0.00/0.00 % Leo-III: Strategy 1 (for '60') 120.24/30.27 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 120.24/30.27 % [INFO] Parsing done (229ms). 120.24/30.27 % [INFO] Running in sequential loop mode. 120.24/30.27 % [CONFIG] Using configuration: timeout(60) with strategy 120.24/30.27 % [INFO] eprover registered as external prover. 120.24/30.27 % [INFO] cvc4 registered as external prover. 120.24/30.27 % [INFO] Parsing finished. Scanning for conjecture ... 120.24/30.27 % [INFO] Found a conjecture and 0 axioms. Running axiom selection ... 120.24/30.27 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms). 120.24/30.27 % [INFO] Problem is higher-order (TPTP THF). 120.24/30.27 % [INFO] Type checking passed. Searching for refutation ... 120.24/30.27 % External prover 'cvc4' found a proof! 120.24/30.27 % [INFO] Killing All external provers ... 120.24/30.27 % Time passed: 23763ms (effective reasoning time: 23185ms) 120.24/30.27 % Solved by strategy 120.24/30.27 % Axioms used in derivation (0): 120.24/30.27 % No. of inferences in proof: 4 120.24/30.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 23763 ms resp. 23185 ms w/o parsing 120.24/30.27 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 120.24/30.27 thf(in_type, type, in: ($i > ($i > $o))). 120.24/30.27 thf(setextAx_type, type, setextAx: $o). 120.24/30.27 thf(setextAx_def, definition, (setextAx = (! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ A) = (in @ C @ B))) => (A = B))))). 120.24/30.27 thf(emptyset_type, type, emptyset: $i). 120.24/30.27 thf(emptysetAx_type, type, emptysetAx: $o). 120.24/30.27 thf(emptysetAx_def, definition, (emptysetAx = (! [A:$i]: ~ (in @ A @ emptyset)))). 120.24/30.27 thf(setadjoin_type, type, setadjoin: ($i > ($i > $i))). 120.24/30.27 thf(setadjoinAx_type, type, setadjoinAx: $o). 120.24/30.27 thf(setadjoinAx_def, definition, (setadjoinAx = (! [A:$i,B:$i,C:$i]: ((in @ C @ (setadjoin @ A @ B)) = ((C = A) | (in @ C @ B)))))). 120.24/30.27 thf(powerset_type, type, powerset: ($i > $i)). 120.24/30.27 thf(powersetAx_type, type, powersetAx: $o). 120.24/30.27 thf(powersetAx_def, definition, (powersetAx = (! [A:$i,B:$i]: ((in @ B @ (powerset @ A)) = (! [C:$i]: ((in @ C @ B) => (in @ C @ A))))))). 120.24/30.27 thf(setunion_type, type, setunion: ($i > $i)). 120.24/30.27 thf(setunionAx_type, type, setunionAx: $o). 120.24/30.27 thf(setunionAx_def, definition, (setunionAx = (! [A:$i,B:$i]: ((in @ B @ (setunion @ A)) = (? [C:$i]: ((in @ B @ C) & (in @ C @ A))))))). 120.24/30.27 thf(omega_type, type, omega: $i). 120.24/30.27 thf(omega0Ax_type, type, omega0Ax: $o). 120.24/30.27 thf(omega0Ax_def, definition, (omega0Ax = (in @ emptyset @ omega))). 120.24/30.27 thf(omegaSAx_type, type, omegaSAx: $o). 120.24/30.27 thf(omegaSAx_def, definition, (omegaSAx = (! [A:$i]: ((in @ A @ omega) => (in @ (setadjoin @ A @ A) @ omega))))). 120.24/30.27 thf(omegaIndAx_type, type, omegaIndAx: $o). 120.24/30.27 thf(omegaIndAx_def, definition, (omegaIndAx = (! [A:$i]: (((in @ emptyset @ A) & ! [B:$i]: (((in @ B @ omega) & (in @ B @ A)) => (in @ (setadjoin @ B @ B) @ A))) => (! [B:$i]: ((in @ B @ omega) => (in @ B @ A))))))). 120.24/30.27 thf(replAx_type, type, replAx: $o). 120.24/30.27 thf(replAx_def, definition, (replAx = (! [A:($i > ($i > $o)),B:$i]: ((! [C:$i]: ((in @ C @ B) => (exu @ (A @ C)))) => (? [C:$i]: ! [D:$i]: ((in @ D @ C) = (? [E:$i]: ((in @ E @ B) & (A @ E @ D))))))))). 120.24/30.27 thf(foundationAx_type, type, foundationAx: $o). 120.24/30.27 thf(foundationAx_def, definition, (foundationAx = (! [A:$i]: ((? [B:$i]: (in @ B @ A)) => (? [B:$i]: ((in @ B @ A) & ~ (? [C:$i]: ((in @ C @ B) & (in @ C @ A))))))))). 120.24/30.27 thf(wellorderingAx_type, type, wellorderingAx: $o). 120.24/30.27 thf(wellorderingAx_def, definition, (wellorderingAx = (! [A:$i]: ? [B:$i]: (! [C:$i]: ((in @ C @ B) => (! [D:$i]: ((in @ D @ C) => (in @ D @ A)))) & ! [C:$i,D:$i]: (((in @ C @ A) & (in @ D @ A)) => ((! [E:$i]: ((in @ E @ B) => ((in @ C @ E) = (in @ D @ E)))) => (C = D))) & ! [C:$i,D:$i]: (((in @ C @ B) & (in @ D @ B)) => (! [E:$i]: ((in @ E @ C) => (in @ E @ D)) | ! [E:$i]: ((in @ E @ D) => (in @ E @ C)))) & ! [C:$i]: ((! [D:$i]: ((in @ D @ C) => (in @ D @ A)) & ? [D:$i]: (in @ D @ C)) => (? [D:$i,E:$i]: ((in @ D @ B) & (in @ E @ C) & ~ (? [F:$i]: ((in @ F @ D) & (in @ F @ C))) & ! [F:$i]: ((in @ F @ B) => (! [G:$i]: ((in @ G @ F) => (in @ G @ D)) | (in @ E @ F)))))))))). 120.24/30.27 thf(descr_type, type, descr: (($i > $o) > $i)). 120.24/30.27 thf(descrp_type, type, descrp: $o). 120.24/30.27 thf(descrp_def, definition, (descrp = (! [A:($i > $o)]: ((exu @ (A)) => (A @ (descr @ (A))))))). 120.24/30.27 thf(dsetconstr_type, type, dsetconstr: ($i > (($i > $o) > $i))). 120.24/30.27 thf(dsetconstrI_type, type, dsetconstrI: $o). 120.24/30.27 thf(dsetconstrI_def, definition, (dsetconstrI = (! [A:$i,B:($i > $o),C:$i]: ((in @ C @ A) => ((B @ C) => (in @ C @ (dsetconstr @ A @ (B)))))))). 120.24/30.27 thf(dsetconstrEL_type, type, dsetconstrEL: $o). 120.24/30.27 thf(dsetconstrEL_def, definition, (dsetconstrEL = (! [A:$i,B:($i > $o),C:$i]: ((in @ C @ (dsetconstr @ A @ (B))) => (in @ C @ A))))). 120.24/30.27 thf(dsetconstrER_type, type, dsetconstrER: $o). 120.24/30.27 thf(dsetconstrER_def, definition, (dsetconstrER = (! [A:$i,B:($i > $o),C:$i]: ((in @ C @ (dsetconstr @ A @ (B))) => (B @ C))))). 120.24/30.27 thf(exuE1_type, type, exuE1: $o). 120.24/30.27 thf(exuE1_def, definition, (exuE1 = (! [A:($i > $o)]: ((exu @ (A)) => (? [B:$i]: ((A @ B) & ! [C:$i]: ((A @ C) => (B = C)))))))). 120.24/30.27 thf(prop2set_type, type, prop2set: ($o > $i)). 120.24/30.27 thf(prop2setE_type, type, prop2setE: $o). 120.24/30.27 thf(prop2setE_def, definition, (prop2setE = (! [A:$o,B:$i]: ((in @ B @ (prop2set @ A)) => (A))))). 120.24/30.27 thf(emptysetE_type, type, emptysetE: $o). 120.24/30.27 thf(emptysetE_def, definition, (emptysetE = (! [A:$i]: ((in @ A @ emptyset) => (! [B:$o]: (B)))))). 120.24/30.27 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o). 120.24/30.27 thf(emptysetimpfalse_def, definition, (emptysetimpfalse = (! [A:$i]: ((in @ A @ emptyset) => ($false))))). 120.24/30.27 thf(notinemptyset_type, type, notinemptyset: $o). 120.24/30.27 thf(notinemptyset_def, definition, (notinemptyset = (! [A:$i]: ~ (in @ A @ emptyset)))). 120.24/30.27 thf(exuE3e_type, type, exuE3e: $o). 120.24/30.27 thf(exuE3e_def, definition, (exuE3e = (! [A:($i > $o)]: ((exu @ (A)) => (? [B:$i]: (A @ B)))))). 120.24/30.27 thf(setext_type, type, setext: $o). 120.24/30.27 thf(setext_def, definition, (setext = (! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ A) => (in @ C @ B))) => ((! [C:$i]: ((in @ C @ B) => (in @ C @ A))) => (A = B)))))). 120.24/30.27 thf(emptyI_type, type, emptyI: $o). 120.24/30.27 thf(emptyI_def, definition, (emptyI = (! [A:$i]: ((! [B:$i]: ~ (in @ B @ A)) => (A = emptyset))))). 120.24/30.27 thf(noeltsimpempty_type, type, noeltsimpempty: $o). 120.24/30.27 thf(noeltsimpempty_def, definition, (noeltsimpempty = (! [A:$i]: ((! [B:$i]: ~ (in @ B @ A)) => (A = emptyset))))). 120.24/30.27 thf(setbeta_type, type, setbeta: $o). 120.24/30.27 thf(setbeta_def, definition, (setbeta = (! [A:$i,B:($i > $o),C:$i]: ((in @ C @ A) => ((in @ C @ (dsetconstr @ A @ (B))) = (B @ C)))))). 120.24/30.27 thf(nonemptyE1_type, type, nonemptyE1: $o). 120.24/30.27 thf(nonemptyE1_def, definition, (nonemptyE1 = (! [A:$i]: ((nonempty @ A) => (? [B:$i]: (in @ B @ A)))))). 120.24/30.27 thf(nonemptyI_type, type, nonemptyI: $o). 120.24/30.27 thf(nonemptyI_def, definition, (nonemptyI = (! [A:$i,B:($i > $o),C:$i]: ((in @ C @ A) => ((B @ C) => (nonempty @ (dsetconstr @ A @ (B)))))))). 120.24/30.27 thf(nonemptyI1_type, type, nonemptyI1: $o). 120.24/30.27 thf(nonemptyI1_def, definition, (nonemptyI1 = (! [A:$i]: ((? [B:$i]: (in @ B @ A)) => (nonempty @ A))))). 120.24/30.27 thf(setadjoinIL_type, type, setadjoinIL: $o). 120.24/30.27 thf(setadjoinIL_def, definition, (setadjoinIL = (! [A:$i,B:$i]: (in @ A @ (setadjoin @ A @ B))))). 120.24/30.27 thf(emptyinunitempty_type, type, emptyinunitempty: $o). 120.24/30.27 thf(emptyinunitempty_def, definition, (emptyinunitempty = (in @ emptyset @ (setadjoin @ emptyset @ emptyset)))). 120.24/30.27 thf(setadjoinIR_type, type, setadjoinIR: $o). 120.24/30.27 thf(setadjoinIR_def, definition, (setadjoinIR = (! [A:$i,B:$i,C:$i]: ((in @ C @ B) => (in @ C @ (setadjoin @ A @ B)))))). 120.24/30.27 thf(setadjoinE_type, type, setadjoinE: $o). 120.24/30.27 thf(setadjoinE_def, definition, (setadjoinE = (! [A:$i,B:$i,C:$i]: ((in @ C @ (setadjoin @ A @ B)) => (! [D:$o]: (((C = A) => (D)) => (((in @ C @ B) => (D)) => (D)))))))). 120.24/30.27 thf(setadjoinOr_type, type, setadjoinOr: $o). 120.24/30.27 thf(setadjoinOr_def, definition, (setadjoinOr = (! [A:$i,B:$i,C:$i]: ((in @ C @ (setadjoin @ A @ B)) => ((C = A) | (in @ C @ B)))))). 120.24/30.27 thf(setoftrueEq_type, type, setoftrueEq: $o). 120.24/30.27 thf(setoftrueEq_def, definition, (setoftrueEq = (! [A:$i]: ((dsetconstr @ A @ (^ [B:$i]: ($true))) = A)))). 120.24/30.27 thf(powersetI_type, type, powersetI: $o). 120.24/30.27 thf(powersetI_def, definition, (powersetI = (! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ B) => (in @ C @ A))) => (in @ B @ (powerset @ A)))))). 120.24/30.27 thf(emptyinPowerset_type, type, emptyinPowerset: $o). 120.24/30.27 thf(emptyinPowerset_def, definition, (emptyinPowerset = (! [A:$i]: (in @ emptyset @ (powerset @ A))))). 120.24/30.27 thf(emptyInPowerset_type, type, emptyInPowerset: $o). 120.24/30.27 thf(emptyInPowerset_def, definition, (emptyInPowerset = (! [A:$i]: (in @ emptyset @ (powerset @ A))))). 120.24/30.27 thf(powersetE_type, type, powersetE: $o). 120.24/30.27 thf(powersetE_def, definition, (powersetE = (! [A:$i,B:$i,C:$i]: ((in @ B @ (powerset @ A)) => ((in @ C @ B) => (in @ C @ A)))))). 120.24/30.27 thf(setunionI_type, type, setunionI: $o). 120.24/30.27 thf(setunionI_def, definition, (setunionI = (! [A:$i,B:$i,C:$i]: ((in @ B @ C) => ((in @ C @ A) => (in @ B @ (setunion @ A))))))). 120.24/30.27 thf(setunionE_type, type, setunionE: $o). 120.24/30.27 thf(setunionE_def, definition, (setunionE = (! [A:$i,B:$i]: ((in @ B @ (setunion @ A)) => (! [C:$o]: ((! [D:$i]: ((in @ B @ D) => ((in @ D @ A) => (C)))) => (C))))))). 120.24/30.27 thf(subPowSU_type, type, subPowSU: $o). 120.24/30.27 thf(subPowSU_def, definition, (subPowSU = (! [A:$i,B:$i]: ((in @ B @ A) => (in @ B @ (powerset @ (setunion @ A))))))). 120.24/30.27 thf(exuE2_type, type, exuE2: $o). 120.24/30.27 thf(exuE2_def, definition, (exuE2 = (! [A:($i > $o)]: ((exu @ (A)) => (? [B:$i]: ! [C:$i]: ((A @ C) = (C = B))))))). 120.24/30.27 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o). 120.24/30.27 thf(nonemptyImpWitness_def, definition, (nonemptyImpWitness = (! [A:$i]: ((nonempty @ A) => (? [B:$i]: ((in @ B @ A) & ($true))))))). 120.24/30.27 thf(uniqinunit_type, type, uniqinunit: $o). 120.24/30.27 thf(uniqinunit_def, definition, (uniqinunit = (! [A:$i,B:$i]: ((in @ A @ (setadjoin @ B @ emptyset)) => (A = B))))). 120.24/30.27 thf(notinsingleton_type, type, notinsingleton: $o). 120.24/30.27 thf(notinsingleton_def, definition, (notinsingleton = (! [A:$i,B:$i]: ((A != B) => (~ (in @ B @ (setadjoin @ A @ emptyset))))))). 120.24/30.27 thf(eqinunit_type, type, eqinunit: $o). 120.24/30.27 thf(eqinunit_def, definition, (eqinunit = (! [A:$i,B:$i]: ((A = B) => (in @ A @ (setadjoin @ B @ emptyset)))))). 120.24/30.27 thf(singletonsswitch_type, type, singletonsswitch: $o). 120.24/30.27 thf(singletonsswitch_def, definition, (singletonsswitch = (! [A:$i,B:$i]: ((in @ A @ (setadjoin @ B @ emptyset)) => (in @ B @ (setadjoin @ A @ emptyset)))))). 120.24/30.27 thf(upairsetE_type, type, upairsetE: $o). 120.24/30.27 thf(upairsetE_def, definition, (upairsetE = (! [A:$i,B:$i,C:$i]: ((in @ C @ (setadjoin @ A @ (setadjoin @ B @ emptyset))) => ((C = A) | (C = B)))))). 120.24/30.27 thf(upairsetIL_type, type, upairsetIL: $o). 120.24/30.27 thf(upairsetIL_def, definition, (upairsetIL = (! [A:$i,B:$i]: (in @ A @ (setadjoin @ A @ (setadjoin @ B @ emptyset)))))). 120.24/30.27 thf(upairsetIR_type, type, upairsetIR: $o). 120.24/30.27 thf(upairsetIR_def, definition, (upairsetIR = (! [A:$i,B:$i]: (in @ B @ (setadjoin @ A @ (setadjoin @ B @ emptyset)))))). 120.24/30.27 thf(emptyE1_type, type, emptyE1: $o). 120.24/30.27 thf(emptyE1_def, definition, (emptyE1 = (! [A:$i,B:($i > $o)]: ((? [C:$i]: ((in @ C @ A) & (B @ C))) => (((dsetconstr @ A @ (B)) = emptyset) => ($false)))))). 120.24/30.27 thf(vacuousDall_type, type, vacuousDall: $o). 120.24/30.27 thf(vacuousDall_def, definition, (vacuousDall = (! [A:($i > $o),B:$i]: ((in @ B @ emptyset) => (A @ B))))). 120.24/30.27 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o). 120.24/30.27 thf(quantDeMorgan1_def, definition, (quantDeMorgan1 = (! [A:$i,B:($i > $o)]: ((~ (! [C:$i]: ((in @ C @ A) => (B @ C)))) => (? [C:$i]: ((in @ C @ A) & ~ (B @ C))))))). 120.24/30.27 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o). 120.24/30.27 thf(quantDeMorgan2_def, definition, (quantDeMorgan2 = (! [A:$i,B:($i > $o)]: ((! [C:$i]: ((in @ C @ A) => (~ (B @ C)))) => (~ (? [C:$i]: ((in @ C @ A) & (B @ C)))))))). 120.24/30.27 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o). 120.24/30.27 thf(quantDeMorgan3_def, definition, (quantDeMorgan3 = (! [A:$i,B:($i > $o)]: ((~ (? [C:$i]: ((in @ C @ A) & (B @ C)))) => (! [C:$i]: ((in @ C @ A) => (~ (B @ C)))))))). 120.24/30.27 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o). 120.24/30.27 thf(quantDeMorgan4_def, definition, (quantDeMorgan4 = (! [A:$i,B:($i > $o)]: ((? [C:$i]: ((in @ C @ A) & ~ (B @ C))) => (~ (! [C:$i]: ((in @ C @ A) => (B @ C)))))))). 120.24/30.27 thf(prop2setI_type, type, prop2setI: $o). 120.24/30.27 thf(prop2setI_def, definition, (prop2setI = (! [A:$o]: ((A) => (in @ emptyset @ (prop2set @ A)))))). 120.24/30.27 thf(set2prop_type, type, set2prop: ($i > $o)). 120.24/30.27 thf(prop2set2propI_type, type, prop2set2propI: $o). 120.24/30.27 thf(prop2set2propI_def, definition, (prop2set2propI = (! [A:$o]: ((A) => (set2prop @ (prop2set @ A)))))). 120.24/30.27 thf(notdexE_type, type, notdexE: $o). 120.24/30.27 thf(notdexE_def, definition, (notdexE = (! [A:$i,B:($i > $o)]: ((~ (? [C:$i]: ((in @ C @ A) & (B @ C)))) => (! [C:$i]: ((in @ C @ A) => (~ (B @ C)))))))). 120.24/30.27 thf(notdallE_type, type, notdallE: $o). 120.24/30.27 thf(notdallE_def, definition, (notdallE = (! [A:$i,B:($i > $o)]: ((~ (! [C:$i]: ((in @ C @ A) => (B @ C)))) => (? [C:$i]: ((in @ C @ A) & ~ (B @ C))))))). 120.24/30.27 thf(exuI1_type, type, exuI1: $o). 120.24/30.27 thf(exuI1_def, definition, (exuI1 = (! [A:($i > $o)]: ((? [B:$i]: ((A @ B) & ! [C:$i]: ((A @ C) => (B = C)))) => (exu @ (A)))))). 120.24/30.27 thf(exuI3_type, type, exuI3: $o). 120.24/30.27 thf(exuI3_def, definition, (exuI3 = (! [A:($i > $o)]: ((? [B:$i]: (A @ B)) => ((! [B:$i,C:$i]: ((A @ B) => ((A @ C) => (B = C)))) => (exu @ (A))))))). 120.24/30.27 thf(exuI2_type, type, exuI2: $o). 120.24/30.27 thf(exuI2_def, definition, (exuI2 = (! [A:($i > $o)]: ((? [B:$i]: ! [C:$i]: ((A @ C) = (C = B))) => (exu @ (A)))))). 120.24/30.27 thf(inCongP_type, type, inCongP: $o). 120.24/30.27 thf(inCongP_def, definition, (inCongP = (! [A:$i,B:$i]: ((A = B) => (! [C:$i,D:$i]: ((C = D) => ((in @ C @ A) => (in @ D @ B)))))))). 120.24/30.27 thf(in__Cong_type, type, in__Cong: $o). 120.24/30.27 thf(in__Cong_def, definition, (in__Cong = (! [A:$i,B:$i]: ((A = B) => (! [C:$i,D:$i]: ((C = D) => ((in @ C @ A) = (in @ D @ B)))))))). 120.24/30.27 thf(exuE3u_type, type, exuE3u: $o). 120.24/30.27 thf(exuE3u_def, definition, (exuE3u = (! [A:($i > $o)]: ((exu @ (A)) => (! [B:$i,C:$i]: ((A @ B) => ((A @ C) => (B = C)))))))). 120.24/30.27 thf(exu__Cong_type, type, exu__Cong: $o). 120.24/30.27 thf(exu__Cong_def, definition, (exu__Cong = (! [A:($i > $o),B:($i > $o)]: ((! [C:$i,D:$i]: ((C = D) => ((A @ C) = (B @ D)))) => ((exu @ (A)) = (exu @ (B))))))). 120.24/30.27 thf(emptyset__Cong_type, type, emptyset__Cong: $o). 120.24/30.27 thf(emptyset__Cong_def, definition, (emptyset__Cong = (emptyset = emptyset))). 120.24/30.27 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o). 120.24/30.27 thf(setadjoin__Cong_def, definition, (setadjoin__Cong = (! [A:$i,B:$i]: ((A = B) => (! [C:$i,D:$i]: ((C = D) => ((setadjoin @ A @ C) = (setadjoin @ B @ D)))))))). 120.24/30.27 thf(powerset__Cong_type, type, powerset__Cong: $o). 120.24/30.27 thf(powerset__Cong_def, definition, (powerset__Cong = (! [A:$i,B:$i]: ((A = B) => ((powerset @ A) = (powerset @ B)))))). 120.24/30.27 thf(setunion__Cong_type, type, setunion__Cong: $o). 120.24/30.27 thf(setunion__Cong_def, definition, (setunion__Cong = (! [A:$i,B:$i]: ((A = B) => ((setunion @ A) = (setunion @ B)))))). 120.24/30.27 thf(omega__Cong_type, type, omega__Cong: $o). 120.24/30.27 thf(omega__Cong_def, definition, (omega__Cong = (omega = omega))). 120.24/30.27 thf(exuEu_type, type, exuEu: $o). 120.24/30.27 thf(exuEu_def, definition, (exuEu = (! [A:($i > $o)]: ((exu @ (A)) => (! [B:$i,C:$i]: ((A @ B) => ((A @ C) => (B = C)))))))). 120.24/30.27 thf(descr__Cong_type, type, descr__Cong: $o). 120.24/30.27 thf(descr__Cong_def, definition, (descr__Cong = (! [A:($i > $o),B:($i > $o)]: ((! [C:$i,D:$i]: ((C = D) => ((A @ C) = (B @ D)))) => ((exu @ (A)) => ((exu @ (B)) => ((descr @ (A)) = (descr @ (B))))))))). 120.24/30.27 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o). 120.24/30.27 thf(dsetconstr__Cong_def, definition, (dsetconstr__Cong = (! [A:$i,B:$i]: ((A = B) => (! [C:($i > $o),D:($i > $o)]: ((! [E:$i]: ((in @ E @ A) => (! [F:$i]: ((in @ F @ B) => ((E = F) => ((C @ E) = (D @ F))))))) => ((dsetconstr @ A @ (C)) = (dsetconstr @ B @ (D))))))))). 120.24/30.27 thf(subset_type, type, subset: ($i > ($i > $o))). 120.24/30.27 thf(subsetI1_type, type, subsetI1: $o). 120.24/30.27 thf(subsetI1_def, definition, (subsetI1 = (! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ A) => (in @ C @ B))) => (subset @ A @ B))))). 120.24/30.27 thf(eqimpsubset2_type, type, eqimpsubset2: $o). 120.24/30.27 thf(eqimpsubset2_def, definition, (eqimpsubset2 = (! [A:$i,B:$i]: ((A = B) => (subset @ B @ A))))). 120.24/30.27 thf(eqimpsubset1_type, type, eqimpsubset1: $o). 120.24/30.27 thf(eqimpsubset1_def, definition, (eqimpsubset1 = (! [A:$i,B:$i]: ((A = B) => (subset @ A @ B))))). 120.24/30.27 thf(subsetI2_type, type, subsetI2: $o). 120.24/30.27 thf(subsetI2_def, definition, (subsetI2 = (! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ A) => (in @ C @ B))) => (subset @ A @ B))))). 120.24/30.27 thf(emptysetsubset_type, type, emptysetsubset: $o). 120.24/30.27 thf(emptysetsubset_def, definition, (emptysetsubset = (! [A:$i]: (subset @ emptyset @ A)))). 120.24/30.27 thf(subsetE_type, type, subsetE: $o). 120.24/30.27 thf(subsetE_def, definition, (subsetE = (! [A:$i,B:$i,C:$i]: ((subset @ A @ B) => ((in @ C @ A) => (in @ C @ B)))))). 120.24/30.27 thf(subsetE2_type, type, subsetE2: $o). 120.24/30.27 thf(subsetE2_def, definition, (subsetE2 = (! [A:$i,B:$i,C:$i]: ((subset @ A @ B) => ((~ (in @ C @ B)) => (~ (in @ C @ A))))))). 120.24/30.27 thf(notsubsetI_type, type, notsubsetI: $o). 120.24/30.27 thf(notsubsetI_def, definition, (notsubsetI = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => ((~ (in @ C @ B)) => (~ (subset @ A @ B))))))). 120.24/30.27 thf(notequalI1_type, type, notequalI1: $o). 120.24/30.27 thf(notequalI1_def, definition, (notequalI1 = (! [A:$i,B:$i]: ((~ (subset @ A @ B)) => (A != B))))). 120.24/30.27 thf(notequalI2_type, type, notequalI2: $o). 120.24/30.27 thf(notequalI2_def, definition, (notequalI2 = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => ((~ (in @ C @ B)) => (A != B)))))). 120.24/30.27 thf(subsetRefl_type, type, subsetRefl: $o). 120.24/30.27 thf(subsetRefl_def, definition, (subsetRefl = (! [A:$i]: (subset @ A @ A)))). 120.24/30.27 thf(subsetTrans_type, type, subsetTrans: $o). 120.24/30.27 thf(subsetTrans_def, definition, (subsetTrans = (! [A:$i,B:$i,C:$i]: ((subset @ A @ B) => ((subset @ B @ C) => (subset @ A @ C)))))). 120.24/30.27 thf(setadjoinSub_type, type, setadjoinSub: $o). 120.24/30.27 thf(setadjoinSub_def, definition, (setadjoinSub = (! [A:$i,B:$i]: (subset @ B @ (setadjoin @ A @ B))))). 120.24/30.27 thf(setadjoinSub2_type, type, setadjoinSub2: $o). 120.24/30.27 thf(setadjoinSub2_def, definition, (setadjoinSub2 = (! [A:$i,B:$i,C:$i]: ((subset @ A @ C) => (subset @ A @ (setadjoin @ B @ C)))))). 120.24/30.27 thf(subset2powerset_type, type, subset2powerset: $o). 120.24/30.27 thf(subset2powerset_def, definition, (subset2powerset = (! [A:$i,B:$i]: ((subset @ A @ B) => (in @ A @ (powerset @ B)))))). 120.24/30.27 thf(setextsub_type, type, setextsub: $o). 120.24/30.27 thf(setextsub_def, definition, (setextsub = (! [A:$i,B:$i]: ((subset @ A @ B) => ((subset @ B @ A) => (A = B)))))). 120.24/30.27 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o). 120.24/30.27 thf(subsetemptysetimpeq_def, definition, (subsetemptysetimpeq = (! [A:$i]: ((subset @ A @ emptyset) => (A = emptyset))))). 120.24/30.27 thf(powersetI1_type, type, powersetI1: $o). 120.24/30.27 thf(powersetI1_def, definition, (powersetI1 = (! [A:$i,B:$i]: ((subset @ B @ A) => (in @ B @ (powerset @ A)))))). 120.24/30.27 thf(powersetE1_type, type, powersetE1: $o). 120.24/30.27 thf(powersetE1_def, definition, (powersetE1 = (! [A:$i,B:$i]: ((in @ B @ (powerset @ A)) => (subset @ B @ A))))). 120.24/30.27 thf(inPowerset_type, type, inPowerset: $o). 120.24/30.27 thf(inPowerset_def, definition, (inPowerset = (! [A:$i]: (in @ A @ (powerset @ A))))). 120.24/30.27 thf(powersetsubset_type, type, powersetsubset: $o). 120.24/30.27 thf(powersetsubset_def, definition, (powersetsubset = (! [A:$i,B:$i]: ((subset @ A @ B) => (subset @ (powerset @ A) @ (powerset @ B)))))). 120.24/30.27 thf(sepInPowerset_type, type, sepInPowerset: $o). 120.24/30.27 thf(sepInPowerset_def, definition, (sepInPowerset = (! [A:$i,B:($i > $o)]: (in @ (dsetconstr @ A @ (B)) @ (powerset @ A))))). 120.24/30.27 thf(sepSubset_type, type, sepSubset: $o). 120.24/30.27 thf(sepSubset_def, definition, (sepSubset = (! [A:$i,B:($i > $o)]: (subset @ (dsetconstr @ A @ (B)) @ A)))). 120.24/30.27 thf(binunion_type, type, binunion: ($i > ($i > $i))). 120.24/30.27 thf(binunionIL_type, type, binunionIL: $o). 120.24/30.27 thf(binunionIL_def, definition, (binunionIL = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (in @ C @ (binunion @ A @ B)))))). 120.24/30.27 thf(upairset2IR_type, type, upairset2IR: $o). 120.24/30.27 thf(upairset2IR_def, definition, (upairset2IR = (! [A:$i,B:$i]: (in @ B @ (setadjoin @ A @ (setadjoin @ B @ emptyset)))))). 120.24/30.27 thf(binunionIR_type, type, binunionIR: $o). 120.24/30.27 thf(binunionIR_def, definition, (binunionIR = (! [A:$i,B:$i,C:$i]: ((in @ C @ B) => (in @ C @ (binunion @ A @ B)))))). 120.24/30.27 thf(binunionEcases_type, type, binunionEcases: $o). 120.24/30.27 thf(binunionEcases_def, definition, (binunionEcases = (! [A:$i,B:$i,C:$i,D:$o]: ((in @ C @ (binunion @ A @ B)) => (((in @ C @ A) => (D)) => (((in @ C @ B) => (D)) => (D))))))). 120.24/30.27 thf(binunionE_type, type, binunionE: $o). 120.24/30.27 thf(binunionE_def, definition, (binunionE = (! [A:$i,B:$i,C:$i]: ((in @ C @ (binunion @ A @ B)) => ((in @ C @ A) | (in @ C @ B)))))). 120.24/30.27 thf(binunionLsub_type, type, binunionLsub: $o). 120.24/30.27 thf(binunionLsub_def, definition, (binunionLsub = (! [A:$i,B:$i]: (subset @ A @ (binunion @ A @ B))))). 120.24/30.27 thf(binunionRsub_type, type, binunionRsub: $o). 120.24/30.27 thf(binunionRsub_def, definition, (binunionRsub = (! [A:$i,B:$i]: (subset @ B @ (binunion @ A @ B))))). 120.24/30.27 thf(binintersect_type, type, binintersect: ($i > ($i > $i))). 120.24/30.27 thf(binintersectI_type, type, binintersectI: $o). 120.24/30.27 thf(binintersectI_def, definition, (binintersectI = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => ((in @ C @ B) => (in @ C @ (binintersect @ A @ B))))))). 120.24/30.27 thf(binintersectSubset5_type, type, binintersectSubset5: $o). 120.24/30.27 thf(binintersectSubset5_def, definition, (binintersectSubset5 = (! [A:$i,B:$i,C:$i]: ((subset @ C @ A) => ((subset @ C @ B) => (subset @ C @ (binintersect @ A @ B))))))). 120.24/30.27 thf(binintersectEL_type, type, binintersectEL: $o). 120.24/30.27 thf(binintersectEL_def, definition, (binintersectEL = (! [A:$i,B:$i,C:$i]: ((in @ C @ (binintersect @ A @ B)) => (in @ C @ A))))). 120.24/30.27 thf(binintersectLsub_type, type, binintersectLsub: $o). 120.24/30.27 thf(binintersectLsub_def, definition, (binintersectLsub = (! [A:$i,B:$i]: (subset @ (binintersect @ A @ B) @ A)))). 120.24/30.27 thf(binintersectSubset2_type, type, binintersectSubset2: $o). 120.24/30.27 thf(binintersectSubset2_def, definition, (binintersectSubset2 = (! [A:$i,B:$i]: ((subset @ A @ B) => ((binintersect @ A @ B) = A))))). 120.24/30.27 thf(binintersectSubset3_type, type, binintersectSubset3: $o). 120.24/30.27 thf(binintersectSubset3_def, definition, (binintersectSubset3 = (! [A:$i,B:$i]: (((binintersect @ A @ B) = B) => (subset @ B @ A))))). 120.24/30.27 thf(binintersectER_type, type, binintersectER: $o). 120.24/30.27 thf(binintersectER_def, definition, (binintersectER = (! [A:$i,B:$i,C:$i]: ((in @ C @ (binintersect @ A @ B)) => (in @ C @ B))))). 120.24/30.27 thf(disjointsetsI1_type, type, disjointsetsI1: $o). 120.24/30.27 thf(disjointsetsI1_def, definition, (disjointsetsI1 = (! [A:$i,B:$i]: ((~ (? [C:$i]: ((in @ C @ A) & (in @ C @ B)))) => ((binintersect @ A @ B) = emptyset))))). 120.24/30.27 thf(binintersectRsub_type, type, binintersectRsub: $o). 120.24/30.27 thf(binintersectRsub_def, definition, (binintersectRsub = (! [A:$i,B:$i]: (subset @ (binintersect @ A @ B) @ B)))). 120.24/30.27 thf(binintersectSubset4_type, type, binintersectSubset4: $o). 120.24/30.27 thf(binintersectSubset4_def, definition, (binintersectSubset4 = (! [A:$i,B:$i]: ((subset @ B @ A) => ((binintersect @ A @ B) = B))))). 120.24/30.27 thf(binintersectSubset1_type, type, binintersectSubset1: $o). 120.24/30.27 thf(binintersectSubset1_def, definition, (binintersectSubset1 = (! [A:$i,B:$i]: (((binintersect @ A @ B) = A) => (subset @ A @ B))))). 120.24/30.27 thf(bs114d_type, type, bs114d: $o). 120.24/30.27 thf(bs114d_def, definition, (bs114d = (! [A:$i,B:$i,C:$i]: ((binintersect @ A @ (binunion @ B @ C)) = (binunion @ (binintersect @ A @ B) @ (binintersect @ A @ C)))))). 120.24/30.27 thf(setminus_type, type, setminus: ($i > ($i > $i))). 120.24/30.27 thf(setminusI_type, type, setminusI: $o). 120.24/30.27 thf(setminusI_def, definition, (setminusI = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => ((~ (in @ C @ B)) => (in @ C @ (setminus @ A @ B))))))). 120.24/30.27 thf(setminusEL_type, type, setminusEL: $o). 120.24/30.27 thf(setminusEL_def, definition, (setminusEL = (! [A:$i,B:$i,C:$i]: ((in @ C @ (setminus @ A @ B)) => (in @ C @ A))))). 120.24/30.27 thf(setminusER_type, type, setminusER: $o). 120.24/30.27 thf(setminusER_def, definition, (setminusER = (! [A:$i,B:$i,C:$i]: ((in @ C @ (setminus @ A @ B)) => (~ (in @ C @ B)))))). 120.24/30.27 thf(setminusSubset2_type, type, setminusSubset2: $o). 120.24/30.27 thf(setminusSubset2_def, definition, (setminusSubset2 = (! [A:$i,B:$i]: ((subset @ A @ B) => ((setminus @ A @ B) = emptyset))))). 120.24/30.27 thf(setminusERneg_type, type, setminusERneg: $o). 120.24/30.27 thf(setminusERneg_def, definition, (setminusERneg = (! [A:$i,B:$i,C:$i]: ((~ (in @ C @ (setminus @ A @ B))) => ((in @ C @ A) => (in @ C @ B)))))). 120.24/30.27 thf(setminusELneg_type, type, setminusELneg: $o). 120.24/30.27 thf(setminusELneg_def, definition, (setminusELneg = (! [A:$i,B:$i,C:$i]: ((~ (in @ C @ (setminus @ A @ B))) => ((~ (in @ C @ B)) => (~ (in @ C @ A))))))). 120.24/30.27 thf(setminusILneg_type, type, setminusILneg: $o). 120.24/30.27 thf(setminusILneg_def, definition, (setminusILneg = (! [A:$i,B:$i,C:$i]: ((~ (in @ C @ A)) => (~ (in @ C @ (setminus @ A @ B))))))). 120.24/30.27 thf(setminusIRneg_type, type, setminusIRneg: $o). 120.24/30.27 thf(setminusIRneg_def, definition, (setminusIRneg = (! [A:$i,B:$i,C:$i]: ((in @ C @ B) => (~ (in @ C @ (setminus @ A @ B))))))). 120.24/30.27 thf(setminusLsub_type, type, setminusLsub: $o). 120.24/30.27 thf(setminusLsub_def, definition, (setminusLsub = (! [A:$i,B:$i]: (subset @ (setminus @ A @ B) @ A)))). 120.24/30.27 thf(setminusSubset1_type, type, setminusSubset1: $o). 120.24/30.27 thf(setminusSubset1_def, definition, (setminusSubset1 = (! [A:$i,B:$i]: (((setminus @ A @ B) = emptyset) => (subset @ A @ B))))). 120.24/30.27 thf(symdiff_type, type, symdiff: ($i > ($i > $i))). 120.24/30.27 thf(symdiffE_type, type, symdiffE: $o). 120.24/30.27 thf(symdiffE_def, definition, (symdiffE = (! [A:$i,B:$i,C:$i]: ((in @ C @ (symdiff @ A @ B)) => (! [D:$o]: (((in @ C @ A) => ((~ (in @ C @ B)) => (D))) => (((~ (in @ C @ A)) => ((in @ C @ B) => (D))) => (D)))))))). 120.24/30.27 thf(symdiffI1_type, type, symdiffI1: $o). 120.24/30.27 thf(symdiffI1_def, definition, (symdiffI1 = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => ((~ (in @ C @ B)) => (in @ C @ (symdiff @ A @ B))))))). 120.24/30.27 thf(symdiffI2_type, type, symdiffI2: $o). 120.24/30.27 thf(symdiffI2_def, definition, (symdiffI2 = (! [A:$i,B:$i,C:$i]: ((~ (in @ C @ A)) => ((in @ C @ B) => (in @ C @ (symdiff @ A @ B))))))). 120.24/30.27 thf(symdiffIneg1_type, type, symdiffIneg1: $o). 120.24/30.27 thf(symdiffIneg1_def, definition, (symdiffIneg1 = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => ((in @ C @ B) => (~ (in @ C @ (symdiff @ A @ B)))))))). 120.24/30.27 thf(symdiffIneg2_type, type, symdiffIneg2: $o). 120.24/30.27 thf(symdiffIneg2_def, definition, (symdiffIneg2 = (! [A:$i,B:$i,C:$i]: ((~ (in @ C @ A)) => ((~ (in @ C @ B)) => (~ (in @ C @ (symdiff @ A @ B)))))))). 120.24/30.27 thf(iskpair_type, type, iskpair: ($i > $o)). 120.24/30.27 thf(secondinupair_type, type, secondinupair: $o). 120.24/30.27 thf(secondinupair_def, definition, (secondinupair = (! [A:$i,B:$i]: (in @ B @ (setadjoin @ A @ (setadjoin @ B @ emptyset)))))). 120.24/30.27 thf(setukpairIL_type, type, setukpairIL: $o). 120.24/30.27 thf(setukpairIL_def, definition, (setukpairIL = (! [A:$i,B:$i]: (in @ A @ (setunion @ (setadjoin @ (setadjoin @ A @ emptyset) @ (setadjoin @ (setadjoin @ A @ (setadjoin @ B @ emptyset)) @ emptyset))))))). 120.24/30.27 thf(setukpairIR_type, type, setukpairIR: $o). 120.24/30.27 thf(setukpairIR_def, definition, (setukpairIR = (! [A:$i,B:$i]: (in @ B @ (setunion @ (setadjoin @ (setadjoin @ A @ emptyset) @ (setadjoin @ (setadjoin @ A @ (setadjoin @ B @ emptyset)) @ emptyset))))))). 120.24/30.27 thf(kpairiskpair_type, type, kpairiskpair: $o). 120.24/30.27 thf(kpairiskpair_def, definition, (kpairiskpair = (! [A:$i,B:$i]: (iskpair @ (setadjoin @ (setadjoin @ A @ emptyset) @ (setadjoin @ (setadjoin @ A @ (setadjoin @ B @ emptyset)) @ emptyset)))))). 120.24/30.27 thf(kpair_type, type, kpair: ($i > ($i > $i))). 120.24/30.27 thf(kpairp_type, type, kpairp: $o). 120.24/30.27 thf(kpairp_def, definition, (kpairp = (! [A:$i,B:$i]: (iskpair @ (kpair @ A @ B))))). 120.24/30.27 thf(cartprod_type, type, cartprod: ($i > ($i > $i))). 120.24/30.27 thf(singletonsubset_type, type, singletonsubset: $o). 120.24/30.27 thf(singletonsubset_def, definition, (singletonsubset = (! [A:$i,B:$i]: ((in @ B @ A) => (subset @ (setadjoin @ B @ emptyset) @ A))))). 120.24/30.27 thf(singletoninpowerset_type, type, singletoninpowerset: $o). 120.24/30.27 thf(singletoninpowerset_def, definition, (singletoninpowerset = (! [A:$i,B:$i]: ((in @ B @ A) => (in @ (setadjoin @ B @ emptyset) @ (powerset @ A)))))). 120.24/30.27 thf(singletoninpowunion_type, type, singletoninpowunion: $o). 120.24/30.27 thf(singletoninpowunion_def, definition, (singletoninpowunion = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (in @ (setadjoin @ C @ emptyset) @ (powerset @ (binunion @ A @ B))))))). 120.24/30.27 thf(upairset2E_type, type, upairset2E: $o). 120.24/30.27 thf(upairset2E_def, definition, (upairset2E = (! [A:$i,B:$i,C:$i]: ((in @ C @ (setadjoin @ A @ (setadjoin @ B @ emptyset))) => ((C = A) | (C = B)))))). 120.24/30.27 thf(upairsubunion_type, type, upairsubunion: $o). 120.24/30.27 thf(upairsubunion_def, definition, (upairsubunion = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ B) => (subset @ (setadjoin @ C @ (setadjoin @ D @ emptyset)) @ (binunion @ A @ B)))))))). 120.24/30.27 thf(upairinpowunion_type, type, upairinpowunion: $o). 120.24/30.27 thf(upairinpowunion_def, definition, (upairinpowunion = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ B) => (in @ (setadjoin @ C @ (setadjoin @ D @ emptyset)) @ (powerset @ (binunion @ A @ B))))))))). 120.24/30.27 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o). 120.24/30.27 thf(ubforcartprodlem1_def, definition, (ubforcartprodlem1 = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ B) => (subset @ (setadjoin @ (setadjoin @ C @ emptyset) @ (setadjoin @ (setadjoin @ C @ (setadjoin @ D @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ A @ B))))))))). 120.24/30.27 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o). 120.24/30.27 thf(ubforcartprodlem2_def, definition, (ubforcartprodlem2 = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ B) => (in @ (setadjoin @ (setadjoin @ C @ emptyset) @ (setadjoin @ (setadjoin @ C @ (setadjoin @ D @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ A @ B)))))))))). 120.24/30.27 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o). 120.24/30.27 thf(ubforcartprodlem3_def, definition, (ubforcartprodlem3 = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ B) => (in @ (kpair @ C @ D) @ (powerset @ (powerset @ (binunion @ A @ B)))))))))). 120.24/30.27 thf(cartprodpairin_type, type, cartprodpairin: $o). 120.24/30.27 thf(cartprodpairin_def, definition, (cartprodpairin = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ B) => (in @ (kpair @ C @ D) @ (cartprod @ A @ B)))))))). 120.24/30.27 thf(cartprodmempair1_type, type, cartprodmempair1: $o). 120.24/30.27 thf(cartprodmempair1_def, definition, (cartprodmempair1 = (! [A:$i,B:$i,C:$i]: ((in @ C @ (cartprod @ A @ B)) => (? [D:$i]: ((in @ D @ A) & ? [E:$i]: ((in @ E @ B) & (C = (kpair @ D @ E))))))))). 120.24/30.27 thf(cartprodmempair_type, type, cartprodmempair: $o). 120.24/30.27 thf(cartprodmempair_def, definition, (cartprodmempair = (! [A:$i,B:$i,C:$i]: ((in @ C @ (cartprod @ A @ B)) => (iskpair @ C))))). 120.24/30.27 thf(setunionE2_type, type, setunionE2: $o). 120.24/30.27 thf(setunionE2_def, definition, (setunionE2 = (! [A:$i,B:$i]: ((in @ B @ (setunion @ A)) => (? [C:$i]: ((in @ C @ A) & (in @ B @ C))))))). 120.24/30.27 thf(setunionsingleton1_type, type, setunionsingleton1: $o). 120.24/30.27 thf(setunionsingleton1_def, definition, (setunionsingleton1 = (! [A:$i]: (subset @ (setunion @ (setadjoin @ A @ emptyset)) @ A)))). 120.24/30.27 thf(setunionsingleton2_type, type, setunionsingleton2: $o). 120.24/30.27 thf(setunionsingleton2_def, definition, (setunionsingleton2 = (! [A:$i]: (subset @ A @ (setunion @ (setadjoin @ A @ emptyset)))))). 120.24/30.27 thf(setunionsingleton_type, type, setunionsingleton: $o). 120.24/30.27 thf(setunionsingleton_def, definition, (setunionsingleton = (! [A:$i]: ((setunion @ (setadjoin @ A @ emptyset)) = A)))). 120.24/30.27 thf(singleton_type, type, singleton: ($i > $o)). 120.24/30.27 thf(singletonprop_type, type, singletonprop: $o). 120.24/30.27 thf(singletonprop_def, definition, (singletonprop = (! [A:$i,B:($i > $o)]: ((! [C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ A) => ((B @ C) => ((B @ D) => (C = D))))))) => ((? [C:$i]: ((in @ C @ A) & (B @ C))) => (singleton @ (dsetconstr @ A @ (B)))))))). 120.24/30.27 thf(ex1E1_type, type, ex1E1: $o). 120.24/30.27 thf(ex1E1_def, definition, (ex1E1 = (! [A:$i,B:($i > $o)]: ((ex1 @ A @ (B)) => (? [C:$i]: ((in @ C @ A) & (B @ C))))))). 120.24/30.27 thf(ex1I_type, type, ex1I: $o). 120.24/30.27 thf(ex1I_def, definition, (ex1I = (! [A:$i,B:($i > $o),C:$i]: ((in @ C @ A) => ((B @ C) => ((! [D:$i]: ((in @ D @ A) => ((B @ D) => (D = C)))) => (ex1 @ A @ (B)))))))). 120.24/30.27 thf(ex1I2_type, type, ex1I2: $o). 120.24/30.27 thf(ex1I2_def, definition, (ex1I2 = (! [A:$i,B:($i > $o)]: ((! [C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ A) => ((B @ C) => ((B @ D) => (C = D))))))) => ((? [C:$i]: ((in @ C @ A) & (B @ C))) => (ex1 @ A @ (B))))))). 120.24/30.27 thf(singletonsuniq_type, type, singletonsuniq: $o). 120.24/30.27 thf(singletonsuniq_def, definition, (singletonsuniq = (! [A:$i,B:$i]: (((setadjoin @ A @ emptyset) = (setadjoin @ B @ emptyset)) => (A = B))))). 120.24/30.27 thf(setukpairinjL1_type, type, setukpairinjL1: $o). 120.24/30.27 thf(setukpairinjL1_def, definition, (setukpairinjL1 = (! [A:$i,B:$i,C:$i]: ((in @ (setadjoin @ C @ emptyset) @ (setadjoin @ (setadjoin @ A @ emptyset) @ (setadjoin @ (setadjoin @ A @ (setadjoin @ B @ emptyset)) @ emptyset))) => (A = C))))). 120.24/30.27 thf(kfstsingleton_type, type, kfstsingleton: $o). 120.24/30.27 thf(kfstsingleton_def, definition, (kfstsingleton = (! [A:$i]: ((iskpair @ A) => (singleton @ (dsetconstr @ (setunion @ A) @ (^ [B:$i]: (in @ (setadjoin @ B @ emptyset) @ A)))))))). 120.24/30.27 thf(theprop_type, type, theprop: $o). 120.24/30.27 thf(theprop_def, definition, (theprop = (! [A:$i]: ((singleton @ A) => (in @ (setunion @ A) @ A))))). 120.24/30.27 thf(kfst_type, type, kfst: ($i > $i)). 120.24/30.27 thf(kfstpairEq_type, type, kfstpairEq: $o). 120.24/30.27 thf(kfstpairEq_def, definition, (kfstpairEq = (! [A:$i,B:$i]: ((kfst @ (kpair @ A @ B)) = A)))). 120.24/30.27 thf(cartprodfstin_type, type, cartprodfstin: $o). 120.24/30.27 thf(cartprodfstin_def, definition, (cartprodfstin = (! [A:$i,B:$i,C:$i]: ((in @ C @ (cartprod @ A @ B)) => (in @ (kfst @ C) @ A))))). 120.24/30.27 thf(setukpairinjL2_type, type, setukpairinjL2: $o). 120.24/30.27 thf(setukpairinjL2_def, definition, (setukpairinjL2 = (! [A:$i,B:$i,C:$i,D:$i]: (((setadjoin @ (setadjoin @ A @ emptyset) @ (setadjoin @ (setadjoin @ A @ (setadjoin @ B @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ C @ emptyset) @ (setadjoin @ (setadjoin @ C @ (setadjoin @ D @ emptyset)) @ emptyset))) => (A = C))))). 120.24/30.27 thf(setukpairinjL_type, type, setukpairinjL: $o). 120.24/30.27 thf(setukpairinjL_def, definition, (setukpairinjL = (! [A:$i,B:$i,C:$i,D:$i]: (((kpair @ A @ B) = (kpair @ C @ D)) => (A = C))))). 120.24/30.27 thf(setukpairinjR11_type, type, setukpairinjR11: $o). 120.24/30.27 thf(setukpairinjR11_def, definition, (setukpairinjR11 = (! [A:$i,B:$i]: ((A = B) => ((setadjoin @ A @ (setadjoin @ B @ emptyset)) = (setadjoin @ A @ emptyset)))))). 120.24/30.27 thf(setukpairinjR12_type, type, setukpairinjR12: $o). 120.24/30.27 thf(setukpairinjR12_def, definition, (setukpairinjR12 = (! [A:$i,B:$i]: ((A = B) => ((setadjoin @ (setadjoin @ A @ emptyset) @ (setadjoin @ (setadjoin @ A @ (setadjoin @ B @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ A @ emptyset) @ emptyset)))))). 120.24/30.27 thf(setukpairinjR1_type, type, setukpairinjR1: $o). 120.24/30.27 thf(setukpairinjR1_def, definition, (setukpairinjR1 = (! [A:$i,B:$i,C:$i,D:$i]: (((setadjoin @ (setadjoin @ A @ emptyset) @ (setadjoin @ (setadjoin @ A @ (setadjoin @ B @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ C @ emptyset) @ (setadjoin @ (setadjoin @ C @ (setadjoin @ D @ emptyset)) @ emptyset))) => ((C = D) => (B = D)))))). 120.24/30.27 thf(upairequniteq_type, type, upairequniteq: $o). 120.24/30.27 thf(upairequniteq_def, definition, (upairequniteq = (! [A:$i,B:$i,C:$i]: (((setadjoin @ A @ (setadjoin @ B @ emptyset)) = (setadjoin @ C @ emptyset)) => (A = B))))). 120.24/30.27 thf(setukpairinjR2_type, type, setukpairinjR2: $o). 120.24/30.27 thf(setukpairinjR2_def, definition, (setukpairinjR2 = (! [A:$i,B:$i,C:$i,D:$i]: (((setadjoin @ (setadjoin @ A @ emptyset) @ (setadjoin @ (setadjoin @ A @ (setadjoin @ B @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ C @ emptyset) @ (setadjoin @ (setadjoin @ C @ (setadjoin @ D @ emptyset)) @ emptyset))) => (B = D))))). 120.24/30.27 thf(setukpairinjR_type, type, setukpairinjR: $o). 120.24/30.27 thf(setukpairinjR_def, definition, (setukpairinjR = (! [A:$i,B:$i,C:$i,D:$i]: (((kpair @ A @ B) = (kpair @ C @ D)) => (B = D))))). 120.24/30.27 thf(ksndsingleton_type, type, ksndsingleton: $o). 120.24/30.27 thf(ksndsingleton_def, definition, (ksndsingleton = (! [A:$i]: ((iskpair @ A) => (singleton @ (dsetconstr @ (setunion @ A) @ (^ [B:$i]: (A = (kpair @ (kfst @ A) @ B))))))))). 120.24/30.27 thf(ksnd_type, type, ksnd: ($i > $i)). 120.24/30.27 thf(ksndpairEq_type, type, ksndpairEq: $o). 120.24/30.27 thf(ksndpairEq_def, definition, (ksndpairEq = (! [A:$i,B:$i]: ((ksnd @ (kpair @ A @ B)) = B)))). 120.24/30.27 thf(kpairsurjEq_type, type, kpairsurjEq: $o). 120.24/30.27 thf(kpairsurjEq_def, definition, (kpairsurjEq = (! [A:$i]: ((iskpair @ A) => ((kpair @ (kfst @ A) @ (ksnd @ A)) = A))))). 120.24/30.27 thf(cartprodsndin_type, type, cartprodsndin: $o). 120.24/30.27 thf(cartprodsndin_def, definition, (cartprodsndin = (! [A:$i,B:$i,C:$i]: ((in @ C @ (cartprod @ A @ B)) => (in @ (ksnd @ C) @ B))))). 120.24/30.27 thf(cartprodpairmemEL_type, type, cartprodpairmemEL: $o). 120.24/30.27 thf(cartprodpairmemEL_def, definition, (cartprodpairmemEL = (! [A:$i,B:$i,C:$i,D:$i]: ((in @ (kpair @ C @ D) @ (cartprod @ A @ B)) => (in @ C @ A))))). 120.24/30.27 thf(cartprodpairmemER_type, type, cartprodpairmemER: $o). 120.24/30.27 thf(cartprodpairmemER_def, definition, (cartprodpairmemER = (! [A:$i,B:$i,C:$i,D:$i]: ((in @ (kpair @ C @ D) @ (cartprod @ A @ B)) => (in @ D @ B))))). 120.24/30.27 thf(cartprodmempaircEq_type, type, cartprodmempaircEq: $o). 120.24/30.27 thf(cartprodmempaircEq_def, definition, (cartprodmempaircEq = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ B) => ((kpair @ C @ D) = (kpair @ C @ D)))))))). 120.24/30.27 thf(cartprodfstpairEq_type, type, cartprodfstpairEq: $o). 120.24/30.27 thf(cartprodfstpairEq_def, definition, (cartprodfstpairEq = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ B) => ((kfst @ (kpair @ C @ D)) = C))))))). 120.24/30.27 thf(cartprodsndpairEq_type, type, cartprodsndpairEq: $o). 120.24/30.27 thf(cartprodsndpairEq_def, definition, (cartprodsndpairEq = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ B) => ((ksnd @ (kpair @ C @ D)) = D))))))). 120.24/30.27 thf(cartprodpairsurjEq_type, type, cartprodpairsurjEq: $o). 120.24/30.27 thf(cartprodpairsurjEq_def, definition, (cartprodpairsurjEq = (! [A:$i,B:$i,C:$i]: ((in @ C @ (cartprod @ A @ B)) => ((kpair @ (kfst @ C) @ (ksnd @ C)) = C))))). 120.24/30.27 thf(dpsetconstr_type, type, dpsetconstr: ($i > ($i > (($i > ($i > $o)) > $i)))). 120.24/30.27 thf(dpsetconstrI_type, type, dpsetconstrI: $o). 120.24/30.27 thf(dpsetconstrI_def, definition, (dpsetconstrI = (! [A:$i,B:$i,C:($i > ($i > $o)),D:$i]: ((in @ D @ A) => (! [E:$i]: ((in @ E @ B) => ((C @ D @ E) => (in @ (kpair @ D @ E) @ (dpsetconstr @ A @ B @ (C)))))))))). 120.24/30.27 thf(dpsetconstrSub_type, type, dpsetconstrSub: $o). 120.24/30.27 thf(dpsetconstrSub_def, definition, (dpsetconstrSub = (! [A:$i,B:$i,C:($i > ($i > $o))]: (subset @ (dpsetconstr @ A @ B @ (C)) @ (cartprod @ A @ B))))). 120.24/30.27 thf(setOfPairsIsBReln_type, type, setOfPairsIsBReln: $o). 120.24/30.27 thf(setOfPairsIsBReln_def, definition, (setOfPairsIsBReln = (! [A:$i,B:$i,C:($i > ($i > $o))]: (breln @ A @ B @ (dpsetconstr @ A @ B @ (C)))))). 120.24/30.27 thf(dpsetconstrERa_type, type, dpsetconstrERa: $o). 120.24/30.27 thf(dpsetconstrERa_def, definition, (dpsetconstrERa = (! [A:$i,B:$i,C:($i > ($i > $o)),D:$i]: ((in @ D @ A) => (! [E:$i]: ((in @ E @ B) => ((in @ (kpair @ D @ E) @ (dpsetconstr @ A @ B @ (C))) => (C @ D @ E)))))))). 120.24/30.27 thf(dpsetconstrEL1_type, type, dpsetconstrEL1: $o). 120.24/30.27 thf(dpsetconstrEL1_def, definition, (dpsetconstrEL1 = (! [A:$i,B:$i,C:($i > ($i > $o)),D:$i,E:$i]: ((in @ (kpair @ D @ E) @ (dpsetconstr @ A @ B @ (C))) => (in @ D @ A))))). 120.24/30.27 thf(dpsetconstrEL2_type, type, dpsetconstrEL2: $o). 120.24/30.27 thf(dpsetconstrEL2_def, definition, (dpsetconstrEL2 = (! [A:$i,B:$i,C:($i > ($i > $o)),D:$i,E:$i]: ((in @ (kpair @ D @ E) @ (dpsetconstr @ A @ B @ (C))) => (in @ E @ B))))). 120.24/30.27 thf(dpsetconstrER_type, type, dpsetconstrER: $o). 120.24/30.27 thf(dpsetconstrER_def, definition, (dpsetconstrER = (! [A:$i,B:$i,C:($i > ($i > $o)),D:$i,E:$i]: ((in @ (kpair @ D @ E) @ (dpsetconstr @ A @ B @ (C))) => (C @ D @ E))))). 120.24/30.27 thf(func_type, type, func: ($i > ($i > ($i > $o)))). 120.24/30.27 thf(funcSet_type, type, funcSet: ($i > ($i > $i))). 120.24/30.27 thf(funcImageSingleton_type, type, funcImageSingleton: $o). 120.24/30.27 thf(funcImageSingleton_def, definition, (funcImageSingleton = (! [A:$i,B:$i,C:$i]: ((func @ A @ B @ C) => (! [D:$i]: ((in @ D @ A) => (singleton @ (dsetconstr @ B @ (^ [E:$i]: (in @ (kpair @ D @ E) @ C)))))))))). 120.24/30.27 thf(apProp_type, type, apProp: $o). 120.24/30.27 thf(apProp_def, definition, (apProp = (! [A:$i,B:$i,C:$i]: ((func @ A @ B @ C) => (! [D:$i]: ((in @ D @ A) => (in @ (setunion @ (dsetconstr @ B @ (^ [E:$i]: (in @ (kpair @ D @ E) @ C)))) @ B))))))). 120.24/30.27 thf(ap_type, type, ap: ($i > ($i > ($i > ($i > $i))))). 120.24/30.27 thf(app_type, type, app: $o). 120.24/30.27 thf(app_def, definition, (app = (! [A:$i,B:$i,C:$i]: ((func @ A @ B @ C) => (! [D:$i]: ((in @ D @ A) => (in @ (ap @ A @ B @ C @ D) @ B))))))). 120.24/30.27 thf(infuncsetfunc_type, type, infuncsetfunc: $o). 120.24/30.27 thf(infuncsetfunc_def, definition, (infuncsetfunc = (! [A:$i,B:$i,C:$i]: ((in @ C @ (funcSet @ A @ B)) => (func @ A @ B @ C))))). 120.24/30.27 thf(ap2p_type, type, ap2p: $o). 120.24/30.27 thf(ap2p_def, definition, (ap2p = (! [A:$i,B:$i,C:$i]: ((in @ C @ (funcSet @ A @ B)) => (! [D:$i]: ((in @ D @ A) => (in @ (ap @ A @ B @ C @ D) @ B))))))). 120.24/30.27 thf(funcinfuncset_type, type, funcinfuncset: $o). 120.24/30.27 thf(funcinfuncset_def, definition, (funcinfuncset = (! [A:$i,B:$i,C:$i]: ((func @ A @ B @ C) => (in @ C @ (funcSet @ A @ B)))))). 120.24/30.27 thf(lamProp_type, type, lamProp: $o). 120.24/30.27 thf(lamProp_def, definition, (lamProp = (! [A:$i,B:$i,C:($i > $i)]: ((! [D:$i]: ((in @ D @ A) => (in @ (C @ D) @ B))) => (func @ A @ B @ (dpsetconstr @ A @ B @ (^ [D:$i]: (= @ $i @ (C @ D))))))))). 120.24/30.27 thf(lam_type, type, lam: ($i > ($i > (($i > $i) > $i)))). 120.24/30.27 thf(lamp_type, type, lamp: $o). 120.24/30.27 thf(lamp_def, definition, (lamp = (! [A:$i,B:$i,C:($i > $i)]: ((! [D:$i]: ((in @ D @ A) => (in @ (C @ D) @ B))) => (func @ A @ B @ (lam @ A @ B @ (C))))))). 120.24/30.27 thf(lam2p_type, type, lam2p: $o). 120.24/30.27 thf(lam2p_def, definition, (lam2p = (! [A:$i,B:$i,C:($i > $i)]: ((! [D:$i]: ((in @ D @ A) => (in @ (C @ D) @ B))) => (in @ (lam @ A @ B @ (C)) @ (funcSet @ A @ B)))))). 120.24/30.27 thf(brelnall1_type, type, brelnall1: $o). 120.24/30.27 thf(brelnall1_def, definition, (brelnall1 = (! [A:$i,B:$i,C:$i]: ((breln @ A @ B @ C) => (! [D:($i > $o)]: ((! [E:$i]: ((in @ E @ A) => (! [F:$i]: ((in @ F @ B) => ((in @ (kpair @ E @ F) @ C) => (D @ (kpair @ E @ F))))))) => (! [E:$i]: ((in @ E @ C) => (D @ E))))))))). 120.24/30.27 thf(brelnall2_type, type, brelnall2: $o). 120.24/30.27 thf(brelnall2_def, definition, (brelnall2 = (! [A:$i,B:$i,C:$i]: ((breln @ A @ B @ C) => (! [D:($i > $o)]: ((! [E:$i]: ((in @ E @ A) => (! [F:$i]: ((in @ F @ B) => ((in @ (kpair @ E @ F) @ C) => (D @ (kpair @ E @ F))))))) => (! [E:$i]: ((in @ E @ C) => (D @ E))))))))). 120.24/30.27 thf(ex1E2_type, type, ex1E2: $o). 120.24/30.27 thf(ex1E2_def, definition, (ex1E2 = (! [A:$i,B:($i > $o)]: ((ex1 @ A @ (B)) => (! [C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ A) => ((B @ C) => ((B @ D) => (C = D))))))))))). 120.24/30.27 thf(funcGraphProp1_type, type, funcGraphProp1: $o). 120.24/30.27 thf(funcGraphProp1_def, definition, (funcGraphProp1 = (! [A:$i,B:$i,C:$i]: ((func @ A @ B @ C) => (! [D:$i]: ((in @ D @ A) => (in @ (kpair @ D @ (ap @ A @ B @ C @ D)) @ C))))))). 120.24/30.27 thf(funcGraphProp3_type, type, funcGraphProp3: $o). 120.24/30.27 thf(funcGraphProp3_def, definition, (funcGraphProp3 = (! [A:$i,B:$i,C:$i]: ((in @ C @ (funcSet @ A @ B)) => (! [D:$i]: ((in @ D @ A) => (in @ (kpair @ D @ (ap @ A @ B @ C @ D)) @ C))))))). 120.24/30.27 thf(funcGraphProp2_type, type, funcGraphProp2: $o). 120.24/30.27 thf(funcGraphProp2_def, definition, (funcGraphProp2 = (! [A:$i,B:$i,C:$i]: ((func @ A @ B @ C) => (! [D:$i]: ((in @ D @ A) => (! [E:$i]: ((in @ E @ B) => ((in @ (kpair @ D @ E) @ C) => ((ap @ A @ B @ C @ D) = E)))))))))). 120.24/30.27 thf(funcextLem_type, type, funcextLem: $o). 120.24/30.27 thf(funcextLem_def, definition, (funcextLem = (! [A:$i,B:$i,C:$i]: ((func @ A @ B @ C) => (! [D:$i]: ((func @ A @ B @ D) => ((! [E:$i]: ((in @ E @ A) => ((ap @ A @ B @ C @ E) = (ap @ A @ B @ D @ E)))) => (! [E:$i]: ((in @ E @ A) => (! [F:$i]: ((in @ F @ B) => ((in @ (kpair @ E @ F) @ D) => (in @ (kpair @ E @ F) @ C))))))))))))). 120.24/30.27 thf(funcGraphProp4_type, type, funcGraphProp4: $o). 120.24/30.27 thf(funcGraphProp4_def, definition, (funcGraphProp4 = (! [A:$i,B:$i,C:$i]: ((in @ C @ (funcSet @ A @ B)) => (! [D:$i]: ((in @ D @ A) => (! [E:$i]: ((in @ E @ B) => ((in @ (kpair @ D @ E) @ C) => ((ap @ A @ B @ C @ D) = E)))))))))). 120.24/30.27 thf(subbreln_type, type, subbreln: $o). 120.24/30.27 thf(subbreln_def, definition, (subbreln = (! [A:$i,B:$i,C:$i]: ((breln @ A @ B @ C) => (! [D:$i]: ((breln @ A @ B @ D) => ((! [E:$i]: ((in @ E @ A) => (! [F:$i]: ((in @ F @ B) => ((in @ (kpair @ E @ F) @ C) => (in @ (kpair @ E @ F) @ D)))))) => (subset @ C @ D)))))))). 120.24/30.27 thf(eqbreln_type, type, eqbreln: $o). 120.24/30.27 thf(eqbreln_def, definition, (eqbreln = (! [A:$i,B:$i,C:$i]: ((breln @ A @ B @ C) => (! [D:$i]: ((breln @ A @ B @ D) => ((! [E:$i]: ((in @ E @ A) => (! [F:$i]: ((in @ F @ B) => ((in @ (kpair @ E @ F) @ C) => (in @ (kpair @ E @ F) @ D)))))) => ((! [E:$i]: ((in @ E @ A) => (! [F:$i]: ((in @ F @ B) => ((in @ (kpair @ E @ F) @ D) => (in @ (kpair @ E @ F) @ C)))))) => (C = D))))))))). 120.24/30.27 thf(funcext_type, type, funcext: $o). 120.24/30.27 thf(funcext_def, definition, (funcext = (! [A:$i,B:$i,C:$i]: ((func @ A @ B @ C) => (! [D:$i]: ((func @ A @ B @ D) => ((! [E:$i]: ((in @ E @ A) => ((ap @ A @ B @ C @ E) = (ap @ A @ B @ D @ E)))) => (C = D)))))))). 120.24/30.27 thf(funcext2_type, type, funcext2: $o). 120.24/30.27 thf(funcext2_def, definition, (funcext2 = (! [A:$i,B:$i,C:$i]: ((in @ C @ (funcSet @ A @ B)) => (! [D:$i]: ((in @ D @ (funcSet @ A @ B)) => ((! [E:$i]: ((in @ E @ A) => ((ap @ A @ B @ C @ E) = (ap @ A @ B @ D @ E)))) => (C = D)))))))). 120.24/30.27 thf(ap2apEq1_type, type, ap2apEq1: $o). 120.24/30.27 thf(ap2apEq1_def, definition, (ap2apEq1 = (! [A:$i,B:$i,C:$i]: ((in @ C @ (funcSet @ A @ B)) => (! [D:$i]: ((in @ D @ A) => ((ap @ A @ B @ C @ D) = (ap @ A @ B @ C @ D)))))))). 120.24/30.27 thf(ap2apEq2_type, type, ap2apEq2: $o). 120.24/30.27 thf(ap2apEq2_def, definition, (ap2apEq2 = (! [A:$i,B:$i,C:$i]: ((func @ A @ B @ C) => (! [D:$i]: ((in @ D @ A) => ((ap @ A @ B @ C @ D) = (ap @ A @ B @ C @ D)))))))). 120.24/30.27 thf(beta1_type, type, beta1: $o). 120.24/30.27 thf(beta1_def, definition, (beta1 = (! [A:$i,B:$i,C:($i > $i)]: ((! [D:$i]: ((in @ D @ A) => (in @ (C @ D) @ B))) => (! [D:$i]: ((in @ D @ A) => ((ap @ A @ B @ (lam @ A @ B @ (C)) @ D) = (C @ D)))))))). 120.24/30.27 thf(eta1_type, type, eta1: $o). 120.24/30.27 thf(eta1_def, definition, (eta1 = (! [A:$i,B:$i,C:$i]: ((func @ A @ B @ C) => ((lam @ A @ B @ (ap @ A @ B @ C)) = C))))). 120.24/30.27 thf(lam2lamEq_type, type, lam2lamEq: $o). 120.24/30.27 thf(lam2lamEq_def, definition, (lam2lamEq = (! [A:$i,B:$i,C:($i > $i)]: ((! [D:$i]: ((in @ D @ A) => (in @ (C @ D) @ B))) => ((lam @ A @ B @ (C)) = (lam @ A @ B @ (C))))))). 120.24/30.27 thf(beta2_type, type, beta2: $o). 120.24/30.27 thf(beta2_def, definition, (beta2 = (! [A:$i,B:$i,C:($i > $i)]: ((! [D:$i]: ((in @ D @ A) => (in @ (C @ D) @ B))) => (! [D:$i]: ((in @ D @ A) => ((ap @ A @ B @ (lam @ A @ B @ (C)) @ D) = (C @ D)))))))). 120.24/30.27 thf(eta2_type, type, eta2: $o). 120.24/30.27 thf(eta2_def, definition, (eta2 = (! [A:$i,B:$i,C:$i]: ((in @ C @ (funcSet @ A @ B)) => ((lam @ A @ B @ (ap @ A @ B @ C)) = C))))). 120.24/30.27 thf(iffalseProp1_type, type, iffalseProp1: $o). 120.24/30.27 thf(iffalseProp1_def, definition, (iffalseProp1 = (! [A:$i,B:$o,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ A) => ((~ (B)) => (in @ D @ (dsetconstr @ A @ (^ [E:$i]: (((B) & (E = C)) | (~ (B) & (E = D))))))))))))). 120.24/30.27 thf(iffalseProp2_type, type, iffalseProp2: $o). 120.24/30.27 thf(iffalseProp2_def, definition, (iffalseProp2 = (! [A:$i,B:$o,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ A) => ((~ (B)) => ((dsetconstr @ A @ (^ [E:$i]: (((B) & (E = C)) | (~ (B) & (E = D))))) = (setadjoin @ D @ emptyset))))))))). 120.24/30.27 thf(iftrueProp1_type, type, iftrueProp1: $o). 120.24/30.27 thf(iftrueProp1_def, definition, (iftrueProp1 = (! [A:$i,B:$o,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ A) => ((B) => (in @ C @ (dsetconstr @ A @ (^ [E:$i]: (((B) & (E = C)) | (~ (B) & (E = D))))))))))))). 120.24/30.27 thf(iftrueProp2_type, type, iftrueProp2: $o). 120.24/30.27 thf(iftrueProp2_def, definition, (iftrueProp2 = (! [A:$i,B:$o,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ A) => ((B) => ((dsetconstr @ A @ (^ [E:$i]: (((B) & (E = C)) | (~ (B) & (E = D))))) = (setadjoin @ C @ emptyset))))))))). 120.24/30.27 thf(ifSingleton_type, type, ifSingleton: $o). 120.24/30.27 thf(ifSingleton_def, definition, (ifSingleton = (! [A:$i,B:$o,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ A) => (singleton @ (dsetconstr @ A @ (^ [E:$i]: (((B) & (E = C)) | (~ (B) & (E = D)))))))))))). 120.24/30.27 thf(if_type, type, if: ($i > ($o > ($i > ($i > $i))))). 120.24/30.27 thf(ifp_type, type, ifp: $o). 120.24/30.27 thf(ifp_def, definition, (ifp = (! [A:$i,B:$o,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ A) => (in @ (if @ A @ B @ C @ D) @ A))))))). 120.24/30.27 thf(theeq_type, type, theeq: $o). 120.24/30.27 thf(theeq_def, definition, (theeq = (! [A:$i]: ((singleton @ A) => (! [B:$i]: ((in @ B @ A) => ((setunion @ A) = B))))))). 120.24/30.27 thf(iftrue_type, type, iftrue: $o). 120.24/30.27 thf(iftrue_def, definition, (iftrue = (! [A:$i,B:$o,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ A) => ((B) => ((if @ A @ B @ C @ D) = C)))))))). 120.24/30.27 thf(iffalse_type, type, iffalse: $o). 120.24/30.27 thf(iffalse_def, definition, (iffalse = (! [A:$i,B:$o,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ A) => ((~ (B)) => ((if @ A @ B @ C @ D) = D)))))))). 120.24/30.27 thf(iftrueorfalse_type, type, iftrueorfalse: $o). 120.24/30.27 thf(iftrueorfalse_def, definition, (iftrueorfalse = (! [A:$i,B:$o,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ A) => (in @ (if @ A @ B @ C @ D) @ (setadjoin @ C @ (setadjoin @ D @ emptyset))))))))). 120.24/30.27 thf(binintersectT_lem_type, type, binintersectT_lem: $o). 120.24/30.27 thf(binintersectT_lem_def, definition, (binintersectT_lem = (! [A:$i,B:$i]: ((in @ B @ (powerset @ A)) => (! [C:$i]: ((in @ C @ (powerset @ A)) => (in @ (binintersect @ B @ C) @ (powerset @ A)))))))). 120.24/30.27 thf(binunionT_lem_type, type, binunionT_lem: $o). 120.24/30.27 thf(binunionT_lem_def, definition, (binunionT_lem = (! [A:$i,B:$i]: ((in @ B @ (powerset @ A)) => (! [C:$i]: ((in @ C @ (powerset @ A)) => (in @ (binunion @ B @ C) @ (powerset @ A)))))))). 120.24/30.27 thf(powersetT_lem_type, type, powersetT_lem: $o). 120.24/30.27 thf(powersetT_lem_def, definition, (powersetT_lem = (! [A:$i,B:$i]: ((in @ B @ (powerset @ A)) => (in @ (powerset @ B) @ (powerset @ (powerset @ A))))))). 120.24/30.27 thf(setminusT_lem_type, type, setminusT_lem: $o). 120.24/30.27 thf(setminusT_lem_def, definition, (setminusT_lem = (! [A:$i,B:$i]: ((in @ B @ (powerset @ A)) => (! [C:$i]: ((in @ C @ (powerset @ A)) => (in @ (setminus @ B @ C) @ (powerset @ A)))))))). 120.24/30.27 thf(complementT_lem_type, type, complementT_lem: $o). 120.24/30.27 thf(complementT_lem_def, definition, (complementT_lem = (! [A:$i,B:$i]: ((in @ B @ (powerset @ A)) => (in @ (setminus @ A @ B) @ (powerset @ A)))))). 120.24/30.27 thf(setextT_type, type, setextT: $o). 120.24/30.27 thf(setextT_def, definition, (setextT = (! [A:$i,B:$i]: ((in @ B @ (powerset @ A)) => (! [C:$i]: ((in @ C @ (powerset @ A)) => ((! [D:$i]: ((in @ D @ A) => ((in @ D @ B) => (in @ D @ C)))) => ((! [D:$i]: ((in @ D @ A) => ((in @ D @ C) => (in @ D @ B)))) => (B = C))))))))). 120.24/30.27 thf(subsetTI_type, type, subsetTI: $o). 120.24/30.27 thf(subsetTI_def, definition, (subsetTI = (! [A:$i,B:$i]: ((in @ B @ (powerset @ A)) => (! [C:$i]: ((in @ C @ (powerset @ A)) => ((! [D:$i]: ((in @ D @ A) => ((in @ D @ B) => (in @ D @ C)))) => (subset @ B @ C)))))))). 120.24/30.27 thf(powersetTI1_type, type, powersetTI1: $o). 120.24/30.27 thf(powersetTI1_def, definition, (powersetTI1 = (! [A:$i,B:$i]: ((in @ B @ (powerset @ A)) => (! [C:$i]: ((in @ C @ (powerset @ A)) => ((! [D:$i]: ((in @ D @ A) => ((in @ D @ B) => (in @ D @ C)))) => (in @ B @ (powerset @ C))))))))). 120.24/30.27 thf(powersetTE1_type, type, powersetTE1: $o). 120.24/30.27 thf(powersetTE1_def, definition, (powersetTE1 = (! [A:$i,B:$i]: ((in @ B @ (powerset @ A)) => (! [C:$i]: ((in @ C @ (powerset @ A)) => (! [D:$i]: ((in @ D @ A) => ((in @ B @ (powerset @ C)) => ((in @ D @ B) => (in @ D @ C))))))))))). 120.24/30.27 thf(complementTI1_type, type, complementTI1: $o). 120.24/30.27 thf(complementTI1_def, definition, (complementTI1 = (! [A:$i,B:$i]: ((in @ B @ (powerset @ A)) => (! [C:$i]: ((in @ C @ A) => ((in @ C @ B) => (~ (in @ C @ (setminus @ A @ B)))))))))). 120.24/30.27 thf(complementTE1_type, type, complementTE1: $o). 120.24/30.27 thf(complementTE1_def, definition, (complementTE1 = (! [A:$i,B:$i]: ((in @ B @ (powerset @ A)) => (! [C:$i]: ((in @ C @ A) => ((~ (in @ C @ (setminus @ A @ B))) => (in @ C @ B)))))))). 120.24/30.27 thf(binintersectTELcontra_type, type, binintersectTELcontra: $o). 120.24/30.27 thf(binintersectTELcontra_def, definition, (binintersectTELcontra = (! [A:$i,B:$i]: ((in @ B @ (powerset @ A)) => (! [C:$i]: ((in @ C @ (powerset @ A)) => (! [D:$i]: ((in @ D @ A) => ((~ (in @ D @ B)) => (~ (in @ D @ (binintersect @ B @ C)))))))))))). 120.24/30.27 thf(binintersectTERcontra_type, type, binintersectTERcontra: $o). 120.24/30.27 thf(binintersectTERcontra_def, definition, (binintersectTERcontra = (! [A:$i,B:$i]: ((in @ B @ (powerset @ A)) => (! [C:$i]: ((in @ C @ (powerset @ A)) => (! [D:$i]: ((in @ D @ A) => ((~ (in @ D @ C)) => (~ (in @ D @ (binintersect @ B @ C)))))))))))). 120.24/30.27 thf(contrasubsetT_type, type, contrasubsetT: $o). 120.24/30.27 thf(contrasubsetT_def, definition, (contrasubsetT = (! [A:$i,B:$i]: ((in @ B @ (powerset @ A)) => (! [C:$i]: ((in @ C @ (powerset @ A)) => (! [D:$i]: ((in @ D @ A) => ((subset @ B @ (setminus @ A @ C)) => ((in @ D @ C) => (~ (in @ D @ B)))))))))))). 120.24/30.27 thf(contrasubsetT1_type, type, contrasubsetT1: $o). 120.24/30.27 thf(contrasubsetT1_def, definition, (contrasubsetT1 = (! [A:$i,B:$i]: ((in @ B @ (powerset @ A)) => (! [C:$i]: ((in @ C @ (powerset @ A)) => (! [D:$i]: ((in @ D @ A) => ((subset @ B @ C) => ((~ (in @ D @ C)) => (~ (in @ D @ B)))))))))))). 120.24/30.27 thf(1,conjecture,(((setextAx) => ((emptysetAx) => (((powersetAx) => ((setunionAx) => ((omega0Ax) => (((omegaIndAx) => (((foundationAx) => (((descrp) => (((dsetconstrEL) => ((dsetconstrER) => ((exuE1) => (((((notinemptyset) => ((exuE3e) => ((setext) => (((noeltsimpempty) => ((setbeta) => ((((((((setadjoinE) => ((setadjoinOr) => (((powersetI) => ((((((((exuE2) => ((nonemptyImpWitness) => ((((((upairsetE) => (((((vacuousDall) => ((((((prop2setI) => ((prop2set2propI) => ((notdexE) => (((exuI1) => (((((in__Cong) => (((exu__Cong) => ((emptyset__Cong) => ((setadjoin__Cong) => ((((omega__Cong) => ((((((eqimpsubset2) => ((eqimpsubset1) => (((((subsetE2) => (((notequalI1) => ((((subsetTrans) => ((((((((powersetE1) => (((powersetsubset) => (((((upairset2IR) => ((binunionIR) => ((binunionEcases) => ((binunionE) => ((binunionLsub) => ((((binintersectSubset5) => (((((binintersectSubset3) => ((((binintersectRsub) => ((binintersectSubset4) => (((((setminusEL) => ((setminusER) => ((setminusSubset2) => (((setminusELneg) => ((setminusILneg) => ((setminusIRneg) => ((setminusLsub) => (((((((symdiffIneg2) => ((((setukpairIR) => ((kpairiskpair) => ((kpairp) => ((((singletoninpowunion) => ((upairset2E) => ((upairsubunion) => ((((ubforcartprodlem2) => ((ubforcartprodlem3) => (((((setunionE2) => (((((singletonprop) => (((((singletonsuniq) => ((setukpairinjL1) => (((theprop) => ((kfstpairEq) => ((cartprodfstin) => ((((((setukpairinjR1) => (((((ksndsingleton) => (((kpairsurjEq) => ((cartprodsndin) => (((((cartprodfstpairEq) => ((cartprodsndpairEq) => ((((dpsetconstrSub) => ((setOfPairsIsBReln) => (((dpsetconstrEL1) => (((dpsetconstrER) => ((funcImageSingleton) => ((apProp) => ((((ap2p) => (((lamProp) => (((lam2p) => ((brelnall1) => (((ex1E2) => (((funcGraphProp3) => ((funcGraphProp2) => ((funcextLem) => (((((((((((lam2lamEq) => ((((iffalseProp1) => ((((((ifp) => (((((iftrueorfalse) => ((binintersectT_lem) => (((powersetT_lem) => ((setminusT_lem) => ((complementT_lem) => ((((((complementTI1) => (((binintersectTELcontra) => (((contrasubsetT) => ((! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ (powerset @ A)) => ((subset @ B @ C) => (subset @ (setminus @ A @ C) @ (setminus @ A @ B))))) <= (in @ B @ (powerset @ A)))) <= (contrasubsetT1))) <= (binintersectTERcontra))) <= (complementTE1))) <= (powersetTE1)) <= (powersetTI1)) <= (subsetTI)) <= (setextT))))) <= (binunionT_lem)))) <= (iffalse)) <= (iftrue)) <= (theeq))) <= (ifSingleton)) <= (iftrueProp2)) <= (iftrueProp1)) <= (iffalseProp2))) <= (eta2)) <= (beta2))) <= (eta1)) <= (beta1)) <= (ap2apEq2)) <= (ap2apEq1)) <= (funcext2)) <= (funcext)) <= (eqbreln)) <= (subbreln)) <= (funcGraphProp4))))) <= (funcGraphProp1))) <= (brelnall2)))) <= (lamp))) <= (funcinfuncset))) <= (infuncsetfunc)) <= (app))))) <= (dpsetconstrEL2))) <= (dpsetconstrERa)))) <= (dpsetconstrI)) <= (cartprodpairsurjEq)))) <= (cartprodmempaircEq)) <= (cartprodpairmemER)) <= (cartprodpairmemEL)))) <= (ksndpairEq))) <= (setukpairinjR)) <= (setukpairinjR2)) <= (upairequniteq))) <= (setukpairinjR12)) <= (setukpairinjR11)) <= (setukpairinjL)) <= (setukpairinjL2))))) <= (kfstsingleton)))) <= (ex1I2)) <= (ex1I)) <= (ex1E1))) <= (setunionsingleton)) <= (setunionsingleton2)) <= (setunionsingleton1))) <= (cartprodmempair)) <= (cartprodmempair1)) <= (cartprodpairin)))) <= (ubforcartprodlem1)) <= (upairinpowunion))))) <= (singletoninpowerset)) <= (singletonsubset))))) <= (setukpairIL)) <= (secondinupair))) <= (symdiffIneg1)) <= (symdiffI2)) <= (symdiffI1)) <= (symdiffE)) <= (setminusSubset1)))))) <= (setminusERneg))))) <= (setminusI)) <= (bs114d)) <= (binintersectSubset1)))) <= (disjointsetsI1)) <= (binintersectER))) <= (binintersectSubset2)) <= (binintersectLsub)) <= (binintersectEL))) <= (binintersectI)) <= (binunionRsub))))))) <= (binunionIL)) <= (sepSubset)) <= (sepInPowerset))) <= (inPowerset))) <= (powersetI1)) <= (subsetemptysetimpeq)) <= (setextsub)) <= (subset2powerset)) <= (setadjoinSub2)) <= (setadjoinSub))) <= (subsetRefl)) <= (notequalI2))) <= (notsubsetI))) <= (subsetE)) <= (emptysetsubset)) <= (subsetI2)))) <= (subsetI1)) <= (dsetconstr__Cong)) <= (descr__Cong)) <= (exuEu))) <= (setunion__Cong)) <= (powerset__Cong))))) <= (exuE3u))) <= (inCongP)) <= (exuI2)) <= (exuI3))) <= (notdallE))))) <= (quantDeMorgan4)) <= (quantDeMorgan3)) <= (quantDeMorgan2)) <= (quantDeMorgan1))) <= (emptyE1)) <= (upairsetIR)) <= (upairsetIL))) <= (singletonsswitch)) <= (eqinunit)) <= (notinsingleton)) <= (uniqinunit)))) <= (subPowSU)) <= (setunionE)) <= (setunionI)) <= (powersetE)) <= (emptyInPowerset)) <= (emptyinPowerset))) <= (setoftrueEq)))) <= (setadjoinIR)) <= (emptyinunitempty)) <= (setadjoinIL)) <= (nonemptyI1)) <= (nonemptyI)) <= (nonemptyE1)))) <= (emptyI))))) <= (emptysetimpfalse)) <= (emptysetE)) <= (prop2setE))))) <= (dsetconstrI))) <= (wellorderingAx))) <= (replAx))) <= (omegaSAx))))) <= (setadjoinAx))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',contrasubsetT2)). 120.24/30.27 thf(2,negated_conjecture,((~ ((setextAx) => ((emptysetAx) => (((powersetAx) => ((setunionAx) => ((omega0Ax) => (((omegaIndAx) => (((foundationAx) => (((descrp) => (((dsetconstrEL) => ((dsetconstrER) => ((exuE1) => (((((notinemptyset) => ((exuE3e) => ((setext) => (((noeltsimpempty) => ((setbeta) => ((((((((setadjoinE) => ((setadjoinOr) => (((powersetI) => ((((((((exuE2) => ((nonemptyImpWitness) => ((((((upairsetE) => (((((vacuousDall) => ((((((prop2setI) => ((prop2set2propI) => ((notdexE) => (((exuI1) => (((((in__Cong) => (((exu__Cong) => ((emptyset__Cong) => ((setadjoin__Cong) => ((((omega__Cong) => ((((((eqimpsubset2) => ((eqimpsubset1) => (((((subsetE2) => (((notequalI1) => ((((subsetTrans) => ((((((((powersetE1) => (((powersetsubset) => (((((upairset2IR) => ((binunionIR) => ((binunionEcases) => ((binunionE) => ((binunionLsub) => ((((binintersectSubset5) => (((((binintersectSubset3) => ((((binintersectRsub) => ((binintersectSubset4) => (((((setminusEL) => ((setminusER) => ((setminusSubset2) => (((setminusELneg) => ((setminusILneg) => ((setminusIRneg) => ((setminusLsub) => (((((((symdiffIneg2) => ((((setukpairIR) => ((kpairiskpair) => ((kpairp) => ((((singletoninpowunion) => ((upairset2E) => ((upairsubunion) => ((((ubforcartprodlem2) => ((ubforcartprodlem3) => (((((setunionE2) => (((((singletonprop) => (((((singletonsuniq) => ((setukpairinjL1) => (((theprop) => ((kfstpairEq) => ((cartprodfstin) => ((((((setukpairinjR1) => (((((ksndsingleton) => (((kpairsurjEq) => ((cartprodsndin) => (((((cartprodfstpairEq) => ((cartprodsndpairEq) => ((((dpsetconstrSub) => ((setOfPairsIsBReln) => (((dpsetconstrEL1) => (((dpsetconstrER) => ((funcImageSingleton) => ((apProp) => ((((ap2p) => (((lamProp) => (((lam2p) => ((brelnall1) => (((ex1E2) => (((funcGraphProp3) => ((funcGraphProp2) => ((funcextLem) => (((((((((((lam2lamEq) => ((((iffalseProp1) => ((((((ifp) => (((((iftrueorfalse) => ((binintersectT_lem) => (((powersetT_lem) => ((setminusT_lem) => ((complementT_lem) => ((((((complementTI1) => (((binintersectTELcontra) => (((contrasubsetT) => ((! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ (powerset @ A)) => ((subset @ B @ C) => (subset @ (setminus @ A @ C) @ (setminus @ A @ B))))) <= (in @ B @ (powerset @ A)))) <= (contrasubsetT1))) <= (binintersectTERcontra))) <= (complementTE1))) <= (powersetTE1)) <= (powersetTI1)) <= (subsetTI)) <= (setextT))))) <= (binunionT_lem)))) <= (iffalse)) <= (iftrue)) <= (theeq))) <= (ifSingleton)) <= (iftrueProp2)) <= (iftrueProp1)) <= (iffalseProp2))) <= (eta2)) <= (beta2))) <= (eta1)) <= (beta1)) <= (ap2apEq2)) <= (ap2apEq1)) <= (funcext2)) <= (funcext)) <= (eqbreln)) <= (subbreln)) <= (funcGraphProp4))))) <= (funcGraphProp1))) <= (brelnall2)))) <= (lamp))) <= (funcinfuncset))) <= (infuncsetfunc)) <= (app))))) <= (dpsetconstrEL2))) <= (dpsetconstrERa)))) <= (dpsetconstrI)) <= (cartprodpairsurjEq)))) <= (cartprodmempaircEq)) <= (cartprodpairmemER)) <= (cartprodpairmemEL)))) <= (ksndpairEq))) <= (setukpairinjR)) <= (setukpairinjR2)) <= (upairequniteq))) <= (setukpairinjR12)) <= (setukpairinjR11)) <= (setukpairinjL)) <= (setukpairinjL2))))) <= (kfstsingleton)))) <= (ex1I2)) <= (ex1I)) <= (ex1E1))) <= (setunionsingleton)) <= (setunionsingleton2)) <= (setunionsingleton1))) <= (cartprodmempair)) <= (cartprodmempair1)) <= (cartprodpairin)))) <= (ubforcartprodlem1)) <= (upairinpowunion))))) <= (singletoninpowerset)) <= (singletonsubset))))) <= (setukpairIL)) <= (secondinupair))) <= (symdiffIneg1)) <= (symdiffI2)) <= (symdiffI1)) <= (symdiffE)) <= (setminusSubset1)))))) <= (setminusERneg))))) <= (setminusI)) <= (bs114d)) <= (binintersectSubset1)))) <= (disjointsetsI1)) <= (binintersectER))) <= (binintersectSubset2)) <= (binintersectLsub)) <= (binintersectEL))) <= (binintersectI)) <= (binunionRsub))))))) <= (binunionIL)) <= (sepSubset)) <= (sepInPowerset))) <= (inPowerset))) <= (powersetI1)) <= (subsetemptysetimpeq)) <= (setextsub)) <= (subset2powerset)) <= (setadjoinSub2)) <= (setadjoinSub))) <= (subsetRefl)) <= (notequalI2))) <= (notsubsetI))) <= (subsetE)) <= (emptysetsubset)) <= (subsetI2)))) <= (subsetI1)) <= (dsetconstr__Cong)) <= (descr__Cong)) <= (exuEu))) <= (setunion__Cong)) <= (powerset__Cong))))) <= (exuE3u))) <= (inCongP)) <= (exuI2)) <= (exuI3))) <= (notdallE))))) <= (quantDeMorgan4)) <= (quantDeMorgan3)) <= (quantDeMorgan2)) <= (quantDeMorgan1))) <= (emptyE1)) <= (upairsetIR)) <= (upairsetIL))) <= (singletonsswitch)) <= (eqinunit)) <= (notinsingleton)) <= (uniqinunit)))) <= (subPowSU)) <= (setunionE)) <= (setunionI)) <= (powersetE)) <= (emptyInPowerset)) <= (emptyinPowerset))) <= (setoftrueEq)))) <= (setadjoinIR)) <= (emptyinunitempty)) <= (setadjoinIL)) <= (nonemptyI1)) <= (nonemptyI)) <= (nonemptyE1)))) <= (emptyI))))) <= (emptysetimpfalse)) <= (emptysetE)) <= (prop2setE))))) <= (dsetconstrI))) <= (wellorderingAx))) <= (replAx))) <= (omegaSAx))))) <= (setadjoinAx)))))),inference(neg_conjecture,[status(cth)],[1])). 120.24/30.27 thf(3,plain,((~ ((! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ A) = (in @ C @ B))) => (A = B))) => ((! [A:$i]: ~ (in @ A @ emptyset)) => (((! [A:$i,B:$i]: ((in @ B @ (powerset @ A)) = (! [C:$i]: ((in @ C @ B) => (in @ C @ A))))) => ((! [A:$i,B:$i]: ((in @ B @ (setunion @ A)) = (? [C:$i]: ((in @ B @ C) & (in @ C @ A))))) => ((in @ emptyset @ omega) => (((! [A:$i]: (((in @ emptyset @ A) & ! [B:$i]: (((in @ B @ omega) & (in @ B @ A)) => (in @ (setadjoin @ B @ B) @ A))) => (! [B:$i]: ((in @ B @ omega) => (in @ B @ A))))) => (((! [A:$i]: ((? [B:$i]: (in @ B @ A)) => (? [B:$i]: ((in @ B @ A) & ~ (? [C:$i]: ((in @ C @ B) & (in @ C @ A))))))) => (((! [A:($i > $o)]: ((? [B:$i]: ((A @ B) & ! [C:$i]: ((A @ C) => (B = C)))) => (A @ (descr @ (A))))) => (((! [A:$i,B:($i > $o),C:$i]: ((in @ C @ (dsetconstr @ A @ (B))) => (in @ C @ A))) => ((! [A:$i,B:($i > $o),C:$i]: ((in @ C @ (dsetconstr @ A @ (B))) => (B @ C))) => (((! [A:$i]: ~ (in @ A @ emptyset)) => ((! [A:($i > $o)]: ((? [B:$i]: ((A @ B) & ! [C:$i]: ((A @ C) => (B = C)))) => (? [B:$i]: (A @ B)))) => ((! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ A) => (in @ C @ B))) => ((! [C:$i]: ((in @ C @ B) => (in @ C @ A))) => (A = B)))) => (((! [A:$i]: ((! [B:$i]: ~ (in @ B @ A)) => (A = emptyset))) => ((! [A:$i,B:($i > $o),C:$i]: ((in @ C @ A) => ((in @ C @ (dsetconstr @ A @ (B))) = (B @ C)))) => (((! [A:$i,B:$i,C:$i]: ((in @ C @ (setadjoin @ A @ B)) => (! [D:$o]: (((C = A) => (D)) => (((in @ C @ B) => (D)) => (D)))))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ (setadjoin @ A @ B)) => ((C = A) | (in @ C @ B)))) => (((! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ B) => (in @ C @ A))) => (in @ B @ (powerset @ A)))) => (((! [A:($i > $o)]: ((? [B:$i]: ((A @ B) & ! [C:$i]: ((A @ C) => (B = C)))) => (? [B:$i]: ! [C:$i]: ((A @ C) = (C = B))))) => ((! [A:$i]: ((~ (A = emptyset)) => (? [B:$i]: (in @ B @ A)))) => (((! [A:$i,B:$i,C:$i]: ((in @ C @ (setadjoin @ A @ (setadjoin @ B @ emptyset))) => ((C = A) | (C = B)))) => (((! [A:($i > $o),B:$i]: ((in @ B @ emptyset) => (A @ B))) => (((! [A:$o]: ((A) => (in @ emptyset @ (prop2set @ A)))) => ((! [A:$o]: ((A) => (set2prop @ (prop2set @ A)))) => ((! [A:$i,B:($i > $o)]: ((~ (? [C:$i]: ((in @ C @ A) & (B @ C)))) => (! [C:$i]: ((in @ C @ A) => (~ (B @ C)))))) => (((! [A:$i,B:$i]: ((A = B) => (! [C:$i,D:$i]: ((C = D) => ((in @ C @ A) = (in @ D @ B)))))) => (((! [A:($i > $o),B:($i > $o)]: ((! [C:$i,D:$i]: ((C = D) => ((A @ C) = (B @ D)))) => ((? [C:$i]: ((A @ C) & ! [D:$i]: ((A @ D) => (C = D)))) = (? [C:$i]: ((B @ C) & ! [D:$i]: ((B @ D) => (C = D))))))) => ((! [A:$i,B:$i]: ((A = B) => (! [C:$i,D:$i]: ((C = D) => ((setadjoin @ A @ C) = (setadjoin @ B @ D)))))) => (((! [A:$i,B:$i]: ((A = B) => (subset @ B @ A))) => ((! [A:$i,B:$i]: ((A = B) => (subset @ A @ B))) => (((! [A:$i,B:$i,C:$i]: ((subset @ A @ B) => ((~ (in @ C @ B)) => (~ (in @ C @ A))))) => (((! [A:$i,B:$i]: ((~ (subset @ A @ B)) => (~ (A = B)))) => (((! [A:$i,B:$i,C:$i]: ((subset @ A @ B) => ((subset @ B @ C) => (subset @ A @ C)))) => (((! [A:$i,B:$i]: ((in @ B @ (powerset @ A)) => (subset @ B @ A))) => (((! [A:$i,B:$i]: ((subset @ A @ B) => (subset @ (powerset @ A) @ (powerset @ B)))) => (((! [A:$i,B:$i]: (in @ B @ (setadjoin @ A @ (setadjoin @ B @ emptyset)))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ B) => (in @ C @ (binunion @ A @ B)))) => ((! [A:$i,B:$i,C:$i,D:$o]: ((in @ C @ (binunion @ A @ B)) => (((in @ C @ A) => (D)) => (((in @ C @ B) => (D)) => (D))))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ (binunion @ A @ B)) => ((in @ C @ A) | (in @ C @ B)))) => ((! [A:$i,B:$i]: (subset @ A @ (binunion @ A @ B))) => (((! [A:$i,B:$i,C:$i]: ((subset @ C @ A) => ((subset @ C @ B) => (subset @ C @ (binintersect @ A @ B))))) => (((! [A:$i,B:$i]: (((binintersect @ A @ B) = B) => (subset @ B @ A))) => (((! [A:$i,B:$i]: (subset @ (binintersect @ A @ B) @ B)) => ((! [A:$i,B:$i]: ((subset @ B @ A) => ((binintersect @ A @ B) = B))) => (((! [A:$i,B:$i,C:$i]: ((in @ C @ (setminus @ A @ B)) => (in @ C @ A))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ (setminus @ A @ B)) => (~ (in @ C @ B)))) => ((! [A:$i,B:$i]: ((subset @ A @ B) => ((setminus @ A @ B) = emptyset))) => (((! [A:$i,B:$i,C:$i]: ((~ (in @ C @ (setminus @ A @ B))) => ((~ (in @ C @ B)) => (~ (in @ C @ A))))) => ((! [A:$i,B:$i,C:$i]: ((~ (in @ C @ A)) => (~ (in @ C @ (setminus @ A @ B))))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ B) => (~ (in @ C @ (setminus @ A @ B))))) => ((! [A:$i,B:$i]: (subset @ (setminus @ A @ B) @ A)) => (((! [A:$i,B:$i,C:$i]: ((~ (in @ C @ A)) => ((~ (in @ C @ B)) => (~ (in @ C @ (symdiff @ A @ B)))))) => (((! [A:$i,B:$i]: (in @ B @ (setunion @ (setadjoin @ (setadjoin @ A @ emptyset) @ (setadjoin @ (setadjoin @ A @ (setadjoin @ B @ emptyset)) @ emptyset))))) => ((! [A:$i,B:$i]: (iskpair @ (setadjoin @ (setadjoin @ A @ emptyset) @ (setadjoin @ (setadjoin @ A @ (setadjoin @ B @ emptyset)) @ emptyset)))) => ((! [A:$i,B:$i]: (iskpair @ (kpair @ A @ B))) => (((! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (in @ (setadjoin @ C @ emptyset) @ (powerset @ (binunion @ A @ B))))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ (setadjoin @ A @ (setadjoin @ B @ emptyset))) => ((C = A) | (C = B)))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ B) => (subset @ (setadjoin @ C @ (setadjoin @ D @ emptyset)) @ (binunion @ A @ B)))))) => (((! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ B) => (in @ (setadjoin @ (setadjoin @ C @ emptyset) @ (setadjoin @ (setadjoin @ C @ (setadjoin @ D @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ A @ B)))))))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ B) => (in @ (kpair @ C @ D) @ (powerset @ (powerset @ (binunion @ A @ B)))))))) => (((! [A:$i,B:$i]: ((in @ B @ (setunion @ A)) => (? [C:$i]: ((in @ C @ A) & (in @ B @ C))))) => (((! [A:$i,B:($i > $o)]: ((! [C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ A) => ((B @ C) => ((B @ D) => (C = D))))))) => ((? [C:$i]: ((in @ C @ A) & (B @ C))) => (singleton @ (dsetconstr @ A @ (B)))))) => (((! [A:$i,B:$i]: (((setadjoin @ A @ emptyset) = (setadjoin @ B @ emptyset)) => (A = B))) => ((! [A:$i,B:$i,C:$i]: ((in @ (setadjoin @ C @ emptyset) @ (setadjoin @ (setadjoin @ A @ emptyset) @ (setadjoin @ (setadjoin @ A @ (setadjoin @ B @ emptyset)) @ emptyset))) => (A = C))) => (((! [A:$i]: ((singleton @ A) => (in @ (setunion @ A) @ A))) => ((! [A:$i,B:$i]: ((kfst @ (kpair @ A @ B)) = A)) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ (cartprod @ A @ B)) => (in @ (kfst @ C) @ A))) => (((! [A:$i,B:$i,C:$i,D:$i]: (((setadjoin @ (setadjoin @ A @ emptyset) @ (setadjoin @ (setadjoin @ A @ (setadjoin @ B @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ C @ emptyset) @ (setadjoin @ (setadjoin @ C @ (setadjoin @ D @ emptyset)) @ emptyset))) => ((C = D) => (B = D)))) => (((! [A:$i]: ((iskpair @ A) => (singleton @ (dsetconstr @ (setunion @ A) @ (^ [B:$i]: (A = (kpair @ (kfst @ A) @ B))))))) => (((! [A:$i]: ((iskpair @ A) => ((kpair @ (kfst @ A) @ (ksnd @ A)) = A))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ (cartprod @ A @ B)) => (in @ (ksnd @ C) @ B))) => (((! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ B) => ((kfst @ (kpair @ C @ D)) = C))))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ B) => ((ksnd @ (kpair @ C @ D)) = D))))) => (((! [A:$i,B:$i,C:($i > ($i > $o))]: (subset @ (dpsetconstr @ A @ B @ (C)) @ (cartprod @ A @ B))) => ((! [A:$i,B:$i,C:($i > ($i > $o))]: (subset @ (dpsetconstr @ A @ B @ (C)) @ (cartprod @ A @ B))) => (((! [A:$i,B:$i,C:($i > ($i > $o)),D:$i,E:$i]: ((in @ (kpair @ D @ E) @ (dpsetconstr @ A @ B @ (C))) => (in @ D @ A))) => (((! [A:$i,B:$i,C:($i > ($i > $o)),D:$i,E:$i]: ((in @ (kpair @ D @ E) @ (dpsetconstr @ A @ B @ (C))) => (C @ D @ E))) => ((! [A:$i,B:$i,C:$i]: ((func @ A @ B @ C) => (! [D:$i]: ((in @ D @ A) => (singleton @ (dsetconstr @ B @ (^ [E:$i]: (in @ (kpair @ D @ E) @ C)))))))) => ((! [A:$i,B:$i,C:$i]: ((func @ A @ B @ C) => (! [D:$i]: ((in @ D @ A) => (in @ (setunion @ (dsetconstr @ B @ (^ [E:$i]: (in @ (kpair @ D @ E) @ C)))) @ B))))) => (((! [A:$i,B:$i,C:$i]: ((in @ C @ (funcSet @ A @ B)) => (! [D:$i]: ((in @ D @ A) => (in @ (ap @ A @ B @ C @ D) @ B))))) => (((! [A:$i,B:$i,C:($i > $i)]: ((! [D:$i]: ((in @ D @ A) => (in @ (C @ D) @ B))) => (func @ A @ B @ (dpsetconstr @ A @ B @ (^ [D:$i]: (= @ $i @ (C @ D))))))) => (((! [A:$i,B:$i,C:($i > $i)]: ((! [D:$i]: ((in @ D @ A) => (in @ (C @ D) @ B))) => (in @ (lam @ A @ B @ (C)) @ (funcSet @ A @ B)))) => ((! [A:$i,B:$i,C:$i]: ((subset @ C @ (cartprod @ A @ B)) => (! [D:($i > $o)]: ((! [E:$i]: ((in @ E @ A) => (! [F:$i]: ((in @ F @ B) => ((in @ (kpair @ E @ F) @ C) => (D @ (kpair @ E @ F))))))) => (! [E:$i]: ((in @ E @ C) => (D @ E))))))) => (((! [A:$i,B:($i > $o)]: ((singleton @ (dsetconstr @ A @ (B))) => (! 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[A:$i,B:$o,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ A) => (in @ (if @ A @ B @ C @ D) @ (setadjoin @ C @ (setadjoin @ D @ emptyset))))))) => ((! [A:$i,B:$i]: ((in @ B @ (powerset @ A)) => (! [C:$i]: ((in @ C @ (powerset @ A)) => (in @ (binintersect @ B @ C) @ (powerset @ A)))))) => (((! [A:$i,B:$i]: ((in @ B @ (powerset @ A)) => (in @ (powerset @ B) @ (powerset @ (powerset @ A))))) => ((! [A:$i,B:$i]: ((in @ B @ (powerset @ A)) => (! [C:$i]: ((in @ C @ (powerset @ A)) => (in @ (setminus @ B @ C) @ (powerset @ A)))))) => ((! [A:$i,B:$i]: ((in @ B @ (powerset @ A)) => (in @ (setminus @ A @ B) @ (powerset @ A)))) => (((! [A:$i,B:$i]: ((in @ B @ (powerset @ A)) => (! [C:$i]: ((in @ C @ A) => ((in @ C @ B) => (~ (in @ C @ (setminus @ A @ B)))))))) => (((! [A:$i,B:$i]: ((in @ B @ (powerset @ A)) => (! [C:$i]: ((in @ C @ (powerset @ A)) => (! [D:$i]: ((in @ D @ A) => ((~ (in @ D @ B)) => (~ (in @ D @ (binintersect @ B @ C)))))))))) => (((! [A:$i,B:$i]: ((in @ B @ (powerset @ A)) => (! 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[D:$i]: ((in @ D @ A) => ((in @ B @ (powerset @ C)) => ((in @ D @ B) => (in @ D @ C))))))))) | ~ (! [A:$i,B:$i]: ((in @ B @ (powerset @ A)) => (! [C:$i]: ((in @ C @ (powerset @ A)) => ((! [D:$i]: ((in @ D @ A) => ((in @ D @ B) => (in @ D @ C)))) => (in @ B @ (powerset @ C))))))) | ~ (! [A:$i,B:$i]: ((in @ B @ (powerset @ A)) => (! [C:$i]: ((in @ C @ (powerset @ A)) => ((! [D:$i]: ((in @ D @ A) => ((in @ D @ B) => (in @ D @ C)))) => (subset @ B @ C)))))) | ~ (! [A:$i,B:$i]: ((in @ B @ (powerset @ A)) => (! [C:$i]: ((in @ C @ (powerset @ A)) => ((! [D:$i]: ((in @ D @ A) => ((in @ D @ B) => (in @ D @ C)))) => ((! [D:$i]: ((in @ D @ A) => ((in @ D @ C) => (in @ D @ B)))) => (B = C))))))))))) | ~ (! [A:$i,B:$i]: ((in @ B @ (powerset @ A)) => (! [C:$i]: ((in @ C @ (powerset @ A)) => (in @ (binunion @ B @ C) @ (powerset @ A))))))))) | ~ (! [A:$i,B:$o,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ A) => ((~ (B)) => ((if @ A @ B @ C @ D) = D)))))) | ~ (! [A:$i,B:$o,C:$i]: ((in @ C @ A) => (! 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[A:$i,B:$i]: ((A = B) => ((powerset @ A) = (powerset @ B))))))) | ~ (! [A:($i > $o)]: ((? [B:$i]: ((A @ B) & ! [C:$i]: ((A @ C) => (B = C)))) => (! [B:$i,C:$i]: ((A @ B) => ((A @ C) => (B = C)))))))) | ~ (! [A:$i,B:$i]: ((A = B) => (! [C:$i,D:$i]: ((C = D) => ((in @ C @ A) => (in @ D @ B)))))) | ~ (! [A:($i > $o)]: ((? [B:$i]: ! [C:$i]: ((A @ C) = (C = B))) => (? [B:$i]: ((A @ B) & ! [C:$i]: ((A @ C) => (B = C)))))) | ~ (! [A:($i > $o)]: ((? [B:$i]: (A @ B)) => ((! [B:$i,C:$i]: ((A @ B) => ((A @ C) => (B = C)))) => (? [B:$i]: ((A @ B) & ! [C:$i]: ((A @ C) => (B = C))))))) | ~ (! [A:$i,B:($i > $o)]: ((~ (! [C:$i]: ((in @ C @ A) => (B @ C)))) => (? [C:$i]: ((in @ C @ A) & ~ (B @ C))))))))) | ~ (! [A:$i,B:($i > $o)]: ((? [C:$i]: ((in @ C @ A) & ~ (B @ C))) => (~ (! [C:$i]: ((in @ C @ A) => (B @ C)))))) | ~ (! [A:$i,B:($i > $o)]: ((~ (? [C:$i]: ((in @ C @ A) & (B @ C)))) => (! [C:$i]: ((in @ C @ A) => (~ (B @ C)))))) | ~ (! [A:$i,B:($i > $o)]: ((! [C:$i]: ((in @ C @ A) => (~ (B @ C)))) => (~ (? [C:$i]: ((in @ C @ A) & (B @ C)))))) | ~ (! [A:$i,B:($i > $o)]: ((~ (! [C:$i]: ((in @ C @ A) => (B @ C)))) => (? [C:$i]: ((in @ C @ A) & ~ (B @ C))))))) | ~ (! [A:$i,B:($i > $o)]: ((? [C:$i]: ((in @ C @ A) & (B @ C))) => (~ ((dsetconstr @ A @ (B)) = emptyset)))) | ~ (! [A:$i,B:$i]: (in @ B @ (setadjoin @ A @ (setadjoin @ B @ emptyset)))) | ~ (! [A:$i,B:$i]: (in @ A @ (setadjoin @ A @ (setadjoin @ B @ emptyset)))))) | ~ (! [A:$i,B:$i]: ((in @ A @ (setadjoin @ B @ emptyset)) => (in @ B @ (setadjoin @ A @ emptyset)))) | ~ (! [A:$i,B:$i]: ((A = B) => (in @ A @ (setadjoin @ B @ emptyset)))) | ~ (! [A:$i,B:$i]: ((~ (A = B)) => (~ (in @ B @ (setadjoin @ A @ emptyset))))) | ~ (! [A:$i,B:$i]: ((in @ A @ (setadjoin @ B @ emptyset)) => (A = B)))))) | ~ (! [A:$i,B:$i]: ((in @ B @ A) => (in @ B @ (powerset @ (setunion @ A))))) | ~ (! [A:$i,B:$i]: ((in @ B @ (setunion @ A)) => (! [C:$o]: ((! [D:$i]: ((in @ B @ D) => ((in @ D @ A) => (C)))) => (C))))) | ~ (! [A:$i,B:$i,C:$i]: ((in @ B @ C) => ((in @ C @ A) => (in @ B @ (setunion @ A))))) | ~ (! [A:$i,B:$i,C:$i]: ((in @ B @ (powerset @ A)) => ((in @ C @ B) => (in @ C @ A)))) | ~ (! [A:$i]: (in @ emptyset @ (powerset @ A))) | ~ (! [A:$i]: (in @ emptyset @ (powerset @ A))))) | ~ (! [A:$i]: ((dsetconstr @ A @ (^ [B:$i]: ($true))) = A))))) | ~ (! [A:$i,B:$i,C:$i]: ((in @ C @ B) => (in @ C @ (setadjoin @ A @ B)))) | ~ (in @ emptyset @ (setadjoin @ emptyset @ emptyset)) | ~ (! [A:$i,B:$i]: (in @ A @ (setadjoin @ A @ B))) | ~ (! [A:$i]: ((? [B:$i]: (in @ B @ A)) => (~ (A = emptyset)))) | ~ (! [A:$i,B:($i > $o),C:$i]: ((in @ C @ A) => ((B @ C) => (~ ((dsetconstr @ A @ (B)) = emptyset))))) | ~ (! [A:$i]: ((~ (A = emptyset)) => (? [B:$i]: (in @ B @ A))))))) | ~ (! [A:$i]: ((! [B:$i]: ~ (in @ B @ A)) => (A = emptyset))))))) | ~ (! [A:$i]: ~ (in @ A @ emptyset)) | ~ (! [A:$i]: ((in @ A @ emptyset) => (! [B:$o]: (B)))) | ~ (! [A:$o,B:$i]: ((in @ B @ (prop2set @ A)) => (A)))))) | ~ (! [A:$i,B:($i > $o),C:$i]: ((in @ C @ A) => ((B @ C) => (in @ C @ (dsetconstr @ A @ (B)))))))) | ~ (! [A:$i]: ? [B:$i]: (! [C:$i]: ((in @ C @ B) => (! [D:$i]: ((in @ D @ C) => (in @ D @ A)))) & ! [C:$i,D:$i]: (((in @ C @ A) & (in @ D @ A)) => ((! [E:$i]: ((in @ E @ B) => ((in @ C @ E) = (in @ D @ E)))) => (C = D))) & ! [C:$i,D:$i]: (((in @ C @ B) & (in @ D @ B)) => (! [E:$i]: ((in @ E @ C) => (in @ E @ D)) | ! [E:$i]: ((in @ E @ D) => (in @ E @ C)))) & ! [C:$i]: ((! [D:$i]: ((in @ D @ C) => (in @ D @ A)) & ? [D:$i]: (in @ D @ C)) => (? [D:$i,E:$i]: ((in @ D @ B) & (in @ E @ C) & ~ (? [F:$i]: ((in @ F @ D) & (in @ F @ C))) & ! [F:$i]: ((in @ F @ B) => (! [G:$i]: ((in @ G @ F) => (in @ G @ D)) | (in @ E @ F)))))))))) | ~ (! [A:($i > ($i > $o)),B:$i]: ((! [C:$i]: ((in @ C @ B) => (? [D:$i]: ((A @ C @ D) & ! [E:$i]: ((A @ C @ E) => (D = E)))))) => (? [C:$i]: ! [D:$i]: ((in @ D @ C) = (? [E:$i]: ((in @ E @ B) & (A @ E @ D))))))))) | ~ (! [A:$i]: ((in @ A @ omega) => (in @ (setadjoin @ A @ A) @ omega))))))) | ~ (! [A:$i,B:$i,C:$i]: ((in @ C @ (setadjoin @ A @ B)) = ((C = A) | (in @ C @ B))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])). 120.24/30.27 thf(43908,plain,($false),inference(cvc4,[status(thm)],[3])). 120.24/30.27 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 120.24/30.27 % [INFO] Killing All external provers ... 120.24/30.27 WARNING: TreeLimitedRun lost 41.79s, total lost is 41.79s 120.24/30.27 FINAL WATCH: 103.2 CPU 24.1 WC 120.24/30.27 Killed 3 orphans 120.24/30.27 Killed 3 orphans 120.24/30.27 EOF