0.00/0.01 % Leo-III: Strategy 1 (for '60') 5.31/6.63 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 5.31/6.63 % [INFO] Parsing done (223ms). 5.31/6.63 % [INFO] Running in sequential loop mode. 5.31/6.63 % [CONFIG] Using configuration: timeout(60) with strategy 5.31/6.63 % [INFO] eprover registered as external prover. 5.31/6.63 % [INFO] cvc4 registered as external prover. 5.31/6.63 % [INFO] Parsing finished. Scanning for conjecture ... 5.31/6.63 % [INFO] Found a conjecture and 0 axioms. Running axiom selection ... 5.31/6.63 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms). 5.31/6.63 % [INFO] Problem is higher-order (TPTP THF). 5.31/6.63 % [INFO] Type checking passed. Searching for refutation ... 5.31/6.63 % External prover 'e' found a proof! 5.31/6.63 % [INFO] Killing All external provers ... 5.31/6.63 % Time passed: 2304ms (effective reasoning time: 1576ms) 5.31/6.63 % Solved by strategy 5.31/6.63 % Axioms used in derivation (0): 5.31/6.63 % No. of inferences in proof: 4 5.31/6.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2304 ms resp. 1576 ms w/o parsing 5.31/6.63 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 5.31/6.63 thf(in_type, type, in: ($i > ($i > $o))). 5.31/6.63 thf(setextAx_type, type, setextAx: $o). 5.31/6.63 thf(setextAx_def, definition, (setextAx = (! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ A) = (in @ C @ B))) => (A = B))))). 5.31/6.63 thf(emptyset_type, type, emptyset: $i). 5.31/6.63 thf(emptysetAx_type, type, emptysetAx: $o). 5.31/6.63 thf(emptysetAx_def, definition, (emptysetAx = (! [A:$i]: ~ (in @ A @ emptyset)))). 5.31/6.63 thf(setadjoin_type, type, setadjoin: ($i > ($i > $i))). 5.31/6.63 thf(setadjoinAx_type, type, setadjoinAx: $o). 5.31/6.63 thf(setadjoinAx_def, definition, (setadjoinAx = (! [A:$i,B:$i,C:$i]: ((in @ C @ (setadjoin @ A @ B)) = ((C = A) | (in @ C @ B)))))). 5.31/6.63 thf(powerset_type, type, powerset: ($i > $i)). 5.31/6.63 thf(powersetAx_type, type, powersetAx: $o). 5.31/6.63 thf(powersetAx_def, definition, (powersetAx = (! [A:$i,B:$i]: ((in @ B @ (powerset @ A)) = (! [C:$i]: ((in @ C @ B) => (in @ C @ A))))))). 5.31/6.63 thf(setunion_type, type, setunion: ($i > $i)). 5.31/6.63 thf(setunionAx_type, type, setunionAx: $o). 5.31/6.63 thf(setunionAx_def, definition, (setunionAx = (! [A:$i,B:$i]: ((in @ B @ (setunion @ A)) = (? [C:$i]: ((in @ B @ C) & (in @ C @ A))))))). 5.31/6.63 thf(omega_type, type, omega: $i). 5.31/6.63 thf(omega0Ax_type, type, omega0Ax: $o). 5.31/6.63 thf(omega0Ax_def, definition, (omega0Ax = (in @ emptyset @ omega))). 5.31/6.63 thf(omegaSAx_type, type, omegaSAx: $o). 5.31/6.63 thf(omegaSAx_def, definition, (omegaSAx = (! [A:$i]: ((in @ A @ omega) => (in @ (setadjoin @ A @ A) @ omega))))). 5.31/6.63 thf(omegaIndAx_type, type, omegaIndAx: $o). 5.31/6.63 thf(omegaIndAx_def, definition, (omegaIndAx = (! [A:$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))))))). 5.31/6.63 thf(replAx_type, type, replAx: $o). 5.31/6.63 thf(replAx_def, definition, (replAx = (! [A:($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))))))))). 5.31/6.63 thf(foundationAx_type, type, foundationAx: $o). 5.31/6.63 thf(foundationAx_def, definition, (foundationAx = (! [A:$i]: ((? [B:$i]: (in @ B @ A)) => (? [B:$i]: ((in @ B @ A) & ~ (? [C:$i]: ((in @ C @ B) & (in @ C @ A))))))))). 5.31/6.63 thf(wellorderingAx_type, type, wellorderingAx: $o). 5.31/6.63 thf(wellorderingAx_def, definition, (wellorderingAx = (! [A:$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)))))))))). 5.31/6.63 thf(descrp_type, type, descrp: $o). 5.31/6.63 thf(descrp_def, definition, (descrp = (! [A:($i > $o)]: ((exu @ (A)) => (A @ (descr @ (A))))))). 5.31/6.63 thf(dsetconstr_type, type, dsetconstr: ($i > (($i > $o) > $i))). 5.31/6.63 thf(dsetconstrI_type, type, dsetconstrI: $o). 5.31/6.63 thf(dsetconstrI_def, definition, (dsetconstrI = (! [A:$i,B:($i > $o),C:$i]: ((in @ C @ A) => ((B @ C) => (in @ C @ (dsetconstr @ A @ (B)))))))). 5.31/6.63 thf(dsetconstrEL_type, type, dsetconstrEL: $o). 5.31/6.63 thf(dsetconstrEL_def, definition, (dsetconstrEL = (! [A:$i,B:($i > $o),C:$i]: ((in @ C @ (dsetconstr @ A @ (B))) => (in @ C @ A))))). 5.31/6.63 thf(dsetconstrER_type, type, dsetconstrER: $o). 5.31/6.63 thf(dsetconstrER_def, definition, (dsetconstrER = (! [A:$i,B:($i > $o),C:$i]: ((in @ C @ (dsetconstr @ A @ (B))) => (B @ C))))). 5.31/6.63 thf(exuE1_type, type, exuE1: $o). 5.31/6.63 thf(exuE1_def, definition, (exuE1 = (! [A:($i > $o)]: ((exu @ (A)) => (? [B:$i]: ((A @ B) & ! [C:$i]: ((A @ C) => (B = C)))))))). 5.31/6.63 thf(prop2setE_type, type, prop2setE: $o). 5.31/6.63 thf(prop2setE_def, definition, (prop2setE = (! [A:$o,B:$i]: ((in @ B @ (prop2set @ A)) => (A))))). 5.31/6.63 thf(emptysetE_type, type, emptysetE: $o). 5.31/6.63 thf(emptysetE_def, definition, (emptysetE = (! [A:$i]: ((in @ A @ emptyset) => (! [B:$o]: (B)))))). 5.31/6.63 thf(emptysetimpfalse_type, type, emptysetimpfalse: $o). 5.31/6.63 thf(emptysetimpfalse_def, definition, (emptysetimpfalse = (! [A:$i]: ((in @ A @ emptyset) => ($false))))). 5.31/6.63 thf(notinemptyset_type, type, notinemptyset: $o). 5.31/6.63 thf(notinemptyset_def, definition, (notinemptyset = (! [A:$i]: ~ (in @ A @ emptyset)))). 5.31/6.63 thf(exuE3e_type, type, exuE3e: $o). 5.31/6.63 thf(exuE3e_def, definition, (exuE3e = (! [A:($i > $o)]: ((exu @ (A)) => (? [B:$i]: (A @ B)))))). 5.31/6.63 thf(setext_type, type, setext: $o). 5.31/6.63 thf(setext_def, definition, (setext = (! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ A) => (in @ C @ B))) => ((! [C:$i]: ((in @ C @ B) => (in @ C @ A))) => (A = B)))))). 5.31/6.63 thf(emptyI_type, type, emptyI: $o). 5.31/6.63 thf(emptyI_def, definition, (emptyI = (! [A:$i]: ((! [B:$i]: ~ (in @ B @ A)) => (A = emptyset))))). 5.31/6.63 thf(noeltsimpempty_type, type, noeltsimpempty: $o). 5.31/6.63 thf(noeltsimpempty_def, definition, (noeltsimpempty = (! [A:$i]: ((! [B:$i]: ~ (in @ B @ A)) => (A = emptyset))))). 5.31/6.63 thf(setbeta_type, type, setbeta: $o). 5.31/6.63 thf(setbeta_def, definition, (setbeta = (! [A:$i,B:($i > $o),C:$i]: ((in @ C @ A) => ((in @ C @ (dsetconstr @ A @ (B))) = (B @ C)))))). 5.31/6.63 thf(nonempty_type, type, nonempty: ($i > $o)). 5.31/6.63 thf(nonempty_def, definition, (nonempty = (^ [A:$i]: (A != emptyset)))). 5.31/6.63 thf(nonemptyE1_type, type, nonemptyE1: $o). 5.31/6.63 thf(nonemptyE1_def, definition, (nonemptyE1 = (! [A:$i]: ((nonempty @ A) => (? [B:$i]: (in @ B @ A)))))). 5.31/6.63 thf(1,conjecture,(((setextAx) => (((((((omegaSAx) => ((omegaIndAx) => (((foundationAx) => ((wellorderingAx) => ((descrp) => (((dsetconstrEL) => ((((prop2setE) => ((emptysetE) => ((emptysetimpfalse) => ((notinemptyset) => (((setext) => (((noeltsimpempty) => (((nonemptyE1) => (! [A:$i,B:($i > $o),C:$i]: ((in @ C @ A) => ((nonempty @ (dsetconstr @ A @ (B))) <= (B @ C))))) <= (setbeta))) <= (emptyI))) <= (exuE3e)))))) <= (exuE1)) <= (dsetconstrER))) <= (dsetconstrI))))) <= (replAx)))) <= (omega0Ax)) <= (setunionAx)) <= (powersetAx)) <= (setadjoinAx)) <= (emptysetAx)))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyI)). 5.31/6.63 thf(2,negated_conjecture,((~ ((setextAx) => (((((((omegaSAx) => ((omegaIndAx) => (((foundationAx) => ((wellorderingAx) => ((descrp) => (((dsetconstrEL) => ((((prop2setE) => ((emptysetE) => ((emptysetimpfalse) => ((notinemptyset) => (((setext) => (((noeltsimpempty) => (((nonemptyE1) => (! [A:$i,B:($i > $o),C:$i]: ((in @ C @ A) => ((nonempty @ (dsetconstr @ A @ (B))) <= (B @ C))))) <= (setbeta))) <= (emptyI))) <= (exuE3e)))))) <= (exuE1)) <= (dsetconstrER))) <= (dsetconstrI))))) <= (replAx)))) <= (omega0Ax)) <= (setunionAx)) <= (powersetAx)) <= (setadjoinAx)) <= (emptysetAx))))),inference(neg_conjecture,[status(cth)],[1])). 5.31/6.63 thf(3,plain,((~ ((! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ A) = (in @ C @ B))) => (A = B))) => (((! [A:$i]: ((in @ A @ omega) => (in @ (setadjoin @ A @ A) @ omega))) => ((! [A:$i]: (((in @ emptyset @ A) & ! [B:$i]: (((in @ B @ omega) & (in @ B @ A)) => (in @ (setadjoin @ B @ B) @ A))) => (! [B:$i]: ((in @ B @ omega) => (in @ B @ A))))) => (((! [A:$i]: ((? [B:$i]: (in @ B @ A)) => (? [B:$i]: ((in @ B @ A) & ~ (? [C:$i]: ((in @ C @ B) & (in @ C @ A))))))) => ((! [A:$i]: ? [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 > $o)]: ((? [B:$i]: ((A @ B) & ! [C:$i]: ((A @ C) => (B = C)))) => (A @ (descr @ (A))))) => (((! [A:$i,B:($i > $o),C:$i]: ((in @ C @ (dsetconstr @ A @ (B))) => (in @ C @ A))) => (((! [A:$o,B:$i]: ((in @ B @ (dsetconstr @ (powerset @ emptyset) @ (^ [C:$i]: (A)))) => (A))) => ((! [A:$i]: ((in @ A @ emptyset) => (! [B:$o]: (B)))) => ((! [A:$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]: ((~ (A = emptyset)) => (? [B:$i]: (in @ B @ A)))) => (! [A:$i,B:($i > $o),C:$i]: ((in @ C @ A) => (~ ((dsetconstr @ A @ (B)) = emptyset) | ~ (B @ C))))) | ~ (! [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 > $o)]: ((? [B:$i]: ((A @ B) & ! [C:$i]: ((A @ C) => (B = C)))) => (? [B:$i]: (A @ B))))))))) | ~ (! [A:$i,B:($i > $o),C:$i]: ((in @ C @ (dsetconstr @ A @ (B))) => (B @ C))))) | ~ (! [A:$i,B:($i > $o),C:$i]: ((in @ C @ A) => ((B @ C) => (in @ C @ (dsetconstr @ A @ (B)))))))))) | ~ (! [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)))))))))) | ~ (in @ emptyset @ omega) | ~ (! [A:$i,B:$i]: ((in @ B @ (setunion @ A)) = (? [C:$i]: ((in @ B @ C) & (in @ C @ A))))) | ~ (! [A:$i,B:$i]: ((in @ B @ (powerset @ A)) = (! [C:$i]: ((in @ C @ B) => (in @ C @ A))))) | ~ (! [A:$i,B:$i,C:$i]: ((in @ C @ (setadjoin @ A @ B)) = ((C = A) | (in @ C @ B)))) | ~ (! [A:$i]: ~ (in @ A @ emptyset)))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])). 5.31/6.63 thf(114,plain,($false),inference(e,[status(thm)],[3])). 5.31/6.63 % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p 5.31/6.63 % [INFO] Killing All external provers ... 5.31/6.63 FINAL WATCH: 5.2 CPU 2.6 WC 5.31/6.63 Killed 1 orphans 5.31/6.63 Killed 2 orphans 5.31/6.63 Killed 1 orphans 5.31/6.63 EOF