TSTP Solution File: SYO436^1 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO436^1 : TPTP v8.1.0. Released v4.0.0.
% 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 21 19:32:04 EDT 2022
% Result : Theorem 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO436^1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n022.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 : Fri Jul 8 20:01:26 EDT 2022
% 0.19/0.34 % CPUTime :
% 0.19/0.38 % SZS status Theorem
% 0.19/0.38 % Mode: mode213
% 0.19/0.38 % Inferences: 40
% 0.19/0.38 % SZS output start Proof
% 0.19/0.38 thf(ty_eigen__6, type, eigen__6 : $i).
% 0.19/0.38 thf(ty_p, type, p : ($i>$o)).
% 0.19/0.38 thf(ty_rel_s4, type, rel_s4 : ($i>$i>$o)).
% 0.19/0.38 thf(ty_eigen__2, type, eigen__2 : $i).
% 0.19/0.38 thf(ty_q, type, q : ($i>$o)).
% 0.19/0.38 thf(ty_eigen__1, type, eigen__1 : $i).
% 0.19/0.38 thf(ty_eigen__0, type, eigen__0 : $i).
% 0.19/0.38 thf(ty_eigen__4, type, eigen__4 : $i).
% 0.19/0.38 thf(ty_eigen__5, type, eigen__5 : $i).
% 0.19/0.38 thf(ty_eigen__3, type, eigen__3 : $i).
% 0.19/0.38 thf(sP1,plain,sP1 <=> (![X1:$i]:((~((((rel_s4 @ eigen__0) @ eigen__1) => (~(((rel_s4 @ eigen__1) @ X1)))))) => ((rel_s4 @ eigen__0) @ X1))),introduced(definition,[new_symbols(definition,[sP1])])).
% 0.19/0.38 thf(sP2,plain,sP2 <=> (((rel_s4 @ eigen__0) @ eigen__6) => (q @ eigen__6)),introduced(definition,[new_symbols(definition,[sP2])])).
% 0.19/0.38 thf(sP3,plain,sP3 <=> (![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((rel_s4 @ X1) @ X2) => (~(((rel_s4 @ X2) @ X3)))))) => ((rel_s4 @ X1) @ X3))))),introduced(definition,[new_symbols(definition,[sP3])])).
% 0.19/0.38 thf(sP4,plain,sP4 <=> ((rel_s4 @ eigen__0) @ eigen__1),introduced(definition,[new_symbols(definition,[sP4])])).
% 0.19/0.38 thf(sP5,plain,sP5 <=> (q @ eigen__6),introduced(definition,[new_symbols(definition,[sP5])])).
% 0.19/0.38 thf(sP6,plain,sP6 <=> ((rel_s4 @ eigen__0) @ eigen__6),introduced(definition,[new_symbols(definition,[sP6])])).
% 0.19/0.38 thf(sP7,plain,sP7 <=> ((~((((rel_s4 @ eigen__0) @ eigen__4) => (~(((rel_s4 @ eigen__4) @ eigen__6)))))) => sP6),introduced(definition,[new_symbols(definition,[sP7])])).
% 0.19/0.38 thf(sP8,plain,sP8 <=> (![X1:$i]:(((rel_s4 @ eigen__0) @ X1) => (q @ X1))),introduced(definition,[new_symbols(definition,[sP8])])).
% 0.19/0.38 thf(sP9,plain,sP9 <=> (![X1:$i]:(((rel_s4 @ eigen__0) @ X1) => (p @ X1))),introduced(definition,[new_symbols(definition,[sP9])])).
% 0.19/0.38 thf(sP10,plain,sP10 <=> ((~((sP4 => (~(((rel_s4 @ eigen__1) @ eigen__2)))))) => ((rel_s4 @ eigen__0) @ eigen__2)),introduced(definition,[new_symbols(definition,[sP10])])).
% 0.19/0.38 thf(sP11,plain,sP11 <=> ((rel_s4 @ eigen__0) @ eigen__2),introduced(definition,[new_symbols(definition,[sP11])])).
% 0.19/0.38 thf(sP12,plain,sP12 <=> ((rel_s4 @ eigen__0) @ eigen__4),introduced(definition,[new_symbols(definition,[sP12])])).
% 0.19/0.38 thf(sP13,plain,sP13 <=> (sP12 => (~(((rel_s4 @ eigen__4) @ eigen__6)))),introduced(definition,[new_symbols(definition,[sP13])])).
% 0.19/0.38 thf(sP14,plain,sP14 <=> (![X1:$i]:(![X2:$i]:((~((((rel_s4 @ eigen__0) @ X1) => (~(((rel_s4 @ X1) @ X2)))))) => ((rel_s4 @ eigen__0) @ X2)))),introduced(definition,[new_symbols(definition,[sP14])])).
% 0.19/0.38 thf(sP15,plain,sP15 <=> (p @ eigen__2),introduced(definition,[new_symbols(definition,[sP15])])).
% 0.19/0.38 thf(sP16,plain,sP16 <=> ((rel_s4 @ eigen__4) @ eigen__6),introduced(definition,[new_symbols(definition,[sP16])])).
% 0.19/0.38 thf(sP17,plain,sP17 <=> (![X1:$i]:((~((sP12 => (~(((rel_s4 @ eigen__4) @ X1)))))) => ((rel_s4 @ eigen__0) @ X1))),introduced(definition,[new_symbols(definition,[sP17])])).
% 0.19/0.38 thf(sP18,plain,sP18 <=> (sP11 => sP15),introduced(definition,[new_symbols(definition,[sP18])])).
% 0.19/0.38 thf(sP19,plain,sP19 <=> ((rel_s4 @ eigen__1) @ eigen__2),introduced(definition,[new_symbols(definition,[sP19])])).
% 0.19/0.38 thf(sP20,plain,sP20 <=> (sP4 => (~(sP19))),introduced(definition,[new_symbols(definition,[sP20])])).
% 0.19/0.38 thf(def_meq_ind,definition,(meq_ind = (^[X1:mu]:(^[X2:mu]:(^[X3:$i]:(X1 = X2)))))).
% 0.19/0.38 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))).
% 0.19/0.38 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))).
% 0.19/0.38 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))).
% 0.19/0.38 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))).
% 0.19/0.38 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))).
% 0.19/0.38 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))).
% 0.19/0.38 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))).
% 0.19/0.38 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))).
% 0.19/0.38 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:((X1 @ X3) @ X2)))))).
% 0.19/0.38 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))).
% 0.19/0.38 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))).
% 0.19/0.38 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))).
% 0.19/0.38 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))).
% 0.19/0.38 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))).
% 0.19/0.38 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))).
% 0.19/0.38 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))).
% 0.19/0.38 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))).
% 0.19/0.38 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))).
% 0.19/0.38 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3)))))))))).
% 0.19/0.38 thf(def_mtransitive,definition,(mtransitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))).
% 0.19/0.38 thf(def_meuclidean,definition,(meuclidean = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))).
% 0.19/0.38 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)))))))).
% 0.19/0.38 thf(def_mfunctional,definition,(mfunctional = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(((X1 @ X2) @ X3) => (~((![X4:$i]:(((X1 @ X2) @ X4) => (X3 = X4))))))))))))).
% 0.19/0.38 thf(def_mweakly_dense,definition,(mweakly_dense = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((X1 @ X2) @ X3) => (~((![X5:$i]:(((X1 @ X2) @ X5) => (~(((X1 @ X5) @ X3)))))))))))))).
% 0.19/0.38 thf(def_mweakly_connected,definition,(mweakly_connected = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((~(((~(((X1 @ X3) @ X4))) => (X3 = X4)))) => ((X1 @ X4) @ X3))))))))).
% 0.19/0.38 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (~((![X5:$i]:(((X1 @ X3) @ X5) => (~(((X1 @ X4) @ X5)))))))))))))).
% 0.19/0.38 thf(def_mvalid,definition,(mvalid = (!!))).
% 0.19/0.38 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))).
% 0.19/0.38 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))).
% 0.19/0.38 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))).
% 0.19/0.38 thf(def_mbox_s4,definition,(mbox_s4 = (^[X1:$i>$o]:(^[X2:$i]:(![X3:$i]:(((rel_s4 @ X2) @ X3) => (X1 @ X3))))))).
% 0.19/0.38 thf(def_mdia_s4,definition,(mdia_s4 = (^[X1:$i>$o]:(mnot @ (mbox_s4 @ (mnot @ X1)))))).
% 0.19/0.38 thf(prove,conjecture,(![X1:$i]:((~((~(((~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (p @ X2))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (q @ X2)))))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => ((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (p @ X3))))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (q @ X3))))))))).
% 0.19/0.38 thf(h0,negated_conjecture,(~((![X1:$i]:(((~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (p @ X2))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (q @ X2)))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => ((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (p @ X3))))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (q @ X3)))))))))),inference(assume_negation,[status(cth)],[prove])).
% 0.19/0.38 thf(h1,assumption,(~((((~(sP9)) => sP8) => (![X1:$i]:(((rel_s4 @ eigen__0) @ X1) => ((~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (p @ X2))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (q @ X2))))))))),introduced(assumption,[])).
% 0.19/0.38 thf(h2,assumption,((~(sP9)) => sP8),introduced(assumption,[])).
% 0.19/0.38 thf(h3,assumption,(~((![X1:$i]:(((rel_s4 @ eigen__0) @ X1) => ((~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (p @ X2))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (q @ X2)))))))),introduced(assumption,[])).
% 0.19/0.38 thf(h4,assumption,sP9,introduced(assumption,[])).
% 0.19/0.38 thf(h5,assumption,sP8,introduced(assumption,[])).
% 0.19/0.38 thf(h6,assumption,(~((sP4 => ((~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (p @ X1))))) => (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (q @ X1))))))),introduced(assumption,[])).
% 0.19/0.38 thf(h7,assumption,sP4,introduced(assumption,[])).
% 0.19/0.38 thf(h8,assumption,(~(((~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (p @ X1))))) => (![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (q @ X1)))))),introduced(assumption,[])).
% 0.19/0.38 thf(h9,assumption,(~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (p @ X1))))),introduced(assumption,[])).
% 0.19/0.38 thf(h10,assumption,(~((![X1:$i]:(((rel_s4 @ eigen__1) @ X1) => (q @ X1))))),introduced(assumption,[])).
% 0.19/0.38 thf(h11,assumption,(~((sP19 => sP15))),introduced(assumption,[])).
% 0.19/0.38 thf(h12,assumption,sP19,introduced(assumption,[])).
% 0.19/0.38 thf(h13,assumption,(~(sP15)),introduced(assumption,[])).
% 0.19/0.38 thf(h14,assumption,(~((((rel_s4 @ eigen__1) @ eigen__3) => (q @ eigen__3)))),introduced(assumption,[])).
% 0.19/0.38 thf(h15,assumption,((rel_s4 @ eigen__1) @ eigen__3),introduced(assumption,[])).
% 0.19/0.38 thf(h16,assumption,(~((q @ eigen__3))),introduced(assumption,[])).
% 0.19/0.38 thf(1,plain,(~(sP3) | sP14),inference(all_rule,[status(thm)],[])).
% 0.19/0.38 thf(2,plain,(~(sP14) | sP1),inference(all_rule,[status(thm)],[])).
% 0.19/0.38 thf(3,plain,(~(sP1) | sP10),inference(all_rule,[status(thm)],[])).
% 0.19/0.38 thf(4,plain,((~(sP10) | sP20) | sP11),inference(prop_rule,[status(thm)],[])).
% 0.19/0.38 thf(5,plain,((~(sP20) | ~(sP4)) | ~(sP19)),inference(prop_rule,[status(thm)],[])).
% 0.19/0.38 thf(6,plain,(~(sP9) | sP18),inference(all_rule,[status(thm)],[])).
% 0.19/0.38 thf(7,plain,((~(sP18) | ~(sP11)) | sP15),inference(prop_rule,[status(thm)],[])).
% 0.19/0.38 thf(a2,axiom,(mtransitive @ rel_s4)).
% 0.19/0.38 thf(8,plain,sP3,inference(preprocess,[status(thm)],[a2]).
% 0.19/0.38 thf(9,plain,$false,inference(prop_unsat,[status(thm),assumptions([h15,h16,h14,h12,h13,h11,h9,h10,h7,h8,h6,h4,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,h4,h7,h12,h13])).
% 0.19/0.38 thf(10,plain,$false,inference(tab_negimp,[status(thm),assumptions([h14,h12,h13,h11,h9,h10,h7,h8,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h15,h16])],[h14,9,h15,h16])).
% 0.19/0.38 thf(11,plain,$false,inference(tab_negall,[status(thm),assumptions([h12,h13,h11,h9,h10,h7,h8,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h14]),tab_negall(eigenvar,eigen__3)],[h10,10,h14])).
% 0.19/0.38 thf(12,plain,$false,inference(tab_negimp,[status(thm),assumptions([h11,h9,h10,h7,h8,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h12,h13])],[h11,11,h12,h13])).
% 0.19/0.38 thf(13,plain,$false,inference(tab_negall,[status(thm),assumptions([h9,h10,h7,h8,h6,h4,h2,h3,h1,h0]),tab_negall(discharge,[h11]),tab_negall(eigenvar,eigen__2)],[h9,12,h11])).
% 0.19/0.38 thf(14,plain,$false,inference(tab_negimp,[status(thm),assumptions([h7,h8,h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h9,h10])],[h8,13,h9,h10])).
% 0.19/0.38 thf(15,plain,$false,inference(tab_negimp,[status(thm),assumptions([h6,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,14,h7,h8])).
% 0.19/0.38 thf(16,plain,$false,inference(tab_negall,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__1)],[h3,15,h6])).
% 0.19/0.38 thf(h17,assumption,(~((sP12 => ((~((![X1:$i]:(((rel_s4 @ eigen__4) @ X1) => (p @ X1))))) => (![X1:$i]:(((rel_s4 @ eigen__4) @ X1) => (q @ X1))))))),introduced(assumption,[])).
% 0.19/0.38 thf(h18,assumption,sP12,introduced(assumption,[])).
% 0.19/0.38 thf(h19,assumption,(~(((~((![X1:$i]:(((rel_s4 @ eigen__4) @ X1) => (p @ X1))))) => (![X1:$i]:(((rel_s4 @ eigen__4) @ X1) => (q @ X1)))))),introduced(assumption,[])).
% 0.19/0.38 thf(h20,assumption,(~((![X1:$i]:(((rel_s4 @ eigen__4) @ X1) => (p @ X1))))),introduced(assumption,[])).
% 0.19/0.38 thf(h21,assumption,(~((![X1:$i]:(((rel_s4 @ eigen__4) @ X1) => (q @ X1))))),introduced(assumption,[])).
% 0.19/0.38 thf(h22,assumption,(~((((rel_s4 @ eigen__4) @ eigen__5) => (p @ eigen__5)))),introduced(assumption,[])).
% 0.19/0.38 thf(h23,assumption,((rel_s4 @ eigen__4) @ eigen__5),introduced(assumption,[])).
% 0.19/0.38 thf(h24,assumption,(~((p @ eigen__5))),introduced(assumption,[])).
% 0.19/0.38 thf(h25,assumption,(~((sP16 => sP5))),introduced(assumption,[])).
% 0.19/0.38 thf(h26,assumption,sP16,introduced(assumption,[])).
% 0.19/0.38 thf(h27,assumption,(~(sP5)),introduced(assumption,[])).
% 0.19/0.38 thf(17,plain,(~(sP17) | sP7),inference(all_rule,[status(thm)],[])).
% 0.19/0.38 thf(18,plain,((~(sP7) | sP13) | sP6),inference(prop_rule,[status(thm)],[])).
% 0.19/0.38 thf(19,plain,((~(sP13) | ~(sP12)) | ~(sP16)),inference(prop_rule,[status(thm)],[])).
% 0.19/0.38 thf(20,plain,(~(sP3) | sP14),inference(all_rule,[status(thm)],[])).
% 0.19/0.38 thf(21,plain,(~(sP14) | sP17),inference(all_rule,[status(thm)],[])).
% 0.19/0.38 thf(22,plain,(~(sP8) | sP2),inference(all_rule,[status(thm)],[])).
% 0.19/0.38 thf(23,plain,((~(sP2) | ~(sP6)) | sP5),inference(prop_rule,[status(thm)],[])).
% 0.19/0.38 thf(24,plain,$false,inference(prop_unsat,[status(thm),assumptions([h26,h27,h25,h23,h24,h22,h20,h21,h18,h19,h17,h5,h2,h3,h1,h0])],[17,18,19,20,21,22,23,8,h5,h18,h26,h27])).
% 0.19/0.38 thf(25,plain,$false,inference(tab_negimp,[status(thm),assumptions([h25,h23,h24,h22,h20,h21,h18,h19,h17,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h26,h27])],[h25,24,h26,h27])).
% 0.19/0.38 thf(26,plain,$false,inference(tab_negall,[status(thm),assumptions([h23,h24,h22,h20,h21,h18,h19,h17,h5,h2,h3,h1,h0]),tab_negall(discharge,[h25]),tab_negall(eigenvar,eigen__6)],[h21,25,h25])).
% 0.19/0.38 thf(27,plain,$false,inference(tab_negimp,[status(thm),assumptions([h22,h20,h21,h18,h19,h17,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h23,h24])],[h22,26,h23,h24])).
% 0.19/0.38 thf(28,plain,$false,inference(tab_negall,[status(thm),assumptions([h20,h21,h18,h19,h17,h5,h2,h3,h1,h0]),tab_negall(discharge,[h22]),tab_negall(eigenvar,eigen__5)],[h20,27,h22])).
% 0.19/0.38 thf(29,plain,$false,inference(tab_negimp,[status(thm),assumptions([h18,h19,h17,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h20,h21])],[h19,28,h20,h21])).
% 0.19/0.38 thf(30,plain,$false,inference(tab_negimp,[status(thm),assumptions([h17,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h18,h19])],[h17,29,h18,h19])).
% 0.19/0.38 thf(31,plain,$false,inference(tab_negall,[status(thm),assumptions([h5,h2,h3,h1,h0]),tab_negall(discharge,[h17]),tab_negall(eigenvar,eigen__4)],[h3,30,h17])).
% 0.19/0.38 thf(32,plain,$false,inference(tab_imp,[status(thm),assumptions([h2,h3,h1,h0]),tab_imp(discharge,[h4]),tab_imp(discharge,[h5])],[h2,16,31,h4,h5])).
% 0.19/0.38 thf(33,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,32,h2,h3])).
% 0.19/0.38 thf(34,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,33,h1])).
% 0.19/0.38 thf(0,theorem,(![X1:$i]:((~((~(((~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (p @ X2))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (q @ X2)))))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => ((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (p @ X3))))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (q @ X3)))))))),inference(contra,[status(thm),contra(discharge,[h0])],[34,h0])).
% 0.19/0.38 % SZS output end Proof
%------------------------------------------------------------------------------