%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SET619^5 : TPTP v9.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n002.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 : Thu Oct 9 02:24:27 PM UTC 2025
% Result : Theorem 0.20s 0.41s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET619^5 : TPTP v9.2.0. Released v4.0.0.
% 0.03/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n002.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Oct 8 14:47:53 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.20/0.41 % SZS status Theorem
% 0.20/0.41 % Mode: cade22grackle2xfee4
% 0.20/0.41 % Steps: 24
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 thf(ty_a, type, a : $tType).
% 0.20/0.41 thf(ty_eigen__0, type, eigen__0 : (a>$o)).
% 0.20/0.41 thf(ty_eigen__1, type, eigen__1 : (a>$o)).
% 0.20/0.41 thf(ty_eigen__2, type, eigen__2 : a).
% 0.20/0.41 thf(sP1,plain,sP1 <=> ((eigen__1 @ eigen__2) => (eigen__0 @ eigen__2)),introduced(definition,[new_symbols(definition,[sP1])])).
% 0.20/0.41 thf(sP2,plain,sP2 <=> ((~((((eigen__0 @ eigen__2) => (eigen__1 @ eigen__2)) => (~(sP1))))) => (~(((eigen__0 @ eigen__2) => (~((eigen__1 @ eigen__2))))))),introduced(definition,[new_symbols(definition,[sP2])])).
% 0.20/0.41 thf(sP3,plain,sP3 <=> (eigen__0 @ eigen__2),introduced(definition,[new_symbols(definition,[sP3])])).
% 0.20/0.41 thf(sP4,plain,sP4 <=> (eigen__1 @ eigen__2),introduced(definition,[new_symbols(definition,[sP4])])).
% 0.20/0.41 thf(sP5,plain,sP5 <=> (sP3 => sP4),introduced(definition,[new_symbols(definition,[sP5])])).
% 0.20/0.41 thf(sP6,plain,sP6 <=> (sP3 => (~(sP4))),introduced(definition,[new_symbols(definition,[sP6])])).
% 0.20/0.41 thf(sP7,plain,sP7 <=> (sP5 => (~(sP1))),introduced(definition,[new_symbols(definition,[sP7])])).
% 0.20/0.41 thf(cBOOL_PROP_95_pme,conjecture,(![X1:a>$o]:(![X2:a>$o]:((^[X3:a]:((~((X1 @ X3))) => (X2 @ X3))) = (^[X3:a]:((~((((X1 @ X3) => (X2 @ X3)) => (~(((X2 @ X3) => (X1 @ X3))))))) => (~(((X1 @ X3) => (~((X2 @ X3)))))))))))).
% 0.20/0.41 thf(h0,negated_conjecture,(~((![X1:a>$o]:(![X2:a>$o]:((^[X3:a]:((~((X1 @ X3))) => (X2 @ X3))) = (^[X3:a]:((~((((X1 @ X3) => (X2 @ X3)) => (~(((X2 @ X3) => (X1 @ X3))))))) => (~(((X1 @ X3) => (~((X2 @ X3))))))))))))),inference(assume_negation,[status(cth)],[cBOOL_PROP_95_pme])).
% 0.20/0.41 thf(h1,assumption,(~((![X1:a>$o]:((^[X2:a]:((~((eigen__0 @ X2))) => (X1 @ X2))) = (^[X2:a]:((~((((eigen__0 @ X2) => (X1 @ X2)) => (~(((X1 @ X2) => (eigen__0 @ X2))))))) => (~(((eigen__0 @ X2) => (~((X1 @ X2)))))))))))),introduced(assumption,[])).
% 0.20/0.41 thf(h2,assumption,(~(((^[X1:a]:((~((eigen__0 @ X1))) => (eigen__1 @ X1))) = (^[X1:a]:((~((((eigen__0 @ X1) => (eigen__1 @ X1)) => (~(((eigen__1 @ X1) => (eigen__0 @ X1))))))) => (~(((eigen__0 @ X1) => (~((eigen__1 @ X1))))))))))),introduced(assumption,[])).
% 0.20/0.41 thf(h3,assumption,(~((![X1:a]:(((~((eigen__0 @ X1))) => (eigen__1 @ X1)) = ((~((((eigen__0 @ X1) => (eigen__1 @ X1)) => (~(((eigen__1 @ X1) => (eigen__0 @ X1))))))) => (~(((eigen__0 @ X1) => (~((eigen__1 @ X1))))))))))),introduced(assumption,[])).
% 0.20/0.41 thf(h4,assumption,(~((((~(sP3)) => sP4) = sP2))),introduced(assumption,[])).
% 0.20/0.41 thf(h5,assumption,(~(sP3)),introduced(assumption,[])).
% 0.20/0.41 thf(h6,assumption,(~(sP4)),introduced(assumption,[])).
% 0.20/0.41 thf(1,plain,(sP1 | sP4),inference(prop_rule,[status(thm)],[])).
% 0.20/0.41 thf(2,plain,(sP5 | sP3),inference(prop_rule,[status(thm)],[])).
% 0.20/0.41 thf(3,plain,(sP6 | sP3),inference(prop_rule,[status(thm)],[])).
% 0.20/0.41 thf(4,plain,((~(sP7) | ~(sP5)) | ~(sP1)),inference(prop_rule,[status(thm)],[])).
% 0.20/0.41 thf(5,plain,((~(sP2) | sP7) | ~(sP6)),inference(prop_rule,[status(thm)],[])).
% 0.20/0.41 1:332: Could not find hyp name
% 0.20/0.41 s = imp (imp (imp (imp (__0 __2) (__1 __2)) (imp (imp (__1 __2) (__0 __2)) False)) False) (imp (imp (__0 __2) (imp (__1 __2) False)) False)
% 0.20/0.41 hyp:
% 0.20/0.41 [321] h5: imp (__0 __2) False
% 0.20/0.41 [329] h6: imp (__1 __2) False
% 0.20/0.41 [334] h4: imp (eq:$o (imp (imp (__0 __2) False) (__1 __2)) (imp (imp (imp (imp (__0 __2) (__1 __2)) (imp (imp (__1 __2) (__0 __2)) False)) False) (imp (imp (__0 __2) (imp (__1 __2) False)) False))) False
% 0.20/0.41 [318] h3: imp (Pi:a (\_:a.eq:$o (imp (imp (__0 ^0) False) (__1 ^0)) (imp (imp (imp (imp (__0 ^0) (__1 ^0)) (imp (imp (__1 ^0) (__0 ^0)) False)) False) (imp (imp (__0 ^0) (imp (__1 ^0) False)) False)))) False
% 0.20/0.41 [315] h2: imp (eq:a>$o (\_:a.imp (imp (__0 ^0) False) (__1 ^0)) (\_:a.imp (imp (imp (imp (__0 ^0) (__1 ^0)) (imp (imp (__1 ^0) (__0 ^0)) False)) False) (imp (imp (__0 ^0) (imp (__1 ^0) False)) False))) False
% 0.20/0.41 [299] h1: imp (Pi:a>$o (\_:a>$o.eq:a>$o (\_:a.imp (imp (__0 ^0) False) (^1 ^0)) (\_:a.imp (imp (imp (imp (__0 ^0) (^1 ^0)) (imp (imp (^1 ^0) (__0 ^0)) False)) False) (imp (imp (__0 ^0) (imp (^1 ^0) False)) False)))) False
% 0.20/0.41 [282] h0: imp (Pi:a>$o (\_:a>$o.Pi:a>$o (\_:a>$o.eq:a>$o (\_:a.imp (imp (^2 ^0) False) (^1 ^0)) (\_:a.imp (imp (imp (imp (^2 ^0) (^1 ^0)) (imp (imp (^1 ^0) (^2 ^0)) False)) False) (imp (imp (^2 ^0) (imp (^1 ^0) False)) False))))) False
% 0.20/0.41 % SZS status Error
% 0.20/0.41 Exception: Failure("Could not find hyp name")
% 0.20/0.44 % SZS status Theorem
% 0.20/0.44 % Mode: cade22grackle2x798d
% 0.20/0.44 % Steps: 44
%------------------------------------------------------------------------------