TSTP Solution File: LCL944^8 by Satallax---3.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : LCL944^8 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n011.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 14:12:07 EDT 2022
% Result : Theorem 8.34s 8.76s
% Output : Proof 8.34s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL944^8 : TPTP v8.1.0. Released v8.1.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n011.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 : Mon Jul 4 23:58:52 EDT 2022
% 0.13/0.34 % CPUTime :
% 8.34/8.76 % SZS status Theorem
% 8.34/8.76 % Mode: mode8a:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=16:SINE_RANK_LIMIT=3.:SINE_DEPTH=0
% 8.34/8.76 % Inferences: 8450
% 8.34/8.76 % SZS output start Proof
% 8.34/8.76 thf(ty_mworld, type, mworld : $tType).
% 8.34/8.76 thf(ty_r4, type, r4 : (mworld>$o)).
% 8.34/8.76 thf(ty_eiw_di, type, eiw_di : ($i>mworld>$o)).
% 8.34/8.76 thf(ty_modus_tollens, type, modus_tollens : (mworld>$o)).
% 8.34/8.76 thf(ty_and_3, type, and_3 : (mworld>$o)).
% 8.34/8.76 thf(ty_and_1, type, and_1 : (mworld>$o)).
% 8.34/8.76 thf(ty_or_3, type, or_3 : (mworld>$o)).
% 8.34/8.76 thf(ty_r3, type, r3 : (mworld>$o)).
% 8.34/8.76 thf(ty_or_2, type, or_2 : (mworld>$o)).
% 8.34/8.76 thf(ty_and_2, type, and_2 : (mworld>$o)).
% 8.34/8.76 thf(ty_or, type, or : ($i>$i>$i)).
% 8.34/8.76 thf(ty_eigen__0, type, eigen__0 : mworld).
% 8.34/8.76 thf(ty_is_a_theorem, type, is_a_theorem : ($i>mworld>$o)).
% 8.34/8.76 thf(ty_kn1, type, kn1 : (mworld>$o)).
% 8.34/8.76 thf(ty_cn3, type, cn3 : (mworld>$o)).
% 8.34/8.76 thf(ty_and, type, and : ($i>$i>$i)).
% 8.34/8.76 thf(ty_implies, type, implies : ($i>$i>$i)).
% 8.34/8.76 thf(ty_or_1, type, or_1 : (mworld>$o)).
% 8.34/8.76 thf(ty_mrel, type, mrel : (mworld>mworld>$o)).
% 8.34/8.76 thf(ty_r5, type, r5 : (mworld>$o)).
% 8.34/8.76 thf(ty_r1, type, r1 : (mworld>$o)).
% 8.34/8.76 thf(ty_r2, type, r2 : (mworld>$o)).
% 8.34/8.76 thf(ty_mactual, type, mactual : mworld).
% 8.34/8.76 thf(ty_kn3, type, kn3 : (mworld>$o)).
% 8.34/8.76 thf(ty_kn2, type, kn2 : (mworld>$o)).
% 8.34/8.76 thf(ty_cn2, type, cn2 : (mworld>$o)).
% 8.34/8.76 thf(ty_not, type, not : ($i>$i)).
% 8.34/8.76 thf(sP1,plain,sP1 <=> (![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => ((is_a_theorem @ ((implies @ X5) @ ((or @ X3) @ X5))) @ X6))))))))))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (r2 @ X2)))))),introduced(definition,[new_symbols(definition,[sP1])])).
% 8.34/8.76 thf(sP2,plain,sP2 <=> (((mrel @ mactual) @ eigen__0) => (r2 @ eigen__0)),introduced(definition,[new_symbols(definition,[sP2])])).
% 8.34/8.76 thf(sP3,plain,sP3 <=> (![X1:mworld]:(((mrel @ mactual) @ X1) => (r2 @ X1))),introduced(definition,[new_symbols(definition,[sP3])])).
% 8.34/8.76 thf(sP4,plain,sP4 <=> (r2 @ eigen__0),introduced(definition,[new_symbols(definition,[sP4])])).
% 8.34/8.76 thf(sP5,plain,sP5 <=> (![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (or_2 @ X2))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => ((is_a_theorem @ ((implies @ X5) @ ((or @ X3) @ X5))) @ X6)))))))))))))),introduced(definition,[new_symbols(definition,[sP5])])).
% 8.34/8.76 thf(sP6,plain,sP6 <=> (![X1:mworld]:(((mrel @ mactual) @ X1) => (![X2:$i]:(((eiw_di @ X2) @ X1) => (![X3:mworld]:(((mrel @ X1) @ X3) => (![X4:$i]:(((eiw_di @ X4) @ X3) => (![X5:mworld]:(((mrel @ X3) @ X5) => ((is_a_theorem @ ((implies @ X4) @ ((or @ X2) @ X4))) @ X5))))))))))),introduced(definition,[new_symbols(definition,[sP6])])).
% 8.34/8.76 thf(sP7,plain,sP7 <=> (![X1:mworld]:(((mrel @ mactual) @ X1) => (or_2 @ X1))),introduced(definition,[new_symbols(definition,[sP7])])).
% 8.34/8.76 thf(sP8,plain,sP8 <=> (sP6 => sP3),introduced(definition,[new_symbols(definition,[sP8])])).
% 8.34/8.76 thf(sP9,plain,sP9 <=> (sP7 => sP6),introduced(definition,[new_symbols(definition,[sP9])])).
% 8.34/8.76 thf(sP10,plain,sP10 <=> (![X1:mworld]:((mrel @ X1) @ X1)),introduced(definition,[new_symbols(definition,[sP10])])).
% 8.34/8.76 thf(sP11,plain,sP11 <=> (((mrel @ mactual) @ mactual) => sP8),introduced(definition,[new_symbols(definition,[sP11])])).
% 8.34/8.76 thf(sP12,plain,sP12 <=> ((mrel @ mactual) @ mactual),introduced(definition,[new_symbols(definition,[sP12])])).
% 8.34/8.76 thf(sP13,plain,sP13 <=> (sP12 => sP9),introduced(definition,[new_symbols(definition,[sP13])])).
% 8.34/8.76 thf(sP14,plain,sP14 <=> ((mrel @ mactual) @ eigen__0),introduced(definition,[new_symbols(definition,[sP14])])).
% 8.34/8.76 thf(def_mlocal,definition,(mlocal = (^[X1:mworld>$o]:(X1 @ mactual)))).
% 8.34/8.76 thf(def_mand,definition,(mand = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))).
% 8.34/8.76 thf(def_mimplies,definition,(mimplies = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((X1 @ X3) => (X2 @ X3))))))).
% 8.34/8.76 thf(def_mbox,definition,(mbox = (^[X1:mworld>$o]:(^[X2:mworld]:(![X3:mworld]:(((mrel @ X2) @ X3) => (X1 @ X3))))))).
% 8.34/8.76 thf(def_mforall_di,definition,(mforall_di = (^[X1:$i>mworld>$o]:(^[X2:mworld]:(![X3:$i]:(((eiw_di @ X3) @ X2) => ((X1 @ X3) @ X2))))))).
% 8.34/8.76 thf(principia_r2,conjecture,sP3).
% 8.34/8.76 thf(h0,negated_conjecture,(~(sP3)),inference(assume_negation,[status(cth)],[principia_r2])).
% 8.34/8.76 thf(h1,assumption,(~(sP2)),introduced(assumption,[])).
% 8.34/8.76 thf(h2,assumption,sP14,introduced(assumption,[])).
% 8.34/8.76 thf(h3,assumption,(~(sP4)),introduced(assumption,[])).
% 8.34/8.76 thf(h4,assumption,(![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (r5 @ X2))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => (![X7:$i]:(((eiw_di @ X7) @ X6) => (![X8:mworld]:(((mrel @ X6) @ X8) => ((is_a_theorem @ ((implies @ ((implies @ X5) @ X7)) @ ((implies @ ((or @ X3) @ X5)) @ ((or @ X3) @ X7)))) @ X8)))))))))))))))))),introduced(assumption,[])).
% 8.34/8.76 thf(h5,assumption,(![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => (![X7:$i]:(((eiw_di @ X7) @ X6) => (![X8:mworld]:(((mrel @ X6) @ X8) => ((is_a_theorem @ ((implies @ ((implies @ X5) @ X7)) @ ((implies @ ((or @ X3) @ X5)) @ ((or @ X3) @ X7)))) @ X8))))))))))))))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (r5 @ X2)))))),introduced(assumption,[])).
% 8.34/8.76 thf(h6,assumption,(![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (r4 @ X2))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => (![X7:$i]:(((eiw_di @ X7) @ X6) => (![X8:mworld]:(((mrel @ X6) @ X8) => ((is_a_theorem @ ((implies @ ((or @ X3) @ ((or @ X5) @ X7))) @ ((or @ X5) @ ((or @ X3) @ X7)))) @ X8)))))))))))))))))),introduced(assumption,[])).
% 8.34/8.76 thf(h7,assumption,(![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => (![X7:$i]:(((eiw_di @ X7) @ X6) => (![X8:mworld]:(((mrel @ X6) @ X8) => ((is_a_theorem @ ((implies @ ((or @ X3) @ ((or @ X5) @ X7))) @ ((or @ X5) @ ((or @ X3) @ X7)))) @ X8))))))))))))))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (r4 @ X2)))))),introduced(assumption,[])).
% 8.34/8.76 thf(h8,assumption,(![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (r3 @ X2))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => ((is_a_theorem @ ((implies @ ((or @ X3) @ X5)) @ ((or @ X5) @ X3))) @ X6)))))))))))))),introduced(assumption,[])).
% 8.34/8.76 thf(h9,assumption,(![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => ((is_a_theorem @ ((implies @ ((or @ X3) @ X5)) @ ((or @ X5) @ X3))) @ X6))))))))))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (r3 @ X2)))))),introduced(assumption,[])).
% 8.34/8.76 thf(h10,assumption,(![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (r2 @ X2))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => ((is_a_theorem @ ((implies @ X5) @ ((or @ X3) @ X5))) @ X6)))))))))))))),introduced(assumption,[])).
% 8.34/8.76 thf(h11,assumption,sP1,introduced(assumption,[])).
% 8.34/8.76 thf(h12,assumption,(![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (r1 @ X2))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => ((is_a_theorem @ ((implies @ ((or @ X3) @ X3)) @ X3)) @ X4)))))))))),introduced(assumption,[])).
% 8.34/8.76 thf(h13,assumption,(![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => ((is_a_theorem @ ((implies @ ((or @ X3) @ X3)) @ X3)) @ X4))))))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (r1 @ X2)))))),introduced(assumption,[])).
% 8.34/8.76 thf(h14,assumption,(![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (cn3 @ X2))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => ((is_a_theorem @ ((implies @ ((implies @ (not @ X3)) @ X3)) @ X3)) @ X4)))))))))),introduced(assumption,[])).
% 8.34/8.76 thf(h15,assumption,(![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => ((is_a_theorem @ ((implies @ ((implies @ (not @ X3)) @ X3)) @ X3)) @ X4))))))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (cn3 @ X2)))))),introduced(assumption,[])).
% 8.34/8.76 thf(h16,assumption,(![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (cn2 @ X2))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => ((is_a_theorem @ ((implies @ X3) @ ((implies @ (not @ X3)) @ X5))) @ X6)))))))))))))),introduced(assumption,[])).
% 8.34/8.76 thf(h17,assumption,(![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => ((is_a_theorem @ ((implies @ X3) @ ((implies @ (not @ X3)) @ X5))) @ X6))))))))))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (cn2 @ X2)))))),introduced(assumption,[])).
% 8.34/8.76 thf(h18,assumption,(![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (kn3 @ X2))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => (![X7:$i]:(((eiw_di @ X7) @ X6) => (![X8:mworld]:(((mrel @ X6) @ X8) => ((is_a_theorem @ ((implies @ ((implies @ X3) @ X5)) @ ((implies @ (not @ ((and @ X5) @ X7))) @ (not @ ((and @ X7) @ X3))))) @ X8)))))))))))))))))),introduced(assumption,[])).
% 8.34/8.76 thf(h19,assumption,(![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => (![X7:$i]:(((eiw_di @ X7) @ X6) => (![X8:mworld]:(((mrel @ X6) @ X8) => ((is_a_theorem @ ((implies @ ((implies @ X3) @ X5)) @ ((implies @ (not @ ((and @ X5) @ X7))) @ (not @ ((and @ X7) @ X3))))) @ X8))))))))))))))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (kn3 @ X2)))))),introduced(assumption,[])).
% 8.34/8.76 thf(h20,assumption,(![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (kn2 @ X2))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => ((is_a_theorem @ ((implies @ ((and @ X3) @ X5)) @ X3)) @ X6)))))))))))))),introduced(assumption,[])).
% 8.34/8.76 thf(h21,assumption,(![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => ((is_a_theorem @ ((implies @ ((and @ X3) @ X5)) @ X3)) @ X6))))))))))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (kn2 @ X2)))))),introduced(assumption,[])).
% 8.34/8.76 thf(h22,assumption,(![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (kn1 @ X2))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => ((is_a_theorem @ ((implies @ X3) @ ((and @ X3) @ X3))) @ X4)))))))))),introduced(assumption,[])).
% 8.34/8.76 thf(h23,assumption,(![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => ((is_a_theorem @ ((implies @ X3) @ ((and @ X3) @ X3))) @ X4))))))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (kn1 @ X2)))))),introduced(assumption,[])).
% 8.34/8.76 thf(h24,assumption,(![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (or_3 @ X2))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => (![X7:$i]:(((eiw_di @ X7) @ X6) => (![X8:mworld]:(((mrel @ X6) @ X8) => ((is_a_theorem @ ((implies @ ((implies @ X3) @ X7)) @ ((implies @ ((implies @ X5) @ X7)) @ ((implies @ ((or @ X3) @ X5)) @ X7)))) @ X8)))))))))))))))))),introduced(assumption,[])).
% 8.34/8.76 thf(h25,assumption,(![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => (![X7:$i]:(((eiw_di @ X7) @ X6) => (![X8:mworld]:(((mrel @ X6) @ X8) => ((is_a_theorem @ ((implies @ ((implies @ X3) @ X7)) @ ((implies @ ((implies @ X5) @ X7)) @ ((implies @ ((or @ X3) @ X5)) @ X7)))) @ X8))))))))))))))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (or_3 @ X2)))))),introduced(assumption,[])).
% 8.34/8.76 thf(h26,assumption,sP5,introduced(assumption,[])).
% 8.34/8.76 thf(h27,assumption,(![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => ((is_a_theorem @ ((implies @ X5) @ ((or @ X3) @ X5))) @ X6))))))))))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (or_2 @ X2)))))),introduced(assumption,[])).
% 8.34/8.76 thf(h28,assumption,(![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (or_1 @ X2))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => ((is_a_theorem @ ((implies @ X3) @ ((or @ X3) @ X5))) @ X6)))))))))))))),introduced(assumption,[])).
% 8.34/8.76 thf(h29,assumption,(![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => ((is_a_theorem @ ((implies @ X3) @ ((or @ X3) @ X5))) @ X6))))))))))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (or_1 @ X2)))))),introduced(assumption,[])).
% 8.34/8.76 thf(h30,assumption,(![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (and_3 @ X2))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => ((is_a_theorem @ ((implies @ X3) @ ((implies @ X5) @ ((and @ X3) @ X5)))) @ X6)))))))))))))),introduced(assumption,[])).
% 8.34/8.76 thf(h31,assumption,(![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => ((is_a_theorem @ ((implies @ X3) @ ((implies @ X5) @ ((and @ X3) @ X5)))) @ X6))))))))))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (and_3 @ X2)))))),introduced(assumption,[])).
% 8.34/8.76 thf(h32,assumption,(![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (and_2 @ X2))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => ((is_a_theorem @ ((implies @ ((and @ X3) @ X5)) @ X5)) @ X6)))))))))))))),introduced(assumption,[])).
% 8.34/8.76 thf(h33,assumption,(![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => ((is_a_theorem @ ((implies @ ((and @ X3) @ X5)) @ X5)) @ X6))))))))))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (and_2 @ X2)))))),introduced(assumption,[])).
% 8.34/8.76 thf(h34,assumption,(![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (and_1 @ X2))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => ((is_a_theorem @ ((implies @ ((and @ X3) @ X5)) @ X3)) @ X6)))))))))))))),introduced(assumption,[])).
% 8.34/8.76 thf(h35,assumption,(![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => ((is_a_theorem @ ((implies @ ((and @ X3) @ X5)) @ X3)) @ X6))))))))))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (and_1 @ X2)))))),introduced(assumption,[])).
% 8.34/8.76 thf(h36,assumption,(![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (modus_tollens @ X2))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => ((is_a_theorem @ ((implies @ ((implies @ (not @ X5)) @ (not @ X3))) @ ((implies @ X3) @ X5))) @ X6)))))))))))))),introduced(assumption,[])).
% 8.34/8.76 thf(h37,assumption,(![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => ((is_a_theorem @ ((implies @ ((implies @ (not @ X5)) @ (not @ X3))) @ ((implies @ X3) @ X5))) @ X6))))))))))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (modus_tollens @ X2)))))),introduced(assumption,[])).
% 8.34/8.76 thf(1,plain,((~(sP2) | ~(sP14)) | sP4),inference(prop_rule,[status(thm)],[])).
% 8.34/8.76 thf(2,plain,(~(sP3) | sP2),inference(all_rule,[status(thm)],[])).
% 8.34/8.76 thf(3,plain,((~(sP8) | ~(sP6)) | sP3),inference(prop_rule,[status(thm)],[])).
% 8.34/8.76 thf(4,plain,((~(sP9) | ~(sP7)) | sP6),inference(prop_rule,[status(thm)],[])).
% 8.34/8.76 thf(5,plain,((~(sP13) | ~(sP12)) | sP9),inference(prop_rule,[status(thm)],[])).
% 8.34/8.76 thf(6,plain,((~(sP11) | ~(sP12)) | sP8),inference(prop_rule,[status(thm)],[])).
% 8.34/8.76 thf(7,plain,(~(sP1) | sP11),inference(all_rule,[status(thm)],[])).
% 8.34/8.76 thf(8,plain,(~(sP5) | sP13),inference(all_rule,[status(thm)],[])).
% 8.34/8.76 thf(9,plain,(~(sP10) | sP12),inference(all_rule,[status(thm)],[])).
% 8.34/8.76 thf(hilbert_or_2,axiom,(mlocal @ (mbox @ or_2))).
% 8.34/8.76 thf(10,plain,sP7,inference(preprocess,[status(thm)],[hilbert_or_2]).
% 8.34/8.76 thf(mrel_reflexive,axiom,sP10).
% 8.34/8.76 thf(11,plain,$false,inference(prop_unsat,[status(thm),assumptions([h36,h37,h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,h2,h3,10,h11,h26,mrel_reflexive])).
% 8.34/8.76 thf(modus_tollens_0,axiom,(mlocal @ ((mand @ (mbox @ ((mimplies @ (mbox @ modus_tollens)) @ (mbox @ (mforall_di @ (^[X1:$i]:(mbox @ (mforall_di @ (^[X2:$i]:(mbox @ (is_a_theorem @ ((implies @ ((implies @ (not @ X2)) @ (not @ X1))) @ ((implies @ X1) @ X2))))))))))))) @ (mbox @ ((mimplies @ (mbox @ (mforall_di @ (^[X1:$i]:(mbox @ (mforall_di @ (^[X2:$i]:(mbox @ (is_a_theorem @ ((implies @ ((implies @ (not @ X2)) @ (not @ X1))) @ ((implies @ X1) @ X2))))))))))) @ (mbox @ modus_tollens)))))).
% 8.34/8.76 thf(12,plain,(~(((![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (modus_tollens @ X2))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => ((is_a_theorem @ ((implies @ ((implies @ (not @ X5)) @ (not @ X3))) @ ((implies @ X3) @ X5))) @ X6)))))))))))))) => (~((![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => ((is_a_theorem @ ((implies @ ((implies @ (not @ X5)) @ (not @ X3))) @ ((implies @ X3) @ X5))) @ X6))))))))))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (modus_tollens @ X2))))))))))),inference(preprocess,[status(thm)],[modus_tollens_0]).
% 8.34/8.76 thf(13,plain,$false,inference(tab_negimp,[status(thm),assumptions([h34,h35,h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h36,h37])],[12,11,h36,h37])).
% 8.34/8.76 thf(and_1_0,axiom,(mlocal @ ((mand @ (mbox @ ((mimplies @ (mbox @ and_1)) @ (mbox @ (mforall_di @ (^[X1:$i]:(mbox @ (mforall_di @ (^[X2:$i]:(mbox @ (is_a_theorem @ ((implies @ ((and @ X1) @ X2)) @ X1)))))))))))) @ (mbox @ ((mimplies @ (mbox @ (mforall_di @ (^[X1:$i]:(mbox @ (mforall_di @ (^[X2:$i]:(mbox @ (is_a_theorem @ ((implies @ ((and @ X1) @ X2)) @ X1)))))))))) @ (mbox @ and_1)))))).
% 8.34/8.76 thf(14,plain,(~(((![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (and_1 @ X2))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => ((is_a_theorem @ ((implies @ ((and @ X3) @ X5)) @ X3)) @ X6)))))))))))))) => (~((![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => ((is_a_theorem @ ((implies @ ((and @ X3) @ X5)) @ X3)) @ X6))))))))))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (and_1 @ X2))))))))))),inference(preprocess,[status(thm)],[and_1_0]).
% 8.34/8.76 thf(15,plain,$false,inference(tab_negimp,[status(thm),assumptions([h32,h33,h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h34,h35])],[14,13,h34,h35])).
% 8.34/8.76 thf(and_2_0,axiom,(mlocal @ ((mand @ (mbox @ ((mimplies @ (mbox @ and_2)) @ (mbox @ (mforall_di @ (^[X1:$i]:(mbox @ (mforall_di @ (^[X2:$i]:(mbox @ (is_a_theorem @ ((implies @ ((and @ X1) @ X2)) @ X2)))))))))))) @ (mbox @ ((mimplies @ (mbox @ (mforall_di @ (^[X1:$i]:(mbox @ (mforall_di @ (^[X2:$i]:(mbox @ (is_a_theorem @ ((implies @ ((and @ X1) @ X2)) @ X2)))))))))) @ (mbox @ and_2)))))).
% 8.34/8.76 thf(16,plain,(~(((![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (and_2 @ X2))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => ((is_a_theorem @ ((implies @ ((and @ X3) @ X5)) @ X5)) @ X6)))))))))))))) => (~((![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => ((is_a_theorem @ ((implies @ ((and @ X3) @ X5)) @ X5)) @ X6))))))))))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (and_2 @ X2))))))))))),inference(preprocess,[status(thm)],[and_2_0]).
% 8.34/8.76 thf(17,plain,$false,inference(tab_negimp,[status(thm),assumptions([h30,h31,h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h32,h33])],[16,15,h32,h33])).
% 8.34/8.76 thf(and_3_0,axiom,(mlocal @ ((mand @ (mbox @ ((mimplies @ (mbox @ and_3)) @ (mbox @ (mforall_di @ (^[X1:$i]:(mbox @ (mforall_di @ (^[X2:$i]:(mbox @ (is_a_theorem @ ((implies @ X1) @ ((implies @ X2) @ ((and @ X1) @ X2)))))))))))))) @ (mbox @ ((mimplies @ (mbox @ (mforall_di @ (^[X1:$i]:(mbox @ (mforall_di @ (^[X2:$i]:(mbox @ (is_a_theorem @ ((implies @ X1) @ ((implies @ X2) @ ((and @ X1) @ X2)))))))))))) @ (mbox @ and_3)))))).
% 8.34/8.76 thf(18,plain,(~(((![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (and_3 @ X2))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => ((is_a_theorem @ ((implies @ X3) @ ((implies @ X5) @ ((and @ X3) @ X5)))) @ X6)))))))))))))) => (~((![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => ((is_a_theorem @ ((implies @ X3) @ ((implies @ X5) @ ((and @ X3) @ X5)))) @ X6))))))))))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (and_3 @ X2))))))))))),inference(preprocess,[status(thm)],[and_3_0]).
% 8.34/8.76 thf(19,plain,$false,inference(tab_negimp,[status(thm),assumptions([h28,h29,h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h30,h31])],[18,17,h30,h31])).
% 8.34/8.76 thf(or_1_0,axiom,(mlocal @ ((mand @ (mbox @ ((mimplies @ (mbox @ or_1)) @ (mbox @ (mforall_di @ (^[X1:$i]:(mbox @ (mforall_di @ (^[X2:$i]:(mbox @ (is_a_theorem @ ((implies @ X1) @ ((or @ X1) @ X2))))))))))))) @ (mbox @ ((mimplies @ (mbox @ (mforall_di @ (^[X1:$i]:(mbox @ (mforall_di @ (^[X2:$i]:(mbox @ (is_a_theorem @ ((implies @ X1) @ ((or @ X1) @ X2))))))))))) @ (mbox @ or_1)))))).
% 8.34/8.76 thf(20,plain,(~(((![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (or_1 @ X2))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => ((is_a_theorem @ ((implies @ X3) @ ((or @ X3) @ X5))) @ X6)))))))))))))) => (~((![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => ((is_a_theorem @ ((implies @ X3) @ ((or @ X3) @ X5))) @ X6))))))))))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (or_1 @ X2))))))))))),inference(preprocess,[status(thm)],[or_1_0]).
% 8.34/8.76 thf(21,plain,$false,inference(tab_negimp,[status(thm),assumptions([h26,h27,h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h28,h29])],[20,19,h28,h29])).
% 8.34/8.76 thf(or_2_0,axiom,(mlocal @ ((mand @ (mbox @ ((mimplies @ (mbox @ or_2)) @ (mbox @ (mforall_di @ (^[X1:$i]:(mbox @ (mforall_di @ (^[X2:$i]:(mbox @ (is_a_theorem @ ((implies @ X2) @ ((or @ X1) @ X2))))))))))))) @ (mbox @ ((mimplies @ (mbox @ (mforall_di @ (^[X1:$i]:(mbox @ (mforall_di @ (^[X2:$i]:(mbox @ (is_a_theorem @ ((implies @ X2) @ ((or @ X1) @ X2))))))))))) @ (mbox @ or_2)))))).
% 8.34/8.76 thf(22,plain,(~((sP5 => (~((![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => ((is_a_theorem @ ((implies @ X5) @ ((or @ X3) @ X5))) @ X6))))))))))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (or_2 @ X2))))))))))),inference(preprocess,[status(thm)],[or_2_0]).
% 8.34/8.76 thf(23,plain,$false,inference(tab_negimp,[status(thm),assumptions([h24,h25,h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h26,h27])],[22,21,h26,h27])).
% 8.34/8.76 thf(or_3_0,axiom,(mlocal @ ((mand @ (mbox @ ((mimplies @ (mbox @ or_3)) @ (mbox @ (mforall_di @ (^[X1:$i]:(mbox @ (mforall_di @ (^[X2:$i]:(mbox @ (mforall_di @ (^[X3:$i]:(mbox @ (is_a_theorem @ ((implies @ ((implies @ X1) @ X3)) @ ((implies @ ((implies @ X2) @ X3)) @ ((implies @ ((or @ X1) @ X2)) @ X3))))))))))))))))) @ (mbox @ ((mimplies @ (mbox @ (mforall_di @ (^[X1:$i]:(mbox @ (mforall_di @ (^[X2:$i]:(mbox @ (mforall_di @ (^[X3:$i]:(mbox @ (is_a_theorem @ ((implies @ ((implies @ X1) @ X3)) @ ((implies @ ((implies @ X2) @ X3)) @ ((implies @ ((or @ X1) @ X2)) @ X3))))))))))))))) @ (mbox @ or_3)))))).
% 8.34/8.76 thf(24,plain,(~(((![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (or_3 @ X2))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => (![X7:$i]:(((eiw_di @ X7) @ X6) => (![X8:mworld]:(((mrel @ X6) @ X8) => ((is_a_theorem @ ((implies @ ((implies @ X3) @ X7)) @ ((implies @ ((implies @ X5) @ X7)) @ ((implies @ ((or @ X3) @ X5)) @ X7)))) @ X8)))))))))))))))))) => (~((![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => (![X7:$i]:(((eiw_di @ X7) @ X6) => (![X8:mworld]:(((mrel @ X6) @ X8) => ((is_a_theorem @ ((implies @ ((implies @ X3) @ X7)) @ ((implies @ ((implies @ X5) @ X7)) @ ((implies @ ((or @ X3) @ X5)) @ X7)))) @ X8))))))))))))))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (or_3 @ X2))))))))))),inference(preprocess,[status(thm)],[or_3_0]).
% 8.34/8.76 thf(25,plain,$false,inference(tab_negimp,[status(thm),assumptions([h22,h23,h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h24,h25])],[24,23,h24,h25])).
% 8.34/8.76 thf(kn1_0,axiom,(mlocal @ ((mand @ (mbox @ ((mimplies @ (mbox @ kn1)) @ (mbox @ (mforall_di @ (^[X1:$i]:(mbox @ (is_a_theorem @ ((implies @ X1) @ ((and @ X1) @ X1)))))))))) @ (mbox @ ((mimplies @ (mbox @ (mforall_di @ (^[X1:$i]:(mbox @ (is_a_theorem @ ((implies @ X1) @ ((and @ X1) @ X1)))))))) @ (mbox @ kn1)))))).
% 8.34/8.76 thf(26,plain,(~(((![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (kn1 @ X2))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => ((is_a_theorem @ ((implies @ X3) @ ((and @ X3) @ X3))) @ X4)))))))))) => (~((![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => ((is_a_theorem @ ((implies @ X3) @ ((and @ X3) @ X3))) @ X4))))))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (kn1 @ X2))))))))))),inference(preprocess,[status(thm)],[kn1_0]).
% 8.34/8.76 thf(27,plain,$false,inference(tab_negimp,[status(thm),assumptions([h20,h21,h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h22,h23])],[26,25,h22,h23])).
% 8.34/8.76 thf(kn2_0,axiom,(mlocal @ ((mand @ (mbox @ ((mimplies @ (mbox @ kn2)) @ (mbox @ (mforall_di @ (^[X1:$i]:(mbox @ (mforall_di @ (^[X2:$i]:(mbox @ (is_a_theorem @ ((implies @ ((and @ X1) @ X2)) @ X1)))))))))))) @ (mbox @ ((mimplies @ (mbox @ (mforall_di @ (^[X1:$i]:(mbox @ (mforall_di @ (^[X2:$i]:(mbox @ (is_a_theorem @ ((implies @ ((and @ X1) @ X2)) @ X1)))))))))) @ (mbox @ kn2)))))).
% 8.34/8.76 thf(28,plain,(~(((![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (kn2 @ X2))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => ((is_a_theorem @ ((implies @ ((and @ X3) @ X5)) @ X3)) @ X6)))))))))))))) => (~((![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => ((is_a_theorem @ ((implies @ ((and @ X3) @ X5)) @ X3)) @ X6))))))))))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (kn2 @ X2))))))))))),inference(preprocess,[status(thm)],[kn2_0]).
% 8.34/8.76 thf(29,plain,$false,inference(tab_negimp,[status(thm),assumptions([h18,h19,h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h20,h21])],[28,27,h20,h21])).
% 8.34/8.76 thf(kn3_0,axiom,(mlocal @ ((mand @ (mbox @ ((mimplies @ (mbox @ kn3)) @ (mbox @ (mforall_di @ (^[X1:$i]:(mbox @ (mforall_di @ (^[X2:$i]:(mbox @ (mforall_di @ (^[X3:$i]:(mbox @ (is_a_theorem @ ((implies @ ((implies @ X1) @ X2)) @ ((implies @ (not @ ((and @ X2) @ X3))) @ (not @ ((and @ X3) @ X1)))))))))))))))))) @ (mbox @ ((mimplies @ (mbox @ (mforall_di @ (^[X1:$i]:(mbox @ (mforall_di @ (^[X2:$i]:(mbox @ (mforall_di @ (^[X3:$i]:(mbox @ (is_a_theorem @ ((implies @ ((implies @ X1) @ X2)) @ ((implies @ (not @ ((and @ X2) @ X3))) @ (not @ ((and @ X3) @ X1)))))))))))))))) @ (mbox @ kn3)))))).
% 8.34/8.76 thf(30,plain,(~(((![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (kn3 @ X2))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => (![X7:$i]:(((eiw_di @ X7) @ X6) => (![X8:mworld]:(((mrel @ X6) @ X8) => ((is_a_theorem @ ((implies @ ((implies @ X3) @ X5)) @ ((implies @ (not @ ((and @ X5) @ X7))) @ (not @ ((and @ X7) @ X3))))) @ X8)))))))))))))))))) => (~((![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => (![X7:$i]:(((eiw_di @ X7) @ X6) => (![X8:mworld]:(((mrel @ X6) @ X8) => ((is_a_theorem @ ((implies @ ((implies @ X3) @ X5)) @ ((implies @ (not @ ((and @ X5) @ X7))) @ (not @ ((and @ X7) @ X3))))) @ X8))))))))))))))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (kn3 @ X2))))))))))),inference(preprocess,[status(thm)],[kn3_0]).
% 8.34/8.76 thf(31,plain,$false,inference(tab_negimp,[status(thm),assumptions([h16,h17,h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h18,h19])],[30,29,h18,h19])).
% 8.34/8.76 thf(cn2_0,axiom,(mlocal @ ((mand @ (mbox @ ((mimplies @ (mbox @ cn2)) @ (mbox @ (mforall_di @ (^[X1:$i]:(mbox @ (mforall_di @ (^[X2:$i]:(mbox @ (is_a_theorem @ ((implies @ X1) @ ((implies @ (not @ X1)) @ X2))))))))))))) @ (mbox @ ((mimplies @ (mbox @ (mforall_di @ (^[X1:$i]:(mbox @ (mforall_di @ (^[X2:$i]:(mbox @ (is_a_theorem @ ((implies @ X1) @ ((implies @ (not @ X1)) @ X2))))))))))) @ (mbox @ cn2)))))).
% 8.34/8.76 thf(32,plain,(~(((![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (cn2 @ X2))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => ((is_a_theorem @ ((implies @ X3) @ ((implies @ (not @ X3)) @ X5))) @ X6)))))))))))))) => (~((![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => ((is_a_theorem @ ((implies @ X3) @ ((implies @ (not @ X3)) @ X5))) @ X6))))))))))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (cn2 @ X2))))))))))),inference(preprocess,[status(thm)],[cn2_0]).
% 8.34/8.76 thf(33,plain,$false,inference(tab_negimp,[status(thm),assumptions([h14,h15,h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h16,h17])],[32,31,h16,h17])).
% 8.34/8.76 thf(cn3_0,axiom,(mlocal @ ((mand @ (mbox @ ((mimplies @ (mbox @ cn3)) @ (mbox @ (mforall_di @ (^[X1:$i]:(mbox @ (is_a_theorem @ ((implies @ ((implies @ (not @ X1)) @ X1)) @ X1))))))))) @ (mbox @ ((mimplies @ (mbox @ (mforall_di @ (^[X1:$i]:(mbox @ (is_a_theorem @ ((implies @ ((implies @ (not @ X1)) @ X1)) @ X1))))))) @ (mbox @ cn3)))))).
% 8.34/8.76 thf(34,plain,(~(((![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (cn3 @ X2))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => ((is_a_theorem @ ((implies @ ((implies @ (not @ X3)) @ X3)) @ X3)) @ X4)))))))))) => (~((![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => ((is_a_theorem @ ((implies @ ((implies @ (not @ X3)) @ X3)) @ X3)) @ X4))))))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (cn3 @ X2))))))))))),inference(preprocess,[status(thm)],[cn3_0]).
% 8.34/8.76 thf(35,plain,$false,inference(tab_negimp,[status(thm),assumptions([h12,h13,h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h14,h15])],[34,33,h14,h15])).
% 8.34/8.76 thf(r1_0,axiom,(mlocal @ ((mand @ (mbox @ ((mimplies @ (mbox @ r1)) @ (mbox @ (mforall_di @ (^[X1:$i]:(mbox @ (is_a_theorem @ ((implies @ ((or @ X1) @ X1)) @ X1))))))))) @ (mbox @ ((mimplies @ (mbox @ (mforall_di @ (^[X1:$i]:(mbox @ (is_a_theorem @ ((implies @ ((or @ X1) @ X1)) @ X1))))))) @ (mbox @ r1)))))).
% 8.34/8.76 thf(36,plain,(~(((![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (r1 @ X2))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => ((is_a_theorem @ ((implies @ ((or @ X3) @ X3)) @ X3)) @ X4)))))))))) => (~((![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => ((is_a_theorem @ ((implies @ ((or @ X3) @ X3)) @ X3)) @ X4))))))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (r1 @ X2))))))))))),inference(preprocess,[status(thm)],[r1_0]).
% 8.34/8.76 thf(37,plain,$false,inference(tab_negimp,[status(thm),assumptions([h10,h11,h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h12,h13])],[36,35,h12,h13])).
% 8.34/8.76 thf(r2_0,axiom,(mlocal @ ((mand @ (mbox @ ((mimplies @ (mbox @ r2)) @ (mbox @ (mforall_di @ (^[X1:$i]:(mbox @ (mforall_di @ (^[X2:$i]:(mbox @ (is_a_theorem @ ((implies @ X2) @ ((or @ X1) @ X2))))))))))))) @ (mbox @ ((mimplies @ (mbox @ (mforall_di @ (^[X1:$i]:(mbox @ (mforall_di @ (^[X2:$i]:(mbox @ (is_a_theorem @ ((implies @ X2) @ ((or @ X1) @ X2))))))))))) @ (mbox @ r2)))))).
% 8.34/8.76 thf(38,plain,(~(((![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (r2 @ X2))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => ((is_a_theorem @ ((implies @ X5) @ ((or @ X3) @ X5))) @ X6)))))))))))))) => (~(sP1))))),inference(preprocess,[status(thm)],[r2_0]).
% 8.34/8.76 thf(39,plain,$false,inference(tab_negimp,[status(thm),assumptions([h8,h9,h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h10,h11])],[38,37,h10,h11])).
% 8.34/8.76 thf(r3_0,axiom,(mlocal @ ((mand @ (mbox @ ((mimplies @ (mbox @ r3)) @ (mbox @ (mforall_di @ (^[X1:$i]:(mbox @ (mforall_di @ (^[X2:$i]:(mbox @ (is_a_theorem @ ((implies @ ((or @ X1) @ X2)) @ ((or @ X2) @ X1))))))))))))) @ (mbox @ ((mimplies @ (mbox @ (mforall_di @ (^[X1:$i]:(mbox @ (mforall_di @ (^[X2:$i]:(mbox @ (is_a_theorem @ ((implies @ ((or @ X1) @ X2)) @ ((or @ X2) @ X1))))))))))) @ (mbox @ r3)))))).
% 8.34/8.76 thf(40,plain,(~(((![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (r3 @ X2))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => ((is_a_theorem @ ((implies @ ((or @ X3) @ X5)) @ ((or @ X5) @ X3))) @ X6)))))))))))))) => (~((![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => ((is_a_theorem @ ((implies @ ((or @ X3) @ X5)) @ ((or @ X5) @ X3))) @ X6))))))))))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (r3 @ X2))))))))))),inference(preprocess,[status(thm)],[r3_0]).
% 8.34/8.76 thf(41,plain,$false,inference(tab_negimp,[status(thm),assumptions([h6,h7,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[40,39,h8,h9])).
% 8.34/8.76 thf(r4_0,axiom,(mlocal @ ((mand @ (mbox @ ((mimplies @ (mbox @ r4)) @ (mbox @ (mforall_di @ (^[X1:$i]:(mbox @ (mforall_di @ (^[X2:$i]:(mbox @ (mforall_di @ (^[X3:$i]:(mbox @ (is_a_theorem @ ((implies @ ((or @ X1) @ ((or @ X2) @ X3))) @ ((or @ X2) @ ((or @ X1) @ X3))))))))))))))))) @ (mbox @ ((mimplies @ (mbox @ (mforall_di @ (^[X1:$i]:(mbox @ (mforall_di @ (^[X2:$i]:(mbox @ (mforall_di @ (^[X3:$i]:(mbox @ (is_a_theorem @ ((implies @ ((or @ X1) @ ((or @ X2) @ X3))) @ ((or @ X2) @ ((or @ X1) @ X3))))))))))))))) @ (mbox @ r4)))))).
% 8.34/8.76 thf(42,plain,(~(((![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (r4 @ X2))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => (![X7:$i]:(((eiw_di @ X7) @ X6) => (![X8:mworld]:(((mrel @ X6) @ X8) => ((is_a_theorem @ ((implies @ ((or @ X3) @ ((or @ X5) @ X7))) @ ((or @ X5) @ ((or @ X3) @ X7)))) @ X8)))))))))))))))))) => (~((![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => (![X7:$i]:(((eiw_di @ X7) @ X6) => (![X8:mworld]:(((mrel @ X6) @ X8) => ((is_a_theorem @ ((implies @ ((or @ X3) @ ((or @ X5) @ X7))) @ ((or @ X5) @ ((or @ X3) @ X7)))) @ X8))))))))))))))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (r4 @ X2))))))))))),inference(preprocess,[status(thm)],[r4_0]).
% 8.34/8.76 thf(43,plain,$false,inference(tab_negimp,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h6,h7])],[42,41,h6,h7])).
% 8.34/8.76 thf(r5_0,axiom,(mlocal @ ((mand @ (mbox @ ((mimplies @ (mbox @ r5)) @ (mbox @ (mforall_di @ (^[X1:$i]:(mbox @ (mforall_di @ (^[X2:$i]:(mbox @ (mforall_di @ (^[X3:$i]:(mbox @ (is_a_theorem @ ((implies @ ((implies @ X2) @ X3)) @ ((implies @ ((or @ X1) @ X2)) @ ((or @ X1) @ X3))))))))))))))))) @ (mbox @ ((mimplies @ (mbox @ (mforall_di @ (^[X1:$i]:(mbox @ (mforall_di @ (^[X2:$i]:(mbox @ (mforall_di @ (^[X3:$i]:(mbox @ (is_a_theorem @ ((implies @ ((implies @ X2) @ X3)) @ ((implies @ ((or @ X1) @ X2)) @ ((or @ X1) @ X3))))))))))))))) @ (mbox @ r5)))))).
% 8.34/8.76 thf(44,plain,(~(((![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (r5 @ X2))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => (![X7:$i]:(((eiw_di @ X7) @ X6) => (![X8:mworld]:(((mrel @ X6) @ X8) => ((is_a_theorem @ ((implies @ ((implies @ X5) @ X7)) @ ((implies @ ((or @ X3) @ X5)) @ ((or @ X3) @ X7)))) @ X8)))))))))))))))))) => (~((![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (![X3:$i]:(((eiw_di @ X3) @ X2) => (![X4:mworld]:(((mrel @ X2) @ X4) => (![X5:$i]:(((eiw_di @ X5) @ X4) => (![X6:mworld]:(((mrel @ X4) @ X6) => (![X7:$i]:(((eiw_di @ X7) @ X6) => (![X8:mworld]:(((mrel @ X6) @ X8) => ((is_a_theorem @ ((implies @ ((implies @ X5) @ X7)) @ ((implies @ ((or @ X3) @ X5)) @ ((or @ X3) @ X7)))) @ X8))))))))))))))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (r5 @ X2))))))))))),inference(preprocess,[status(thm)],[r5_0]).
% 8.34/8.76 thf(45,plain,$false,inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[44,43,h4,h5])).
% 8.34/8.76 thf(46,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,45,h2,h3])).
% 8.34/8.76 thf(47,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,46,h1])).
% 8.34/8.76 thf(0,theorem,sP3,inference(contra,[status(thm),contra(discharge,[h0])],[47,h0])).
% 8.34/8.76 % SZS output end Proof
%------------------------------------------------------------------------------