],[])).
% 5.31/5.48 tff(103,plain,
% 5.31/5.48 ((~![W0: $i, W1: $i] : ((sdtpldt0(W0, W1) = sdtpldt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (sdtpldt0(xn, sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, W0!2), xn))),
% 5.31/5.48 inference(modus_ponens,[status(thm)],[102, 101])).
% 5.31/5.48 tff(104,plain,
% 5.31/5.48 ((~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (sdtpldt0(xn, sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, W0!2), xn))),
% 5.31/5.48 inference(unit_resolution,[status(thm)],[103, 69, 97])).
% 5.31/5.48 tff(105,plain,
% 5.31/5.48 (sdtpldt0(xn, sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, W0!2), xn)),
% 5.31/5.48 inference(unit_resolution,[status(thm)],[104, 17])).
% 5.31/5.48 tff(106,plain,
% 5.31/5.48 (sdtpldt0(xn, sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, xr), sdtasdt0(xl, W0!2))),
% 5.31/5.48 inference(transitivity,[status(thm)],[105, 94, 93, 90, 86, 78])).
% 5.31/5.48 tff(107,plain,
% 5.31/5.48 (((sdtpldt0(xn, sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, xr), sdtasdt0(xl, W0!2))) | (sdtpldt0(sdtasdt0(xl, W0!2), xn) = sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, xr)))) | (~(sdtpldt0(xn, sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, xr), sdtasdt0(xl, W0!2))))),
% 5.31/5.48 inference(tautology,[status(thm)],[])).
% 5.31/5.48 tff(108,plain,
% 5.31/5.48 ((sdtpldt0(xn, sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, xr), sdtasdt0(xl, W0!2))) | (sdtpldt0(sdtasdt0(xl, W0!2), xn) = sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, xr)))),
% 5.31/5.48 inference(unit_resolution,[status(thm)],[107, 106])).
% 5.31/5.48 tff(109,plain,
% 5.31/5.48 ((~(xn = sdtasdt0(xl, xr))) <=> (~(xn = sdtasdt0(xl, xr)))),
% 5.31/5.48 inference(rewrite,[status(thm)],[])).
% 5.31/5.48 tff(110,axiom,(~(xn = sdtasdt0(xl, xr))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 5.31/5.48 tff(111,plain,
% 5.31/5.48 (~(xn = sdtasdt0(xl, xr))),
% 5.31/5.48 inference(modus_ponens,[status(thm)],[110, 109])).
% 5.31/5.48 tff(112,plain,
% 5.31/5.48 (^[W0: $i, W1: $i, W2: $i] : refl(((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))),
% 5.31/5.48 inference(bind,[status(th)],[])).
% 5.31/5.48 tff(113,plain,
% 5.31/5.48 (![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 5.31/5.48 inference(quant_intro,[status(thm)],[112])).
% 5.31/5.48 tff(114,plain,
% 5.31/5.48 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(trans(monotonicity(rewrite((aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2)) <=> (~((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))), ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) <=> (~(~((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))))), rewrite((~(~((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))) <=> ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) <=> ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))), (((W1 = W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2))))) <=> ((W1 = W2) | ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2))))))), rewrite(((W1 = W2) | ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2))))) <=> ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), (((W1 = W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2))))) <=> ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))))),
% 5.31/5.48 inference(bind,[status(th)],[])).
% 5.31/5.48 tff(115,plain,
% 5.31/5.48 (![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2))))) <=> ![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 5.31/5.48 inference(quant_intro,[status(thm)],[114])).
% 5.31/5.48 tff(116,plain,
% 5.31/5.48 (![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2))))) <=> ![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))))),
% 5.31/5.48 inference(rewrite,[status(thm)],[])).
% 5.31/5.48 tff(117,plain,
% 5.31/5.48 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) <=> (aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))), trans(monotonicity(rewrite(((sdtpldt0(W0, W1) = sdtpldt0(W0, W2)) | (sdtpldt0(W1, W0) = sdtpldt0(W2, W0))) <=> ((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))), ((((sdtpldt0(W0, W1) = sdtpldt0(W0, W2)) | (sdtpldt0(W1, W0) = sdtpldt0(W2, W0))) => (W1 = W2)) <=> (((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2))) => (W1 = W2)))), rewrite((((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2))) => (W1 = W2)) <=> ((~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (W1 = W2))), ((((sdtpldt0(W0, W1) = sdtpldt0(W0, W2)) | (sdtpldt0(W1, W0) = sdtpldt0(W2, W0))) => (W1 = W2)) <=> ((~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (W1 = W2)))), ((((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => (((sdtpldt0(W0, W1) = sdtpldt0(W0, W2)) | (sdtpldt0(W1, W0) = sdtpldt0(W2, W0))) => (W1 = W2))) <=> ((aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2)) => ((~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (W1 = W2))))), rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2)) => ((~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (W1 = W2))) <=> ((W1 = W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))))), ((((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => (((sdtpldt0(W0, W1) = sdtpldt0(W0, W2)) | (sdtpldt0(W1, W0) = sdtpldt0(W2, W0))) => (W1 = W2))) <=> ((W1 = W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))))))),
% 5.31/5.48 inference(bind,[status(th)],[])).
% 5.31/5.48 tff(118,plain,
% 5.31/5.48 (![W0: $i, W1: $i, W2: $i] : (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => (((sdtpldt0(W0, W1) = sdtpldt0(W0, W2)) | (sdtpldt0(W1, W0) = sdtpldt0(W2, W0))) => (W1 = W2))) <=> ![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))))),
% 5.31/5.48 inference(quant_intro,[status(thm)],[117])).
% 5.31/5.48 tff(119,axiom,(![W0: $i, W1: $i, W2: $i] : (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => (((sdtpldt0(W0, W1) = sdtpldt0(W0, W2)) | (sdtpldt0(W1, W0) = sdtpldt0(W2, W0))) => (W1 = W2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mAddCanc')).
% 5.31/5.48 tff(120,plain,
% 5.31/5.48 (![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))))),
% 5.31/5.48 inference(modus_ponens,[status(thm)],[119, 118])).
% 5.31/5.48 tff(121,plain,
% 5.31/5.48 (![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))))),
% 5.31/5.48 inference(modus_ponens,[status(thm)],[120, 116])).
% 5.31/5.48 tff(122,plain,(
% 5.31/5.48 ![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))))),
% 5.31/5.48 inference(skolemize,[status(sab)],[121])).
% 5.31/5.48 tff(123,plain,
% 5.31/5.48 (![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 5.31/5.48 inference(modus_ponens,[status(thm)],[122, 115])).
% 5.31/5.48 tff(124,plain,
% 5.31/5.48 (![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 5.31/5.48 inference(modus_ponens,[status(thm)],[123, 113])).
% 5.31/5.48 tff(125,plain,
% 5.31/5.48 (((~![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((xn = sdtasdt0(xl, xr)) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (~aNaturalNumber0(sdtasdt0(xl, xr))) | (~((sdtpldt0(xn, sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, xr), sdtasdt0(xl, W0!2))) | (sdtpldt0(sdtasdt0(xl, W0!2), xn) = sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, xr))))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (xn = sdtasdt0(xl, xr)) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (~aNaturalNumber0(sdtasdt0(xl, xr))) | (~((sdtpldt0(xn, sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, xr), sdtasdt0(xl, W0!2))) | (sdtpldt0(sdtasdt0(xl, W0!2), xn) = sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, xr))))))),
% 5.31/5.48 inference(rewrite,[status(thm)],[])).
% 5.31/5.48 tff(126,plain,
% 5.31/5.48 (((xn = sdtasdt0(xl, xr)) | (~aNaturalNumber0(sdtasdt0(xl, xr))) | (~((sdtpldt0(xn, sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, xr), sdtasdt0(xl, W0!2))) | (sdtpldt0(sdtasdt0(xl, W0!2), xn) = sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, xr))))) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(sdtasdt0(xl, W0!2)))) <=> ((xn = sdtasdt0(xl, xr)) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (~aNaturalNumber0(sdtasdt0(xl, xr))) | (~((sdtpldt0(xn, sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, xr), sdtasdt0(xl, W0!2))) | (sdtpldt0(sdtasdt0(xl, W0!2), xn) = sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, xr))))))),
% 5.31/5.48 inference(rewrite,[status(thm)],[])).
% 5.31/5.48 tff(127,plain,
% 5.31/5.48 (((~![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((xn = sdtasdt0(xl, xr)) | (~aNaturalNumber0(sdtasdt0(xl, xr))) | (~((sdtpldt0(xn, sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, xr), sdtasdt0(xl, W0!2))) | (sdtpldt0(sdtasdt0(xl, W0!2), xn) = sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, xr))))) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((xn = sdtasdt0(xl, xr)) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (~aNaturalNumber0(sdtasdt0(xl, xr))) | (~((sdtpldt0(xn, sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, xr), sdtasdt0(xl, W0!2))) | (sdtpldt0(sdtasdt0(xl, W0!2), xn) = sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, xr)))))))),
% 5.31/5.48 inference(monotonicity,[status(thm)],[126])).
% 5.31/5.48 tff(128,plain,
% 5.31/5.48 (((~![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((xn = sdtasdt0(xl, xr)) | (~aNaturalNumber0(sdtasdt0(xl, xr))) | (~((sdtpldt0(xn, sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, xr), sdtasdt0(xl, W0!2))) | (sdtpldt0(sdtasdt0(xl, W0!2), xn) = sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, xr))))) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (xn = sdtasdt0(xl, xr)) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (~aNaturalNumber0(sdtasdt0(xl, xr))) | (~((sdtpldt0(xn, sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, xr), sdtasdt0(xl, W0!2))) | (sdtpldt0(sdtasdt0(xl, W0!2), xn) = sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, xr))))))),
% 5.35/5.51 inference(transitivity,[status(thm)],[127, 125])).
% 5.35/5.51 tff(129,plain,
% 5.35/5.51 ((~![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((xn = sdtasdt0(xl, xr)) | (~aNaturalNumber0(sdtasdt0(xl, xr))) | (~((sdtpldt0(xn, sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, xr), sdtasdt0(xl, W0!2))) | (sdtpldt0(sdtasdt0(xl, W0!2), xn) = sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, xr))))) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))))),
% 5.35/5.51 inference(quant_inst,[status(thm)],[])).
% 5.35/5.51 tff(130,plain,
% 5.35/5.51 ((~![W0: $i, W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtpldt0(W1, W0) = sdtpldt0(W2, W0)) | (sdtpldt0(W0, W1) = sdtpldt0(W0, W2)))) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (xn = sdtasdt0(xl, xr)) | (~aNaturalNumber0(xn)) | (~aNaturalNumber0(sdtasdt0(xl, W0!2))) | (~aNaturalNumber0(sdtasdt0(xl, xr))) | (~((sdtpldt0(xn, sdtasdt0(xl, W0!2)) = sdtpldt0(sdtasdt0(xl, xr), sdtasdt0(xl, W0!2))) | (sdtpldt0(sdtasdt0(xl, W0!2), xn) = sdtpldt0(sdtasdt0(xl, W0!2), sdtasdt0(xl, xr)))))),
% 5.35/5.51 inference(modus_ponens,[status(thm)],[129, 128])).
% 5.35/5.51 tff(131,plain,
% 5.35/5.51 ($false),
% 5.35/5.51 inference(unit_resolution,[status(thm)],[130, 124, 97, 111, 17, 56, 108])).
% 5.35/5.51 % SZS output end Proof
% 5.35/5.51 % E exiting
%------------------------------------------------------------------------------