%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM525+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:21:17 AM UTC 2025
% Result : Theorem 0.47s 0.65s
% Output : Proof 0.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.14 % Problem : NUM525+3 : TPTP v9.0.0. Released v4.0.0.
% 0.05/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n002.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 01:24:01 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.47/0.65 % SZS status Theorem
% 0.47/0.65 % SZS output start Proof
% 0.47/0.65 tff(sdtasdt0_type, type, (
% 0.47/0.65 sdtasdt0: ( $i * $i ) > $i)).
% 0.47/0.65 tff(xq_type, type, (
% 0.47/0.65 xq: $i)).
% 0.47/0.65 tff(xp_type, type, (
% 0.47/0.65 xp: $i)).
% 0.47/0.65 tff(xm_type, type, (
% 0.47/0.65 xm: $i)).
% 0.47/0.65 tff(xn_type, type, (
% 0.47/0.65 xn: $i)).
% 0.47/0.65 tff(tptp_fun_W0_7_type, type, (
% 0.47/0.65 tptp_fun_W0_7: $i)).
% 0.47/0.65 tff(aNaturalNumber0_type, type, (
% 0.47/0.65 aNaturalNumber0: $i > $o)).
% 0.47/0.65 tff(doDivides0_type, type, (
% 0.47/0.65 doDivides0: ( $i * $i ) > $o)).
% 0.47/0.65 tff(sz00_type, type, (
% 0.47/0.65 sz00: $i)).
% 0.47/0.65 tff(sdtsldt0_type, type, (
% 0.47/0.65 sdtsldt0: ( $i * $i ) > $i)).
% 0.47/0.65 tff(1,plain,
% 0.47/0.65 ((sdtasdt0(xp, sdtasdt0(xm, xm)) = sdtasdt0(xn, xn)) <=> (sdtasdt0(xp, sdtasdt0(xm, xm)) = sdtasdt0(xn, xn))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(2,axiom,(sdtasdt0(xp, sdtasdt0(xm, xm)) = sdtasdt0(xn, xn)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__3014')).
% 0.47/0.65 tff(3,plain,
% 0.47/0.65 (sdtasdt0(xp, sdtasdt0(xm, xm)) = sdtasdt0(xn, xn)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[2, 1])).
% 0.47/0.65 tff(4,plain,
% 0.47/0.65 (sdtasdt0(xn, xn) = sdtasdt0(xp, sdtasdt0(xm, xm))),
% 0.47/0.65 inference(symmetry,[status(thm)],[3])).
% 0.47/0.65 tff(5,plain,
% 0.47/0.65 (?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xp, W0))) <=> ?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xp, W0)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(6,axiom,(((?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xn, xn) = sdtasdt0(xp, W0))) & doDivides0(xp, sdtasdt0(xn, xn))) & ?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xp, W0)))) & doDivides0(xp, xn)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__3046')).
% 0.47/0.65 tff(7,plain,
% 0.47/0.65 ((?[W0: $i] : (aNaturalNumber0(W0) & (sdtasdt0(xn, xn) = sdtasdt0(xp, W0))) & doDivides0(xp, sdtasdt0(xn, xn))) & ?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xp, W0)))),
% 0.47/0.65 inference(and_elim,[status(thm)],[6])).
% 0.47/0.65 tff(8,plain,
% 0.47/0.65 (?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xp, W0)))),
% 0.47/0.65 inference(and_elim,[status(thm)],[7])).
% 0.47/0.65 tff(9,plain,
% 0.47/0.65 (?[W0: $i] : (aNaturalNumber0(W0) & (xn = sdtasdt0(xp, W0)))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[8, 5])).
% 0.47/0.65 tff(10,plain,(
% 0.47/0.65 aNaturalNumber0(W0!7) & (xn = sdtasdt0(xp, W0!7))),
% 0.47/0.65 inference(skolemize,[status(sab)],[9])).
% 0.47/0.65 tff(11,plain,
% 0.47/0.65 (xn = sdtasdt0(xp, W0!7)),
% 0.47/0.65 inference(and_elim,[status(thm)],[10])).
% 0.47/0.65 tff(12,plain,
% 0.47/0.65 (sdtasdt0(xp, W0!7) = xn),
% 0.47/0.65 inference(symmetry,[status(thm)],[11])).
% 0.47/0.65 tff(13,plain,
% 0.47/0.65 (aNaturalNumber0(W0!7)),
% 0.47/0.65 inference(and_elim,[status(thm)],[10])).
% 0.47/0.65 tff(14,plain,
% 0.47/0.65 (aNaturalNumber0(xp) <=> aNaturalNumber0(xp)),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(15,axiom,(((((aNaturalNumber0(xn) & aNaturalNumber0(xm)) & aNaturalNumber0(xp)) & (~(xn = sz00))) & (~(xm = sz00))) & (~(xp = sz00))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__2987')).
% 0.47/0.65 tff(16,plain,
% 0.47/0.65 ((((aNaturalNumber0(xn) & aNaturalNumber0(xm)) & aNaturalNumber0(xp)) & (~(xn = sz00))) & (~(xm = sz00))),
% 0.47/0.65 inference(and_elim,[status(thm)],[15])).
% 0.47/0.65 tff(17,plain,
% 0.47/0.65 (((aNaturalNumber0(xn) & aNaturalNumber0(xm)) & aNaturalNumber0(xp)) & (~(xn = sz00))),
% 0.47/0.65 inference(and_elim,[status(thm)],[16])).
% 0.47/0.65 tff(18,plain,
% 0.47/0.65 ((aNaturalNumber0(xn) & aNaturalNumber0(xm)) & aNaturalNumber0(xp)),
% 0.47/0.65 inference(and_elim,[status(thm)],[17])).
% 0.47/0.65 tff(19,plain,
% 0.47/0.65 (aNaturalNumber0(xp)),
% 0.47/0.65 inference(and_elim,[status(thm)],[18])).
% 0.47/0.65 tff(20,plain,
% 0.47/0.65 (aNaturalNumber0(xp)),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[19, 14])).
% 0.47/0.65 tff(21,plain,
% 0.47/0.65 (^[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))))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(22,plain,
% 0.47/0.65 (![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)))),
% 0.47/0.65 inference(quant_intro,[status(thm)],[21])).
% 0.47/0.65 tff(23,plain,
% 0.47/0.65 (^[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)))))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(24,plain,
% 0.47/0.65 (![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)))),
% 0.47/0.65 inference(quant_intro,[status(thm)],[23])).
% 0.47/0.65 tff(25,plain,
% 0.47/0.65 (![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)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(26,plain,
% 0.47/0.65 (^[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))))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(27,plain,
% 0.47/0.65 (![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)))),
% 0.47/0.65 inference(quant_intro,[status(thm)],[26])).
% 0.47/0.65 tff(28,axiom,(![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mMulComm')).
% 0.47/0.65 tff(29,plain,
% 0.47/0.65 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.47/0.65 tff(30,plain,
% 0.47/0.65 (![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.47/0.65 tff(31,plain,(
% 0.47/0.65 ![W0: $i, W1: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1))) | (sdtasdt0(W0, W1) = sdtasdt0(W1, W0)))),
% 0.47/0.65 inference(skolemize,[status(sab)],[30])).
% 0.47/0.65 tff(32,plain,
% 0.47/0.65 (![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.47/0.65 tff(33,plain,
% 0.47/0.65 (![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[32, 22])).
% 0.47/0.65 tff(34,plain,
% 0.47/0.65 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!7)) | (sdtasdt0(W0!7, xp) = sdtasdt0(xp, W0!7)))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!7)) | (sdtasdt0(W0!7, xp) = sdtasdt0(xp, W0!7)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(35,plain,
% 0.47/0.65 (((sdtasdt0(W0!7, xp) = sdtasdt0(xp, W0!7)) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!7))) <=> ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!7)) | (sdtasdt0(W0!7, xp) = sdtasdt0(xp, W0!7)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(36,plain,
% 0.47/0.65 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(W0!7, xp) = sdtasdt0(xp, W0!7)) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!7)))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!7)) | (sdtasdt0(W0!7, xp) = sdtasdt0(xp, W0!7))))),
% 0.47/0.66 inference(monotonicity,[status(thm)],[35])).
% 0.47/0.66 tff(37,plain,
% 0.47/0.66 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(W0!7, xp) = sdtasdt0(xp, W0!7)) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!7)))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!7)) | (sdtasdt0(W0!7, xp) = sdtasdt0(xp, W0!7)))),
% 0.47/0.66 inference(transitivity,[status(thm)],[36, 34])).
% 0.47/0.66 tff(38,plain,
% 0.47/0.66 ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(W0!7, xp) = sdtasdt0(xp, W0!7)) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!7)))),
% 0.47/0.66 inference(quant_inst,[status(thm)],[])).
% 0.47/0.66 tff(39,plain,
% 0.47/0.66 ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!7)) | (sdtasdt0(W0!7, xp) = sdtasdt0(xp, W0!7))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[38, 37])).
% 0.47/0.66 tff(40,plain,
% 0.47/0.66 (sdtasdt0(W0!7, xp) = sdtasdt0(xp, W0!7)),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[39, 33, 20, 13])).
% 0.47/0.66 tff(41,plain,
% 0.47/0.66 (sdtasdt0(W0!7, xp) = xn),
% 0.47/0.66 inference(transitivity,[status(thm)],[40, 12])).
% 0.47/0.66 tff(42,plain,
% 0.47/0.66 (sdtasdt0(sdtasdt0(xp, W0!7), sdtasdt0(W0!7, xp)) = sdtasdt0(xn, xn)),
% 0.47/0.66 inference(monotonicity,[status(thm)],[12, 41])).
% 0.47/0.66 tff(43,plain,
% 0.47/0.66 (aNaturalNumber0(sdtasdt0(xp, W0!7)) <=> aNaturalNumber0(xn)),
% 0.47/0.66 inference(monotonicity,[status(thm)],[12])).
% 0.47/0.66 tff(44,plain,
% 0.47/0.66 (aNaturalNumber0(xn) <=> aNaturalNumber0(sdtasdt0(xp, W0!7))),
% 0.47/0.66 inference(symmetry,[status(thm)],[43])).
% 0.47/0.66 tff(45,plain,
% 0.47/0.66 (aNaturalNumber0(xn) <=> aNaturalNumber0(xn)),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(46,plain,
% 0.47/0.66 (aNaturalNumber0(xn) & aNaturalNumber0(xm)),
% 0.47/0.66 inference(and_elim,[status(thm)],[18])).
% 0.47/0.66 tff(47,plain,
% 0.47/0.66 (aNaturalNumber0(xn)),
% 0.47/0.66 inference(and_elim,[status(thm)],[46])).
% 0.47/0.66 tff(48,plain,
% 0.47/0.66 (aNaturalNumber0(xn)),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[47, 45])).
% 0.47/0.66 tff(49,plain,
% 0.47/0.66 (aNaturalNumber0(sdtasdt0(xp, W0!7))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.47/0.66 tff(50,plain,
% 0.47/0.66 (^[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))))),
% 0.47/0.66 inference(bind,[status(th)],[])).
% 0.47/0.66 tff(51,plain,
% 0.47/0.66 (![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)))),
% 0.47/0.66 inference(quant_intro,[status(thm)],[50])).
% 0.47/0.66 tff(52,plain,
% 0.47/0.66 (^[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)))))),
% 0.47/0.66 inference(bind,[status(th)],[])).
% 0.47/0.66 tff(53,plain,
% 0.47/0.66 (![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)))),
% 0.47/0.66 inference(quant_intro,[status(thm)],[52])).
% 0.47/0.66 tff(54,plain,
% 0.47/0.66 (![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))))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(55,plain,
% 0.47/0.66 (^[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))))))),
% 0.47/0.66 inference(bind,[status(th)],[])).
% 0.47/0.66 tff(56,plain,
% 0.47/0.66 (![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))))),
% 0.47/0.66 inference(quant_intro,[status(thm)],[55])).
% 0.47/0.66 tff(57,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/sandbox/benchmark/theBenchmark.p','mMulAsso')).
% 0.47/0.66 tff(58,plain,
% 0.47/0.66 (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.47/0.66 tff(59,plain,
% 0.47/0.66 (![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.47/0.66 tff(60,plain,(
% 0.47/0.66 ![W0: $i, W1: $i, W2: $i] : ((~(aNaturalNumber0(W0) & aNaturalNumber0(W1) & aNaturalNumber0(W2))) | (sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))))),
% 0.47/0.66 inference(skolemize,[status(sab)],[59])).
% 0.47/0.66 tff(61,plain,
% 0.47/0.66 (![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[60, 53])).
% 0.47/0.66 tff(62,plain,
% 0.47/0.66 (![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[61, 51])).
% 0.47/0.66 tff(63,plain,
% 0.47/0.66 (((~![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(W0!7)) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | (sdtasdt0(sdtasdt0(sdtasdt0(xp, W0!7), W0!7), xp) = sdtasdt0(sdtasdt0(xp, W0!7), sdtasdt0(W0!7, 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(W0!7)) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | (sdtasdt0(sdtasdt0(sdtasdt0(xp, W0!7), W0!7), xp) = sdtasdt0(sdtasdt0(xp, W0!7), sdtasdt0(W0!7, xp))))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(64,plain,
% 0.47/0.66 (((sdtasdt0(sdtasdt0(sdtasdt0(xp, W0!7), W0!7), xp) = sdtasdt0(sdtasdt0(xp, W0!7), sdtasdt0(W0!7, xp))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!7)) | (~aNaturalNumber0(sdtasdt0(xp, W0!7)))) <=> ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!7)) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | (sdtasdt0(sdtasdt0(sdtasdt0(xp, W0!7), W0!7), xp) = sdtasdt0(sdtasdt0(xp, W0!7), sdtasdt0(W0!7, xp))))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(65,plain,
% 0.47/0.66 (((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtasdt0(sdtasdt0(xp, W0!7), W0!7), xp) = sdtasdt0(sdtasdt0(xp, W0!7), sdtasdt0(W0!7, xp))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!7)) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))))) <=> ((~![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(W0!7)) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | (sdtasdt0(sdtasdt0(sdtasdt0(xp, W0!7), W0!7), xp) = sdtasdt0(sdtasdt0(xp, W0!7), sdtasdt0(W0!7, xp)))))),
% 0.47/0.66 inference(monotonicity,[status(thm)],[64])).
% 0.47/0.66 tff(66,plain,
% 0.47/0.66 (((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtasdt0(sdtasdt0(xp, W0!7), W0!7), xp) = sdtasdt0(sdtasdt0(xp, W0!7), sdtasdt0(W0!7, xp))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!7)) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))))) <=> ((~![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(W0!7)) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | (sdtasdt0(sdtasdt0(sdtasdt0(xp, W0!7), W0!7), xp) = sdtasdt0(sdtasdt0(xp, W0!7), sdtasdt0(W0!7, xp))))),
% 0.47/0.66 inference(transitivity,[status(thm)],[65, 63])).
% 0.47/0.66 tff(67,plain,
% 0.47/0.66 ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtasdt0(sdtasdt0(xp, W0!7), W0!7), xp) = sdtasdt0(sdtasdt0(xp, W0!7), sdtasdt0(W0!7, xp))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(W0!7)) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))))),
% 0.47/0.66 inference(quant_inst,[status(thm)],[])).
% 0.47/0.66 tff(68,plain,
% 0.47/0.66 ((~![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(W0!7)) | (~aNaturalNumber0(sdtasdt0(xp, W0!7))) | (sdtasdt0(sdtasdt0(sdtasdt0(xp, W0!7), W0!7), xp) = sdtasdt0(sdtasdt0(xp, W0!7), sdtasdt0(W0!7, xp)))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.47/0.66 tff(69,plain,
% 0.47/0.66 (sdtasdt0(sdtasdt0(sdtasdt0(xp, W0!7), W0!7), xp) = sdtasdt0(sdtasdt0(xp, W0!7), sdtasdt0(W0!7, xp))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[68, 62, 20, 13, 49])).
% 0.47/0.66 tff(70,plain,
% 0.47/0.66 ((sdtasdt0(xp, sdtsldt0(xn, xp)) = sdtasdt0(xp, W0!7)) <=> (sdtasdt0(xp, W0!7) = sdtasdt0(xp, sdtsldt0(xn, xp)))),
% 0.47/0.66 inference(commutativity,[status(thm)],[])).
% 0.47/0.66 tff(71,plain,
% 0.47/0.66 ((sdtasdt0(xp, W0!7) = sdtasdt0(xp, sdtsldt0(xn, xp))) <=> (sdtasdt0(xp, sdtsldt0(xn, xp)) = sdtasdt0(xp, W0!7))),
% 0.47/0.66 inference(symmetry,[status(thm)],[70])).
% 0.47/0.66 tff(72,plain,
% 0.47/0.66 ((xq = sdtsldt0(xn, xp)) <=> (xq = sdtsldt0(xn, xp))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(73,axiom,((aNaturalNumber0(xq) & (xn = sdtasdt0(xp, xq))) & (xq = sdtsldt0(xn, xp))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__3059')).
% 0.47/0.66 tff(74,plain,
% 0.47/0.66 (xq = sdtsldt0(xn, xp)),
% 0.47/0.66 inference(and_elim,[status(thm)],[73])).
% 0.47/0.66 tff(75,plain,
% 0.47/0.66 (xq = sdtsldt0(xn, xp)),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[74, 72])).
% 0.47/0.66 tff(76,plain,
% 0.47/0.66 (sdtsldt0(xn, xp) = xq),
% 0.47/0.66 inference(symmetry,[status(thm)],[75])).
% 0.47/0.66 tff(77,plain,
% 0.47/0.66 (sdtasdt0(xp, sdtsldt0(xn, xp)) = sdtasdt0(xp, xq)),
% 0.47/0.66 inference(monotonicity,[status(thm)],[76])).
% 0.47/0.66 tff(78,plain,
% 0.47/0.66 (sdtasdt0(xp, xq) = sdtasdt0(xp, sdtsldt0(xn, xp))),
% 0.47/0.66 inference(symmetry,[status(thm)],[77])).
% 0.47/0.66 tff(79,plain,
% 0.47/0.66 ((xn = sdtasdt0(xp, xq)) <=> (xn = sdtasdt0(xp, xq))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(80,plain,
% 0.47/0.66 (aNaturalNumber0(xq) & (xn = sdtasdt0(xp, xq))),
% 0.47/0.66 inference(and_elim,[status(thm)],[73])).
% 0.47/0.66 tff(81,plain,
% 0.47/0.66 (xn = sdtasdt0(xp, xq)),
% 0.47/0.66 inference(and_elim,[status(thm)],[80])).
% 0.47/0.66 tff(82,plain,
% 0.47/0.66 (xn = sdtasdt0(xp, xq)),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[81, 79])).
% 0.47/0.66 tff(83,plain,
% 0.47/0.66 (sdtasdt0(xp, W0!7) = sdtasdt0(xp, sdtsldt0(xn, xp))),
% 0.47/0.66 inference(transitivity,[status(thm)],[12, 82, 78])).
% 0.47/0.66 tff(84,plain,
% 0.47/0.66 (sdtasdt0(xp, sdtsldt0(xn, xp)) = sdtasdt0(xp, W0!7)),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[83, 71])).
% 0.47/0.66 tff(85,plain,
% 0.47/0.66 (((sdtasdt0(xp, sdtsldt0(xn, xp)) = sdtasdt0(xp, W0!7)) | (sdtasdt0(sdtsldt0(xn, xp), xp) = sdtasdt0(W0!7, xp))) | (~(sdtasdt0(xp, sdtsldt0(xn, xp)) = sdtasdt0(xp, W0!7)))),
% 0.47/0.66 inference(tautology,[status(thm)],[])).
% 0.47/0.66 tff(86,plain,
% 0.47/0.66 ((sdtasdt0(xp, sdtsldt0(xn, xp)) = sdtasdt0(xp, W0!7)) | (sdtasdt0(sdtsldt0(xn, xp), xp) = sdtasdt0(W0!7, xp))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.47/0.66 tff(87,plain,
% 0.47/0.66 ((~(xp = sz00)) <=> (~(xp = sz00))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(88,plain,
% 0.47/0.66 (~(xp = sz00)),
% 0.47/0.66 inference(and_elim,[status(thm)],[15])).
% 0.47/0.66 tff(89,plain,
% 0.47/0.66 (~(xp = sz00)),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.47/0.66 tff(90,plain,
% 0.47/0.66 (^[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)))))),
% 0.47/0.66 inference(bind,[status(th)],[])).
% 0.47/0.66 tff(91,plain,
% 0.47/0.66 (![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))))),
% 0.47/0.66 inference(quant_intro,[status(thm)],[90])).
% 0.47/0.66 tff(92,plain,
% 0.47/0.66 (^[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)))))),
% 0.47/0.66 inference(bind,[status(th)],[])).
% 0.47/0.66 tff(93,plain,
% 0.47/0.66 (![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))))),
% 0.47/0.66 inference(quant_intro,[status(thm)],[92])).
% 0.47/0.66 tff(94,plain,
% 0.47/0.66 (![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))))),
% 0.47/0.66 inference(transitivity,[status(thm)],[93, 91])).
% 0.47/0.66 tff(95,plain,
% 0.47/0.66 (^[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))))))),
% 0.47/0.66 inference(bind,[status(th)],[])).
% 0.47/0.66 tff(96,plain,
% 0.47/0.66 (![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))))),
% 0.47/0.66 inference(quant_intro,[status(thm)],[95])).
% 0.47/0.66 tff(97,plain,
% 0.47/0.66 (![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))))))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(98,plain,
% 0.47/0.66 (^[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))))))))),
% 0.47/0.66 inference(bind,[status(th)],[])).
% 0.47/0.66 tff(99,plain,
% 0.47/0.66 (![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))))))),
% 0.47/0.66 inference(quant_intro,[status(thm)],[98])).
% 0.47/0.66 tff(100,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/sandbox/benchmark/theBenchmark.p','mMulCanc')).
% 0.47/0.66 tff(101,plain,
% 0.47/0.66 (![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))))))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.47/0.66 tff(102,plain,
% 0.47/0.66 (![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))))))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[101, 97])).
% 0.47/0.66 tff(103,plain,(
% 0.47/0.66 ![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))))))),
% 0.47/0.66 inference(skolemize,[status(sab)],[102])).
% 0.47/0.66 tff(104,plain,
% 0.47/0.66 (![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))))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[103, 96])).
% 0.47/0.66 tff(105,plain,
% 0.47/0.66 (![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))))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[104, 94])).
% 0.47/0.66 tff(106,plain,
% 0.47/0.66 (((~![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))))) | ((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp))))))) <=> ((~![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))))) | (xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp))))))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(107,plain,
% 0.47/0.66 (((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) <=> ((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp))))))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(108,plain,
% 0.47/0.66 (^[W1: $i, W2: $i] : rewrite(((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))) | (~aNaturalNumber0(W1))) <=> ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp))))))),
% 0.47/0.66 inference(bind,[status(th)],[])).
% 0.47/0.66 tff(109,plain,
% 0.47/0.66 (![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))) | (~aNaturalNumber0(W1))) <=> ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))),
% 0.47/0.66 inference(quant_intro,[status(thm)],[108])).
% 0.47/0.66 tff(110,plain,
% 0.47/0.66 (((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))) | (~aNaturalNumber0(W1)))) <=> ((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp))))))),
% 0.47/0.66 inference(monotonicity,[status(thm)],[109])).
% 0.47/0.66 tff(111,plain,
% 0.47/0.66 (((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))) | (~aNaturalNumber0(W1)))) <=> ((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp))))))),
% 0.47/0.66 inference(transitivity,[status(thm)],[110, 107])).
% 0.47/0.66 tff(112,plain,
% 0.47/0.66 (((~![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))))) | ((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))) | (~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))))) | ((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))))),
% 0.47/0.67 inference(monotonicity,[status(thm)],[111])).
% 0.47/0.67 tff(113,plain,
% 0.47/0.67 (((~![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))))) | ((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))) | (~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))))) | (xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp))))))),
% 0.47/0.67 inference(transitivity,[status(thm)],[112, 106])).
% 0.47/0.67 tff(114,plain,
% 0.47/0.67 ((~![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))))) | ((xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))) | (~aNaturalNumber0(W1))))),
% 0.47/0.67 inference(quant_inst,[status(thm)],[])).
% 0.47/0.67 tff(115,plain,
% 0.47/0.67 ((~![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))))) | (xp = sz00) | (~aNaturalNumber0(xp)) | ![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.47/0.67 tff(116,plain,
% 0.47/0.67 (![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[115, 105, 20, 89])).
% 0.47/0.67 tff(117,plain,
% 0.47/0.67 (aNaturalNumber0(sdtsldt0(xn, xp)) <=> aNaturalNumber0(xq)),
% 0.47/0.67 inference(monotonicity,[status(thm)],[76])).
% 0.47/0.67 tff(118,plain,
% 0.47/0.67 (aNaturalNumber0(xq) <=> aNaturalNumber0(sdtsldt0(xn, xp))),
% 0.47/0.67 inference(symmetry,[status(thm)],[117])).
% 0.47/0.67 tff(119,plain,
% 0.47/0.67 (aNaturalNumber0(xq) <=> aNaturalNumber0(xq)),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(120,plain,
% 0.47/0.67 (aNaturalNumber0(xq)),
% 0.47/0.67 inference(and_elim,[status(thm)],[80])).
% 0.47/0.67 tff(121,plain,
% 0.47/0.67 (aNaturalNumber0(xq)),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.47/0.67 tff(122,plain,
% 0.47/0.67 (aNaturalNumber0(sdtsldt0(xn, xp))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[121, 118])).
% 0.47/0.67 tff(123,plain,
% 0.47/0.67 (((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | ((~aNaturalNumber0(W0!7)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (sdtsldt0(xn, xp) = W0!7) | (~((sdtasdt0(xp, sdtsldt0(xn, xp)) = sdtasdt0(xp, W0!7)) | (sdtasdt0(sdtsldt0(xn, xp), xp) = sdtasdt0(W0!7, xp)))))) <=> ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | (~aNaturalNumber0(W0!7)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (sdtsldt0(xn, xp) = W0!7) | (~((sdtasdt0(xp, sdtsldt0(xn, xp)) = sdtasdt0(xp, W0!7)) | (sdtasdt0(sdtsldt0(xn, xp), xp) = sdtasdt0(W0!7, xp)))))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(124,plain,
% 0.47/0.67 (((sdtsldt0(xn, xp) = W0!7) | (~aNaturalNumber0(W0!7)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~((sdtasdt0(xp, sdtsldt0(xn, xp)) = sdtasdt0(xp, W0!7)) | (sdtasdt0(sdtsldt0(xn, xp), xp) = sdtasdt0(W0!7, xp))))) <=> ((~aNaturalNumber0(W0!7)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (sdtsldt0(xn, xp) = W0!7) | (~((sdtasdt0(xp, sdtsldt0(xn, xp)) = sdtasdt0(xp, W0!7)) | (sdtasdt0(sdtsldt0(xn, xp), xp) = sdtasdt0(W0!7, xp)))))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(125,plain,
% 0.47/0.67 (((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | ((sdtsldt0(xn, xp) = W0!7) | (~aNaturalNumber0(W0!7)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~((sdtasdt0(xp, sdtsldt0(xn, xp)) = sdtasdt0(xp, W0!7)) | (sdtasdt0(sdtsldt0(xn, xp), xp) = sdtasdt0(W0!7, xp)))))) <=> ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | ((~aNaturalNumber0(W0!7)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (sdtsldt0(xn, xp) = W0!7) | (~((sdtasdt0(xp, sdtsldt0(xn, xp)) = sdtasdt0(xp, W0!7)) | (sdtasdt0(sdtsldt0(xn, xp), xp) = sdtasdt0(W0!7, xp))))))),
% 0.47/0.67 inference(monotonicity,[status(thm)],[124])).
% 0.47/0.67 tff(126,plain,
% 0.47/0.67 (((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | ((sdtsldt0(xn, xp) = W0!7) | (~aNaturalNumber0(W0!7)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~((sdtasdt0(xp, sdtsldt0(xn, xp)) = sdtasdt0(xp, W0!7)) | (sdtasdt0(sdtsldt0(xn, xp), xp) = sdtasdt0(W0!7, xp)))))) <=> ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | (~aNaturalNumber0(W0!7)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (sdtsldt0(xn, xp) = W0!7) | (~((sdtasdt0(xp, sdtsldt0(xn, xp)) = sdtasdt0(xp, W0!7)) | (sdtasdt0(sdtsldt0(xn, xp), xp) = sdtasdt0(W0!7, xp)))))),
% 0.47/0.67 inference(transitivity,[status(thm)],[125, 123])).
% 0.47/0.67 tff(127,plain,
% 0.47/0.67 ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | ((sdtsldt0(xn, xp) = W0!7) | (~aNaturalNumber0(W0!7)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~((sdtasdt0(xp, sdtsldt0(xn, xp)) = sdtasdt0(xp, W0!7)) | (sdtasdt0(sdtsldt0(xn, xp), xp) = sdtasdt0(W0!7, xp)))))),
% 0.47/0.67 inference(quant_inst,[status(thm)],[])).
% 0.47/0.67 tff(128,plain,
% 0.47/0.67 ((~![W1: $i, W2: $i] : ((W1 = W2) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~((sdtasdt0(xp, W1) = sdtasdt0(xp, W2)) | (sdtasdt0(W1, xp) = sdtasdt0(W2, xp)))))) | (~aNaturalNumber0(W0!7)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (sdtsldt0(xn, xp) = W0!7) | (~((sdtasdt0(xp, sdtsldt0(xn, xp)) = sdtasdt0(xp, W0!7)) | (sdtasdt0(sdtsldt0(xn, xp), xp) = sdtasdt0(W0!7, xp))))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.47/0.67 tff(129,plain,
% 0.47/0.67 (sdtsldt0(xn, xp) = W0!7),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[128, 13, 122, 116, 86])).
% 0.47/0.67 tff(130,plain,
% 0.47/0.67 (W0!7 = sdtsldt0(xn, xp)),
% 0.47/0.67 inference(symmetry,[status(thm)],[129])).
% 0.47/0.67 tff(131,plain,
% 0.47/0.67 (sdtasdt0(sdtasdt0(xp, W0!7), W0!7) = sdtasdt0(sdtasdt0(xp, sdtsldt0(xn, xp)), sdtsldt0(xn, xp))),
% 0.47/0.67 inference(monotonicity,[status(thm)],[83, 130])).
% 0.47/0.67 tff(132,plain,
% 0.47/0.67 (sdtasdt0(sdtasdt0(xp, sdtsldt0(xn, xp)), sdtsldt0(xn, xp)) = sdtasdt0(sdtasdt0(xp, W0!7), W0!7)),
% 0.47/0.67 inference(symmetry,[status(thm)],[131])).
% 0.47/0.67 tff(133,plain,
% 0.47/0.67 (((~![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(sdtsldt0(xn, xp))) | (sdtasdt0(sdtasdt0(xp, sdtsldt0(xn, xp)), sdtsldt0(xn, xp)) = sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, 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(sdtsldt0(xn, xp))) | (sdtasdt0(sdtasdt0(xp, sdtsldt0(xn, xp)), sdtsldt0(xn, xp)) = sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(134,plain,
% 0.47/0.67 (((sdtasdt0(sdtasdt0(xp, sdtsldt0(xn, xp)), sdtsldt0(xn, xp)) = sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~aNaturalNumber0(xp))) <=> ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (sdtasdt0(sdtasdt0(xp, sdtsldt0(xn, xp)), sdtsldt0(xn, xp)) = sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(135,plain,
% 0.47/0.67 (((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtasdt0(xp, sdtsldt0(xn, xp)), sdtsldt0(xn, xp)) = sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~aNaturalNumber0(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(sdtsldt0(xn, xp))) | (sdtasdt0(sdtasdt0(xp, sdtsldt0(xn, xp)), sdtsldt0(xn, xp)) = sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))))))),
% 0.47/0.67 inference(monotonicity,[status(thm)],[134])).
% 0.47/0.67 tff(136,plain,
% 0.47/0.67 (((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtasdt0(xp, sdtsldt0(xn, xp)), sdtsldt0(xn, xp)) = sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~aNaturalNumber0(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(sdtsldt0(xn, xp))) | (sdtasdt0(sdtasdt0(xp, sdtsldt0(xn, xp)), sdtsldt0(xn, xp)) = sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))))),
% 0.47/0.67 inference(transitivity,[status(thm)],[135, 133])).
% 0.47/0.67 tff(137,plain,
% 0.47/0.67 ((~![W0: $i, W1: $i, W2: $i] : ((sdtasdt0(sdtasdt0(W0, W1), W2) = sdtasdt0(W0, sdtasdt0(W1, W2))) | (~aNaturalNumber0(W2)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtasdt0(xp, sdtsldt0(xn, xp)), sdtsldt0(xn, xp)) = sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~aNaturalNumber0(xp)))),
% 0.47/0.67 inference(quant_inst,[status(thm)],[])).
% 0.47/0.67 tff(138,plain,
% 0.47/0.67 ((~![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(sdtsldt0(xn, xp))) | (sdtasdt0(sdtasdt0(xp, sdtsldt0(xn, xp)), sdtsldt0(xn, xp)) = sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[137, 136])).
% 0.47/0.67 tff(139,plain,
% 0.47/0.67 ((~aNaturalNumber0(sdtsldt0(xn, xp))) | (sdtasdt0(sdtasdt0(xp, sdtsldt0(xn, xp)), sdtsldt0(xn, xp)) = sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[138, 62, 20])).
% 0.47/0.67 tff(140,plain,
% 0.47/0.67 (sdtasdt0(sdtasdt0(xp, sdtsldt0(xn, xp)), sdtsldt0(xn, xp)) = sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[139, 122])).
% 0.47/0.67 tff(141,plain,
% 0.47/0.67 (sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))) = sdtasdt0(sdtasdt0(xp, sdtsldt0(xn, xp)), sdtsldt0(xn, xp))),
% 0.47/0.67 inference(symmetry,[status(thm)],[140])).
% 0.47/0.67 tff(142,plain,
% 0.47/0.67 (sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)) = sdtasdt0(xq, xq)),
% 0.47/0.67 inference(monotonicity,[status(thm)],[76, 76])).
% 0.47/0.67 tff(143,plain,
% 0.47/0.67 (sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))) = sdtasdt0(xp, sdtasdt0(xq, xq))),
% 0.47/0.67 inference(monotonicity,[status(thm)],[142])).
% 0.47/0.67 tff(144,plain,
% 0.47/0.67 (sdtasdt0(xp, sdtasdt0(xq, xq)) = sdtasdt0(xp, sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))),
% 0.47/0.67 inference(symmetry,[status(thm)],[143])).
% 0.47/0.67 tff(145,plain,
% 0.47/0.67 (sdtasdt0(xp, sdtasdt0(xq, xq)) = sdtasdt0(sdtasdt0(xp, W0!7), W0!7)),
% 0.47/0.67 inference(transitivity,[status(thm)],[144, 141, 132])).
% 0.47/0.67 tff(146,plain,
% 0.47/0.67 (sdtasdt0(sdtasdt0(xp, sdtasdt0(xq, xq)), xp) = sdtasdt0(sdtasdt0(sdtasdt0(xp, W0!7), W0!7), xp)),
% 0.47/0.67 inference(monotonicity,[status(thm)],[145])).
% 0.47/0.67 tff(147,plain,
% 0.47/0.67 (sdtasdt0(sdtasdt0(xp, sdtasdt0(xq, xq)), xp) = sdtasdt0(xp, sdtasdt0(xm, xm))),
% 0.47/0.67 inference(transitivity,[status(thm)],[146, 69, 42, 4])).
% 0.47/0.67 tff(148,plain,
% 0.47/0.67 ((sdtasdt0(sdtasdt0(xp, sdtasdt0(xq, xq)), xp) = sdtasdt0(xp, sdtasdt0(xp, sdtasdt0(xq, xq)))) <=> (sdtasdt0(xp, sdtasdt0(xm, xm)) = sdtasdt0(xp, sdtasdt0(xp, sdtasdt0(xq, xq))))),
% 0.47/0.67 inference(monotonicity,[status(thm)],[147])).
% 0.47/0.67 tff(149,plain,
% 0.47/0.67 ((sdtasdt0(xp, sdtasdt0(xm, xm)) = sdtasdt0(xp, sdtasdt0(xp, sdtasdt0(xq, xq)))) <=> (sdtasdt0(sdtasdt0(xp, sdtasdt0(xq, xq)), xp) = sdtasdt0(xp, sdtasdt0(xp, sdtasdt0(xq, xq))))),
% 0.47/0.67 inference(symmetry,[status(thm)],[148])).
% 0.47/0.67 tff(150,plain,
% 0.47/0.67 ((~(sdtasdt0(xp, sdtasdt0(xm, xm)) = sdtasdt0(xp, sdtasdt0(xp, sdtasdt0(xq, xq))))) <=> (~(sdtasdt0(sdtasdt0(xp, sdtasdt0(xq, xq)), xp) = sdtasdt0(xp, sdtasdt0(xp, sdtasdt0(xq, xq)))))),
% 0.47/0.67 inference(monotonicity,[status(thm)],[149])).
% 0.47/0.67 tff(151,plain,
% 0.47/0.67 ((~(sdtasdt0(xp, sdtasdt0(xm, xm)) = sdtasdt0(xp, sdtasdt0(xp, sdtasdt0(xq, xq))))) <=> (~(sdtasdt0(xp, sdtasdt0(xm, xm)) = sdtasdt0(xp, sdtasdt0(xp, sdtasdt0(xq, xq)))))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(152,axiom,(~(sdtasdt0(xp, sdtasdt0(xm, xm)) = sdtasdt0(xp, sdtasdt0(xp, sdtasdt0(xq, xq))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 0.47/0.67 tff(153,plain,
% 0.47/0.67 (~(sdtasdt0(xp, sdtasdt0(xm, xm)) = sdtasdt0(xp, sdtasdt0(xp, sdtasdt0(xq, xq))))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.47/0.67 tff(154,plain,
% 0.47/0.67 (~(sdtasdt0(sdtasdt0(xp, sdtasdt0(xq, xq)), xp) = sdtasdt0(xp, sdtasdt0(xp, sdtasdt0(xq, xq))))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[153, 150])).
% 0.47/0.67 tff(155,plain,
% 0.47/0.67 (aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))) <=> aNaturalNumber0(sdtasdt0(xq, xq))),
% 0.47/0.67 inference(monotonicity,[status(thm)],[142])).
% 0.47/0.67 tff(156,plain,
% 0.47/0.67 (^[W0: $i, W1: $i] : refl((aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))))),
% 0.47/0.67 inference(bind,[status(th)],[])).
% 0.47/0.67 tff(157,plain,
% 0.47/0.67 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.47/0.67 inference(quant_intro,[status(thm)],[156])).
% 0.47/0.67 tff(158,plain,
% 0.47/0.67 (^[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)))))),
% 0.47/0.67 inference(bind,[status(th)],[])).
% 0.47/0.67 tff(159,plain,
% 0.47/0.67 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.47/0.67 inference(quant_intro,[status(thm)],[158])).
% 0.47/0.67 tff(160,plain,
% 0.47/0.67 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(161,plain,
% 0.47/0.67 (^[W0: $i, W1: $i] : rewrite(((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtasdt0(W0, W1))) <=> (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1)))))),
% 0.47/0.67 inference(bind,[status(th)],[])).
% 0.47/0.67 tff(162,plain,
% 0.47/0.67 (![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtasdt0(W0, W1))) <=> ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.47/0.67 inference(quant_intro,[status(thm)],[161])).
% 0.47/0.67 tff(163,axiom,(![W0: $i, W1: $i] : ((aNaturalNumber0(W0) & aNaturalNumber0(W1)) => aNaturalNumber0(sdtasdt0(W0, W1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mSortsB_02')).
% 0.47/0.67 tff(164,plain,
% 0.47/0.67 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.47/0.67 tff(165,plain,
% 0.47/0.67 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[164, 160])).
% 0.47/0.67 tff(166,plain,(
% 0.47/0.67 ![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~(aNaturalNumber0(W0) & aNaturalNumber0(W1))))),
% 0.47/0.67 inference(skolemize,[status(sab)],[165])).
% 0.47/0.67 tff(167,plain,
% 0.47/0.67 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[166, 159])).
% 0.47/0.67 tff(168,plain,
% 0.47/0.67 (![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[167, 157])).
% 0.47/0.67 tff(169,plain,
% 0.47/0.67 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(sdtsldt0(xn, xp))) | aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(170,plain,
% 0.47/0.67 ((aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~aNaturalNumber0(sdtsldt0(xn, xp)))) <=> ((~aNaturalNumber0(sdtsldt0(xn, xp))) | aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(171,plain,
% 0.47/0.67 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~aNaturalNumber0(sdtsldt0(xn, xp))))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(sdtsldt0(xn, xp))) | aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))))),
% 0.47/0.67 inference(monotonicity,[status(thm)],[170])).
% 0.47/0.67 tff(172,plain,
% 0.47/0.67 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~aNaturalNumber0(sdtsldt0(xn, xp))))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))))),
% 0.47/0.67 inference(transitivity,[status(thm)],[171, 169])).
% 0.47/0.67 tff(173,plain,
% 0.47/0.67 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp))) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | (~aNaturalNumber0(sdtsldt0(xn, xp))))),
% 0.47/0.67 inference(quant_inst,[status(thm)],[])).
% 0.47/0.67 tff(174,plain,
% 0.47/0.67 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(sdtsldt0(xn, xp))) | aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.47/0.67 tff(175,plain,
% 0.47/0.67 ((~aNaturalNumber0(sdtsldt0(xn, xp))) | aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[174, 168])).
% 0.47/0.67 tff(176,plain,
% 0.47/0.67 (aNaturalNumber0(sdtasdt0(sdtsldt0(xn, xp), sdtsldt0(xn, xp)))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[175, 122])).
% 0.47/0.67 tff(177,plain,
% 0.47/0.67 (aNaturalNumber0(sdtasdt0(xq, xq))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[176, 155])).
% 0.47/0.67 tff(178,plain,
% 0.47/0.67 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xq, xq))) | aNaturalNumber0(sdtasdt0(xp, sdtasdt0(xq, xq))))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xq, xq))) | aNaturalNumber0(sdtasdt0(xp, sdtasdt0(xq, xq))))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(179,plain,
% 0.47/0.67 ((aNaturalNumber0(sdtasdt0(xp, sdtasdt0(xq, xq))) | (~aNaturalNumber0(sdtasdt0(xq, xq))) | (~aNaturalNumber0(xp))) <=> ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xq, xq))) | aNaturalNumber0(sdtasdt0(xp, sdtasdt0(xq, xq))))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(180,plain,
% 0.47/0.67 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(xp, sdtasdt0(xq, xq))) | (~aNaturalNumber0(sdtasdt0(xq, xq))) | (~aNaturalNumber0(xp)))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xq, xq))) | aNaturalNumber0(sdtasdt0(xp, sdtasdt0(xq, xq)))))),
% 0.47/0.67 inference(monotonicity,[status(thm)],[179])).
% 0.47/0.67 tff(181,plain,
% 0.47/0.67 (((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(xp, sdtasdt0(xq, xq))) | (~aNaturalNumber0(sdtasdt0(xq, xq))) | (~aNaturalNumber0(xp)))) <=> ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xq, xq))) | aNaturalNumber0(sdtasdt0(xp, sdtasdt0(xq, xq))))),
% 0.47/0.67 inference(transitivity,[status(thm)],[180, 178])).
% 0.47/0.67 tff(182,plain,
% 0.47/0.67 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (aNaturalNumber0(sdtasdt0(xp, sdtasdt0(xq, xq))) | (~aNaturalNumber0(sdtasdt0(xq, xq))) | (~aNaturalNumber0(xp)))),
% 0.47/0.67 inference(quant_inst,[status(thm)],[])).
% 0.47/0.67 tff(183,plain,
% 0.47/0.67 ((~![W0: $i, W1: $i] : (aNaturalNumber0(sdtasdt0(W0, W1)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xq, xq))) | aNaturalNumber0(sdtasdt0(xp, sdtasdt0(xq, xq)))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.47/0.67 tff(184,plain,
% 0.47/0.67 ((~aNaturalNumber0(sdtasdt0(xq, xq))) | aNaturalNumber0(sdtasdt0(xp, sdtasdt0(xq, xq)))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[183, 168, 20])).
% 0.47/0.67 tff(185,plain,
% 0.47/0.67 (aNaturalNumber0(sdtasdt0(xp, sdtasdt0(xq, xq)))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[184, 177])).
% 0.47/0.67 tff(186,plain,
% 0.47/0.67 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xp, sdtasdt0(xq, xq)))) | (sdtasdt0(sdtasdt0(xp, sdtasdt0(xq, xq)), xp) = sdtasdt0(xp, sdtasdt0(xp, sdtasdt0(xq, xq)))))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xp, sdtasdt0(xq, xq)))) | (sdtasdt0(sdtasdt0(xp, sdtasdt0(xq, xq)), xp) = sdtasdt0(xp, sdtasdt0(xp, sdtasdt0(xq, xq)))))),
% 0.47/0.68 inference(rewrite,[status(thm)],[])).
% 0.47/0.68 tff(187,plain,
% 0.47/0.68 (((sdtasdt0(sdtasdt0(xp, sdtasdt0(xq, xq)), xp) = sdtasdt0(xp, sdtasdt0(xp, sdtasdt0(xq, xq)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xp, sdtasdt0(xq, xq))))) <=> ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xp, sdtasdt0(xq, xq)))) | (sdtasdt0(sdtasdt0(xp, sdtasdt0(xq, xq)), xp) = sdtasdt0(xp, sdtasdt0(xp, sdtasdt0(xq, xq)))))),
% 0.47/0.68 inference(rewrite,[status(thm)],[])).
% 0.47/0.68 tff(188,plain,
% 0.47/0.68 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtasdt0(xp, sdtasdt0(xq, xq)), xp) = sdtasdt0(xp, sdtasdt0(xp, sdtasdt0(xq, xq)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xp, sdtasdt0(xq, xq)))))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xp, sdtasdt0(xq, xq)))) | (sdtasdt0(sdtasdt0(xp, sdtasdt0(xq, xq)), xp) = sdtasdt0(xp, sdtasdt0(xp, sdtasdt0(xq, xq))))))),
% 0.47/0.68 inference(monotonicity,[status(thm)],[187])).
% 0.47/0.68 tff(189,plain,
% 0.47/0.68 (((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtasdt0(xp, sdtasdt0(xq, xq)), xp) = sdtasdt0(xp, sdtasdt0(xp, sdtasdt0(xq, xq)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xp, sdtasdt0(xq, xq)))))) <=> ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xp, sdtasdt0(xq, xq)))) | (sdtasdt0(sdtasdt0(xp, sdtasdt0(xq, xq)), xp) = sdtasdt0(xp, sdtasdt0(xp, sdtasdt0(xq, xq)))))),
% 0.47/0.68 inference(transitivity,[status(thm)],[188, 186])).
% 0.47/0.68 tff(190,plain,
% 0.47/0.68 ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | ((sdtasdt0(sdtasdt0(xp, sdtasdt0(xq, xq)), xp) = sdtasdt0(xp, sdtasdt0(xp, sdtasdt0(xq, xq)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xp, sdtasdt0(xq, xq)))))),
% 0.47/0.68 inference(quant_inst,[status(thm)],[])).
% 0.47/0.68 tff(191,plain,
% 0.47/0.68 ((~![W0: $i, W1: $i] : ((sdtasdt0(W0, W1) = sdtasdt0(W1, W0)) | (~aNaturalNumber0(W1)) | (~aNaturalNumber0(W0)))) | (~aNaturalNumber0(xp)) | (~aNaturalNumber0(sdtasdt0(xp, sdtasdt0(xq, xq)))) | (sdtasdt0(sdtasdt0(xp, sdtasdt0(xq, xq)), xp) = sdtasdt0(xp, sdtasdt0(xp, sdtasdt0(xq, xq))))),
% 0.47/0.68 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.47/0.68 tff(192,plain,
% 0.47/0.68 ((~aNaturalNumber0(sdtasdt0(xp, sdtasdt0(xq, xq)))) | (sdtasdt0(sdtasdt0(xp, sdtasdt0(xq, xq)), xp) = sdtasdt0(xp, sdtasdt0(xp, sdtasdt0(xq, xq))))),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[191, 33, 20])).
% 0.47/0.68 tff(193,plain,
% 0.47/0.68 ($false),
% 0.47/0.68 inference(unit_resolution,[status(thm)],[192, 185, 154])).
% 0.47/0.68 % SZS output end Proof
% 0.47/0.68 % E exiting
%------------------------------------------------------------------------------