TSTP Solution File: KRS275^7 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : KRS275^7 : 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 : n018.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 : Sun Jul 17 03:27:31 EDT 2022
% Result : Theorem 0.41s 0.58s
% Output : Proof 0.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KRS275^7 : TPTP v8.1.0. Released v5.5.0.
% 0.12/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 7 17:43:21 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.41/0.58 % SZS status Theorem
% 0.41/0.58 % Mode: mode213
% 0.41/0.58 % Inferences: 954
% 0.41/0.58 % SZS output start Proof
% 0.41/0.58 thf(ty_mu, type, mu : $tType).
% 0.41/0.58 thf(ty_eigen__12, type, eigen__12 : $i).
% 0.41/0.58 thf(ty_rel_s4, type, rel_s4 : ($i>$i>$o)).
% 0.41/0.58 thf(ty_eigen__0, type, eigen__0 : $i).
% 0.41/0.58 thf(ty_john, type, john : mu).
% 0.41/0.58 thf(ty_math, type, math : mu).
% 0.41/0.58 thf(ty_exists_in_world, type, exists_in_world : (mu>$i>$o)).
% 0.41/0.58 thf(ty_psych, type, psych : mu).
% 0.41/0.58 thf(ty_teach, type, teach : (mu>mu>$i>$o)).
% 0.41/0.58 thf(ty_cs, type, cs : mu).
% 0.41/0.58 thf(ty_mary, type, mary : mu).
% 0.41/0.58 thf(ty_sue, type, sue : mu).
% 0.41/0.58 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])).
% 0.41/0.58 thf(eigendef_eigen__12, definition, eigen__12 = (eps__0 @ (^[X1:$i]:(~((((rel_s4 @ eigen__0) @ X1) => (((teach @ john) @ math) @ X1)))))), introduced(definition,[new_symbols(definition,[eigen__12])])).
% 0.41/0.58 thf(sP1,plain,sP1 <=> (![X1:$i]:(![X2:$i]:(((rel_s4 @ X1) @ X2) => (~(((((teach @ john) @ math) @ X2) => ((~((![X3:mu]:(((exists_in_world @ X3) @ X2) => (~((((teach @ X3) @ cs) @ X2))))))) => ((((teach @ mary) @ psych) @ X2) => (~((((teach @ sue) @ psych) @ X2))))))))))),introduced(definition,[new_symbols(definition,[sP1])])).
% 0.41/0.58 thf(sP2,plain,sP2 <=> (((exists_in_world @ math) @ eigen__0) => (~((![X1:$i]:(((rel_s4 @ eigen__0) @ X1) => (((teach @ john) @ math) @ X1)))))),introduced(definition,[new_symbols(definition,[sP2])])).
% 0.41/0.58 thf(sP3,plain,sP3 <=> ((((teach @ john) @ math) @ eigen__12) => ((~((![X1:mu]:(((exists_in_world @ X1) @ eigen__12) => (~((((teach @ X1) @ cs) @ eigen__12))))))) => ((((teach @ mary) @ psych) @ eigen__12) => (~((((teach @ sue) @ psych) @ eigen__12)))))),introduced(definition,[new_symbols(definition,[sP3])])).
% 0.41/0.58 thf(sP4,plain,sP4 <=> (((rel_s4 @ eigen__0) @ eigen__12) => (((teach @ john) @ math) @ eigen__12)),introduced(definition,[new_symbols(definition,[sP4])])).
% 0.41/0.58 thf(sP5,plain,sP5 <=> ((rel_s4 @ eigen__0) @ eigen__12),introduced(definition,[new_symbols(definition,[sP5])])).
% 0.41/0.58 thf(sP6,plain,sP6 <=> (![X1:$i]:(((rel_s4 @ eigen__0) @ X1) => (((teach @ john) @ math) @ X1))),introduced(definition,[new_symbols(definition,[sP6])])).
% 0.41/0.58 thf(sP7,plain,sP7 <=> (((teach @ john) @ math) @ eigen__12),introduced(definition,[new_symbols(definition,[sP7])])).
% 0.41/0.58 thf(sP8,plain,sP8 <=> (![X1:$i]:(((rel_s4 @ eigen__0) @ X1) => (~(((((teach @ john) @ math) @ X1) => ((~((![X2:mu]:(((exists_in_world @ X2) @ X1) => (~((((teach @ X2) @ cs) @ X1))))))) => ((((teach @ mary) @ psych) @ X1) => (~((((teach @ sue) @ psych) @ X1)))))))))),introduced(definition,[new_symbols(definition,[sP8])])).
% 0.41/0.58 thf(sP9,plain,sP9 <=> ((exists_in_world @ math) @ eigen__0),introduced(definition,[new_symbols(definition,[sP9])])).
% 0.41/0.58 thf(sP10,plain,sP10 <=> (![X1:mu]:(((exists_in_world @ X1) @ eigen__0) => (~((![X2:$i]:(((rel_s4 @ eigen__0) @ X2) => (((teach @ john) @ X1) @ X2))))))),introduced(definition,[new_symbols(definition,[sP10])])).
% 0.41/0.58 thf(sP11,plain,sP11 <=> (sP5 => (~(sP3))),introduced(definition,[new_symbols(definition,[sP11])])).
% 0.41/0.58 thf(sP12,plain,sP12 <=> ((!!) @ (exists_in_world @ math)),introduced(definition,[new_symbols(definition,[sP12])])).
% 0.41/0.58 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))).
% 0.41/0.58 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))).
% 0.41/0.58 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))).
% 0.41/0.58 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))).
% 0.41/0.58 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))).
% 0.41/0.58 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))).
% 0.41/0.58 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))).
% 0.41/0.58 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))).
% 0.41/0.58 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))).
% 0.41/0.58 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))).
% 0.41/0.58 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))).
% 0.41/0.58 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))).
% 0.41/0.58 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))).
% 0.41/0.58 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:(((exists_in_world @ X3) @ X2) => ((X1 @ X3) @ X2))))))).
% 0.41/0.58 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))).
% 0.41/0.58 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))).
% 0.41/0.58 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))).
% 0.41/0.58 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))).
% 0.41/0.58 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3)))))))))).
% 0.41/0.58 thf(def_mtransitive,definition,(mtransitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))).
% 0.41/0.58 thf(def_meuclidean,definition,(meuclidean = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))).
% 0.41/0.58 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)))))))).
% 0.41/0.58 thf(def_mfunctional,definition,(mfunctional = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(((X1 @ X2) @ X3) => (~((![X4:$i]:(((X1 @ X2) @ X4) => (X3 = X4))))))))))))).
% 0.41/0.58 thf(def_mweakly_dense,definition,(mweakly_dense = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((X1 @ X2) @ X3) => (~((![X5:$i]:(((X1 @ X2) @ X5) => (~(((X1 @ X5) @ X3)))))))))))))).
% 0.41/0.58 thf(def_mweakly_connected,definition,(mweakly_connected = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((~(((~(((X1 @ X3) @ X4))) => (X3 = X4)))) => ((X1 @ X4) @ X3))))))))).
% 0.41/0.58 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (~((![X5:$i]:(((X1 @ X3) @ X5) => (~(((X1 @ X4) @ X5)))))))))))))).
% 0.41/0.58 thf(def_mvalid,definition,(mvalid = (!!))).
% 0.41/0.58 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))).
% 0.41/0.58 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))).
% 0.41/0.58 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))).
% 0.41/0.58 thf(def_mbox_s4,definition,(mbox_s4 = (^[X1:$i>$o]:(^[X2:$i]:(![X3:$i]:(((rel_s4 @ X2) @ X3) => (X1 @ X3))))))).
% 0.41/0.58 thf(def_mdia_s4,definition,(mdia_s4 = (^[X1:$i>$o]:(mnot @ (mbox_s4 @ (mnot @ X1)))))).
% 0.41/0.58 thf(query,conjecture,(![X1:$i]:(~((![X2:mu]:(((exists_in_world @ X2) @ X1) => (~((![X3:$i]:(((rel_s4 @ X1) @ X3) => (((teach @ john) @ X2) @ X3))))))))))).
% 0.41/0.58 thf(h1,negated_conjecture,(~((![X1:$i]:(~((![X2:mu]:(((exists_in_world @ X2) @ X1) => (~((![X3:$i]:(((rel_s4 @ X1) @ X3) => (((teach @ john) @ X2) @ X3)))))))))))),inference(assume_negation,[status(cth)],[query])).
% 0.41/0.58 thf(h2,assumption,sP10,introduced(assumption,[])).
% 0.41/0.58 thf(1,plain,(sP3 | sP7),inference(prop_rule,[status(thm)],[])).
% 0.41/0.58 thf(2,plain,(~(sP8) | sP11),inference(all_rule,[status(thm)],[])).
% 0.41/0.58 thf(3,plain,((~(sP11) | ~(sP5)) | ~(sP3)),inference(prop_rule,[status(thm)],[])).
% 0.41/0.58 thf(4,plain,(sP4 | ~(sP7)),inference(prop_rule,[status(thm)],[])).
% 0.41/0.58 thf(5,plain,(sP4 | sP5),inference(prop_rule,[status(thm)],[])).
% 0.41/0.58 thf(6,plain,(sP6 | ~(sP4)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__12])).
% 0.41/0.58 thf(7,plain,(~(sP10) | sP2),inference(all_rule,[status(thm)],[])).
% 0.41/0.58 thf(8,plain,((~(sP2) | ~(sP9)) | ~(sP6)),inference(prop_rule,[status(thm)],[])).
% 0.41/0.58 thf(9,plain,(~(sP12) | sP9),inference(all_rule,[status(thm)],[])).
% 0.41/0.58 thf(10,plain,(~(sP1) | sP8),inference(all_rule,[status(thm)],[])).
% 0.41/0.58 thf(existence_of_math_ax,axiom,sP12).
% 0.41/0.58 thf(db,axiom,(mvalid @ (mbox_s4 @ ((mand @ ((teach @ john) @ math)) @ ((mand @ (mexists_ind @ (^[X1:mu]:((teach @ X1) @ cs)))) @ ((mand @ ((teach @ mary) @ psych)) @ ((teach @ sue) @ psych))))))).
% 0.41/0.58 thf(11,plain,sP1,inference(preprocess,[status(thm)],[db]).
% 0.41/0.58 thf(12,plain,$false,inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,existence_of_math_ax,11,h2])).
% 0.41/0.58 thf(13,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,12,h2])).
% 0.41/0.58 thf(14,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[13,h0])).
% 0.41/0.58 thf(0,theorem,(![X1:$i]:(~((![X2:mu]:(((exists_in_world @ X2) @ X1) => (~((![X3:$i]:(((rel_s4 @ X1) @ X3) => (((teach @ john) @ X2) @ X3)))))))))),inference(contra,[status(thm),contra(discharge,[h1])],[13,h1])).
% 0.41/0.58 % SZS output end Proof
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