TSTP Solution File: SYO536^1 by Lash---1.13
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% File : Lash---1.13
% Problem : SYO536^1 : 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 : n022.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 : Fri Sep 1 04:47:24 EDT 2023
% Result : Theorem 0.20s 0.42s
% Output : Proof 0.20s
% 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 : SYO536^1 : 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 : n022.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 : Sat Aug 26 02:09:55 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.42 % SZS status Theorem
% 0.20/0.42 % Mode: cade22grackle2xfee4
% 0.20/0.42 % Steps: 32
% 0.20/0.42 % SZS output start Proof
% 0.20/0.42 thf(ty_epsii, type, epsii : ((($i>$i)>$o)>$i>$i)).
% 0.20/0.42 thf(ty_eigen__2, type, eigen__2 : $i).
% 0.20/0.42 thf(ty_eigen__0, type, eigen__0 : (($i>$i)>$i>$o)).
% 0.20/0.42 thf(ty_eigen__1, type, eigen__1 : ($i>$i)).
% 0.20/0.42 thf(ty_eps, type, eps : (($i>$o)>$i)).
% 0.20/0.42 thf(sP1,plain,sP1 <=> ((eigen__0 @ eigen__1) @ eigen__2),introduced(definition,[new_symbols(definition,[sP1])])).
% 0.20/0.42 thf(sP2,plain,sP2 <=> (![X1:$i]:(~(((eigen__0 @ (epsii @ (^[X2:$i>$i]:(~((![X3:$i]:(~(((eigen__0 @ X2) @ X3))))))))) @ X1)))),introduced(definition,[new_symbols(definition,[sP2])])).
% 0.20/0.42 thf(sP3,plain,sP3 <=> (![X1:$i]:(~(((eigen__0 @ eigen__1) @ X1)))),introduced(definition,[new_symbols(definition,[sP3])])).
% 0.20/0.42 thf(sP4,plain,sP4 <=> ((eigen__0 @ (epsii @ (^[X1:$i>$i]:(~((![X2:$i]:(~(((eigen__0 @ X1) @ X2))))))))) @ (eps @ (eigen__0 @ (epsii @ (^[X1:$i>$i]:(~((![X2:$i]:(~(((eigen__0 @ X1) @ X2))))))))))),introduced(definition,[new_symbols(definition,[sP4])])).
% 0.20/0.42 thf(sP5,plain,sP5 <=> (![X1:$i>$i]:(![X2:$i]:(~(((eigen__0 @ X1) @ X2))))),introduced(definition,[new_symbols(definition,[sP5])])).
% 0.20/0.42 thf(def_epsa,definition,(epsa = (^[X1:($i>$i)>$i>$o]:(epsii @ (^[X2:$i>$i]:(?[X3:$i]:((X1 @ X2) @ X3))))))).
% 0.20/0.42 thf(def_epsb,definition,(epsb = (^[X1:($i>$i)>$i>$o]:(eps @ (^[X2:$i]:((X1 @ (epsa @ X1)) @ X2)))))).
% 0.20/0.42 thf(conj,conjecture,(![X1:($i>$i)>$i>$o]:((~((![X2:$i>$i]:(![X3:$i]:(~(((X1 @ X2) @ X3))))))) => ((X1 @ (epsii @ (^[X2:$i>$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3))))))))) @ (eps @ (X1 @ (epsii @ (^[X2:$i>$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3)))))))))))))).
% 0.20/0.42 thf(h0,negated_conjecture,(~((![X1:($i>$i)>$i>$o]:((~((![X2:$i>$i]:(![X3:$i]:(~(((X1 @ X2) @ X3))))))) => ((X1 @ (epsii @ (^[X2:$i>$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3))))))))) @ (eps @ (X1 @ (epsii @ (^[X2:$i>$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3))))))))))))))),inference(assume_negation,[status(cth)],[conj])).
% 0.20/0.42 thf(h1,assumption,(~(((~(sP5)) => sP4))),introduced(assumption,[])).
% 0.20/0.42 thf(h2,assumption,(~(sP5)),introduced(assumption,[])).
% 0.20/0.42 thf(h3,assumption,(~(sP4)),introduced(assumption,[])).
% 0.20/0.42 thf(h4,assumption,(~(sP3)),introduced(assumption,[])).
% 0.20/0.42 thf(h5,assumption,sP1,introduced(assumption,[])).
% 0.20/0.42 thf(1,plain,(~(sP3) | ~(sP1)),inference(all_rule,[status(thm)],[])).
% 0.20/0.42 thf(2,plain,(~(sP5) | sP3),inference(all_rule,[status(thm)],[])).
% 0.20/0.42 thf(choiceaxii,axiom,(![X1:($i>$i)>$o]:((~((![X2:$i>$i]:(~((X1 @ X2)))))) => (X1 @ (epsii @ X1))))).
% 0.20/0.42 thf(3,plain,(![X1:($i>$i)>$o]:((~((![X2:$i>$i]:(~((X1 @ X2)))))) => (X1 @ (epsii @ X1)))),inference(preprocess,[status(thm)],[3]).
% 0.20/0.42 thf(4,plain,(~(sP2) | sP5),inference(choice_rule,[status(thm)],[3])).
% 0.20/0.42 thf(choiceax,axiom,(![X1:$i>$o]:((~((![X2:$i]:(~((X1 @ X2)))))) => (X1 @ (eps @ X1))))).
% 0.20/0.42 thf(5,plain,(![X1:$i>$o]:((~((![X2:$i]:(~((X1 @ X2)))))) => (X1 @ (eps @ X1)))),inference(preprocess,[status(thm)],[5]).
% 0.20/0.42 thf(6,plain,(sP4 | sP2),inference(choice_rule,[status(thm)],[5])).
% 0.20/0.42 thf(7,plain,$false,inference(prop_unsat,[status(thm),assumptions([h5,h4,h2,h3,h1,h0])],[1,2,4,6,h5,h3])).
% 0.20/0.42 thf(8,plain,$false,inference(tab_negall,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__2)],[h4,7,h5])).
% 0.20/0.42 thf(9,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h2,8,h4])).
% 0.20/0.42 thf(10,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,9,h2,h3])).
% 0.20/0.42 thf(11,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,10,h1])).
% 0.20/0.42 thf(0,theorem,(![X1:($i>$i)>$i>$o]:((~((![X2:$i>$i]:(![X3:$i]:(~(((X1 @ X2) @ X3))))))) => ((X1 @ (epsii @ (^[X2:$i>$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3))))))))) @ (eps @ (X1 @ (epsii @ (^[X2:$i>$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3))))))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[11,h0])).
% 0.20/0.42 % SZS output end Proof
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