TSTP Solution File: SYO005^1 by Satallax---3.5
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% File : Satallax---3.5
% Problem : SYO005^1 : 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 : 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 : Thu Jul 21 19:29:28 EDT 2022
% Result : Theorem 0.14s 0.39s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SYO005^1 : TPTP v8.1.0. Released v3.7.0.
% 0.08/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.36 % Computer : n017.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Sat Jul 9 10:19:17 EDT 2022
% 0.14/0.37 % CPUTime :
% 0.14/0.39 % SZS status Theorem
% 0.14/0.39 % Mode: mode213
% 0.14/0.39 % Inferences: 7
% 0.14/0.39 % SZS output start Proof
% 0.14/0.39 thf(ty_eigen__2, type, eigen__2 : $i).
% 0.14/0.39 thf(ty_eigen__1, type, eigen__1 : ($i>$i)).
% 0.14/0.39 thf(ty_eigen__0, type, eigen__0 : ($i>$i)).
% 0.14/0.39 thf(ty_eigen__3, type, eigen__3 : ($i>$o)).
% 0.14/0.39 thf(sP1,plain,sP1 <=> (eigen__3 @ (eigen__0 @ eigen__2)),introduced(definition,[new_symbols(definition,[sP1])])).
% 0.14/0.39 thf(sP2,plain,sP2 <=> (![X1:$i]:((eigen__0 @ X1) = (eigen__1 @ X1))),introduced(definition,[new_symbols(definition,[sP2])])).
% 0.14/0.39 thf(sP3,plain,sP3 <=> ((eigen__0 @ eigen__2) = (eigen__1 @ eigen__2)),introduced(definition,[new_symbols(definition,[sP3])])).
% 0.14/0.39 thf(sP4,plain,sP4 <=> (eigen__0 = eigen__1),introduced(definition,[new_symbols(definition,[sP4])])).
% 0.14/0.39 thf(sP5,plain,sP5 <=> (eigen__3 @ (eigen__1 @ eigen__2)),introduced(definition,[new_symbols(definition,[sP5])])).
% 0.14/0.39 thf(def_leibeq1,definition,(leibeq1 = (^[X1:$i]:(^[X2:$i]:(![X3:$i>$o]:((X3 @ X1) => (X3 @ X2))))))).
% 0.14/0.39 thf(def_leibeq2,definition,(leibeq2 = (^[X1:$i>$i]:(^[X2:$i>$i]:(![X3:($i>$i)>$o]:((X3 @ X1) => (X3 @ X2))))))).
% 0.14/0.39 thf(conj,conjecture,(![X1:$i>$i]:(![X2:$i>$i]:((![X3:($i>$i)>$o]:((X3 @ X1) => (X3 @ X2))) => (![X3:$i]:(![X4:$i>$o]:((X4 @ (X1 @ X3)) => (X4 @ (X2 @ X3))))))))).
% 0.14/0.39 thf(h0,negated_conjecture,(~((![X1:$i>$i]:(![X2:$i>$i]:((![X3:($i>$i)>$o]:((X3 @ X1) => (X3 @ X2))) => (![X3:$i]:(![X4:$i>$o]:((X4 @ (X1 @ X3)) => (X4 @ (X2 @ X3)))))))))),inference(assume_negation,[status(cth)],[conj])).
% 0.14/0.39 thf(h1,assumption,(~((![X1:$i>$i]:((![X2:($i>$i)>$o]:((X2 @ eigen__0) => (X2 @ X1))) => (![X2:$i]:(![X3:$i>$o]:((X3 @ (eigen__0 @ X2)) => (X3 @ (X1 @ X2))))))))),introduced(assumption,[])).
% 0.14/0.39 thf(h2,assumption,(~(((![X1:($i>$i)>$o]:((X1 @ eigen__0) => (X1 @ eigen__1))) => (![X1:$i]:(![X2:$i>$o]:((X2 @ (eigen__0 @ X1)) => (X2 @ (eigen__1 @ X1)))))))),introduced(assumption,[])).
% 0.14/0.39 thf(h3,assumption,(![X1:($i>$i)>$o]:((X1 @ eigen__0) => (X1 @ eigen__1))),introduced(assumption,[])).
% 0.14/0.39 thf(h4,assumption,(~((![X1:$i]:(![X2:$i>$o]:((X2 @ (eigen__0 @ X1)) => (X2 @ (eigen__1 @ X1))))))),introduced(assumption,[])).
% 0.14/0.39 thf(h5,assumption,(~((![X1:$i>$o]:((X1 @ (eigen__0 @ eigen__2)) => (X1 @ (eigen__1 @ eigen__2)))))),introduced(assumption,[])).
% 0.14/0.39 thf(h6,assumption,(~((sP1 => sP5))),introduced(assumption,[])).
% 0.14/0.39 thf(h7,assumption,sP1,introduced(assumption,[])).
% 0.14/0.39 thf(h8,assumption,(~(sP5)),introduced(assumption,[])).
% 0.14/0.39 thf(1,plain,(~(sP2) | sP3),inference(all_rule,[status(thm)],[])).
% 0.14/0.39 thf(2,plain,((~(sP1) | sP5) | ~(sP3)),inference(mating_rule,[status(thm)],[])).
% 0.14/0.39 thf(3,plain,(~(sP4) | sP2),inference(prop_rule,[status(thm)],[])).
% 0.14/0.39 thf(4,plain,sP4,inference(normalize,[status(thm)],[h3]).
% 0.14/0.39 thf(5,plain,$false,inference(prop_unsat,[status(thm),assumptions([h7,h8,h6,h5,h3,h4,h2,h1,h0])],[1,2,3,4,h7,h8])).
% 0.14/0.39 thf(6,plain,$false,inference(tab_negimp,[status(thm),assumptions([h6,h5,h3,h4,h2,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,5,h7,h8])).
% 0.14/0.39 thf(7,plain,$false,inference(tab_negall,[status(thm),assumptions([h5,h3,h4,h2,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__3)],[h5,6,h6])).
% 0.14/0.39 thf(8,plain,$false,inference(tab_negall,[status(thm),assumptions([h3,h4,h2,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__2)],[h4,7,h5])).
% 0.14/0.39 thf(9,plain,$false,inference(tab_negimp,[status(thm),assumptions([h2,h1,h0]),tab_negimp(discharge,[h3,h4])],[h2,8,h3,h4])).
% 0.14/0.39 thf(10,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__1)],[h1,9,h2])).
% 0.14/0.39 thf(11,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,10,h1])).
% 0.14/0.39 thf(0,theorem,(![X1:$i>$i]:(![X2:$i>$i]:((![X3:($i>$i)>$o]:((X3 @ X1) => (X3 @ X2))) => (![X3:$i]:(![X4:$i>$o]:((X4 @ (X1 @ X3)) => (X4 @ (X2 @ X3)))))))),inference(contra,[status(thm),contra(discharge,[h0])],[11,h0])).
% 0.14/0.39 % SZS output end Proof
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