TSTP Solution File: SWV061^7 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SWV061^7 : 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 : n012.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 : Wed Jul 20 21:23:34 EDT 2022
% Result : Theorem 24.14s 23.52s
% Output : Proof 24.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWV061^7 : TPTP v8.1.0. Released v5.5.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jun 15 09:34:10 EDT 2022
% 0.13/0.35 % CPUTime :
% 24.14/23.52 % SZS status Theorem
% 24.14/23.52 % Mode: mode84:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=2.:SINE_DEPTH=0
% 24.14/23.52 % Inferences: 156
% 24.14/23.52 % SZS output start Proof
% 24.14/23.52 thf(ty_mu, type, mu : $tType).
% 24.14/23.52 thf(ty_eigen__6, type, eigen__6 : $i).
% 24.14/23.52 thf(ty_rel_s4, type, rel_s4 : ($i>$i>$o)).
% 24.14/23.52 thf(ty_eigen__2, type, eigen__2 : $i).
% 24.14/23.52 thf(ty_gt, type, gt : (mu>mu>$i>$o)).
% 24.14/23.52 thf(ty_eigen__4, type, eigen__4 : $i).
% 24.14/23.52 thf(ty_eigen__3, type, eigen__3 : $i).
% 24.14/23.52 thf(ty_n1, type, n1 : mu).
% 24.14/23.52 thf(ty_loopcounter, type, loopcounter : mu).
% 24.14/23.52 thf(ty_true, type, true : ($i>$o)).
% 24.14/23.52 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])).
% 24.14/23.52 thf(eigendef_eigen__3, definition, eigen__3 = (eps__0 @ (^[X1:$i]:(~((((rel_s4 @ eigen__2) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (true @ X2))) => (~(((![X2:$i]:(((rel_s4 @ X1) @ X2) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((gt @ loopcounter) @ n1) @ X4))))))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (true @ X3)))))) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((gt @ loopcounter) @ n1) @ X3))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (true @ X3))))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__3])])).
% 24.14/23.52 thf(eigendef_eigen__6, definition, eigen__6 = (eps__0 @ (^[X1:$i]:(~((((rel_s4 @ eigen__3) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((gt @ loopcounter) @ n1) @ X3))))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (true @ X2))))))))), introduced(definition,[new_symbols(definition,[eigen__6])])).
% 24.14/23.52 thf(eigendef_eigen__2, definition, eigen__2 = (eps__0 @ (^[X1:$i]:(~((![X2:$i]:(((rel_s4 @ X1) @ X2) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (true @ X3))) => (~(((![X3:$i]:(((rel_s4 @ X2) @ X3) => ((![X4:$i]:(((rel_s4 @ X3) @ X4) => (~((![X5:$i]:(((rel_s4 @ X4) @ X5) => (((gt @ loopcounter) @ n1) @ X5))))))) => (![X4:$i]:(((rel_s4 @ X3) @ X4) => (true @ X4)))))) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => ((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((gt @ loopcounter) @ n1) @ X4))) => (![X4:$i]:(((rel_s4 @ X3) @ X4) => (true @ X4)))))))))))))))))), introduced(definition,[new_symbols(definition,[eigen__2])])).
% 24.14/23.52 thf(eigendef_eigen__4, definition, eigen__4 = (eps__0 @ (^[X1:$i]:(~((((rel_s4 @ eigen__3) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((gt @ loopcounter) @ n1) @ X2))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (true @ X2))))))))), introduced(definition,[new_symbols(definition,[eigen__4])])).
% 24.14/23.52 thf(sP1,plain,sP1 <=> (![X1:$i]:(((rel_s4 @ eigen__4) @ X1) => (true @ X1))),introduced(definition,[new_symbols(definition,[sP1])])).
% 24.14/23.52 thf(sP2,plain,sP2 <=> ((![X1:$i]:(((rel_s4 @ eigen__3) @ X1) => (true @ X1))) => (~(((![X1:$i]:(((rel_s4 @ eigen__3) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((gt @ loopcounter) @ n1) @ X3))))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (true @ X2)))))) => (~((![X1:$i]:(((rel_s4 @ eigen__3) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((gt @ loopcounter) @ n1) @ X2))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (true @ X2)))))))))))),introduced(definition,[new_symbols(definition,[sP2])])).
% 24.14/23.52 thf(sP3,plain,sP3 <=> (![X1:$i]:(((rel_s4 @ eigen__3) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((gt @ loopcounter) @ n1) @ X3))))))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (true @ X2)))))),introduced(definition,[new_symbols(definition,[sP3])])).
% 24.14/23.52 thf(sP4,plain,sP4 <=> (![X1:$i]:(((rel_s4 @ eigen__3) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((gt @ loopcounter) @ n1) @ X2))) => (![X2:$i]:(((rel_s4 @ X1) @ X2) => (true @ X2)))))),introduced(definition,[new_symbols(definition,[sP4])])).
% 24.14/23.52 thf(sP5,plain,sP5 <=> (((rel_s4 @ eigen__3) @ eigen__4) => ((![X1:$i]:(((rel_s4 @ eigen__4) @ X1) => (((gt @ loopcounter) @ n1) @ X1))) => sP1)),introduced(definition,[new_symbols(definition,[sP5])])).
% 24.14/23.52 thf(sP6,plain,sP6 <=> (![X1:$i]:(![X2:$i]:(((rel_s4 @ X1) @ X2) => (true @ X2)))),introduced(definition,[new_symbols(definition,[sP6])])).
% 24.14/23.52 thf(sP7,plain,sP7 <=> (((rel_s4 @ eigen__3) @ eigen__6) => ((![X1:$i]:(((rel_s4 @ eigen__6) @ X1) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((gt @ loopcounter) @ n1) @ X2))))))) => (![X1:$i]:(((rel_s4 @ eigen__6) @ X1) => (true @ X1))))),introduced(definition,[new_symbols(definition,[sP7])])).
% 24.14/23.52 thf(sP8,plain,sP8 <=> (![X1:$i]:(((rel_s4 @ eigen__2) @ X1) => ((![X2:$i]:(((rel_s4 @ X1) @ X2) => (true @ X2))) => (~(((![X2:$i]:(((rel_s4 @ X1) @ X2) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((gt @ loopcounter) @ n1) @ X4))))))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (true @ X3)))))) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (((gt @ loopcounter) @ n1) @ X3))) => (![X3:$i]:(((rel_s4 @ X2) @ X3) => (true @ X3)))))))))))))),introduced(definition,[new_symbols(definition,[sP8])])).
% 24.14/23.52 thf(sP9,plain,sP9 <=> (((rel_s4 @ eigen__2) @ eigen__3) => sP2),introduced(definition,[new_symbols(definition,[sP9])])).
% 24.14/23.52 thf(sP10,plain,sP10 <=> (![X1:$i]:(((rel_s4 @ eigen__6) @ X1) => (true @ X1))),introduced(definition,[new_symbols(definition,[sP10])])).
% 24.14/23.52 thf(sP11,plain,sP11 <=> (sP3 => (~(sP4))),introduced(definition,[new_symbols(definition,[sP11])])).
% 24.14/23.52 thf(sP12,plain,sP12 <=> ((![X1:$i]:(((rel_s4 @ eigen__6) @ X1) => (~((![X2:$i]:(((rel_s4 @ X1) @ X2) => (((gt @ loopcounter) @ n1) @ X2))))))) => sP10),introduced(definition,[new_symbols(definition,[sP12])])).
% 24.14/23.52 thf(sP13,plain,sP13 <=> (![X1:$i]:(![X2:$i]:(((rel_s4 @ X1) @ X2) => ((![X3:$i]:(((rel_s4 @ X2) @ X3) => (true @ X3))) => (~(((![X3:$i]:(((rel_s4 @ X2) @ X3) => ((![X4:$i]:(((rel_s4 @ X3) @ X4) => (~((![X5:$i]:(((rel_s4 @ X4) @ X5) => (((gt @ loopcounter) @ n1) @ X5))))))) => (![X4:$i]:(((rel_s4 @ X3) @ X4) => (true @ X4)))))) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => ((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((gt @ loopcounter) @ n1) @ X4))) => (![X4:$i]:(((rel_s4 @ X3) @ X4) => (true @ X4))))))))))))))),introduced(definition,[new_symbols(definition,[sP13])])).
% 24.14/23.52 thf(sP14,plain,sP14 <=> ((![X1:$i]:(((rel_s4 @ eigen__4) @ X1) => (((gt @ loopcounter) @ n1) @ X1))) => sP1),introduced(definition,[new_symbols(definition,[sP14])])).
% 24.14/23.52 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))).
% 24.14/23.52 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))).
% 24.14/23.52 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))).
% 24.14/23.52 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))).
% 24.14/23.52 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:(((exists_in_world @ X3) @ X2) => ((X1 @ X3) @ X2))))))).
% 24.14/23.52 thf(def_mvalid,definition,(mvalid = (!!))).
% 24.14/23.52 thf(def_mbox_s4,definition,(mbox_s4 = (^[X1:$i>$o]:(^[X2:$i]:(![X3:$i]:(((rel_s4 @ X2) @ X3) => (X1 @ X3))))))).
% 24.14/23.52 thf(cl5_nebula_array_0002,conjecture,(![X1:$i]:(![X2:$i]:(((rel_s4 @ X1) @ X2) => ((~((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (true @ X3))))))) => (~(((~((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => ((~((~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (~((![X5:$i]:(((rel_s4 @ X4) @ X5) => (((gt @ loopcounter) @ n1) @ X5))))))))))) => (![X4:$i]:(((rel_s4 @ X3) @ X4) => (true @ X4)))))))))) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => ((~((~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((gt @ loopcounter) @ n1) @ X4))))))) => (![X4:$i]:(((rel_s4 @ X3) @ X4) => (true @ X4)))))))))))))))).
% 24.14/23.52 thf(h1,negated_conjecture,(~(sP13)),inference(assume_negation,[status(cth)],[cl5_nebula_array_0002])).
% 24.14/23.52 thf(1,plain,(~(sP6) | sP10),inference(all_rule,[status(thm)],[])).
% 24.14/23.52 thf(2,plain,(~(sP6) | sP1),inference(all_rule,[status(thm)],[])).
% 24.14/23.52 thf(3,plain,(sP12 | ~(sP10)),inference(prop_rule,[status(thm)],[])).
% 24.14/23.52 thf(4,plain,(sP7 | ~(sP12)),inference(prop_rule,[status(thm)],[])).
% 24.14/23.52 thf(5,plain,(sP3 | ~(sP7)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__6])).
% 24.14/23.52 thf(6,plain,(sP14 | ~(sP1)),inference(prop_rule,[status(thm)],[])).
% 24.14/23.52 thf(7,plain,(sP5 | ~(sP14)),inference(prop_rule,[status(thm)],[])).
% 24.14/23.52 thf(8,plain,(sP4 | ~(sP5)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4])).
% 24.14/23.52 thf(9,plain,((~(sP11) | ~(sP3)) | ~(sP4)),inference(prop_rule,[status(thm)],[])).
% 24.14/23.52 thf(10,plain,(sP2 | sP11),inference(prop_rule,[status(thm)],[])).
% 24.14/23.52 thf(11,plain,(sP9 | ~(sP2)),inference(prop_rule,[status(thm)],[])).
% 24.14/23.52 thf(12,plain,(sP8 | ~(sP9)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3])).
% 24.14/23.52 thf(13,plain,(sP13 | ~(sP8)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__2])).
% 24.14/23.52 thf(ttrue,axiom,(mvalid @ (mbox_s4 @ true))).
% 24.14/23.52 thf(14,plain,sP6,inference(preprocess,[status(thm)],[ttrue]).
% 24.14/23.52 thf(15,plain,$false,inference(prop_unsat,[status(thm),assumptions([h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,h1])).
% 24.14/23.52 thf(16,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[15,h0])).
% 24.14/23.52 thf(0,theorem,(![X1:$i]:(![X2:$i]:(((rel_s4 @ X1) @ X2) => ((~((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => (true @ X3))))))) => (~(((~((~((![X3:$i]:(((rel_s4 @ X2) @ X3) => ((~((~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (~((![X5:$i]:(((rel_s4 @ X4) @ X5) => (((gt @ loopcounter) @ n1) @ X5))))))))))) => (![X4:$i]:(((rel_s4 @ X3) @ X4) => (true @ X4)))))))))) => (~((![X3:$i]:(((rel_s4 @ X2) @ X3) => ((~((~((![X4:$i]:(((rel_s4 @ X3) @ X4) => (((gt @ loopcounter) @ n1) @ X4))))))) => (![X4:$i]:(((rel_s4 @ X3) @ X4) => (true @ X4))))))))))))))),inference(contra,[status(thm),contra(discharge,[h1])],[15,h1])).
% 24.14/23.52 % SZS output end Proof
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