0.07/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.14 % Command : run_Leo-III---1.5 %s %d 0.15/0.35 % Computer : n021.cluster.edu 0.15/0.35 % Model : x86_64 x86_64 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.15/0.35 % Memory : 8042.1875MB 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.15/0.35 % CPULimit : 960 0.15/0.35 % WCLimit : 120 0.15/0.35 % DateTime : Thu Jul 2 08:56:23 EDT 2020 0.15/0.35 % CPUTime : 0.15/0.36 % Leo-III: Strategy 1 (for '60') 41.01/17.88 % [INFO] Running in sequential loop mode. 41.01/17.88 % [CONFIG] Using configuration: timeout(60) with strategy 41.01/17.88 % [INFO] eprover registered as external prover. 41.01/17.88 % [INFO] cvc4 registered as external prover. 41.01/17.88 % [INFO] Parsing finished. Scanning for conjecture ... 41.01/17.88 % [INFO] Found a conjecture and 0 axioms. Running axiom selection ... 41.01/17.88 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms). 41.01/17.88 % [INFO] Type checking passed. Searching for refutation ... 41.01/17.88 % [INFO] Killing All external provers ... 41.01/17.88 % Time passed: 15157ms 41.01/17.88 % Effective reasoning time: 4355ms 41.01/17.88 % Solved by strategy 41.01/17.88 % Axioms used in derivation (0): 41.01/17.88 % No. of inferences in proof: 4 41.01/17.88 % No. of processed clauses: 9 41.01/17.88 % No. of generated clauses: 53 41.01/17.88 % No. of forward subsumed clauses: 1 41.01/17.88 % No. of backward subsumed clauses: 0 41.01/17.88 % No. of ground rewrite rules in store: 4 41.01/17.88 % No. of non-ground rewrite rules in store: 2 41.01/17.88 % No. of positive (non-rewrite) units in store: 0 41.01/17.88 % No. of negative (non-rewrite) units in store: 1 41.01/17.88 % No. of choice functions detected: 0 41.01/17.88 % No. of choice instantiations: 0 41.01/17.88 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 15157 ms resp. 4355 ms w/o parsing 41.01/17.88 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 41.01/17.88 thf(in_type, type, in: ($i > ($i > $o))). 41.01/17.88 thf(setextAx_type, type, setextAx: $o). 41.01/17.88 thf(setextAx_def, definition, (setextAx = (! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ A) = (in @ C @ B))) => (A = B))))). 41.01/17.88 thf(emptyset_type, type, emptyset: $i). 41.01/17.88 thf(emptysetAx_type, type, emptysetAx: $o). 41.01/17.88 thf(emptysetAx_def, definition, (emptysetAx = (! [A:$i]: ~ (in @ A @ emptyset)))). 41.01/17.88 thf(setadjoin_type, type, setadjoin: ($i > ($i > $i))). 41.01/17.88 thf(setadjoinAx_type, type, setadjoinAx: $o). 41.01/17.88 thf(setadjoinAx_def, definition, (setadjoinAx = (! [A:$i,B:$i,C:$i]: ((in @ C @ (setadjoin @ A @ B)) = ((C = A) | (in @ C @ B)))))). 41.01/17.88 thf(powerset_type, type, powerset: ($i > $i)). 41.01/17.88 thf(powersetAx_type, type, powersetAx: $o). 41.01/17.88 thf(powersetAx_def, definition, (powersetAx = (! [A:$i,B:$i]: ((in @ B @ (powerset @ A)) = (! [C:$i]: ((in @ C @ B) => (in @ C @ A))))))). 41.01/17.88 thf(setunion_type, type, setunion: ($i > $i)). 41.01/17.88 thf(setunionAx_type, type, setunionAx: $o). 41.01/17.88 thf(setunionAx_def, definition, (setunionAx = (! [A:$i,B:$i]: ((in @ B @ (setunion @ A)) = (? [C:$i]: ((in @ B @ C) & (in @ C @ A))))))). 41.01/17.88 thf(omega_type, type, omega: $i). 41.01/17.88 thf(omega0Ax_type, type, omega0Ax: $o). 41.01/17.88 thf(omega0Ax_def, definition, (omega0Ax = (in @ emptyset @ omega))). 41.01/17.88 thf(omegaSAx_type, type, omegaSAx: $o). 41.01/17.88 thf(omegaSAx_def, definition, (omegaSAx = (! [A:$i]: ((in @ A @ omega) => (in @ (setadjoin @ A @ A) @ omega))))). 41.01/17.88 thf(omegaIndAx_type, type, omegaIndAx: $o). 41.01/17.88 thf(omegaIndAx_def, definition, (omegaIndAx = (! [A:$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))))))). 41.01/17.88 thf(replAx_type, type, replAx: $o). 41.01/17.88 thf(replAx_def, definition, (replAx = (! [A:($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))))))))). 41.01/17.88 thf(foundationAx_type, type, foundationAx: $o). 41.01/17.88 thf(foundationAx_def, definition, (foundationAx = (! [A:$i]: ((? [B:$i]: (in @ B @ A)) => (? [B:$i]: ((in @ B @ A) & ~ (? [C:$i]: ((in @ C @ B) & (in @ C @ A))))))))). 41.01/17.88 thf(wellorderingAx_type, type, wellorderingAx: $o). 41.01/17.88 thf(wellorderingAx_def, definition, (wellorderingAx = (! [A:$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)))))))))). 41.01/17.88 thf(descr_type, type, descr: (($i > $o) > $i)). 41.01/17.88 thf(descrp_type, type, descrp: $o). 41.01/17.88 thf(descrp_def, definition, (descrp = (! [A:($i > $o)]: ((exu @ (A)) => (A @ (descr @ (A))))))). 41.01/17.88 thf(dsetconstr_type, type, dsetconstr: ($i > (($i > $o) > $i))). 41.01/17.88 thf(dsetconstrI_type, type, dsetconstrI: $o). 41.01/17.88 thf(dsetconstrI_def, definition, (dsetconstrI = (! [A:$i,B:($i > $o),C:$i]: ((in @ C @ A) => ((B @ C) => (in @ C @ (dsetconstr @ A @ (B)))))))). 41.01/17.88 thf(dsetconstrEL_type, type, dsetconstrEL: $o). 41.01/17.88 thf(dsetconstrEL_def, definition, (dsetconstrEL = (! [A:$i,B:($i > $o),C:$i]: ((in @ C @ (dsetconstr @ A @ (B))) => (in @ C @ A))))). 41.01/17.88 thf(dsetconstrER_type, type, dsetconstrER: $o). 41.01/17.88 thf(dsetconstrER_def, definition, (dsetconstrER = (! [A:$i,B:($i > $o),C:$i]: ((in @ C @ (dsetconstr @ A @ (B))) => (B @ C))))). 41.01/17.88 thf(exuE1_type, type, exuE1: $o). 41.01/17.88 thf(exuE1_def, definition, (exuE1 = (! [A:($i > $o)]: ((exu @ (A)) => (? [B:$i]: ((A @ B) & ! [C:$i]: ((A @ C) => (B = C)))))))). 41.01/17.88 thf(prop2set_type, type, prop2set: ($o > $i)). 41.01/17.88 thf(prop2setE_type, type, prop2setE: $o). 41.01/17.88 thf(prop2setE_def, definition, (prop2setE = (! [A:$o,B:$i]: ((in @ B @ (prop2set @ A)) => (A))))). 41.01/17.88 thf(emptysetE_type, type, emptysetE: $o). 41.01/17.88 thf(emptysetE_def, definition, (emptysetE = (! [A:$i]: ((in @ A @ emptyset) => (! [B:$o]: (B)))))). 41.01/17.88 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o). 41.01/17.88 thf(emptysetimpfalse_def, definition, (emptysetimpfalse = (! [A:$i]: ((in @ A @ emptyset) => ($false))))). 41.01/17.88 thf(notinemptyset_type, type, notinemptyset: $o). 41.01/17.88 thf(notinemptyset_def, definition, (notinemptyset = (! [A:$i]: ~ (in @ A @ emptyset)))). 41.01/17.88 thf(exuE3e_type, type, exuE3e: $o). 41.01/17.88 thf(exuE3e_def, definition, (exuE3e = (! [A:($i > $o)]: ((exu @ (A)) => (? [B:$i]: (A @ B)))))). 41.01/17.88 thf(setext_type, type, setext: $o). 41.01/17.88 thf(setext_def, definition, (setext = (! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ A) => (in @ C @ B))) => ((! [C:$i]: ((in @ C @ B) => (in @ C @ A))) => (A = B)))))). 41.01/17.88 thf(emptyI_type, type, emptyI: $o). 41.01/17.88 thf(emptyI_def, definition, (emptyI = (! [A:$i]: ((! [B:$i]: ~ (in @ B @ A)) => (A = emptyset))))). 41.01/17.88 thf(noeltsimpempty_type, type, noeltsimpempty: $o). 41.01/17.88 thf(noeltsimpempty_def, definition, (noeltsimpempty = (! [A:$i]: ((! [B:$i]: ~ (in @ B @ A)) => (A = emptyset))))). 41.01/17.88 thf(setbeta_type, type, setbeta: $o). 41.01/17.88 thf(setbeta_def, definition, (setbeta = (! [A:$i,B:($i > $o),C:$i]: ((in @ C @ A) => ((in @ C @ (dsetconstr @ A @ (B))) = (B @ C)))))). 41.01/17.88 thf(nonemptyE1_type, type, nonemptyE1: $o). 41.01/17.88 thf(nonemptyE1_def, definition, (nonemptyE1 = (! [A:$i]: ((nonempty @ A) => (? [B:$i]: (in @ B @ A)))))). 41.01/17.88 thf(nonemptyI_type, type, nonemptyI: $o). 41.01/17.88 thf(nonemptyI_def, definition, (nonemptyI = (! [A:$i,B:($i > $o),C:$i]: ((in @ C @ A) => ((B @ C) => (nonempty @ (dsetconstr @ A @ (B)))))))). 41.01/17.88 thf(nonemptyI1_type, type, nonemptyI1: $o). 41.01/17.88 thf(nonemptyI1_def, definition, (nonemptyI1 = (! [A:$i]: ((? [B:$i]: (in @ B @ A)) => (nonempty @ A))))). 41.01/17.88 thf(setadjoinIL_type, type, setadjoinIL: $o). 41.01/17.88 thf(setadjoinIL_def, definition, (setadjoinIL = (! [A:$i,B:$i]: (in @ A @ (setadjoin @ A @ B))))). 41.01/17.88 thf(emptyinunitempty_type, type, emptyinunitempty: $o). 41.01/17.88 thf(emptyinunitempty_def, definition, (emptyinunitempty = (in @ emptyset @ (setadjoin @ emptyset @ emptyset)))). 41.01/17.88 thf(setadjoinIR_type, type, setadjoinIR: $o). 41.01/17.88 thf(setadjoinIR_def, definition, (setadjoinIR = (! [A:$i,B:$i,C:$i]: ((in @ C @ B) => (in @ C @ (setadjoin @ A @ B)))))). 41.01/17.88 thf(setadjoinE_type, type, setadjoinE: $o). 41.01/17.88 thf(setadjoinE_def, definition, (setadjoinE = (! [A:$i,B:$i,C:$i]: ((in @ C @ (setadjoin @ A @ B)) => (! [D:$o]: (((C = A) => (D)) => (((in @ C @ B) => (D)) => (D)))))))). 41.01/17.88 thf(setadjoinOr_type, type, setadjoinOr: $o). 41.01/17.88 thf(setadjoinOr_def, definition, (setadjoinOr = (! [A:$i,B:$i,C:$i]: ((in @ C @ (setadjoin @ A @ B)) => ((C = A) | (in @ C @ B)))))). 41.01/17.88 thf(setoftrueEq_type, type, setoftrueEq: $o). 41.01/17.88 thf(setoftrueEq_def, definition, (setoftrueEq = (! [A:$i]: ((dsetconstr @ A @ (^ [B:$i]: ($true))) = A)))). 41.01/17.88 thf(powersetI_type, type, powersetI: $o). 41.01/17.88 thf(powersetI_def, definition, (powersetI = (! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ B) => (in @ C @ A))) => (in @ B @ (powerset @ A)))))). 41.01/17.88 thf(emptyinPowerset_type, type, emptyinPowerset: $o). 41.01/17.88 thf(emptyinPowerset_def, definition, (emptyinPowerset = (! [A:$i]: (in @ emptyset @ (powerset @ A))))). 41.01/17.88 thf(emptyInPowerset_type, type, emptyInPowerset: $o). 41.01/17.88 thf(emptyInPowerset_def, definition, (emptyInPowerset = (! [A:$i]: (in @ emptyset @ (powerset @ A))))). 41.01/17.88 thf(powersetE_type, type, powersetE: $o). 41.01/17.88 thf(powersetE_def, definition, (powersetE = (! [A:$i,B:$i,C:$i]: ((in @ B @ (powerset @ A)) => ((in @ C @ B) => (in @ C @ A)))))). 41.01/17.88 thf(setunionI_type, type, setunionI: $o). 41.01/17.88 thf(setunionI_def, definition, (setunionI = (! [A:$i,B:$i,C:$i]: ((in @ B @ C) => ((in @ C @ A) => (in @ B @ (setunion @ A))))))). 41.01/17.88 thf(setunionE_type, type, setunionE: $o). 41.01/17.88 thf(setunionE_def, definition, (setunionE = (! [A:$i,B:$i]: ((in @ B @ (setunion @ A)) => (! [C:$o]: ((! [D:$i]: ((in @ B @ D) => ((in @ D @ A) => (C)))) => (C))))))). 41.01/17.88 thf(subPowSU_type, type, subPowSU: $o). 41.01/17.88 thf(subPowSU_def, definition, (subPowSU = (! [A:$i,B:$i]: ((in @ B @ A) => (in @ B @ (powerset @ (setunion @ A))))))). 41.01/17.88 thf(exuE2_type, type, exuE2: $o). 41.01/17.88 thf(exuE2_def, definition, (exuE2 = (! [A:($i > $o)]: ((exu @ (A)) => (? [B:$i]: ! [C:$i]: ((A @ C) = (C = B))))))). 41.01/17.88 thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o). 41.01/17.88 thf(nonemptyImpWitness_def, definition, (nonemptyImpWitness = (! [A:$i]: ((nonempty @ A) => (? [B:$i]: ((in @ B @ A) & ($true))))))). 41.01/17.88 thf(uniqinunit_type, type, uniqinunit: $o). 41.01/17.88 thf(uniqinunit_def, definition, (uniqinunit = (! [A:$i,B:$i]: ((in @ A @ (setadjoin @ B @ emptyset)) => (A = B))))). 41.01/17.88 thf(notinsingleton_type, type, notinsingleton: $o). 41.01/17.88 thf(notinsingleton_def, definition, (notinsingleton = (! [A:$i,B:$i]: ((A != B) => (~ (in @ B @ (setadjoin @ A @ emptyset))))))). 41.01/17.88 thf(eqinunit_type, type, eqinunit: $o). 41.01/17.88 thf(eqinunit_def, definition, (eqinunit = (! [A:$i,B:$i]: ((A = B) => (in @ A @ (setadjoin @ B @ emptyset)))))). 41.01/17.88 thf(singletonsswitch_type, type, singletonsswitch: $o). 41.01/17.88 thf(singletonsswitch_def, definition, (singletonsswitch = (! [A:$i,B:$i]: ((in @ A @ (setadjoin @ B @ emptyset)) => (in @ B @ (setadjoin @ A @ emptyset)))))). 41.01/17.88 thf(upairsetE_type, type, upairsetE: $o). 41.01/17.88 thf(upairsetE_def, definition, (upairsetE = (! [A:$i,B:$i,C:$i]: ((in @ C @ (setadjoin @ A @ (setadjoin @ B @ emptyset))) => ((C = A) | (C = B)))))). 41.01/17.88 thf(upairsetIL_type, type, upairsetIL: $o). 41.01/17.88 thf(upairsetIL_def, definition, (upairsetIL = (! [A:$i,B:$i]: (in @ A @ (setadjoin @ A @ (setadjoin @ B @ emptyset)))))). 41.01/17.88 thf(upairsetIR_type, type, upairsetIR: $o). 41.01/17.88 thf(upairsetIR_def, definition, (upairsetIR = (! [A:$i,B:$i]: (in @ B @ (setadjoin @ A @ (setadjoin @ B @ emptyset)))))). 41.01/17.88 thf(emptyE1_type, type, emptyE1: $o). 41.01/17.88 thf(emptyE1_def, definition, (emptyE1 = (! [A:$i,B:($i > $o)]: ((? [C:$i]: ((in @ C @ A) & (B @ C))) => (((dsetconstr @ A @ (B)) = emptyset) => ($false)))))). 41.01/17.88 thf(vacuousDall_type, type, vacuousDall: $o). 41.01/17.88 thf(vacuousDall_def, definition, (vacuousDall = (! [A:($i > $o),B:$i]: ((in @ B @ emptyset) => (A @ B))))). 41.01/17.88 thf(quantDeMorgan1_type, type, quantDeMorgan1: $o). 41.01/17.88 thf(quantDeMorgan1_def, definition, (quantDeMorgan1 = (! [A:$i,B:($i > $o)]: ((~ (! [C:$i]: ((in @ C @ A) => (B @ C)))) => (? [C:$i]: ((in @ C @ A) & ~ (B @ C))))))). 41.01/17.88 thf(quantDeMorgan2_type, type, quantDeMorgan2: $o). 41.01/17.88 thf(quantDeMorgan2_def, definition, (quantDeMorgan2 = (! [A:$i,B:($i > $o)]: ((! [C:$i]: ((in @ C @ A) => (~ (B @ C)))) => (~ (? [C:$i]: ((in @ C @ A) & (B @ C)))))))). 41.01/17.88 thf(quantDeMorgan3_type, type, quantDeMorgan3: $o). 41.01/17.88 thf(quantDeMorgan3_def, definition, (quantDeMorgan3 = (! [A:$i,B:($i > $o)]: ((~ (? [C:$i]: ((in @ C @ A) & (B @ C)))) => (! [C:$i]: ((in @ C @ A) => (~ (B @ C)))))))). 41.01/17.88 thf(quantDeMorgan4_type, type, quantDeMorgan4: $o). 41.01/17.88 thf(quantDeMorgan4_def, definition, (quantDeMorgan4 = (! [A:$i,B:($i > $o)]: ((? [C:$i]: ((in @ C @ A) & ~ (B @ C))) => (~ (! [C:$i]: ((in @ C @ A) => (B @ C)))))))). 41.01/17.88 thf(prop2setI_type, type, prop2setI: $o). 41.01/17.88 thf(prop2setI_def, definition, (prop2setI = (! [A:$o]: ((A) => (in @ emptyset @ (prop2set @ A)))))). 41.01/17.88 thf(set2prop_type, type, set2prop: ($i > $o)). 41.01/17.88 thf(prop2set2propI_type, type, prop2set2propI: $o). 41.01/17.88 thf(prop2set2propI_def, definition, (prop2set2propI = (! [A:$o]: ((A) => (set2prop @ (prop2set @ A)))))). 41.01/17.88 thf(notdexE_type, type, notdexE: $o). 41.01/17.88 thf(notdexE_def, definition, (notdexE = (! [A:$i,B:($i > $o)]: ((~ (? [C:$i]: ((in @ C @ A) & (B @ C)))) => (! [C:$i]: ((in @ C @ A) => (~ (B @ C)))))))). 41.01/17.88 thf(notdallE_type, type, notdallE: $o). 41.01/17.88 thf(notdallE_def, definition, (notdallE = (! [A:$i,B:($i > $o)]: ((~ (! [C:$i]: ((in @ C @ A) => (B @ C)))) => (? [C:$i]: ((in @ C @ A) & ~ (B @ C))))))). 41.01/17.88 thf(exuI1_type, type, exuI1: $o). 41.01/17.88 thf(exuI1_def, definition, (exuI1 = (! [A:($i > $o)]: ((? [B:$i]: ((A @ B) & ! [C:$i]: ((A @ C) => (B = C)))) => (exu @ (A)))))). 41.01/17.88 thf(exuI3_type, type, exuI3: $o). 41.01/17.88 thf(exuI3_def, definition, (exuI3 = (! [A:($i > $o)]: ((? [B:$i]: (A @ B)) => ((! [B:$i,C:$i]: ((A @ B) => ((A @ C) => (B = C)))) => (exu @ (A))))))). 41.01/17.88 thf(exuI2_type, type, exuI2: $o). 41.01/17.88 thf(exuI2_def, definition, (exuI2 = (! [A:($i > $o)]: ((? [B:$i]: ! [C:$i]: ((A @ C) = (C = B))) => (exu @ (A)))))). 41.01/17.88 thf(inCongP_type, type, inCongP: $o). 41.01/17.88 thf(inCongP_def, definition, (inCongP = (! [A:$i,B:$i]: ((A = B) => (! [C:$i,D:$i]: ((C = D) => ((in @ C @ A) => (in @ D @ B)))))))). 41.01/17.88 thf(in__Cong_type, type, in__Cong: $o). 41.01/17.88 thf(in__Cong_def, definition, (in__Cong = (! [A:$i,B:$i]: ((A = B) => (! [C:$i,D:$i]: ((C = D) => ((in @ C @ A) = (in @ D @ B)))))))). 41.01/17.88 thf(exuE3u_type, type, exuE3u: $o). 41.01/17.88 thf(exuE3u_def, definition, (exuE3u = (! [A:($i > $o)]: ((exu @ (A)) => (! [B:$i,C:$i]: ((A @ B) => ((A @ C) => (B = C)))))))). 41.01/17.88 thf(exu__Cong_type, type, exu__Cong: $o). 41.01/17.88 thf(exu__Cong_def, definition, (exu__Cong = (! [A:($i > $o),B:($i > $o)]: ((! [C:$i,D:$i]: ((C = D) => ((A @ C) = (B @ D)))) => ((exu @ (A)) = (exu @ (B))))))). 41.01/17.88 thf(emptyset__Cong_type, type, emptyset__Cong: $o). 41.01/17.88 thf(emptyset__Cong_def, definition, (emptyset__Cong = (emptyset = emptyset))). 41.01/17.88 thf(setadjoin__Cong_type, type, setadjoin__Cong: $o). 41.01/17.88 thf(setadjoin__Cong_def, definition, (setadjoin__Cong = (! [A:$i,B:$i]: ((A = B) => (! [C:$i,D:$i]: ((C = D) => ((setadjoin @ A @ C) = (setadjoin @ B @ D)))))))). 41.01/17.88 thf(powerset__Cong_type, type, powerset__Cong: $o). 41.01/17.88 thf(powerset__Cong_def, definition, (powerset__Cong = (! [A:$i,B:$i]: ((A = B) => ((powerset @ A) = (powerset @ B)))))). 41.01/17.88 thf(setunion__Cong_type, type, setunion__Cong: $o). 41.01/17.88 thf(setunion__Cong_def, definition, (setunion__Cong = (! [A:$i,B:$i]: ((A = B) => ((setunion @ A) = (setunion @ B)))))). 41.01/17.88 thf(omega__Cong_type, type, omega__Cong: $o). 41.01/17.88 thf(omega__Cong_def, definition, (omega__Cong = (omega = omega))). 41.01/17.88 thf(exuEu_type, type, exuEu: $o). 41.01/17.88 thf(exuEu_def, definition, (exuEu = (! [A:($i > $o)]: ((exu @ (A)) => (! [B:$i,C:$i]: ((A @ B) => ((A @ C) => (B = C)))))))). 41.01/17.88 thf(descr__Cong_type, type, descr__Cong: $o). 41.01/17.88 thf(descr__Cong_def, definition, (descr__Cong = (! [A:($i > $o),B:($i > $o)]: ((! [C:$i,D:$i]: ((C = D) => ((A @ C) = (B @ D)))) => ((exu @ (A)) => ((exu @ (B)) => ((descr @ (A)) = (descr @ (B))))))))). 41.01/17.88 thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o). 41.01/17.88 thf(dsetconstr__Cong_def, definition, (dsetconstr__Cong = (! [A:$i,B:$i]: ((A = B) => (! [C:($i > $o),D:($i > $o)]: ((! [E:$i]: ((in @ E @ A) => (! [F:$i]: ((in @ F @ B) => ((E = F) => ((C @ E) = (D @ F))))))) => ((dsetconstr @ A @ (C)) = (dsetconstr @ B @ (D))))))))). 41.01/17.88 thf(subset_type, type, subset: ($i > ($i > $o))). 41.01/17.88 thf(subsetI1_type, type, subsetI1: $o). 41.01/17.88 thf(subsetI1_def, definition, (subsetI1 = (! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ A) => (in @ C @ B))) => (subset @ A @ B))))). 41.01/17.88 thf(eqimpsubset2_type, type, eqimpsubset2: $o). 41.01/17.88 thf(eqimpsubset2_def, definition, (eqimpsubset2 = (! [A:$i,B:$i]: ((A = B) => (subset @ B @ A))))). 41.01/17.88 thf(eqimpsubset1_type, type, eqimpsubset1: $o). 41.01/17.88 thf(eqimpsubset1_def, definition, (eqimpsubset1 = (! [A:$i,B:$i]: ((A = B) => (subset @ A @ B))))). 41.01/17.88 thf(subsetI2_type, type, subsetI2: $o). 41.01/17.88 thf(subsetI2_def, definition, (subsetI2 = (! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ A) => (in @ C @ B))) => (subset @ A @ B))))). 41.01/17.88 thf(emptysetsubset_type, type, emptysetsubset: $o). 41.01/17.88 thf(emptysetsubset_def, definition, (emptysetsubset = (! [A:$i]: (subset @ emptyset @ A)))). 41.01/17.88 thf(subsetE_type, type, subsetE: $o). 41.01/17.88 thf(subsetE_def, definition, (subsetE = (! [A:$i,B:$i,C:$i]: ((subset @ A @ B) => ((in @ C @ A) => (in @ C @ B)))))). 41.01/17.88 thf(subsetE2_type, type, subsetE2: $o). 41.01/17.88 thf(subsetE2_def, definition, (subsetE2 = (! [A:$i,B:$i,C:$i]: ((subset @ A @ B) => ((~ (in @ C @ B)) => (~ (in @ C @ A))))))). 41.01/17.88 thf(notsubsetI_type, type, notsubsetI: $o). 41.01/17.88 thf(notsubsetI_def, definition, (notsubsetI = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => ((~ (in @ C @ B)) => (~ (subset @ A @ B))))))). 41.01/17.88 thf(notequalI1_type, type, notequalI1: $o). 41.01/17.88 thf(notequalI1_def, definition, (notequalI1 = (! [A:$i,B:$i]: ((~ (subset @ A @ B)) => (A != B))))). 41.01/17.88 thf(notequalI2_type, type, notequalI2: $o). 41.01/17.88 thf(notequalI2_def, definition, (notequalI2 = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => ((~ (in @ C @ B)) => (A != B)))))). 41.01/17.88 thf(subsetRefl_type, type, subsetRefl: $o). 41.01/17.88 thf(subsetRefl_def, definition, (subsetRefl = (! [A:$i]: (subset @ A @ A)))). 41.01/17.88 thf(subsetTrans_type, type, subsetTrans: $o). 41.01/17.88 thf(subsetTrans_def, definition, (subsetTrans = (! [A:$i,B:$i,C:$i]: ((subset @ A @ B) => ((subset @ B @ C) => (subset @ A @ C)))))). 41.01/17.88 thf(setadjoinSub_type, type, setadjoinSub: $o). 41.01/17.88 thf(setadjoinSub_def, definition, (setadjoinSub = (! [A:$i,B:$i]: (subset @ B @ (setadjoin @ A @ B))))). 41.01/17.88 thf(setadjoinSub2_type, type, setadjoinSub2: $o). 41.01/17.88 thf(setadjoinSub2_def, definition, (setadjoinSub2 = (! [A:$i,B:$i,C:$i]: ((subset @ A @ C) => (subset @ A @ (setadjoin @ B @ C)))))). 41.01/17.88 thf(subset2powerset_type, type, subset2powerset: $o). 41.01/17.88 thf(subset2powerset_def, definition, (subset2powerset = (! [A:$i,B:$i]: ((subset @ A @ B) => (in @ A @ (powerset @ B)))))). 41.01/17.88 thf(setextsub_type, type, setextsub: $o). 41.01/17.88 thf(setextsub_def, definition, (setextsub = (! [A:$i,B:$i]: ((subset @ A @ B) => ((subset @ B @ A) => (A = B)))))). 41.01/17.88 thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o). 41.01/17.88 thf(subsetemptysetimpeq_def, definition, (subsetemptysetimpeq = (! [A:$i]: ((subset @ A @ emptyset) => (A = emptyset))))). 41.01/17.88 thf(powersetI1_type, type, powersetI1: $o). 41.01/17.88 thf(powersetI1_def, definition, (powersetI1 = (! [A:$i,B:$i]: ((subset @ B @ A) => (in @ B @ (powerset @ A)))))). 41.01/17.88 thf(powersetE1_type, type, powersetE1: $o). 41.01/17.88 thf(powersetE1_def, definition, (powersetE1 = (! [A:$i,B:$i]: ((in @ B @ (powerset @ A)) => (subset @ B @ A))))). 41.01/17.88 thf(inPowerset_type, type, inPowerset: $o). 41.01/17.88 thf(inPowerset_def, definition, (inPowerset = (! [A:$i]: (in @ A @ (powerset @ A))))). 41.01/17.88 thf(powersetsubset_type, type, powersetsubset: $o). 41.01/17.88 thf(powersetsubset_def, definition, (powersetsubset = (! [A:$i,B:$i]: ((subset @ A @ B) => (subset @ (powerset @ A) @ (powerset @ B)))))). 41.01/17.88 thf(sepInPowerset_type, type, sepInPowerset: $o). 41.01/17.88 thf(sepInPowerset_def, definition, (sepInPowerset = (! [A:$i,B:($i > $o)]: (in @ (dsetconstr @ A @ (B)) @ (powerset @ A))))). 41.01/17.88 thf(sepSubset_type, type, sepSubset: $o). 41.01/17.88 thf(sepSubset_def, definition, (sepSubset = (! [A:$i,B:($i > $o)]: (subset @ (dsetconstr @ A @ (B)) @ A)))). 41.01/17.88 thf(binunion_type, type, binunion: ($i > ($i > $i))). 41.01/17.88 thf(binunionIL_type, type, binunionIL: $o). 41.01/17.88 thf(binunionIL_def, definition, (binunionIL = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (in @ C @ (binunion @ A @ B)))))). 41.01/17.88 thf(upairset2IR_type, type, upairset2IR: $o). 41.01/17.88 thf(upairset2IR_def, definition, (upairset2IR = (! [A:$i,B:$i]: (in @ B @ (setadjoin @ A @ (setadjoin @ B @ emptyset)))))). 41.01/17.88 thf(binunionIR_type, type, binunionIR: $o). 41.01/17.88 thf(binunionIR_def, definition, (binunionIR = (! [A:$i,B:$i,C:$i]: ((in @ C @ B) => (in @ C @ (binunion @ A @ B)))))). 41.01/17.88 thf(binunionEcases_type, type, binunionEcases: $o). 41.01/17.88 thf(binunionEcases_def, definition, (binunionEcases = (! [A:$i,B:$i,C:$i,D:$o]: ((in @ C @ (binunion @ A @ B)) => (((in @ C @ A) => (D)) => (((in @ C @ B) => (D)) => (D))))))). 41.01/17.88 thf(binunionE_type, type, binunionE: $o). 41.01/17.88 thf(binunionE_def, definition, (binunionE = (! [A:$i,B:$i,C:$i]: ((in @ C @ (binunion @ A @ B)) => ((in @ C @ A) | (in @ C @ B)))))). 41.01/17.88 thf(binunionLsub_type, type, binunionLsub: $o). 41.01/17.88 thf(binunionLsub_def, definition, (binunionLsub = (! [A:$i,B:$i]: (subset @ A @ (binunion @ A @ B))))). 41.01/17.88 thf(binunionRsub_type, type, binunionRsub: $o). 41.01/17.88 thf(binunionRsub_def, definition, (binunionRsub = (! [A:$i,B:$i]: (subset @ B @ (binunion @ A @ B))))). 41.01/17.88 thf(binintersect_type, type, binintersect: ($i > ($i > $i))). 41.01/17.88 thf(binintersectI_type, type, binintersectI: $o). 41.01/17.88 thf(binintersectI_def, definition, (binintersectI = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => ((in @ C @ B) => (in @ C @ (binintersect @ A @ B))))))). 41.01/17.88 thf(binintersectSubset5_type, type, binintersectSubset5: $o). 41.01/17.88 thf(binintersectSubset5_def, definition, (binintersectSubset5 = (! [A:$i,B:$i,C:$i]: ((subset @ C @ A) => ((subset @ C @ B) => (subset @ C @ (binintersect @ A @ B))))))). 41.01/17.88 thf(binintersectEL_type, type, binintersectEL: $o). 41.01/17.88 thf(binintersectEL_def, definition, (binintersectEL = (! [A:$i,B:$i,C:$i]: ((in @ C @ (binintersect @ A @ B)) => (in @ C @ A))))). 41.01/17.88 thf(binintersectLsub_type, type, binintersectLsub: $o). 41.01/17.88 thf(binintersectLsub_def, definition, (binintersectLsub = (! [A:$i,B:$i]: (subset @ (binintersect @ A @ B) @ A)))). 41.01/17.88 thf(binintersectSubset2_type, type, binintersectSubset2: $o). 41.01/17.88 thf(binintersectSubset2_def, definition, (binintersectSubset2 = (! [A:$i,B:$i]: ((subset @ A @ B) => ((binintersect @ A @ B) = A))))). 41.01/17.88 thf(binintersectSubset3_type, type, binintersectSubset3: $o). 41.01/17.88 thf(binintersectSubset3_def, definition, (binintersectSubset3 = (! [A:$i,B:$i]: (((binintersect @ A @ B) = B) => (subset @ B @ A))))). 41.01/17.88 thf(binintersectER_type, type, binintersectER: $o). 41.01/17.88 thf(binintersectER_def, definition, (binintersectER = (! [A:$i,B:$i,C:$i]: ((in @ C @ (binintersect @ A @ B)) => (in @ C @ B))))). 41.01/17.88 thf(disjointsetsI1_type, type, disjointsetsI1: $o). 41.01/17.88 thf(disjointsetsI1_def, definition, (disjointsetsI1 = (! [A:$i,B:$i]: ((~ (? [C:$i]: ((in @ C @ A) & (in @ C @ B)))) => ((binintersect @ A @ B) = emptyset))))). 41.01/17.88 thf(binintersectRsub_type, type, binintersectRsub: $o). 41.01/17.88 thf(binintersectRsub_def, definition, (binintersectRsub = (! [A:$i,B:$i]: (subset @ (binintersect @ A @ B) @ B)))). 41.01/17.88 thf(binintersectSubset4_type, type, binintersectSubset4: $o). 41.01/17.88 thf(binintersectSubset4_def, definition, (binintersectSubset4 = (! [A:$i,B:$i]: ((subset @ B @ A) => ((binintersect @ A @ B) = B))))). 41.01/17.88 thf(binintersectSubset1_type, type, binintersectSubset1: $o). 41.01/17.88 thf(binintersectSubset1_def, definition, (binintersectSubset1 = (! [A:$i,B:$i]: (((binintersect @ A @ B) = A) => (subset @ A @ B))))). 41.01/17.88 thf(bs114d_type, type, bs114d: $o). 41.01/17.88 thf(bs114d_def, definition, (bs114d = (! [A:$i,B:$i,C:$i]: ((binintersect @ A @ (binunion @ B @ C)) = (binunion @ (binintersect @ A @ B) @ (binintersect @ A @ C)))))). 41.01/17.88 thf(setminus_type, type, setminus: ($i > ($i > $i))). 41.01/17.88 thf(setminusI_type, type, setminusI: $o). 41.01/17.88 thf(setminusI_def, definition, (setminusI = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => ((~ (in @ C @ B)) => (in @ C @ (setminus @ A @ B))))))). 41.01/17.88 thf(setminusEL_type, type, setminusEL: $o). 41.01/17.88 thf(setminusEL_def, definition, (setminusEL = (! [A:$i,B:$i,C:$i]: ((in @ C @ (setminus @ A @ B)) => (in @ C @ A))))). 41.01/17.88 thf(setminusER_type, type, setminusER: $o). 41.01/17.88 thf(setminusER_def, definition, (setminusER = (! [A:$i,B:$i,C:$i]: ((in @ C @ (setminus @ A @ B)) => (~ (in @ C @ B)))))). 41.01/17.88 thf(setminusSubset2_type, type, setminusSubset2: $o). 41.01/17.88 thf(setminusSubset2_def, definition, (setminusSubset2 = (! [A:$i,B:$i]: ((subset @ A @ B) => ((setminus @ A @ B) = emptyset))))). 41.01/17.88 thf(setminusERneg_type, type, setminusERneg: $o). 41.01/17.88 thf(setminusERneg_def, definition, (setminusERneg = (! [A:$i,B:$i,C:$i]: ((~ (in @ C @ (setminus @ A @ B))) => ((in @ C @ A) => (in @ C @ B)))))). 41.01/17.88 thf(setminusELneg_type, type, setminusELneg: $o). 41.01/17.88 thf(setminusELneg_def, definition, (setminusELneg = (! [A:$i,B:$i,C:$i]: ((~ (in @ C @ (setminus @ A @ B))) => ((~ (in @ C @ B)) => (~ (in @ C @ A))))))). 41.01/17.88 thf(setminusILneg_type, type, setminusILneg: $o). 41.01/17.88 thf(setminusILneg_def, definition, (setminusILneg = (! [A:$i,B:$i,C:$i]: ((~ (in @ C @ A)) => (~ (in @ C @ (setminus @ A @ B))))))). 41.01/17.88 thf(setminusIRneg_type, type, setminusIRneg: $o). 41.01/17.88 thf(setminusIRneg_def, definition, (setminusIRneg = (! [A:$i,B:$i,C:$i]: ((in @ C @ B) => (~ (in @ C @ (setminus @ A @ B))))))). 41.01/17.88 thf(setminusLsub_type, type, setminusLsub: $o). 41.01/17.88 thf(setminusLsub_def, definition, (setminusLsub = (! [A:$i,B:$i]: (subset @ (setminus @ A @ B) @ A)))). 41.01/17.88 thf(setminusSubset1_type, type, setminusSubset1: $o). 41.01/17.88 thf(setminusSubset1_def, definition, (setminusSubset1 = (! [A:$i,B:$i]: (((setminus @ A @ B) = emptyset) => (subset @ A @ B))))). 41.01/17.88 thf(symdiff_type, type, symdiff: ($i > ($i > $i))). 41.01/17.88 thf(symdiffE_type, type, symdiffE: $o). 41.01/17.88 thf(symdiffE_def, definition, (symdiffE = (! [A:$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)))))))). 41.01/17.88 thf(symdiffI1_type, type, symdiffI1: $o). 41.01/17.88 thf(symdiffI1_def, definition, (symdiffI1 = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => ((~ (in @ C @ B)) => (in @ C @ (symdiff @ A @ B))))))). 41.01/17.88 thf(symdiffI2_type, type, symdiffI2: $o). 41.01/17.88 thf(symdiffI2_def, definition, (symdiffI2 = (! [A:$i,B:$i,C:$i]: ((~ (in @ C @ A)) => ((in @ C @ B) => (in @ C @ (symdiff @ A @ B))))))). 41.01/17.88 thf(symdiffIneg1_type, type, symdiffIneg1: $o). 41.01/17.88 thf(symdiffIneg1_def, definition, (symdiffIneg1 = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => ((in @ C @ B) => (~ (in @ C @ (symdiff @ A @ B)))))))). 41.01/17.88 thf(symdiffIneg2_type, type, symdiffIneg2: $o). 41.01/17.88 thf(symdiffIneg2_def, definition, (symdiffIneg2 = (! [A:$i,B:$i,C:$i]: ((~ (in @ C @ A)) => ((~ (in @ C @ B)) => (~ (in @ C @ (symdiff @ A @ B)))))))). 41.01/17.88 thf(secondinupair_type, type, secondinupair: $o). 41.01/17.88 thf(secondinupair_def, definition, (secondinupair = (! [A:$i,B:$i]: (in @ B @ (setadjoin @ A @ (setadjoin @ B @ emptyset)))))). 41.01/17.88 thf(setukpairIL_type, type, setukpairIL: $o). 41.01/17.88 thf(setukpairIL_def, definition, (setukpairIL = (! [A:$i,B:$i]: (in @ A @ (setunion @ (setadjoin @ (setadjoin @ A @ emptyset) @ (setadjoin @ (setadjoin @ A @ (setadjoin @ B @ emptyset)) @ emptyset))))))). 41.01/17.88 thf(setukpairIR_type, type, setukpairIR: $o). 41.01/17.88 thf(setukpairIR_def, definition, (setukpairIR = (! [A:$i,B:$i]: (in @ B @ (setunion @ (setadjoin @ (setadjoin @ A @ emptyset) @ (setadjoin @ (setadjoin @ A @ (setadjoin @ B @ emptyset)) @ emptyset))))))). 41.01/17.88 thf(kpairiskpair_type, type, kpairiskpair: $o). 41.01/17.88 thf(kpairiskpair_def, definition, (kpairiskpair = (! [A:$i,B:$i]: (iskpair @ (setadjoin @ (setadjoin @ A @ emptyset) @ (setadjoin @ (setadjoin @ A @ (setadjoin @ B @ emptyset)) @ emptyset)))))). 41.01/17.88 thf(kpairp_type, type, kpairp: $o). 41.01/17.88 thf(kpairp_def, definition, (kpairp = (! [A:$i,B:$i]: (iskpair @ (kpair @ A @ B))))). 41.01/17.88 thf(cartprod_type, type, cartprod: ($i > ($i > $i))). 41.01/17.88 thf(singletonsubset_type, type, singletonsubset: $o). 41.01/17.88 thf(singletonsubset_def, definition, (singletonsubset = (! [A:$i,B:$i]: ((in @ B @ A) => (subset @ (setadjoin @ B @ emptyset) @ A))))). 41.01/17.88 thf(singletoninpowerset_type, type, singletoninpowerset: $o). 41.01/17.88 thf(singletoninpowerset_def, definition, (singletoninpowerset = (! [A:$i,B:$i]: ((in @ B @ A) => (in @ (setadjoin @ B @ emptyset) @ (powerset @ A)))))). 41.01/17.88 thf(singletoninpowunion_type, type, singletoninpowunion: $o). 41.01/17.88 thf(singletoninpowunion_def, definition, (singletoninpowunion = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (in @ (setadjoin @ C @ emptyset) @ (powerset @ (binunion @ A @ B))))))). 41.01/17.88 thf(upairset2E_type, type, upairset2E: $o). 41.01/17.88 thf(upairset2E_def, definition, (upairset2E = (! [A:$i,B:$i,C:$i]: ((in @ C @ (setadjoin @ A @ (setadjoin @ B @ emptyset))) => ((C = A) | (C = B)))))). 41.01/17.88 thf(upairsubunion_type, type, upairsubunion: $o). 41.01/17.88 thf(upairsubunion_def, definition, (upairsubunion = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ B) => (subset @ (setadjoin @ C @ (setadjoin @ D @ emptyset)) @ (binunion @ A @ B)))))))). 41.01/17.88 thf(upairinpowunion_type, type, upairinpowunion: $o). 41.01/17.88 thf(upairinpowunion_def, definition, (upairinpowunion = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ B) => (in @ (setadjoin @ C @ (setadjoin @ D @ emptyset)) @ (powerset @ (binunion @ A @ B))))))))). 41.01/17.88 thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o). 41.01/17.88 thf(ubforcartprodlem1_def, definition, (ubforcartprodlem1 = (! [A:$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))))))))). 41.01/17.88 thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o). 41.01/17.88 thf(ubforcartprodlem2_def, definition, (ubforcartprodlem2 = (! [A:$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)))))))))). 41.01/17.88 thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o). 41.01/17.88 thf(ubforcartprodlem3_def, definition, (ubforcartprodlem3 = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ B) => (in @ (kpair @ C @ D) @ (powerset @ (powerset @ (binunion @ A @ B)))))))))). 41.01/17.88 thf(cartprodpairin_type, type, cartprodpairin: $o). 41.01/17.88 thf(cartprodpairin_def, definition, (cartprodpairin = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ B) => (in @ (kpair @ C @ D) @ (cartprod @ A @ B)))))))). 41.01/17.88 thf(cartprodmempair1_type, type, cartprodmempair1: $o). 41.01/17.88 thf(cartprodmempair1_def, definition, (cartprodmempair1 = (! [A:$i,B:$i,C:$i]: ((in @ C @ (cartprod @ A @ B)) => (? [D:$i]: ((in @ D @ A) & ? [E:$i]: ((in @ E @ B) & (C = (kpair @ D @ E))))))))). 41.01/17.88 thf(cartprodmempair_type, type, cartprodmempair: $o). 41.01/17.88 thf(cartprodmempair_def, definition, (cartprodmempair = (! [A:$i,B:$i,C:$i]: ((in @ C @ (cartprod @ A @ B)) => (iskpair @ C))))). 41.01/17.88 thf(setunionE2_type, type, setunionE2: $o). 41.01/17.88 thf(setunionE2_def, definition, (setunionE2 = (! [A:$i,B:$i]: ((in @ B @ (setunion @ A)) => (? [C:$i]: ((in @ C @ A) & (in @ B @ C))))))). 41.01/17.88 thf(setunionsingleton1_type, type, setunionsingleton1: $o). 41.01/17.88 thf(setunionsingleton1_def, definition, (setunionsingleton1 = (! [A:$i]: (subset @ (setunion @ (setadjoin @ A @ emptyset)) @ A)))). 41.01/17.88 thf(setunionsingleton2_type, type, setunionsingleton2: $o). 41.01/17.88 thf(setunionsingleton2_def, definition, (setunionsingleton2 = (! [A:$i]: (subset @ A @ (setunion @ (setadjoin @ A @ emptyset)))))). 41.01/17.88 thf(setunionsingleton_type, type, setunionsingleton: $o). 41.01/17.88 thf(setunionsingleton_def, definition, (setunionsingleton = (! [A:$i]: ((setunion @ (setadjoin @ A @ emptyset)) = A)))). 41.01/17.88 thf(singletonprop_type, type, singletonprop: $o). 41.01/17.88 thf(singletonprop_def, definition, (singletonprop = (! [A:$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)))))))). 41.01/17.88 thf(ex1E1_type, type, ex1E1: $o). 41.01/17.88 thf(ex1E1_def, definition, (ex1E1 = (! [A:$i,B:($i > $o)]: ((ex1 @ A @ (B)) => (? [C:$i]: ((in @ C @ A) & (B @ C))))))). 41.01/17.88 thf(ex1I_type, type, ex1I: $o). 41.01/17.88 thf(ex1I_def, definition, (ex1I = (! [A:$i,B:($i > $o),C:$i]: ((in @ C @ A) => ((B @ C) => ((! [D:$i]: ((in @ D @ A) => ((B @ D) => (D = C)))) => (ex1 @ A @ (B)))))))). 41.01/17.88 thf(ex1I2_type, type, ex1I2: $o). 41.01/17.88 thf(ex1I2_def, definition, (ex1I2 = (! [A:$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))))))). 41.01/17.88 thf(singletonsuniq_type, type, singletonsuniq: $o). 41.01/17.88 thf(singletonsuniq_def, definition, (singletonsuniq = (! [A:$i,B:$i]: (((setadjoin @ A @ emptyset) = (setadjoin @ B @ emptyset)) => (A = B))))). 41.01/17.88 thf(setukpairinjL1_type, type, setukpairinjL1: $o). 41.01/17.88 thf(setukpairinjL1_def, definition, (setukpairinjL1 = (! [A:$i,B:$i,C:$i]: ((in @ (setadjoin @ C @ emptyset) @ (setadjoin @ (setadjoin @ A @ emptyset) @ (setadjoin @ (setadjoin @ A @ (setadjoin @ B @ emptyset)) @ emptyset))) => (A = C))))). 41.01/17.88 thf(kfstsingleton_type, type, kfstsingleton: $o). 41.01/17.88 thf(kfstsingleton_def, definition, (kfstsingleton = (! [A:$i]: ((iskpair @ A) => (singleton @ (dsetconstr @ (setunion @ A) @ (^ [B:$i]: (in @ (setadjoin @ B @ emptyset) @ A)))))))). 41.01/17.88 thf(theprop_type, type, theprop: $o). 41.01/17.88 thf(theprop_def, definition, (theprop = (! [A:$i]: ((singleton @ A) => (in @ (setunion @ A) @ A))))). 41.01/17.88 thf(kfst_type, type, kfst: ($i > $i)). 41.01/17.88 thf(kfstpairEq_type, type, kfstpairEq: $o). 41.01/17.88 thf(kfstpairEq_def, definition, (kfstpairEq = (! [A:$i,B:$i]: ((kfst @ (kpair @ A @ B)) = A)))). 41.01/17.88 thf(1,conjecture,(((setextAx) => ((emptysetAx) => ((setadjoinAx) => ((powersetAx) => (((omega0Ax) => ((((((wellorderingAx) => (((dsetconstrI) => ((dsetconstrEL) => ((dsetconstrER) => ((exuE1) => ((prop2setE) => (((emptysetimpfalse) => ((notinemptyset) => (((setext) => (((noeltsimpempty) => ((setbeta) => ((((nonemptyI1) => ((setadjoinIL) => (((setadjoinIR) => ((setadjoinE) => (((setoftrueEq) => (((((powersetE) => (((setunionE) => ((((nonemptyImpWitness) => (((notinsingleton) => (((singletonsswitch) => ((upairsetE) => ((((((quantDeMorgan1) => ((quantDeMorgan2) => (((quantDeMorgan4) => ((prop2setI) => ((prop2set2propI) => (((notdallE) => (((exuI3) => (((inCongP) => ((((exu__Cong) => ((((powerset__Cong) => (((((((subsetI1) => ((eqimpsubset2) => ((((emptysetsubset) => (((subsetE2) => ((notsubsetI) => (((notequalI2) => ((subsetRefl) => (((setadjoinSub) => ((((setextsub) => (((powersetI1) => ((powersetE1) => ((inPowerset) => ((powersetsubset) => ((sepInPowerset) => ((sepSubset) => ((((binunionIR) => ((binunionEcases) => ((binunionE) => ((((binintersectI) => (((((binintersectSubset2) => ((binintersectSubset3) => ((binintersectER) => ((disjointsetsI1) => (((binintersectSubset4) => (((((setminusEL) => ((((setminusERneg) => (((setminusILneg) => ((setminusIRneg) => ((setminusLsub) => (((symdiffE) => (((((((setukpairIL) => ((setukpairIR) => (((kpairp) => ((singletonsubset) => ((((upairset2E) => (((((ubforcartprodlem2) => ((((cartprodmempair1) => ((cartprodmempair) => ((setunionE2) => ((setunionsingleton1) => ((((((ex1I) => ((ex1I2) => ((singletonsuniq) => (((kfstsingleton) => (((kfstpairEq) => (! [A:$i,B:$i,C:$i]: ((in @ C @ (cartprod @ A @ B)) => (in @ (kfst @ C) @ A)))) <= (theprop))) <= (setukpairinjL1))))) <= (ex1E1)) <= (singletonprop)) <= (setunionsingleton)) <= (setunionsingleton2)))))) <= (cartprodpairin)) <= (ubforcartprodlem3))) <= (ubforcartprodlem1)) <= (upairinpowunion)) <= (upairsubunion))) <= (singletoninpowunion)) <= (singletoninpowerset)))) <= (kpairiskpair)))) <= (secondinupair)) <= (symdiffIneg2)) <= (symdiffIneg1)) <= (symdiffI2)) <= (symdiffI1))) <= (setminusSubset1))))) <= (setminusELneg))) <= (setminusSubset2)) <= (setminusER))) <= (setminusI)) <= (bs114d)) <= (binintersectSubset1))) <= (binintersectRsub)))))) <= (binintersectLsub)) <= (binintersectEL)) <= (binintersectSubset5))) <= (binunionRsub)) <= (binunionLsub))))) <= (upairset2IR)) <= (binunionIL)))))))) <= (subsetemptysetimpeq))) <= (subset2powerset)) <= (setadjoinSub2))) <= (subsetTrans)))) <= (notequalI1)))) <= (subsetE))) <= (subsetI2)) <= (eqimpsubset1)))) <= (dsetconstr__Cong)) <= (descr__Cong)) <= (exuEu)) <= (omega__Cong)) <= (setunion__Cong))) <= (setadjoin__Cong)) <= (emptyset__Cong))) <= (exuE3u)) <= (in__Cong))) <= (exuI2))) <= (exuI1))) <= (notdexE))))) <= (quantDeMorgan3)))) <= (vacuousDall)) <= (emptyE1)) <= (upairsetIR)) <= (upairsetIL)))) <= (eqinunit))) <= (uniqinunit))) <= (exuE2)) <= (subPowSU))) <= (setunionI))) <= (emptyInPowerset)) <= (emptyinPowerset)) <= (powersetI))) <= (setadjoinOr)))) <= (emptyinunitempty)))) <= (nonemptyI)) <= (nonemptyE1)))) <= (emptyI))) <= (exuE3e)))) <= (emptysetE))))))) <= (descrp))) <= (foundationAx)) <= (replAx)) <= (omegaIndAx)) <= (omegaSAx))) <= (setunionAx))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodfstin)). 41.01/17.88 thf(2,negated_conjecture,((~ ((setextAx) => ((emptysetAx) => ((setadjoinAx) => ((powersetAx) => (((omega0Ax) => ((((((wellorderingAx) => (((dsetconstrI) => ((dsetconstrEL) => ((dsetconstrER) => ((exuE1) => ((prop2setE) => (((emptysetimpfalse) => ((notinemptyset) => (((setext) => (((noeltsimpempty) => ((setbeta) => ((((nonemptyI1) => ((setadjoinIL) => (((setadjoinIR) => ((setadjoinE) => (((setoftrueEq) => (((((powersetE) => (((setunionE) => ((((nonemptyImpWitness) => (((notinsingleton) => (((singletonsswitch) => ((upairsetE) => ((((((quantDeMorgan1) => ((quantDeMorgan2) => (((quantDeMorgan4) => ((prop2setI) => ((prop2set2propI) => (((notdallE) => (((exuI3) => (((inCongP) => ((((exu__Cong) => ((((powerset__Cong) => (((((((subsetI1) => ((eqimpsubset2) => ((((emptysetsubset) => (((subsetE2) => ((notsubsetI) => (((notequalI2) => ((subsetRefl) => (((setadjoinSub) => ((((setextsub) => (((powersetI1) => ((powersetE1) => ((inPowerset) => ((powersetsubset) => ((sepInPowerset) => ((sepSubset) => ((((binunionIR) => ((binunionEcases) => ((binunionE) => ((((binintersectI) => (((((binintersectSubset2) => ((binintersectSubset3) => ((binintersectER) => ((disjointsetsI1) => (((binintersectSubset4) => (((((setminusEL) => ((((setminusERneg) => (((setminusILneg) => ((setminusIRneg) => ((setminusLsub) => (((symdiffE) => (((((((setukpairIL) => ((setukpairIR) => (((kpairp) => ((singletonsubset) => ((((upairset2E) => (((((ubforcartprodlem2) => ((((cartprodmempair1) => ((cartprodmempair) => ((setunionE2) => ((setunionsingleton1) => ((((((ex1I) => ((ex1I2) => ((singletonsuniq) => (((kfstsingleton) => (((kfstpairEq) => (! [A:$i,B:$i,C:$i]: ((in @ C @ (cartprod @ A @ B)) => (in @ (kfst @ C) @ A)))) <= (theprop))) <= (setukpairinjL1))))) <= (ex1E1)) <= (singletonprop)) <= (setunionsingleton)) <= (setunionsingleton2)))))) <= (cartprodpairin)) <= (ubforcartprodlem3))) <= (ubforcartprodlem1)) <= (upairinpowunion)) <= (upairsubunion))) <= (singletoninpowunion)) <= (singletoninpowerset)))) <= (kpairiskpair)))) <= (secondinupair)) <= (symdiffIneg2)) <= (symdiffIneg1)) <= (symdiffI2)) <= (symdiffI1))) <= (setminusSubset1))))) <= (setminusELneg))) <= (setminusSubset2)) <= (setminusER))) <= (setminusI)) <= (bs114d)) <= (binintersectSubset1))) <= (binintersectRsub)))))) <= (binintersectLsub)) <= (binintersectEL)) <= (binintersectSubset5))) <= (binunionRsub)) <= (binunionLsub))))) <= (upairset2IR)) <= (binunionIL)))))))) <= (subsetemptysetimpeq))) <= (subset2powerset)) <= (setadjoinSub2))) <= (subsetTrans)))) <= (notequalI1)))) <= (subsetE))) <= (subsetI2)) <= (eqimpsubset1)))) <= (dsetconstr__Cong)) <= (descr__Cong)) <= (exuEu)) <= (omega__Cong)) <= (setunion__Cong))) <= (setadjoin__Cong)) <= (emptyset__Cong))) <= (exuE3u)) <= (in__Cong))) <= (exuI2))) <= (exuI1))) <= (notdexE))))) <= (quantDeMorgan3)))) <= (vacuousDall)) <= (emptyE1)) <= (upairsetIR)) <= (upairsetIL)))) <= (eqinunit))) <= (uniqinunit))) <= (exuE2)) <= (subPowSU))) <= (setunionI))) <= (emptyInPowerset)) <= (emptyinPowerset)) <= (powersetI))) <= (setadjoinOr)))) <= (emptyinunitempty)))) <= (nonemptyI)) <= (nonemptyE1)))) <= (emptyI))) <= (exuE3e)))) <= (emptysetE))))))) <= (descrp))) <= (foundationAx)) <= (replAx)) <= (omegaIndAx)) <= (omegaSAx))) <= (setunionAx)))))))),inference(neg_conjecture,[status(cth)],[1])). 41.01/17.88 thf(3,plain,((~ ((! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ A) = (in @ C @ B))) => (A = B))) => ((! [A:$i]: ~ (in @ A @ emptyset)) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ (setadjoin @ A @ B)) = ((C = A) | (in @ C @ B)))) => ((! [A:$i,B:$i]: ((in @ B @ (powerset @ A)) = (! [C:$i]: ((in @ C @ B) => (in @ C @ A))))) => (((in @ emptyset @ omega) => (((! [A:$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 > $o),C:$i]: ((in @ C @ A) => ((B @ C) => (in @ C @ (dsetconstr @ A @ (B)))))) => ((! [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:$o,B:$i]: ((in @ B @ (prop2set @ A)) => (A))) => (((! [A:$i]: ~ (in @ A @ emptyset)) => ((! [A:$i]: ~ (in @ A @ emptyset)) => (((! [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]: (in @ B @ A)) => (~ (A = emptyset)))) => ((! [A:$i,B:$i]: (in @ A @ (setadjoin @ A @ B))) => (((! [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)) => (! [D:$o]: (((C = A) => (D)) => (((in @ C @ B) => (D)) => (D)))))) => (((! [A:$i]: ((dsetconstr @ A @ (^ [B:$i]: ($true))) = A)) => (((! [A:$i,B:$i,C:$i]: ((in @ B @ (powerset @ A)) => ((in @ C @ B) => (in @ C @ A)))) => (((! [A:$i,B:$i]: ((in @ B @ (setunion @ A)) => (! [C:$o]: ((! [D:$i]: ((in @ B @ D) => ((in @ D @ A) => (C)))) => (C))))) => (((! [A:$i]: ((~ (A = emptyset)) => (? [B:$i]: (in @ B @ A)))) => (((! [A:$i,B:$i]: ((~ (A = B)) => (~ (in @ B @ (setadjoin @ A @ emptyset))))) => (((! [A:$i,B:$i]: ((in @ A @ (setadjoin @ B @ emptyset)) => (in @ B @ (setadjoin @ A @ emptyset)))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ (setadjoin @ A @ (setadjoin @ B @ emptyset))) => ((C = A) | (C = 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:$i]: ((in @ C @ A) => (B @ C)))))) => ((! [A:$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 > $o)]: ((? [B:$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 > $o),B:($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:$i]: ((A = B) => ((powerset @ A) = (powerset @ B)))) => (((! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ A) => (in @ C @ B))) => (subset @ A @ B))) => ((! [A:$i,B:$i]: ((A = B) => (subset @ B @ A))) => (((! [A:$i]: (subset @ emptyset @ A)) => (((! [A:$i,B:$i,C:$i]: ((subset @ A @ B) => ((~ (in @ C @ B)) => (~ (in @ C @ A))))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ A) => ((~ (in @ C @ B)) => (~ (subset @ A @ B))))) => (((! [A:$i,B:$i,C:$i]: ((in @ C @ A) => ((~ (in @ C @ B)) => (~ (A = B))))) => ((! [A:$i]: (subset @ A @ A)) => (((! [A:$i,B:$i]: (subset @ B @ (setadjoin @ A @ B))) => (((! [A:$i,B:$i]: ((subset @ A @ B) => ((subset @ B @ A) => (A = B)))) => (((! [A:$i,B:$i]: ((subset @ B @ A) => (in @ B @ (powerset @ A)))) => ((! [A:$i,B:$i]: ((in @ B @ (powerset @ A)) => (subset @ B @ A))) => ((! [A:$i]: (in @ A @ (powerset @ A))) => ((! [A:$i,B:$i]: ((subset @ A @ B) => (subset @ (powerset @ A) @ (powerset @ B)))) => ((! [A:$i,B:($i > $o)]: (in @ (dsetconstr @ A @ (B)) @ (powerset @ A))) => ((! [A:$i,B:($i > $o)]: (subset @ (dsetconstr @ A @ (B)) @ A)) => (((! [A:$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:$i,C:$i]: ((in @ C @ A) => ((in @ C @ B) => (in @ C @ (binintersect @ A @ B))))) => (((! [A:$i,B:$i]: ((subset @ A @ B) => ((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:$i]: ((~ (? [C:$i]: ((in @ C @ A) & (in @ C @ B)))) => ((binintersect @ A @ B) = emptyset))) => (((! [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 @ A) => (in @ C @ B)))) => (((! [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:$i]: ((in @ C @ (symdiff @ A @ B)) => (! [D:$o]: (((in @ C @ A) => ((~ (in @ C @ B)) => (D))) => (((~ (in @ C @ A)) => ((in @ C @ B) => (D))) => (D)))))) => (((! [A:$i,B:$i]: (in @ A @ (setunion @ (setadjoin @ (setadjoin @ A @ emptyset) @ (setadjoin @ (setadjoin @ A @ (setadjoin @ B @ emptyset)) @ emptyset))))) => ((! [A:$i,B:$i]: (in @ B @ (setunion @ (setadjoin @ (setadjoin @ A @ emptyset) @ (setadjoin @ (setadjoin @ A @ (setadjoin @ B @ emptyset)) @ emptyset))))) => (((! [A:$i,B:$i]: ? [C:$i]: ((in @ C @ (setunion @ (setadjoin @ (setadjoin @ A @ emptyset) @ (setadjoin @ (setadjoin @ A @ (setadjoin @ B @ emptyset)) @ emptyset)))) & ? [D:$i]: ((in @ D @ (setunion @ (setadjoin @ (setadjoin @ A @ emptyset) @ (setadjoin @ (setadjoin @ A @ (setadjoin @ B @ emptyset)) @ emptyset)))) & ((setadjoin @ (setadjoin @ A @ emptyset) @ (setadjoin @ (setadjoin @ A @ (setadjoin @ B @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ C @ emptyset) @ (setadjoin @ (setadjoin @ C @ (setadjoin @ D @ emptyset)) @ emptyset)))))) => ((! [A:$i,B:$i]: ((in @ B @ A) => (subset @ (setadjoin @ B @ emptyset) @ A))) => (((! [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:$i]: ((in @ D @ B) => (in @ (setadjoin @ (setadjoin @ C @ emptyset) @ (setadjoin @ (setadjoin @ C @ (setadjoin @ D @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ A @ B)))))))) => (((! [A:$i,B:$i,C:$i]: ((in @ C @ (cartprod @ A @ B)) => (? [D:$i]: ((in @ D @ A) & ? [E:$i]: ((in @ E @ B) & (C = (setadjoin @ (setadjoin @ D @ emptyset) @ (setadjoin @ (setadjoin @ D @ (setadjoin @ E @ emptyset)) @ emptyset)))))))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ (cartprod @ A @ B)) => (? [D:$i]: ((in @ D @ (setunion @ C)) & ? [E:$i]: ((in @ E @ (setunion @ C)) & (C = (setadjoin @ (setadjoin @ D @ emptyset) @ (setadjoin @ (setadjoin @ D @ (setadjoin @ E @ emptyset)) @ emptyset)))))))) => ((! [A:$i,B:$i]: ((in @ B @ (setunion @ A)) => (? [C:$i]: ((in @ C @ A) & (in @ B @ C))))) => ((! [A:$i]: (subset @ (setunion @ (setadjoin @ A @ emptyset)) @ A)) => (((! [A:$i,B:($i > $o),C:$i]: ((in @ C @ A) => ((B @ C) => ((! [D:$i]: ((in @ D @ A) => ((B @ D) => (D = C)))) => (? [D:$i]: ((in @ D @ (dsetconstr @ A @ (B))) & ((dsetconstr @ A @ (B)) = (setadjoin @ D @ emptyset)))))))) => ((! [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))) => (? [C:$i]: ((in @ C @ (dsetconstr @ A @ (B))) & ((dsetconstr @ A @ (B)) = (setadjoin @ C @ emptyset))))))) => ((! [A:$i,B:$i]: (((setadjoin @ A @ emptyset) = (setadjoin @ B @ emptyset)) => (A = B))) => (((! [A:$i]: ((? [B:$i]: ((in @ B @ (setunion @ A)) & ? [C:$i]: ((in @ C @ (setunion @ A)) & (A = (setadjoin @ (setadjoin @ B @ emptyset) @ (setadjoin @ (setadjoin @ B @ (setadjoin @ C @ emptyset)) @ emptyset)))))) => (? [B:$i]: ((in @ B @ (dsetconstr @ (setunion @ A) @ (^ [C:$i]: (in @ (setadjoin @ C @ emptyset) @ A)))) & ((dsetconstr @ (setunion @ A) @ (^ [C:$i]: (in @ (setadjoin @ C @ emptyset) @ A))) = (setadjoin @ B @ emptyset)))))) => (((! [A:$i,B:$i]: ((kfst @ (setadjoin @ (setadjoin @ A @ emptyset) @ (setadjoin @ (setadjoin @ A @ (setadjoin @ B @ emptyset)) @ emptyset))) = A)) => (! [A:$i,B:$i,C:$i]: ((in @ C @ (cartprod @ A @ B)) => (in @ (kfst @ C) @ A)))) | ~ (! [A:$i]: ((? [B:$i]: ((in @ B @ A) & (A = (setadjoin @ B @ emptyset)))) => (in @ (setunion @ A) @ A))))) | ~ (! [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,B:($i > $o)]: ((? [C:$i]: ((in @ C @ (dsetconstr @ A @ (B))) & ((dsetconstr @ A @ (B)) = (setadjoin @ C @ emptyset)))) => (? [C:$i]: ((in @ C @ A) & (B @ C))))) | ~ (! [A:$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))) => (? [C:$i]: ((in @ C @ (dsetconstr @ A @ (B))) & ((dsetconstr @ A @ (B)) = (setadjoin @ C @ emptyset))))))) | ~ (! [A:$i]: ((setunion @ (setadjoin @ A @ emptyset)) = A)) | ~ (! [A:$i]: (subset @ A @ (setunion @ (setadjoin @ A @ emptyset))))))))) | ~ (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ B) => (in @ (setadjoin @ (setadjoin @ C @ emptyset) @ (setadjoin @ (setadjoin @ C @ (setadjoin @ D @ emptyset)) @ emptyset)) @ (cartprod @ A @ B)))))) | ~ (! [A:$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:$i]: ((in @ D @ B) => (subset @ (setadjoin @ (setadjoin @ C @ emptyset) @ (setadjoin @ (setadjoin @ C @ (setadjoin @ D @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ A @ B))))))) | ~ (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (! [D:$i]: ((in @ D @ B) => (in @ (setadjoin @ C @ (setadjoin @ D @ emptyset)) @ (powerset @ (binunion @ A @ B))))))) | ~ (! [A:$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) => (in @ (setadjoin @ C @ emptyset) @ (powerset @ (binunion @ A @ B))))) | ~ (! [A:$i,B:$i]: ((in @ B @ A) => (in @ (setadjoin @ B @ emptyset) @ (powerset @ A))))))) | ~ (! [A:$i,B:$i]: ? [C:$i]: ((in @ C @ (setunion @ (setadjoin @ (setadjoin @ A @ emptyset) @ (setadjoin @ (setadjoin @ A @ (setadjoin @ B @ emptyset)) @ emptyset)))) & ? [D:$i]: ((in @ D @ (setunion @ (setadjoin @ (setadjoin @ A @ emptyset) @ (setadjoin @ (setadjoin @ A @ (setadjoin @ B @ emptyset)) @ emptyset)))) & ((setadjoin @ (setadjoin @ A @ emptyset) @ (setadjoin @ (setadjoin @ A @ (setadjoin @ B @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ C @ emptyset) @ (setadjoin @ (setadjoin @ C @ (setadjoin @ D @ emptyset)) @ emptyset))))))))) | ~ (! [A:$i,B:$i]: (in @ B @ (setadjoin @ A @ (setadjoin @ B @ emptyset)))) | ~ (! [A:$i,B:$i,C:$i]: ((~ (in @ C @ A)) => ((~ (in @ C @ B)) => (~ (in @ C @ (symdiff @ A @ B)))))) | ~ (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => ((in @ C @ B) => (~ (in @ C @ (symdiff @ A @ B)))))) | ~ (! [A:$i,B:$i,C:$i]: ((~ (in @ C @ A)) => ((in @ C @ B) => (in @ C @ (symdiff @ A @ B))))) | ~ (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => ((~ (in @ C @ B)) => (in @ C @ (symdiff @ A @ B))))))) | ~ (! [A:$i,B:$i]: (((setminus @ A @ B) = emptyset) => (subset @ A @ B))))))) | ~ (! [A:$i,B:$i,C:$i]: ((~ (in @ C @ (setminus @ A @ B))) => ((~ (in @ C @ B)) => (~ (in @ C @ A))))))) | ~ (! [A:$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]: (((binintersect @ A @ B) = A) => (subset @ A @ B))))) | ~ (! [A:$i,B:$i]: (subset @ (binintersect @ A @ B) @ B))))))) | ~ (! [A:$i,B:$i]: (subset @ (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]: (subset @ B @ (binunion @ A @ B))) | ~ (! [A:$i,B:$i]: (subset @ A @ (binunion @ A @ B))))))) | ~ (! [A:$i,B:$i]: (in @ B @ (setadjoin @ A @ (setadjoin @ B @ emptyset)))) | ~ (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (in @ C @ (binunion @ A @ B))))))))))) | ~ (! [A:$i]: ((subset @ A @ emptyset) => (A = emptyset))))) | ~ (! [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:$i,C:$i]: ((subset @ A @ B) => ((subset @ B @ C) => (subset @ A @ C))))))) | ~ (! [A:$i,B:$i]: ((~ (subset @ A @ B)) => (~ (A = B))))))) | ~ (! [A:$i,B:$i,C:$i]: ((subset @ A @ B) => ((in @ C @ A) => (in @ C @ B)))))) | ~ (! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ A) => (in @ C @ B))) => (subset @ A @ B))) | ~ (! [A:$i,B:$i]: ((A = 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 > $o)]: ((? [B:$i]: ((A @ B) & ! [C:$i]: ((A @ C) => (B = C)))) => (! [B:$i,C:$i]: ((A @ B) => ((A @ C) => (B = C)))))) | ~ (! [A:$i,B:$i]: ((A = B) => ((setunion @ A) = (setunion @ B)))))) | ~ (! [A:$i,B:$i]: ((A = B) => (! [C:$i,D:$i]: ((C = D) => ((setadjoin @ A @ C) = (setadjoin @ B @ D)))))))) | ~ (! [A:($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,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]: ((in @ B @ emptyset) => (A @ B))) | ~ (! [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]: ((A = B) => (in @ A @ (setadjoin @ B @ emptyset)))))) | ~ (! [A:$i,B:$i]: ((in @ A @ (setadjoin @ B @ emptyset)) => (A = B))))) | ~ (! [A:($i > $o)]: ((? [B:$i]: ((A @ B) & ! [C:$i]: ((A @ C) => (B = C)))) => (? [B:$i]: ! [C:$i]: ((A @ C) = (C = B))))) | ~ (! [A:$i,B:$i]: ((in @ B @ A) => (in @ B @ (powerset @ (setunion @ A))))))) | ~ (! [A:$i,B:$i,C:$i]: ((in @ B @ C) => ((in @ C @ A) => (in @ B @ (setunion @ A))))))) | ~ (! [A:$i]: (in @ emptyset @ (powerset @ A))) | ~ (! [A:$i]: (in @ emptyset @ (powerset @ A))) | ~ (! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ B) => (in @ C @ A))) => (in @ B @ (powerset @ A)))))) | ~ (! [A:$i,B:$i,C:$i]: ((in @ C @ (setadjoin @ A @ B)) => ((C = A) | (in @ C @ B))))))) | ~ (in @ emptyset @ (setadjoin @ emptyset @ 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 > $o)]: ((? [B:$i]: ((A @ B) & ! [C:$i]: ((A @ C) => (B = C)))) => (? [B:$i]: (A @ B))))))) | ~ (! [A:$i]: ((in @ A @ emptyset) => (! [B:$o]: (B))))))))) | ~ (! [A:($i > $o)]: ((? [B:$i]: ((A @ B) & ! [C:$i]: ((A @ C) => (B = C)))) => (A @ (descr @ (A))))))) | ~ (! [A:$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:$i]: ((in @ B @ omega) => (in @ B @ A))))) | ~ (! [A:$i]: ((in @ A @ omega) => (in @ (setadjoin @ A @ A) @ omega))))) | ~ (! [A:$i,B:$i]: ((in @ B @ (setunion @ A)) = (? [C:$i]: ((in @ B @ C) & (in @ C @ A)))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])). 41.01/17.88 thf(731,plain,($false),inference(cvc4,[status(thm)],[3])). 41.01/17.88 % SZS output end CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 41.01/17.88 % [INFO] Killing All external provers ... 41.01/17.88 FINAL WATCH: 40.7 CPU 15.5 WC 41.01/17.88 Killed 1 orphans 41.01/17.88 Killed 1 orphans 41.01/17.88 EOF