TSTP Solution File: LCL623^1 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : LCL623^1 : TPTP v8.1.0. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n020.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 14:09:08 EDT 2022
% Result : Theorem 1.25s 1.46s
% Output : Proof 1.25s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : LCL623^1 : TPTP v8.1.0. Bugfixed v7.3.0.
% 0.08/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.15/0.35 % Computer : n020.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Mon Jul 4 11:03:44 EDT 2022
% 0.15/0.36 % CPUTime :
% 1.25/1.46 % SZS status Theorem
% 1.25/1.46 % Mode: mode213
% 1.25/1.46 % Inferences: 1152
% 1.25/1.46 % SZS output start Proof
% 1.25/1.46 thf(ty_eigen__2, type, eigen__2 : $i).
% 1.25/1.46 thf(ty_eigen__1, type, eigen__1 : $i).
% 1.25/1.46 thf(ty_eigen__0, type, eigen__0 : ($i>$o)).
% 1.25/1.46 thf(ty_r, type, r : ($i>$i>$o)).
% 1.25/1.46 thf(sP1,plain,sP1 <=> ((r @ eigen__1) @ eigen__2),introduced(definition,[new_symbols(definition,[sP1])])).
% 1.25/1.46 thf(sP2,plain,sP2 <=> (sP1 => (eigen__0 @ eigen__2)),introduced(definition,[new_symbols(definition,[sP2])])).
% 1.25/1.46 thf(sP3,plain,sP3 <=> ((![X1:$i]:(((r @ eigen__1) @ X1) => ((![X2:$i]:(((r @ X1) @ X2) => (eigen__0 @ X2))) => (eigen__0 @ X1)))) => (![X1:$i]:(((r @ eigen__1) @ X1) => (eigen__0 @ X1)))),introduced(definition,[new_symbols(definition,[sP3])])).
% 1.25/1.46 thf(sP4,plain,sP4 <=> (![X1:$i]:(((r @ eigen__1) @ X1) => ((![X2:$i]:(((r @ X1) @ X2) => (eigen__0 @ X2))) => (eigen__0 @ X1)))),introduced(definition,[new_symbols(definition,[sP4])])).
% 1.25/1.46 thf(sP5,plain,sP5 <=> (eigen__0 @ eigen__2),introduced(definition,[new_symbols(definition,[sP5])])).
% 1.25/1.46 thf(sP6,plain,sP6 <=> (![X1:$i]:(((r @ eigen__1) @ X1) => (eigen__0 @ X1))),introduced(definition,[new_symbols(definition,[sP6])])).
% 1.25/1.46 thf(sP7,plain,sP7 <=> (![X1:$i>$o]:(![X2:$i]:((![X3:$i]:(((r @ X2) @ X3) => ((![X4:$i]:(((r @ X3) @ X4) => (X1 @ X4))) => (X1 @ X3)))) => (![X3:$i]:(((r @ X2) @ X3) => (X1 @ X3)))))),introduced(definition,[new_symbols(definition,[sP7])])).
% 1.25/1.46 thf(sP8,plain,sP8 <=> (![X1:$i]:((![X2:$i]:(((r @ X1) @ X2) => ((![X3:$i]:(((r @ X2) @ X3) => (eigen__0 @ X3))) => (eigen__0 @ X2)))) => (![X2:$i]:(((r @ X1) @ X2) => (eigen__0 @ X2))))),introduced(definition,[new_symbols(definition,[sP8])])).
% 1.25/1.46 thf(def_mfalse,definition,(mfalse = (^[X1:$i]:$false))).
% 1.25/1.46 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))).
% 1.25/1.46 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))).
% 1.25/1.46 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))).
% 1.25/1.46 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))).
% 1.25/1.46 thf(def_mimpl,definition,(mimpl = (^[X1:$i>$o]:(mor @ (mnot @ X1))))).
% 1.25/1.46 thf(def_miff,definition,(miff = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimpl @ X1) @ X2)) @ ((mimpl @ X2) @ X1)))))).
% 1.25/1.46 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))).
% 1.25/1.46 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~((![X4:$i]:(((X1 @ X3) @ X4) => (~((X2 @ X4)))))))))))).
% 1.25/1.46 thf(def_mall,definition,(mall = (^[X1:individuals>$i>$o]:(^[X2:$i]:(![X3:individuals]:((X1 @ X3) @ X2)))))).
% 1.25/1.46 thf(def_mexists,definition,(mexists = (^[X1:individuals>$i>$o]:(^[X2:$i]:(~((![X3:individuals]:(~(((X1 @ X3) @ X2)))))))))).
% 1.25/1.46 thf(def_mvalid,definition,(mvalid = (!!))).
% 1.25/1.46 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))).
% 1.25/1.46 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))).
% 1.25/1.46 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))).
% 1.25/1.46 thf(loeb,conjecture,(![X1:$i>$o]:(![X2:$i]:((~((~((![X3:$i]:(((r @ X2) @ X3) => ((~((~((![X4:$i]:(((r @ X3) @ X4) => (X1 @ X4))))))) => (X1 @ X3)))))))) => (![X3:$i]:(((r @ X2) @ X3) => (X1 @ X3))))))).
% 1.25/1.46 thf(h0,negated_conjecture,(~(sP7)),inference(assume_negation,[status(cth)],[loeb])).
% 1.25/1.46 thf(h1,assumption,(~(sP8)),introduced(assumption,[])).
% 1.25/1.46 thf(h2,assumption,(~(sP3)),introduced(assumption,[])).
% 1.25/1.46 thf(h3,assumption,sP4,introduced(assumption,[])).
% 1.25/1.46 thf(h4,assumption,(~(sP6)),introduced(assumption,[])).
% 1.25/1.46 thf(h5,assumption,(~(sP2)),introduced(assumption,[])).
% 1.25/1.46 thf(h6,assumption,sP1,introduced(assumption,[])).
% 1.25/1.46 thf(h7,assumption,(~(sP5)),introduced(assumption,[])).
% 1.25/1.46 thf(1,plain,(~(sP6) | sP2),inference(all_rule,[status(thm)],[])).
% 1.25/1.46 thf(2,plain,((~(sP2) | ~(sP1)) | sP5),inference(prop_rule,[status(thm)],[])).
% 1.25/1.46 thf(3,plain,(~(sP8) | sP3),inference(all_rule,[status(thm)],[])).
% 1.25/1.46 thf(4,plain,((~(sP3) | ~(sP4)) | sP6),inference(prop_rule,[status(thm)],[])).
% 1.25/1.46 thf(5,plain,(~(sP7) | sP8),inference(all_rule,[status(thm)],[])).
% 1.25/1.46 thf(gl,axiom,(![X1:$i>$o]:(mvalid @ ((mimpl @ ((mbox @ r) @ ((mimpl @ ((mbox @ r) @ X1)) @ X1))) @ ((mbox @ r) @ X1))))).
% 1.25/1.46 thf(6,plain,sP7,inference(preprocess,[status(thm)],[gl]).
% 1.25/1.46 thf(7,plain,$false,inference(prop_unsat,[status(thm),assumptions([h6,h7,h5,h3,h4,h2,h1,h0])],[1,2,3,4,5,6,h3,h6,h7])).
% 1.25/1.46 thf(8,plain,$false,inference(tab_negimp,[status(thm),assumptions([h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,7,h6,h7])).
% 1.25/1.46 thf(9,plain,$false,inference(tab_negall,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__2)],[h4,8,h5])).
% 1.25/1.46 thf(10,plain,$false,inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,9,h3,h4])).
% 1.25/1.46 thf(11,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,10,h2])).
% 1.25/1.46 thf(12,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,11,h1])).
% 1.25/1.46 thf(0,theorem,(![X1:$i>$o]:(![X2:$i]:((~((~((![X3:$i]:(((r @ X2) @ X3) => ((~((~((![X4:$i]:(((r @ X3) @ X4) => (X1 @ X4))))))) => (X1 @ X3)))))))) => (![X3:$i]:(((r @ X2) @ X3) => (X1 @ X3)))))),inference(contra,[status(thm),contra(discharge,[h0])],[12,h0])).
% 1.25/1.46 % SZS output end Proof
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