TSTP Solution File: SYO002^1 by Satallax---3.5
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% File : Satallax---3.5
% Problem : SYO002^1 : 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 : 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 : 600s
% DateTime : Thu Jul 21 19:29:27 EDT 2022
% Result : Theorem 0.12s 0.36s
% 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
% 0.07/0.12 % Problem : SYO002^1 : TPTP v8.1.0. Released v3.7.0.
% 0.07/0.12 % Command : satallax -E eprover-ho -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
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jul 9 13:39:37 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.36 % SZS status Theorem
% 0.12/0.36 % Mode: mode213
% 0.12/0.36 % Inferences: 5
% 0.12/0.36 % SZS output start Proof
% 0.12/0.36 thf(ty_eigen__2, type, eigen__2 : ($i>$i)).
% 0.12/0.36 thf(ty_eigen__1, type, eigen__1 : $i).
% 0.12/0.36 thf(ty_eigen__0, type, eigen__0 : $i).
% 0.12/0.36 thf(ty_eigen__3, type, eigen__3 : ($i>$o)).
% 0.12/0.36 thf(sP1,plain,sP1 <=> (eigen__3 @ (eigen__2 @ eigen__0)),introduced(definition,[new_symbols(definition,[sP1])])).
% 0.12/0.36 thf(sP2,plain,sP2 <=> ((eigen__2 @ eigen__0) = (eigen__2 @ eigen__1)),introduced(definition,[new_symbols(definition,[sP2])])).
% 0.12/0.36 thf(sP3,plain,sP3 <=> (eigen__0 = eigen__1),introduced(definition,[new_symbols(definition,[sP3])])).
% 0.12/0.36 thf(sP4,plain,sP4 <=> (eigen__3 @ (eigen__2 @ eigen__1)),introduced(definition,[new_symbols(definition,[sP4])])).
% 0.12/0.36 thf(def_leibeq,definition,(leibeq = (^[X1:$i]:(^[X2:$i]:(![X3:$i>$o]:((X3 @ X1) => (X3 @ X2))))))).
% 0.12/0.36 thf(conj,conjecture,(![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i>$o]:((X4 @ X1) => (X4 @ X2))) => (![X4:$i>$o]:((X4 @ (X3 @ X1)) => (X4 @ (X3 @ X2))))))))).
% 0.12/0.36 thf(h0,negated_conjecture,(~((![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i>$o]:((X4 @ X1) => (X4 @ X2))) => (![X4:$i>$o]:((X4 @ (X3 @ X1)) => (X4 @ (X3 @ X2)))))))))),inference(assume_negation,[status(cth)],[conj])).
% 0.12/0.36 thf(h1,assumption,(~((![X1:$i]:(![X2:$i>$i]:((![X3:$i>$o]:((X3 @ eigen__0) => (X3 @ X1))) => (![X3:$i>$o]:((X3 @ (X2 @ eigen__0)) => (X3 @ (X2 @ X1))))))))),introduced(assumption,[])).
% 0.12/0.36 thf(h2,assumption,(~((![X1:$i>$i]:((![X2:$i>$o]:((X2 @ eigen__0) => (X2 @ eigen__1))) => (![X2:$i>$o]:((X2 @ (X1 @ eigen__0)) => (X2 @ (X1 @ eigen__1)))))))),introduced(assumption,[])).
% 0.12/0.36 thf(h3,assumption,(~(((![X1:$i>$o]:((X1 @ eigen__0) => (X1 @ eigen__1))) => (![X1:$i>$o]:((X1 @ (eigen__2 @ eigen__0)) => (X1 @ (eigen__2 @ eigen__1))))))),introduced(assumption,[])).
% 0.12/0.36 thf(h4,assumption,(![X1:$i>$o]:((X1 @ eigen__0) => (X1 @ eigen__1))),introduced(assumption,[])).
% 0.12/0.36 thf(h5,assumption,(~((![X1:$i>$o]:((X1 @ (eigen__2 @ eigen__0)) => (X1 @ (eigen__2 @ eigen__1)))))),introduced(assumption,[])).
% 0.12/0.36 thf(h6,assumption,(~((sP1 => sP4))),introduced(assumption,[])).
% 0.12/0.36 thf(h7,assumption,sP1,introduced(assumption,[])).
% 0.12/0.36 thf(h8,assumption,(~(sP4)),introduced(assumption,[])).
% 0.12/0.36 thf(1,plain,(sP2 | ~(sP3)),inference(prop_rule,[status(thm)],[])).
% 0.12/0.36 thf(2,plain,((~(sP1) | sP4) | ~(sP2)),inference(mating_rule,[status(thm)],[])).
% 0.12/0.36 thf(3,plain,sP3,inference(normalize,[status(thm)],[h4]).
% 0.12/0.36 thf(4,plain,$false,inference(prop_unsat,[status(thm),assumptions([h7,h8,h6,h4,h5,h3,h2,h1,h0])],[1,2,3,h7,h8])).
% 0.12/0.36 thf(5,plain,$false,inference(tab_negimp,[status(thm),assumptions([h6,h4,h5,h3,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,4,h7,h8])).
% 0.12/0.36 thf(6,plain,$false,inference(tab_negall,[status(thm),assumptions([h4,h5,h3,h2,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__3)],[h5,5,h6])).
% 0.12/0.36 thf(7,plain,$false,inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,6,h4,h5])).
% 0.12/0.36 thf(8,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__2)],[h2,7,h3])).
% 0.12/0.36 thf(9,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,8,h2])).
% 0.12/0.36 thf(10,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,9,h1])).
% 0.12/0.36 thf(0,theorem,(![X1:$i]:(![X2:$i]:(![X3:$i>$i]:((![X4:$i>$o]:((X4 @ X1) => (X4 @ X2))) => (![X4:$i>$o]:((X4 @ (X3 @ X1)) => (X4 @ (X3 @ X2)))))))),inference(contra,[status(thm),contra(discharge,[h0])],[10,h0])).
% 0.12/0.36 % SZS output end Proof
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