TSTP Solution File: SYO534^1 by Lash---1.13
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SYO534^1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n008.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 : 300s
% DateTime : Fri Sep 1 04:47:24 EDT 2023
% Result : Theorem 0.22s 0.44s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SYO534^1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.15 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.36 % Computer : n008.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 : 300
% 0.14/0.36 % DateTime : Sat Aug 26 05:16:17 EDT 2023
% 0.14/0.37 % CPUTime :
% 0.22/0.44 % SZS status Theorem
% 0.22/0.44 % Mode: cade22grackle2xfee4
% 0.22/0.44 % Steps: 78
% 0.22/0.44 % SZS output start Proof
% 0.22/0.44 thf(ty_eigen__2, type, eigen__2 : $i).
% 0.22/0.44 thf(ty_eigen__0, type, eigen__0 : ($i>$i>$i>$o)).
% 0.22/0.44 thf(ty_eigen__1, type, eigen__1 : $i).
% 0.22/0.44 thf(ty_eps, type, eps : (($i>$o)>$i)).
% 0.22/0.44 thf(ty_eigen__3, type, eigen__3 : $i).
% 0.22/0.44 thf(sP1,plain,sP1 <=> (((eigen__0 @ eigen__1) @ eigen__2) @ eigen__3),introduced(definition,[new_symbols(definition,[sP1])])).
% 0.22/0.44 thf(sP2,plain,sP2 <=> (![X1:$i]:(![X2:$i]:(~((((eigen__0 @ (eps @ (^[X3:$i]:(~((![X4:$i]:(![X5:$i]:(~((((eigen__0 @ X3) @ X4) @ X5)))))))))) @ X1) @ X2))))),introduced(definition,[new_symbols(definition,[sP2])])).
% 0.22/0.44 thf(sP3,plain,sP3 <=> (![X1:$i]:(![X2:$i]:(![X3:$i]:(~((((eigen__0 @ X1) @ X2) @ X3)))))),introduced(definition,[new_symbols(definition,[sP3])])).
% 0.22/0.44 thf(sP4,plain,sP4 <=> (((eigen__0 @ (eps @ (^[X1:$i]:(~((![X2:$i]:(![X3:$i]:(~((((eigen__0 @ X1) @ X2) @ X3)))))))))) @ (eps @ (^[X1:$i]:(~((![X2:$i]:(~((((eigen__0 @ (eps @ (^[X3:$i]:(~((![X4:$i]:(![X5:$i]:(~((((eigen__0 @ X3) @ X4) @ X5)))))))))) @ X1) @ X2))))))))) @ (eps @ ((eigen__0 @ (eps @ (^[X1:$i]:(~((![X2:$i]:(![X3:$i]:(~((((eigen__0 @ X1) @ X2) @ X3)))))))))) @ (eps @ (^[X1:$i]:(~((![X2:$i]:(~((((eigen__0 @ (eps @ (^[X3:$i]:(~((![X4:$i]:(![X5:$i]:(~((((eigen__0 @ X3) @ X4) @ X5)))))))))) @ X1) @ X2))))))))))),introduced(definition,[new_symbols(definition,[sP4])])).
% 0.22/0.44 thf(sP5,plain,sP5 <=> (![X1:$i]:(~((((eigen__0 @ (eps @ (^[X2:$i]:(~((![X3:$i]:(![X4:$i]:(~((((eigen__0 @ X2) @ X3) @ X4)))))))))) @ (eps @ (^[X2:$i]:(~((![X3:$i]:(~((((eigen__0 @ (eps @ (^[X4:$i]:(~((![X5:$i]:(![X6:$i]:(~((((eigen__0 @ X4) @ X5) @ X6)))))))))) @ X2) @ X3))))))))) @ X1)))),introduced(definition,[new_symbols(definition,[sP5])])).
% 0.22/0.44 thf(sP6,plain,sP6 <=> (![X1:$i]:(![X2:$i]:(~((((eigen__0 @ eigen__1) @ X1) @ X2))))),introduced(definition,[new_symbols(definition,[sP6])])).
% 0.22/0.44 thf(sP7,plain,sP7 <=> (![X1:$i]:(~((((eigen__0 @ eigen__1) @ eigen__2) @ X1)))),introduced(definition,[new_symbols(definition,[sP7])])).
% 0.22/0.44 thf(def_epsa,definition,(epsa = (^[X1:$i>$i>$i>$o]:(eps @ (^[X2:$i]:(?[X3:$i]:(?[X4:$i]:(((X1 @ X2) @ X3) @ X4)))))))).
% 0.22/0.44 thf(def_epsb,definition,(epsb = (^[X1:$i>$i>$i>$o]:(eps @ (^[X2:$i]:(?[X3:$i]:(((X1 @ (epsa @ X1)) @ X2) @ X3))))))).
% 0.22/0.44 thf(def_epsc,definition,(epsc = (^[X1:$i>$i>$i>$o]:(eps @ (^[X2:$i]:(((X1 @ (epsa @ X1)) @ (epsb @ X1)) @ X2)))))).
% 0.22/0.44 thf(conj,conjecture,(![X1:$i>$i>$i>$o]:((~((![X2:$i]:(![X3:$i]:(![X4:$i]:(~((((X1 @ X2) @ X3) @ X4)))))))) => (((X1 @ (eps @ (^[X2:$i]:(~((![X3:$i]:(![X4:$i]:(~((((X1 @ X2) @ X3) @ X4)))))))))) @ (eps @ (^[X2:$i]:(~((![X3:$i]:(~((((X1 @ (eps @ (^[X4:$i]:(~((![X5:$i]:(![X6:$i]:(~((((X1 @ X4) @ X5) @ X6)))))))))) @ X2) @ X3))))))))) @ (eps @ ((X1 @ (eps @ (^[X2:$i]:(~((![X3:$i]:(![X4:$i]:(~((((X1 @ X2) @ X3) @ X4)))))))))) @ (eps @ (^[X2:$i]:(~((![X3:$i]:(~((((X1 @ (eps @ (^[X4:$i]:(~((![X5:$i]:(![X6:$i]:(~((((X1 @ X4) @ X5) @ X6)))))))))) @ X2) @ X3)))))))))))))).
% 0.22/0.44 thf(h0,negated_conjecture,(~((![X1:$i>$i>$i>$o]:((~((![X2:$i]:(![X3:$i]:(![X4:$i]:(~((((X1 @ X2) @ X3) @ X4)))))))) => (((X1 @ (eps @ (^[X2:$i]:(~((![X3:$i]:(![X4:$i]:(~((((X1 @ X2) @ X3) @ X4)))))))))) @ (eps @ (^[X2:$i]:(~((![X3:$i]:(~((((X1 @ (eps @ (^[X4:$i]:(~((![X5:$i]:(![X6:$i]:(~((((X1 @ X4) @ X5) @ X6)))))))))) @ X2) @ X3))))))))) @ (eps @ ((X1 @ (eps @ (^[X2:$i]:(~((![X3:$i]:(![X4:$i]:(~((((X1 @ X2) @ X3) @ X4)))))))))) @ (eps @ (^[X2:$i]:(~((![X3:$i]:(~((((X1 @ (eps @ (^[X4:$i]:(~((![X5:$i]:(![X6:$i]:(~((((X1 @ X4) @ X5) @ X6)))))))))) @ X2) @ X3))))))))))))))),inference(assume_negation,[status(cth)],[conj])).
% 0.22/0.44 thf(h1,assumption,(~(((~(sP3)) => sP4))),introduced(assumption,[])).
% 0.22/0.44 thf(h2,assumption,(~(sP3)),introduced(assumption,[])).
% 0.22/0.44 thf(h3,assumption,(~(sP4)),introduced(assumption,[])).
% 0.22/0.44 thf(h4,assumption,(~(sP6)),introduced(assumption,[])).
% 0.22/0.44 thf(h5,assumption,(~(sP7)),introduced(assumption,[])).
% 0.22/0.44 thf(h6,assumption,sP1,introduced(assumption,[])).
% 0.22/0.44 thf(1,plain,(~(sP7) | ~(sP1)),inference(all_rule,[status(thm)],[])).
% 0.22/0.44 thf(choiceax,axiom,(![X1:$i>$o]:((~((![X2:$i]:(~((X1 @ X2)))))) => (X1 @ (eps @ X1))))).
% 0.22/0.44 thf(2,plain,(![X1:$i>$o]:((~((![X2:$i]:(~((X1 @ X2)))))) => (X1 @ (eps @ X1)))),inference(preprocess,[status(thm)],[2]).
% 0.22/0.44 thf(3,plain,(~(sP2) | sP3),inference(choice_rule,[status(thm)],[2])).
% 0.22/0.44 thf(4,plain,(~(sP6) | sP7),inference(all_rule,[status(thm)],[])).
% 0.22/0.44 thf(5,plain,(~(sP3) | sP6),inference(all_rule,[status(thm)],[])).
% 0.22/0.44 thf(6,plain,(![X1:$i>$o]:((~((![X2:$i]:(~((X1 @ X2)))))) => (X1 @ (eps @ X1)))),inference(preprocess,[status(thm)],[6]).
% 0.22/0.44 thf(7,plain,(sP4 | sP5),inference(choice_rule,[status(thm)],[6])).
% 0.22/0.44 thf(8,plain,(![X1:$i>$o]:((~((![X2:$i]:(~((X1 @ X2)))))) => (X1 @ (eps @ X1)))),inference(preprocess,[status(thm)],[8]).
% 0.22/0.44 thf(9,plain,(~(sP5) | sP2),inference(choice_rule,[status(thm)],[8])).
% 0.22/0.44 thf(10,plain,$false,inference(prop_unsat,[status(thm),assumptions([h6,h5,h4,h2,h3,h1,h0])],[1,3,4,5,7,9,h6,h3])).
% 0.22/0.44 thf(11,plain,$false,inference(tab_negall,[status(thm),assumptions([h5,h4,h2,h3,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__3)],[h5,10,h6])).
% 0.22/0.44 thf(12,plain,$false,inference(tab_negall,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__2)],[h4,11,h5])).
% 0.22/0.44 thf(13,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h2,12,h4])).
% 0.22/0.44 thf(14,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,13,h2,h3])).
% 0.22/0.44 thf(15,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,14,h1])).
% 0.22/0.44 thf(0,theorem,(![X1:$i>$i>$i>$o]:((~((![X2:$i]:(![X3:$i]:(![X4:$i]:(~((((X1 @ X2) @ X3) @ X4)))))))) => (((X1 @ (eps @ (^[X2:$i]:(~((![X3:$i]:(![X4:$i]:(~((((X1 @ X2) @ X3) @ X4)))))))))) @ (eps @ (^[X2:$i]:(~((![X3:$i]:(~((((X1 @ (eps @ (^[X4:$i]:(~((![X5:$i]:(![X6:$i]:(~((((X1 @ X4) @ X5) @ X6)))))))))) @ X2) @ X3))))))))) @ (eps @ ((X1 @ (eps @ (^[X2:$i]:(~((![X3:$i]:(![X4:$i]:(~((((X1 @ X2) @ X3) @ X4)))))))))) @ (eps @ (^[X2:$i]:(~((![X3:$i]:(~((((X1 @ (eps @ (^[X4:$i]:(~((![X5:$i]:(![X6:$i]:(~((((X1 @ X4) @ X5) @ X6)))))))))) @ X2) @ X3))))))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[15,h0])).
% 0.22/0.44 % SZS output end Proof
%------------------------------------------------------------------------------