%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM513+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:21:14 AM UTC 2025
% Result : Theorem 0.48s 0.70s
% Output : Proof 0.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : NUM513+3 : TPTP v9.0.0. Released v4.0.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n005.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 01:21:20 EDT 2025
% 0.19/0.34 % CPUTime :
% 0.48/0.70 % SZS status Theorem
% 0.48/0.70 % SZS output start Proof
% 0.48/0.70 tff(sdtasdt0_type, type, (
% 0.48/0.70 sdtasdt0: ( $i * $i ) > $i)).
% 0.48/0.70 tff(xm_type, type, (
% 0.48/0.70 xm: $i)).
% 0.48/0.70 tff(sdtsldt0_type, type, (
% 0.48/0.70 sdtsldt0: ( $i * $i ) > $i)).
% 0.48/0.70 tff(xr_type, type, (
% 0.48/0.70 xr: $i)).
% 0.48/0.70 tff(xn_type, type, (
% 0.48/0.70 xn: $i)).
% 0.48/0.70 tff(xk_type, type, (
% 0.48/0.70 xk: $i)).
% 0.48/0.70 tff(xp_type, type, (
% 0.48/0.70 xp: $i)).
% 0.48/0.70 tff(aNaturalNumber0_type, type, (
% 0.48/0.70 aNaturalNumber0: $i > $o)).
% 0.48/0.70 tff(doDivides0_type, type, (
% 0.48/0.70 doDivides0: ( $i * $i ) > $o)).
% 0.48/0.70 tff(sz00_type, type, (
% 0.48/0.70 sz00: $i)).
% 0.48/0.70 tff(sz10_type, type, (
% 0.48/0.70 sz10: $i)).
% 0.48/0.70 tff(isPrime0_type, type, (
% 0.48/0.70 isPrime0: $i > $o)).
% 0.48/0.70 tff(sdtpldt0_type, type, (
% 0.48/0.70 sdtpldt0: ( $i * $i ) > $i)).
% 0.48/0.70 tff(tptp_fun_W0_10_type, type, (
% 0.48/0.70 tptp_fun_W0_10: $i)).
% 0.48/0.70 tff(sdtlseqdt0_type, type, (
% 0.48/0.70 sdtlseqdt0: ( $i * $i ) > $o)).
% 0.48/0.70 tff(1,plain,
% 0.48/0.70 ((sdtasdt0(xr, sdtasdt0(xp, sdtsldt0(xk, xr))) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm))) <=> (sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(xr, sdtasdt0(xp, sdtsldt0(xk, xr))))),
% 0.48/0.70 inference(commutativity,[status(thm)],[])).
% 0.48/0.70 tff(2,plain,
% 0.48/0.70 ((sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(xr, sdtasdt0(xp, sdtsldt0(xk, xr)))) <=> (sdtasdt0(xr, sdtasdt0(xp, sdtsldt0(xk, xr))) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)))),
% 0.48/0.70 inference(symmetry,[status(thm)],[1])).
% 0.48/0.70 tff(3,plain,
% 0.48/0.70 (aNaturalNumber0(sdtsldt0(xk, xr)) <=> aNaturalNumber0(sdtsldt0(xk, xr))),
% 0.48/0.70 inference(rewrite,[status(thm)],[])).
% 0.48/0.70 tff(4,plain,
% 0.48/0.70 ((~((aNaturalNumber0(sdtsldt0(xk, xr)) & (xk = sdtasdt0(xr, sdtsldt0(xk, xr)))) => ((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (sdtasdt0(xp, sdtsldt0(xk, xr)) = sdtasdt0(sdtsldt0(xn, xr), xm))))) <=> (~((sdtasdt0(xp, sdtsldt0(xk, xr)) = sdtasdt0(sdtsldt0(xn, xr), xm)) | (~(aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr))))) | (~(aNaturalNumber0(sdtsldt0(xk, xr)) & (xk = sdtasdt0(xr, sdtsldt0(xk, xr)))))))),
% 0.48/0.70 inference(rewrite,[status(thm)],[])).
% 0.48/0.70 tff(5,axiom,(~((aNaturalNumber0(sdtsldt0(xk, xr)) & (xk = sdtasdt0(xr, sdtsldt0(xk, xr)))) => ((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (sdtasdt0(xp, sdtsldt0(xk, xr)) = sdtasdt0(sdtsldt0(xn, xr), xm))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__')).
% 0.48/0.70 tff(6,plain,
% 0.48/0.70 (~((sdtasdt0(xp, sdtsldt0(xk, xr)) = sdtasdt0(sdtsldt0(xn, xr), xm)) | (~(aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr))))) | (~(aNaturalNumber0(sdtsldt0(xk, xr)) & (xk = sdtasdt0(xr, sdtsldt0(xk, xr))))))),
% 0.48/0.70 inference(modus_ponens,[status(thm)],[5, 4])).
% 0.48/0.70 tff(7,plain,
% 0.48/0.70 (aNaturalNumber0(sdtsldt0(xk, xr)) & (xk = sdtasdt0(xr, sdtsldt0(xk, xr)))),
% 0.48/0.70 inference(or_elim,[status(thm)],[6])).
% 0.48/0.70 tff(8,plain,
% 0.48/0.70 (aNaturalNumber0(sdtsldt0(xk, xr))),
% 0.48/0.70 inference(and_elim,[status(thm)],[7])).
% 0.48/0.70 tff(9,plain,
% 0.48/0.70 (aNaturalNumber0(sdtsldt0(xk, xr))),
% 0.48/0.70 inference(modus_ponens,[status(thm)],[8, 3])).
% 0.48/0.70 tff(10,plain,
% 0.48/0.70 (aNaturalNumber0(xp) <=> aNaturalNumber0(xp)),
% 0.48/0.70 inference(rewrite,[status(thm)],[])).
% 0.48/0.70 tff(11,axiom,((aNaturalNumber0(xn) & aNaturalNumber0(xm)) & aNaturalNumber0(xp)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__1837')).
% 0.48/0.70 tff(12,plain,
% 0.48/0.70 (aNaturalNumber0(xp)),
% 0.48/0.70 inference(and_elim,[status(thm)],[11])).
% 0.48/0.70 tff(13,plain,
% 0.48/0.70 (aNaturalNumber0(xp)),
% 0.48/0.70 inference(modus_ponens,[status(thm)],[12, 10])).
% 0.48/0.70 tff(14,plain,
% 0.48/0.70 (^[W0: $i, W1: $i] : refl(((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))),
% 0.48/0.70 inference(bind,[status(th)],[])).
% 0.48/0.70 tff(15,plain,
% 0.48/0.70 (![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.48/0.70 inference(quant_intro,[status(thm)],[14])).
% 0.48/0.70 tff(16,plain,
% 0.48/0.70 (^[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))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> (((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))))), rewrite((((~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), (((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))))),
% 0.48/0.70 inference(bind,[status(th)],[])).
% 0.48/0.70 tff(17,plain,
% 0.48/0.70 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.48/0.70 inference(quant_intro,[status(thm)],[16])).
% 0.48/0.70 tff(18,plain,
% 0.48/0.70 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 0.48/0.70 inference(rewrite,[status(thm)],[])).
% 0.48/0.70 tff(19,plain,
% 0.48/0.70 (^[W0: $i, W1: $i] : rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))))),
% 0.48/0.70 inference(bind,[status(th)],[])).
% 0.48/0.70 tff(20,plain,
% 0.48/0.70 (![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtasdt0(W0, W1) = sdtasdt0(W1, W0))) <=> ![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 0.48/0.70 inference(quant_intro,[status(thm)],[19])).
% 0.48/0.70 tff(21,axiom,(![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mMulComm')).
% 0.48/0.70 tff(22,plain,
% 0.48/0.70 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 0.48/0.70 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.48/0.70 tff(23,plain,
% 0.48/0.70 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 0.48/0.70 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.48/0.70 tff(24,plain,(
% 0.48/0.70 ![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 0.48/0.70 inference(skolemize,[status(sab)],[23])).
% 0.48/0.70 tff(25,plain,
% 0.48/0.70 (![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.48/0.70 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.48/0.70 tff(26,plain,
% 0.48/0.70 (![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.48/0.70 inference(modus_ponens,[status(thm)],[25, 15])).
% 0.48/0.70 tff(27,plain,
% 0.48/0.70 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(xk, xr))) | (sdtasdt0(sdtsldt0(xk, xr), xp) = sdtasdt0(xp, sdtsldt0(xk, xr))))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(xk, xr))) | (sdtasdt0(sdtsldt0(xk, xr), xp) = sdtasdt0(xp, sdtsldt0(xk, xr))))),
% 0.48/0.70 inference(rewrite,[status(thm)],[])).
% 0.48/0.70 tff(28,plain,
% 0.48/0.70 (((sdtasdt0(sdtsldt0(xk, xr), xp) = sdtasdt0(xp, sdtsldt0(xk, xr))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(xk, xr)))) <=> ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(xk, xr))) | (sdtasdt0(sdtsldt0(xk, xr), xp) = sdtasdt0(xp, sdtsldt0(xk, xr))))),
% 0.48/0.70 inference(rewrite,[status(thm)],[])).
% 0.48/0.70 tff(29,plain,
% 0.48/0.70 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtsldt0(xk, xr), xp) = sdtasdt0(xp, sdtsldt0(xk, xr))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(xk, xr))))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(xk, xr))) | (sdtasdt0(sdtsldt0(xk, xr), xp) = sdtasdt0(xp, sdtsldt0(xk, xr)))))),
% 0.48/0.70 inference(monotonicity,[status(thm)],[28])).
% 0.48/0.70 tff(30,plain,
% 0.48/0.70 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtsldt0(xk, xr), xp) = sdtasdt0(xp, sdtsldt0(xk, xr))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(xk, xr))))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(xk, xr))) | (sdtasdt0(sdtsldt0(xk, xr), xp) = sdtasdt0(xp, sdtsldt0(xk, xr))))),
% 0.48/0.70 inference(transitivity,[status(thm)],[29, 27])).
% 0.48/0.70 tff(31,plain,
% 0.48/0.70 ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtsldt0(xk, xr), xp) = sdtasdt0(xp, sdtsldt0(xk, xr))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(xk, xr))))),
% 0.48/0.70 inference(quant_inst,[status(thm)],[])).
% 0.48/0.70 tff(32,plain,
% 0.48/0.70 ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(xk, xr))) | (sdtasdt0(sdtsldt0(xk, xr), xp) = sdtasdt0(xp, sdtsldt0(xk, xr)))),
% 0.48/0.70 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.48/0.70 tff(33,plain,
% 0.48/0.70 (sdtasdt0(sdtsldt0(xk, xr), xp) = sdtasdt0(xp, sdtsldt0(xk, xr))),
% 0.48/0.70 inference(unit_resolution,[status(thm)],[32, 26, 13, 9])).
% 0.48/0.70 tff(34,plain,
% 0.48/0.70 (sdtasdt0(xp, sdtsldt0(xk, xr)) = sdtasdt0(sdtsldt0(xk, xr), xp)),
% 0.48/0.70 inference(symmetry,[status(thm)],[33])).
% 0.48/0.70 tff(35,plain,
% 0.48/0.70 (sdtasdt0(xr, sdtasdt0(xp, sdtsldt0(xk, xr))) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xk, xr), xp))),
% 0.48/0.70 inference(monotonicity,[status(thm)],[34])).
% 0.48/0.70 tff(36,plain,
% 0.48/0.70 (sdtasdt0(xr, sdtasdt0(sdtsldt0(xk, xr), xp)) = sdtasdt0(xr, sdtasdt0(xp, sdtsldt0(xk, xr)))),
% 0.48/0.70 inference(symmetry,[status(thm)],[35])).
% 0.48/0.70 tff(37,plain,
% 0.48/0.70 (aNaturalNumber0(xr) <=> aNaturalNumber0(xr)),
% 0.48/0.70 inference(rewrite,[status(thm)],[])).
% 0.48/0.70 tff(38,axiom,((((((aNaturalNumber0(xr) & ?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))) & doDivides0(xr, xk)) & (~(xr = sz00))) & (~(xr = sz10))) & ![W0: $i] : ((aNaturalNumber0(W0) & (?[W1: $i] : (aNaturalNumber0(W1) & (xr = sdtasdt0(W0, W1))) | doDivides0(W0, xr))) => ((W0 = sz10) | (W0 = xr)))) & isPrime0(xr)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2342')).
% 0.48/0.70 tff(39,plain,
% 0.48/0.70 (((((aNaturalNumber0(xr) & ?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))) & doDivides0(xr, xk)) & (~(xr = sz00))) & (~(xr = sz10))) & ![W0: $i] : ((aNaturalNumber0(W0) & (?[W1: $i] : (aNaturalNumber0(W1) & (xr = sdtasdt0(W0, W1))) | doDivides0(W0, xr))) => ((W0 = sz10) | (W0 = xr)))),
% 0.48/0.70 inference(and_elim,[status(thm)],[38])).
% 0.48/0.70 tff(40,plain,
% 0.48/0.70 ((((aNaturalNumber0(xr) & ?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))) & doDivides0(xr, xk)) & (~(xr = sz00))) & (~(xr = sz10))),
% 0.48/0.70 inference(and_elim,[status(thm)],[39])).
% 0.48/0.70 tff(41,plain,
% 0.48/0.70 (((aNaturalNumber0(xr) & ?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))) & doDivides0(xr, xk)) & (~(xr = sz00))),
% 0.48/0.70 inference(and_elim,[status(thm)],[40])).
% 0.48/0.70 tff(42,plain,
% 0.48/0.70 ((aNaturalNumber0(xr) & ?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))) & doDivides0(xr, xk)),
% 0.48/0.70 inference(and_elim,[status(thm)],[41])).
% 0.48/0.70 tff(43,plain,
% 0.48/0.70 (aNaturalNumber0(xr) & ?[W0: $i] : (aNaturalNumber0(W0) & (xk = sdtasdt0(xr, W0)))),
% 0.48/0.70 inference(and_elim,[status(thm)],[42])).
% 0.48/0.70 tff(44,plain,
% 0.48/0.70 (aNaturalNumber0(xr)),
% 0.48/0.70 inference(and_elim,[status(thm)],[43])).
% 0.48/0.70 tff(45,plain,
% 0.48/0.70 (aNaturalNumber0(xr)),
% 0.48/0.70 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.48/0.70 tff(46,plain,
% 0.48/0.70 (^[W0: $i, W1: $i, W2: $i] : refl(((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))),
% 0.48/0.70 inference(bind,[status(th)],[])).
% 0.48/0.70 tff(47,plain,
% 0.48/0.70 (![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.48/0.70 inference(quant_intro,[status(thm)],[46])).
% 0.48/0.70 tff(48,plain,
% 0.48/0.70 (^[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))))), (((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> (((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))))), rewrite((((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))), (((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))))),
% 0.48/0.70 inference(bind,[status(th)],[])).
% 0.48/0.70 tff(49,plain,
% 0.48/0.70 (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.48/0.70 inference(quant_intro,[status(thm)],[48])).
% 0.48/0.70 tff(50,plain,
% 0.48/0.70 (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))),
% 0.48/0.70 inference(rewrite,[status(thm)],[])).
% 0.48/0.70 tff(51,plain,
% 0.48/0.70 (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) <=> (aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))), ((((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ((aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))))), rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))), ((((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))))),
% 0.48/0.71 inference(bind,[status(th)],[])).
% 0.48/0.71 tff(52,plain,
% 0.48/0.71 (![W0: $i, W1: $i, W2: $i] : (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2)))) <=> ![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))),
% 0.48/0.71 inference(quant_intro,[status(thm)],[51])).
% 0.48/0.71 tff(53,axiom,(![W0: $i, W1: $i, W2: $i] : (((aNaturalNumber0(W0) & aNaturalNumber0(W1)) & aNaturalNumber0(W2)) => (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mMulAsso')).
% 0.48/0.71 tff(54,plain,
% 0.48/0.71 (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))),
% 0.48/0.71 inference(modus_ponens,[status(thm)],[53, 52])).
% 0.48/0.71 tff(55,plain,
% 0.48/0.71 (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))),
% 0.48/0.71 inference(modus_ponens,[status(thm)],[54, 50])).
% 0.48/0.71 tff(56,plain,(
% 0.48/0.71 ![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))),
% 0.48/0.71 inference(skolemize,[status(sab)],[55])).
% 0.48/0.71 tff(57,plain,
% 0.48/0.71 (![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.48/0.71 inference(modus_ponens,[status(thm)],[56, 49])).
% 0.48/0.71 tff(58,plain,
% 0.48/0.71 (![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.48/0.71 inference(modus_ponens,[status(thm)],[57, 47])).
% 0.48/0.71 tff(59,plain,
% 0.48/0.71 (((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(sdtsldt0(xk, xr))) | (sdtasdt0(sdtasdt0(xr, sdtsldt0(xk, xr)), xp) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xk, xr), xp))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(sdtsldt0(xk, xr))) | (sdtasdt0(sdtasdt0(xr, sdtsldt0(xk, xr)), xp) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xk, xr), xp))))),
% 0.48/0.71 inference(rewrite,[status(thm)],[])).
% 0.48/0.71 tff(60,plain,
% 0.48/0.71 (((sdtasdt0(sdtasdt0(xr, sdtsldt0(xk, xr)), xp) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xk, xr), xp))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(xk, xr))) | (~aNaturalNumber0(xr))) <=> ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(sdtsldt0(xk, xr))) | (sdtasdt0(sdtasdt0(xr, sdtsldt0(xk, xr)), xp) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xk, xr), xp))))),
% 0.48/0.71 inference(rewrite,[status(thm)],[])).
% 0.48/0.71 tff(61,plain,
% 0.48/0.71 (((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtasdt0(xr, sdtsldt0(xk, xr)), xp) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xk, xr), xp))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(xk, xr))) | (~aNaturalNumber0(xr)))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(sdtsldt0(xk, xr))) | (sdtasdt0(sdtasdt0(xr, sdtsldt0(xk, xr)), xp) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xk, xr), xp)))))),
% 0.55/0.71 inference(monotonicity,[status(thm)],[60])).
% 0.55/0.71 tff(62,plain,
% 0.55/0.71 (((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtasdt0(xr, sdtsldt0(xk, xr)), xp) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xk, xr), xp))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(xk, xr))) | (~aNaturalNumber0(xr)))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(sdtsldt0(xk, xr))) | (sdtasdt0(sdtasdt0(xr, sdtsldt0(xk, xr)), xp) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xk, xr), xp))))),
% 0.55/0.71 inference(transitivity,[status(thm)],[61, 59])).
% 0.55/0.71 tff(63,plain,
% 0.55/0.71 ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtasdt0(xr, sdtsldt0(xk, xr)), xp) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xk, xr), xp))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(xk, xr))) | (~aNaturalNumber0(xr)))),
% 0.55/0.71 inference(quant_inst,[status(thm)],[])).
% 0.55/0.71 tff(64,plain,
% 0.55/0.71 ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(sdtsldt0(xk, xr))) | (sdtasdt0(sdtasdt0(xr, sdtsldt0(xk, xr)), xp) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xk, xr), xp)))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[63, 62])).
% 0.55/0.71 tff(65,plain,
% 0.55/0.71 (sdtasdt0(sdtasdt0(xr, sdtsldt0(xk, xr)), xp) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xk, xr), xp))),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[64, 58, 13, 45, 9])).
% 0.55/0.71 tff(66,plain,
% 0.55/0.71 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp)) <=> ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(67,axiom,((((((~(xn = xp)) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp))) & sdtlseqdt0(xn, xp)) & (~(xm = xp))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp))) & sdtlseqdt0(xm, xp)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2287')).
% 0.55/0.71 tff(68,plain,
% 0.55/0.71 (((((~(xn = xp)) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xn, W0) = xp))) & sdtlseqdt0(xn, xp)) & (~(xm = xp))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp))),
% 0.55/0.71 inference(and_elim,[status(thm)],[67])).
% 0.55/0.71 tff(69,plain,
% 0.55/0.71 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp))),
% 0.55/0.71 inference(and_elim,[status(thm)],[68])).
% 0.55/0.71 tff(70,plain,
% 0.55/0.71 (?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(xm, W0) = xp))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[69, 66])).
% 0.55/0.71 tff(71,plain,(
% 0.55/0.71 aNaturalNumber0(W0!10) & (sdtpldt0(xm, W0!10) = xp)),
% 0.55/0.71 inference(skolemize,[status(sab)],[70])).
% 0.55/0.71 tff(72,plain,
% 0.55/0.71 (sdtpldt0(xm, W0!10) = xp),
% 0.55/0.71 inference(and_elim,[status(thm)],[71])).
% 0.55/0.71 tff(73,plain,
% 0.55/0.71 (xp = sdtpldt0(xm, W0!10)),
% 0.55/0.71 inference(symmetry,[status(thm)],[72])).
% 0.55/0.71 tff(74,plain,
% 0.55/0.71 ((xk = sdtsldt0(sdtasdt0(xn, xm), xp)) <=> (xk = sdtsldt0(sdtasdt0(xn, xm), xp))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(75,axiom,((aNaturalNumber0(xk) & (sdtasdt0(xn, xm) = sdtasdt0(xp, xk))) & (xk = sdtsldt0(sdtasdt0(xn, xm), xp))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2306')).
% 0.55/0.71 tff(76,plain,
% 0.55/0.71 (xk = sdtsldt0(sdtasdt0(xn, xm), xp)),
% 0.55/0.71 inference(and_elim,[status(thm)],[75])).
% 0.55/0.71 tff(77,plain,
% 0.55/0.71 (xk = sdtsldt0(sdtasdt0(xn, xm), xp)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[76, 74])).
% 0.55/0.71 tff(78,plain,
% 0.55/0.71 ((xk = sdtasdt0(xr, sdtsldt0(xk, xr))) <=> (xk = sdtasdt0(xr, sdtsldt0(xk, xr)))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(79,plain,
% 0.55/0.71 (xk = sdtasdt0(xr, sdtsldt0(xk, xr))),
% 0.55/0.71 inference(and_elim,[status(thm)],[7])).
% 0.55/0.71 tff(80,plain,
% 0.55/0.71 (xk = sdtasdt0(xr, sdtsldt0(xk, xr))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.55/0.71 tff(81,plain,
% 0.55/0.71 (sdtasdt0(xr, sdtsldt0(xk, xr)) = xk),
% 0.55/0.71 inference(symmetry,[status(thm)],[80])).
% 0.55/0.71 tff(82,plain,
% 0.55/0.71 (sdtasdt0(xr, sdtsldt0(xk, xr)) = sdtsldt0(sdtasdt0(xn, xm), xp)),
% 0.55/0.71 inference(transitivity,[status(thm)],[81, 77])).
% 0.55/0.71 tff(83,plain,
% 0.55/0.71 (sdtasdt0(sdtasdt0(xr, sdtsldt0(xk, xr)), xp) = sdtasdt0(sdtsldt0(sdtasdt0(xn, xm), xp), sdtpldt0(xm, W0!10))),
% 0.55/0.71 inference(monotonicity,[status(thm)],[82, 73])).
% 0.55/0.71 tff(84,plain,
% 0.55/0.71 (sdtasdt0(sdtsldt0(sdtasdt0(xn, xm), xp), sdtpldt0(xm, W0!10)) = sdtasdt0(sdtasdt0(xr, sdtsldt0(xk, xr)), xp)),
% 0.55/0.71 inference(symmetry,[status(thm)],[83])).
% 0.55/0.71 tff(85,plain,
% 0.55/0.71 (sdtasdt0(sdtsldt0(sdtasdt0(xn, xm), xp), sdtpldt0(xm, W0!10)) = sdtasdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp)),
% 0.55/0.71 inference(monotonicity,[status(thm)],[72])).
% 0.55/0.71 tff(86,plain,
% 0.55/0.71 (sdtasdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp) = sdtasdt0(sdtsldt0(sdtasdt0(xn, xm), xp), sdtpldt0(xm, W0!10))),
% 0.55/0.71 inference(symmetry,[status(thm)],[85])).
% 0.55/0.71 tff(87,plain,
% 0.55/0.71 (sdtsldt0(sdtasdt0(xn, xm), xp) = xk),
% 0.55/0.71 inference(symmetry,[status(thm)],[77])).
% 0.55/0.71 tff(88,plain,
% 0.55/0.71 (aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp)) <=> aNaturalNumber0(xk)),
% 0.55/0.71 inference(monotonicity,[status(thm)],[87])).
% 0.55/0.71 tff(89,plain,
% 0.55/0.71 (aNaturalNumber0(xk) <=> aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))),
% 0.55/0.71 inference(symmetry,[status(thm)],[88])).
% 0.55/0.71 tff(90,plain,
% 0.55/0.71 (aNaturalNumber0(xk) <=> aNaturalNumber0(xk)),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(91,plain,
% 0.55/0.71 (aNaturalNumber0(xk) & (sdtasdt0(xn, xm) = sdtasdt0(xp, xk))),
% 0.55/0.71 inference(and_elim,[status(thm)],[75])).
% 0.55/0.71 tff(92,plain,
% 0.55/0.71 (aNaturalNumber0(xk)),
% 0.55/0.71 inference(and_elim,[status(thm)],[91])).
% 0.55/0.71 tff(93,plain,
% 0.55/0.71 (aNaturalNumber0(xk)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[92, 90])).
% 0.55/0.71 tff(94,plain,
% 0.55/0.71 (aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[93, 89])).
% 0.55/0.71 tff(95,plain,
% 0.55/0.71 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))) | (sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)) = sdtasdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp)))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))) | (sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)) = sdtasdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp)))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(96,plain,
% 0.55/0.71 (((sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)) = sdtasdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp)) | (~aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))) | (~aNaturalNumber0(xp))) <=> ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))) | (sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)) = sdtasdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp)))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(97,plain,
% 0.55/0.71 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)) = sdtasdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp)) | (~aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))) | (~aNaturalNumber0(xp)))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))) | (sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)) = sdtasdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp))))),
% 0.55/0.71 inference(monotonicity,[status(thm)],[96])).
% 0.55/0.71 tff(98,plain,
% 0.55/0.71 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)) = sdtasdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp)) | (~aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))) | (~aNaturalNumber0(xp)))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))) | (sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)) = sdtasdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp)))),
% 0.55/0.71 inference(transitivity,[status(thm)],[97, 95])).
% 0.55/0.71 tff(99,plain,
% 0.55/0.71 ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)) = sdtasdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp)) | (~aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))) | (~aNaturalNumber0(xp)))),
% 0.55/0.71 inference(quant_inst,[status(thm)],[])).
% 0.55/0.71 tff(100,plain,
% 0.55/0.71 ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(sdtasdt0(xn, xm), xp))) | (sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)) = sdtasdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.55/0.71 tff(101,plain,
% 0.55/0.71 (sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)) = sdtasdt0(sdtsldt0(sdtasdt0(xn, xm), xp), xp)),
% 0.55/0.71 inference(unit_resolution,[status(thm)],[100, 26, 13, 94])).
% 0.55/0.71 tff(102,plain,
% 0.55/0.71 (sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp)) = sdtasdt0(xp, xk)),
% 0.55/0.71 inference(monotonicity,[status(thm)],[87])).
% 0.55/0.71 tff(103,plain,
% 0.55/0.71 (sdtasdt0(xp, xk) = sdtasdt0(xp, sdtsldt0(sdtasdt0(xn, xm), xp))),
% 0.55/0.71 inference(symmetry,[status(thm)],[102])).
% 0.55/0.71 tff(104,plain,
% 0.55/0.71 ((sdtasdt0(xn, xm) = sdtasdt0(xp, xk)) <=> (sdtasdt0(xn, xm) = sdtasdt0(xp, xk))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(105,plain,
% 0.55/0.71 (sdtasdt0(xn, xm) = sdtasdt0(xp, xk)),
% 0.55/0.71 inference(and_elim,[status(thm)],[91])).
% 0.55/0.71 tff(106,plain,
% 0.55/0.71 (sdtasdt0(xn, xm) = sdtasdt0(xp, xk)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[105, 104])).
% 0.55/0.71 tff(107,plain,
% 0.55/0.71 ((sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr) = sdtasdt0(xn, xm)) <=> (sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr) = sdtasdt0(xn, xm))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(108,axiom,(((((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) & (sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr) = sdtasdt0(xn, xm))) & aNaturalNumber0(sdtsldt0(sdtasdt0(xp, xk), xr))) & (sdtasdt0(xp, xk) = sdtasdt0(xr, sdtsldt0(sdtasdt0(xp, xk), xr)))) & (sdtasdt0(xn, xm) = sdtasdt0(sdtsldt0(sdtasdt0(xp, xk), xr), xr))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2576')).
% 0.55/0.71 tff(109,plain,
% 0.55/0.71 ((((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) & (sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr) = sdtasdt0(xn, xm))) & aNaturalNumber0(sdtsldt0(sdtasdt0(xp, xk), xr))) & (sdtasdt0(xp, xk) = sdtasdt0(xr, sdtsldt0(sdtasdt0(xp, xk), xr)))),
% 0.55/0.71 inference(and_elim,[status(thm)],[108])).
% 0.55/0.71 tff(110,plain,
% 0.55/0.71 (((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) & (sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr) = sdtasdt0(xn, xm))) & aNaturalNumber0(sdtsldt0(sdtasdt0(xp, xk), xr))),
% 0.55/0.71 inference(and_elim,[status(thm)],[109])).
% 0.55/0.71 tff(111,plain,
% 0.55/0.71 ((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) & (sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr) = sdtasdt0(xn, xm))),
% 0.55/0.71 inference(and_elim,[status(thm)],[110])).
% 0.55/0.71 tff(112,plain,
% 0.55/0.71 (sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr) = sdtasdt0(xn, xm)),
% 0.55/0.71 inference(and_elim,[status(thm)],[111])).
% 0.55/0.71 tff(113,plain,
% 0.55/0.71 (sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr) = sdtasdt0(xn, xm)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[112, 107])).
% 0.55/0.71 tff(114,plain,
% 0.55/0.71 (aNaturalNumber0(sdtsldt0(xn, xr)) <=> aNaturalNumber0(sdtsldt0(xn, xr))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(115,plain,
% 0.55/0.71 ((~((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (sdtsldt0(xn, xr) = xn))) <=> (~((~(aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr))))) | (sdtsldt0(xn, xr) = xn)))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(116,axiom,(((((~((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (sdtsldt0(xn, xr) = xn))) & aNaturalNumber0(sdtsldt0(xn, xr))) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sdtsldt0(xn, xr), W0) = xn))) & sdtlseqdt0(sdtsldt0(xn, xr), xn)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','m__2504')).
% 0.55/0.71 tff(117,plain,
% 0.55/0.71 ((((~((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (sdtsldt0(xn, xr) = xn))) & aNaturalNumber0(sdtsldt0(xn, xr))) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) & ?[W0: $i] : (aNaturalNumber0(W0) & (sdtpldt0(sdtsldt0(xn, xr), W0) = xn))),
% 0.55/0.71 inference(and_elim,[status(thm)],[116])).
% 0.55/0.71 tff(118,plain,
% 0.55/0.71 (((~((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (sdtsldt0(xn, xr) = xn))) & aNaturalNumber0(sdtsldt0(xn, xr))) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))),
% 0.55/0.71 inference(and_elim,[status(thm)],[117])).
% 0.55/0.71 tff(119,plain,
% 0.55/0.71 ((~((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (sdtsldt0(xn, xr) = xn))) & aNaturalNumber0(sdtsldt0(xn, xr))),
% 0.55/0.71 inference(and_elim,[status(thm)],[118])).
% 0.55/0.71 tff(120,plain,
% 0.55/0.71 (~((aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))) => (sdtsldt0(xn, xr) = xn))),
% 0.55/0.71 inference(and_elim,[status(thm)],[119])).
% 0.55/0.71 tff(121,plain,
% 0.55/0.71 (~((~(aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr))))) | (sdtsldt0(xn, xr) = xn))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[120, 115])).
% 0.55/0.71 tff(122,plain,
% 0.55/0.71 (aNaturalNumber0(sdtsldt0(xn, xr)) & (xn = sdtasdt0(xr, sdtsldt0(xn, xr)))),
% 0.55/0.71 inference(or_elim,[status(thm)],[121])).
% 0.55/0.71 tff(123,plain,
% 0.55/0.71 (aNaturalNumber0(sdtsldt0(xn, xr))),
% 0.55/0.71 inference(and_elim,[status(thm)],[122])).
% 0.55/0.71 tff(124,plain,
% 0.55/0.71 (aNaturalNumber0(sdtsldt0(xn, xr))),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[123, 114])).
% 0.55/0.71 tff(125,plain,
% 0.55/0.71 (aNaturalNumber0(xm) <=> aNaturalNumber0(xm)),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(126,plain,
% 0.55/0.71 (aNaturalNumber0(xn) & aNaturalNumber0(xm)),
% 0.55/0.71 inference(and_elim,[status(thm)],[11])).
% 0.55/0.71 tff(127,plain,
% 0.55/0.71 (aNaturalNumber0(xm)),
% 0.55/0.71 inference(and_elim,[status(thm)],[126])).
% 0.55/0.71 tff(128,plain,
% 0.55/0.71 (aNaturalNumber0(xm)),
% 0.55/0.71 inference(modus_ponens,[status(thm)],[127, 125])).
% 0.55/0.71 tff(129,plain,
% 0.55/0.71 (^[W0: $i, W1: $i] : refl((aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))),
% 0.55/0.71 inference(bind,[status(th)],[])).
% 0.55/0.71 tff(130,plain,
% 0.55/0.71 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.55/0.71 inference(quant_intro,[status(thm)],[129])).
% 0.55/0.71 tff(131,plain,
% 0.55/0.71 (^[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)))))),
% 0.55/0.71 inference(bind,[status(th)],[])).
% 0.55/0.71 tff(132,plain,
% 0.55/0.71 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.55/0.71 inference(quant_intro,[status(thm)],[131])).
% 0.55/0.71 tff(133,plain,
% 0.55/0.71 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.55/0.71 inference(rewrite,[status(thm)],[])).
% 0.55/0.71 tff(134,plain,
% 0.55/0.71 (^[W0: $i, W1: $i] : rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtasdt0(W0, W1))) <=> (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))))),
% 0.55/0.71 inference(bind,[status(th)],[])).
% 0.55/0.71 tff(135,plain,
% 0.55/0.71 (![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtasdt0(W0, W1))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.55/0.71 inference(quant_intro,[status(thm)],[134])).
% 0.55/0.71 tff(136,axiom,(![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtasdt0(W0, W1)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mSortsB_02')).
% 0.55/0.71 tff(137,plain,
% 0.55/0.71 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.55/0.72 tff(138,plain,
% 0.55/0.72 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[137, 133])).
% 0.55/0.72 tff(139,plain,(
% 0.55/0.72 ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.55/0.72 inference(skolemize,[status(sab)],[138])).
% 0.55/0.72 tff(140,plain,
% 0.55/0.72 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[139, 132])).
% 0.55/0.72 tff(141,plain,
% 0.55/0.72 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[140, 130])).
% 0.55/0.72 tff(142,plain,
% 0.55/0.72 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xm)) | aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xm)) | aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(143,plain,
% 0.55/0.72 ((aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr)))) <=> ((~aNaturalNumber0(xm)) | aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(144,plain,
% 0.55/0.72 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xm)) | aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr)))))),
% 0.55/0.72 inference(monotonicity,[status(thm)],[143])).
% 0.55/0.72 tff(145,plain,
% 0.55/0.72 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xm)) | aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))))),
% 0.55/0.72 inference(transitivity,[status(thm)],[144, 142])).
% 0.55/0.72 tff(146,plain,
% 0.55/0.72 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm)) | (~aNaturalNumber0(xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr))))),
% 0.55/0.72 inference(quant_inst,[status(thm)],[])).
% 0.55/0.72 tff(147,plain,
% 0.55/0.72 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xm)) | aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm)) | (~aNaturalNumber0(sdtsldt0(xn, xr)))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.55/0.72 tff(148,plain,
% 0.55/0.72 (aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[147, 141, 128, 124])).
% 0.55/0.72 tff(149,plain,
% 0.55/0.72 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xr)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))) | (sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr)))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))) | (sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr)))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(150,plain,
% 0.55/0.72 (((sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))) | (~aNaturalNumber0(xr))) <=> ((~aNaturalNumber0(xr)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))) | (sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr)))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(151,plain,
% 0.55/0.72 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))) | (~aNaturalNumber0(xr)))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xr)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))) | (sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr))))),
% 0.55/0.72 inference(monotonicity,[status(thm)],[150])).
% 0.55/0.72 tff(152,plain,
% 0.55/0.72 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))) | (~aNaturalNumber0(xr)))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))) | (sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr)))),
% 0.55/0.72 inference(transitivity,[status(thm)],[151, 149])).
% 0.55/0.72 tff(153,plain,
% 0.55/0.72 ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))) | (~aNaturalNumber0(xr)))),
% 0.55/0.72 inference(quant_inst,[status(thm)],[])).
% 0.55/0.72 tff(154,plain,
% 0.55/0.72 ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xr)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))) | (sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.55/0.72 tff(155,plain,
% 0.55/0.72 (sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr)),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[154, 26, 45, 148])).
% 0.55/0.72 tff(156,plain,
% 0.55/0.72 (sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)) = sdtasdt0(xr, sdtasdt0(xp, sdtsldt0(xk, xr)))),
% 0.55/0.72 inference(transitivity,[status(thm)],[155, 113, 106, 103, 101, 86, 84, 65, 36])).
% 0.55/0.72 tff(157,plain,
% 0.55/0.72 (sdtasdt0(xr, sdtasdt0(xp, sdtsldt0(xk, xr))) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[156, 2])).
% 0.55/0.72 tff(158,plain,
% 0.55/0.72 ((~(xr = sz00)) <=> (~(xr = sz00))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(159,plain,
% 0.55/0.72 (~(xr = sz00)),
% 0.55/0.72 inference(and_elim,[status(thm)],[41])).
% 0.55/0.72 tff(160,plain,
% 0.55/0.72 (~(xr = sz00)),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.55/0.72 tff(161,plain,
% 0.55/0.72 (^[W0: $i] : refl(((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))))),
% 0.55/0.72 inference(bind,[status(th)],[])).
% 0.55/0.72 tff(162,plain,
% 0.55/0.72 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))) <=> ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))),
% 0.55/0.72 inference(quant_intro,[status(thm)],[161])).
% 0.55/0.72 tff(163,plain,
% 0.55/0.72 (^[W0: $i] : rewrite(((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))))),
% 0.55/0.72 inference(bind,[status(th)],[])).
% 0.55/0.72 tff(164,plain,
% 0.55/0.72 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))) <=> ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))),
% 0.55/0.72 inference(quant_intro,[status(thm)],[163])).
% 0.55/0.72 tff(165,plain,
% 0.55/0.72 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))) <=> ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))),
% 0.55/0.72 inference(transitivity,[status(thm)],[164, 162])).
% 0.55/0.72 tff(166,plain,
% 0.55/0.72 (^[W0: $i] : trans(monotonicity(quant_intro(proof_bind(^[W1: $i, W2: $i] : trans(monotonicity(trans(monotonicity(rewrite((aNaturalNumber0(W1) & aNaturalNumber0(W2)) <=> (~((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1))))), ((~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) <=> (~(~((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1))))))), rewrite((~(~((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1))))) <=> ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)))), ((~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) <=> ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1))))), rewrite((~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) <=> (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))), (((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))) <=> ((W1 = W2) | ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))), rewrite(((W1 = W2) | ((~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))) <=> ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))), (((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))) <=> ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))))), (![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))) <=> ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))), (((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))))), rewrite(((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1)))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))), (((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))))),
% 0.55/0.72 inference(bind,[status(th)],[])).
% 0.55/0.72 tff(167,plain,
% 0.55/0.72 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))) <=> ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))),
% 0.55/0.72 inference(quant_intro,[status(thm)],[166])).
% 0.55/0.72 tff(168,plain,
% 0.55/0.72 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))) <=> ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(169,plain,
% 0.55/0.72 (^[W0: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[W1: $i, W2: $i] : trans(monotonicity(trans(monotonicity(rewrite(((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) <=> ((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))), ((((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)) <=> (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)))), rewrite((((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)) <=> ((~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (W1 = W2))), ((((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)) <=> ((~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (W1 = W2)))), (((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2))) <=> ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => ((~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (W1 = W2))))), rewrite(((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => ((~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (W1 = W2))) <=> ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))), (((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2))) <=> ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))))), (![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2))) <=> ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))), (((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)))) <=> ((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))))), rewrite(((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))) <=> ((W0 = sz00) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))), (((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)))) <=> ((W0 = sz00) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))))))), ((aNaturalNumber0(W0) => ((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2))))) <=> (aNaturalNumber0(W0) => ((W0 = sz00) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))))), rewrite((aNaturalNumber0(W0) => ((W0 = sz00) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))), ((aNaturalNumber0(W0) => ((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2))))) <=> ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))))),
% 0.55/0.72 inference(bind,[status(th)],[])).
% 0.55/0.72 tff(170,plain,
% 0.55/0.72 (![W0: $i] : (aNaturalNumber0(W0) => ((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2))))) <=> ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))),
% 0.55/0.72 inference(quant_intro,[status(thm)],[169])).
% 0.55/0.72 tff(171,axiom,(![W0: $i] : (aNaturalNumber0(W0) => ((~(W0 = sz00)) => ![W1: $i, W2: $i] : ((aNaturalNumber0(W1) & aNaturalNumber0(W2)) => (((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))) => (W1 = W2)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mMulCanc')).
% 0.55/0.72 tff(172,plain,
% 0.55/0.72 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[171, 170])).
% 0.55/0.72 tff(173,plain,
% 0.55/0.72 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[172, 168])).
% 0.55/0.72 tff(174,plain,(
% 0.55/0.72 ![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~(aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0))))))),
% 0.55/0.72 inference(skolemize,[status(sab)],[173])).
% 0.55/0.72 tff(175,plain,
% 0.55/0.72 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[174, 167])).
% 0.55/0.72 tff(176,plain,
% 0.55/0.72 (![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[175, 165])).
% 0.55/0.72 tff(177,plain,
% 0.55/0.72 (((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | ((xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr))))))) <=> ((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | (xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr))))))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(178,plain,
% 0.55/0.72 (((xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))) <=> ((xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr))))))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(179,plain,
% 0.55/0.72 (^[W1: $i, W2: $i] : rewrite(((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))) | (~aNaturalNumber0(W1))) <=> ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr))))))),
% 0.55/0.72 inference(bind,[status(th)],[])).
% 0.55/0.72 tff(180,plain,
% 0.55/0.72 (![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))) | (~aNaturalNumber0(W1))) <=> ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))),
% 0.55/0.72 inference(quant_intro,[status(thm)],[179])).
% 0.55/0.72 tff(181,plain,
% 0.55/0.72 (((xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))) | (~aNaturalNumber0(W1)))) <=> ((xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr))))))),
% 0.55/0.72 inference(monotonicity,[status(thm)],[180])).
% 0.55/0.72 tff(182,plain,
% 0.55/0.72 (((xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))) | (~aNaturalNumber0(W1)))) <=> ((xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr))))))),
% 0.55/0.72 inference(transitivity,[status(thm)],[181, 178])).
% 0.55/0.72 tff(183,plain,
% 0.55/0.72 (((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | ((xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))) | (~aNaturalNumber0(W1))))) <=> ((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | ((xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))))),
% 0.55/0.72 inference(monotonicity,[status(thm)],[182])).
% 0.55/0.72 tff(184,plain,
% 0.55/0.72 (((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | ((xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))) | (~aNaturalNumber0(W1))))) <=> ((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | (xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr))))))),
% 0.55/0.72 inference(transitivity,[status(thm)],[183, 177])).
% 0.55/0.72 tff(185,plain,
% 0.55/0.72 ((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | ((xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))) | (~aNaturalNumber0(W1))))),
% 0.55/0.72 inference(quant_inst,[status(thm)],[])).
% 0.55/0.72 tff(186,plain,
% 0.55/0.72 ((~![W0: $i] : ((W0 = sz00) | (~aNaturalNumber0(W0)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(W0, W1) = sdtasdt0(W0, W2)) | (sdtasdt0(W1, W0) = sdtasdt0(W2, W0)))) | (~aNaturalNumber0(W1))))) | (xr = sz00) | (~aNaturalNumber0(xr)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.55/0.72 tff(187,plain,
% 0.55/0.72 (![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[186, 176, 45, 160])).
% 0.55/0.72 tff(188,plain,
% 0.55/0.72 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(xk, xr))) | aNaturalNumber0(sdtasdt0(xp, sdtsldt0(xk, xr))))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(xk, xr))) | aNaturalNumber0(sdtasdt0(xp, sdtsldt0(xk, xr))))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(189,plain,
% 0.55/0.72 ((aNaturalNumber0(sdtasdt0(xp, sdtsldt0(xk, xr))) | (~aNaturalNumber0(sdtsldt0(xk, xr))) | (~aNaturalNumber0(xp))) <=> ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(xk, xr))) | aNaturalNumber0(sdtasdt0(xp, sdtsldt0(xk, xr))))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(190,plain,
% 0.55/0.72 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(xp, sdtsldt0(xk, xr))) | (~aNaturalNumber0(sdtsldt0(xk, xr))) | (~aNaturalNumber0(xp)))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(xk, xr))) | aNaturalNumber0(sdtasdt0(xp, sdtsldt0(xk, xr)))))),
% 0.55/0.72 inference(monotonicity,[status(thm)],[189])).
% 0.55/0.72 tff(191,plain,
% 0.55/0.72 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(xp, sdtsldt0(xk, xr))) | (~aNaturalNumber0(sdtsldt0(xk, xr))) | (~aNaturalNumber0(xp)))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(xk, xr))) | aNaturalNumber0(sdtasdt0(xp, sdtsldt0(xk, xr))))),
% 0.55/0.72 inference(transitivity,[status(thm)],[190, 188])).
% 0.55/0.72 tff(192,plain,
% 0.55/0.72 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(xp, sdtsldt0(xk, xr))) | (~aNaturalNumber0(sdtsldt0(xk, xr))) | (~aNaturalNumber0(xp)))),
% 0.55/0.72 inference(quant_inst,[status(thm)],[])).
% 0.55/0.72 tff(193,plain,
% 0.55/0.72 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(xk, xr))) | aNaturalNumber0(sdtasdt0(xp, sdtsldt0(xk, xr)))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.55/0.72 tff(194,plain,
% 0.55/0.72 (aNaturalNumber0(sdtasdt0(xp, sdtsldt0(xk, xr)))),
% 0.55/0.72 inference(unit_resolution,[status(thm)],[193, 141, 13, 9])).
% 0.55/0.72 tff(195,plain,
% 0.55/0.72 ((~(sdtasdt0(xp, sdtsldt0(xk, xr)) = sdtasdt0(sdtsldt0(xn, xr), xm))) <=> (~(sdtasdt0(xp, sdtsldt0(xk, xr)) = sdtasdt0(sdtsldt0(xn, xr), xm)))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(196,plain,
% 0.55/0.72 (~(sdtasdt0(xp, sdtsldt0(xk, xr)) = sdtasdt0(sdtsldt0(xn, xr), xm))),
% 0.55/0.72 inference(or_elim,[status(thm)],[6])).
% 0.55/0.72 tff(197,plain,
% 0.55/0.72 (~(sdtasdt0(xp, sdtsldt0(xk, xr)) = sdtasdt0(sdtsldt0(xn, xr), xm))),
% 0.55/0.72 inference(modus_ponens,[status(thm)],[196, 195])).
% 0.55/0.72 tff(198,plain,
% 0.55/0.72 (((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))) | ((sdtasdt0(xp, sdtsldt0(xk, xr)) = sdtasdt0(sdtsldt0(xn, xr), xm)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))) | (~aNaturalNumber0(sdtasdt0(xp, sdtsldt0(xk, xr)))) | (~((sdtasdt0(xr, sdtasdt0(xp, sdtsldt0(xk, xr))) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm))) | (sdtasdt0(sdtasdt0(xp, sdtsldt0(xk, xr)), xr) = sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr)))))) <=> ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))) | (sdtasdt0(xp, sdtsldt0(xk, xr)) = sdtasdt0(sdtsldt0(xn, xr), xm)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))) | (~aNaturalNumber0(sdtasdt0(xp, sdtsldt0(xk, xr)))) | (~((sdtasdt0(xr, sdtasdt0(xp, sdtsldt0(xk, xr))) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm))) | (sdtasdt0(sdtasdt0(xp, sdtsldt0(xk, xr)), xr) = sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr)))))),
% 0.55/0.72 inference(rewrite,[status(thm)],[])).
% 0.55/0.72 tff(199,plain,
% 0.55/0.73 ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))) | ((sdtasdt0(xp, sdtsldt0(xk, xr)) = sdtasdt0(sdtsldt0(xn, xr), xm)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))) | (~aNaturalNumber0(sdtasdt0(xp, sdtsldt0(xk, xr)))) | (~((sdtasdt0(xr, sdtasdt0(xp, sdtsldt0(xk, xr))) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm))) | (sdtasdt0(sdtasdt0(xp, sdtsldt0(xk, xr)), xr) = sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr)))))),
% 0.55/0.73 inference(quant_inst,[status(thm)],[])).
% 0.55/0.73 tff(200,plain,
% 0.55/0.73 ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xr, W1) = sdtasdt0(xr, W2)) | (sdtasdt0(W1, xr) = sdtasdt0(W2, xr)))))) | (sdtasdt0(xp, sdtsldt0(xk, xr)) = sdtasdt0(sdtsldt0(xn, xr), xm)) | (~aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xr), xm))) | (~aNaturalNumber0(sdtasdt0(xp, sdtsldt0(xk, xr)))) | (~((sdtasdt0(xr, sdtasdt0(xp, sdtsldt0(xk, xr))) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm))) | (sdtasdt0(sdtasdt0(xp, sdtsldt0(xk, xr)), xr) = sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr))))),
% 0.55/0.73 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.55/0.73 tff(201,plain,
% 0.55/0.73 (~((sdtasdt0(xr, sdtasdt0(xp, sdtsldt0(xk, xr))) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm))) | (sdtasdt0(sdtasdt0(xp, sdtsldt0(xk, xr)), xr) = sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr)))),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[200, 197, 148, 194, 187])).
% 0.55/0.73 tff(202,plain,
% 0.55/0.73 (((sdtasdt0(xr, sdtasdt0(xp, sdtsldt0(xk, xr))) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm))) | (sdtasdt0(sdtasdt0(xp, sdtsldt0(xk, xr)), xr) = sdtasdt0(sdtasdt0(sdtsldt0(xn, xr), xm), xr))) | (~(sdtasdt0(xr, sdtasdt0(xp, sdtsldt0(xk, xr))) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm))))),
% 0.55/0.73 inference(tautology,[status(thm)],[])).
% 0.55/0.73 tff(203,plain,
% 0.55/0.73 (~(sdtasdt0(xr, sdtasdt0(xp, sdtsldt0(xk, xr))) = sdtasdt0(xr, sdtasdt0(sdtsldt0(xn, xr), xm)))),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[202, 201])).
% 0.55/0.73 tff(204,plain,
% 0.55/0.73 ($false),
% 0.55/0.73 inference(unit_resolution,[status(thm)],[203, 157])).
% 0.55/0.73 % SZS output end Proof
% 0.55/0.73 % E exiting
%------------------------------------------------------------------------------