0.00/0.00 % Leo-III: Strategy 1 (for '60') 29.46/11.17 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 29.46/11.17 % [INFO] Parsing done (203ms). 29.46/11.17 % [INFO] Running in sequential loop mode. 29.46/11.17 % [CONFIG] Using configuration: timeout(60) with strategy 29.46/11.17 % [INFO] eprover registered as external prover. 29.46/11.17 % [INFO] cvc4 registered as external prover. 29.46/11.17 % [INFO] Parsing finished. Scanning for conjecture ... 29.46/11.17 % [INFO] Found a conjecture and 0 axioms. Running axiom selection ... 29.46/11.17 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms). 29.46/11.17 % [INFO] Problem is higher-order (TPTP THF). 29.46/11.17 % [INFO] Type checking passed. Searching for refutation ... 29.46/11.17 % External prover 'e' found a proof! 29.46/11.17 % [INFO] Killing All external provers ... 29.46/11.17 % Time passed: 5750ms (effective reasoning time: 5190ms) 29.46/11.17 % Solved by strategy 29.46/11.17 % Axioms used in derivation (0): 29.46/11.17 % No. of inferences in proof: 4 29.46/11.17 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5750 ms resp. 5190 ms w/o parsing 29.46/11.17 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 29.46/11.17 thf(in_type, type, in: ($i > ($i > $o))). 29.46/11.17 thf(setextAx_type, type, setextAx: $o). 29.46/11.17 thf(setextAx_def, definition, (setextAx = (! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ A) = (in @ C @ B))) => (A = B))))). 29.46/11.17 thf(emptyset_type, type, emptyset: $i). 29.46/11.17 thf(emptysetAx_type, type, emptysetAx: $o). 29.46/11.17 thf(emptysetAx_def, definition, (emptysetAx = (! [A:$i]: ~ (in @ A @ emptyset)))). 29.46/11.17 thf(setadjoin_type, type, setadjoin: ($i > ($i > $i))). 29.46/11.17 thf(setadjoinAx_type, type, setadjoinAx: $o). 29.46/11.17 thf(setadjoinAx_def, definition, (setadjoinAx = (! [A:$i,B:$i,C:$i]: ((in @ C @ (setadjoin @ A @ B)) = ((C = A) | (in @ C @ B)))))). 29.46/11.17 thf(powerset_type, type, powerset: ($i > $i)). 29.46/11.17 thf(powersetAx_type, type, powersetAx: $o). 29.46/11.17 thf(powersetAx_def, definition, (powersetAx = (! [A:$i,B:$i]: ((in @ B @ (powerset @ A)) = (! [C:$i]: ((in @ C @ B) => (in @ C @ A))))))). 29.46/11.17 thf(setunion_type, type, setunion: ($i > $i)). 29.46/11.17 thf(setunionAx_type, type, setunionAx: $o). 29.46/11.17 thf(setunionAx_def, definition, (setunionAx = (! [A:$i,B:$i]: ((in @ B @ (setunion @ A)) = (? [C:$i]: ((in @ B @ C) & (in @ C @ A))))))). 29.46/11.17 thf(omega_type, type, omega: $i). 29.46/11.17 thf(omega0Ax_type, type, omega0Ax: $o). 29.46/11.17 thf(omega0Ax_def, definition, (omega0Ax = (in @ emptyset @ omega))). 29.46/11.17 thf(omegaSAx_type, type, omegaSAx: $o). 29.46/11.17 thf(omegaSAx_def, definition, (omegaSAx = (! [A:$i]: ((in @ A @ omega) => (in @ (setadjoin @ A @ A) @ omega))))). 29.46/11.17 thf(omegaIndAx_type, type, omegaIndAx: $o). 29.46/11.17 thf(omegaIndAx_def, definition, (omegaIndAx = (! [A:$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))))))). 29.46/11.17 thf(replAx_type, type, replAx: $o). 29.46/11.17 thf(replAx_def, definition, (replAx = (! [A:($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))))))))). 29.46/11.17 thf(foundationAx_type, type, foundationAx: $o). 29.46/11.17 thf(foundationAx_def, definition, (foundationAx = (! [A:$i]: ((? [B:$i]: (in @ B @ A)) => (? [B:$i]: ((in @ B @ A) & ~ (? [C:$i]: ((in @ C @ B) & (in @ C @ A))))))))). 29.46/11.17 thf(wellorderingAx_type, type, wellorderingAx: $o). 29.46/11.17 thf(wellorderingAx_def, definition, (wellorderingAx = (! [A:$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)))))))))). 29.46/11.17 thf(descr_type, type, descr: (($i > $o) > $i)). 29.46/11.17 thf(descrp_type, type, descrp: $o). 29.46/11.17 thf(descrp_def, definition, (descrp = (! [A:($i > $o)]: ((exu @ (A)) => (A @ (descr @ (A))))))). 29.46/11.17 thf(dsetconstr_type, type, dsetconstr: ($i > (($i > $o) > $i))). 29.46/11.17 thf(dsetconstrI_type, type, dsetconstrI: $o). 29.46/11.17 thf(dsetconstrI_def, definition, (dsetconstrI = (! [A:$i,B:($i > $o),C:$i]: ((in @ C @ A) => ((B @ C) => (in @ C @ (dsetconstr @ A @ (B)))))))). 29.46/11.17 thf(dsetconstrEL_type, type, dsetconstrEL: $o). 29.46/11.17 thf(dsetconstrEL_def, definition, (dsetconstrEL = (! [A:$i,B:($i > $o),C:$i]: ((in @ C @ (dsetconstr @ A @ (B))) => (in @ C @ A))))). 29.46/11.17 thf(dsetconstrER_type, type, dsetconstrER: $o). 29.46/11.17 thf(dsetconstrER_def, definition, (dsetconstrER = (! [A:$i,B:($i > $o),C:$i]: ((in @ C @ (dsetconstr @ A @ (B))) => (B @ C))))). 29.46/11.17 thf(exuE1_type, type, exuE1: $o). 29.46/11.17 thf(exuE1_def, definition, (exuE1 = (! [A:($i > $o)]: ((exu @ (A)) => (? [B:$i]: ((A @ B) & ! [C:$i]: ((A @ C) => (B = C)))))))). 29.46/11.17 thf(prop2set_type, type, prop2set: ($o > $i)). 29.46/11.17 thf(prop2setE_type, type, prop2setE: $o). 29.46/11.17 thf(prop2setE_def, definition, (prop2setE = (! [A:$o,B:$i]: ((in @ B @ (prop2set @ A)) => (A))))). 29.46/11.17 thf(emptysetE_type, type, emptysetE: $o). 29.46/11.17 thf(emptysetE_def, definition, (emptysetE = (! [A:$i]: ((in @ A @ emptyset) => (! [B:$o]: (B)))))). 29.46/11.17 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o). 29.46/11.17 thf(emptysetimpfalse_def, definition, (emptysetimpfalse = (! [A:$i]: ((in @ A @ emptyset) => ($false))))). 29.46/11.17 thf(notinemptyset_type, type, notinemptyset: $o). 29.46/11.17 thf(notinemptyset_def, definition, (notinemptyset = (! [A:$i]: ~ (in @ A @ emptyset)))). 29.46/11.17 thf(exuE3e_type, type, exuE3e: $o). 29.46/11.17 thf(exuE3e_def, definition, (exuE3e = (! [A:($i > $o)]: ((exu @ (A)) => (? [B:$i]: (A @ B)))))). 29.46/11.17 thf(setext_type, type, setext: $o). 29.46/11.17 thf(setext_def, definition, (setext = (! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ A) => (in @ C @ B))) => ((! [C:$i]: ((in @ C @ B) => (in @ C @ A))) => (A = B)))))). 29.46/11.17 thf(emptyI_type, type, emptyI: $o). 29.46/11.17 thf(emptyI_def, definition, (emptyI = (! [A:$i]: ((! [B:$i]: ~ (in @ B @ A)) => (A = emptyset))))). 29.46/11.17 thf(noeltsimpempty_type, type, noeltsimpempty: $o). 29.46/11.17 thf(noeltsimpempty_def, definition, (noeltsimpempty = (! [A:$i]: ((! [B:$i]: ~ (in @ B @ A)) => (A = emptyset))))). 29.46/11.17 thf(setbeta_type, type, setbeta: $o). 29.46/11.17 thf(setbeta_def, definition, (setbeta = (! [A:$i,B:($i > $o),C:$i]: ((in @ C @ A) => ((in @ C @ (dsetconstr @ A @ (B))) = (B @ C)))))). 29.46/11.17 thf(nonemptyE1_type, type, nonemptyE1: $o). 29.46/11.17 thf(nonemptyE1_def, definition, (nonemptyE1 = (! [A:$i]: ((nonempty @ A) => (? [B:$i]: (in @ B @ A)))))). 29.46/11.17 thf(nonemptyI_type, type, nonemptyI: $o). 29.46/11.17 thf(nonemptyI_def, definition, (nonemptyI = (! [A:$i,B:($i > $o),C:$i]: ((in @ C @ A) => ((B @ C) => (nonempty @ (dsetconstr @ A @ (B)))))))). 29.46/11.17 thf(nonemptyI1_type, type, nonemptyI1: $o). 29.46/11.17 thf(nonemptyI1_def, definition, (nonemptyI1 = (! [A:$i]: ((? [B:$i]: (in @ B @ A)) => (nonempty @ A))))). 29.46/11.17 thf(setadjoinIL_type, type, setadjoinIL: $o). 29.46/11.17 thf(setadjoinIL_def, definition, (setadjoinIL = (! [A:$i,B:$i]: (in @ A @ (setadjoin @ A @ B))))). 29.46/11.17 thf(emptyinunitempty_type, type, emptyinunitempty: $o). 29.46/11.17 thf(emptyinunitempty_def, definition, (emptyinunitempty = (in @ emptyset @ (setadjoin @ emptyset @ emptyset)))). 29.46/11.17 thf(setadjoinIR_type, type, setadjoinIR: $o). 29.46/11.17 thf(setadjoinIR_def, definition, (setadjoinIR = (! [A:$i,B:$i,C:$i]: ((in @ C @ B) => (in @ C @ (setadjoin @ A @ B)))))). 29.46/11.17 thf(setadjoinE_type, type, setadjoinE: $o). 29.46/11.17 thf(setadjoinE_def, definition, (setadjoinE = (! [A:$i,B:$i,C:$i]: ((in @ C @ (setadjoin @ A @ B)) => (! [D:$o]: (((C = A) => (D)) => (((in @ C @ B) => (D)) => (D)))))))). 29.46/11.17 thf(setadjoinOr_type, type, setadjoinOr: $o). 29.46/11.17 thf(setadjoinOr_def, definition, (setadjoinOr = (! [A:$i,B:$i,C:$i]: ((in @ C @ (setadjoin @ A @ B)) => ((C = A) | (in @ C @ B)))))). 29.46/11.17 thf(setoftrueEq_type, type, setoftrueEq: $o). 29.46/11.17 thf(setoftrueEq_def, definition, (setoftrueEq = (! [A:$i]: ((dsetconstr @ A @ (^ [B:$i]: ($true))) = A)))). 29.46/11.17 thf(powersetI_type, type, powersetI: $o). 29.46/11.17 thf(powersetI_def, definition, (powersetI = (! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ B) => (in @ C @ A))) => (in @ B @ (powerset @ A)))))). 29.46/11.17 thf(emptyinPowerset_type, type, emptyinPowerset: $o). 29.46/11.17 thf(emptyinPowerset_def, definition, (emptyinPowerset = (! [A:$i]: (in @ emptyset @ (powerset @ A))))). 29.46/11.17 thf(emptyInPowerset_type, type, emptyInPowerset: $o). 29.46/11.17 thf(emptyInPowerset_def, definition, (emptyInPowerset = (! [A:$i]: (in @ emptyset @ (powerset @ A))))). 29.46/11.17 thf(powersetE_type, type, powersetE: $o). 29.46/11.17 thf(powersetE_def, definition, (powersetE = (! [A:$i,B:$i,C:$i]: ((in @ B @ (powerset @ A)) => ((in @ C @ B) => (in @ C @ A)))))). 29.46/11.17 thf(setunionI_type, type, setunionI: $o). 29.46/11.17 thf(setunionI_def, definition, (setunionI = (! [A:$i,B:$i,C:$i]: ((in @ B @ C) => ((in @ C @ A) => (in @ B @ (setunion @ A))))))). 29.46/11.17 thf(setunionE_type, type, setunionE: $o). 29.46/11.17 thf(setunionE_def, definition, (setunionE = (! [A:$i,B:$i]: ((in @ B @ (setunion @ A)) => (! [C:$o]: ((! [D:$i]: ((in @ B @ D) => ((in @ D @ A) => (C)))) => (C))))))). 29.46/11.17 thf(subPowSU_type, type, subPowSU: $o). 29.46/11.17 thf(subPowSU_def, definition, (subPowSU = (! [A:$i,B:$i]: ((in @ B @ A) => (in @ B @ (powerset @ (setunion @ A))))))). 29.46/11.17 thf(exuE2_type, type, exuE2: $o). 29.46/11.17 thf(exuE2_def, definition, (exuE2 = (! [A:($i > $o)]: ((exu @ (A)) => (? [B:$i]: ! [C:$i]: ((A @ C) = (C = B))))))). 29.46/11.17 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o). 29.46/11.17 thf(nonemptyImpWitness_def, definition, (nonemptyImpWitness = (! [A:$i]: ((nonempty @ A) => (? [B:$i]: ((in @ B @ A) & ($true))))))). 29.46/11.17 thf(uniqinunit_type, type, uniqinunit: $o). 29.46/11.17 thf(uniqinunit_def, definition, (uniqinunit = (! [A:$i,B:$i]: ((in @ A @ (setadjoin @ B @ emptyset)) => (A = B))))). 29.46/11.17 thf(notinsingleton_type, type, notinsingleton: $o). 29.46/11.17 thf(notinsingleton_def, definition, (notinsingleton = (! [A:$i,B:$i]: ((A != B) => (~ (in @ B @ (setadjoin @ A @ emptyset))))))). 29.46/11.17 thf(eqinunit_type, type, eqinunit: $o). 29.46/11.17 thf(eqinunit_def, definition, (eqinunit = (! [A:$i,B:$i]: ((A = B) => (in @ A @ (setadjoin @ B @ emptyset)))))). 29.46/11.17 thf(singletonsswitch_type, type, singletonsswitch: $o). 29.46/11.17 thf(singletonsswitch_def, definition, (singletonsswitch = (! [A:$i,B:$i]: ((in @ A @ (setadjoin @ B @ emptyset)) => (in @ B @ (setadjoin @ A @ emptyset)))))). 29.46/11.17 thf(upairsetE_type, type, upairsetE: $o). 29.46/11.17 thf(upairsetE_def, definition, (upairsetE = (! [A:$i,B:$i,C:$i]: ((in @ C @ (setadjoin @ A @ (setadjoin @ B @ emptyset))) => ((C = A) | (C = B)))))). 29.46/11.17 thf(upairsetIL_type, type, upairsetIL: $o). 29.46/11.17 thf(upairsetIL_def, definition, (upairsetIL = (! [A:$i,B:$i]: (in @ A @ (setadjoin @ A @ (setadjoin @ B @ emptyset)))))). 29.46/11.17 thf(upairsetIR_type, type, upairsetIR: $o). 29.46/11.17 thf(upairsetIR_def, definition, (upairsetIR = (! [A:$i,B:$i]: (in @ B @ (setadjoin @ A @ (setadjoin @ B @ emptyset)))))). 29.46/11.17 thf(emptyE1_type, type, emptyE1: $o). 29.46/11.17 thf(emptyE1_def, definition, (emptyE1 = (! [A:$i,B:($i > $o)]: ((? [C:$i]: ((in @ C @ A) & (B @ C))) => (((dsetconstr @ A @ (B)) = emptyset) => ($false)))))). 29.46/11.17 thf(vacuousDall_type, type, vacuousDall: $o). 29.46/11.17 thf(vacuousDall_def, definition, (vacuousDall = (! [A:($i > $o),B:$i]: ((in @ B @ emptyset) => (A @ B))))). 29.46/11.17 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o). 29.46/11.17 thf(quantDeMorgan1_def, definition, (quantDeMorgan1 = (! [A:$i,B:($i > $o)]: ((~ (! [C:$i]: ((in @ C @ A) => (B @ C)))) => (? [C:$i]: ((in @ C @ A) & ~ (B @ C))))))). 29.46/11.17 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o). 29.46/11.17 thf(quantDeMorgan2_def, definition, (quantDeMorgan2 = (! [A:$i,B:($i > $o)]: ((! [C:$i]: ((in @ C @ A) => (~ (B @ C)))) => (~ (? [C:$i]: ((in @ C @ A) & (B @ C)))))))). 29.46/11.17 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o). 29.46/11.17 thf(quantDeMorgan3_def, definition, (quantDeMorgan3 = (! [A:$i,B:($i > $o)]: ((~ (? [C:$i]: ((in @ C @ A) & (B @ C)))) => (! [C:$i]: ((in @ C @ A) => (~ (B @ C)))))))). 29.46/11.17 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o). 29.46/11.17 thf(quantDeMorgan4_def, definition, (quantDeMorgan4 = (! [A:$i,B:($i > $o)]: ((? [C:$i]: ((in @ C @ A) & ~ (B @ C))) => (~ (! [C:$i]: ((in @ C @ A) => (B @ C)))))))). 29.46/11.17 thf(prop2setI_type, type, prop2setI: $o). 29.46/11.17 thf(prop2setI_def, definition, (prop2setI = (! [A:$o]: ((A) => (in @ emptyset @ (prop2set @ A)))))). 29.46/11.17 thf(set2prop_type, type, set2prop: ($i > $o)). 29.46/11.17 thf(prop2set2propI_type, type, prop2set2propI: $o). 29.46/11.17 thf(prop2set2propI_def, definition, (prop2set2propI = (! [A:$o]: ((A) => (set2prop @ (prop2set @ A)))))). 29.46/11.17 thf(notdexE_type, type, notdexE: $o). 29.46/11.17 thf(notdexE_def, definition, (notdexE = (! [A:$i,B:($i > $o)]: ((~ (? [C:$i]: ((in @ C @ A) & (B @ C)))) => (! [C:$i]: ((in @ C @ A) => (~ (B @ C)))))))). 29.46/11.17 thf(notdallE_type, type, notdallE: $o). 29.46/11.17 thf(notdallE_def, definition, (notdallE = (! [A:$i,B:($i > $o)]: ((~ (! [C:$i]: ((in @ C @ A) => (B @ C)))) => (? [C:$i]: ((in @ C @ A) & ~ (B @ C))))))). 29.46/11.17 thf(exuI1_type, type, exuI1: $o). 29.46/11.17 thf(exuI1_def, definition, (exuI1 = (! [A:($i > $o)]: ((? [B:$i]: ((A @ B) & ! [C:$i]: ((A @ C) => (B = C)))) => (exu @ (A)))))). 29.46/11.17 thf(exuI3_type, type, exuI3: $o). 29.46/11.17 thf(exuI3_def, definition, (exuI3 = (! [A:($i > $o)]: ((? [B:$i]: (A @ B)) => ((! [B:$i,C:$i]: ((A @ B) => ((A @ C) => (B = C)))) => (exu @ (A))))))). 29.46/11.17 thf(exuI2_type, type, exuI2: $o). 29.46/11.17 thf(exuI2_def, definition, (exuI2 = (! [A:($i > $o)]: ((? [B:$i]: ! [C:$i]: ((A @ C) = (C = B))) => (exu @ (A)))))). 29.46/11.17 thf(inCongP_type, type, inCongP: $o). 29.46/11.17 thf(inCongP_def, definition, (inCongP = (! [A:$i,B:$i]: ((A = B) => (! [C:$i,D:$i]: ((C = D) => ((in @ C @ A) => (in @ D @ B)))))))). 29.46/11.17 thf(in__Cong_type, type, in__Cong: $o). 29.46/11.17 thf(in__Cong_def, definition, (in__Cong = (! [A:$i,B:$i]: ((A = B) => (! [C:$i,D:$i]: ((C = D) => ((in @ C @ A) = (in @ D @ B)))))))). 29.46/11.17 thf(exuE3u_type, type, exuE3u: $o). 29.46/11.17 thf(exuE3u_def, definition, (exuE3u = (! [A:($i > $o)]: ((exu @ (A)) => (! [B:$i,C:$i]: ((A @ B) => ((A @ C) => (B = C)))))))). 29.46/11.17 thf(exu__Cong_type, type, exu__Cong: $o). 29.46/11.17 thf(exu__Cong_def, definition, (exu__Cong = (! [A:($i > $o),B:($i > $o)]: ((! [C:$i,D:$i]: ((C = D) => ((A @ C) = (B @ D)))) => ((exu @ (A)) = (exu @ (B))))))). 29.46/11.17 thf(emptyset__Cong_type, type, emptyset__Cong: $o). 29.46/11.17 thf(emptyset__Cong_def, definition, (emptyset__Cong = (emptyset = emptyset))). 29.46/11.17 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o). 29.46/11.17 thf(setadjoin__Cong_def, definition, (setadjoin__Cong = (! [A:$i,B:$i]: ((A = B) => (! [C:$i,D:$i]: ((C = D) => ((setadjoin @ A @ C) = (setadjoin @ B @ D)))))))). 29.46/11.17 thf(powerset__Cong_type, type, powerset__Cong: $o). 29.46/11.17 thf(powerset__Cong_def, definition, (powerset__Cong = (! [A:$i,B:$i]: ((A = B) => ((powerset @ A) = (powerset @ B)))))). 29.46/11.17 thf(setunion__Cong_type, type, setunion__Cong: $o). 29.46/11.17 thf(setunion__Cong_def, definition, (setunion__Cong = (! [A:$i,B:$i]: ((A = B) => ((setunion @ A) = (setunion @ B)))))). 29.46/11.17 thf(omega__Cong_type, type, omega__Cong: $o). 29.46/11.17 thf(omega__Cong_def, definition, (omega__Cong = (omega = omega))). 29.46/11.17 thf(exuEu_type, type, exuEu: $o). 29.46/11.17 thf(exuEu_def, definition, (exuEu = (! [A:($i > $o)]: ((exu @ (A)) => (! [B:$i,C:$i]: ((A @ B) => ((A @ C) => (B = C)))))))). 29.46/11.17 thf(descr__Cong_type, type, descr__Cong: $o). 29.46/11.17 thf(descr__Cong_def, definition, (descr__Cong = (! [A:($i > $o),B:($i > $o)]: ((! [C:$i,D:$i]: ((C = D) => ((A @ C) = (B @ D)))) => ((exu @ (A)) => ((exu @ (B)) => ((descr @ (A)) = (descr @ (B))))))))). 29.46/11.17 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o). 29.46/11.17 thf(dsetconstr__Cong_def, definition, (dsetconstr__Cong = (! [A:$i,B:$i]: ((A = B) => (! [C:($i > $o),D:($i > $o)]: ((! [E:$i]: ((in @ E @ A) => (! [F:$i]: ((in @ F @ B) => ((E = F) => ((C @ E) = (D @ F))))))) => ((dsetconstr @ A @ (C)) = (dsetconstr @ B @ (D))))))))). 29.46/11.17 thf(subset_type, type, subset: ($i > ($i > $o))). 29.46/11.17 thf(subsetI1_type, type, subsetI1: $o). 29.46/11.17 thf(subsetI1_def, definition, (subsetI1 = (! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ A) => (in @ C @ B))) => (subset @ A @ B))))). 29.46/11.17 thf(eqimpsubset2_type, type, eqimpsubset2: $o). 29.46/11.17 thf(eqimpsubset2_def, definition, (eqimpsubset2 = (! [A:$i,B:$i]: ((A = B) => (subset @ B @ A))))). 29.46/11.17 thf(eqimpsubset1_type, type, eqimpsubset1: $o). 29.46/11.17 thf(eqimpsubset1_def, definition, (eqimpsubset1 = (! [A:$i,B:$i]: ((A = B) => (subset @ A @ B))))). 29.46/11.17 thf(subsetI2_type, type, subsetI2: $o). 29.46/11.17 thf(subsetI2_def, definition, (subsetI2 = (! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ A) => (in @ C @ B))) => (subset @ A @ B))))). 29.46/11.17 thf(emptysetsubset_type, type, emptysetsubset: $o). 29.46/11.17 thf(emptysetsubset_def, definition, (emptysetsubset = (! [A:$i]: (subset @ emptyset @ A)))). 29.46/11.17 thf(subsetE_type, type, subsetE: $o). 29.46/11.17 thf(subsetE_def, definition, (subsetE = (! [A:$i,B:$i,C:$i]: ((subset @ A @ B) => ((in @ C @ A) => (in @ C @ B)))))). 29.46/11.17 thf(subsetE2_type, type, subsetE2: $o). 29.46/11.17 thf(subsetE2_def, definition, (subsetE2 = (! [A:$i,B:$i,C:$i]: ((subset @ A @ B) => ((~ (in @ C @ B)) => (~ (in @ C @ A))))))). 29.46/11.17 thf(notsubsetI_type, type, notsubsetI: $o). 29.46/11.17 thf(notsubsetI_def, definition, (notsubsetI = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => ((~ (in @ C @ B)) => (~ (subset @ A @ B))))))). 29.46/11.17 thf(notequalI1_type, type, notequalI1: $o). 29.46/11.17 thf(notequalI1_def, definition, (notequalI1 = (! [A:$i,B:$i]: ((~ (subset @ A @ B)) => (A != B))))). 29.46/11.17 thf(notequalI2_type, type, notequalI2: $o). 29.46/11.17 thf(notequalI2_def, definition, (notequalI2 = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => ((~ (in @ C @ B)) => (A != B)))))). 29.46/11.17 thf(subsetRefl_type, type, subsetRefl: $o). 29.46/11.17 thf(subsetRefl_def, definition, (subsetRefl = (! [A:$i]: (subset @ A @ A)))). 29.46/11.17 thf(subsetTrans_type, type, subsetTrans: $o). 29.46/11.17 thf(subsetTrans_def, definition, (subsetTrans = (! [A:$i,B:$i,C:$i]: ((subset @ A @ B) => ((subset @ B @ C) => (subset @ A @ C)))))). 29.46/11.17 thf(setadjoinSub_type, type, setadjoinSub: $o). 29.46/11.17 thf(setadjoinSub_def, definition, (setadjoinSub = (! [A:$i,B:$i]: (subset @ B @ (setadjoin @ A @ B))))). 29.46/11.17 thf(setadjoinSub2_type, type, setadjoinSub2: $o). 29.46/11.17 thf(setadjoinSub2_def, definition, (setadjoinSub2 = (! [A:$i,B:$i,C:$i]: ((subset @ A @ C) => (subset @ A @ (setadjoin @ B @ C)))))). 29.46/11.17 thf(subset2powerset_type, type, subset2powerset: $o). 29.46/11.17 thf(subset2powerset_def, definition, (subset2powerset = (! [A:$i,B:$i]: ((subset @ A @ B) => (in @ A @ (powerset @ B)))))). 29.46/11.17 thf(setextsub_type, type, setextsub: $o). 29.46/11.17 thf(setextsub_def, definition, (setextsub = (! [A:$i,B:$i]: ((subset @ A @ B) => ((subset @ B @ A) => (A = B)))))). 29.46/11.17 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o). 29.46/11.17 thf(subsetemptysetimpeq_def, definition, (subsetemptysetimpeq = (! [A:$i]: ((subset @ A @ emptyset) => (A = emptyset))))). 29.46/11.17 thf(powersetI1_type, type, powersetI1: $o). 29.46/11.17 thf(powersetI1_def, definition, (powersetI1 = (! [A:$i,B:$i]: ((subset @ B @ A) => (in @ B @ (powerset @ A)))))). 29.46/11.17 thf(powersetE1_type, type, powersetE1: $o). 29.46/11.17 thf(powersetE1_def, definition, (powersetE1 = (! [A:$i,B:$i]: ((in @ B @ (powerset @ A)) => (subset @ B @ A))))). 29.46/11.17 thf(inPowerset_type, type, inPowerset: $o). 29.46/11.17 thf(inPowerset_def, definition, (inPowerset = (! [A:$i]: (in @ A @ (powerset @ A))))). 29.46/11.17 thf(powersetsubset_type, type, powersetsubset: $o). 29.46/11.17 thf(powersetsubset_def, definition, (powersetsubset = (! [A:$i,B:$i]: ((subset @ A @ B) => (subset @ (powerset @ A) @ (powerset @ B)))))). 29.46/11.17 thf(sepInPowerset_type, type, sepInPowerset: $o). 29.46/11.17 thf(sepInPowerset_def, definition, (sepInPowerset = (! [A:$i,B:($i > $o)]: (in @ (dsetconstr @ A @ (B)) @ (powerset @ A))))). 29.46/11.17 thf(sepSubset_type, type, sepSubset: $o). 29.46/11.17 thf(sepSubset_def, definition, (sepSubset = (! [A:$i,B:($i > $o)]: (subset @ (dsetconstr @ A @ (B)) @ A)))). 29.46/11.17 thf(binunion_type, type, binunion: ($i > ($i > $i))). 29.46/11.17 thf(binunionIL_type, type, binunionIL: $o). 29.46/11.17 thf(binunionIL_def, definition, (binunionIL = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (in @ C @ (binunion @ A @ B)))))). 29.46/11.17 thf(upairset2IR_type, type, upairset2IR: $o). 29.46/11.17 thf(upairset2IR_def, definition, (upairset2IR = (! [A:$i,B:$i]: (in @ B @ (setadjoin @ A @ (setadjoin @ B @ emptyset)))))). 29.46/11.17 thf(binunionIR_type, type, binunionIR: $o). 29.46/11.17 thf(binunionIR_def, definition, (binunionIR = (! [A:$i,B:$i,C:$i]: ((in @ C @ B) => (in @ C @ (binunion @ A @ B)))))). 29.46/11.17 thf(binunionEcases_type, type, binunionEcases: $o). 29.46/11.17 thf(binunionEcases_def, definition, (binunionEcases = (! [A:$i,B:$i,C:$i,D:$o]: ((in @ C @ (binunion @ A @ B)) => (((in @ C @ A) => (D)) => (((in @ C @ B) => (D)) => (D))))))). 29.46/11.17 thf(binunionE_type, type, binunionE: $o). 29.46/11.17 thf(binunionE_def, definition, (binunionE = (! [A:$i,B:$i,C:$i]: ((in @ C @ (binunion @ A @ B)) => ((in @ C @ A) | (in @ C @ B)))))). 29.46/11.17 thf(binunionLsub_type, type, binunionLsub: $o). 29.46/11.17 thf(binunionLsub_def, definition, (binunionLsub = (! [A:$i,B:$i]: (subset @ A @ (binunion @ A @ B))))). 29.46/11.17 thf(binunionRsub_type, type, binunionRsub: $o). 29.46/11.17 thf(binunionRsub_def, definition, (binunionRsub = (! [A:$i,B:$i]: (subset @ B @ (binunion @ A @ B))))). 29.46/11.17 thf(binintersect_type, type, binintersect: ($i > ($i > $i))). 29.46/11.17 thf(binintersectI_type, type, binintersectI: $o). 29.46/11.17 thf(binintersectI_def, definition, (binintersectI = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => ((in @ C @ B) => (in @ C @ (binintersect @ A @ B))))))). 29.46/11.17 thf(binintersectSubset5_type, type, binintersectSubset5: $o). 29.46/11.17 thf(binintersectSubset5_def, definition, (binintersectSubset5 = (! [A:$i,B:$i,C:$i]: ((subset @ C @ A) => ((subset @ C @ B) => (subset @ C @ (binintersect @ A @ B))))))). 29.46/11.17 thf(binintersectEL_type, type, binintersectEL: $o). 29.46/11.17 thf(binintersectEL_def, definition, (binintersectEL = (! [A:$i,B:$i,C:$i]: ((in @ C @ (binintersect @ A @ B)) => (in @ C @ A))))). 29.46/11.17 thf(binintersectLsub_type, type, binintersectLsub: $o). 29.46/11.17 thf(binintersectLsub_def, definition, (binintersectLsub = (! [A:$i,B:$i]: (subset @ (binintersect @ A @ B) @ A)))). 29.46/11.17 thf(binintersectSubset2_type, type, binintersectSubset2: $o). 29.46/11.17 thf(binintersectSubset2_def, definition, (binintersectSubset2 = (! [A:$i,B:$i]: ((subset @ A @ B) => ((binintersect @ A @ B) = A))))). 29.46/11.17 thf(binintersectSubset3_type, type, binintersectSubset3: $o). 29.46/11.17 thf(binintersectSubset3_def, definition, (binintersectSubset3 = (! [A:$i,B:$i]: (((binintersect @ A @ B) = B) => (subset @ B @ A))))). 29.46/11.17 thf(binintersectER_type, type, binintersectER: $o). 29.46/11.17 thf(binintersectER_def, definition, (binintersectER = (! [A:$i,B:$i,C:$i]: ((in @ C @ (binintersect @ A @ B)) => (in @ C @ B))))). 29.46/11.17 thf(disjointsetsI1_type, type, disjointsetsI1: $o). 29.46/11.17 thf(disjointsetsI1_def, definition, (disjointsetsI1 = (! [A:$i,B:$i]: ((~ (? [C:$i]: ((in @ C @ A) & (in @ C @ B)))) => ((binintersect @ A @ B) = emptyset))))). 29.46/11.17 thf(binintersectRsub_type, type, binintersectRsub: $o). 29.46/11.17 thf(binintersectRsub_def, definition, (binintersectRsub = (! [A:$i,B:$i]: (subset @ (binintersect @ A @ B) @ B)))). 29.46/11.17 thf(binintersectSubset4_type, type, binintersectSubset4: $o). 29.46/11.17 thf(binintersectSubset4_def, definition, (binintersectSubset4 = (! [A:$i,B:$i]: ((subset @ B @ A) => ((binintersect @ A @ B) = B))))). 29.46/11.17 thf(binintersectSubset1_type, type, binintersectSubset1: $o). 29.46/11.17 thf(binintersectSubset1_def, definition, (binintersectSubset1 = (! [A:$i,B:$i]: (((binintersect @ A @ B) = A) => (subset @ A @ B))))). 29.46/11.17 thf(bs114d_type, type, bs114d: $o). 29.46/11.17 thf(bs114d_def, definition, (bs114d = (! [A:$i,B:$i,C:$i]: ((binintersect @ A @ (binunion @ B @ C)) = (binunion @ (binintersect @ A @ B) @ (binintersect @ A @ C)))))). 29.46/11.17 thf(setminus_type, type, setminus: ($i > ($i > $i))). 29.46/11.17 thf(setminusI_type, type, setminusI: $o). 29.46/11.17 thf(setminusI_def, definition, (setminusI = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => ((~ (in @ C @ B)) => (in @ C @ (setminus @ A @ B))))))). 29.46/11.17 thf(setminusEL_type, type, setminusEL: $o). 29.46/11.17 thf(setminusEL_def, definition, (setminusEL = (! [A:$i,B:$i,C:$i]: ((in @ C @ (setminus @ A @ B)) => (in @ C @ A))))). 29.46/11.17 thf(setminusER_type, type, setminusER: $o). 29.46/11.17 thf(setminusER_def, definition, (setminusER = (! [A:$i,B:$i,C:$i]: ((in @ C @ (setminus @ A @ B)) => (~ (in @ C @ B)))))). 29.46/11.17 thf(setminusSubset2_type, type, setminusSubset2: $o). 29.46/11.17 thf(setminusSubset2_def, definition, (setminusSubset2 = (! [A:$i,B:$i]: ((subset @ A @ B) => ((setminus @ A @ B) = emptyset))))). 29.46/11.17 thf(setminusERneg_type, type, setminusERneg: $o). 29.46/11.17 thf(setminusERneg_def, definition, (setminusERneg = (! [A:$i,B:$i,C:$i]: ((~ (in @ C @ (setminus @ A @ B))) => ((in @ C @ A) => (in @ C @ B)))))). 29.46/11.17 thf(setminusELneg_type, type, setminusELneg: $o). 29.46/11.17 thf(setminusELneg_def, definition, (setminusELneg = (! [A:$i,B:$i,C:$i]: ((~ (in @ C @ (setminus @ A @ B))) => ((~ (in @ C @ B)) => (~ (in @ C @ A))))))). 29.46/11.17 thf(setminusILneg_type, type, setminusILneg: $o). 29.46/11.17 thf(setminusILneg_def, definition, (setminusILneg = (! [A:$i,B:$i,C:$i]: ((~ (in @ C @ A)) => (~ (in @ C @ (setminus @ A @ B))))))). 29.46/11.17 thf(setminusIRneg_type, type, setminusIRneg: $o). 29.46/11.17 thf(setminusIRneg_def, definition, (setminusIRneg = (! [A:$i,B:$i,C:$i]: ((in @ C @ B) => (~ (in @ C @ (setminus @ A @ B))))))). 29.46/11.17 thf(setminusLsub_type, type, setminusLsub: $o). 29.46/11.17 thf(setminusLsub_def, definition, (setminusLsub = (! [A:$i,B:$i]: (subset @ (setminus @ A @ B) @ A)))). 29.46/11.17 thf(setminusSubset1_type, type, setminusSubset1: $o). 29.46/11.17 thf(setminusSubset1_def, definition, (setminusSubset1 = (! [A:$i,B:$i]: (((setminus @ A @ B) = emptyset) => (subset @ A @ B))))). 29.46/11.17 thf(symdiff_type, type, symdiff: ($i > ($i > $i))). 29.46/11.17 thf(symdiff_def, definition, (symdiff = (^ [A:$i,B:$i]: (dsetconstr @ (binunion @ A @ B) @ (^ [C:$i]: (~ (in @ C @ A) | ~ (in @ C @ B))))))). 29.46/11.17 thf(symdiffE_type, type, symdiffE: $o). 29.46/11.17 thf(symdiffE_def, definition, (symdiffE = (! [A:$i,B:$i,C:$i]: ((in @ C @ (symdiff @ A @ B)) => (! [D:$o]: (((in @ C @ A) => ((~ (in @ C @ B)) => (D))) => (((~ (in @ C @ A)) => ((in @ C @ B) => (D))) => (D)))))))). 29.46/11.17 thf(1,conjecture,(((setextAx) => ((emptysetAx) => ((((setunionAx) => (((omegaSAx) => ((((((descrp) => ((((dsetconstrER) => ((((emptysetE) => ((emptysetimpfalse) => (((exuE3e) => ((setext) => ((emptyI) => ((noeltsimpempty) => (((((nonemptyI1) => (((emptyinunitempty) => ((setadjoinIR) => (((setadjoinOr) => ((setoftrueEq) => ((powersetI) => ((emptyinPowerset) => ((((setunionI) => (((subPowSU) => ((exuE2) => ((nonemptyImpWitness) => ((uniqinunit) => ((notinsingleton) => ((eqinunit) => (((upairsetE) => (((upairsetIR) => ((emptyE1) => ((vacuousDall) => (((((quantDeMorgan4) => ((((notdexE) => ((notdallE) => ((exuI1) => ((exuI3) => (((inCongP) => ((in__Cong) => (((exu__Cong) => ((emptyset__Cong) => ((setadjoin__Cong) => ((powerset__Cong) => (((omega__Cong) => ((exuEu) => (((((((subsetI2) => ((((((notequalI1) => ((notequalI2) => ((subsetRefl) => ((subsetTrans) => ((((((subsetemptysetimpeq) => ((powersetI1) => ((((powersetsubset) => (((sepSubset) => (((upairset2IR) => ((binunionIR) => ((((binunionLsub) => ((binunionRsub) => ((binintersectI) => ((((binintersectLsub) => (((binintersectSubset3) => ((binintersectER) => ((((binintersectSubset4) => ((binintersectSubset1) => ((((setminusEL) => (((((setminusELneg) => ((setminusILneg) => ((setminusIRneg) => (((setminusSubset1) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ A) => ((~ (in @ C @ B)) => (in @ C @ (symdiff @ A @ B))))) <= (symdiffE))) <= (setminusLsub))))) <= (setminusERneg)) <= (setminusSubset2)) <= (setminusER))) <= (setminusI)) <= (bs114d)))) <= (binintersectRsub)) <= (disjointsetsI1)))) <= (binintersectSubset2))) <= (binintersectEL)) <= (binintersectSubset5))))) <= (binunionE)) <= (binunionEcases)))) <= (binunionIL))) <= (sepInPowerset))) <= (inPowerset)) <= (powersetE1)))) <= (setextsub)) <= (subset2powerset)) <= (setadjoinSub2)) <= (setadjoinSub)))))) <= (notsubsetI)) <= (subsetE2)) <= (subsetE)) <= (emptysetsubset))) <= (eqimpsubset1)) <= (eqimpsubset2)) <= (subsetI1)) <= (dsetconstr__Cong)) <= (descr__Cong)))) <= (setunion__Cong)))))) <= (exuE3u)))) <= (exuI2)))))) <= (prop2set2propI)) <= (prop2setI))) <= (quantDeMorgan3)) <= (quantDeMorgan2)) <= (quantDeMorgan1))))) <= (upairsetIL))) <= (singletonsswitch)))))))) <= (setunionE))) <= (powersetE)) <= (emptyInPowerset)))))) <= (setadjoinE)))) <= (setadjoinIL))) <= (nonemptyI)) <= (nonemptyE1)) <= (setbeta)))))) <= (notinemptyset)))) <= (prop2setE)) <= (exuE1))) <= (dsetconstrEL)) <= (dsetconstrI))) <= (wellorderingAx)) <= (foundationAx)) <= (replAx)) <= (omegaIndAx))) <= (omega0Ax))) <= (powersetAx)) <= (setadjoinAx))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffI1)). 29.46/11.17 thf(2,negated_conjecture,((~ ((setextAx) => ((emptysetAx) => ((((setunionAx) => (((omegaSAx) => ((((((descrp) => ((((dsetconstrER) => ((((emptysetE) => ((emptysetimpfalse) => (((exuE3e) => ((setext) => ((emptyI) => ((noeltsimpempty) => (((((nonemptyI1) => (((emptyinunitempty) => ((setadjoinIR) => (((setadjoinOr) => ((setoftrueEq) => ((powersetI) => ((emptyinPowerset) => ((((setunionI) => (((subPowSU) => ((exuE2) => ((nonemptyImpWitness) => ((uniqinunit) => ((notinsingleton) => ((eqinunit) => (((upairsetE) => (((upairsetIR) => ((emptyE1) => ((vacuousDall) => (((((quantDeMorgan4) => ((((notdexE) => ((notdallE) => ((exuI1) => ((exuI3) => (((inCongP) => ((in__Cong) => (((exu__Cong) => ((emptyset__Cong) => ((setadjoin__Cong) => ((powerset__Cong) => (((omega__Cong) => ((exuEu) => (((((((subsetI2) => ((((((notequalI1) => ((notequalI2) => ((subsetRefl) => ((subsetTrans) => ((((((subsetemptysetimpeq) => ((powersetI1) => ((((powersetsubset) => (((sepSubset) => (((upairset2IR) => ((binunionIR) => ((((binunionLsub) => ((binunionRsub) => ((binintersectI) => ((((binintersectLsub) => (((binintersectSubset3) => ((binintersectER) => ((((binintersectSubset4) => ((binintersectSubset1) => ((((setminusEL) => (((((setminusELneg) => ((setminusILneg) => ((setminusIRneg) => (((setminusSubset1) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ A) => ((~ (in @ C @ B)) => (in @ C @ (symdiff @ A @ B))))) <= (symdiffE))) <= (setminusLsub))))) <= (setminusERneg)) <= (setminusSubset2)) <= (setminusER))) <= (setminusI)) <= (bs114d)))) <= (binintersectRsub)) <= (disjointsetsI1)))) <= (binintersectSubset2))) <= (binintersectEL)) <= (binintersectSubset5))))) <= (binunionE)) <= (binunionEcases)))) <= (binunionIL))) <= (sepInPowerset))) <= (inPowerset)) <= (powersetE1)))) <= (setextsub)) <= (subset2powerset)) <= (setadjoinSub2)) <= (setadjoinSub)))))) <= (notsubsetI)) <= (subsetE2)) <= (subsetE)) <= (emptysetsubset))) <= (eqimpsubset1)) <= (eqimpsubset2)) <= (subsetI1)) <= (dsetconstr__Cong)) <= (descr__Cong)))) <= (setunion__Cong)))))) <= (exuE3u)))) <= (exuI2)))))) <= (prop2set2propI)) <= (prop2setI))) <= (quantDeMorgan3)) <= (quantDeMorgan2)) <= (quantDeMorgan1))))) <= (upairsetIL))) <= (singletonsswitch)))))))) <= (setunionE))) <= (powersetE)) <= (emptyInPowerset)))))) <= (setadjoinE)))) <= (setadjoinIL))) <= (nonemptyI)) <= (nonemptyE1)) <= (setbeta)))))) <= (notinemptyset)))) <= (prop2setE)) <= (exuE1))) <= (dsetconstrEL)) <= (dsetconstrI))) <= (wellorderingAx)) <= (foundationAx)) <= (replAx)) <= (omegaIndAx))) <= (omega0Ax))) <= (powersetAx)) <= (setadjoinAx)))))),inference(neg_conjecture,[status(cth)],[1])). 29.46/11.17 thf(3,plain,((~ ((! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ A) = (in @ C @ B))) => (A = B))) => ((! [A:$i]: ~ (in @ A @ emptyset)) => (((! [A:$i,B:$i]: ((in @ B @ (setunion @ A)) = (? [C:$i]: ((in @ B @ C) & (in @ C @ A))))) => (((! [A:$i]: ((in @ A @ omega) => (in @ (setadjoin @ A @ A) @ omega))) => (((! [A:($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))) => (B @ C))) => (((! [A:$i]: ((in @ A @ emptyset) => (! [B:$o]: (B)))) => ((! [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]: ~ (in @ B @ A)) => (A = emptyset))) => (((! [A:$i]: ((? [B:$i]: (in @ B @ A)) => (~ (A = emptyset)))) => (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ B) => (in @ C @ (setadjoin @ A @ B)))) => (((! [A:$i,B:$i,C:$i]: ((in @ C @ (setadjoin @ A @ B)) => ((C = A) | (in @ C @ B)))) => ((! [A:$i]: ((dsetconstr @ A @ (^ [B:$i]: ($true))) = A)) => ((! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ B) => (in @ C @ A))) => (in @ B @ (powerset @ A)))) => ((! [A:$i]: (in @ emptyset @ (powerset @ A))) => (((! [A:$i,B:$i,C:$i]: ((in @ B @ C) => ((in @ C @ A) => (in @ B @ (setunion @ A))))) => (((! [A:$i,B:$i]: ((in @ B @ A) => (in @ B @ (powerset @ (setunion @ 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:$i]: ((in @ A @ (setadjoin @ B @ emptyset)) => (A = B))) => ((! [A:$i,B:$i]: ((~ (A = B)) => (~ (in @ B @ (setadjoin @ A @ emptyset))))) => ((! [A:$i,B:$i]: ((A = B) => (in @ A @ (setadjoin @ B @ emptyset)))) => (((! [A:$i,B:$i,C:$i]: ((in @ C @ (setadjoin @ A @ (setadjoin @ B @ emptyset))) => ((C = A) | (C = B)))) => (((! [A:$i,B:$i]: (in @ B @ (setadjoin @ A @ (setadjoin @ B @ emptyset)))) => ((! [A:$i,B:($i > $o)]: ((? [C:$i]: ((in @ C @ A) & (B @ C))) => (~ ((dsetconstr @ A @ (B)) = emptyset)))) => ((! [A:($i > $o),B:$i]: ((in @ B @ emptyset) => (A @ B))) => (((! [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 > $o)]: ((? [B:$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]: ((A = B) => (! [C:$i,D:$i]: ((C = D) => ((in @ C @ A) => (in @ D @ B)))))) => ((! [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:$i]: ((A = B) => ((powerset @ A) = (powerset @ B)))) => (((! [A:($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:$i]: ((! [C:$i]: ((in @ C @ A) => (in @ C @ B))) => (subset @ A @ B))) => (((! [A:$i,B:$i]: ((~ (subset @ A @ B)) => (~ (A = B)))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ A) => ((~ (in @ C @ B)) => (~ (A = B))))) => ((! [A:$i]: (subset @ A @ A)) => ((! [A:$i,B:$i,C:$i]: ((subset @ A @ B) => ((subset @ B @ C) => (subset @ A @ C)))) => (((! [A:$i]: ((subset @ A @ emptyset) => (A = emptyset))) => ((! [A:$i,B:$i]: ((subset @ B @ A) => (in @ B @ (powerset @ A)))) => (((! [A:$i,B:$i]: ((subset @ A @ B) => (subset @ (powerset @ A) @ (powerset @ B)))) => (((! [A:$i,B:($i > $o)]: (subset @ (dsetconstr @ A @ (B)) @ A)) => (((! [A:$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]: (subset @ A @ (binunion @ A @ B))) => ((! [A:$i,B:$i]: (subset @ B @ (binunion @ A @ B))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ A) => ((in @ C @ B) => (in @ C @ (binintersect @ A @ B))))) => (((! [A:$i,B:$i]: (subset @ (binintersect @ A @ B) @ A)) => (((! [A:$i,B:$i]: (((binintersect @ A @ B) = B) => (subset @ B @ A))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ (binintersect @ A @ B)) => (in @ C @ B))) => (((! [A:$i,B:$i]: ((subset @ B @ A) => ((binintersect @ A @ B) = B))) => ((! [A:$i,B:$i]: (((binintersect @ A @ B) = A) => (subset @ A @ 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)) => (~ (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]: (((setminus @ A @ B) = emptyset) => (subset @ A @ B))) => (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => ((~ (in @ C @ B)) => (in @ C @ (dsetconstr @ (binunion @ A @ B) @ (^ [D:$i]: (~ (in @ D @ A) | ~ (in @ D @ B))))))) | ~ (! [A:$i,B:$i,C:$i]: ((in @ C @ (dsetconstr @ (binunion @ A @ B) @ (^ [D:$i]: (~ (in @ D @ A) | ~ (in @ D @ B))))) => (! [D:$o]: (((in @ C @ A) => ((~ (in @ C @ B)) => (D))) => (((~ (in @ C @ A)) => ((in @ C @ B) => (D))) => (D)))))))) | ~ (! [A:$i,B:$i]: (subset @ (setminus @ A @ B) @ A)))))) | ~ (! [A:$i,B:$i,C:$i]: ((~ (in @ C @ (setminus @ A @ B))) => ((in @ C @ A) => (in @ C @ B)))) | ~ (! [A:$i,B:$i]: ((subset @ A @ B) => ((setminus @ A @ B) = emptyset))) | ~ (! [A:$i,B:$i,C:$i]: ((in @ C @ (setminus @ A @ B)) => (~ (in @ C @ B)))))) | ~ (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => ((~ (in @ C @ B)) => (in @ C @ (setminus @ A @ B))))) | ~ (! [A:$i,B:$i,C:$i]: ((binintersect @ A @ (binunion @ B @ C)) = (binunion @ (binintersect @ A @ B) @ (binintersect @ A @ C))))))) | ~ (! [A:$i,B:$i]: (subset @ (binintersect @ A @ B) @ B)) | ~ (! [A:$i,B:$i]: ((~ (? [C:$i]: ((in @ C @ A) & (in @ C @ B)))) => ((binintersect @ A @ B) = emptyset)))))) | ~ (! [A:$i,B:$i]: ((subset @ A @ B) => ((binintersect @ A @ B) = A))))) | ~ (! [A:$i,B:$i,C:$i]: ((in @ C @ (binintersect @ A @ B)) => (in @ C @ A))) | ~ (! [A:$i,B:$i,C:$i]: ((subset @ C @ A) => ((subset @ C @ B) => (subset @ C @ (binintersect @ A @ B))))))))) | ~ (! [A:$i,B:$i,C:$i]: ((in @ C @ (binunion @ A @ B)) => ((in @ C @ A) | (in @ C @ B)))) | ~ (! [A:$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 @ A) => (in @ C @ (binunion @ A @ B)))))) | ~ (! [A:$i,B:($i > $o)]: (in @ (dsetconstr @ A @ (B)) @ (powerset @ A))))) | ~ (! [A:$i]: (in @ A @ (powerset @ A))) | ~ (! [A:$i,B:$i]: ((in @ B @ (powerset @ A)) => (subset @ B @ A)))))) | ~ (! [A:$i,B:$i]: ((subset @ A @ B) => ((subset @ B @ A) => (A = B)))) | ~ (! [A:$i,B:$i]: ((subset @ A @ B) => (in @ A @ (powerset @ B)))) | ~ (! [A:$i,B:$i,C:$i]: ((subset @ A @ C) => (subset @ A @ (setadjoin @ B @ C)))) | ~ (! [A:$i,B:$i]: (subset @ B @ (setadjoin @ A @ B)))))))) | ~ (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => ((~ (in @ C @ B)) => (~ (subset @ A @ B))))) | ~ (! [A:$i,B:$i,C:$i]: ((subset @ A @ B) => ((~ (in @ C @ B)) => (~ (in @ C @ A))))) | ~ (! [A:$i,B:$i,C:$i]: ((subset @ A @ B) => ((in @ C @ A) => (in @ C @ B)))) | ~ (! [A:$i]: (subset @ emptyset @ A)))) | ~ (! [A:$i,B:$i]: ((A = B) => (subset @ A @ B))) | ~ (! [A:$i,B:$i]: ((A = B) => (subset @ B @ A))) | ~ (! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ A) => (in @ C @ B))) => (subset @ A @ B))) | ~ (! [A:$i,B:$i]: ((A = B) => (! [C:($i > $o),D:($i > $o)]: ((! [E:$i]: ((in @ E @ A) => (! [F:$i]: ((in @ F @ B) => ((E = F) => ((C @ E) = (D @ F))))))) => ((dsetconstr @ A @ (C)) = (dsetconstr @ B @ (D))))))) | ~ (! [A:($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:$i]: ((B @ D) => (C = D)))) => ((descr @ (A)) = (descr @ (B))))))))) | ~ (! [A:$i,B:$i]: ((A = B) => ((setunion @ A) = (setunion @ B)))))))) | ~ (! [A:($i > $o)]: ((? [B:$i]: ((A @ B) & ! [C:$i]: ((A @ C) => (B = C)))) => (! [B:$i,C:$i]: ((A @ B) => ((A @ C) => (B = C))))))))) | ~ (! [A:($i > $o)]: ((? [B:$i]: ! [C:$i]: ((A @ C) = (C = B))) => (? [B:$i]: ((A @ B) & ! [C:$i]: ((A @ C) => (B = C)))))))))) | ~ (! [A:$o]: ((A) => (set2prop @ (prop2set @ A)))) | ~ (! [A:$o]: ((A) => (in @ emptyset @ (prop2set @ A)))))) | ~ (! [A:$i,B:($i > $o)]: ((~ (? [C:$i]: ((in @ C @ A) & (B @ C)))) => (! [C:$i]: ((in @ C @ A) => (~ (B @ C)))))) | ~ (! [A:$i,B:($i > $o)]: ((! [C:$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:$i]: (in @ A @ (setadjoin @ A @ (setadjoin @ B @ emptyset)))))) | ~ (! [A:$i,B:$i]: ((in @ A @ (setadjoin @ B @ emptyset)) => (in @ B @ (setadjoin @ A @ emptyset))))))))))) | ~ (! [A:$i,B:$i]: ((in @ B @ (setunion @ A)) => (! [C:$o]: ((! [D:$i]: ((in @ B @ D) => ((in @ D @ A) => (C)))) => (C))))))) | ~ (! [A:$i,B:$i,C:$i]: ((in @ B @ (powerset @ A)) => ((in @ C @ B) => (in @ C @ A)))) | ~ (! [A:$i]: (in @ emptyset @ (powerset @ A)))))))) | ~ (! [A:$i,B:$i,C:$i]: ((in @ C @ (setadjoin @ A @ B)) => (! [D:$o]: (((C = A) => (D)) => (((in @ C @ B) => (D)) => (D))))))))) | ~ (! [A:$i,B:$i]: (in @ A @ (setadjoin @ A @ B))))) | ~ (! [A:$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 > $o),C:$i]: ((in @ C @ A) => ((in @ C @ (dsetconstr @ A @ (B))) = (B @ C))))))))) | ~ (! [A:$i]: ~ (in @ A @ emptyset))))) | ~ (! [A:$o,B:$i]: ((in @ B @ (prop2set @ A)) => (A))))) | ~ (! [A:$i,B:($i > $o),C:$i]: ((in @ C @ (dsetconstr @ A @ (B))) => (in @ C @ A))) | ~ (! [A:$i,B:($i > $o),C:$i]: ((in @ C @ 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]: ((? [B:$i]: (in @ B @ A)) => (? [B:$i]: ((in @ B @ A) & ~ (? [C:$i]: ((in @ C @ B) & (in @ C @ A))))))) | ~ (! [A:($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:$i]: (((in @ emptyset @ A) & ! [B:$i]: (((in @ B @ omega) & (in @ B @ A)) => (in @ (setadjoin @ B @ B) @ A))) => (! [B:$i]: ((in @ B @ omega) => (in @ B @ A))))))) | ~ (in @ emptyset @ omega))) | ~ (! [A:$i,B:$i]: ((in @ B @ (powerset @ A)) = (! [C:$i]: ((in @ C @ B) => (in @ C @ A))))) | ~ (! [A:$i,B:$i,C:$i]: ((in @ C @ (setadjoin @ A @ B)) = ((C = A) | (in @ C @ B))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])). 29.46/11.17 thf(4205,plain,($false),inference(e,[status(thm)],[3])). 29.46/11.17 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 29.46/11.17 % [INFO] Killing All external provers ... 29.46/11.17 FINAL WATCH: 22.9 CPU 6.1 WC 29.46/11.17 Killed 3 orphans 29.46/11.17 Killed 1 orphans 29.46/11.17 Killed 1 orphans 29.46/11.17 EOF