TSTP Solution File: SYO277^5 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SYO277^5 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n029.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 19:31:13 EDT 2022
% Result : Theorem 0.13s 0.36s
% Output : Proof 0.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SYO277^5 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.33 % Computer : n029.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sat Jul 9 02:31:00 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.36 % SZS status Theorem
% 0.13/0.36 % Mode: mode213
% 0.13/0.36 % Inferences: 19
% 0.13/0.36 % SZS output start Proof
% 0.13/0.36 thf(ty_eigen__2, type, eigen__2 : ($i>$i>$o)).
% 0.13/0.36 thf(ty_eigen__1, type, eigen__1 : $i).
% 0.13/0.36 thf(ty_eigen__0, type, eigen__0 : $i).
% 0.13/0.36 thf(ty_eigen__4, type, eigen__4 : ($i>$o)).
% 0.13/0.36 thf(sP1,plain,sP1 <=> (![X1:$i]:((eigen__2 @ X1) @ X1)),introduced(definition,[new_symbols(definition,[sP1])])).
% 0.13/0.36 thf(sP2,plain,sP2 <=> ((eigen__2 @ eigen__0) @ eigen__0),introduced(definition,[new_symbols(definition,[sP2])])).
% 0.13/0.36 thf(sP3,plain,sP3 <=> (eigen__4 @ eigen__1),introduced(definition,[new_symbols(definition,[sP3])])).
% 0.13/0.36 thf(sP4,plain,sP4 <=> (eigen__0 = eigen__1),introduced(definition,[new_symbols(definition,[sP4])])).
% 0.13/0.36 thf(sP5,plain,sP5 <=> ((eigen__2 @ eigen__0) @ eigen__1),introduced(definition,[new_symbols(definition,[sP5])])).
% 0.13/0.36 thf(sP6,plain,sP6 <=> (eigen__4 @ eigen__0),introduced(definition,[new_symbols(definition,[sP6])])).
% 0.13/0.36 thf(sP7,plain,sP7 <=> (eigen__0 = eigen__0),introduced(definition,[new_symbols(definition,[sP7])])).
% 0.13/0.36 thf(cTHM47D,conjecture,(![X1:$i]:(![X2:$i]:((![X3:$i>$o]:((X3 @ X1) => (X3 @ X2))) = (![X3:$i>$i>$o]:((![X4:$i]:((X3 @ X4) @ X4)) => ((X3 @ X1) @ X2))))))).
% 0.13/0.36 thf(h0,negated_conjecture,(~((![X1:$i]:(![X2:$i]:((![X3:$i>$o]:((X3 @ X1) => (X3 @ X2))) = (![X3:$i>$i>$o]:((![X4:$i]:((X3 @ X4) @ X4)) => ((X3 @ X1) @ X2)))))))),inference(assume_negation,[status(cth)],[cTHM47D])).
% 0.13/0.36 thf(h1,assumption,(~((![X1:$i]:((![X2:$i>$o]:((X2 @ eigen__0) => (X2 @ X1))) = (![X2:$i>$i>$o]:((![X3:$i]:((X2 @ X3) @ X3)) => ((X2 @ eigen__0) @ X1))))))),introduced(assumption,[])).
% 0.13/0.36 thf(h2,assumption,(~(((![X1:$i>$o]:((X1 @ eigen__0) => (X1 @ eigen__1))) = (![X1:$i>$i>$o]:((![X2:$i]:((X1 @ X2) @ X2)) => ((X1 @ eigen__0) @ eigen__1)))))),introduced(assumption,[])).
% 0.13/0.36 thf(h3,assumption,(![X1:$i>$o]:((X1 @ eigen__0) => (X1 @ eigen__1))),introduced(assumption,[])).
% 0.13/0.36 thf(h4,assumption,(![X1:$i>$i>$o]:((![X2:$i]:((X1 @ X2) @ X2)) => ((X1 @ eigen__0) @ eigen__1))),introduced(assumption,[])).
% 0.13/0.36 thf(h5,assumption,(~((![X1:$i>$o]:((X1 @ eigen__0) => (X1 @ eigen__1))))),introduced(assumption,[])).
% 0.13/0.36 thf(h6,assumption,(~((![X1:$i>$i>$o]:((![X2:$i]:((X1 @ X2) @ X2)) => ((X1 @ eigen__0) @ eigen__1))))),introduced(assumption,[])).
% 0.13/0.36 thf(h7,assumption,(~((sP1 => sP5))),introduced(assumption,[])).
% 0.13/0.36 thf(h8,assumption,sP1,introduced(assumption,[])).
% 0.13/0.36 thf(h9,assumption,(~(sP5)),introduced(assumption,[])).
% 0.13/0.36 thf(1,plain,sP7,inference(prop_rule,[status(thm)],[])).
% 0.13/0.36 thf(2,plain,(((~(sP2) | sP5) | ~(sP7)) | ~(sP4)),inference(mating_rule,[status(thm)],[])).
% 0.13/0.36 thf(3,plain,(~(sP1) | sP2),inference(all_rule,[status(thm)],[])).
% 0.13/0.36 1: Could not find hyp name
% 0.13/0.36 s = Pi:$i>$i>$o (\_:$i>$i>$o.imp (Pi:$i (\_:$i.^1 ^0 ^0)) (^0 __0 __1))
% 0.13/0.36 hyp:
% 0.13/0.36 h8: Pi:$i (\_:$i.__2 ^0 ^0)
% 0.13/0.36 h9: imp (__2 __0 __1) False
% 0.13/0.36 h7: imp (imp (Pi:$i (\_:$i.__2 ^0 ^0)) (__2 __0 __1)) False
% 0.13/0.36 h3: Pi:$i>$o (\_:$i>$o.imp (^0 __0) (^0 __1))
% 0.13/0.36 h4: imp (Pi:$i>$i>$o (\_:$i>$i>$o.imp (Pi:$i (\_:$i.^1 ^0 ^0)) (^0 __0 __1))) False
% 0.13/0.36 h2: imp (eq:$o (Pi:$i>$o (\_:$i>$o.imp (^0 __0) (^0 __1))) (Pi:$i>$i>$o (\_:$i>$i>$o.imp (Pi:$i (\_:$i.^1 ^0 ^0)) (^0 __0 __1)))) False
% 0.13/0.36 h1: imp (Pi:$i (\_:$i.eq:$o (Pi:$i>$o (\_:$i>$o.imp (^0 __0) (^0 ^1))) (Pi:$i>$i>$o (\_:$i>$i>$o.imp (Pi:$i (\_:$i.^1 ^0 ^0)) (^0 __0 ^1))))) False
% 0.13/0.36 h0: imp (Pi:$i (\_:$i.Pi:$i (\_:$i.eq:$o (Pi:$i>$o (\_:$i>$o.imp (^0 ^2) (^0 ^1))) (Pi:$i>$i>$o (\_:$i>$i>$o.imp (Pi:$i (\_:$i.^1 ^0 ^0)) (^0 ^2 ^1)))))) False
% 0.43/0.72 % SZS status Theorem
% 0.43/0.72 % Mode: mode506
% 0.43/0.72 % Inferences: 88827
% 0.43/0.72 % SZS output start Proof
% 0.43/0.72 thf(ty_eigen__2, type, eigen__2 : ($i>$o)).
% 0.43/0.72 thf(ty_eigen__25, type, eigen__25 : $i).
% 0.43/0.72 thf(ty_eigen__1, type, eigen__1 : $i).
% 0.43/0.72 thf(ty_eigen__0, type, eigen__0 : $i).
% 0.43/0.72 thf(ty_eigen__3, type, eigen__3 : ($i>$i>$o)).
% 0.43/0.72 thf(h0, assumption, (![X1:($i>$i>$o)>$o]:(![X2:$i>$i>$o]:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])).
% 0.43/0.72 thf(eigendef_eigen__3, definition, eigen__3 = (eps__0 @ (^[X1:$i>$i>$o]:(~(((![X2:$i]:((X1 @ X2) @ X2)) => ((X1 @ eigen__0) @ eigen__1)))))), introduced(definition,[new_symbols(definition,[eigen__3])])).
% 0.43/0.72 thf(h1, assumption, (![X1:$i>$o]:(![X2:$i]:((X1 @ X2) => (X1 @ (eps__1 @ X1))))),introduced(assumption,[])).
% 0.43/0.72 thf(eigendef_eigen__1, definition, eigen__1 = (eps__1 @ (^[X1:$i]:(~(((![X2:$i>$o]:((X2 @ eigen__0) => (X2 @ X1))) = (![X2:$i>$i>$o]:((![X3:$i]:((X2 @ X3) @ X3)) => ((X2 @ eigen__0) @ X1)))))))), introduced(definition,[new_symbols(definition,[eigen__1])])).
% 0.43/0.72 thf(eigendef_eigen__0, definition, eigen__0 = (eps__1 @ (^[X1:$i]:(~((![X2:$i]:((![X3:$i>$o]:((X3 @ X1) => (X3 @ X2))) = (![X3:$i>$i>$o]:((![X4:$i]:((X3 @ X4) @ X4)) => ((X3 @ X1) @ X2))))))))), introduced(definition,[new_symbols(definition,[eigen__0])])).
% 0.43/0.72 thf(h2, assumption, (![X1:($i>$o)>$o]:(![X2:$i>$o]:((X1 @ X2) => (X1 @ (eps__2 @ X1))))),introduced(assumption,[])).
% 0.43/0.72 thf(eigendef_eigen__2, definition, eigen__2 = (eps__2 @ (^[X1:$i>$o]:(~(((X1 @ eigen__0) => (X1 @ eigen__1)))))), introduced(definition,[new_symbols(definition,[eigen__2])])).
% 0.43/0.72 thf(eigendef_eigen__25, definition, eigen__25 = (eps__1 @ (^[X1:$i]:(~((X1 = X1))))), introduced(definition,[new_symbols(definition,[eigen__25])])).
% 0.43/0.72 thf(sP1,plain,sP1 <=> (![X1:$i]:((![X2:$i>$o]:((X2 @ eigen__0) => (X2 @ X1))) = (![X2:$i>$i>$o]:((![X3:$i]:((X2 @ X3) @ X3)) => ((X2 @ eigen__0) @ X1))))),introduced(definition,[new_symbols(definition,[sP1])])).
% 0.43/0.72 thf(sP2,plain,sP2 <=> (((eigen__3 @ eigen__0) @ eigen__0) => ((eigen__3 @ eigen__0) @ eigen__1)),introduced(definition,[new_symbols(definition,[sP2])])).
% 0.43/0.72 thf(sP3,plain,sP3 <=> (![X1:$i]:(X1 = X1)),introduced(definition,[new_symbols(definition,[sP3])])).
% 0.43/0.72 thf(sP4,plain,sP4 <=> (![X1:$i>$o]:((X1 @ eigen__0) => (X1 @ eigen__1))),introduced(definition,[new_symbols(definition,[sP4])])).
% 0.43/0.72 thf(sP5,plain,sP5 <=> ((eigen__3 @ eigen__0) @ eigen__0),introduced(definition,[new_symbols(definition,[sP5])])).
% 0.43/0.72 thf(sP6,plain,sP6 <=> ((eigen__3 @ eigen__0) @ eigen__1),introduced(definition,[new_symbols(definition,[sP6])])).
% 0.43/0.72 thf(sP7,plain,sP7 <=> (![X1:$i]:((eigen__3 @ X1) @ X1)),introduced(definition,[new_symbols(definition,[sP7])])).
% 0.43/0.72 thf(sP8,plain,sP8 <=> (eigen__2 @ eigen__0),introduced(definition,[new_symbols(definition,[sP8])])).
% 0.43/0.72 thf(sP9,plain,sP9 <=> (![X1:$i>$i>$o]:((![X2:$i]:((X1 @ X2) @ X2)) => ((X1 @ eigen__0) @ eigen__1))),introduced(definition,[new_symbols(definition,[sP9])])).
% 0.43/0.72 thf(sP10,plain,sP10 <=> (sP7 => sP6),introduced(definition,[new_symbols(definition,[sP10])])).
% 0.43/0.72 thf(sP11,plain,sP11 <=> (eigen__0 = eigen__1),introduced(definition,[new_symbols(definition,[sP11])])).
% 0.43/0.72 thf(sP12,plain,sP12 <=> (sP4 = sP9),introduced(definition,[new_symbols(definition,[sP12])])).
% 0.43/0.72 thf(sP13,plain,sP13 <=> (![X1:$i]:(![X2:$i]:((![X3:$i>$o]:((X3 @ X1) => (X3 @ X2))) = (![X3:$i>$i>$o]:((![X4:$i]:((X3 @ X4) @ X4)) => ((X3 @ X1) @ X2)))))),introduced(definition,[new_symbols(definition,[sP13])])).
% 0.43/0.72 thf(sP14,plain,sP14 <=> (sP8 => (eigen__2 @ eigen__1)),introduced(definition,[new_symbols(definition,[sP14])])).
% 0.43/0.72 thf(sP15,plain,sP15 <=> (eigen__25 = eigen__25),introduced(definition,[new_symbols(definition,[sP15])])).
% 0.43/0.72 thf(sP16,plain,sP16 <=> (eigen__2 @ eigen__1),introduced(definition,[new_symbols(definition,[sP16])])).
% 0.43/0.72 thf(sP17,plain,sP17 <=> (sP3 => sP11),introduced(definition,[new_symbols(definition,[sP17])])).
% 0.43/0.72 thf(cTHM47D,conjecture,sP13).
% 0.43/0.72 thf(h3,negated_conjecture,(~(sP13)),inference(assume_negation,[status(cth)],[cTHM47D])).
% 0.43/0.72 thf(1,plain,sP15,inference(prop_rule,[status(thm)],[])).
% 0.43/0.72 thf(2,plain,(sP3 | ~(sP15)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__25])).
% 0.43/0.72 thf(3,plain,((~(sP17) | ~(sP3)) | sP11),inference(prop_rule,[status(thm)],[])).
% 0.43/0.72 thf(4,plain,(~(sP9) | sP17),inference(all_rule,[status(thm)],[])).
% 0.43/0.72 thf(5,plain,(~(sP7) | sP5),inference(all_rule,[status(thm)],[])).
% 0.43/0.72 thf(6,plain,((~(sP2) | ~(sP5)) | sP6),inference(prop_rule,[status(thm)],[])).
% 0.43/0.72 thf(7,plain,(~(sP4) | sP2),inference(all_rule,[status(thm)],[])).
% 0.43/0.72 thf(8,plain,(sP10 | ~(sP6)),inference(prop_rule,[status(thm)],[])).
% 0.43/0.72 thf(9,plain,(sP10 | sP7),inference(prop_rule,[status(thm)],[])).
% 0.43/0.72 thf(10,plain,(sP9 | ~(sP10)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__3])).
% 0.43/0.72 thf(11,plain,((~(sP8) | sP16) | ~(sP11)),inference(mating_rule,[status(thm)],[])).
% 0.43/0.72 thf(12,plain,(sP14 | ~(sP16)),inference(prop_rule,[status(thm)],[])).
% 0.43/0.72 thf(13,plain,(sP14 | sP8),inference(prop_rule,[status(thm)],[])).
% 0.43/0.72 thf(14,plain,(sP4 | ~(sP14)),inference(eigen_choice_rule,[status(thm),assumptions([h2])],[h2,eigendef_eigen__2])).
% 0.43/0.72 thf(15,plain,((sP12 | ~(sP4)) | ~(sP9)),inference(prop_rule,[status(thm)],[])).
% 0.43/0.72 thf(16,plain,((sP12 | sP4) | sP9),inference(prop_rule,[status(thm)],[])).
% 0.43/0.72 thf(17,plain,(sP1 | ~(sP12)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__1])).
% 0.43/0.72 thf(18,plain,(sP13 | ~(sP1)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__0])).
% 0.43/0.72 thf(19,plain,$false,inference(prop_unsat,[status(thm),assumptions([h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,h3])).
% 0.43/0.72 thf(20,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h3,h1,h0]),eigenvar_choice(discharge,[h2])],[19,h2])).
% 0.43/0.72 thf(21,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h3,h0]),eigenvar_choice(discharge,[h1])],[20,h1])).
% 0.43/0.72 thf(22,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h3]),eigenvar_choice(discharge,[h0])],[21,h0])).
% 0.43/0.72 thf(0,theorem,sP13,inference(contra,[status(thm),contra(discharge,[h3])],[19,h3])).
% 0.43/0.72 % SZS output end Proof
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