TSTP Solution File: SYO568^7 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO568^7 : 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 : n010.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 21 19:33:29 EDT 2022
% Result : Theorem 0.36s 0.55s
% Output : Proof 0.36s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYO568^7 : TPTP v8.1.0. Released v5.5.0.
% 0.06/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n010.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 11:55:31 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.36/0.55 % SZS status Theorem
% 0.36/0.55 % Mode: mode213
% 0.36/0.55 % Inferences: 2812
% 0.36/0.55 % SZS output start Proof
% 0.36/0.55 thf(ty_mu, type, mu : $tType).
% 0.36/0.55 thf(ty_a, type, a : mu).
% 0.36/0.55 thf(ty_rel_s4, type, rel_s4 : ($i>$i>$o)).
% 0.36/0.55 thf(ty_eigen__2, type, eigen__2 : $i).
% 0.36/0.55 thf(ty_eigen__1, type, eigen__1 : $i).
% 0.36/0.55 thf(ty_eigen__0, type, eigen__0 : $i).
% 0.36/0.55 thf(ty_exists_in_world, type, exists_in_world : (mu>$i>$o)).
% 0.36/0.55 thf(ty_f, type, f : (mu>$i>$o)).
% 0.36/0.55 thf(sP1,plain,sP1 <=> (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => ((f @ a) @ X1))),introduced(definition,[new_symbols(definition,[sP1])])).
% 0.36/0.55 thf(sP2,plain,sP2 <=> ((rel_s4 @ eigen__0) @ eigen__2),introduced(definition,[new_symbols(definition,[sP2])])).
% 0.36/0.55 thf(sP3,plain,sP3 <=> (![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((rel_s4 @ X1) @ X2) => (~(((rel_s4 @ X2) @ X3)))))) => ((rel_s4 @ X1) @ X3))))),introduced(definition,[new_symbols(definition,[sP3])])).
% 0.36/0.55 thf(sP4,plain,sP4 <=> (![X1:$i]:(![X2:$i]:((~((((rel_s4 @ eigen__0) @ X1) => (~(((rel_s4 @ X1) @ X2)))))) => ((rel_s4 @ eigen__0) @ X2)))),introduced(definition,[new_symbols(definition,[sP4])])).
% 0.36/0.55 thf(sP5,plain,sP5 <=> ((rel_s4 @ eigen__1) @ eigen__1),introduced(definition,[new_symbols(definition,[sP5])])).
% 0.36/0.55 thf(sP6,plain,sP6 <=> ((~((((rel_s4 @ eigen__0) @ eigen__1) => (~(((rel_s4 @ eigen__1) @ eigen__2)))))) => sP2),introduced(definition,[new_symbols(definition,[sP6])])).
% 0.36/0.55 thf(sP7,plain,sP7 <=> ((!!) @ (exists_in_world @ a)),introduced(definition,[new_symbols(definition,[sP7])])).
% 0.36/0.55 thf(sP8,plain,sP8 <=> ((rel_s4 @ eigen__1) @ eigen__2),introduced(definition,[new_symbols(definition,[sP8])])).
% 0.36/0.55 thf(sP9,plain,sP9 <=> (![X1:$i]:((~((((rel_s4 @ eigen__0) @ eigen__1) => (~(((rel_s4 @ eigen__1) @ X1)))))) => ((rel_s4 @ eigen__0) @ X1))),introduced(definition,[new_symbols(definition,[sP9])])).
% 0.36/0.55 thf(sP10,plain,sP10 <=> ((f @ a) @ eigen__2),introduced(definition,[new_symbols(definition,[sP10])])).
% 0.36/0.55 thf(sP11,plain,sP11 <=> (((exists_in_world @ a) @ eigen__0) => ((~((![X1:$i]:(((rel_s4 @ eigen__0) @ X1) => ((f @ a) @ X1))))) => (![X1:$i]:(((rel_s4 @ eigen__0) @ X1) => (~(((f @ a) @ X1))))))),introduced(definition,[new_symbols(definition,[sP11])])).
% 0.36/0.55 thf(sP12,plain,sP12 <=> (![X1:$i]:(((rel_s4 @ eigen__0) @ X1) => (~(((f @ a) @ X1))))),introduced(definition,[new_symbols(definition,[sP12])])).
% 0.36/0.55 thf(sP13,plain,sP13 <=> (sP5 => ((f @ a) @ eigen__1)),introduced(definition,[new_symbols(definition,[sP13])])).
% 0.36/0.55 thf(sP14,plain,sP14 <=> (((rel_s4 @ eigen__0) @ eigen__1) => (~(sP8))),introduced(definition,[new_symbols(definition,[sP14])])).
% 0.36/0.55 thf(sP15,plain,sP15 <=> ((~((![X1:$i]:(((rel_s4 @ eigen__0) @ X1) => ((f @ a) @ X1))))) => sP12),introduced(definition,[new_symbols(definition,[sP15])])).
% 0.36/0.55 thf(sP16,plain,sP16 <=> ((rel_s4 @ eigen__0) @ eigen__1),introduced(definition,[new_symbols(definition,[sP16])])).
% 0.36/0.55 thf(sP17,plain,sP17 <=> ((f @ a) @ eigen__1),introduced(definition,[new_symbols(definition,[sP17])])).
% 0.36/0.55 thf(sP18,plain,sP18 <=> (![X1:$i]:((rel_s4 @ X1) @ X1)),introduced(definition,[new_symbols(definition,[sP18])])).
% 0.36/0.55 thf(sP19,plain,sP19 <=> ((exists_in_world @ a) @ eigen__0),introduced(definition,[new_symbols(definition,[sP19])])).
% 0.36/0.55 thf(sP20,plain,sP20 <=> (![X1:$i]:(((rel_s4 @ eigen__0) @ X1) => ((f @ a) @ X1))),introduced(definition,[new_symbols(definition,[sP20])])).
% 0.36/0.55 thf(sP21,plain,sP21 <=> (sP2 => sP10),introduced(definition,[new_symbols(definition,[sP21])])).
% 0.36/0.55 thf(sP22,plain,sP22 <=> (![X1:mu]:(((exists_in_world @ X1) @ eigen__0) => ((~((![X2:$i]:(((rel_s4 @ eigen__0) @ X2) => ((f @ X1) @ X2))))) => (![X2:$i]:(((rel_s4 @ eigen__0) @ X2) => (~(((f @ X1) @ X2)))))))),introduced(definition,[new_symbols(definition,[sP22])])).
% 0.36/0.55 thf(sP23,plain,sP23 <=> (sP16 => (~(sP17))),introduced(definition,[new_symbols(definition,[sP23])])).
% 0.36/0.55 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))).
% 0.36/0.55 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))).
% 0.36/0.55 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))).
% 0.36/0.55 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))).
% 0.36/0.55 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))).
% 0.36/0.55 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))).
% 0.36/0.55 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))).
% 0.36/0.55 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))).
% 0.36/0.55 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))).
% 0.36/0.55 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))).
% 0.36/0.55 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))).
% 0.36/0.55 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))).
% 0.36/0.55 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))).
% 0.36/0.55 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:(((exists_in_world @ X3) @ X2) => ((X1 @ X3) @ X2))))))).
% 0.36/0.55 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))).
% 0.36/0.55 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))).
% 0.36/0.55 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))).
% 0.36/0.55 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))).
% 0.36/0.55 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3)))))))))).
% 0.36/0.55 thf(def_mtransitive,definition,(mtransitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))).
% 0.36/0.55 thf(def_meuclidean,definition,(meuclidean = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))).
% 0.36/0.55 thf(def_mpartially_functional,definition,(mpartially_functional = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (X3 = X4)))))))).
% 0.36/0.55 thf(def_mfunctional,definition,(mfunctional = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(((X1 @ X2) @ X3) => (~((![X4:$i]:(((X1 @ X2) @ X4) => (X3 = X4))))))))))))).
% 0.36/0.55 thf(def_mweakly_dense,definition,(mweakly_dense = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((X1 @ X2) @ X3) => (~((![X5:$i]:(((X1 @ X2) @ X5) => (~(((X1 @ X5) @ X3)))))))))))))).
% 0.36/0.55 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))))))))).
% 0.36/0.55 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (~((![X5:$i]:(((X1 @ X3) @ X5) => (~(((X1 @ X4) @ X5)))))))))))))).
% 0.36/0.55 thf(def_mvalid,definition,(mvalid = (!!))).
% 0.36/0.55 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))).
% 0.36/0.55 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))).
% 0.36/0.55 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))).
% 0.36/0.55 thf(def_mbox_s4,definition,(mbox_s4 = (^[X1:$i>$o]:(^[X2:$i]:(![X3:$i]:(((rel_s4 @ X2) @ X3) => (X1 @ X3))))))).
% 0.36/0.55 thf(def_mdia_s4,definition,(mdia_s4 = (^[X1:$i>$o]:(mnot @ (mbox_s4 @ (mnot @ X1)))))).
% 0.36/0.55 thf(con,conjecture,(![X1:$i]:((~((~((![X2:mu]:(((exists_in_world @ X2) @ X1) => ((~((![X3:$i]:(((rel_s4 @ X1) @ X3) => ((f @ X2) @ X3))))) => (![X3:$i]:(((rel_s4 @ X1) @ X3) => (~(((f @ X2) @ X3)))))))))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (~(((~((~(((~((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => ((f @ a) @ X3))))))) => ((f @ a) @ X2)))))) => (~(((~((~(((f @ a) @ X2))))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => ((f @ a) @ X3)))))))))))))).
% 0.36/0.55 thf(h0,negated_conjecture,(~((![X1:$i]:((![X2:mu]:(((exists_in_world @ X2) @ X1) => ((~((![X3:$i]:(((rel_s4 @ X1) @ X3) => ((f @ X2) @ X3))))) => (![X3:$i]:(((rel_s4 @ X1) @ X3) => (~(((f @ X2) @ X3)))))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (~((((![X3:$i]:(((rel_s4 @ X2) @ X3) => ((f @ a) @ X3))) => ((f @ a) @ X2)) => (~((((f @ a) @ X2) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => ((f @ a) @ X3))))))))))))))),inference(assume_negation,[status(cth)],[con])).
% 0.36/0.55 thf(h1,assumption,(~((sP22 => (![X1:$i]:(((rel_s4 @ eigen__0) @ X1) => (~((((![X2:$i]:(((rel_s4 @ X1) @ X2) => ((f @ a) @ X2))) => ((f @ a) @ X1)) => (~((((f @ a) @ X1) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => ((f @ a) @ X2)))))))))))))),introduced(assumption,[])).
% 0.36/0.55 thf(h2,assumption,sP22,introduced(assumption,[])).
% 0.36/0.55 thf(h3,assumption,(~((![X1:$i]:(((rel_s4 @ eigen__0) @ X1) => (~((((![X2:$i]:(((rel_s4 @ X1) @ X2) => ((f @ a) @ X2))) => ((f @ a) @ X1)) => (~((((f @ a) @ X1) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => ((f @ a) @ X2))))))))))))),introduced(assumption,[])).
% 0.36/0.55 thf(h4,assumption,(~((sP16 => (~(((sP1 => sP17) => (~((sP17 => sP1))))))))),introduced(assumption,[])).
% 0.36/0.55 thf(h5,assumption,sP16,introduced(assumption,[])).
% 0.36/0.55 thf(h6,assumption,((sP1 => sP17) => (~((sP17 => sP1)))),introduced(assumption,[])).
% 0.36/0.55 thf(h7,assumption,(~((sP1 => sP17))),introduced(assumption,[])).
% 0.36/0.55 thf(h8,assumption,(~((sP17 => sP1))),introduced(assumption,[])).
% 0.36/0.55 thf(h9,assumption,sP1,introduced(assumption,[])).
% 0.36/0.55 thf(h10,assumption,(~(sP17)),introduced(assumption,[])).
% 0.36/0.55 thf(1,plain,(~(sP18) | sP5),inference(all_rule,[status(thm)],[])).
% 0.36/0.55 thf(2,plain,(~(sP1) | sP13),inference(all_rule,[status(thm)],[])).
% 0.36/0.55 thf(3,plain,((~(sP13) | ~(sP5)) | sP17),inference(prop_rule,[status(thm)],[])).
% 0.36/0.55 thf(a1,axiom,(mreflexive @ rel_s4)).
% 0.36/0.55 thf(4,plain,sP18,inference(preprocess,[status(thm)],[a1]).
% 0.36/0.55 thf(5,plain,$false,inference(prop_unsat,[status(thm),assumptions([h9,h10,h7,h5,h6,h4,h2,h3,h1,h0])],[1,2,3,4,h9,h10])).
% 0.36/0.55 thf(6,plain,$false,inference(tab_negimp,[status(thm),assumptions([h7,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h9,h10])],[h7,5,h9,h10])).
% 0.36/0.55 thf(h11,assumption,sP17,introduced(assumption,[])).
% 0.36/0.55 thf(h12,assumption,(~(sP1)),introduced(assumption,[])).
% 0.36/0.55 thf(h13,assumption,(~((sP8 => sP10))),introduced(assumption,[])).
% 0.36/0.55 thf(h14,assumption,sP8,introduced(assumption,[])).
% 0.36/0.55 thf(h15,assumption,(~(sP10)),introduced(assumption,[])).
% 0.36/0.55 thf(7,plain,(~(sP7) | sP19),inference(all_rule,[status(thm)],[])).
% 0.36/0.55 thf(8,plain,(~(sP3) | sP4),inference(all_rule,[status(thm)],[])).
% 0.36/0.55 thf(9,plain,(~(sP4) | sP9),inference(all_rule,[status(thm)],[])).
% 0.36/0.55 thf(10,plain,(~(sP9) | sP6),inference(all_rule,[status(thm)],[])).
% 0.36/0.55 thf(11,plain,((~(sP6) | sP14) | sP2),inference(prop_rule,[status(thm)],[])).
% 0.36/0.55 thf(12,plain,((~(sP14) | ~(sP16)) | ~(sP8)),inference(prop_rule,[status(thm)],[])).
% 0.36/0.55 thf(13,plain,(~(sP22) | sP11),inference(all_rule,[status(thm)],[])).
% 0.36/0.55 thf(14,plain,((~(sP11) | ~(sP19)) | sP15),inference(prop_rule,[status(thm)],[])).
% 0.36/0.55 thf(15,plain,((~(sP15) | sP20) | sP12),inference(prop_rule,[status(thm)],[])).
% 0.36/0.55 thf(16,plain,(~(sP20) | sP21),inference(all_rule,[status(thm)],[])).
% 0.36/0.55 thf(17,plain,((~(sP21) | ~(sP2)) | sP10),inference(prop_rule,[status(thm)],[])).
% 0.36/0.55 thf(18,plain,(~(sP12) | sP23),inference(all_rule,[status(thm)],[])).
% 0.36/0.55 thf(19,plain,((~(sP23) | ~(sP16)) | ~(sP17)),inference(prop_rule,[status(thm)],[])).
% 0.36/0.55 thf(a2,axiom,(mtransitive @ rel_s4)).
% 0.36/0.55 thf(20,plain,sP3,inference(preprocess,[status(thm)],[a2]).
% 0.36/0.55 thf(existence_of_a_ax,axiom,sP7).
% 0.36/0.55 thf(21,plain,$false,inference(prop_unsat,[status(thm),assumptions([h14,h15,h13,h11,h12,h8,h5,h6,h4,h2,h3,h1,h0])],[7,8,9,10,11,12,13,14,15,16,17,18,19,20,existence_of_a_ax,h2,h5,h11,h14,h15])).
% 0.36/0.55 thf(22,plain,$false,inference(tab_negimp,[status(thm),assumptions([h13,h11,h12,h8,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h14,h15])],[h13,21,h14,h15])).
% 0.36/0.55 thf(23,plain,$false,inference(tab_negall,[status(thm),assumptions([h11,h12,h8,h5,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h13]),tab_negall(eigenvar,eigen__2)],[h12,22,h13])).
% 0.36/0.55 thf(24,plain,$false,inference(tab_negimp,[status(thm),assumptions([h8,h5,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h11,h12])],[h8,23,h11,h12])).
% 0.36/0.55 thf(25,plain,$false,inference(tab_imp,[status(thm),assumptions([h5,h6,h4,h2,h3,h1,h0]),tab_imp(discharge,[h7]),tab_imp(discharge,[h8])],[h6,6,24,h7,h8])).
% 0.36/0.55 thf(26,plain,$false,inference(tab_negimp,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,25,h5,h6])).
% 0.36/0.55 thf(27,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,26,h4])).
% 0.36/0.55 thf(28,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,27,h2,h3])).
% 0.36/0.55 thf(29,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,28,h1])).
% 0.36/0.55 thf(0,theorem,(![X1:$i]:((~((~((![X2:mu]:(((exists_in_world @ X2) @ X1) => ((~((![X3:$i]:(((rel_s4 @ X1) @ X3) => ((f @ X2) @ X3))))) => (![X3:$i]:(((rel_s4 @ X1) @ X3) => (~(((f @ X2) @ X3)))))))))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (~(((~((~(((~((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => ((f @ a) @ X3))))))) => ((f @ a) @ X2)))))) => (~(((~((~(((f @ a) @ X2))))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => ((f @ a) @ X3))))))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[29,h0])).
% 0.36/0.55 % SZS output end Proof
%------------------------------------------------------------------------------