TSTP Solution File: SET925^7 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SET925^7 : TPTP v8.1.0. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 04:56:41 EDT 2022
% Result : Theorem 1.95s 2.16s
% Output : Proof 1.95s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET925^7 : TPTP v8.1.0. Released v5.5.0.
% 0.11/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jul 9 21:28:44 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.95/2.16 % SZS status Theorem
% 1.95/2.16 % Mode: mode506
% 1.95/2.16 % Inferences: 0
% 1.95/2.16 % SZS output start Proof
% 1.95/2.16 thf(ty_mu, type, mu : $tType).
% 1.95/2.16 thf(ty_singleton, type, singleton : (mu>mu)).
% 1.95/2.16 thf(ty_rel_s4, type, rel_s4 : ($i>$i>$o)).
% 1.95/2.16 thf(ty_exists_in_world, type, exists_in_world : (mu>$i>$o)).
% 1.95/2.16 thf(ty_qmltpeq, type, qmltpeq : (mu>mu>$i>$o)).
% 1.95/2.16 thf(ty_empty_set, type, empty_set : mu).
% 1.95/2.16 thf(ty_set_difference, type, set_difference : (mu>mu>mu)).
% 1.95/2.16 thf(ty_in, type, in : (mu>mu>$i>$o)).
% 1.95/2.16 thf(sP1,plain,sP1 <=> (![X1:$i]:(![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (![X4:$i]:(((rel_s4 @ X2) @ X4) => (![X5:mu]:(((exists_in_world @ X5) @ X4) => (~(((![X6:$i]:(((rel_s4 @ X4) @ X6) => ((![X7:$i]:(((rel_s4 @ X6) @ X7) => (((qmltpeq @ ((set_difference @ (singleton @ X3)) @ X5)) @ empty_set) @ X7))) => (![X7:$i]:(((rel_s4 @ X6) @ X7) => (((in @ X3) @ X5) @ X7)))))) => (~((![X6:$i]:(((rel_s4 @ X4) @ X6) => ((![X7:$i]:(((rel_s4 @ X6) @ X7) => (((in @ X3) @ X5) @ X7))) => (![X7:$i]:(((rel_s4 @ X6) @ X7) => (((qmltpeq @ ((set_difference @ (singleton @ X3)) @ X5)) @ empty_set) @ X7)))))))))))))))))))),introduced(definition,[new_symbols(definition,[sP1])])).
% 1.95/2.16 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))).
% 1.95/2.16 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))).
% 1.95/2.16 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))).
% 1.95/2.16 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))).
% 1.95/2.16 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))).
% 1.95/2.16 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))).
% 1.95/2.16 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))).
% 1.95/2.16 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))).
% 1.95/2.16 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))).
% 1.95/2.16 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))).
% 1.95/2.16 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))).
% 1.95/2.16 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))).
% 1.95/2.16 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))).
% 1.95/2.16 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:(((exists_in_world @ X3) @ X2) => ((X1 @ X3) @ X2))))))).
% 1.95/2.16 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))).
% 1.95/2.16 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))).
% 1.95/2.16 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))).
% 1.95/2.16 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))).
% 1.95/2.16 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3)))))))))).
% 1.95/2.16 thf(def_mtransitive,definition,(mtransitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))).
% 1.95/2.16 thf(def_meuclidean,definition,(meuclidean = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))).
% 1.95/2.16 thf(def_mpartially_functional,definition,(mpartially_functional = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (X3 = X4)))))))).
% 1.95/2.16 thf(def_mfunctional,definition,(mfunctional = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(((X1 @ X2) @ X3) => (~((![X4:$i]:(((X1 @ X2) @ X4) => (X3 = X4))))))))))))).
% 1.95/2.16 thf(def_mweakly_dense,definition,(mweakly_dense = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((X1 @ X2) @ X3) => (~((![X5:$i]:(((X1 @ X2) @ X5) => (~(((X1 @ X5) @ X3)))))))))))))).
% 1.95/2.16 thf(def_mweakly_connected,definition,(mweakly_connected = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((~(((~(((X1 @ X3) @ X4))) => (X3 = X4)))) => ((X1 @ X4) @ X3))))))))).
% 1.95/2.16 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (~((![X5:$i]:(((X1 @ X3) @ X5) => (~(((X1 @ X4) @ X5)))))))))))))).
% 1.95/2.16 thf(def_mvalid,definition,(mvalid = (!!))).
% 1.95/2.16 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))).
% 1.95/2.16 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))).
% 1.95/2.16 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))).
% 1.95/2.16 thf(def_mbox_s4,definition,(mbox_s4 = (^[X1:$i>$o]:(^[X2:$i]:(![X3:$i]:(((rel_s4 @ X2) @ X3) => (X1 @ X3))))))).
% 1.95/2.16 thf(def_mdia_s4,definition,(mdia_s4 = (^[X1:$i>$o]:(mnot @ (mbox_s4 @ (mnot @ X1)))))).
% 1.95/2.16 thf(t68_zfmisc_1,conjecture,(![X1:$i]:(![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (![X4:$i]:(((rel_s4 @ X2) @ X4) => (![X5:mu]:(((exists_in_world @ X5) @ X4) => (~(((~((~((![X6:$i]:(((rel_s4 @ X4) @ X6) => ((~((~((![X7:$i]:(((rel_s4 @ X6) @ X7) => (((qmltpeq @ ((set_difference @ (singleton @ X3)) @ X5)) @ empty_set) @ X7))))))) => (![X7:$i]:(((rel_s4 @ X6) @ X7) => (((in @ X3) @ X5) @ X7)))))))))) => (~((![X6:$i]:(((rel_s4 @ X4) @ X6) => ((~((~((![X7:$i]:(((rel_s4 @ X6) @ X7) => (((in @ X3) @ X5) @ X7))))))) => (![X7:$i]:(((rel_s4 @ X6) @ X7) => (((qmltpeq @ ((set_difference @ (singleton @ X3)) @ X5)) @ empty_set) @ X7))))))))))))))))))))).
% 1.95/2.16 thf(h0,negated_conjecture,(~(sP1)),inference(assume_negation,[status(cth)],[t68_zfmisc_1])).
% 1.95/2.16 thf(l36_zfmisc_1,axiom,(mvalid @ (mbox_s4 @ (mforall_ind @ (^[X1:mu]:(mbox_s4 @ (mforall_ind @ (^[X2:mu]:((mand @ (mbox_s4 @ ((mimplies @ (mbox_s4 @ ((qmltpeq @ ((set_difference @ (singleton @ X1)) @ X2)) @ empty_set))) @ (mbox_s4 @ ((in @ X1) @ X2))))) @ (mbox_s4 @ ((mimplies @ (mbox_s4 @ ((in @ X1) @ X2))) @ (mbox_s4 @ ((qmltpeq @ ((set_difference @ (singleton @ X1)) @ X2)) @ empty_set))))))))))))).
% 1.95/2.16 thf(1,plain,sP1,inference(preprocess,[status(thm)],[l36_zfmisc_1]).
% 1.95/2.16 thf(2,plain,$false,inference(tab_conflict,[status(thm),assumptions([h0])],[1,h0])).
% 1.95/2.16 thf(0,theorem,(![X1:$i]:(![X2:$i]:(((rel_s4 @ X1) @ X2) => (![X3:mu]:(((exists_in_world @ X3) @ X2) => (![X4:$i]:(((rel_s4 @ X2) @ X4) => (![X5:mu]:(((exists_in_world @ X5) @ X4) => (~(((~((~((![X6:$i]:(((rel_s4 @ X4) @ X6) => ((~((~((![X7:$i]:(((rel_s4 @ X6) @ X7) => (((qmltpeq @ ((set_difference @ (singleton @ X3)) @ X5)) @ empty_set) @ X7))))))) => (![X7:$i]:(((rel_s4 @ X6) @ X7) => (((in @ X3) @ X5) @ X7)))))))))) => (~((![X6:$i]:(((rel_s4 @ X4) @ X6) => ((~((~((![X7:$i]:(((rel_s4 @ X6) @ X7) => (((in @ X3) @ X5) @ X7))))))) => (![X7:$i]:(((rel_s4 @ X6) @ X7) => (((qmltpeq @ ((set_difference @ (singleton @ X3)) @ X5)) @ empty_set) @ X7)))))))))))))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[2,h0])).
% 1.95/2.16 % SZS output end Proof
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