TSTP Solution File: SYO035^1 by Satallax---3.5
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% File : Satallax---3.5
% Problem : SYO035^1 : TPTP v8.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n020.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 : Thu Jul 21 19:29:40 EDT 2022
% Result : Theorem 0.12s 0.35s
% Output : Proof 0.12s
% 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 : SYO035^1 : TPTP v8.1.0. Released v3.7.0.
% 0.03/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n020.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
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jul 9 04:37:58 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.35 % SZS status Theorem
% 0.12/0.35 % Mode: mode213
% 0.12/0.35 % Inferences: 13
% 0.12/0.35 % SZS output start Proof
% 0.12/0.35 thf(ty_eigen__2, type, eigen__2 : ($i>$o)).
% 0.12/0.35 thf(ty_eigen__1, type, eigen__1 : $i).
% 0.12/0.35 thf(ty_eigen__0, type, eigen__0 : $i).
% 0.12/0.35 thf(sP1,plain,sP1 <=> (eigen__2 @ eigen__0),introduced(definition,[new_symbols(definition,[sP1])])).
% 0.12/0.35 thf(sP2,plain,sP2 <=> (![X1:$i]:((X1 = eigen__0) = (X1 = eigen__1))),introduced(definition,[new_symbols(definition,[sP2])])).
% 0.12/0.35 thf(sP3,plain,sP3 <=> (eigen__0 = eigen__1),introduced(definition,[new_symbols(definition,[sP3])])).
% 0.12/0.35 thf(sP4,plain,sP4 <=> (eigen__0 = eigen__0),introduced(definition,[new_symbols(definition,[sP4])])).
% 0.12/0.35 thf(sP5,plain,sP5 <=> ((^[X1:$i]:(X1 = eigen__0)) = (^[X1:$i]:(X1 = eigen__1))),introduced(definition,[new_symbols(definition,[sP5])])).
% 0.12/0.35 thf(sP6,plain,sP6 <=> (eigen__2 @ eigen__1),introduced(definition,[new_symbols(definition,[sP6])])).
% 0.12/0.35 thf(sP7,plain,sP7 <=> (sP4 = sP3),introduced(definition,[new_symbols(definition,[sP7])])).
% 0.12/0.35 thf(def_leibeq1,definition,(leibeq1 = (^[X1:$i]:(^[X2:$i]:(![X3:$i>$o]:((X3 @ X1) => (X3 @ X2))))))).
% 0.12/0.35 thf(def_leibeq2,definition,(leibeq2 = (^[X1:$i>$o]:(^[X2:$i>$o]:(![X3:($i>$o)>$o]:((X3 @ X1) => (X3 @ X2))))))).
% 0.12/0.35 thf(conj,conjecture,(![X1:$i]:(![X2:$i]:((![X3:($i>$o)>$o]:((X3 @ (^[X4:$i]:(X4 = X1))) => (X3 @ (^[X4:$i]:(X4 = X2))))) => (![X3:$i>$o]:((X3 @ X1) => (X3 @ X2))))))).
% 0.12/0.35 thf(h0,negated_conjecture,(~((![X1:$i]:(![X2:$i]:((![X3:($i>$o)>$o]:((X3 @ (^[X4:$i]:(X4 = X1))) => (X3 @ (^[X4:$i]:(X4 = X2))))) => (![X3:$i>$o]:((X3 @ X1) => (X3 @ X2)))))))),inference(assume_negation,[status(cth)],[conj])).
% 0.12/0.35 thf(h1,assumption,(~((![X1:$i]:((![X2:($i>$o)>$o]:((X2 @ (^[X3:$i]:(X3 = eigen__0))) => (X2 @ (^[X3:$i]:(X3 = X1))))) => (![X2:$i>$o]:((X2 @ eigen__0) => (X2 @ X1))))))),introduced(assumption,[])).
% 0.12/0.35 thf(h2,assumption,(~(((![X1:($i>$o)>$o]:((X1 @ (^[X2:$i]:(X2 = eigen__0))) => (X1 @ (^[X2:$i]:(X2 = eigen__1))))) => (![X1:$i>$o]:((X1 @ eigen__0) => (X1 @ eigen__1)))))),introduced(assumption,[])).
% 0.12/0.35 thf(h3,assumption,(![X1:($i>$o)>$o]:((X1 @ (^[X2:$i]:(X2 = eigen__0))) => (X1 @ (^[X2:$i]:(X2 = eigen__1))))),introduced(assumption,[])).
% 0.12/0.35 thf(h4,assumption,(~((![X1:$i>$o]:((X1 @ eigen__0) => (X1 @ eigen__1))))),introduced(assumption,[])).
% 0.12/0.35 thf(h5,assumption,(~((sP1 => sP6))),introduced(assumption,[])).
% 0.12/0.35 thf(h6,assumption,sP1,introduced(assumption,[])).
% 0.12/0.35 thf(h7,assumption,(~(sP6)),introduced(assumption,[])).
% 0.12/0.35 thf(1,plain,sP4,inference(prop_rule,[status(thm)],[])).
% 0.12/0.35 thf(2,plain,((~(sP7) | ~(sP4)) | sP3),inference(prop_rule,[status(thm)],[])).
% 0.12/0.35 thf(3,plain,(~(sP2) | sP7),inference(all_rule,[status(thm)],[])).
% 0.12/0.35 thf(4,plain,((~(sP1) | sP6) | ~(sP3)),inference(mating_rule,[status(thm)],[])).
% 0.12/0.35 thf(5,plain,(~(sP5) | sP2),inference(prop_rule,[status(thm)],[])).
% 0.12/0.35 thf(6,plain,sP5,inference(normalize,[status(thm)],[h3]).
% 0.12/0.35 thf(7,plain,$false,inference(prop_unsat,[status(thm),assumptions([h6,h7,h5,h3,h4,h2,h1,h0])],[1,2,3,4,5,6,h6,h7])).
% 0.12/0.35 thf(8,plain,$false,inference(tab_negimp,[status(thm),assumptions([h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h6,h7])],[h5,7,h6,h7])).
% 0.12/0.35 thf(9,plain,$false,inference(tab_negall,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__2)],[h4,8,h5])).
% 0.12/0.35 thf(10,plain,$false,inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,9,h3,h4])).
% 0.12/0.35 thf(11,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,10,h2])).
% 0.12/0.35 thf(12,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,11,h1])).
% 0.12/0.35 thf(0,theorem,(![X1:$i]:(![X2:$i]:((![X3:($i>$o)>$o]:((X3 @ (^[X4:$i]:(X4 = X1))) => (X3 @ (^[X4:$i]:(X4 = X2))))) => (![X3:$i>$o]:((X3 @ X1) => (X3 @ X2)))))),inference(contra,[status(thm),contra(discharge,[h0])],[12,h0])).
% 0.12/0.35 % SZS output end Proof
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