%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU826^1 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -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 : 300s
% DateTime : Thu Oct 9 02:41:59 PM UTC 2025
% Result : Theorem 0.14s 0.40s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU826^1 : TPTP v9.2.0. Released v3.7.0.
% 0.07/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35 % Computer : n005.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Oct 8 21:17:38 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.14/0.40 % SZS status Theorem
% 0.14/0.40 % Mode: cade22grackle2xfee4
% 0.14/0.40 % Steps: 28
% 0.14/0.40 % SZS output start Proof
% 0.14/0.40 thf(ty_eigen__0, type, eigen__0 : $i).
% 0.14/0.40 thf(ty_b, type, b : ($i>$o)).
% 0.14/0.40 thf(ty_c, type, c : ($i>$o)).
% 0.14/0.40 thf(ty_a, type, a : ($i>$o)).
% 0.14/0.40 thf(sP1,plain,sP1 <=> ((~((a @ eigen__0))) => (b @ eigen__0)),introduced(definition,[new_symbols(definition,[sP1])])).
% 0.14/0.40 thf(sP2,plain,sP2 <=> (b @ eigen__0),introduced(definition,[new_symbols(definition,[sP2])])).
% 0.14/0.40 thf(sP3,plain,sP3 <=> (c @ eigen__0),introduced(definition,[new_symbols(definition,[sP3])])).
% 0.14/0.40 thf(sP4,plain,sP4 <=> (a @ eigen__0),introduced(definition,[new_symbols(definition,[sP4])])).
% 0.14/0.40 thf(sP5,plain,sP5 <=> ((~(sP4)) => sP3),introduced(definition,[new_symbols(definition,[sP5])])).
% 0.14/0.40 thf(sP6,plain,sP6 <=> (sP2 => (~(sP3))),introduced(definition,[new_symbols(definition,[sP6])])).
% 0.14/0.40 thf(def_seteq,definition,(seteq = (^[X1:$i>$o]:(^[X2:$i>$o]:(![X3:$i]:((X1 @ X3) <=> (X2 @ X3))))))).
% 0.14/0.40 thf(def_u,definition,(u = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) | (X2 @ X3))))))).
% 0.14/0.40 thf(def_n,definition,(n = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) & (X2 @ X3))))))).
% 0.14/0.40 thf(conj,conjecture,(![X1:$i]:(((~((a @ X1))) => (~(((b @ X1) => (~((c @ X1))))))) = (~((((~((a @ X1))) => (b @ X1)) => (~(((~((a @ X1))) => (c @ X1)))))))))).
% 0.14/0.40 thf(h0,negated_conjecture,(~((![X1:$i]:(((~((a @ X1))) => (~(((b @ X1) => (~((c @ X1))))))) = (~((((~((a @ X1))) => (b @ X1)) => (~(((~((a @ X1))) => (c @ X1))))))))))),inference(assume_negation,[status(cth)],[conj])).
% 0.14/0.40 thf(h1,assumption,(~((((~(sP4)) => (~(sP6))) = (~((sP1 => (~(sP5)))))))),introduced(assumption,[])).
% 0.14/0.40 thf(h2,assumption,(~(sP4)),introduced(assumption,[])).
% 0.14/0.40 thf(h3,assumption,sP6,introduced(assumption,[])).
% 0.14/0.40 thf(h4,assumption,sP1,introduced(assumption,[])).
% 0.14/0.40 thf(h5,assumption,sP5,introduced(assumption,[])).
% 0.14/0.40 thf(1,plain,((~(sP6) | ~(sP2)) | ~(sP3)),inference(prop_rule,[status(thm)],[])).
% 0.14/0.40 thf(2,plain,((~(sP1) | sP4) | sP2),inference(prop_rule,[status(thm)],[])).
% 0.14/0.40 thf(3,plain,((~(sP5) | sP4) | sP3),inference(prop_rule,[status(thm)],[])).
% 0.14/0.40 thf(4,plain,$false,inference(prop_unsat,[status(thm),assumptions([h4,h5,h2,h3,h1,h0])],[1,2,3,h2,h3,h4,h5])).
% 0.14/0.40 7:334: Could not find hyp name
% 0.14/0.40 s = imp (imp (imp (imp (a __0) False) (b __0)) (imp (imp (imp (a __0) False) (c __0)) False)) False
% 0.14/0.40 hyp:
% 0.14/0.40 [323] h2: imp (a __0) False
% 0.14/0.40 [327] h3: imp (b __0) (imp (c __0) False)
% 0.14/0.40 [336] h1: imp (eq:$o (imp (imp (a __0) False) (imp (imp (b __0) (imp (c __0) False)) False)) (imp (imp (imp (imp (a __0) False) (b __0)) (imp (imp (imp (a __0) False) (c __0)) False)) False)) False
% 0.14/0.40 [320] h0: imp (Pi:$i (\_:$i.eq:$o (imp (imp (a ^0) False) (imp (imp (b ^0) (imp (c ^0) False)) False)) (imp (imp (imp (imp (a ^0) False) (b ^0)) (imp (imp (imp (a ^0) False) (c ^0)) False)) False))) False
% 0.14/0.40 % SZS status Error
% 0.14/0.40 Exception: Failure("Could not find hyp name")
% 0.21/0.43 % SZS status Theorem
% 0.21/0.43 % Mode: cade22grackle2x798d
% 0.21/0.43 % Steps: 52
%------------------------------------------------------------------------------