%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SET144^5 : 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 : n031.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 02:23:48 PM UTC 2025
% Result : Theorem 0.18s 0.39s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET144^5 : TPTP v9.2.0. Released v4.0.0.
% 0.06/0.12 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n031.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Oct 8 14:51:08 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.18/0.39 % SZS status Theorem
% 0.18/0.39 % Mode: cade22grackle2xfee4
% 0.18/0.39 % Steps: 29
% 0.18/0.39 % SZS output start Proof
% 0.18/0.39 thf(ty_a, type, a : $tType).
% 0.18/0.39 thf(ty_eigen__0, type, eigen__0 : (a>$o)).
% 0.18/0.39 thf(ty_eigen__3, type, eigen__3 : a).
% 0.18/0.39 thf(ty_eigen__1, type, eigen__1 : (a>$o)).
% 0.18/0.39 thf(ty_eigen__2, type, eigen__2 : (a>$o)).
% 0.18/0.39 thf(sP1,plain,sP1 <=> ((eigen__1 @ eigen__3) => (~((eigen__2 @ eigen__3)))),introduced(definition,[new_symbols(definition,[sP1])])).
% 0.18/0.39 thf(sP2,plain,sP2 <=> (eigen__2 @ eigen__3),introduced(definition,[new_symbols(definition,[sP2])])).
% 0.18/0.39 thf(sP3,plain,sP3 <=> (eigen__0 @ eigen__3),introduced(definition,[new_symbols(definition,[sP3])])).
% 0.18/0.39 thf(sP4,plain,sP4 <=> (eigen__1 @ eigen__3),introduced(definition,[new_symbols(definition,[sP4])])).
% 0.18/0.39 thf(sP5,plain,sP5 <=> ((~(sP3)) => sP4),introduced(definition,[new_symbols(definition,[sP5])])).
% 0.18/0.39 thf(cBOOL_PROP_44_pme,conjecture,(![X1:a>$o]:(![X2:a>$o]:(![X3:a>$o]:((![X4:a]:((X1 @ X4) => (X3 @ X4))) => ((^[X4:a]:((~((X1 @ X4))) => (~(((X2 @ X4) => (~((X3 @ X4)))))))) = (^[X4:a]:(~((((~((X1 @ X4))) => (X2 @ X4)) => (~((X3 @ X4))))))))))))).
% 0.18/0.39 thf(h0,negated_conjecture,(~((![X1:a>$o]:(![X2:a>$o]:(![X3:a>$o]:((![X4:a]:((X1 @ X4) => (X3 @ X4))) => ((^[X4:a]:((~((X1 @ X4))) => (~(((X2 @ X4) => (~((X3 @ X4)))))))) = (^[X4:a]:(~((((~((X1 @ X4))) => (X2 @ X4)) => (~((X3 @ X4)))))))))))))),inference(assume_negation,[status(cth)],[cBOOL_PROP_44_pme])).
% 0.18/0.39 thf(h1,assumption,(~((![X1:a>$o]:(![X2:a>$o]:((![X3:a]:((eigen__0 @ X3) => (X2 @ X3))) => ((^[X3:a]:((~((eigen__0 @ X3))) => (~(((X1 @ X3) => (~((X2 @ X3)))))))) = (^[X3:a]:(~((((~((eigen__0 @ X3))) => (X1 @ X3)) => (~((X2 @ X3))))))))))))),introduced(assumption,[])).
% 0.18/0.39 thf(h2,assumption,(~((![X1:a>$o]:((![X2:a]:((eigen__0 @ X2) => (X1 @ X2))) => ((^[X2:a]:((~((eigen__0 @ X2))) => (~(((eigen__1 @ X2) => (~((X1 @ X2)))))))) = (^[X2:a]:(~((((~((eigen__0 @ X2))) => (eigen__1 @ X2)) => (~((X1 @ X2)))))))))))),introduced(assumption,[])).
% 0.18/0.39 thf(h3,assumption,(~(((![X1:a]:((eigen__0 @ X1) => (eigen__2 @ X1))) => ((^[X1:a]:((~((eigen__0 @ X1))) => (~(((eigen__1 @ X1) => (~((eigen__2 @ X1)))))))) = (^[X1:a]:(~((((~((eigen__0 @ X1))) => (eigen__1 @ X1)) => (~((eigen__2 @ X1))))))))))),introduced(assumption,[])).
% 0.18/0.39 thf(h4,assumption,(![X1:a]:((eigen__0 @ X1) => (eigen__2 @ X1))),introduced(assumption,[])).
% 0.18/0.39 thf(h5,assumption,(~(((^[X1:a]:((~((eigen__0 @ X1))) => (~(((eigen__1 @ X1) => (~((eigen__2 @ X1)))))))) = (^[X1:a]:(~((((~((eigen__0 @ X1))) => (eigen__1 @ X1)) => (~((eigen__2 @ X1)))))))))),introduced(assumption,[])).
% 0.18/0.39 thf(h6,assumption,(~((![X1:a]:(((~((eigen__0 @ X1))) => (~(((eigen__1 @ X1) => (~((eigen__2 @ X1))))))) = (~((((~((eigen__0 @ X1))) => (eigen__1 @ X1)) => (~((eigen__2 @ X1)))))))))),introduced(assumption,[])).
% 0.18/0.39 thf(h7,assumption,(~((((~(sP3)) => (~(sP1))) = (~((sP5 => (~(sP2)))))))),introduced(assumption,[])).
% 0.18/0.39 thf(h8,assumption,(~(sP3)),introduced(assumption,[])).
% 0.18/0.39 thf(h9,assumption,sP1,introduced(assumption,[])).
% 0.18/0.39 thf(h10,assumption,sP5,introduced(assumption,[])).
% 0.18/0.39 thf(h11,assumption,sP2,introduced(assumption,[])).
% 0.18/0.39 thf(1,plain,((~(sP1) | ~(sP4)) | ~(sP2)),inference(prop_rule,[status(thm)],[])).
% 0.18/0.39 thf(2,plain,((~(sP5) | sP3) | sP4),inference(prop_rule,[status(thm)],[])).
% 0.18/0.39 thf(3,plain,$false,inference(prop_unsat,[status(thm),assumptions([h10,h11,h8,h9,h7,h6,h4,h5,h3,h2,h1,h0])],[1,2,h8,h9,h10,h11])).
% 0.18/0.39 7:352: Could not find hyp name
% 0.18/0.39 s = imp (imp (imp (imp (__0 __3) False) (__1 __3)) (imp (__2 __3) False)) False
% 0.18/0.39 hyp:
% 0.18/0.39 [343] h8: imp (__0 __3) False
% 0.18/0.39 [347] h9: imp (__1 __3) (imp (__2 __3) False)
% 0.18/0.39 [354] h7: imp (eq:$o (imp (imp (__0 __3) False) (imp (imp (__1 __3) (imp (__2 __3) False)) False)) (imp (imp (imp (imp (__0 __3) False) (__1 __3)) (imp (__2 __3) False)) False)) False
% 0.18/0.39 [340] h6: imp (Pi:a (\_:a.eq:$o (imp (imp (__0 ^0) False) (imp (imp (__1 ^0) (imp (__2 ^0) False)) False)) (imp (imp (imp (imp (__0 ^0) False) (__1 ^0)) (imp (__2 ^0) False)) False))) False
% 0.18/0.39 [325] h4: Pi:a (\_:a.imp (__0 ^0) (__2 ^0))
% 0.18/0.39 [337] h5: imp (eq:a>$o (\_:a.imp (imp (__0 ^0) False) (imp (imp (__1 ^0) (imp (__2 ^0) False)) False)) (\_:a.imp (imp (imp (imp (__0 ^0) False) (__1 ^0)) (imp (__2 ^0) False)) False)) False
% 0.18/0.39 [336] h3: imp (imp (Pi:a (\_:a.imp (__0 ^0) (__2 ^0))) (eq:a>$o (\_:a.imp (imp (__0 ^0) False) (imp (imp (__1 ^0) (imp (__2 ^0) False)) False)) (\_:a.imp (imp (imp (imp (__0 ^0) False) (__1 ^0)) (imp (__2 ^0) False)) False))) False
% 0.18/0.39 [321] h2: imp (Pi:a>$o (\_:a>$o.imp (Pi:a (\_:a.imp (__0 ^0) (^1 ^0))) (eq:a>$o (\_:a.imp (imp (__0 ^0) False) (imp (imp (__1 ^0) (imp (^1 ^0) False)) False)) (\_:a.imp (imp (imp (imp (__0 ^0) False) (__1 ^0)) (imp (^1 ^0) False)) False)))) False
% 0.18/0.39 [307] h1: imp (Pi:a>$o (\_:a>$o.Pi:a>$o (\_:a>$o.imp (Pi:a (\_:a.imp (__0 ^0) (^1 ^0))) (eq:a>$o (\_:a.imp (imp (__0 ^0) False) (imp (imp (^2 ^0) (imp (^1 ^0) False)) False)) (\_:a.imp (imp (imp (imp (__0 ^0) False) (^2 ^0)) (imp (^1 ^0) False)) False))))) False
% 0.18/0.39 [291] h0: imp (Pi:a>$o (\_:a>$o.Pi:a>$o (\_:a>$o.Pi:a>$o (\_:a>$o.imp (Pi:a (\_:a.imp (^3 ^0) (^1 ^0))) (eq:a>$o (\_:a.imp (imp (^3 ^0) False) (imp (imp (^2 ^0) (imp (^1 ^0) False)) False)) (\_:a.imp (imp (imp (imp (^3 ^0) False) (^2 ^0)) (imp (^1 ^0) False)) False)))))) False
% 0.18/0.39 % SZS status Error
% 0.18/0.39 Exception: Failure("Could not find hyp name")
% 0.18/0.43 % SZS status Theorem
% 0.18/0.43 % Mode: cade22grackle2x798d
% 0.18/0.43 % Steps: 53
%------------------------------------------------------------------------------