TSTP Solution File: QUA004^1 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : QUA004^1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n017.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 : 600s
% DateTime : Mon Jul 18 18:39:55 EDT 2022
% Result : Theorem 64.67s 64.42s
% Output : Proof 64.67s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : QUA004^1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.11/0.31 % Computer : n017.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 600
% 0.11/0.31 % DateTime : Mon Jul 11 10:26:18 EDT 2022
% 0.11/0.32 % CPUTime :
% 64.67/64.42 % SZS status Theorem
% 64.67/64.42 % Mode: mode453
% 64.67/64.42 % Inferences: 521
% 64.67/64.42 % SZS output start Proof
% 64.67/64.42 thf(ty_eigen__1, type, eigen__1 : $i).
% 64.67/64.42 thf(ty_eigen__0, type, eigen__0 : $i).
% 64.67/64.42 thf(ty_sup, type, sup : (($i>$o)>$i)).
% 64.67/64.42 thf(h0, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])).
% 64.67/64.42 thf(eigendef_eigen__1, definition, eigen__1 = (eps__0 @ (^[X1:$i]:(~(((X1 = eigen__0) = ((~((X1 = eigen__0))) => (X1 = eigen__0))))))), introduced(definition,[new_symbols(definition,[eigen__1])])).
% 64.67/64.42 thf(sP1,plain,sP1 <=> (![X1:$i]:((sup @ (^[X2:$i]:(X2 = X1))) = X1)),introduced(definition,[new_symbols(definition,[sP1])])).
% 64.67/64.42 thf(sP2,plain,sP2 <=> ((^[X1:$i]:(X1 = eigen__0)) = (^[X1:$i]:((~((X1 = eigen__0))) => (X1 = eigen__0)))),introduced(definition,[new_symbols(definition,[sP2])])).
% 64.67/64.42 thf(sP3,plain,sP3 <=> ((sup @ (^[X1:$i]:(X1 = eigen__0))) = eigen__0),introduced(definition,[new_symbols(definition,[sP3])])).
% 64.67/64.42 thf(sP4,plain,sP4 <=> ((~((eigen__1 = eigen__0))) => (eigen__1 = eigen__0)),introduced(definition,[new_symbols(definition,[sP4])])).
% 64.67/64.42 thf(sP5,plain,sP5 <=> ((sup @ (^[X1:$i]:(X1 = eigen__0))) = (sup @ (^[X1:$i]:((~((X1 = eigen__0))) => (X1 = eigen__0))))),introduced(definition,[new_symbols(definition,[sP5])])).
% 64.67/64.42 thf(sP6,plain,sP6 <=> ((eigen__1 = eigen__0) = sP4),introduced(definition,[new_symbols(definition,[sP6])])).
% 64.67/64.42 thf(sP7,plain,sP7 <=> (eigen__1 = eigen__0),introduced(definition,[new_symbols(definition,[sP7])])).
% 64.67/64.42 thf(sP8,plain,sP8 <=> ((sup @ (^[X1:$i]:((~((X1 = eigen__0))) => (X1 = eigen__0)))) = eigen__0),introduced(definition,[new_symbols(definition,[sP8])])).
% 64.67/64.42 thf(sP9,plain,sP9 <=> (![X1:$i]:((X1 = eigen__0) = ((~((X1 = eigen__0))) => (X1 = eigen__0)))),introduced(definition,[new_symbols(definition,[sP9])])).
% 64.67/64.42 thf(def_emptyset,definition,(emptyset = (^[X1:$i]:$false))).
% 64.67/64.42 thf(def_union,definition,(union = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))).
% 64.67/64.42 thf(def_singleton,definition,(singleton = (^[X1:$i]:(^[X2:$i]:(X2 = X1))))).
% 64.67/64.42 thf(def_supset,definition,(supset = (^[X1:($i>$o)>$o]:(^[X2:$i]:(~((![X3:$i>$o]:((X1 @ X3) => (~(((sup @ X3) = X2))))))))))).
% 64.67/64.42 thf(def_unionset,definition,(unionset = (^[X1:($i>$o)>$o]:(^[X2:$i]:(~((![X3:$i>$o]:((X1 @ X3) => (~((X3 @ X2))))))))))).
% 64.67/64.42 thf(def_addition,definition,(addition = (^[X1:$i]:(^[X2:$i]:(sup @ ((union @ (singleton @ X1)) @ (singleton @ X2))))))).
% 64.67/64.42 thf(def_crossmult,definition,(crossmult = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(~((![X4:$i]:(![X5:$i]:((~(((X1 @ X4) => (~((X2 @ X5)))))) => (~((X3 = ((multiplication @ X4) @ X5)))))))))))))).
% 64.67/64.42 thf(addition_idemp,conjecture,(![X1:$i]:((sup @ (^[X2:$i]:((~((X2 = X1))) => (X2 = X1)))) = X1))).
% 64.67/64.42 thf(h1,negated_conjecture,(~((![X1:$i]:((sup @ (^[X2:$i]:((~((X2 = X1))) => (X2 = X1)))) = X1)))),inference(assume_negation,[status(cth)],[addition_idemp])).
% 64.67/64.42 thf(h2,assumption,(~(sP8)),introduced(assumption,[])).
% 64.67/64.42 thf(1,plain,((~(sP4) | sP7) | sP7),inference(prop_rule,[status(thm)],[])).
% 64.67/64.42 thf(2,plain,(sP4 | ~(sP7)),inference(prop_rule,[status(thm)],[])).
% 64.67/64.42 thf(3,plain,((sP6 | ~(sP7)) | ~(sP4)),inference(prop_rule,[status(thm)],[])).
% 64.67/64.42 thf(4,plain,((sP6 | sP7) | sP4),inference(prop_rule,[status(thm)],[])).
% 64.67/64.42 thf(5,plain,(sP9 | ~(sP6)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1])).
% 64.67/64.42 thf(6,plain,(sP2 | ~(sP9)),inference(prop_rule,[status(thm)],[])).
% 64.67/64.42 thf(7,plain,(sP5 | ~(sP2)),inference(prop_rule,[status(thm)],[])).
% 64.67/64.42 thf(8,plain,(((~(sP3) | sP8) | ~(sP5)) | ~(sP3)),inference(confrontation_rule,[status(thm)],[])).
% 64.67/64.42 thf(9,plain,(~(sP1) | sP3),inference(all_rule,[status(thm)],[])).
% 64.67/64.42 thf(sup_singleset,axiom,(![X1:$i]:((sup @ (singleton @ X1)) = X1))).
% 64.67/64.42 thf(10,plain,sP1,inference(preprocess,[status(thm)],[sup_singleset]).
% 64.67/64.42 thf(11,plain,$false,inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,h2,10])).
% 64.67/64.42 thf(12,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,11,h2])).
% 64.67/64.42 thf(13,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[12,h0])).
% 64.67/64.42 thf(0,theorem,(![X1:$i]:((sup @ (^[X2:$i]:((~((X2 = X1))) => (X2 = X1)))) = X1)),inference(contra,[status(thm),contra(discharge,[h1])],[12,h1])).
% 64.67/64.42 % SZS output end Proof
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