Z3---4.15.1.THM-Prf.s

%------------------------------------------------------------------------------
% File     : Z3---4.15.1
% Problem  : NUM454+6 : TPTP v9.0.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp
% Command  : run_E %s %d THM

% Computer : n003.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 05:21:02 AM UTC 2025

% Result   : Theorem 0.20s 0.65s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : NUM454+6 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.12  % Command    : run_E %s %d THM
% 0.12/0.34  % Computer : n003.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 01:12:54 EDT 2025
% 0.12/0.34  % CPUTime    : 
% 0.20/0.65  % SZS status Theorem
% 0.20/0.65  % SZS output start Proof
% 0.20/0.65  tff(sz00_type, type, (
% 0.20/0.65     sz00: $i)).
% 0.20/0.65  tff(sdtasdt0_type, type, (
% 0.20/0.65     sdtasdt0: ( $i * $i ) > $i)).
% 0.20/0.65  tff(sdtpldt0_type, type, (
% 0.20/0.65     sdtpldt0: ( $i * $i ) > $i)).
% 0.20/0.65  tff(smndt0_type, type, (
% 0.20/0.65     smndt0: $i > $i)).
% 0.20/0.65  tff(sz10_type, type, (
% 0.20/0.65     sz10: $i)).
% 0.20/0.65  tff(xp_type, type, (
% 0.20/0.65     xp: $i)).
% 0.20/0.65  tff(aInteger0_type, type, (
% 0.20/0.65     aInteger0: $i > $o)).
% 0.20/0.65  tff(aSet0_type, type, (
% 0.20/0.65     aSet0: $i > $o)).
% 0.20/0.65  tff(szAzrzSzezqlpdtcmdtrp0_type, type, (
% 0.20/0.65     szAzrzSzezqlpdtcmdtrp0: ( $i * $i ) > $i)).
% 0.20/0.65  tff(aElementOf0_type, type, (
% 0.20/0.65     aElementOf0: ( $i * $i ) > $o)).
% 0.20/0.65  tff(sdteqdtlpzmzozddtrp0_type, type, (
% 0.20/0.65     sdteqdtlpzmzozddtrp0: ( $i * $i * $i ) > $o)).
% 0.20/0.65  tff(aDivisorOf0_type, type, (
% 0.20/0.65     aDivisorOf0: ( $i * $i ) > $o)).
% 0.20/0.65  tff(sbsmnsldt0_type, type, (
% 0.20/0.65     sbsmnsldt0: $i > $i)).
% 0.20/0.65  tff(xS_type, type, (
% 0.20/0.65     xS: $i)).
% 0.20/0.65  tff(stldt0_type, type, (
% 0.20/0.65     stldt0: $i > $i)).
% 0.20/0.65  tff(aSubsetOf0_type, type, (
% 0.20/0.65     aSubsetOf0: ( $i * $i ) > $o)).
% 0.20/0.65  tff(tptp_fun_W0_22_type, type, (
% 0.20/0.65     tptp_fun_W0_22: $i)).
% 0.20/0.65  tff(1,plain,
% 0.20/0.65      (aInteger0(xp) <=> aInteger0(xp)),
% 0.20/0.65      inference(rewrite,[status(thm)],[])).
% 0.20/0.65  tff(2,axiom,((((((((aInteger0(xp) & (~(xp = sz00))) & aSet0(szAzrzSzezqlpdtcmdtrp0(sz10, xp))) & ![W0: $i] : ((aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp)) => (((aInteger0(W0) & ?[W1: $i] : (aInteger0(W1) & (sdtasdt0(xp, W1) = sdtpldt0(W0, smndt0(sz10))))) & aDivisorOf0(xp, sdtpldt0(W0, smndt0(sz10)))) & sdteqdtlpzmzozddtrp0(W0, sz10, xp))) & ((aInteger0(W0) & ((?[W1: $i] : (aInteger0(W1) & (sdtasdt0(xp, W1) = sdtpldt0(W0, smndt0(sz10)))) | aDivisorOf0(xp, sdtpldt0(W0, smndt0(sz10)))) | sdteqdtlpzmzozddtrp0(W0, sz10, xp))) => aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp))))) & aSet0(sbsmnsldt0(xS))) & ![W0: $i] : (aElementOf0(W0, sbsmnsldt0(xS)) <=> (aInteger0(W0) & ?[W1: $i] : (aElementOf0(W1, xS) & aElementOf0(W0, W1))))) & ![W0: $i] : (aElementOf0(W0, stldt0(sbsmnsldt0(xS))) <=> (aInteger0(W0) & (~aElementOf0(W0, sbsmnsldt0(xS)))))) & ![W0: $i] : (aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp)) => aElementOf0(W0, stldt0(sbsmnsldt0(xS))))) & aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10, xp), stldt0(sbsmnsldt0(xS)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__2171')).
% 0.20/0.65  tff(3,plain,
% 0.20/0.65      (((((((aInteger0(xp) & (~(xp = sz00))) & aSet0(szAzrzSzezqlpdtcmdtrp0(sz10, xp))) & ![W0: $i] : ((aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp)) => (((aInteger0(W0) & ?[W1: $i] : (aInteger0(W1) & (sdtasdt0(xp, W1) = sdtpldt0(W0, smndt0(sz10))))) & aDivisorOf0(xp, sdtpldt0(W0, smndt0(sz10)))) & sdteqdtlpzmzozddtrp0(W0, sz10, xp))) & ((aInteger0(W0) & ((?[W1: $i] : (aInteger0(W1) & (sdtasdt0(xp, W1) = sdtpldt0(W0, smndt0(sz10)))) | aDivisorOf0(xp, sdtpldt0(W0, smndt0(sz10)))) | sdteqdtlpzmzozddtrp0(W0, sz10, xp))) => aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp))))) & aSet0(sbsmnsldt0(xS))) & ![W0: $i] : (aElementOf0(W0, sbsmnsldt0(xS)) <=> (aInteger0(W0) & ?[W1: $i] : (aElementOf0(W1, xS) & aElementOf0(W0, W1))))) & ![W0: $i] : (aElementOf0(W0, stldt0(sbsmnsldt0(xS))) <=> (aInteger0(W0) & (~aElementOf0(W0, sbsmnsldt0(xS)))))) & ![W0: $i] : (aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp)) => aElementOf0(W0, stldt0(sbsmnsldt0(xS))))),
% 0.20/0.65      inference(and_elim,[status(thm)],[2])).
% 0.20/0.65  tff(4,plain,
% 0.20/0.65      ((((((aInteger0(xp) & (~(xp = sz00))) & aSet0(szAzrzSzezqlpdtcmdtrp0(sz10, xp))) & ![W0: $i] : ((aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp)) => (((aInteger0(W0) & ?[W1: $i] : (aInteger0(W1) & (sdtasdt0(xp, W1) = sdtpldt0(W0, smndt0(sz10))))) & aDivisorOf0(xp, sdtpldt0(W0, smndt0(sz10)))) & sdteqdtlpzmzozddtrp0(W0, sz10, xp))) & ((aInteger0(W0) & ((?[W1: $i] : (aInteger0(W1) & (sdtasdt0(xp, W1) = sdtpldt0(W0, smndt0(sz10)))) | aDivisorOf0(xp, sdtpldt0(W0, smndt0(sz10)))) | sdteqdtlpzmzozddtrp0(W0, sz10, xp))) => aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp))))) & aSet0(sbsmnsldt0(xS))) & ![W0: $i] : (aElementOf0(W0, sbsmnsldt0(xS)) <=> (aInteger0(W0) & ?[W1: $i] : (aElementOf0(W1, xS) & aElementOf0(W0, W1))))) & ![W0: $i] : (aElementOf0(W0, stldt0(sbsmnsldt0(xS))) <=> (aInteger0(W0) & (~aElementOf0(W0, sbsmnsldt0(xS)))))),
% 0.20/0.65      inference(and_elim,[status(thm)],[3])).
% 0.20/0.65  tff(5,plain,
% 0.20/0.65      (((((aInteger0(xp) & (~(xp = sz00))) & aSet0(szAzrzSzezqlpdtcmdtrp0(sz10, xp))) & ![W0: $i] : ((aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp)) => (((aInteger0(W0) & ?[W1: $i] : (aInteger0(W1) & (sdtasdt0(xp, W1) = sdtpldt0(W0, smndt0(sz10))))) & aDivisorOf0(xp, sdtpldt0(W0, smndt0(sz10)))) & sdteqdtlpzmzozddtrp0(W0, sz10, xp))) & ((aInteger0(W0) & ((?[W1: $i] : (aInteger0(W1) & (sdtasdt0(xp, W1) = sdtpldt0(W0, smndt0(sz10)))) | aDivisorOf0(xp, sdtpldt0(W0, smndt0(sz10)))) | sdteqdtlpzmzozddtrp0(W0, sz10, xp))) => aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp))))) & aSet0(sbsmnsldt0(xS))) & ![W0: $i] : (aElementOf0(W0, sbsmnsldt0(xS)) <=> (aInteger0(W0) & ?[W1: $i] : (aElementOf0(W1, xS) & aElementOf0(W0, W1))))),
% 0.20/0.65      inference(and_elim,[status(thm)],[4])).
% 0.20/0.65  tff(6,plain,
% 0.20/0.65      ((((aInteger0(xp) & (~(xp = sz00))) & aSet0(szAzrzSzezqlpdtcmdtrp0(sz10, xp))) & ![W0: $i] : ((aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp)) => (((aInteger0(W0) & ?[W1: $i] : (aInteger0(W1) & (sdtasdt0(xp, W1) = sdtpldt0(W0, smndt0(sz10))))) & aDivisorOf0(xp, sdtpldt0(W0, smndt0(sz10)))) & sdteqdtlpzmzozddtrp0(W0, sz10, xp))) & ((aInteger0(W0) & ((?[W1: $i] : (aInteger0(W1) & (sdtasdt0(xp, W1) = sdtpldt0(W0, smndt0(sz10)))) | aDivisorOf0(xp, sdtpldt0(W0, smndt0(sz10)))) | sdteqdtlpzmzozddtrp0(W0, sz10, xp))) => aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp))))) & aSet0(sbsmnsldt0(xS))),
% 0.20/0.65      inference(and_elim,[status(thm)],[5])).
% 0.20/0.65  tff(7,plain,
% 0.20/0.65      (((aInteger0(xp) & (~(xp = sz00))) & aSet0(szAzrzSzezqlpdtcmdtrp0(sz10, xp))) & ![W0: $i] : ((aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp)) => (((aInteger0(W0) & ?[W1: $i] : (aInteger0(W1) & (sdtasdt0(xp, W1) = sdtpldt0(W0, smndt0(sz10))))) & aDivisorOf0(xp, sdtpldt0(W0, smndt0(sz10)))) & sdteqdtlpzmzozddtrp0(W0, sz10, xp))) & ((aInteger0(W0) & ((?[W1: $i] : (aInteger0(W1) & (sdtasdt0(xp, W1) = sdtpldt0(W0, smndt0(sz10)))) | aDivisorOf0(xp, sdtpldt0(W0, smndt0(sz10)))) | sdteqdtlpzmzozddtrp0(W0, sz10, xp))) => aElementOf0(W0, szAzrzSzezqlpdtcmdtrp0(sz10, xp))))),
% 0.20/0.65      inference(and_elim,[status(thm)],[6])).
% 0.20/0.65  tff(8,plain,
% 0.20/0.65      ((aInteger0(xp) & (~(xp = sz00))) & aSet0(szAzrzSzezqlpdtcmdtrp0(sz10, xp))),
% 0.20/0.65      inference(and_elim,[status(thm)],[7])).
% 0.20/0.65  tff(9,plain,
% 0.20/0.65      (aInteger0(xp) & (~(xp = sz00))),
% 0.20/0.65      inference(and_elim,[status(thm)],[8])).
% 0.20/0.65  tff(10,plain,
% 0.20/0.65      (aInteger0(xp)),
% 0.20/0.65      inference(and_elim,[status(thm)],[9])).
% 0.20/0.65  tff(11,plain,
% 0.20/0.65      (aInteger0(xp)),
% 0.20/0.65      inference(modus_ponens,[status(thm)],[10, 1])).
% 0.20/0.65  tff(12,plain,
% 0.20/0.65      (^[W0: $i] : refl(((~aInteger0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0)))))) <=> ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0)))))))),
% 0.20/0.65      inference(bind,[status(th)],[])).
% 0.20/0.65  tff(13,plain,
% 0.20/0.65      (![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0)))))) <=> ![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0))))))),
% 0.20/0.65      inference(quant_intro,[status(thm)],[12])).
% 0.20/0.65  tff(14,plain,
% 0.20/0.65      (^[W0: $i] : rewrite(((~aInteger0(W0)) | ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0)))) <=> ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0)))))))),
% 0.20/0.65      inference(bind,[status(th)],[])).
% 0.20/0.65  tff(15,plain,
% 0.20/0.65      (![W0: $i] : ((~aInteger0(W0)) | ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0)))) <=> ![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0))))))),
% 0.20/0.65      inference(quant_intro,[status(thm)],[14])).
% 0.20/0.65  tff(16,plain,
% 0.20/0.65      (![W0: $i] : ((~aInteger0(W0)) | ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0)))) <=> ![W0: $i] : ((~aInteger0(W0)) | ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0))))),
% 0.20/0.65      inference(rewrite,[status(thm)],[])).
% 0.20/0.65  tff(17,plain,
% 0.20/0.65      (^[W0: $i] : rewrite((aInteger0(W0) => ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0)))) <=> ((~aInteger0(W0)) | ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0)))))),
% 0.20/0.65      inference(bind,[status(th)],[])).
% 0.20/0.65  tff(18,plain,
% 0.20/0.65      (![W0: $i] : (aInteger0(W0) => ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0)))) <=> ![W0: $i] : ((~aInteger0(W0)) | ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0))))),
% 0.20/0.65      inference(quant_intro,[status(thm)],[17])).
% 0.20/0.65  tff(19,axiom,(![W0: $i] : (aInteger0(W0) => ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mAddNeg')).
% 0.20/0.65  tff(20,plain,
% 0.20/0.65      (![W0: $i] : ((~aInteger0(W0)) | ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0))))),
% 0.20/0.65      inference(modus_ponens,[status(thm)],[19, 18])).
% 0.20/0.65  tff(21,plain,
% 0.20/0.65      (![W0: $i] : ((~aInteger0(W0)) | ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0))))),
% 0.20/0.65      inference(modus_ponens,[status(thm)],[20, 16])).
% 0.20/0.65  tff(22,plain,(
% 0.20/0.65      ![W0: $i] : ((~aInteger0(W0)) | ((sdtpldt0(W0, smndt0(W0)) = sz00) & (sz00 = sdtpldt0(smndt0(W0), W0))))),
% 0.20/0.65      inference(skolemize,[status(sab)],[21])).
% 0.20/0.65  tff(23,plain,
% 0.20/0.65      (![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0))))))),
% 0.20/0.65      inference(modus_ponens,[status(thm)],[22, 15])).
% 0.20/0.65  tff(24,plain,
% 0.20/0.65      (![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0))))))),
% 0.20/0.65      inference(modus_ponens,[status(thm)],[23, 13])).
% 0.20/0.65  tff(25,plain,
% 0.20/0.65      (((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0))))))) | ((~aInteger0(xp)) | (~((~(sdtpldt0(xp, smndt0(xp)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(xp), xp))))))) <=> ((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0))))))) | (~aInteger0(xp)) | (~((~(sdtpldt0(xp, smndt0(xp)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(xp), xp))))))),
% 0.20/0.65      inference(rewrite,[status(thm)],[])).
% 0.20/0.65  tff(26,plain,
% 0.20/0.65      ((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0))))))) | ((~aInteger0(xp)) | (~((~(sdtpldt0(xp, smndt0(xp)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(xp), xp))))))),
% 0.20/0.65      inference(quant_inst,[status(thm)],[])).
% 0.20/0.65  tff(27,plain,
% 0.20/0.65      ((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0))))))) | (~aInteger0(xp)) | (~((~(sdtpldt0(xp, smndt0(xp)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(xp), xp)))))),
% 0.20/0.65      inference(modus_ponens,[status(thm)],[26, 25])).
% 0.20/0.65  tff(28,plain,
% 0.20/0.65      (~((~(sdtpldt0(xp, smndt0(xp)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(xp), xp))))),
% 0.20/0.65      inference(unit_resolution,[status(thm)],[27, 24, 11])).
% 0.20/0.65  tff(29,plain,
% 0.20/0.65      (((~(sdtpldt0(xp, smndt0(xp)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(xp), xp)))) | (sdtpldt0(xp, smndt0(xp)) = sz00)),
% 0.20/0.65      inference(tautology,[status(thm)],[])).
% 0.20/0.65  tff(30,plain,
% 0.20/0.65      (sdtpldt0(xp, smndt0(xp)) = sz00),
% 0.20/0.65      inference(unit_resolution,[status(thm)],[29, 28])).
% 0.20/0.65  tff(31,plain,
% 0.20/0.65      (^[W0: $i] : refl((aInteger0(smndt0(W0)) | (~aInteger0(W0))) <=> (aInteger0(smndt0(W0)) | (~aInteger0(W0))))),
% 0.20/0.65      inference(bind,[status(th)],[])).
% 0.20/0.65  tff(32,plain,
% 0.20/0.65      (![W0: $i] : (aInteger0(smndt0(W0)) | (~aInteger0(W0))) <=> ![W0: $i] : (aInteger0(smndt0(W0)) | (~aInteger0(W0)))),
% 0.20/0.65      inference(quant_intro,[status(thm)],[31])).
% 0.20/0.65  tff(33,plain,
% 0.20/0.65      (![W0: $i] : (aInteger0(smndt0(W0)) | (~aInteger0(W0))) <=> ![W0: $i] : (aInteger0(smndt0(W0)) | (~aInteger0(W0)))),
% 0.20/0.65      inference(rewrite,[status(thm)],[])).
% 0.20/0.65  tff(34,plain,
% 0.20/0.65      (^[W0: $i] : rewrite((aInteger0(W0) => aInteger0(smndt0(W0))) <=> (aInteger0(smndt0(W0)) | (~aInteger0(W0))))),
% 0.20/0.65      inference(bind,[status(th)],[])).
% 0.20/0.65  tff(35,plain,
% 0.20/0.65      (![W0: $i] : (aInteger0(W0) => aInteger0(smndt0(W0))) <=> ![W0: $i] : (aInteger0(smndt0(W0)) | (~aInteger0(W0)))),
% 0.20/0.65      inference(quant_intro,[status(thm)],[34])).
% 0.20/0.65  tff(36,axiom,(![W0: $i] : (aInteger0(W0) => aInteger0(smndt0(W0)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mIntNeg')).
% 0.20/0.65  tff(37,plain,
% 0.20/0.65      (![W0: $i] : (aInteger0(smndt0(W0)) | (~aInteger0(W0)))),
% 0.20/0.65      inference(modus_ponens,[status(thm)],[36, 35])).
% 0.20/0.65  tff(38,plain,
% 0.20/0.65      (![W0: $i] : (aInteger0(smndt0(W0)) | (~aInteger0(W0)))),
% 0.20/0.65      inference(modus_ponens,[status(thm)],[37, 33])).
% 0.20/0.65  tff(39,plain,(
% 0.20/0.65      ![W0: $i] : (aInteger0(smndt0(W0)) | (~aInteger0(W0)))),
% 0.20/0.65      inference(skolemize,[status(sab)],[38])).
% 0.20/0.65  tff(40,plain,
% 0.20/0.65      (![W0: $i] : (aInteger0(smndt0(W0)) | (~aInteger0(W0)))),
% 0.20/0.65      inference(modus_ponens,[status(thm)],[39, 32])).
% 0.20/0.65  tff(41,plain,
% 0.20/0.65      (((~![W0: $i] : (aInteger0(smndt0(W0)) | (~aInteger0(W0)))) | (aInteger0(smndt0(xp)) | (~aInteger0(xp)))) <=> ((~![W0: $i] : (aInteger0(smndt0(W0)) | (~aInteger0(W0)))) | aInteger0(smndt0(xp)) | (~aInteger0(xp)))),
% 0.20/0.65      inference(rewrite,[status(thm)],[])).
% 0.20/0.65  tff(42,plain,
% 0.20/0.65      ((~![W0: $i] : (aInteger0(smndt0(W0)) | (~aInteger0(W0)))) | (aInteger0(smndt0(xp)) | (~aInteger0(xp)))),
% 0.20/0.65      inference(quant_inst,[status(thm)],[])).
% 0.20/0.65  tff(43,plain,
% 0.20/0.65      ((~![W0: $i] : (aInteger0(smndt0(W0)) | (~aInteger0(W0)))) | aInteger0(smndt0(xp)) | (~aInteger0(xp))),
% 0.20/0.65      inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.65  tff(44,plain,
% 0.20/0.65      (aInteger0(smndt0(xp))),
% 0.20/0.65      inference(unit_resolution,[status(thm)],[43, 40, 11])).
% 0.20/0.65  tff(45,plain,
% 0.20/0.65      (^[W0: $i] : refl(((~aInteger0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0)))))) <=> ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0)))))))),
% 0.20/0.65      inference(bind,[status(th)],[])).
% 0.20/0.65  tff(46,plain,
% 0.20/0.65      (![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0)))))) <=> ![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))),
% 0.20/0.65      inference(quant_intro,[status(thm)],[45])).
% 0.20/0.65  tff(47,plain,
% 0.20/0.65      (^[W0: $i] : rewrite(((~aInteger0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))) <=> ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0)))))))),
% 0.20/0.65      inference(bind,[status(th)],[])).
% 0.20/0.65  tff(48,plain,
% 0.20/0.65      (![W0: $i] : ((~aInteger0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))) <=> ![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))),
% 0.20/0.65      inference(quant_intro,[status(thm)],[47])).
% 0.20/0.65  tff(49,plain,
% 0.20/0.65      (![W0: $i] : ((~aInteger0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))) <=> ![W0: $i] : ((~aInteger0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))),
% 0.20/0.65      inference(rewrite,[status(thm)],[])).
% 0.20/0.65  tff(50,plain,
% 0.20/0.65      (^[W0: $i] : rewrite((aInteger0(W0) => ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))) <=> ((~aInteger0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))))),
% 0.20/0.65      inference(bind,[status(th)],[])).
% 0.20/0.65  tff(51,plain,
% 0.20/0.65      (![W0: $i] : (aInteger0(W0) => ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0)))) <=> ![W0: $i] : ((~aInteger0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))),
% 0.20/0.65      inference(quant_intro,[status(thm)],[50])).
% 0.20/0.65  tff(52,axiom,(![W0: $i] : (aInteger0(W0) => ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mAddZero')).
% 0.20/0.65  tff(53,plain,
% 0.20/0.65      (![W0: $i] : ((~aInteger0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))),
% 0.20/0.65      inference(modus_ponens,[status(thm)],[52, 51])).
% 0.20/0.65  tff(54,plain,
% 0.20/0.65      (![W0: $i] : ((~aInteger0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))),
% 0.20/0.65      inference(modus_ponens,[status(thm)],[53, 49])).
% 0.20/0.65  tff(55,plain,(
% 0.20/0.65      ![W0: $i] : ((~aInteger0(W0)) | ((sdtpldt0(W0, sz00) = W0) & (W0 = sdtpldt0(sz00, W0))))),
% 0.20/0.65      inference(skolemize,[status(sab)],[54])).
% 0.20/0.65  tff(56,plain,
% 0.20/0.65      (![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))),
% 0.20/0.65      inference(modus_ponens,[status(thm)],[55, 48])).
% 0.20/0.65  tff(57,plain,
% 0.20/0.65      (![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))),
% 0.20/0.65      inference(modus_ponens,[status(thm)],[56, 46])).
% 0.20/0.65  tff(58,plain,
% 0.20/0.65      (((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | ((~aInteger0(smndt0(xp))) | (~((~(smndt0(xp) = sdtpldt0(sz00, smndt0(xp)))) | (~(sdtpldt0(smndt0(xp), sz00) = smndt0(xp))))))) <=> ((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | (~aInteger0(smndt0(xp))) | (~((~(smndt0(xp) = sdtpldt0(sz00, smndt0(xp)))) | (~(sdtpldt0(smndt0(xp), sz00) = smndt0(xp))))))),
% 0.20/0.65      inference(rewrite,[status(thm)],[])).
% 0.20/0.65  tff(59,plain,
% 0.20/0.65      (((~aInteger0(smndt0(xp))) | (~((~(sdtpldt0(smndt0(xp), sz00) = smndt0(xp))) | (~(smndt0(xp) = sdtpldt0(sz00, smndt0(xp))))))) <=> ((~aInteger0(smndt0(xp))) | (~((~(smndt0(xp) = sdtpldt0(sz00, smndt0(xp)))) | (~(sdtpldt0(smndt0(xp), sz00) = smndt0(xp))))))),
% 0.20/0.65      inference(rewrite,[status(thm)],[])).
% 0.20/0.65  tff(60,plain,
% 0.20/0.65      (((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | ((~aInteger0(smndt0(xp))) | (~((~(sdtpldt0(smndt0(xp), sz00) = smndt0(xp))) | (~(smndt0(xp) = sdtpldt0(sz00, smndt0(xp)))))))) <=> ((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | ((~aInteger0(smndt0(xp))) | (~((~(smndt0(xp) = sdtpldt0(sz00, smndt0(xp)))) | (~(sdtpldt0(smndt0(xp), sz00) = smndt0(xp)))))))),
% 0.20/0.65      inference(monotonicity,[status(thm)],[59])).
% 0.20/0.65  tff(61,plain,
% 0.20/0.65      (((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | ((~aInteger0(smndt0(xp))) | (~((~(sdtpldt0(smndt0(xp), sz00) = smndt0(xp))) | (~(smndt0(xp) = sdtpldt0(sz00, smndt0(xp)))))))) <=> ((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | (~aInteger0(smndt0(xp))) | (~((~(smndt0(xp) = sdtpldt0(sz00, smndt0(xp)))) | (~(sdtpldt0(smndt0(xp), sz00) = smndt0(xp))))))),
% 0.20/0.65      inference(transitivity,[status(thm)],[60, 58])).
% 0.20/0.65  tff(62,plain,
% 0.20/0.65      ((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | ((~aInteger0(smndt0(xp))) | (~((~(sdtpldt0(smndt0(xp), sz00) = smndt0(xp))) | (~(smndt0(xp) = sdtpldt0(sz00, smndt0(xp)))))))),
% 0.20/0.65      inference(quant_inst,[status(thm)],[])).
% 0.20/0.65  tff(63,plain,
% 0.20/0.65      ((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | (~aInteger0(smndt0(xp))) | (~((~(smndt0(xp) = sdtpldt0(sz00, smndt0(xp)))) | (~(sdtpldt0(smndt0(xp), sz00) = smndt0(xp)))))),
% 0.20/0.65      inference(modus_ponens,[status(thm)],[62, 61])).
% 0.20/0.65  tff(64,plain,
% 0.20/0.65      (~((~(smndt0(xp) = sdtpldt0(sz00, smndt0(xp)))) | (~(sdtpldt0(smndt0(xp), sz00) = smndt0(xp))))),
% 0.20/0.65      inference(unit_resolution,[status(thm)],[63, 57, 44])).
% 0.20/0.65  tff(65,plain,
% 0.20/0.65      (((~(smndt0(xp) = sdtpldt0(sz00, smndt0(xp)))) | (~(sdtpldt0(smndt0(xp), sz00) = smndt0(xp)))) | (smndt0(xp) = sdtpldt0(sz00, smndt0(xp)))),
% 0.20/0.65      inference(tautology,[status(thm)],[])).
% 0.20/0.65  tff(66,plain,
% 0.20/0.65      (smndt0(xp) = sdtpldt0(sz00, smndt0(xp))),
% 0.20/0.65      inference(unit_resolution,[status(thm)],[65, 64])).
% 0.20/0.65  tff(67,plain,
% 0.20/0.65      (sdtpldt0(sz00, smndt0(xp)) = smndt0(xp)),
% 0.20/0.65      inference(symmetry,[status(thm)],[66])).
% 0.20/0.65  tff(68,plain,
% 0.20/0.65      (aInteger0(sz10) <=> aInteger0(sz10)),
% 0.20/0.65      inference(rewrite,[status(thm)],[])).
% 0.20/0.65  tff(69,axiom,(aInteger0(sz10)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mIntOne')).
% 0.20/0.65  tff(70,plain,
% 0.20/0.65      (aInteger0(sz10)),
% 0.20/0.65      inference(modus_ponens,[status(thm)],[69, 68])).
% 0.20/0.65  tff(71,plain,
% 0.20/0.65      (((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0))))))) | ((~aInteger0(sz10)) | (~((~(sdtpldt0(sz10, smndt0(sz10)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(sz10), sz10))))))) <=> ((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0))))))) | (~aInteger0(sz10)) | (~((~(sdtpldt0(sz10, smndt0(sz10)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(sz10), sz10))))))),
% 0.20/0.65      inference(rewrite,[status(thm)],[])).
% 0.20/0.65  tff(72,plain,
% 0.20/0.65      ((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0))))))) | ((~aInteger0(sz10)) | (~((~(sdtpldt0(sz10, smndt0(sz10)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(sz10), sz10))))))),
% 0.20/0.65      inference(quant_inst,[status(thm)],[])).
% 0.20/0.65  tff(73,plain,
% 0.20/0.65      ((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, smndt0(W0)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(W0), W0))))))) | (~aInteger0(sz10)) | (~((~(sdtpldt0(sz10, smndt0(sz10)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(sz10), sz10)))))),
% 0.20/0.65      inference(modus_ponens,[status(thm)],[72, 71])).
% 0.20/0.65  tff(74,plain,
% 0.20/0.65      (~((~(sdtpldt0(sz10, smndt0(sz10)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(sz10), sz10))))),
% 0.20/0.65      inference(unit_resolution,[status(thm)],[73, 70, 24])).
% 0.20/0.65  tff(75,plain,
% 0.20/0.65      (((~(sdtpldt0(sz10, smndt0(sz10)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(sz10), sz10)))) | (sz00 = sdtpldt0(smndt0(sz10), sz10))),
% 0.20/0.65      inference(tautology,[status(thm)],[])).
% 0.20/0.65  tff(76,plain,
% 0.20/0.65      (sz00 = sdtpldt0(smndt0(sz10), sz10)),
% 0.20/0.65      inference(unit_resolution,[status(thm)],[75, 74])).
% 0.20/0.65  tff(77,plain,
% 0.20/0.65      (sdtpldt0(sz00, smndt0(xp)) = sdtpldt0(sdtpldt0(smndt0(sz10), sz10), smndt0(xp))),
% 0.20/0.65      inference(monotonicity,[status(thm)],[76])).
% 0.20/0.65  tff(78,plain,
% 0.20/0.65      (sdtpldt0(sdtpldt0(smndt0(sz10), sz10), smndt0(xp)) = sdtpldt0(sz00, smndt0(xp))),
% 0.20/0.65      inference(symmetry,[status(thm)],[77])).
% 0.20/0.65  tff(79,plain,
% 0.20/0.65      (((~![W0: $i] : (aInteger0(smndt0(W0)) | (~aInteger0(W0)))) | (aInteger0(smndt0(sz10)) | (~aInteger0(sz10)))) <=> ((~![W0: $i] : (aInteger0(smndt0(W0)) | (~aInteger0(W0)))) | aInteger0(smndt0(sz10)) | (~aInteger0(sz10)))),
% 0.20/0.65      inference(rewrite,[status(thm)],[])).
% 0.20/0.65  tff(80,plain,
% 0.20/0.65      ((~![W0: $i] : (aInteger0(smndt0(W0)) | (~aInteger0(W0)))) | (aInteger0(smndt0(sz10)) | (~aInteger0(sz10)))),
% 0.20/0.65      inference(quant_inst,[status(thm)],[])).
% 0.20/0.65  tff(81,plain,
% 0.20/0.65      ((~![W0: $i] : (aInteger0(smndt0(W0)) | (~aInteger0(W0)))) | aInteger0(smndt0(sz10)) | (~aInteger0(sz10))),
% 0.20/0.65      inference(modus_ponens,[status(thm)],[80, 79])).
% 0.20/0.65  tff(82,plain,
% 0.20/0.65      (aInteger0(smndt0(sz10))),
% 0.20/0.65      inference(unit_resolution,[status(thm)],[81, 70, 40])).
% 0.20/0.65  tff(83,plain,
% 0.20/0.65      (^[W0: $i, W1: $i, W2: $i] : refl(((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0))) <=> ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0))))),
% 0.20/0.65      inference(bind,[status(th)],[])).
% 0.20/0.65  tff(84,plain,
% 0.20/0.65      (![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0))) <=> ![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))),
% 0.20/0.65      inference(quant_intro,[status(thm)],[83])).
% 0.20/0.65  tff(85,plain,
% 0.20/0.65      (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(trans(monotonicity(rewrite((aInteger0(W0) & aInteger0(W1) & aInteger0(W2)) <=> (~((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0))))), ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) <=> (~(~((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0))))))), rewrite((~(~((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0))))) <=> ((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))), ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) <=> ((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0))))), (((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | (sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2))) <=> (((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0))) | (sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2))))), rewrite((((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0))) | (sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2))) <=> ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))), (((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | (sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2))) <=> ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))))),
% 0.20/0.65      inference(bind,[status(th)],[])).
% 0.20/0.65  tff(86,plain,
% 0.20/0.65      (![W0: $i, W1: $i, W2: $i] : ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | (sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2))) <=> ![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))),
% 0.20/0.65      inference(quant_intro,[status(thm)],[85])).
% 0.20/0.65  tff(87,plain,
% 0.20/0.65      (![W0: $i, W1: $i, W2: $i] : ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | (sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2))) <=> ![W0: $i, W1: $i, W2: $i] : ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | (sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)))),
% 0.20/0.65      inference(rewrite,[status(thm)],[])).
% 0.20/0.65  tff(88,plain,
% 0.20/0.65      (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(rewrite(((aInteger0(W0) & aInteger0(W1)) & aInteger0(W2)) <=> (aInteger0(W0) & aInteger0(W1) & aInteger0(W2))), ((((aInteger0(W0) & aInteger0(W1)) & aInteger0(W2)) => (sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2))) <=> ((aInteger0(W0) & aInteger0(W1) & aInteger0(W2)) => (sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2))))), rewrite(((aInteger0(W0) & aInteger0(W1) & aInteger0(W2)) => (sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2))) <=> ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | (sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)))), ((((aInteger0(W0) & aInteger0(W1)) & aInteger0(W2)) => (sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2))) <=> ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | (sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)))))),
% 0.20/0.65      inference(bind,[status(th)],[])).
% 0.20/0.65  tff(89,plain,
% 0.20/0.65      (![W0: $i, W1: $i, W2: $i] : (((aInteger0(W0) & aInteger0(W1)) & aInteger0(W2)) => (sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2))) <=> ![W0: $i, W1: $i, W2: $i] : ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | (sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)))),
% 0.20/0.65      inference(quant_intro,[status(thm)],[88])).
% 0.20/0.65  tff(90,axiom,(![W0: $i, W1: $i, W2: $i] : (((aInteger0(W0) & aInteger0(W1)) & aInteger0(W2)) => (sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mAddAsso')).
% 0.20/0.65  tff(91,plain,
% 0.20/0.65      (![W0: $i, W1: $i, W2: $i] : ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | (sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)))),
% 0.20/0.65      inference(modus_ponens,[status(thm)],[90, 89])).
% 0.20/0.65  tff(92,plain,
% 0.20/0.65      (![W0: $i, W1: $i, W2: $i] : ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | (sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)))),
% 0.20/0.65      inference(modus_ponens,[status(thm)],[91, 87])).
% 0.20/0.65  tff(93,plain,(
% 0.20/0.65      ![W0: $i, W1: $i, W2: $i] : ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | (sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)))),
% 0.20/0.65      inference(skolemize,[status(sab)],[92])).
% 0.20/0.65  tff(94,plain,
% 0.20/0.65      (![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))),
% 0.20/0.65      inference(modus_ponens,[status(thm)],[93, 86])).
% 0.20/0.65  tff(95,plain,
% 0.20/0.65      (![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))),
% 0.20/0.65      inference(modus_ponens,[status(thm)],[94, 84])).
% 0.20/0.65  tff(96,plain,
% 0.20/0.65      (((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | ((sdtpldt0(smndt0(sz10), sdtpldt0(sz10, smndt0(xp))) = sdtpldt0(sdtpldt0(smndt0(sz10), sz10), smndt0(xp))) | (~aInteger0(smndt0(xp))) | (~aInteger0(sz10)) | (~aInteger0(smndt0(sz10))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | (sdtpldt0(smndt0(sz10), sdtpldt0(sz10, smndt0(xp))) = sdtpldt0(sdtpldt0(smndt0(sz10), sz10), smndt0(xp))) | (~aInteger0(smndt0(xp))) | (~aInteger0(sz10)) | (~aInteger0(smndt0(sz10))))),
% 0.20/0.65      inference(rewrite,[status(thm)],[])).
% 0.20/0.65  tff(97,plain,
% 0.20/0.65      ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | ((sdtpldt0(smndt0(sz10), sdtpldt0(sz10, smndt0(xp))) = sdtpldt0(sdtpldt0(smndt0(sz10), sz10), smndt0(xp))) | (~aInteger0(smndt0(xp))) | (~aInteger0(sz10)) | (~aInteger0(smndt0(sz10))))),
% 0.20/0.66      inference(quant_inst,[status(thm)],[])).
% 0.20/0.66  tff(98,plain,
% 0.20/0.66      ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | (sdtpldt0(smndt0(sz10), sdtpldt0(sz10, smndt0(xp))) = sdtpldt0(sdtpldt0(smndt0(sz10), sz10), smndt0(xp))) | (~aInteger0(smndt0(xp))) | (~aInteger0(sz10)) | (~aInteger0(smndt0(sz10)))),
% 0.20/0.66      inference(modus_ponens,[status(thm)],[97, 96])).
% 0.20/0.66  tff(99,plain,
% 0.20/0.66      (sdtpldt0(smndt0(sz10), sdtpldt0(sz10, smndt0(xp))) = sdtpldt0(sdtpldt0(smndt0(sz10), sz10), smndt0(xp))),
% 0.20/0.66      inference(unit_resolution,[status(thm)],[98, 70, 95, 44, 82])).
% 0.20/0.66  tff(100,plain,
% 0.20/0.66      ((sdtpldt0(sz10, smndt0(xp)) = smndt0(sz10)) <=> (sdtpldt0(sz10, smndt0(xp)) = smndt0(sz10))),
% 0.20/0.66      inference(rewrite,[status(thm)],[])).
% 0.20/0.66  tff(101,axiom,(~((~(sdtpldt0(sz10, xp) = smndt0(sz10))) | (~(sdtpldt0(sz10, smndt0(xp)) = smndt0(sz10))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__')).
% 0.20/0.66  tff(102,plain,
% 0.20/0.66      (sdtpldt0(sz10, smndt0(xp)) = smndt0(sz10)),
% 0.20/0.66      inference(or_elim,[status(thm)],[101])).
% 0.20/0.66  tff(103,plain,
% 0.20/0.66      (sdtpldt0(sz10, smndt0(xp)) = smndt0(sz10)),
% 0.20/0.66      inference(modus_ponens,[status(thm)],[102, 100])).
% 0.20/0.66  tff(104,plain,
% 0.20/0.66      ((sdtpldt0(sz10, xp) = smndt0(sz10)) <=> (sdtpldt0(sz10, xp) = smndt0(sz10))),
% 0.20/0.66      inference(rewrite,[status(thm)],[])).
% 0.20/0.66  tff(105,plain,
% 0.20/0.66      (sdtpldt0(sz10, xp) = smndt0(sz10)),
% 0.20/0.66      inference(or_elim,[status(thm)],[101])).
% 0.20/0.66  tff(106,plain,
% 0.20/0.66      (sdtpldt0(sz10, xp) = smndt0(sz10)),
% 0.20/0.66      inference(modus_ponens,[status(thm)],[105, 104])).
% 0.20/0.66  tff(107,plain,
% 0.20/0.66      (smndt0(sz10) = sdtpldt0(sz10, xp)),
% 0.20/0.66      inference(symmetry,[status(thm)],[106])).
% 0.20/0.66  tff(108,plain,
% 0.20/0.66      (sdtpldt0(smndt0(sz10), sdtpldt0(sz10, smndt0(xp))) = sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10))),
% 0.20/0.66      inference(monotonicity,[status(thm)],[107, 103])).
% 0.20/0.66  tff(109,plain,
% 0.20/0.66      (sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)) = sdtpldt0(smndt0(sz10), sdtpldt0(sz10, smndt0(xp)))),
% 0.20/0.66      inference(symmetry,[status(thm)],[108])).
% 0.20/0.66  tff(110,plain,
% 0.20/0.66      (sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)) = smndt0(xp)),
% 0.20/0.66      inference(transitivity,[status(thm)],[109, 99, 78, 67])).
% 0.20/0.66  tff(111,plain,
% 0.20/0.66      (((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | ((~aInteger0(xp)) | (~((~(sdtpldt0(xp, sz00) = xp)) | (~(xp = sdtpldt0(sz00, xp))))))) <=> ((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | (~aInteger0(xp)) | (~((~(sdtpldt0(xp, sz00) = xp)) | (~(xp = sdtpldt0(sz00, xp))))))),
% 0.20/0.66      inference(rewrite,[status(thm)],[])).
% 0.20/0.66  tff(112,plain,
% 0.20/0.66      ((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | ((~aInteger0(xp)) | (~((~(sdtpldt0(xp, sz00) = xp)) | (~(xp = sdtpldt0(sz00, xp))))))),
% 0.20/0.66      inference(quant_inst,[status(thm)],[])).
% 0.20/0.66  tff(113,plain,
% 0.20/0.66      ((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | (~aInteger0(xp)) | (~((~(sdtpldt0(xp, sz00) = xp)) | (~(xp = sdtpldt0(sz00, xp)))))),
% 0.20/0.66      inference(modus_ponens,[status(thm)],[112, 111])).
% 0.20/0.66  tff(114,plain,
% 0.20/0.66      (~((~(sdtpldt0(xp, sz00) = xp)) | (~(xp = sdtpldt0(sz00, xp))))),
% 0.20/0.66      inference(unit_resolution,[status(thm)],[113, 57, 11])).
% 0.20/0.66  tff(115,plain,
% 0.20/0.66      (((~(sdtpldt0(xp, sz00) = xp)) | (~(xp = sdtpldt0(sz00, xp)))) | (xp = sdtpldt0(sz00, xp))),
% 0.20/0.66      inference(tautology,[status(thm)],[])).
% 0.20/0.66  tff(116,plain,
% 0.20/0.66      (xp = sdtpldt0(sz00, xp)),
% 0.20/0.66      inference(unit_resolution,[status(thm)],[115, 114])).
% 0.20/0.66  tff(117,plain,
% 0.20/0.66      (sdtpldt0(sz00, xp) = xp),
% 0.20/0.66      inference(symmetry,[status(thm)],[116])).
% 0.20/0.66  tff(118,plain,
% 0.20/0.66      (sdtpldt0(sz00, xp) = sdtpldt0(sdtpldt0(smndt0(sz10), sz10), xp)),
% 0.20/0.66      inference(monotonicity,[status(thm)],[76])).
% 0.20/0.66  tff(119,plain,
% 0.20/0.66      (sdtpldt0(sdtpldt0(smndt0(sz10), sz10), xp) = sdtpldt0(sz00, xp)),
% 0.20/0.66      inference(symmetry,[status(thm)],[118])).
% 0.20/0.66  tff(120,plain,
% 0.20/0.66      (((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | ((~aInteger0(sz10)) | (~aInteger0(smndt0(sz10))) | (sdtpldt0(smndt0(sz10), sdtpldt0(sz10, xp)) = sdtpldt0(sdtpldt0(smndt0(sz10), sz10), xp)) | (~aInteger0(xp)))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | (~aInteger0(sz10)) | (~aInteger0(smndt0(sz10))) | (sdtpldt0(smndt0(sz10), sdtpldt0(sz10, xp)) = sdtpldt0(sdtpldt0(smndt0(sz10), sz10), xp)) | (~aInteger0(xp)))),
% 0.20/0.66      inference(rewrite,[status(thm)],[])).
% 0.20/0.66  tff(121,plain,
% 0.20/0.66      (((sdtpldt0(smndt0(sz10), sdtpldt0(sz10, xp)) = sdtpldt0(sdtpldt0(smndt0(sz10), sz10), xp)) | (~aInteger0(xp)) | (~aInteger0(sz10)) | (~aInteger0(smndt0(sz10)))) <=> ((~aInteger0(sz10)) | (~aInteger0(smndt0(sz10))) | (sdtpldt0(smndt0(sz10), sdtpldt0(sz10, xp)) = sdtpldt0(sdtpldt0(smndt0(sz10), sz10), xp)) | (~aInteger0(xp)))),
% 0.20/0.66      inference(rewrite,[status(thm)],[])).
% 0.20/0.66  tff(122,plain,
% 0.20/0.66      (((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | ((sdtpldt0(smndt0(sz10), sdtpldt0(sz10, xp)) = sdtpldt0(sdtpldt0(smndt0(sz10), sz10), xp)) | (~aInteger0(xp)) | (~aInteger0(sz10)) | (~aInteger0(smndt0(sz10))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | ((~aInteger0(sz10)) | (~aInteger0(smndt0(sz10))) | (sdtpldt0(smndt0(sz10), sdtpldt0(sz10, xp)) = sdtpldt0(sdtpldt0(smndt0(sz10), sz10), xp)) | (~aInteger0(xp))))),
% 0.20/0.66      inference(monotonicity,[status(thm)],[121])).
% 0.20/0.66  tff(123,plain,
% 0.20/0.66      (((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | ((sdtpldt0(smndt0(sz10), sdtpldt0(sz10, xp)) = sdtpldt0(sdtpldt0(smndt0(sz10), sz10), xp)) | (~aInteger0(xp)) | (~aInteger0(sz10)) | (~aInteger0(smndt0(sz10))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | (~aInteger0(sz10)) | (~aInteger0(smndt0(sz10))) | (sdtpldt0(smndt0(sz10), sdtpldt0(sz10, xp)) = sdtpldt0(sdtpldt0(smndt0(sz10), sz10), xp)) | (~aInteger0(xp)))),
% 0.20/0.66      inference(transitivity,[status(thm)],[122, 120])).
% 0.20/0.66  tff(124,plain,
% 0.20/0.66      ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | ((sdtpldt0(smndt0(sz10), sdtpldt0(sz10, xp)) = sdtpldt0(sdtpldt0(smndt0(sz10), sz10), xp)) | (~aInteger0(xp)) | (~aInteger0(sz10)) | (~aInteger0(smndt0(sz10))))),
% 0.20/0.66      inference(quant_inst,[status(thm)],[])).
% 0.20/0.66  tff(125,plain,
% 0.20/0.66      ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | (~aInteger0(sz10)) | (~aInteger0(smndt0(sz10))) | (sdtpldt0(smndt0(sz10), sdtpldt0(sz10, xp)) = sdtpldt0(sdtpldt0(smndt0(sz10), sz10), xp)) | (~aInteger0(xp))),
% 0.20/0.66      inference(modus_ponens,[status(thm)],[124, 123])).
% 0.20/0.66  tff(126,plain,
% 0.20/0.66      (sdtpldt0(smndt0(sz10), sdtpldt0(sz10, xp)) = sdtpldt0(sdtpldt0(smndt0(sz10), sz10), xp)),
% 0.20/0.66      inference(unit_resolution,[status(thm)],[125, 70, 95, 11, 82])).
% 0.20/0.66  tff(127,plain,
% 0.20/0.66      (sdtpldt0(smndt0(sz10), sdtpldt0(sz10, xp)) = sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10))),
% 0.20/0.66      inference(monotonicity,[status(thm)],[107, 106])).
% 0.20/0.66  tff(128,plain,
% 0.20/0.66      (sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)) = sdtpldt0(smndt0(sz10), sdtpldt0(sz10, xp))),
% 0.20/0.66      inference(symmetry,[status(thm)],[127])).
% 0.20/0.66  tff(129,plain,
% 0.20/0.66      (sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)) = xp),
% 0.20/0.66      inference(transitivity,[status(thm)],[128, 126, 119, 117])).
% 0.20/0.66  tff(130,plain,
% 0.20/0.66      (sdtpldt0(sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)), sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10))) = sdtpldt0(xp, smndt0(xp))),
% 0.20/0.66      inference(monotonicity,[status(thm)],[129, 110])).
% 0.20/0.66  tff(131,plain,
% 0.20/0.66      (sdtpldt0(sdtpldt0(smndt0(sz10), sz10), smndt0(xp)) = sdtpldt0(smndt0(sz10), sdtpldt0(sz10, smndt0(xp)))),
% 0.20/0.66      inference(symmetry,[status(thm)],[99])).
% 0.20/0.66  tff(132,plain,
% 0.20/0.66      (smndt0(xp) = sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10))),
% 0.20/0.66      inference(transitivity,[status(thm)],[66, 77, 131, 108])).
% 0.20/0.66  tff(133,plain,
% 0.20/0.66      (sdtpldt0(smndt0(xp), smndt0(xp)) = sdtpldt0(sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)), sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)))),
% 0.20/0.66      inference(monotonicity,[status(thm)],[132, 132])).
% 0.20/0.66  tff(134,plain,
% 0.20/0.66      (^[W0: $i] : refl(((~aInteger0(W0)) | (~((~(sdtasdt0(W0, sz10) = W0)) | (~(W0 = sdtasdt0(sz10, W0)))))) <=> ((~aInteger0(W0)) | (~((~(sdtasdt0(W0, sz10) = W0)) | (~(W0 = sdtasdt0(sz10, W0)))))))),
% 0.20/0.66      inference(bind,[status(th)],[])).
% 0.20/0.66  tff(135,plain,
% 0.20/0.66      (![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtasdt0(W0, sz10) = W0)) | (~(W0 = sdtasdt0(sz10, W0)))))) <=> ![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtasdt0(W0, sz10) = W0)) | (~(W0 = sdtasdt0(sz10, W0))))))),
% 0.20/0.66      inference(quant_intro,[status(thm)],[134])).
% 0.20/0.66  tff(136,plain,
% 0.20/0.66      (^[W0: $i] : rewrite(((~aInteger0(W0)) | ((sdtasdt0(W0, sz10) = W0) & (W0 = sdtasdt0(sz10, W0)))) <=> ((~aInteger0(W0)) | (~((~(sdtasdt0(W0, sz10) = W0)) | (~(W0 = sdtasdt0(sz10, W0)))))))),
% 0.20/0.66      inference(bind,[status(th)],[])).
% 0.20/0.66  tff(137,plain,
% 0.20/0.66      (![W0: $i] : ((~aInteger0(W0)) | ((sdtasdt0(W0, sz10) = W0) & (W0 = sdtasdt0(sz10, W0)))) <=> ![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtasdt0(W0, sz10) = W0)) | (~(W0 = sdtasdt0(sz10, W0))))))),
% 0.20/0.66      inference(quant_intro,[status(thm)],[136])).
% 0.20/0.66  tff(138,plain,
% 0.20/0.66      (![W0: $i] : ((~aInteger0(W0)) | ((sdtasdt0(W0, sz10) = W0) & (W0 = sdtasdt0(sz10, W0)))) <=> ![W0: $i] : ((~aInteger0(W0)) | ((sdtasdt0(W0, sz10) = W0) & (W0 = sdtasdt0(sz10, W0))))),
% 0.20/0.66      inference(rewrite,[status(thm)],[])).
% 0.20/0.66  tff(139,plain,
% 0.20/0.66      (^[W0: $i] : rewrite((aInteger0(W0) => ((sdtasdt0(W0, sz10) = W0) & (W0 = sdtasdt0(sz10, W0)))) <=> ((~aInteger0(W0)) | ((sdtasdt0(W0, sz10) = W0) & (W0 = sdtasdt0(sz10, W0)))))),
% 0.20/0.66      inference(bind,[status(th)],[])).
% 0.20/0.66  tff(140,plain,
% 0.20/0.66      (![W0: $i] : (aInteger0(W0) => ((sdtasdt0(W0, sz10) = W0) & (W0 = sdtasdt0(sz10, W0)))) <=> ![W0: $i] : ((~aInteger0(W0)) | ((sdtasdt0(W0, sz10) = W0) & (W0 = sdtasdt0(sz10, W0))))),
% 0.20/0.66      inference(quant_intro,[status(thm)],[139])).
% 0.20/0.66  tff(141,axiom,(![W0: $i] : (aInteger0(W0) => ((sdtasdt0(W0, sz10) = W0) & (W0 = sdtasdt0(sz10, W0))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mMulOne')).
% 0.20/0.66  tff(142,plain,
% 0.20/0.66      (![W0: $i] : ((~aInteger0(W0)) | ((sdtasdt0(W0, sz10) = W0) & (W0 = sdtasdt0(sz10, W0))))),
% 0.20/0.66      inference(modus_ponens,[status(thm)],[141, 140])).
% 0.20/0.66  tff(143,plain,
% 0.20/0.66      (![W0: $i] : ((~aInteger0(W0)) | ((sdtasdt0(W0, sz10) = W0) & (W0 = sdtasdt0(sz10, W0))))),
% 0.20/0.66      inference(modus_ponens,[status(thm)],[142, 138])).
% 0.20/0.66  tff(144,plain,(
% 0.20/0.66      ![W0: $i] : ((~aInteger0(W0)) | ((sdtasdt0(W0, sz10) = W0) & (W0 = sdtasdt0(sz10, W0))))),
% 0.20/0.66      inference(skolemize,[status(sab)],[143])).
% 0.20/0.66  tff(145,plain,
% 0.20/0.66      (![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtasdt0(W0, sz10) = W0)) | (~(W0 = sdtasdt0(sz10, W0))))))),
% 0.20/0.66      inference(modus_ponens,[status(thm)],[144, 137])).
% 0.20/0.66  tff(146,plain,
% 0.20/0.66      (![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtasdt0(W0, sz10) = W0)) | (~(W0 = sdtasdt0(sz10, W0))))))),
% 0.20/0.66      inference(modus_ponens,[status(thm)],[145, 135])).
% 0.20/0.66  tff(147,plain,
% 0.20/0.66      (((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtasdt0(W0, sz10) = W0)) | (~(W0 = sdtasdt0(sz10, W0))))))) | ((~aInteger0(smndt0(xp))) | (~((~(sdtasdt0(smndt0(xp), sz10) = smndt0(xp))) | (~(smndt0(xp) = sdtasdt0(sz10, smndt0(xp)))))))) <=> ((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtasdt0(W0, sz10) = W0)) | (~(W0 = sdtasdt0(sz10, W0))))))) | (~aInteger0(smndt0(xp))) | (~((~(sdtasdt0(smndt0(xp), sz10) = smndt0(xp))) | (~(smndt0(xp) = sdtasdt0(sz10, smndt0(xp)))))))),
% 0.20/0.66      inference(rewrite,[status(thm)],[])).
% 0.20/0.66  tff(148,plain,
% 0.20/0.66      ((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtasdt0(W0, sz10) = W0)) | (~(W0 = sdtasdt0(sz10, W0))))))) | ((~aInteger0(smndt0(xp))) | (~((~(sdtasdt0(smndt0(xp), sz10) = smndt0(xp))) | (~(smndt0(xp) = sdtasdt0(sz10, smndt0(xp)))))))),
% 0.20/0.66      inference(quant_inst,[status(thm)],[])).
% 0.20/0.66  tff(149,plain,
% 0.20/0.66      ((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtasdt0(W0, sz10) = W0)) | (~(W0 = sdtasdt0(sz10, W0))))))) | (~aInteger0(smndt0(xp))) | (~((~(sdtasdt0(smndt0(xp), sz10) = smndt0(xp))) | (~(smndt0(xp) = sdtasdt0(sz10, smndt0(xp))))))),
% 0.20/0.66      inference(modus_ponens,[status(thm)],[148, 147])).
% 0.20/0.66  tff(150,plain,
% 0.20/0.66      (~((~(sdtasdt0(smndt0(xp), sz10) = smndt0(xp))) | (~(smndt0(xp) = sdtasdt0(sz10, smndt0(xp)))))),
% 0.20/0.66      inference(unit_resolution,[status(thm)],[149, 146, 44])).
% 0.20/0.66  tff(151,plain,
% 0.20/0.66      (((~(sdtasdt0(smndt0(xp), sz10) = smndt0(xp))) | (~(smndt0(xp) = sdtasdt0(sz10, smndt0(xp))))) | (smndt0(xp) = sdtasdt0(sz10, smndt0(xp)))),
% 0.20/0.66      inference(tautology,[status(thm)],[])).
% 0.20/0.66  tff(152,plain,
% 0.20/0.66      (smndt0(xp) = sdtasdt0(sz10, smndt0(xp))),
% 0.20/0.66      inference(unit_resolution,[status(thm)],[151, 150])).
% 0.20/0.66  tff(153,plain,
% 0.20/0.66      (sdtasdt0(sz10, smndt0(xp)) = smndt0(xp)),
% 0.20/0.66      inference(symmetry,[status(thm)],[152])).
% 0.20/0.66  tff(154,plain,
% 0.20/0.66      (sdtpldt0(sdtasdt0(sz10, smndt0(xp)), sdtasdt0(sz10, smndt0(xp))) = sdtpldt0(smndt0(xp), smndt0(xp))),
% 0.20/0.66      inference(monotonicity,[status(thm)],[153, 153])).
% 0.20/0.66  tff(155,plain,
% 0.20/0.66      (^[W0: $i, W1: $i, W2: $i] : refl(((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)) | (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2))))))) <=> ((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)) | (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2))))))))),
% 0.20/0.66      inference(bind,[status(th)],[])).
% 0.20/0.66  tff(156,plain,
% 0.20/0.66      (![W0: $i, W1: $i, W2: $i] : ((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)) | (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2))))))) <=> ![W0: $i, W1: $i, W2: $i] : ((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)) | (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2)))))))),
% 0.20/0.66      inference(quant_intro,[status(thm)],[155])).
% 0.20/0.66  tff(157,plain,
% 0.20/0.66      (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(trans(monotonicity(rewrite((aInteger0(W0) & aInteger0(W1) & aInteger0(W2)) <=> (~((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0))))), ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) <=> (~(~((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0))))))), rewrite((~(~((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0))))) <=> ((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))), ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) <=> ((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0))))), rewrite(((sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2)))) <=> (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2))))))), (((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | ((sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2))))) <=> (((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0))) | (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2))))))))), rewrite((((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0))) | (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2))))))) <=> ((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)) | (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2)))))))), (((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | ((sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2))))) <=> ((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)) | (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2)))))))))),
% 0.20/0.66      inference(bind,[status(th)],[])).
% 0.20/0.66  tff(158,plain,
% 0.20/0.66      (![W0: $i, W1: $i, W2: $i] : ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | ((sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2))))) <=> ![W0: $i, W1: $i, W2: $i] : ((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)) | (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2)))))))),
% 0.20/0.66      inference(quant_intro,[status(thm)],[157])).
% 0.20/0.66  tff(159,plain,
% 0.20/0.66      (![W0: $i, W1: $i, W2: $i] : ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | ((sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2))))) <=> ![W0: $i, W1: $i, W2: $i] : ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | ((sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2)))))),
% 0.20/0.66      inference(rewrite,[status(thm)],[])).
% 0.20/0.66  tff(160,plain,
% 0.20/0.66      (^[W0: $i, W1: $i, W2: $i] : trans(monotonicity(rewrite(((aInteger0(W0) & aInteger0(W1)) & aInteger0(W2)) <=> (aInteger0(W0) & aInteger0(W1) & aInteger0(W2))), ((((aInteger0(W0) & aInteger0(W1)) & aInteger0(W2)) => ((sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2))))) <=> ((aInteger0(W0) & aInteger0(W1) & aInteger0(W2)) => ((sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2))))))), rewrite(((aInteger0(W0) & aInteger0(W1) & aInteger0(W2)) => ((sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2))))) <=> ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | ((sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2)))))), ((((aInteger0(W0) & aInteger0(W1)) & aInteger0(W2)) => ((sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2))))) <=> ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | ((sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2)))))))),
% 0.20/0.66      inference(bind,[status(th)],[])).
% 0.20/0.66  tff(161,plain,
% 0.20/0.66      (![W0: $i, W1: $i, W2: $i] : (((aInteger0(W0) & aInteger0(W1)) & aInteger0(W2)) => ((sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2))))) <=> ![W0: $i, W1: $i, W2: $i] : ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | ((sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2)))))),
% 0.20/0.66      inference(quant_intro,[status(thm)],[160])).
% 0.20/0.66  tff(162,axiom,(![W0: $i, W1: $i, W2: $i] : (((aInteger0(W0) & aInteger0(W1)) & aInteger0(W2)) => ((sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mDistrib')).
% 0.20/0.66  tff(163,plain,
% 0.20/0.66      (![W0: $i, W1: $i, W2: $i] : ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | ((sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2)))))),
% 0.20/0.66      inference(modus_ponens,[status(thm)],[162, 161])).
% 0.20/0.66  tff(164,plain,
% 0.20/0.66      (![W0: $i, W1: $i, W2: $i] : ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | ((sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2)))))),
% 0.20/0.66      inference(modus_ponens,[status(thm)],[163, 159])).
% 0.20/0.66  tff(165,plain,(
% 0.20/0.66      ![W0: $i, W1: $i, W2: $i] : ((~(aInteger0(W0) & aInteger0(W1) & aInteger0(W2))) | ((sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2))) & (sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2)))))),
% 0.20/0.66      inference(skolemize,[status(sab)],[164])).
% 0.20/0.66  tff(166,plain,
% 0.20/0.66      (![W0: $i, W1: $i, W2: $i] : ((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)) | (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2)))))))),
% 0.20/0.66      inference(modus_ponens,[status(thm)],[165, 158])).
% 0.20/0.66  tff(167,plain,
% 0.20/0.66      (![W0: $i, W1: $i, W2: $i] : ((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)) | (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2)))))))),
% 0.20/0.66      inference(modus_ponens,[status(thm)],[166, 156])).
% 0.20/0.66  tff(168,plain,
% 0.20/0.66      (((~![W0: $i, W1: $i, W2: $i] : ((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)) | (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2)))))))) | ((~aInteger0(smndt0(xp))) | (~aInteger0(sz10)) | (~((~(sdtasdt0(sz10, sdtpldt0(sz10, smndt0(xp))) = sdtpldt0(sdtasdt0(sz10, sz10), sdtasdt0(sz10, smndt0(xp))))) | (~(sdtasdt0(sdtpldt0(sz10, sz10), smndt0(xp)) = sdtpldt0(sdtasdt0(sz10, smndt0(xp)), sdtasdt0(sz10, smndt0(xp))))))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)) | (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2)))))))) | (~aInteger0(smndt0(xp))) | (~aInteger0(sz10)) | (~((~(sdtasdt0(sz10, sdtpldt0(sz10, smndt0(xp))) = sdtpldt0(sdtasdt0(sz10, sz10), sdtasdt0(sz10, smndt0(xp))))) | (~(sdtasdt0(sdtpldt0(sz10, sz10), smndt0(xp)) = sdtpldt0(sdtasdt0(sz10, smndt0(xp)), sdtasdt0(sz10, smndt0(xp))))))))),
% 0.20/0.66      inference(rewrite,[status(thm)],[])).
% 0.20/0.66  tff(169,plain,
% 0.20/0.66      (((~aInteger0(smndt0(xp))) | (~aInteger0(sz10)) | (~aInteger0(sz10)) | (~((~(sdtasdt0(sz10, sdtpldt0(sz10, smndt0(xp))) = sdtpldt0(sdtasdt0(sz10, sz10), sdtasdt0(sz10, smndt0(xp))))) | (~(sdtasdt0(sdtpldt0(sz10, sz10), smndt0(xp)) = sdtpldt0(sdtasdt0(sz10, smndt0(xp)), sdtasdt0(sz10, smndt0(xp)))))))) <=> ((~aInteger0(smndt0(xp))) | (~aInteger0(sz10)) | (~((~(sdtasdt0(sz10, sdtpldt0(sz10, smndt0(xp))) = sdtpldt0(sdtasdt0(sz10, sz10), sdtasdt0(sz10, smndt0(xp))))) | (~(sdtasdt0(sdtpldt0(sz10, sz10), smndt0(xp)) = sdtpldt0(sdtasdt0(sz10, smndt0(xp)), sdtasdt0(sz10, smndt0(xp))))))))),
% 0.20/0.66      inference(rewrite,[status(thm)],[])).
% 0.20/0.66  tff(170,plain,
% 0.20/0.66      ((~((~(sdtasdt0(sz10, sdtpldt0(sz10, smndt0(xp))) = sdtpldt0(sdtasdt0(sz10, sz10), sdtasdt0(sz10, smndt0(xp))))) | (~(sdtasdt0(sdtpldt0(sz10, sz10), smndt0(xp)) = sdtpldt0(sdtasdt0(sz10, smndt0(xp)), sdtasdt0(sz10, smndt0(xp))))))) <=> (~((~(sdtasdt0(sz10, sdtpldt0(sz10, smndt0(xp))) = sdtpldt0(sdtasdt0(sz10, sz10), sdtasdt0(sz10, smndt0(xp))))) | (~(sdtasdt0(sdtpldt0(sz10, sz10), smndt0(xp)) = sdtpldt0(sdtasdt0(sz10, smndt0(xp)), sdtasdt0(sz10, smndt0(xp)))))))),
% 0.20/0.66      inference(rewrite,[status(thm)],[])).
% 0.20/0.66  tff(171,plain,
% 0.20/0.66      (((~aInteger0(smndt0(xp))) | (~aInteger0(sz10)) | (~aInteger0(sz10)) | (~((~(sdtasdt0(sz10, sdtpldt0(sz10, smndt0(xp))) = sdtpldt0(sdtasdt0(sz10, sz10), sdtasdt0(sz10, smndt0(xp))))) | (~(sdtasdt0(sdtpldt0(sz10, sz10), smndt0(xp)) = sdtpldt0(sdtasdt0(sz10, smndt0(xp)), sdtasdt0(sz10, smndt0(xp)))))))) <=> ((~aInteger0(smndt0(xp))) | (~aInteger0(sz10)) | (~aInteger0(sz10)) | (~((~(sdtasdt0(sz10, sdtpldt0(sz10, smndt0(xp))) = sdtpldt0(sdtasdt0(sz10, sz10), sdtasdt0(sz10, smndt0(xp))))) | (~(sdtasdt0(sdtpldt0(sz10, sz10), smndt0(xp)) = sdtpldt0(sdtasdt0(sz10, smndt0(xp)), sdtasdt0(sz10, smndt0(xp))))))))),
% 0.20/0.66      inference(monotonicity,[status(thm)],[170])).
% 0.20/0.66  tff(172,plain,
% 0.20/0.66      (((~aInteger0(smndt0(xp))) | (~aInteger0(sz10)) | (~aInteger0(sz10)) | (~((~(sdtasdt0(sz10, sdtpldt0(sz10, smndt0(xp))) = sdtpldt0(sdtasdt0(sz10, sz10), sdtasdt0(sz10, smndt0(xp))))) | (~(sdtasdt0(sdtpldt0(sz10, sz10), smndt0(xp)) = sdtpldt0(sdtasdt0(sz10, smndt0(xp)), sdtasdt0(sz10, smndt0(xp)))))))) <=> ((~aInteger0(smndt0(xp))) | (~aInteger0(sz10)) | (~((~(sdtasdt0(sz10, sdtpldt0(sz10, smndt0(xp))) = sdtpldt0(sdtasdt0(sz10, sz10), sdtasdt0(sz10, smndt0(xp))))) | (~(sdtasdt0(sdtpldt0(sz10, sz10), smndt0(xp)) = sdtpldt0(sdtasdt0(sz10, smndt0(xp)), sdtasdt0(sz10, smndt0(xp))))))))),
% 0.20/0.66      inference(transitivity,[status(thm)],[171, 169])).
% 0.20/0.66  tff(173,plain,
% 0.20/0.66      (((~![W0: $i, W1: $i, W2: $i] : ((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)) | (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2)))))))) | ((~aInteger0(smndt0(xp))) | (~aInteger0(sz10)) | (~aInteger0(sz10)) | (~((~(sdtasdt0(sz10, sdtpldt0(sz10, smndt0(xp))) = sdtpldt0(sdtasdt0(sz10, sz10), sdtasdt0(sz10, smndt0(xp))))) | (~(sdtasdt0(sdtpldt0(sz10, sz10), smndt0(xp)) = sdtpldt0(sdtasdt0(sz10, smndt0(xp)), sdtasdt0(sz10, smndt0(xp))))))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)) | (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2)))))))) | ((~aInteger0(smndt0(xp))) | (~aInteger0(sz10)) | (~((~(sdtasdt0(sz10, sdtpldt0(sz10, smndt0(xp))) = sdtpldt0(sdtasdt0(sz10, sz10), sdtasdt0(sz10, smndt0(xp))))) | (~(sdtasdt0(sdtpldt0(sz10, sz10), smndt0(xp)) = sdtpldt0(sdtasdt0(sz10, smndt0(xp)), sdtasdt0(sz10, smndt0(xp)))))))))),
% 0.20/0.66      inference(monotonicity,[status(thm)],[172])).
% 0.20/0.66  tff(174,plain,
% 0.20/0.66      (((~![W0: $i, W1: $i, W2: $i] : ((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)) | (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2)))))))) | ((~aInteger0(smndt0(xp))) | (~aInteger0(sz10)) | (~aInteger0(sz10)) | (~((~(sdtasdt0(sz10, sdtpldt0(sz10, smndt0(xp))) = sdtpldt0(sdtasdt0(sz10, sz10), sdtasdt0(sz10, smndt0(xp))))) | (~(sdtasdt0(sdtpldt0(sz10, sz10), smndt0(xp)) = sdtpldt0(sdtasdt0(sz10, smndt0(xp)), sdtasdt0(sz10, smndt0(xp))))))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)) | (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2)))))))) | (~aInteger0(smndt0(xp))) | (~aInteger0(sz10)) | (~((~(sdtasdt0(sz10, sdtpldt0(sz10, smndt0(xp))) = sdtpldt0(sdtasdt0(sz10, sz10), sdtasdt0(sz10, smndt0(xp))))) | (~(sdtasdt0(sdtpldt0(sz10, sz10), smndt0(xp)) = sdtpldt0(sdtasdt0(sz10, smndt0(xp)), sdtasdt0(sz10, smndt0(xp))))))))),
% 0.20/0.66      inference(transitivity,[status(thm)],[173, 168])).
% 0.20/0.66  tff(175,plain,
% 0.20/0.66      ((~![W0: $i, W1: $i, W2: $i] : ((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)) | (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2)))))))) | ((~aInteger0(smndt0(xp))) | (~aInteger0(sz10)) | (~aInteger0(sz10)) | (~((~(sdtasdt0(sz10, sdtpldt0(sz10, smndt0(xp))) = sdtpldt0(sdtasdt0(sz10, sz10), sdtasdt0(sz10, smndt0(xp))))) | (~(sdtasdt0(sdtpldt0(sz10, sz10), smndt0(xp)) = sdtpldt0(sdtasdt0(sz10, smndt0(xp)), sdtasdt0(sz10, smndt0(xp))))))))),
% 0.20/0.67      inference(quant_inst,[status(thm)],[])).
% 0.20/0.67  tff(176,plain,
% 0.20/0.67      ((~![W0: $i, W1: $i, W2: $i] : ((~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)) | (~((~(sdtasdt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtasdt0(W0, W1), sdtasdt0(W0, W2)))) | (~(sdtasdt0(sdtpldt0(W0, W1), W2) = sdtpldt0(sdtasdt0(W0, W2), sdtasdt0(W1, W2)))))))) | (~aInteger0(smndt0(xp))) | (~aInteger0(sz10)) | (~((~(sdtasdt0(sz10, sdtpldt0(sz10, smndt0(xp))) = sdtpldt0(sdtasdt0(sz10, sz10), sdtasdt0(sz10, smndt0(xp))))) | (~(sdtasdt0(sdtpldt0(sz10, sz10), smndt0(xp)) = sdtpldt0(sdtasdt0(sz10, smndt0(xp)), sdtasdt0(sz10, smndt0(xp)))))))),
% 0.20/0.67      inference(modus_ponens,[status(thm)],[175, 174])).
% 0.20/0.67  tff(177,plain,
% 0.20/0.67      (~((~(sdtasdt0(sz10, sdtpldt0(sz10, smndt0(xp))) = sdtpldt0(sdtasdt0(sz10, sz10), sdtasdt0(sz10, smndt0(xp))))) | (~(sdtasdt0(sdtpldt0(sz10, sz10), smndt0(xp)) = sdtpldt0(sdtasdt0(sz10, smndt0(xp)), sdtasdt0(sz10, smndt0(xp))))))),
% 0.20/0.67      inference(unit_resolution,[status(thm)],[176, 70, 167, 44])).
% 0.20/0.67  tff(178,plain,
% 0.20/0.67      (((~(sdtasdt0(sz10, sdtpldt0(sz10, smndt0(xp))) = sdtpldt0(sdtasdt0(sz10, sz10), sdtasdt0(sz10, smndt0(xp))))) | (~(sdtasdt0(sdtpldt0(sz10, sz10), smndt0(xp)) = sdtpldt0(sdtasdt0(sz10, smndt0(xp)), sdtasdt0(sz10, smndt0(xp)))))) | (sdtasdt0(sdtpldt0(sz10, sz10), smndt0(xp)) = sdtpldt0(sdtasdt0(sz10, smndt0(xp)), sdtasdt0(sz10, smndt0(xp))))),
% 0.20/0.67      inference(tautology,[status(thm)],[])).
% 0.20/0.67  tff(179,plain,
% 0.20/0.67      (sdtasdt0(sdtpldt0(sz10, sz10), smndt0(xp)) = sdtpldt0(sdtasdt0(sz10, smndt0(xp)), sdtasdt0(sz10, smndt0(xp)))),
% 0.20/0.67      inference(unit_resolution,[status(thm)],[178, 177])).
% 0.20/0.67  tff(180,plain,
% 0.20/0.67      (sdtasdt0(sdtpldt0(sz10, sz10), sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10))) = sdtasdt0(sdtpldt0(sz10, sz10), smndt0(xp))),
% 0.20/0.67      inference(monotonicity,[status(thm)],[110])).
% 0.20/0.67  tff(181,plain,
% 0.20/0.67      (((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | ((~aInteger0(smndt0(xp))) | (~aInteger0(sz10)) | (~aInteger0(smndt0(sz10))) | (sdtpldt0(sz10, sdtpldt0(smndt0(xp), smndt0(sz10))) = sdtpldt0(sdtpldt0(sz10, smndt0(xp)), smndt0(sz10))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | (~aInteger0(smndt0(xp))) | (~aInteger0(sz10)) | (~aInteger0(smndt0(sz10))) | (sdtpldt0(sz10, sdtpldt0(smndt0(xp), smndt0(sz10))) = sdtpldt0(sdtpldt0(sz10, smndt0(xp)), smndt0(sz10))))),
% 0.20/0.67      inference(rewrite,[status(thm)],[])).
% 0.20/0.67  tff(182,plain,
% 0.20/0.67      (((sdtpldt0(sz10, sdtpldt0(smndt0(xp), smndt0(sz10))) = sdtpldt0(sdtpldt0(sz10, smndt0(xp)), smndt0(sz10))) | (~aInteger0(smndt0(sz10))) | (~aInteger0(smndt0(xp))) | (~aInteger0(sz10))) <=> ((~aInteger0(smndt0(xp))) | (~aInteger0(sz10)) | (~aInteger0(smndt0(sz10))) | (sdtpldt0(sz10, sdtpldt0(smndt0(xp), smndt0(sz10))) = sdtpldt0(sdtpldt0(sz10, smndt0(xp)), smndt0(sz10))))),
% 0.20/0.67      inference(rewrite,[status(thm)],[])).
% 0.20/0.67  tff(183,plain,
% 0.20/0.67      (((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | ((sdtpldt0(sz10, sdtpldt0(smndt0(xp), smndt0(sz10))) = sdtpldt0(sdtpldt0(sz10, smndt0(xp)), smndt0(sz10))) | (~aInteger0(smndt0(sz10))) | (~aInteger0(smndt0(xp))) | (~aInteger0(sz10)))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | ((~aInteger0(smndt0(xp))) | (~aInteger0(sz10)) | (~aInteger0(smndt0(sz10))) | (sdtpldt0(sz10, sdtpldt0(smndt0(xp), smndt0(sz10))) = sdtpldt0(sdtpldt0(sz10, smndt0(xp)), smndt0(sz10)))))),
% 0.20/0.67      inference(monotonicity,[status(thm)],[182])).
% 0.20/0.67  tff(184,plain,
% 0.20/0.67      (((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | ((sdtpldt0(sz10, sdtpldt0(smndt0(xp), smndt0(sz10))) = sdtpldt0(sdtpldt0(sz10, smndt0(xp)), smndt0(sz10))) | (~aInteger0(smndt0(sz10))) | (~aInteger0(smndt0(xp))) | (~aInteger0(sz10)))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | (~aInteger0(smndt0(xp))) | (~aInteger0(sz10)) | (~aInteger0(smndt0(sz10))) | (sdtpldt0(sz10, sdtpldt0(smndt0(xp), smndt0(sz10))) = sdtpldt0(sdtpldt0(sz10, smndt0(xp)), smndt0(sz10))))),
% 0.20/0.67      inference(transitivity,[status(thm)],[183, 181])).
% 0.20/0.67  tff(185,plain,
% 0.20/0.67      ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | ((sdtpldt0(sz10, sdtpldt0(smndt0(xp), smndt0(sz10))) = sdtpldt0(sdtpldt0(sz10, smndt0(xp)), smndt0(sz10))) | (~aInteger0(smndt0(sz10))) | (~aInteger0(smndt0(xp))) | (~aInteger0(sz10)))),
% 0.20/0.67      inference(quant_inst,[status(thm)],[])).
% 0.20/0.67  tff(186,plain,
% 0.20/0.67      ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | (~aInteger0(smndt0(xp))) | (~aInteger0(sz10)) | (~aInteger0(smndt0(sz10))) | (sdtpldt0(sz10, sdtpldt0(smndt0(xp), smndt0(sz10))) = sdtpldt0(sdtpldt0(sz10, smndt0(xp)), smndt0(sz10)))),
% 0.20/0.67      inference(modus_ponens,[status(thm)],[185, 184])).
% 0.20/0.67  tff(187,plain,
% 0.20/0.67      ((~aInteger0(smndt0(xp))) | (~aInteger0(smndt0(sz10))) | (sdtpldt0(sz10, sdtpldt0(smndt0(xp), smndt0(sz10))) = sdtpldt0(sdtpldt0(sz10, smndt0(xp)), smndt0(sz10)))),
% 0.20/0.67      inference(unit_resolution,[status(thm)],[186, 70, 95])).
% 0.20/0.67  tff(188,plain,
% 0.20/0.67      (sdtpldt0(sz10, sdtpldt0(smndt0(xp), smndt0(sz10))) = sdtpldt0(sdtpldt0(sz10, smndt0(xp)), smndt0(sz10))),
% 0.20/0.67      inference(unit_resolution,[status(thm)],[187, 44, 82])).
% 0.20/0.67  tff(189,plain,
% 0.20/0.67      (sdtpldt0(sdtpldt0(sz10, smndt0(xp)), smndt0(sz10)) = sdtpldt0(sz10, sdtpldt0(smndt0(xp), smndt0(sz10)))),
% 0.20/0.67      inference(symmetry,[status(thm)],[188])).
% 0.20/0.67  tff(190,plain,
% 0.20/0.67      (sdtpldt0(sz10, smndt0(xp)) = sdtpldt0(sz10, xp)),
% 0.20/0.67      inference(transitivity,[status(thm)],[103, 107])).
% 0.20/0.67  tff(191,plain,
% 0.20/0.67      (sdtpldt0(sdtpldt0(sz10, smndt0(xp)), smndt0(sz10)) = sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10))),
% 0.20/0.67      inference(monotonicity,[status(thm)],[190])).
% 0.20/0.67  tff(192,plain,
% 0.20/0.67      (sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)) = sdtpldt0(sdtpldt0(sz10, smndt0(xp)), smndt0(sz10))),
% 0.20/0.67      inference(symmetry,[status(thm)],[191])).
% 0.20/0.67  tff(193,plain,
% 0.20/0.67      (sdtpldt0(sdtpldt0(smndt0(sz10), sz10), xp) = sdtpldt0(smndt0(sz10), sdtpldt0(sz10, xp))),
% 0.20/0.67      inference(symmetry,[status(thm)],[126])).
% 0.20/0.67  tff(194,plain,
% 0.20/0.67      (xp = sdtpldt0(sz10, sdtpldt0(smndt0(xp), smndt0(sz10)))),
% 0.20/0.67      inference(transitivity,[status(thm)],[116, 118, 193, 127, 192, 189])).
% 0.20/0.67  tff(195,plain,
% 0.20/0.67      (sdtpldt0(xp, smndt0(sz10)) = sdtpldt0(sdtpldt0(sz10, sdtpldt0(smndt0(xp), smndt0(sz10))), smndt0(sz10))),
% 0.20/0.67      inference(monotonicity,[status(thm)],[194])).
% 0.20/0.67  tff(196,plain,
% 0.20/0.67      (sdtpldt0(sdtpldt0(sz10, sdtpldt0(smndt0(xp), smndt0(sz10))), smndt0(sz10)) = sdtpldt0(xp, smndt0(sz10))),
% 0.20/0.67      inference(symmetry,[status(thm)],[195])).
% 0.20/0.67  tff(197,plain,
% 0.20/0.67      (^[W0: $i, W1: $i] : refl((aInteger0(sdtpldt0(W0, W1)) | (~aInteger0(W1)) | (~aInteger0(W0))) <=> (aInteger0(sdtpldt0(W0, W1)) | (~aInteger0(W1)) | (~aInteger0(W0))))),
% 0.20/0.67      inference(bind,[status(th)],[])).
% 0.20/0.67  tff(198,plain,
% 0.20/0.67      (![W0: $i, W1: $i] : (aInteger0(sdtpldt0(W0, W1)) | (~aInteger0(W1)) | (~aInteger0(W0))) <=> ![W0: $i, W1: $i] : (aInteger0(sdtpldt0(W0, W1)) | (~aInteger0(W1)) | (~aInteger0(W0)))),
% 0.20/0.67      inference(quant_intro,[status(thm)],[197])).
% 0.20/0.67  tff(199,plain,
% 0.20/0.67      (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aInteger0(W0) & aInteger0(W1)) <=> (~((~aInteger0(W1)) | (~aInteger0(W0))))), ((~(aInteger0(W0) & aInteger0(W1))) <=> (~(~((~aInteger0(W1)) | (~aInteger0(W0))))))), rewrite((~(~((~aInteger0(W1)) | (~aInteger0(W0))))) <=> ((~aInteger0(W1)) | (~aInteger0(W0)))), ((~(aInteger0(W0) & aInteger0(W1))) <=> ((~aInteger0(W1)) | (~aInteger0(W0))))), ((aInteger0(sdtpldt0(W0, W1)) | (~(aInteger0(W0) & aInteger0(W1)))) <=> (aInteger0(sdtpldt0(W0, W1)) | ((~aInteger0(W1)) | (~aInteger0(W0)))))), rewrite((aInteger0(sdtpldt0(W0, W1)) | ((~aInteger0(W1)) | (~aInteger0(W0)))) <=> (aInteger0(sdtpldt0(W0, W1)) | (~aInteger0(W1)) | (~aInteger0(W0)))), ((aInteger0(sdtpldt0(W0, W1)) | (~(aInteger0(W0) & aInteger0(W1)))) <=> (aInteger0(sdtpldt0(W0, W1)) | (~aInteger0(W1)) | (~aInteger0(W0)))))),
% 0.20/0.67      inference(bind,[status(th)],[])).
% 0.20/0.67  tff(200,plain,
% 0.20/0.67      (![W0: $i, W1: $i] : (aInteger0(sdtpldt0(W0, W1)) | (~(aInteger0(W0) & aInteger0(W1)))) <=> ![W0: $i, W1: $i] : (aInteger0(sdtpldt0(W0, W1)) | (~aInteger0(W1)) | (~aInteger0(W0)))),
% 0.20/0.67      inference(quant_intro,[status(thm)],[199])).
% 0.20/0.67  tff(201,plain,
% 0.20/0.67      (![W0: $i, W1: $i] : (aInteger0(sdtpldt0(W0, W1)) | (~(aInteger0(W0) & aInteger0(W1)))) <=> ![W0: $i, W1: $i] : (aInteger0(sdtpldt0(W0, W1)) | (~(aInteger0(W0) & aInteger0(W1))))),
% 0.20/0.67      inference(rewrite,[status(thm)],[])).
% 0.20/0.67  tff(202,plain,
% 0.20/0.67      (^[W0: $i, W1: $i] : rewrite(((aInteger0(W0) & aInteger0(W1)) => aInteger0(sdtpldt0(W0, W1))) <=> (aInteger0(sdtpldt0(W0, W1)) | (~(aInteger0(W0) & aInteger0(W1)))))),
% 0.20/0.67      inference(bind,[status(th)],[])).
% 0.20/0.67  tff(203,plain,
% 0.20/0.67      (![W0: $i, W1: $i] : ((aInteger0(W0) & aInteger0(W1)) => aInteger0(sdtpldt0(W0, W1))) <=> ![W0: $i, W1: $i] : (aInteger0(sdtpldt0(W0, W1)) | (~(aInteger0(W0) & aInteger0(W1))))),
% 0.20/0.67      inference(quant_intro,[status(thm)],[202])).
% 0.20/0.67  tff(204,axiom,(![W0: $i, W1: $i] : ((aInteger0(W0) & aInteger0(W1)) => aInteger0(sdtpldt0(W0, W1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mIntPlus')).
% 0.20/0.67  tff(205,plain,
% 0.20/0.67      (![W0: $i, W1: $i] : (aInteger0(sdtpldt0(W0, W1)) | (~(aInteger0(W0) & aInteger0(W1))))),
% 0.20/0.67      inference(modus_ponens,[status(thm)],[204, 203])).
% 0.20/0.67  tff(206,plain,
% 0.20/0.67      (![W0: $i, W1: $i] : (aInteger0(sdtpldt0(W0, W1)) | (~(aInteger0(W0) & aInteger0(W1))))),
% 0.20/0.67      inference(modus_ponens,[status(thm)],[205, 201])).
% 0.20/0.67  tff(207,plain,(
% 0.20/0.67      ![W0: $i, W1: $i] : (aInteger0(sdtpldt0(W0, W1)) | (~(aInteger0(W0) & aInteger0(W1))))),
% 0.20/0.67      inference(skolemize,[status(sab)],[206])).
% 0.20/0.67  tff(208,plain,
% 0.20/0.67      (![W0: $i, W1: $i] : (aInteger0(sdtpldt0(W0, W1)) | (~aInteger0(W1)) | (~aInteger0(W0)))),
% 0.20/0.67      inference(modus_ponens,[status(thm)],[207, 200])).
% 0.20/0.67  tff(209,plain,
% 0.20/0.67      (![W0: $i, W1: $i] : (aInteger0(sdtpldt0(W0, W1)) | (~aInteger0(W1)) | (~aInteger0(W0)))),
% 0.20/0.67      inference(modus_ponens,[status(thm)],[208, 198])).
% 0.20/0.67  tff(210,plain,
% 0.20/0.67      (((~![W0: $i, W1: $i] : (aInteger0(sdtpldt0(W0, W1)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | (aInteger0(sdtpldt0(smndt0(xp), smndt0(sz10))) | (~aInteger0(smndt0(sz10))) | (~aInteger0(smndt0(xp))))) <=> ((~![W0: $i, W1: $i] : (aInteger0(sdtpldt0(W0, W1)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | aInteger0(sdtpldt0(smndt0(xp), smndt0(sz10))) | (~aInteger0(smndt0(sz10))) | (~aInteger0(smndt0(xp))))),
% 0.20/0.67      inference(rewrite,[status(thm)],[])).
% 0.20/0.67  tff(211,plain,
% 0.20/0.67      ((~![W0: $i, W1: $i] : (aInteger0(sdtpldt0(W0, W1)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | (aInteger0(sdtpldt0(smndt0(xp), smndt0(sz10))) | (~aInteger0(smndt0(sz10))) | (~aInteger0(smndt0(xp))))),
% 0.20/0.67      inference(quant_inst,[status(thm)],[])).
% 0.20/0.67  tff(212,plain,
% 0.20/0.67      ((~![W0: $i, W1: $i] : (aInteger0(sdtpldt0(W0, W1)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | aInteger0(sdtpldt0(smndt0(xp), smndt0(sz10))) | (~aInteger0(smndt0(sz10))) | (~aInteger0(smndt0(xp)))),
% 0.20/0.67      inference(modus_ponens,[status(thm)],[211, 210])).
% 0.20/0.67  tff(213,plain,
% 0.20/0.67      (aInteger0(sdtpldt0(smndt0(xp), smndt0(sz10)))),
% 0.20/0.67      inference(unit_resolution,[status(thm)],[212, 209, 44, 82])).
% 0.20/0.67  tff(214,plain,
% 0.20/0.67      (((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | ((~aInteger0(sz10)) | (~aInteger0(smndt0(sz10))) | (~aInteger0(sdtpldt0(smndt0(xp), smndt0(sz10)))) | (sdtpldt0(sz10, sdtpldt0(sdtpldt0(smndt0(xp), smndt0(sz10)), smndt0(sz10))) = sdtpldt0(sdtpldt0(sz10, sdtpldt0(smndt0(xp), smndt0(sz10))), smndt0(sz10))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | (~aInteger0(sz10)) | (~aInteger0(smndt0(sz10))) | (~aInteger0(sdtpldt0(smndt0(xp), smndt0(sz10)))) | (sdtpldt0(sz10, sdtpldt0(sdtpldt0(smndt0(xp), smndt0(sz10)), smndt0(sz10))) = sdtpldt0(sdtpldt0(sz10, sdtpldt0(smndt0(xp), smndt0(sz10))), smndt0(sz10))))),
% 0.20/0.67      inference(rewrite,[status(thm)],[])).
% 0.20/0.67  tff(215,plain,
% 0.20/0.67      (((sdtpldt0(sz10, sdtpldt0(sdtpldt0(smndt0(xp), smndt0(sz10)), smndt0(sz10))) = sdtpldt0(sdtpldt0(sz10, sdtpldt0(smndt0(xp), smndt0(sz10))), smndt0(sz10))) | (~aInteger0(smndt0(sz10))) | (~aInteger0(sdtpldt0(smndt0(xp), smndt0(sz10)))) | (~aInteger0(sz10))) <=> ((~aInteger0(sz10)) | (~aInteger0(smndt0(sz10))) | (~aInteger0(sdtpldt0(smndt0(xp), smndt0(sz10)))) | (sdtpldt0(sz10, sdtpldt0(sdtpldt0(smndt0(xp), smndt0(sz10)), smndt0(sz10))) = sdtpldt0(sdtpldt0(sz10, sdtpldt0(smndt0(xp), smndt0(sz10))), smndt0(sz10))))),
% 0.20/0.67      inference(rewrite,[status(thm)],[])).
% 0.20/0.67  tff(216,plain,
% 0.20/0.67      (((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | ((sdtpldt0(sz10, sdtpldt0(sdtpldt0(smndt0(xp), smndt0(sz10)), smndt0(sz10))) = sdtpldt0(sdtpldt0(sz10, sdtpldt0(smndt0(xp), smndt0(sz10))), smndt0(sz10))) | (~aInteger0(smndt0(sz10))) | (~aInteger0(sdtpldt0(smndt0(xp), smndt0(sz10)))) | (~aInteger0(sz10)))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | ((~aInteger0(sz10)) | (~aInteger0(smndt0(sz10))) | (~aInteger0(sdtpldt0(smndt0(xp), smndt0(sz10)))) | (sdtpldt0(sz10, sdtpldt0(sdtpldt0(smndt0(xp), smndt0(sz10)), smndt0(sz10))) = sdtpldt0(sdtpldt0(sz10, sdtpldt0(smndt0(xp), smndt0(sz10))), smndt0(sz10)))))),
% 0.20/0.67      inference(monotonicity,[status(thm)],[215])).
% 0.20/0.67  tff(217,plain,
% 0.20/0.67      (((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | ((sdtpldt0(sz10, sdtpldt0(sdtpldt0(smndt0(xp), smndt0(sz10)), smndt0(sz10))) = sdtpldt0(sdtpldt0(sz10, sdtpldt0(smndt0(xp), smndt0(sz10))), smndt0(sz10))) | (~aInteger0(smndt0(sz10))) | (~aInteger0(sdtpldt0(smndt0(xp), smndt0(sz10)))) | (~aInteger0(sz10)))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | (~aInteger0(sz10)) | (~aInteger0(smndt0(sz10))) | (~aInteger0(sdtpldt0(smndt0(xp), smndt0(sz10)))) | (sdtpldt0(sz10, sdtpldt0(sdtpldt0(smndt0(xp), smndt0(sz10)), smndt0(sz10))) = sdtpldt0(sdtpldt0(sz10, sdtpldt0(smndt0(xp), smndt0(sz10))), smndt0(sz10))))),
% 0.20/0.67      inference(transitivity,[status(thm)],[216, 214])).
% 0.20/0.67  tff(218,plain,
% 0.20/0.67      ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | ((sdtpldt0(sz10, sdtpldt0(sdtpldt0(smndt0(xp), smndt0(sz10)), smndt0(sz10))) = sdtpldt0(sdtpldt0(sz10, sdtpldt0(smndt0(xp), smndt0(sz10))), smndt0(sz10))) | (~aInteger0(smndt0(sz10))) | (~aInteger0(sdtpldt0(smndt0(xp), smndt0(sz10)))) | (~aInteger0(sz10)))),
% 0.20/0.67      inference(quant_inst,[status(thm)],[])).
% 0.20/0.67  tff(219,plain,
% 0.20/0.67      ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | (~aInteger0(sz10)) | (~aInteger0(smndt0(sz10))) | (~aInteger0(sdtpldt0(smndt0(xp), smndt0(sz10)))) | (sdtpldt0(sz10, sdtpldt0(sdtpldt0(smndt0(xp), smndt0(sz10)), smndt0(sz10))) = sdtpldt0(sdtpldt0(sz10, sdtpldt0(smndt0(xp), smndt0(sz10))), smndt0(sz10)))),
% 0.20/0.67      inference(modus_ponens,[status(thm)],[218, 217])).
% 0.20/0.67  tff(220,plain,
% 0.20/0.67      ((~aInteger0(sdtpldt0(smndt0(xp), smndt0(sz10)))) | (sdtpldt0(sz10, sdtpldt0(sdtpldt0(smndt0(xp), smndt0(sz10)), smndt0(sz10))) = sdtpldt0(sdtpldt0(sz10, sdtpldt0(smndt0(xp), smndt0(sz10))), smndt0(sz10)))),
% 0.20/0.67      inference(unit_resolution,[status(thm)],[219, 70, 95, 82])).
% 0.20/0.67  tff(221,plain,
% 0.20/0.67      (sdtpldt0(sz10, sdtpldt0(sdtpldt0(smndt0(xp), smndt0(sz10)), smndt0(sz10))) = sdtpldt0(sdtpldt0(sz10, sdtpldt0(smndt0(xp), smndt0(sz10))), smndt0(sz10))),
% 0.20/0.67      inference(unit_resolution,[status(thm)],[220, 213])).
% 0.20/0.67  tff(222,plain,
% 0.20/0.67      (((~(sdtpldt0(xp, smndt0(xp)) = sz00)) | (~(sz00 = sdtpldt0(smndt0(xp), xp)))) | (sz00 = sdtpldt0(smndt0(xp), xp))),
% 0.20/0.67      inference(tautology,[status(thm)],[])).
% 0.20/0.67  tff(223,plain,
% 0.20/0.67      (sz00 = sdtpldt0(smndt0(xp), xp)),
% 0.20/0.67      inference(unit_resolution,[status(thm)],[222, 28])).
% 0.20/0.67  tff(224,plain,
% 0.20/0.67      (sdtpldt0(smndt0(xp), xp) = sz00),
% 0.20/0.67      inference(symmetry,[status(thm)],[223])).
% 0.20/0.67  tff(225,plain,
% 0.20/0.67      (sdtpldt0(smndt0(sz10), smndt0(sz10)) = sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10))),
% 0.20/0.67      inference(monotonicity,[status(thm)],[107])).
% 0.20/0.67  tff(226,plain,
% 0.20/0.67      (sdtpldt0(smndt0(sz10), smndt0(sz10)) = xp),
% 0.20/0.67      inference(transitivity,[status(thm)],[225, 128, 126, 119, 117])).
% 0.20/0.67  tff(227,plain,
% 0.20/0.67      (sdtpldt0(smndt0(xp), sdtpldt0(smndt0(sz10), smndt0(sz10))) = sdtpldt0(smndt0(xp), xp)),
% 0.20/0.67      inference(monotonicity,[status(thm)],[226])).
% 0.20/0.67  tff(228,plain,
% 0.20/0.67      (((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | ((~aInteger0(smndt0(xp))) | (~aInteger0(smndt0(sz10))) | (sdtpldt0(smndt0(xp), sdtpldt0(smndt0(sz10), smndt0(sz10))) = sdtpldt0(sdtpldt0(smndt0(xp), smndt0(sz10)), smndt0(sz10))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | (~aInteger0(smndt0(xp))) | (~aInteger0(smndt0(sz10))) | (sdtpldt0(smndt0(xp), sdtpldt0(smndt0(sz10), smndt0(sz10))) = sdtpldt0(sdtpldt0(smndt0(xp), smndt0(sz10)), smndt0(sz10))))),
% 0.20/0.67      inference(rewrite,[status(thm)],[])).
% 0.20/0.67  tff(229,plain,
% 0.20/0.67      (((sdtpldt0(smndt0(xp), sdtpldt0(smndt0(sz10), smndt0(sz10))) = sdtpldt0(sdtpldt0(smndt0(xp), smndt0(sz10)), smndt0(sz10))) | (~aInteger0(smndt0(sz10))) | (~aInteger0(smndt0(sz10))) | (~aInteger0(smndt0(xp)))) <=> ((~aInteger0(smndt0(xp))) | (~aInteger0(smndt0(sz10))) | (sdtpldt0(smndt0(xp), sdtpldt0(smndt0(sz10), smndt0(sz10))) = sdtpldt0(sdtpldt0(smndt0(xp), smndt0(sz10)), smndt0(sz10))))),
% 0.20/0.67      inference(rewrite,[status(thm)],[])).
% 0.20/0.67  tff(230,plain,
% 0.20/0.67      (((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | ((sdtpldt0(smndt0(xp), sdtpldt0(smndt0(sz10), smndt0(sz10))) = sdtpldt0(sdtpldt0(smndt0(xp), smndt0(sz10)), smndt0(sz10))) | (~aInteger0(smndt0(sz10))) | (~aInteger0(smndt0(sz10))) | (~aInteger0(smndt0(xp))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | ((~aInteger0(smndt0(xp))) | (~aInteger0(smndt0(sz10))) | (sdtpldt0(smndt0(xp), sdtpldt0(smndt0(sz10), smndt0(sz10))) = sdtpldt0(sdtpldt0(smndt0(xp), smndt0(sz10)), smndt0(sz10)))))),
% 0.20/0.67      inference(monotonicity,[status(thm)],[229])).
% 0.20/0.67  tff(231,plain,
% 0.20/0.67      (((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | ((sdtpldt0(smndt0(xp), sdtpldt0(smndt0(sz10), smndt0(sz10))) = sdtpldt0(sdtpldt0(smndt0(xp), smndt0(sz10)), smndt0(sz10))) | (~aInteger0(smndt0(sz10))) | (~aInteger0(smndt0(sz10))) | (~aInteger0(smndt0(xp))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | (~aInteger0(smndt0(xp))) | (~aInteger0(smndt0(sz10))) | (sdtpldt0(smndt0(xp), sdtpldt0(smndt0(sz10), smndt0(sz10))) = sdtpldt0(sdtpldt0(smndt0(xp), smndt0(sz10)), smndt0(sz10))))),
% 0.20/0.67      inference(transitivity,[status(thm)],[230, 228])).
% 0.20/0.67  tff(232,plain,
% 0.20/0.67      ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | ((sdtpldt0(smndt0(xp), sdtpldt0(smndt0(sz10), smndt0(sz10))) = sdtpldt0(sdtpldt0(smndt0(xp), smndt0(sz10)), smndt0(sz10))) | (~aInteger0(smndt0(sz10))) | (~aInteger0(smndt0(sz10))) | (~aInteger0(smndt0(xp))))),
% 0.20/0.67      inference(quant_inst,[status(thm)],[])).
% 0.20/0.67  tff(233,plain,
% 0.20/0.67      ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | (~aInteger0(smndt0(xp))) | (~aInteger0(smndt0(sz10))) | (sdtpldt0(smndt0(xp), sdtpldt0(smndt0(sz10), smndt0(sz10))) = sdtpldt0(sdtpldt0(smndt0(xp), smndt0(sz10)), smndt0(sz10)))),
% 0.20/0.67      inference(modus_ponens,[status(thm)],[232, 231])).
% 0.20/0.67  tff(234,plain,
% 0.20/0.67      (sdtpldt0(smndt0(xp), sdtpldt0(smndt0(sz10), smndt0(sz10))) = sdtpldt0(sdtpldt0(smndt0(xp), smndt0(sz10)), smndt0(sz10))),
% 0.20/0.67      inference(unit_resolution,[status(thm)],[233, 95, 44, 82])).
% 0.20/0.67  tff(235,plain,
% 0.20/0.67      (sdtpldt0(sdtpldt0(smndt0(xp), smndt0(sz10)), smndt0(sz10)) = sdtpldt0(smndt0(xp), sdtpldt0(smndt0(sz10), smndt0(sz10)))),
% 0.20/0.67      inference(symmetry,[status(thm)],[234])).
% 0.20/0.67  tff(236,plain,
% 0.20/0.67      (sdtpldt0(sdtpldt0(smndt0(xp), smndt0(sz10)), smndt0(sz10)) = sz00),
% 0.20/0.67      inference(transitivity,[status(thm)],[235, 227, 224])).
% 0.20/0.67  tff(237,plain,
% 0.20/0.67      (sdtpldt0(sz10, sdtpldt0(sdtpldt0(smndt0(xp), smndt0(sz10)), smndt0(sz10))) = sdtpldt0(sz10, sz00)),
% 0.20/0.67      inference(monotonicity,[status(thm)],[236])).
% 0.20/0.67  tff(238,plain,
% 0.20/0.67      (sdtpldt0(sz10, sz00) = sdtpldt0(sz10, sdtpldt0(sdtpldt0(smndt0(xp), smndt0(sz10)), smndt0(sz10)))),
% 0.20/0.67      inference(symmetry,[status(thm)],[237])).
% 0.20/0.67  tff(239,plain,
% 0.20/0.67      (((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | ((~aInteger0(sz10)) | (~((~(sdtpldt0(sz10, sz00) = sz10)) | (~(sz10 = sdtpldt0(sz00, sz10))))))) <=> ((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | (~aInteger0(sz10)) | (~((~(sdtpldt0(sz10, sz00) = sz10)) | (~(sz10 = sdtpldt0(sz00, sz10))))))),
% 0.20/0.67      inference(rewrite,[status(thm)],[])).
% 0.20/0.67  tff(240,plain,
% 0.20/0.67      ((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | ((~aInteger0(sz10)) | (~((~(sdtpldt0(sz10, sz00) = sz10)) | (~(sz10 = sdtpldt0(sz00, sz10))))))),
% 0.20/0.67      inference(quant_inst,[status(thm)],[])).
% 0.20/0.67  tff(241,plain,
% 0.20/0.67      ((~![W0: $i] : ((~aInteger0(W0)) | (~((~(sdtpldt0(W0, sz00) = W0)) | (~(W0 = sdtpldt0(sz00, W0))))))) | (~aInteger0(sz10)) | (~((~(sdtpldt0(sz10, sz00) = sz10)) | (~(sz10 = sdtpldt0(sz00, sz10)))))),
% 0.20/0.67      inference(modus_ponens,[status(thm)],[240, 239])).
% 0.20/0.67  tff(242,plain,
% 0.20/0.67      (~((~(sdtpldt0(sz10, sz00) = sz10)) | (~(sz10 = sdtpldt0(sz00, sz10))))),
% 0.20/0.67      inference(unit_resolution,[status(thm)],[241, 70, 57])).
% 0.20/0.67  tff(243,plain,
% 0.20/0.67      (((~(sdtpldt0(sz10, sz00) = sz10)) | (~(sz10 = sdtpldt0(sz00, sz10)))) | (sdtpldt0(sz10, sz00) = sz10)),
% 0.20/0.67      inference(tautology,[status(thm)],[])).
% 0.20/0.67  tff(244,plain,
% 0.20/0.67      (sdtpldt0(sz10, sz00) = sz10),
% 0.20/0.67      inference(unit_resolution,[status(thm)],[243, 242])).
% 0.20/0.67  tff(245,plain,
% 0.20/0.67      (sz10 = sdtpldt0(sz10, sz00)),
% 0.20/0.67      inference(symmetry,[status(thm)],[244])).
% 0.20/0.67  tff(246,plain,
% 0.20/0.67      (sz10 = sdtpldt0(xp, smndt0(sz10))),
% 0.20/0.67      inference(transitivity,[status(thm)],[245, 238, 221, 196])).
% 0.20/0.67  tff(247,plain,
% 0.20/0.67      (sdtpldt0(sz10, sz10) = sdtpldt0(sz10, sdtpldt0(xp, smndt0(sz10)))),
% 0.20/0.67      inference(monotonicity,[status(thm)],[246])).
% 0.20/0.67  tff(248,plain,
% 0.20/0.67      (sdtpldt0(sz10, sdtpldt0(xp, smndt0(sz10))) = sdtpldt0(sz10, sz10)),
% 0.20/0.67      inference(symmetry,[status(thm)],[247])).
% 0.20/0.67  tff(249,plain,
% 0.20/0.67      (((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | ((~aInteger0(sz10)) | (~aInteger0(smndt0(sz10))) | (~aInteger0(xp)) | (sdtpldt0(sz10, sdtpldt0(xp, smndt0(sz10))) = sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10))))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | (~aInteger0(sz10)) | (~aInteger0(smndt0(sz10))) | (~aInteger0(xp)) | (sdtpldt0(sz10, sdtpldt0(xp, smndt0(sz10))) = sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10))))),
% 0.20/0.67      inference(rewrite,[status(thm)],[])).
% 0.20/0.67  tff(250,plain,
% 0.20/0.68      (((sdtpldt0(sz10, sdtpldt0(xp, smndt0(sz10))) = sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10))) | (~aInteger0(smndt0(sz10))) | (~aInteger0(xp)) | (~aInteger0(sz10))) <=> ((~aInteger0(sz10)) | (~aInteger0(smndt0(sz10))) | (~aInteger0(xp)) | (sdtpldt0(sz10, sdtpldt0(xp, smndt0(sz10))) = sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10))))),
% 0.20/0.68      inference(rewrite,[status(thm)],[])).
% 0.20/0.68  tff(251,plain,
% 0.20/0.68      (((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | ((sdtpldt0(sz10, sdtpldt0(xp, smndt0(sz10))) = sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10))) | (~aInteger0(smndt0(sz10))) | (~aInteger0(xp)) | (~aInteger0(sz10)))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | ((~aInteger0(sz10)) | (~aInteger0(smndt0(sz10))) | (~aInteger0(xp)) | (sdtpldt0(sz10, sdtpldt0(xp, smndt0(sz10))) = sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)))))),
% 0.20/0.68      inference(monotonicity,[status(thm)],[250])).
% 0.20/0.68  tff(252,plain,
% 0.20/0.68      (((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | ((sdtpldt0(sz10, sdtpldt0(xp, smndt0(sz10))) = sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10))) | (~aInteger0(smndt0(sz10))) | (~aInteger0(xp)) | (~aInteger0(sz10)))) <=> ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | (~aInteger0(sz10)) | (~aInteger0(smndt0(sz10))) | (~aInteger0(xp)) | (sdtpldt0(sz10, sdtpldt0(xp, smndt0(sz10))) = sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10))))),
% 0.20/0.68      inference(transitivity,[status(thm)],[251, 249])).
% 0.20/0.68  tff(253,plain,
% 0.20/0.68      ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | ((sdtpldt0(sz10, sdtpldt0(xp, smndt0(sz10))) = sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10))) | (~aInteger0(smndt0(sz10))) | (~aInteger0(xp)) | (~aInteger0(sz10)))),
% 0.20/0.68      inference(quant_inst,[status(thm)],[])).
% 0.20/0.68  tff(254,plain,
% 0.20/0.68      ((~![W0: $i, W1: $i, W2: $i] : ((sdtpldt0(W0, sdtpldt0(W1, W2)) = sdtpldt0(sdtpldt0(W0, W1), W2)) | (~aInteger0(W2)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | (~aInteger0(sz10)) | (~aInteger0(smndt0(sz10))) | (~aInteger0(xp)) | (sdtpldt0(sz10, sdtpldt0(xp, smndt0(sz10))) = sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)))),
% 0.20/0.68      inference(modus_ponens,[status(thm)],[253, 252])).
% 0.20/0.68  tff(255,plain,
% 0.20/0.68      ((~aInteger0(smndt0(sz10))) | (sdtpldt0(sz10, sdtpldt0(xp, smndt0(sz10))) = sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)))),
% 0.20/0.68      inference(unit_resolution,[status(thm)],[254, 70, 95, 11])).
% 0.20/0.68  tff(256,plain,
% 0.20/0.68      (sdtpldt0(sz10, sdtpldt0(xp, smndt0(sz10))) = sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10))),
% 0.20/0.68      inference(unit_resolution,[status(thm)],[255, 82])).
% 0.20/0.68  tff(257,plain,
% 0.20/0.68      (sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)) = sdtpldt0(sz10, sdtpldt0(xp, smndt0(sz10)))),
% 0.20/0.68      inference(symmetry,[status(thm)],[256])).
% 0.20/0.68  tff(258,plain,
% 0.20/0.68      (sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)) = sdtpldt0(sz10, sz10)),
% 0.20/0.68      inference(transitivity,[status(thm)],[257, 248])).
% 0.20/0.68  tff(259,plain,
% 0.20/0.68      (sdtasdt0(sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)), sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10))) = sdtasdt0(sdtpldt0(sz10, sz10), sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)))),
% 0.20/0.68      inference(monotonicity,[status(thm)],[258])).
% 0.20/0.68  tff(260,plain,
% 0.20/0.68      (sdtasdt0(sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)), sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10))) = sz00),
% 0.20/0.68      inference(transitivity,[status(thm)],[259, 180, 179, 154, 133, 130, 30])).
% 0.20/0.68  tff(261,plain,
% 0.20/0.68      (?[W0: $i] : (aInteger0(W0) & (sdtasdt0(xp, W0) = sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)))) <=> ?[W0: $i] : (aInteger0(W0) & (sdtasdt0(xp, W0) = sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10))))),
% 0.20/0.68      inference(rewrite,[status(thm)],[])).
% 0.20/0.68  tff(262,axiom,(((((((?[W0: $i] : (aInteger0(W0) & (sdtasdt0(xp, W0) = sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)))) & aDivisorOf0(xp, sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)))) & sdteqdtlpzmzozddtrp0(sdtpldt0(sz10, xp), sz10, xp)) & aElementOf0(sdtpldt0(sz10, xp), szAzrzSzezqlpdtcmdtrp0(sz10, xp))) & ?[W0: $i] : (aInteger0(W0) & (sdtasdt0(xp, W0) = sdtpldt0(sdtpldt0(sz10, smndt0(xp)), smndt0(sz10))))) & aDivisorOf0(xp, sdtpldt0(sdtpldt0(sz10, smndt0(xp)), smndt0(sz10)))) & sdteqdtlpzmzozddtrp0(sdtpldt0(sz10, smndt0(xp)), sz10, xp)) & aElementOf0(sdtpldt0(sz10, smndt0(xp)), szAzrzSzezqlpdtcmdtrp0(sz10, xp))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','m__2232')).
% 0.20/0.68  tff(263,plain,
% 0.20/0.68      ((((((?[W0: $i] : (aInteger0(W0) & (sdtasdt0(xp, W0) = sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)))) & aDivisorOf0(xp, sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)))) & sdteqdtlpzmzozddtrp0(sdtpldt0(sz10, xp), sz10, xp)) & aElementOf0(sdtpldt0(sz10, xp), szAzrzSzezqlpdtcmdtrp0(sz10, xp))) & ?[W0: $i] : (aInteger0(W0) & (sdtasdt0(xp, W0) = sdtpldt0(sdtpldt0(sz10, smndt0(xp)), smndt0(sz10))))) & aDivisorOf0(xp, sdtpldt0(sdtpldt0(sz10, smndt0(xp)), smndt0(sz10)))) & sdteqdtlpzmzozddtrp0(sdtpldt0(sz10, smndt0(xp)), sz10, xp)),
% 0.20/0.68      inference(and_elim,[status(thm)],[262])).
% 0.20/0.68  tff(264,plain,
% 0.20/0.68      (((((?[W0: $i] : (aInteger0(W0) & (sdtasdt0(xp, W0) = sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)))) & aDivisorOf0(xp, sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)))) & sdteqdtlpzmzozddtrp0(sdtpldt0(sz10, xp), sz10, xp)) & aElementOf0(sdtpldt0(sz10, xp), szAzrzSzezqlpdtcmdtrp0(sz10, xp))) & ?[W0: $i] : (aInteger0(W0) & (sdtasdt0(xp, W0) = sdtpldt0(sdtpldt0(sz10, smndt0(xp)), smndt0(sz10))))) & aDivisorOf0(xp, sdtpldt0(sdtpldt0(sz10, smndt0(xp)), smndt0(sz10)))),
% 0.20/0.68      inference(and_elim,[status(thm)],[263])).
% 0.20/0.68  tff(265,plain,
% 0.20/0.68      ((((?[W0: $i] : (aInteger0(W0) & (sdtasdt0(xp, W0) = sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)))) & aDivisorOf0(xp, sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)))) & sdteqdtlpzmzozddtrp0(sdtpldt0(sz10, xp), sz10, xp)) & aElementOf0(sdtpldt0(sz10, xp), szAzrzSzezqlpdtcmdtrp0(sz10, xp))) & ?[W0: $i] : (aInteger0(W0) & (sdtasdt0(xp, W0) = sdtpldt0(sdtpldt0(sz10, smndt0(xp)), smndt0(sz10))))),
% 0.20/0.68      inference(and_elim,[status(thm)],[264])).
% 0.20/0.68  tff(266,plain,
% 0.20/0.68      (((?[W0: $i] : (aInteger0(W0) & (sdtasdt0(xp, W0) = sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)))) & aDivisorOf0(xp, sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)))) & sdteqdtlpzmzozddtrp0(sdtpldt0(sz10, xp), sz10, xp)) & aElementOf0(sdtpldt0(sz10, xp), szAzrzSzezqlpdtcmdtrp0(sz10, xp))),
% 0.20/0.68      inference(and_elim,[status(thm)],[265])).
% 0.20/0.68  tff(267,plain,
% 0.20/0.68      ((?[W0: $i] : (aInteger0(W0) & (sdtasdt0(xp, W0) = sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)))) & aDivisorOf0(xp, sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)))) & sdteqdtlpzmzozddtrp0(sdtpldt0(sz10, xp), sz10, xp)),
% 0.20/0.68      inference(and_elim,[status(thm)],[266])).
% 0.20/0.68  tff(268,plain,
% 0.20/0.68      (?[W0: $i] : (aInteger0(W0) & (sdtasdt0(xp, W0) = sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)))) & aDivisorOf0(xp, sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)))),
% 0.20/0.68      inference(and_elim,[status(thm)],[267])).
% 0.20/0.68  tff(269,plain,
% 0.20/0.68      (?[W0: $i] : (aInteger0(W0) & (sdtasdt0(xp, W0) = sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10))))),
% 0.20/0.68      inference(and_elim,[status(thm)],[268])).
% 0.20/0.68  tff(270,plain,
% 0.20/0.68      (?[W0: $i] : (aInteger0(W0) & (sdtasdt0(xp, W0) = sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10))))),
% 0.20/0.68      inference(modus_ponens,[status(thm)],[269, 261])).
% 0.20/0.68  tff(271,plain,(
% 0.20/0.68      aInteger0(W0!22) & (sdtasdt0(xp, W0!22) = sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)))),
% 0.20/0.68      inference(skolemize,[status(sab)],[270])).
% 0.20/0.68  tff(272,plain,
% 0.20/0.68      (sdtasdt0(xp, W0!22) = sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10))),
% 0.20/0.68      inference(and_elim,[status(thm)],[271])).
% 0.20/0.68  tff(273,plain,
% 0.20/0.68      (sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)) = sdtasdt0(xp, W0!22)),
% 0.20/0.68      inference(symmetry,[status(thm)],[272])).
% 0.20/0.68  tff(274,plain,
% 0.20/0.68      ((sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)) = sz00) <=> (sdtasdt0(xp, W0!22) = sz00)),
% 0.20/0.68      inference(monotonicity,[status(thm)],[273])).
% 0.20/0.68  tff(275,plain,
% 0.20/0.68      ((sdtasdt0(xp, W0!22) = sz00) <=> (sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)) = sz00)),
% 0.20/0.68      inference(symmetry,[status(thm)],[274])).
% 0.20/0.68  tff(276,plain,
% 0.20/0.68      ((~(sdtasdt0(xp, W0!22) = sz00)) <=> (~(sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)) = sz00))),
% 0.20/0.68      inference(monotonicity,[status(thm)],[275])).
% 0.20/0.68  tff(277,plain,
% 0.20/0.68      (xp = sdtasdt0(xp, W0!22)),
% 0.20/0.68      inference(transitivity,[status(thm)],[116, 118, 193, 127, 273])).
% 0.20/0.68  tff(278,plain,
% 0.20/0.68      ((xp = sz00) <=> (sdtasdt0(xp, W0!22) = sz00)),
% 0.20/0.68      inference(monotonicity,[status(thm)],[277])).
% 0.20/0.68  tff(279,plain,
% 0.20/0.68      ((~(xp = sz00)) <=> (~(sdtasdt0(xp, W0!22) = sz00))),
% 0.20/0.68      inference(monotonicity,[status(thm)],[278])).
% 0.20/0.68  tff(280,plain,
% 0.20/0.68      ((~(xp = sz00)) <=> (~(xp = sz00))),
% 0.20/0.68      inference(rewrite,[status(thm)],[])).
% 0.20/0.68  tff(281,plain,
% 0.20/0.68      (~(xp = sz00)),
% 0.20/0.68      inference(and_elim,[status(thm)],[9])).
% 0.20/0.68  tff(282,plain,
% 0.20/0.68      (~(xp = sz00)),
% 0.20/0.68      inference(modus_ponens,[status(thm)],[281, 280])).
% 0.20/0.68  tff(283,plain,
% 0.20/0.68      (~(sdtasdt0(xp, W0!22) = sz00)),
% 0.20/0.68      inference(modus_ponens,[status(thm)],[282, 279])).
% 0.20/0.68  tff(284,plain,
% 0.20/0.68      (~(sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)) = sz00)),
% 0.20/0.68      inference(modus_ponens,[status(thm)],[283, 276])).
% 0.20/0.68  tff(285,plain,
% 0.20/0.68      (aInteger0(sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10))) <=> aInteger0(sdtasdt0(xp, W0!22))),
% 0.20/0.68      inference(monotonicity,[status(thm)],[273])).
% 0.20/0.68  tff(286,plain,
% 0.20/0.68      (aInteger0(sdtasdt0(xp, W0!22)) <=> aInteger0(sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)))),
% 0.20/0.68      inference(symmetry,[status(thm)],[285])).
% 0.20/0.68  tff(287,plain,
% 0.20/0.68      (aInteger0(W0!22)),
% 0.20/0.68      inference(and_elim,[status(thm)],[271])).
% 0.20/0.68  tff(288,plain,
% 0.20/0.68      (^[W0: $i, W1: $i] : refl((aInteger0(sdtasdt0(W0, W1)) | (~aInteger0(W1)) | (~aInteger0(W0))) <=> (aInteger0(sdtasdt0(W0, W1)) | (~aInteger0(W1)) | (~aInteger0(W0))))),
% 0.20/0.68      inference(bind,[status(th)],[])).
% 0.20/0.68  tff(289,plain,
% 0.20/0.68      (![W0: $i, W1: $i] : (aInteger0(sdtasdt0(W0, W1)) | (~aInteger0(W1)) | (~aInteger0(W0))) <=> ![W0: $i, W1: $i] : (aInteger0(sdtasdt0(W0, W1)) | (~aInteger0(W1)) | (~aInteger0(W0)))),
% 0.20/0.68      inference(quant_intro,[status(thm)],[288])).
% 0.20/0.68  tff(290,plain,
% 0.20/0.68      (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aInteger0(W0) & aInteger0(W1)) <=> (~((~aInteger0(W1)) | (~aInteger0(W0))))), ((~(aInteger0(W0) & aInteger0(W1))) <=> (~(~((~aInteger0(W1)) | (~aInteger0(W0))))))), rewrite((~(~((~aInteger0(W1)) | (~aInteger0(W0))))) <=> ((~aInteger0(W1)) | (~aInteger0(W0)))), ((~(aInteger0(W0) & aInteger0(W1))) <=> ((~aInteger0(W1)) | (~aInteger0(W0))))), ((aInteger0(sdtasdt0(W0, W1)) | (~(aInteger0(W0) & aInteger0(W1)))) <=> (aInteger0(sdtasdt0(W0, W1)) | ((~aInteger0(W1)) | (~aInteger0(W0)))))), rewrite((aInteger0(sdtasdt0(W0, W1)) | ((~aInteger0(W1)) | (~aInteger0(W0)))) <=> (aInteger0(sdtasdt0(W0, W1)) | (~aInteger0(W1)) | (~aInteger0(W0)))), ((aInteger0(sdtasdt0(W0, W1)) | (~(aInteger0(W0) & aInteger0(W1)))) <=> (aInteger0(sdtasdt0(W0, W1)) | (~aInteger0(W1)) | (~aInteger0(W0)))))),
% 0.20/0.68      inference(bind,[status(th)],[])).
% 0.20/0.68  tff(291,plain,
% 0.20/0.68      (![W0: $i, W1: $i] : (aInteger0(sdtasdt0(W0, W1)) | (~(aInteger0(W0) & aInteger0(W1)))) <=> ![W0: $i, W1: $i] : (aInteger0(sdtasdt0(W0, W1)) | (~aInteger0(W1)) | (~aInteger0(W0)))),
% 0.20/0.68      inference(quant_intro,[status(thm)],[290])).
% 0.20/0.68  tff(292,plain,
% 0.20/0.68      (![W0: $i, W1: $i] : (aInteger0(sdtasdt0(W0, W1)) | (~(aInteger0(W0) & aInteger0(W1)))) <=> ![W0: $i, W1: $i] : (aInteger0(sdtasdt0(W0, W1)) | (~(aInteger0(W0) & aInteger0(W1))))),
% 0.20/0.68      inference(rewrite,[status(thm)],[])).
% 0.20/0.68  tff(293,plain,
% 0.20/0.68      (^[W0: $i, W1: $i] : rewrite(((aInteger0(W0) & aInteger0(W1)) => aInteger0(sdtasdt0(W0, W1))) <=> (aInteger0(sdtasdt0(W0, W1)) | (~(aInteger0(W0) & aInteger0(W1)))))),
% 0.20/0.68      inference(bind,[status(th)],[])).
% 0.20/0.68  tff(294,plain,
% 0.20/0.68      (![W0: $i, W1: $i] : ((aInteger0(W0) & aInteger0(W1)) => aInteger0(sdtasdt0(W0, W1))) <=> ![W0: $i, W1: $i] : (aInteger0(sdtasdt0(W0, W1)) | (~(aInteger0(W0) & aInteger0(W1))))),
% 0.20/0.68      inference(quant_intro,[status(thm)],[293])).
% 0.20/0.68  tff(295,axiom,(![W0: $i, W1: $i] : ((aInteger0(W0) & aInteger0(W1)) => aInteger0(sdtasdt0(W0, W1)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mIntMult')).
% 0.20/0.68  tff(296,plain,
% 0.20/0.68      (![W0: $i, W1: $i] : (aInteger0(sdtasdt0(W0, W1)) | (~(aInteger0(W0) & aInteger0(W1))))),
% 0.20/0.68      inference(modus_ponens,[status(thm)],[295, 294])).
% 0.20/0.68  tff(297,plain,
% 0.20/0.68      (![W0: $i, W1: $i] : (aInteger0(sdtasdt0(W0, W1)) | (~(aInteger0(W0) & aInteger0(W1))))),
% 0.20/0.68      inference(modus_ponens,[status(thm)],[296, 292])).
% 0.20/0.68  tff(298,plain,(
% 0.20/0.68      ![W0: $i, W1: $i] : (aInteger0(sdtasdt0(W0, W1)) | (~(aInteger0(W0) & aInteger0(W1))))),
% 0.20/0.68      inference(skolemize,[status(sab)],[297])).
% 0.20/0.68  tff(299,plain,
% 0.20/0.68      (![W0: $i, W1: $i] : (aInteger0(sdtasdt0(W0, W1)) | (~aInteger0(W1)) | (~aInteger0(W0)))),
% 0.20/0.68      inference(modus_ponens,[status(thm)],[298, 291])).
% 0.20/0.68  tff(300,plain,
% 0.20/0.68      (![W0: $i, W1: $i] : (aInteger0(sdtasdt0(W0, W1)) | (~aInteger0(W1)) | (~aInteger0(W0)))),
% 0.20/0.68      inference(modus_ponens,[status(thm)],[299, 289])).
% 0.20/0.68  tff(301,plain,
% 0.20/0.68      (((~![W0: $i, W1: $i] : (aInteger0(sdtasdt0(W0, W1)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | (aInteger0(sdtasdt0(xp, W0!22)) | (~aInteger0(W0!22)) | (~aInteger0(xp)))) <=> ((~![W0: $i, W1: $i] : (aInteger0(sdtasdt0(W0, W1)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | aInteger0(sdtasdt0(xp, W0!22)) | (~aInteger0(W0!22)) | (~aInteger0(xp)))),
% 0.20/0.68      inference(rewrite,[status(thm)],[])).
% 0.20/0.68  tff(302,plain,
% 0.20/0.68      ((~![W0: $i, W1: $i] : (aInteger0(sdtasdt0(W0, W1)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | (aInteger0(sdtasdt0(xp, W0!22)) | (~aInteger0(W0!22)) | (~aInteger0(xp)))),
% 0.20/0.68      inference(quant_inst,[status(thm)],[])).
% 0.20/0.68  tff(303,plain,
% 0.20/0.68      ((~![W0: $i, W1: $i] : (aInteger0(sdtasdt0(W0, W1)) | (~aInteger0(W1)) | (~aInteger0(W0)))) | aInteger0(sdtasdt0(xp, W0!22)) | (~aInteger0(W0!22)) | (~aInteger0(xp))),
% 0.20/0.68      inference(modus_ponens,[status(thm)],[302, 301])).
% 0.20/0.68  tff(304,plain,
% 0.20/0.68      (aInteger0(sdtasdt0(xp, W0!22))),
% 0.20/0.68      inference(unit_resolution,[status(thm)],[303, 300, 11, 287])).
% 0.20/0.68  tff(305,plain,
% 0.20/0.68      (aInteger0(sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)))),
% 0.20/0.68      inference(modus_ponens,[status(thm)],[304, 286])).
% 0.20/0.68  tff(306,plain,
% 0.20/0.68      (^[W0: $i, W1: $i] : refl(((W1 = sz00) | (W0 = sz00) | (~aInteger0(W1)) | (~(sdtasdt0(W0, W1) = sz00)) | (~aInteger0(W0))) <=> ((W1 = sz00) | (W0 = sz00) | (~aInteger0(W1)) | (~(sdtasdt0(W0, W1) = sz00)) | (~aInteger0(W0))))),
% 0.20/0.68      inference(bind,[status(th)],[])).
% 0.20/0.68  tff(307,plain,
% 0.20/0.68      (![W0: $i, W1: $i] : ((W1 = sz00) | (W0 = sz00) | (~aInteger0(W1)) | (~(sdtasdt0(W0, W1) = sz00)) | (~aInteger0(W0))) <=> ![W0: $i, W1: $i] : ((W1 = sz00) | (W0 = sz00) | (~aInteger0(W1)) | (~(sdtasdt0(W0, W1) = sz00)) | (~aInteger0(W0)))),
% 0.20/0.68      inference(quant_intro,[status(thm)],[306])).
% 0.20/0.68  tff(308,plain,
% 0.20/0.68      (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite((aInteger0(W0) & aInteger0(W1)) <=> (~((~aInteger0(W1)) | (~aInteger0(W0))))), ((~(aInteger0(W0) & aInteger0(W1))) <=> (~(~((~aInteger0(W1)) | (~aInteger0(W0))))))), rewrite((~(~((~aInteger0(W1)) | (~aInteger0(W0))))) <=> ((~aInteger0(W1)) | (~aInteger0(W0)))), ((~(aInteger0(W0) & aInteger0(W1))) <=> ((~aInteger0(W1)) | (~aInteger0(W0))))), (((W1 = sz00) | (W0 = sz00) | (~(aInteger0(W0) & aInteger0(W1))) | (~(sdtasdt0(W0, W1) = sz00))) <=> ((W1 = sz00) | (W0 = sz00) | ((~aInteger0(W1)) | (~aInteger0(W0))) | (~(sdtasdt0(W0, W1) = sz00))))), rewrite(((W1 = sz00) | (W0 = sz00) | ((~aInteger0(W1)) | (~aInteger0(W0))) | (~(sdtasdt0(W0, W1) = sz00))) <=> ((W1 = sz00) | (W0 = sz00) | (~aInteger0(W1)) | (~(sdtasdt0(W0, W1) = sz00)) | (~aInteger0(W0)))), (((W1 = sz00) | (W0 = sz00) | (~(aInteger0(W0) & aInteger0(W1))) | (~(sdtasdt0(W0, W1) = sz00))) <=> ((W1 = sz00) | (W0 = sz00) | (~aInteger0(W1)) | (~(sdtasdt0(W0, W1) = sz00)) | (~aInteger0(W0)))))),
% 0.20/0.68      inference(bind,[status(th)],[])).
% 0.20/0.68  tff(309,plain,
% 0.20/0.68      (![W0: $i, W1: $i] : ((W1 = sz00) | (W0 = sz00) | (~(aInteger0(W0) & aInteger0(W1))) | (~(sdtasdt0(W0, W1) = sz00))) <=> ![W0: $i, W1: $i] : ((W1 = sz00) | (W0 = sz00) | (~aInteger0(W1)) | (~(sdtasdt0(W0, W1) = sz00)) | (~aInteger0(W0)))),
% 0.20/0.68      inference(quant_intro,[status(thm)],[308])).
% 0.20/0.68  tff(310,plain,
% 0.20/0.68      (![W0: $i, W1: $i] : ((W1 = sz00) | (W0 = sz00) | (~(aInteger0(W0) & aInteger0(W1))) | (~(sdtasdt0(W0, W1) = sz00))) <=> ![W0: $i, W1: $i] : ((W1 = sz00) | (W0 = sz00) | (~(aInteger0(W0) & aInteger0(W1))) | (~(sdtasdt0(W0, W1) = sz00)))),
% 0.20/0.68      inference(rewrite,[status(thm)],[])).
% 0.20/0.68  tff(311,plain,
% 0.20/0.68      (^[W0: $i, W1: $i] : trans(monotonicity(trans(monotonicity(rewrite(((W0 = sz00) | (W1 = sz00)) <=> ((W1 = sz00) | (W0 = sz00))), (((sdtasdt0(W0, W1) = sz00) => ((W0 = sz00) | (W1 = sz00))) <=> ((sdtasdt0(W0, W1) = sz00) => ((W1 = sz00) | (W0 = sz00))))), rewrite(((sdtasdt0(W0, W1) = sz00) => ((W1 = sz00) | (W0 = sz00))) <=> ((W1 = sz00) | (W0 = sz00) | (~(sdtasdt0(W0, W1) = sz00)))), (((sdtasdt0(W0, W1) = sz00) => ((W0 = sz00) | (W1 = sz00))) <=> ((W1 = sz00) | (W0 = sz00) | (~(sdtasdt0(W0, W1) = sz00))))), (((aInteger0(W0) & aInteger0(W1)) => ((sdtasdt0(W0, W1) = sz00) => ((W0 = sz00) | (W1 = sz00)))) <=> ((aInteger0(W0) & aInteger0(W1)) => ((W1 = sz00) | (W0 = sz00) | (~(sdtasdt0(W0, W1) = sz00)))))), rewrite(((aInteger0(W0) & aInteger0(W1)) => ((W1 = sz00) | (W0 = sz00) | (~(sdtasdt0(W0, W1) = sz00)))) <=> ((W1 = sz00) | (W0 = sz00) | (~(aInteger0(W0) & aInteger0(W1))) | (~(sdtasdt0(W0, W1) = sz00)))), (((aInteger0(W0) & aInteger0(W1)) => ((sdtasdt0(W0, W1) = sz00) => ((W0 = sz00) | (W1 = sz00)))) <=> ((W1 = sz00) | (W0 = sz00) | (~(aInteger0(W0) & aInteger0(W1))) | (~(sdtasdt0(W0, W1) = sz00)))))),
% 0.20/0.68      inference(bind,[status(th)],[])).
% 0.20/0.68  tff(312,plain,
% 0.20/0.68      (![W0: $i, W1: $i] : ((aInteger0(W0) & aInteger0(W1)) => ((sdtasdt0(W0, W1) = sz00) => ((W0 = sz00) | (W1 = sz00)))) <=> ![W0: $i, W1: $i] : ((W1 = sz00) | (W0 = sz00) | (~(aInteger0(W0) & aInteger0(W1))) | (~(sdtasdt0(W0, W1) = sz00)))),
% 0.20/0.68      inference(quant_intro,[status(thm)],[311])).
% 0.20/0.68  tff(313,axiom,(![W0: $i, W1: $i] : ((aInteger0(W0) & aInteger0(W1)) => ((sdtasdt0(W0, W1) = sz00) => ((W0 = sz00) | (W1 = sz00))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','mZeroDiv')).
% 0.20/0.68  tff(314,plain,
% 0.20/0.68      (![W0: $i, W1: $i] : ((W1 = sz00) | (W0 = sz00) | (~(aInteger0(W0) & aInteger0(W1))) | (~(sdtasdt0(W0, W1) = sz00)))),
% 0.20/0.68      inference(modus_ponens,[status(thm)],[313, 312])).
% 0.20/0.68  tff(315,plain,
% 0.20/0.68      (![W0: $i, W1: $i] : ((W1 = sz00) | (W0 = sz00) | (~(aInteger0(W0) & aInteger0(W1))) | (~(sdtasdt0(W0, W1) = sz00)))),
% 0.20/0.68      inference(modus_ponens,[status(thm)],[314, 310])).
% 0.20/0.68  tff(316,plain,(
% 0.20/0.68      ![W0: $i, W1: $i] : ((W1 = sz00) | (W0 = sz00) | (~(aInteger0(W0) & aInteger0(W1))) | (~(sdtasdt0(W0, W1) = sz00)))),
% 0.20/0.68      inference(skolemize,[status(sab)],[315])).
% 0.20/0.68  tff(317,plain,
% 0.20/0.68      (![W0: $i, W1: $i] : ((W1 = sz00) | (W0 = sz00) | (~aInteger0(W1)) | (~(sdtasdt0(W0, W1) = sz00)) | (~aInteger0(W0)))),
% 0.20/0.68      inference(modus_ponens,[status(thm)],[316, 309])).
% 0.20/0.68  tff(318,plain,
% 0.20/0.68      (![W0: $i, W1: $i] : ((W1 = sz00) | (W0 = sz00) | (~aInteger0(W1)) | (~(sdtasdt0(W0, W1) = sz00)) | (~aInteger0(W0)))),
% 0.20/0.68      inference(modus_ponens,[status(thm)],[317, 307])).
% 0.20/0.68  tff(319,plain,
% 0.20/0.68      (((~![W0: $i, W1: $i] : ((W1 = sz00) | (W0 = sz00) | (~aInteger0(W1)) | (~(sdtasdt0(W0, W1) = sz00)) | (~aInteger0(W0)))) | ((~aInteger0(sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)))) | (sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)) = sz00) | (~(sdtasdt0(sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)), sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10))) = sz00)))) <=> ((~![W0: $i, W1: $i] : ((W1 = sz00) | (W0 = sz00) | (~aInteger0(W1)) | (~(sdtasdt0(W0, W1) = sz00)) | (~aInteger0(W0)))) | (~aInteger0(sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)))) | (sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)) = sz00) | (~(sdtasdt0(sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)), sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10))) = sz00)))),
% 0.20/0.68      inference(rewrite,[status(thm)],[])).
% 0.20/0.68  tff(320,plain,
% 0.20/0.68      (((sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)) = sz00) | (sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)) = sz00) | (~aInteger0(sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)))) | (~(sdtasdt0(sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)), sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10))) = sz00)) | (~aInteger0(sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10))))) <=> ((~aInteger0(sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)))) | (sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)) = sz00) | (~(sdtasdt0(sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)), sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10))) = sz00)))),
% 0.20/0.68      inference(rewrite,[status(thm)],[])).
% 0.20/0.68  tff(321,plain,
% 0.20/0.68      (((~![W0: $i, W1: $i] : ((W1 = sz00) | (W0 = sz00) | (~aInteger0(W1)) | (~(sdtasdt0(W0, W1) = sz00)) | (~aInteger0(W0)))) | ((sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)) = sz00) | (sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)) = sz00) | (~aInteger0(sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)))) | (~(sdtasdt0(sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)), sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10))) = sz00)) | (~aInteger0(sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)))))) <=> ((~![W0: $i, W1: $i] : ((W1 = sz00) | (W0 = sz00) | (~aInteger0(W1)) | (~(sdtasdt0(W0, W1) = sz00)) | (~aInteger0(W0)))) | ((~aInteger0(sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)))) | (sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)) = sz00) | (~(sdtasdt0(sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)), sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10))) = sz00))))),
% 0.20/0.69      inference(monotonicity,[status(thm)],[320])).
% 0.20/0.69  tff(322,plain,
% 0.20/0.69      (((~![W0: $i, W1: $i] : ((W1 = sz00) | (W0 = sz00) | (~aInteger0(W1)) | (~(sdtasdt0(W0, W1) = sz00)) | (~aInteger0(W0)))) | ((sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)) = sz00) | (sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)) = sz00) | (~aInteger0(sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)))) | (~(sdtasdt0(sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)), sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10))) = sz00)) | (~aInteger0(sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)))))) <=> ((~![W0: $i, W1: $i] : ((W1 = sz00) | (W0 = sz00) | (~aInteger0(W1)) | (~(sdtasdt0(W0, W1) = sz00)) | (~aInteger0(W0)))) | (~aInteger0(sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)))) | (sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)) = sz00) | (~(sdtasdt0(sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)), sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10))) = sz00)))),
% 0.20/0.69      inference(transitivity,[status(thm)],[321, 319])).
% 0.20/0.69  tff(323,plain,
% 0.20/0.69      ((~![W0: $i, W1: $i] : ((W1 = sz00) | (W0 = sz00) | (~aInteger0(W1)) | (~(sdtasdt0(W0, W1) = sz00)) | (~aInteger0(W0)))) | ((sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)) = sz00) | (sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)) = sz00) | (~aInteger0(sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)))) | (~(sdtasdt0(sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)), sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10))) = sz00)) | (~aInteger0(sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)))))),
% 0.20/0.69      inference(quant_inst,[status(thm)],[])).
% 0.20/0.69  tff(324,plain,
% 0.20/0.69      ((~![W0: $i, W1: $i] : ((W1 = sz00) | (W0 = sz00) | (~aInteger0(W1)) | (~(sdtasdt0(W0, W1) = sz00)) | (~aInteger0(W0)))) | (~aInteger0(sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)))) | (sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)) = sz00) | (~(sdtasdt0(sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10)), sdtpldt0(sdtpldt0(sz10, xp), smndt0(sz10))) = sz00))),
% 0.20/0.69      inference(modus_ponens,[status(thm)],[323, 322])).
% 0.20/0.69  tff(325,plain,
% 0.20/0.69      ($false),
% 0.20/0.69      inference(unit_resolution,[status(thm)],[324, 318, 305, 284, 260])).
% 0.20/0.69  % SZS output end Proof
% 0.20/0.69  % E exiting
%------------------------------------------------------------------------------