TSTP Solution File: AGT028^2 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : AGT028^2 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n022.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 : Thu Jul 14 12:03:40 EDT 2022
% Result : Theorem 2.04s 2.28s
% Output : Proof 2.04s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : AGT028^2 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.11/0.32 % Computer : n022.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Sat Jun 4 06:11:51 EDT 2022
% 0.11/0.32 % CPUTime :
% 2.04/2.28 % SZS status Theorem
% 2.04/2.28 % Mode: mode506
% 2.04/2.28 % Inferences: 38778
% 2.04/2.28 % SZS output start Proof
% 2.04/2.28 thf(ty_mu, type, mu : $tType).
% 2.04/2.28 thf(ty_r4, type, r4 : ($i>$i>$o)).
% 2.04/2.28 thf(ty_eigen__0, type, eigen__0 : $i).
% 2.04/2.28 thf(ty_john, type, john : mu).
% 2.04/2.28 thf(ty_good_in_maths, type, good_in_maths : (mu>$i>$o)).
% 2.04/2.28 thf(ty_maths_teacher, type, maths_teacher : (mu>$i>$o)).
% 2.04/2.28 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])).
% 2.04/2.28 thf(eigendef_eigen__0, definition, eigen__0 = (eps__0 @ (^[X1:$i]:(~((~((![X2:mu]:(~((![X3:$i]:(((r4 @ X1) @ X3) => ((good_in_maths @ X2) @ X3)))))))))))), introduced(definition,[new_symbols(definition,[eigen__0])])).
% 2.04/2.28 thf(sP1,plain,sP1 <=> (![X1:$i]:(![X2:mu]:(((maths_teacher @ X2) @ X1) => (![X3:$i]:(((r4 @ X1) @ X3) => ((good_in_maths @ X2) @ X3)))))),introduced(definition,[new_symbols(definition,[sP1])])).
% 2.04/2.28 thf(sP2,plain,sP2 <=> (![X1:mu]:(((maths_teacher @ X1) @ eigen__0) => (![X2:$i]:(((r4 @ eigen__0) @ X2) => ((good_in_maths @ X1) @ X2))))),introduced(definition,[new_symbols(definition,[sP2])])).
% 2.04/2.28 thf(sP3,plain,sP3 <=> (![X1:$i]:(((r4 @ eigen__0) @ X1) => ((good_in_maths @ john) @ X1))),introduced(definition,[new_symbols(definition,[sP3])])).
% 2.04/2.28 thf(sP4,plain,sP4 <=> (((maths_teacher @ john) @ eigen__0) => sP3),introduced(definition,[new_symbols(definition,[sP4])])).
% 2.04/2.28 thf(sP5,plain,sP5 <=> ((!!) @ (maths_teacher @ john)),introduced(definition,[new_symbols(definition,[sP5])])).
% 2.04/2.28 thf(sP6,plain,sP6 <=> (![X1:mu]:(~((![X2:$i]:(((r4 @ eigen__0) @ X2) => ((good_in_maths @ X1) @ X2)))))),introduced(definition,[new_symbols(definition,[sP6])])).
% 2.04/2.28 thf(sP7,plain,sP7 <=> (![X1:$i]:(~((![X2:mu]:(~((![X3:$i]:(((r4 @ X1) @ X3) => ((good_in_maths @ X2) @ X3))))))))),introduced(definition,[new_symbols(definition,[sP7])])).
% 2.04/2.28 thf(sP8,plain,sP8 <=> ((maths_teacher @ john) @ eigen__0),introduced(definition,[new_symbols(definition,[sP8])])).
% 2.04/2.28 thf(def_meq_ind,definition,(meq_ind = (^[X1:mu]:(^[X2:mu]:(^[X3:$i]:(X1 = X2)))))).
% 2.04/2.28 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))).
% 2.04/2.28 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))).
% 2.04/2.28 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))).
% 2.04/2.28 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))).
% 2.04/2.28 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))).
% 2.04/2.28 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))).
% 2.04/2.28 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))).
% 2.04/2.28 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))).
% 2.04/2.28 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:((X1 @ X3) @ X2)))))).
% 2.04/2.28 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))).
% 2.04/2.28 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))).
% 2.04/2.28 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))).
% 2.04/2.28 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))).
% 2.04/2.28 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))).
% 2.04/2.28 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))).
% 2.04/2.28 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))).
% 2.04/2.28 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))).
% 2.04/2.28 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))).
% 2.04/2.28 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3)))))))))).
% 2.04/2.28 thf(def_mtransitive,definition,(mtransitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))).
% 2.04/2.28 thf(def_meuclidean,definition,(meuclidean = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))).
% 2.04/2.28 thf(def_mpartially_functional,definition,(mpartially_functional = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (X3 = X4)))))))).
% 2.04/2.28 thf(def_mfunctional,definition,(mfunctional = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(((X1 @ X2) @ X3) => (~((![X4:$i]:(((X1 @ X2) @ X4) => (X3 = X4))))))))))))).
% 2.04/2.28 thf(def_mweakly_dense,definition,(mweakly_dense = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((X1 @ X2) @ X3) => (~((![X5:$i]:(((X1 @ X2) @ X5) => (~(((X1 @ X5) @ X3)))))))))))))).
% 2.04/2.28 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))))))))).
% 2.04/2.28 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (~((![X5:$i]:(((X1 @ X3) @ X5) => (~(((X1 @ X4) @ X5)))))))))))))).
% 2.04/2.28 thf(def_mvalid,definition,(mvalid = (!!))).
% 2.04/2.28 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))).
% 2.04/2.28 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))).
% 2.04/2.28 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))).
% 2.04/2.28 thf(conj,conjecture,sP7).
% 2.04/2.28 thf(h1,negated_conjecture,(~(sP7)),inference(assume_negation,[status(cth)],[conj])).
% 2.04/2.28 thf(1,plain,(~(sP2) | sP4),inference(all_rule,[status(thm)],[])).
% 2.04/2.28 thf(2,plain,((~(sP4) | ~(sP8)) | sP3),inference(prop_rule,[status(thm)],[])).
% 2.04/2.28 thf(3,plain,(~(sP5) | sP8),inference(all_rule,[status(thm)],[])).
% 2.04/2.28 thf(4,plain,(~(sP1) | sP2),inference(all_rule,[status(thm)],[])).
% 2.04/2.28 thf(5,plain,(~(sP6) | ~(sP3)),inference(all_rule,[status(thm)],[])).
% 2.04/2.28 thf(6,plain,(sP7 | sP6),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__0])).
% 2.04/2.28 thf(axiom_a6,axiom,(mvalid @ (maths_teacher @ john))).
% 2.04/2.28 thf(7,plain,sP5,inference(preprocess,[status(thm)],[axiom_a6]).
% 2.04/2.28 thf(axiom_r1,axiom,(mvalid @ (mforall_ind @ (^[X1:mu]:((mimplies @ (maths_teacher @ X1)) @ ((mbox @ r4) @ (good_in_maths @ X1))))))).
% 2.04/2.28 thf(8,plain,sP1,inference(preprocess,[status(thm)],[axiom_r1]).
% 2.04/2.28 thf(9,plain,$false,inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,h1])).
% 2.04/2.28 thf(10,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[9,h0])).
% 2.04/2.28 thf(0,theorem,sP7,inference(contra,[status(thm),contra(discharge,[h1])],[9,h1])).
% 2.04/2.28 % SZS output end Proof
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