TSTP Solution File: SYO541^1 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO541^1 : 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 : n005.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 0.19s 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
% 0.11/0.12 % Problem : SYO541^1 : TPTP v8.1.2. Released v5.2.0.
% 0.11/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Aug 26 03:34:53 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.40 % SZS status Theorem
% 0.19/0.40 % Mode: cade22grackle2xfee4
% 0.19/0.40 % Steps: 19
% 0.19/0.40 % SZS output start Proof
% 0.19/0.40 thf(ty_eigen__0, type, eigen__0 : ($i>$i)).
% 0.19/0.40 thf(ty_epsii, type, epsii : ((($i>$i)>$o)>$i>$i)).
% 0.19/0.40 thf(ty_eigen__1, type, eigen__1 : ($i>$i)).
% 0.19/0.40 thf(sP1,plain,sP1 <=> ((epsii @ (^[X1:$i>$i]:(X1 = eigen__0))) = eigen__0),introduced(definition,[new_symbols(definition,[sP1])])).
% 0.19/0.40 thf(sP2,plain,sP2 <=> (![X1:$i>$i]:(~((X1 = eigen__1)))),introduced(definition,[new_symbols(definition,[sP2])])).
% 0.19/0.40 thf(sP3,plain,sP3 <=> $false,introduced(definition,[new_symbols(definition,[sP3])])).
% 0.19/0.40 thf(sP4,plain,sP4 <=> ((epsii @ (^[X1:$i>$i]:(X1 = eigen__1))) = eigen__1),introduced(definition,[new_symbols(definition,[sP4])])).
% 0.19/0.40 thf(sP5,plain,sP5 <=> (sP1 => (~(sP4))),introduced(definition,[new_symbols(definition,[sP5])])).
% 0.19/0.40 thf(sP6,plain,sP6 <=> (![X1:$i>$i]:(~((X1 = eigen__0)))),introduced(definition,[new_symbols(definition,[sP6])])).
% 0.19/0.40 thf(def_if,definition,(if = (^[X1:$o]:(^[X2:$i>$i]:(^[X3:$i>$i]:(epsii @ (^[X4:$i>$i]:((X1 & (X4 = X2)) | (((~) @ X1) & (X4 = X3)))))))))).
% 0.19/0.40 thf(conj,conjecture,(![X1:$i>$i]:(![X2:$i>$i]:(~((((epsii @ (^[X3:$i>$i]:(X3 = X1))) = X1) => (~(((epsii @ (^[X3:$i>$i]:(X3 = X2))) = X2))))))))).
% 0.19/0.40 thf(h0,negated_conjecture,(~((![X1:$i>$i]:(![X2:$i>$i]:(~((((epsii @ (^[X3:$i>$i]:(X3 = X1))) = X1) => (~(((epsii @ (^[X3:$i>$i]:(X3 = X2))) = X2)))))))))),inference(assume_negation,[status(cth)],[conj])).
% 0.19/0.40 thf(h1,assumption,(~((![X1:$i>$i]:(~((sP1 => (~(((epsii @ (^[X2:$i>$i]:(X2 = X1))) = X1))))))))),introduced(assumption,[])).
% 0.19/0.40 thf(h2,assumption,sP5,introduced(assumption,[])).
% 0.19/0.40 thf(1,plain,(~(sP2) | sP3),inference(all_rule,[status(thm)],[])).
% 0.19/0.40 thf(2,plain,~(sP3),inference(prop_rule,[status(thm)],[])).
% 0.19/0.40 thf(3,plain,(~(sP6) | sP3),inference(all_rule,[status(thm)],[])).
% 0.19/0.40 thf(choiceaxii,axiom,(![X1:($i>$i)>$o]:((~((![X2:$i>$i]:(~((X1 @ X2)))))) => (X1 @ (epsii @ X1))))).
% 0.19/0.40 thf(4,plain,(![X1:($i>$i)>$o]:((~((![X2:$i>$i]:(~((X1 @ X2)))))) => (X1 @ (epsii @ X1)))),inference(preprocess,[status(thm)],[4]).
% 0.19/0.40 thf(5,plain,(sP4 | sP2),inference(choice_rule,[status(thm)],[4])).
% 0.19/0.40 thf(6,plain,(![X1:($i>$i)>$o]:((~((![X2:$i>$i]:(~((X1 @ X2)))))) => (X1 @ (epsii @ X1)))),inference(preprocess,[status(thm)],[6]).
% 0.19/0.40 thf(7,plain,(sP1 | sP6),inference(choice_rule,[status(thm)],[6])).
% 0.19/0.40 thf(8,plain,((~(sP5) | ~(sP1)) | ~(sP4)),inference(prop_rule,[status(thm)],[])).
% 0.19/0.40 thf(9,plain,$false,inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,5,7,8,h2])).
% 0.19/0.40 thf(10,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,9,h2])).
% 0.19/0.40 thf(11,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,10,h1])).
% 0.19/0.40 thf(0,theorem,(![X1:$i>$i]:(![X2:$i>$i]:(~((((epsii @ (^[X3:$i>$i]:(X3 = X1))) = X1) => (~(((epsii @ (^[X3:$i>$i]:(X3 = X2))) = X2)))))))),inference(contra,[status(thm),contra(discharge,[h0])],[11,h0])).
% 0.19/0.40 % SZS output end Proof
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