TSTP Solution File: SYO539^1 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO539^1 : 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 : n002.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 04:47:25 EDT 2023
% Result : Theorem 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO539^1 : TPTP v8.1.2. Released v5.2.0.
% 0.07/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n002.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.19/0.34 % WCLimit : 300
% 0.19/0.34 % DateTime : Sat Aug 26 04:47:02 EDT 2023
% 0.19/0.34 % CPUTime :
% 0.20/0.40 % SZS status Theorem
% 0.20/0.40 % Mode: cade22grackle2xfee4
% 0.20/0.40 % Steps: 19
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 thf(ty_eigen__2, type, eigen__2 : $i).
% 0.20/0.40 thf(ty_eigen__0, type, eigen__0 : $o).
% 0.20/0.40 thf(ty_eps, type, eps : (($i>$o)>$i)).
% 0.20/0.40 thf(ty_eigen__1, type, eigen__1 : $i).
% 0.20/0.40 thf(sP1,plain,sP1 <=> ((eps @ (^[X1:$i]:((eigen__0 => (~((X1 = eigen__1)))) => (~(((~(eigen__0)) => (~((X1 = eigen__2))))))))) = eigen__1),introduced(definition,[new_symbols(definition,[sP1])])).
% 0.20/0.40 thf(sP2,plain,sP2 <=> eigen__0,introduced(definition,[new_symbols(definition,[sP2])])).
% 0.20/0.40 thf(sP3,plain,sP3 <=> (sP2 => (~(sP1))),introduced(definition,[new_symbols(definition,[sP3])])).
% 0.20/0.40 thf(sP4,plain,sP4 <=> ((~(sP2)) => (~(((eps @ (^[X1:$i]:((sP2 => (~((X1 = eigen__1)))) => (~(((~(sP2)) => (~((X1 = eigen__2))))))))) = eigen__2)))),introduced(definition,[new_symbols(definition,[sP4])])).
% 0.20/0.40 thf(sP5,plain,sP5 <=> ((sP2 => (~((eigen__2 = eigen__1)))) => (~(sP2))),introduced(definition,[new_symbols(definition,[sP5])])).
% 0.20/0.40 thf(sP6,plain,sP6 <=> (![X1:$i]:(~(((sP2 => (~((X1 = eigen__1)))) => (~(((~(sP2)) => (~((X1 = eigen__2)))))))))),introduced(definition,[new_symbols(definition,[sP6])])).
% 0.20/0.40 thf(sP7,plain,sP7 <=> ((eps @ (^[X1:$i]:((sP2 => (~((X1 = eigen__1)))) => (~(((~(sP2)) => (~((X1 = eigen__2))))))))) = eigen__2),introduced(definition,[new_symbols(definition,[sP7])])).
% 0.20/0.40 thf(sP8,plain,sP8 <=> ((~(sP2)) => (~(((~(sP2)) => (~((eigen__1 = eigen__2))))))),introduced(definition,[new_symbols(definition,[sP8])])).
% 0.20/0.40 thf(sP9,plain,sP9 <=> (sP3 => (~(sP4))),introduced(definition,[new_symbols(definition,[sP9])])).
% 0.20/0.40 thf(def_if,definition,(if = (^[X1:$o]:(^[X2:$i]:(^[X3:$i]:(eps @ (^[X4:$i]:((X1 & (X4 = X2)) | (((~) @ X1) & (X4 = X3)))))))))).
% 0.20/0.40 thf(conj,conjecture,(![X1:$o]:(![X2:$i]:(![X3:$i]:((~(((eps @ (^[X4:$i]:((X1 => (~((X4 = X2)))) => (~(((~(X1)) => (~((X4 = X3))))))))) = X2))) => ((eps @ (^[X4:$i]:((X1 => (~((X4 = X2)))) => (~(((~(X1)) => (~((X4 = X3))))))))) = X3)))))).
% 0.20/0.40 thf(h0,negated_conjecture,(~((![X1:$o]:(![X2:$i]:(![X3:$i]:((~(((eps @ (^[X4:$i]:((X1 => (~((X4 = X2)))) => (~(((~(X1)) => (~((X4 = X3))))))))) = X2))) => ((eps @ (^[X4:$i]:((X1 => (~((X4 = X2)))) => (~(((~(X1)) => (~((X4 = X3))))))))) = X3))))))),inference(assume_negation,[status(cth)],[conj])).
% 0.20/0.40 thf(h1,assumption,(~((![X1:$i]:(![X2:$i]:((~(((eps @ (^[X3:$i]:((sP2 => (~((X3 = X1)))) => (~(((~(sP2)) => (~((X3 = X2))))))))) = X1))) => ((eps @ (^[X3:$i]:((sP2 => (~((X3 = X1)))) => (~(((~(sP2)) => (~((X3 = X2))))))))) = X2)))))),introduced(assumption,[])).
% 0.20/0.40 thf(h2,assumption,(~((![X1:$i]:((~(((eps @ (^[X2:$i]:((sP2 => (~((X2 = eigen__1)))) => (~(((~(sP2)) => (~((X2 = X1))))))))) = eigen__1))) => ((eps @ (^[X2:$i]:((sP2 => (~((X2 = eigen__1)))) => (~(((~(sP2)) => (~((X2 = X1))))))))) = X1))))),introduced(assumption,[])).
% 0.20/0.40 thf(h3,assumption,(~(((~(sP1)) => sP7))),introduced(assumption,[])).
% 0.20/0.40 thf(h4,assumption,(~(sP1)),introduced(assumption,[])).
% 0.20/0.40 thf(h5,assumption,(~(sP7)),introduced(assumption,[])).
% 0.20/0.40 thf(1,plain,(sP5 | sP2),inference(prop_rule,[status(thm)],[])).
% 0.20/0.40 thf(2,plain,(~(sP6) | ~(sP5)),inference(all_rule,[status(thm)],[])).
% 0.20/0.40 thf(3,plain,(sP8 | ~(sP2)),inference(prop_rule,[status(thm)],[])).
% 0.20/0.40 thf(4,plain,(~(sP6) | ~(sP8)),inference(all_rule,[status(thm)],[])).
% 0.20/0.40 thf(5,plain,(sP4 | sP7),inference(prop_rule,[status(thm)],[])).
% 0.20/0.40 thf(6,plain,(sP3 | sP1),inference(prop_rule,[status(thm)],[])).
% 0.20/0.40 thf(7,plain,((~(sP9) | ~(sP3)) | ~(sP4)),inference(prop_rule,[status(thm)],[])).
% 0.20/0.40 thf(choiceax,axiom,(![X1:$i>$o]:((~((![X2:$i]:(~((X1 @ X2)))))) => (X1 @ (eps @ X1))))).
% 0.20/0.40 thf(8,plain,(![X1:$i>$o]:((~((![X2:$i]:(~((X1 @ X2)))))) => (X1 @ (eps @ X1)))),inference(preprocess,[status(thm)],[8]).
% 0.20/0.40 thf(9,plain,(sP9 | sP6),inference(choice_rule,[status(thm)],[8])).
% 0.20/0.40 thf(10,plain,$false,inference(prop_unsat,[status(thm),assumptions([h4,h5,h3,h2,h1,h0])],[1,2,3,4,5,6,7,9,h4,h5])).
% 0.20/0.40 thf(11,plain,$false,inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,10,h4,h5])).
% 0.20/0.40 thf(12,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,11,h3])).
% 0.20/0.40 thf(13,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,12,h2])).
% 0.20/0.40 thf(14,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,13,h1])).
% 0.20/0.40 thf(0,theorem,(![X1:$o]:(![X2:$i]:(![X3:$i]:((~(((eps @ (^[X4:$i]:((X1 => (~((X4 = X2)))) => (~(((~(X1)) => (~((X4 = X3))))))))) = X2))) => ((eps @ (^[X4:$i]:((X1 => (~((X4 = X2)))) => (~(((~(X1)) => (~((X4 = X3))))))))) = X3))))),inference(contra,[status(thm),contra(discharge,[h0])],[14,h0])).
% 0.20/0.40 % SZS output end Proof
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