TSTP Solution File: ANA125^1 by Lash---1.13
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% File : Lash---1.13
% Problem : ANA125^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n027.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 : Wed Aug 30 17:19:25 EDT 2023
% Result : Theorem 0.20s 0.42s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : ANA125^1 : TPTP v8.1.2. Released v7.0.0.
% 0.12/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Aug 25 19:15:04 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.42 % SZS status Theorem
% 0.20/0.42 % Mode: cade22grackle2xfee4
% 0.20/0.42 % Steps: 152
% 0.20/0.42 % SZS output start Proof
% 0.20/0.42 thf(ty_'type/realax/real', type, 'type/realax/real' : $tType).
% 0.20/0.42 thf(ty_'const/realax/real_mul', type, 'const/realax/real_mul' : ('type/realax/real'>'type/realax/real'>'type/realax/real')).
% 0.20/0.42 thf(ty_eigen__1, type, eigen__1 : 'type/realax/real').
% 0.20/0.42 thf(ty_'const/iterate/polynomial_function', type, 'const/iterate/polynomial_function' : (('type/realax/real'>'type/realax/real')>$o)).
% 0.20/0.42 thf(ty_eigen__4, type, eigen__4 : 'type/realax/real').
% 0.20/0.42 thf(ty_eigen__0, type, eigen__0 : ('type/realax/real'>'type/realax/real')).
% 0.20/0.42 thf(h0, assumption, (![X1:'type/realax/real'>$o]:(![X2:'type/realax/real']:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])).
% 0.20/0.42 thf(eigendef_eigen__4, definition, eigen__4 = (eps__0 @ (^[X1:'type/realax/real']:(~(((('const/realax/real_mul' @ eigen__1) @ (eigen__0 @ X1)) = (('const/realax/real_mul' @ (eigen__0 @ X1)) @ eigen__1)))))), introduced(definition,[new_symbols(definition,[eigen__4])])).
% 0.20/0.42 thf(sP1,plain,sP1 <=> (![X1:'type/realax/real']:(![X2:'type/realax/real']:((('const/realax/real_mul' @ X1) @ X2) = (('const/realax/real_mul' @ X2) @ X1)))),introduced(definition,[new_symbols(definition,[sP1])])).
% 0.20/0.42 thf(sP2,plain,sP2 <=> (![X1:'type/realax/real']:(('const/iterate/polynomial_function' @ eigen__0) => ('const/iterate/polynomial_function' @ (^[X2:'type/realax/real']:(('const/realax/real_mul' @ X1) @ (eigen__0 @ X2)))))),introduced(definition,[new_symbols(definition,[sP2])])).
% 0.20/0.42 thf(sP3,plain,sP3 <=> (('const/iterate/polynomial_function' @ eigen__0) => ('const/iterate/polynomial_function' @ (^[X1:'type/realax/real']:(('const/realax/real_mul' @ eigen__1) @ (eigen__0 @ X1))))),introduced(definition,[new_symbols(definition,[sP3])])).
% 0.20/0.42 thf(sP4,plain,sP4 <=> (![X1:'type/realax/real']:((('const/realax/real_mul' @ eigen__1) @ (eigen__0 @ X1)) = (('const/realax/real_mul' @ (eigen__0 @ X1)) @ eigen__1))),introduced(definition,[new_symbols(definition,[sP4])])).
% 0.20/0.42 thf(sP5,plain,sP5 <=> ('const/iterate/polynomial_function' @ (^[X1:'type/realax/real']:(('const/realax/real_mul' @ (eigen__0 @ X1)) @ eigen__1))),introduced(definition,[new_symbols(definition,[sP5])])).
% 0.20/0.42 thf(sP6,plain,sP6 <=> (![X1:'type/realax/real'>'type/realax/real']:(![X2:'type/realax/real']:(('const/iterate/polynomial_function' @ X1) => ('const/iterate/polynomial_function' @ (^[X3:'type/realax/real']:(('const/realax/real_mul' @ X2) @ (X1 @ X3))))))),introduced(definition,[new_symbols(definition,[sP6])])).
% 0.20/0.42 thf(sP7,plain,sP7 <=> (![X1:'type/realax/real']:((('const/realax/real_mul' @ eigen__1) @ X1) = (('const/realax/real_mul' @ X1) @ eigen__1))),introduced(definition,[new_symbols(definition,[sP7])])).
% 0.20/0.42 thf(sP8,plain,sP8 <=> ('const/iterate/polynomial_function' @ (^[X1:'type/realax/real']:(('const/realax/real_mul' @ eigen__1) @ (eigen__0 @ X1)))),introduced(definition,[new_symbols(definition,[sP8])])).
% 0.20/0.42 thf(sP9,plain,sP9 <=> ((^[X1:'type/realax/real']:(('const/realax/real_mul' @ eigen__1) @ (eigen__0 @ X1))) = (^[X1:'type/realax/real']:(('const/realax/real_mul' @ (eigen__0 @ X1)) @ eigen__1))),introduced(definition,[new_symbols(definition,[sP9])])).
% 0.20/0.42 thf(sP10,plain,sP10 <=> ('const/iterate/polynomial_function' @ eigen__0),introduced(definition,[new_symbols(definition,[sP10])])).
% 0.20/0.42 thf(sP11,plain,sP11 <=> ((('const/realax/real_mul' @ eigen__1) @ (eigen__0 @ eigen__4)) = (('const/realax/real_mul' @ (eigen__0 @ eigen__4)) @ eigen__1)),introduced(definition,[new_symbols(definition,[sP11])])).
% 0.20/0.42 thf('thm/iterate/POLYNOMIAL_FUNCTION_RMUL_',conjecture,(![X1:'type/realax/real'>'type/realax/real']:(![X2:'type/realax/real']:(('const/iterate/polynomial_function' @ X1) => ('const/iterate/polynomial_function' @ (^[X3:'type/realax/real']:(('const/realax/real_mul' @ (X1 @ X3)) @ X2))))))).
% 0.20/0.42 thf(h1,negated_conjecture,(~((![X1:'type/realax/real'>'type/realax/real']:(![X2:'type/realax/real']:(('const/iterate/polynomial_function' @ X1) => ('const/iterate/polynomial_function' @ (^[X3:'type/realax/real']:(('const/realax/real_mul' @ (X1 @ X3)) @ X2)))))))),inference(assume_negation,[status(cth)],['thm/iterate/POLYNOMIAL_FUNCTION_RMUL_'])).
% 0.20/0.42 thf(h2,assumption,(~((![X1:'type/realax/real']:(sP10 => ('const/iterate/polynomial_function' @ (^[X2:'type/realax/real']:(('const/realax/real_mul' @ (eigen__0 @ X2)) @ X1))))))),introduced(assumption,[])).
% 0.20/0.42 thf(h3,assumption,(~((sP10 => sP5))),introduced(assumption,[])).
% 0.20/0.42 thf(h4,assumption,sP10,introduced(assumption,[])).
% 0.20/0.42 thf(h5,assumption,(~(sP5)),introduced(assumption,[])).
% 0.20/0.42 thf(1,plain,(~(sP7) | sP11),inference(all_rule,[status(thm)],[])).
% 0.20/0.42 thf(2,plain,(sP4 | ~(sP11)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__4])).
% 0.20/0.42 thf(3,plain,(sP9 | ~(sP4)),inference(prop_rule,[status(thm)],[])).
% 0.20/0.42 thf(4,plain,((~(sP8) | sP5) | ~(sP9)),inference(mating_rule,[status(thm)],[])).
% 0.20/0.42 thf(5,plain,((~(sP3) | ~(sP10)) | sP8),inference(prop_rule,[status(thm)],[])).
% 0.20/0.42 thf(6,plain,(~(sP2) | sP3),inference(all_rule,[status(thm)],[])).
% 0.20/0.42 thf(7,plain,(~(sP6) | sP2),inference(all_rule,[status(thm)],[])).
% 0.20/0.42 thf(8,plain,(~(sP1) | sP7),inference(all_rule,[status(thm)],[])).
% 0.20/0.42 thf('thm/realax/REAL_MUL_SYM_',axiom,sP1).
% 0.20/0.42 thf('thm/iterate/POLYNOMIAL_FUNCTION_LMUL_',axiom,sP6).
% 0.20/0.42 thf(9,plain,$false,inference(prop_unsat,[status(thm),assumptions([h4,h5,h3,h2,h1,h0])],[1,2,3,4,5,6,7,8,h4,h5,'thm/realax/REAL_MUL_SYM_','thm/iterate/POLYNOMIAL_FUNCTION_LMUL_'])).
% 0.20/0.42 thf(10,plain,$false,inference(tab_negimp,[status(thm),assumptions([h3,h2,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,9,h4,h5])).
% 0.20/0.42 thf(11,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h1,h0]),tab_negall(discharge,[h3]),tab_negall(eigenvar,eigen__1)],[h2,10,h3])).
% 0.20/0.42 thf(12,plain,$false,inference(tab_negall,[status(thm),assumptions([h1,h0]),tab_negall(discharge,[h2]),tab_negall(eigenvar,eigen__0)],[h1,11,h2])).
% 0.20/0.42 thf(13,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[12,h0])).
% 0.20/0.42 thf(0,theorem,(![X1:'type/realax/real'>'type/realax/real']:(![X2:'type/realax/real']:(('const/iterate/polynomial_function' @ X1) => ('const/iterate/polynomial_function' @ (^[X3:'type/realax/real']:(('const/realax/real_mul' @ (X1 @ X3)) @ X2)))))),inference(contra,[status(thm),contra(discharge,[h1])],[12,h1])).
% 0.20/0.42 % SZS output end Proof
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