0.02/0.10	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.02/0.10	% Command    : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
0.10/0.30	Computer   : n015.cluster.edu
0.10/0.30	Model      : x86_64 x86_64
0.10/0.30	CPUModel   : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.10/0.30	RAMPerCPU  : 8042.1875MB
0.10/0.30	OS         : Linux 3.10.0-693.el7.x86_64
0.10/0.30	% CPULimit   : 960
0.10/0.30	% DateTime   : Tue Aug  9 06:18:26 EDT 2022
0.10/0.30	% CPUTime    : 
69.26/70.53	% SZS status Theorem
69.26/70.53	% Mode: mode454:USE_SINE=true:SINE_TOLERANCE=2.0:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=3.:SINE_DEPTH=0
69.26/70.53	% Inferences: 136
69.26/70.53	% SZS output start Proof
69.26/70.53	thf(ty_mworld, type, mworld : $tType).
69.26/70.53	thf(ty_eiw_di, type, eiw_di : ($i>mworld>$o)).
69.26/70.53	thf(ty_or_2, type, or_2 : (mworld>$o)).
69.26/70.53	thf(ty_or, type, or : ($i>$i>$i)).
69.26/70.53	thf(ty_is_a_theorem, type, is_a_theorem : ($i>mworld>$o)).
69.26/70.53	thf(ty_implies, type, implies : ($i>$i>$i)).
69.26/70.53	thf(ty_mrel, type, mrel : (mworld>mworld>$o)).
69.26/70.53	thf(ty_r2, type, r2 : (mworld>$o)).
69.26/70.53	thf(ty_mactual, type, mactual : mworld).
69.26/70.53	thf(sP1,plain,sP1 <=> (![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,[sP1])])).
69.26/70.53	thf(sP2,plain,sP2 <=> (![X1:mworld]:(((mrel @ mactual) @ X1) => (r2 @ X1))),introduced(definition,[new_symbols(definition,[sP2])])).
69.26/70.53	thf(sP3,plain,sP3 <=> (((mrel @ mactual) @ mactual) => ((![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))))))))))) => sP2)),introduced(definition,[new_symbols(definition,[sP3])])).
69.26/70.53	thf(sP4,plain,sP4 <=> (![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,[sP4])])).
69.26/70.53	thf(sP5,plain,sP5 <=> ((mrel @ mactual) @ mactual),introduced(definition,[new_symbols(definition,[sP5])])).
69.26/70.53	thf(sP6,plain,sP6 <=> (sP5 => ((![X1:mworld]:(((mrel @ mactual) @ X1) => (or_2 @ X1))) => (![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])])).
69.26/70.53	thf(sP7,plain,sP7 <=> (![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,[sP7])])).
69.26/70.53	thf(sP8,plain,sP8 <=> (![X1:mworld]:((mrel @ X1) @ X1)),introduced(definition,[new_symbols(definition,[sP8])])).
69.26/70.53	thf(sP9,plain,sP9 <=> (sP7 => sP2),introduced(definition,[new_symbols(definition,[sP9])])).
69.26/70.53	thf(sP10,plain,sP10 <=> (![X1:mworld]:(((mrel @ mactual) @ X1) => (or_2 @ X1))),introduced(definition,[new_symbols(definition,[sP10])])).
69.26/70.53	thf(sP11,plain,sP11 <=> (sP10 => sP7),introduced(definition,[new_symbols(definition,[sP11])])).
69.26/70.53	thf(sP12,plain,sP12 <=> ((![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)))))))))))))) => (~(sP4))),introduced(definition,[new_symbols(definition,[sP12])])).
69.26/70.53	thf(sP13,plain,sP13 <=> (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) => (or_2 @ X2))))))))),introduced(definition,[new_symbols(definition,[sP13])])).
69.26/70.53	thf(def_mlocal,definition,(mlocal = (^[X1:mworld>$o]:(X1 @ mactual)))).
69.26/70.53	thf(def_mand,definition,(mand = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:(~(((X1 @ X3) => (~((X2 @ X3))))))))))).
69.26/70.53	thf(def_mimplies,definition,(mimplies = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((X1 @ X3) => (X2 @ X3))))))).
69.26/70.53	thf(def_mbox,definition,(mbox = (^[X1:mworld>$o]:(^[X2:mworld]:(![X3:mworld]:(((mrel @ X2) @ X3) => (X1 @ X3))))))).
69.26/70.53	thf(def_mforall_di,definition,(mforall_di = (^[X1:$i>mworld>$o]:(^[X2:mworld]:(![X3:$i]:(((eiw_di @ X3) @ X2) => ((X1 @ X3) @ X2))))))).
69.26/70.53	thf(principia_r2,conjecture,sP2).
69.26/70.53	thf(h0,negated_conjecture,(~(sP2)),inference(assume_negation,[status(cth)],[principia_r2])).
69.26/70.53	thf(1,plain,(~(sP8) | sP5),inference(all_rule,[status(thm)],[])).
69.26/70.53	thf(2,plain,(~(sP4) | sP3),inference(all_rule,[status(thm)],[])).
69.26/70.53	thf(3,plain,((~(sP3) | ~(sP5)) | sP9),inference(prop_rule,[status(thm)],[])).
69.26/70.53	thf(4,plain,((~(sP9) | ~(sP7)) | sP2),inference(prop_rule,[status(thm)],[])).
69.26/70.53	thf(5,plain,(~(sP1) | sP6),inference(all_rule,[status(thm)],[])).
69.26/70.53	thf(6,plain,((~(sP6) | ~(sP5)) | sP11),inference(prop_rule,[status(thm)],[])).
69.26/70.53	thf(7,plain,((~(sP11) | ~(sP10)) | sP7),inference(prop_rule,[status(thm)],[])).
69.26/70.53	thf(8,plain,(sP12 | sP4),inference(prop_rule,[status(thm)],[])).
69.26/70.53	thf(9,plain,(sP13 | sP1),inference(prop_rule,[status(thm)],[])).
69.26/70.53	thf(mrel_reflexive,axiom,sP8).
69.26/70.53	thf(hilbert_or_2,axiom,(mlocal @ (mbox @ or_2))).
69.26/70.53	thf(10,plain,sP10,inference(preprocess,[status(thm)],[hilbert_or_2]).
69.26/70.53	thf(r2_0,axiom,(mlocal @ ((mand @ (mbox @ ((mimplies @ (mbox @ r2)) @ (mbox @ (mforall_di @ (^[X1:$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:$i]:(mbox @ (is_a_theorem @ ((implies @ X2) @ ((or @ X1) @ X2))))))))))) @ (mbox @ r2)))))).
69.26/70.53	thf(11,plain,(~(sP12)),inference(preprocess,[status(thm)],[r2_0]).
69.26/70.53	thf(or_2_0,axiom,(mlocal @ ((mand @ (mbox @ ((mimplies @ (mbox @ or_2)) @ (mbox @ (mforall_di @ (^[X1:$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:$i]:(mbox @ (is_a_theorem @ ((implies @ X2) @ ((or @ X1) @ X2))))))))))) @ (mbox @ or_2)))))).
69.26/70.53	thf(12,plain,(~(sP13)),inference(preprocess,[status(thm)],[or_2_0]).
69.26/70.53	thf(13,plain,$false,inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,mrel_reflexive,10,11,h0,12])).
69.26/70.53	thf(0,theorem,sP2,inference(contra,[status(thm),contra(discharge,[h0])],[13,h0])).
69.26/70.53	% SZS output end Proof
69.26/70.53	EOF