TSTP Solution File: SEV428^1 by Lash---1.13
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% File : Lash---1.13
% Problem : SEV428^1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n004.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 : 300s
% DateTime : Thu Aug 31 19:34:32 EDT 2023
% Result : Theorem 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV428^1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n004.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 : 300
% 0.13/0.34 % DateTime : Thu Aug 24 02:25:53 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.40 % SZS status Theorem
% 0.19/0.40 % Mode: cade22grackle2xfee4
% 0.19/0.40 % Steps: 85
% 0.19/0.40 % SZS output start Proof
% 0.19/0.40 thf(ty_epsio, type, epsio : ((($i>$o)>$o)>$i>$o)).
% 0.19/0.40 thf(ty_eigen__0, type, eigen__0 : ($i>$o)).
% 0.19/0.40 thf(ty_c, type, c : (($i>$o)>$o)).
% 0.19/0.40 thf(ty_a, type, a : $i).
% 0.19/0.40 thf(ty_eps, type, eps : (($i>$o)>$i)).
% 0.19/0.40 thf(sP1,plain,sP1 <=> (c @ eigen__0),introduced(definition,[new_symbols(definition,[sP1])])).
% 0.19/0.40 thf(sP2,plain,sP2 <=> (![X1:$i]:(~(((epsio @ (^[X2:$i>$o]:(~(((c @ X2) => (~((X2 @ (eps @ X2))))))))) @ X1)))),introduced(definition,[new_symbols(definition,[sP2])])).
% 0.19/0.40 thf(sP3,plain,sP3 <=> ((epsio @ (^[X1:$i>$o]:(~(((c @ X1) => (~((X1 @ (eps @ X1))))))))) @ (eps @ (epsio @ (^[X1:$i>$o]:(~(((c @ X1) => (~((X1 @ (eps @ X1))))))))))),introduced(definition,[new_symbols(definition,[sP3])])).
% 0.19/0.40 thf(sP4,plain,sP4 <=> (![X1:$i>$o]:((c @ X1) => (~((X1 @ (eps @ X1)))))),introduced(definition,[new_symbols(definition,[sP4])])).
% 0.19/0.40 thf(sP5,plain,sP5 <=> (eigen__0 @ (eps @ eigen__0)),introduced(definition,[new_symbols(definition,[sP5])])).
% 0.19/0.40 thf(sP6,plain,sP6 <=> (![X1:$i]:(~((eigen__0 @ X1)))),introduced(definition,[new_symbols(definition,[sP6])])).
% 0.19/0.40 thf(sP7,plain,sP7 <=> ((c @ (epsio @ (^[X1:$i>$o]:(~(((c @ X1) => (~((X1 @ (eps @ X1)))))))))) => sP2),introduced(definition,[new_symbols(definition,[sP7])])).
% 0.19/0.40 thf(sP8,plain,sP8 <=> (eigen__0 @ a),introduced(definition,[new_symbols(definition,[sP8])])).
% 0.19/0.40 thf(sP9,plain,sP9 <=> ((c @ (epsio @ (^[X1:$i>$o]:(~(((c @ X1) => (~((X1 @ (eps @ X1)))))))))) => (~(sP3))),introduced(definition,[new_symbols(definition,[sP9])])).
% 0.19/0.40 thf(sP10,plain,sP10 <=> (sP1 => (~(sP5))),introduced(definition,[new_symbols(definition,[sP10])])).
% 0.19/0.40 thf(sP11,plain,sP11 <=> (c @ (epsio @ (^[X1:$i>$o]:(~(((c @ X1) => (~((X1 @ (eps @ X1)))))))))),introduced(definition,[new_symbols(definition,[sP11])])).
% 0.19/0.40 thf(def_setunion,definition,(setunion = (^[X1:($i>$o)>$o]:(^[X2:$i]:(?[X3:$i>$o]:((X1 @ X3) & (X3 @ X2))))))).
% 0.19/0.40 thf(def_choosenonempty,definition,(choosenonempty = (^[X1:($i>$o)>$o]:(epsio @ (^[X2:$i>$o]:((X1 @ X2) & (X2 @ (eps @ X2)))))))).
% 0.19/0.40 thf(conj,conjecture,(~(sP7))).
% 0.19/0.40 thf(h0,negated_conjecture,sP7,inference(assume_negation,[status(cth)],[conj])).
% 0.19/0.40 thf(h1,assumption,(~((sP1 => (~(sP8))))),introduced(assumption,[])).
% 0.19/0.40 thf(h2,assumption,sP1,introduced(assumption,[])).
% 0.19/0.40 thf(h3,assumption,sP8,introduced(assumption,[])).
% 0.19/0.40 thf(1,plain,(~(sP2) | ~(sP3)),inference(all_rule,[status(thm)],[])).
% 0.19/0.40 thf(2,plain,(~(sP6) | ~(sP8)),inference(all_rule,[status(thm)],[])).
% 0.19/0.40 thf(choiceax,axiom,(![X1:$i>$o]:((~((![X2:$i]:(~((X1 @ X2)))))) => (X1 @ (eps @ X1))))).
% 0.19/0.40 thf(3,plain,(![X1:$i>$o]:((~((![X2:$i]:(~((X1 @ X2)))))) => (X1 @ (eps @ X1)))),inference(preprocess,[status(thm)],[3]).
% 0.19/0.40 thf(4,plain,(sP5 | sP6),inference(choice_rule,[status(thm)],[3])).
% 0.19/0.40 thf(5,plain,((~(sP10) | ~(sP1)) | ~(sP5)),inference(prop_rule,[status(thm)],[])).
% 0.19/0.40 thf(6,plain,(~(sP4) | sP10),inference(all_rule,[status(thm)],[])).
% 0.19/0.40 thf(7,plain,(sP9 | sP3),inference(prop_rule,[status(thm)],[])).
% 0.19/0.40 thf(8,plain,(sP9 | sP11),inference(prop_rule,[status(thm)],[])).
% 0.19/0.40 thf(choiceaxio,axiom,(![X1:($i>$o)>$o]:((~((![X2:$i>$o]:(~((X1 @ X2)))))) => (X1 @ (epsio @ X1))))).
% 0.19/0.40 thf(9,plain,(![X1:($i>$o)>$o]:((~((![X2:$i>$o]:(~((X1 @ X2)))))) => (X1 @ (epsio @ X1)))),inference(preprocess,[status(thm)],[9]).
% 0.19/0.40 thf(10,plain,(~(sP9) | sP4),inference(choice_rule,[status(thm)],[9])).
% 0.19/0.40 thf(11,plain,((~(sP7) | ~(sP11)) | sP2),inference(prop_rule,[status(thm)],[])).
% 0.19/0.40 thf(12,plain,$false,inference(prop_unsat,[status(thm),assumptions([h2,h3,h1,h0])],[1,2,4,5,6,7,8,10,11,h0,h2,h3])).
% 0.19/0.40 thf(13,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,12,h2,h3])).
% 0.19/0.40 thf(ca,axiom,(~((![X1:$i>$o]:((c @ X1) => (~((X1 @ a)))))))).
% 0.19/0.40 thf(14,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[ca,13,h1])).
% 0.19/0.40 thf(0,theorem,(~(sP7)),inference(contra,[status(thm),contra(discharge,[h0])],[14,h0])).
% 0.19/0.40 % SZS output end Proof
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