TSTP Solution File: ANA125^1 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ANA125^1 : TPTP v8.1.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n020.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 : 600s
% DateTime : Thu Jul 14 19:25:22 EDT 2022
% Result : Theorem 49.41s 49.59s
% Output : Proof 49.41s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : ANA125^1 : TPTP v8.1.0. Released v7.0.0.
% 0.06/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n020.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 : 600
% 0.12/0.33 % DateTime : Fri Jul 8 06:55:44 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.98/2.18 slave returned with unknown status
% 33.96/34.15 slave returned with unknown status
% 33.96/34.17 slave returned with unknown status
% 35.84/36.08 slave returned with unknown status
% 36.98/37.21 slave returned with unknown status
% 48.24/48.79 slave returned with unknown status
% 49.41/49.59 % SZS status Theorem
% 49.41/49.59 % Mode: mode368
% 49.41/49.59 % Inferences: 13664
% 49.41/49.59 % SZS output start Proof
% 49.41/49.59 thf(ty_'type/realax/real', type, 'type/realax/real' : $tType).
% 49.41/49.59 thf(ty_eigen__2, type, eigen__2 : 'type/realax/real').
% 49.41/49.59 thf(ty_eigen__1, type, eigen__1 : ('type/realax/real'>'type/realax/real')).
% 49.41/49.59 thf(ty_'const/realax/real_mul', type, 'const/realax/real_mul' : ('type/realax/real'>'type/realax/real'>'type/realax/real')).
% 49.41/49.59 thf(ty_eigen__10, type, eigen__10 : 'type/realax/real').
% 49.41/49.59 thf(ty_'const/iterate/polynomial_function', type, 'const/iterate/polynomial_function' : (('type/realax/real'>'type/realax/real')>$o)).
% 49.41/49.59 thf(h0, assumption, (![X1:('type/realax/real'>'type/realax/real')>$o]:(![X2:'type/realax/real'>'type/realax/real']:((X1 @ X2) => (X1 @ (eps__0 @ X1))))),introduced(assumption,[])).
% 49.41/49.59 thf(eigendef_eigen__1, definition, eigen__1 = (eps__0 @ (^[X1:'type/realax/real'>'type/realax/real']:(~((![X2:'type/realax/real']:(('const/iterate/polynomial_function' @ X1) => ('const/iterate/polynomial_function' @ (^[X3:'type/realax/real']:(('const/realax/real_mul' @ (X1 @ X3)) @ X2))))))))), introduced(definition,[new_symbols(definition,[eigen__1])])).
% 49.41/49.59 thf(h1, assumption, (![X1:'type/realax/real'>$o]:(![X2:'type/realax/real']:((X1 @ X2) => (X1 @ (eps__1 @ X1))))),introduced(assumption,[])).
% 49.41/49.59 thf(eigendef_eigen__10, definition, eigen__10 = (eps__1 @ (^[X1:'type/realax/real']:(~(((('const/realax/real_mul' @ eigen__2) @ (eigen__1 @ X1)) = (('const/realax/real_mul' @ (eigen__1 @ X1)) @ eigen__2)))))), introduced(definition,[new_symbols(definition,[eigen__10])])).
% 49.41/49.59 thf(eigendef_eigen__2, definition, eigen__2 = (eps__1 @ (^[X1:'type/realax/real']:(~((('const/iterate/polynomial_function' @ eigen__1) => ('const/iterate/polynomial_function' @ (^[X2:'type/realax/real']:(('const/realax/real_mul' @ (eigen__1 @ X2)) @ X1)))))))), introduced(definition,[new_symbols(definition,[eigen__2])])).
% 49.41/49.59 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])])).
% 49.41/49.59 thf(sP2,plain,sP2 <=> ('const/iterate/polynomial_function' @ eigen__1),introduced(definition,[new_symbols(definition,[sP2])])).
% 49.41/49.59 thf(sP3,plain,sP3 <=> (sP2 => ('const/iterate/polynomial_function' @ (^[X1:'type/realax/real']:(('const/realax/real_mul' @ eigen__2) @ (eigen__1 @ X1))))),introduced(definition,[new_symbols(definition,[sP3])])).
% 49.41/49.59 thf(sP4,plain,sP4 <=> (![X1:'type/realax/real']:((('const/realax/real_mul' @ eigen__2) @ X1) = (('const/realax/real_mul' @ X1) @ eigen__2))),introduced(definition,[new_symbols(definition,[sP4])])).
% 49.41/49.59 thf(sP5,plain,sP5 <=> (![X1:'type/realax/real']:(sP2 => ('const/iterate/polynomial_function' @ (^[X2:'type/realax/real']:(('const/realax/real_mul' @ (eigen__1 @ X2)) @ X1))))),introduced(definition,[new_symbols(definition,[sP5])])).
% 49.41/49.59 thf(sP6,plain,sP6 <=> ((('const/realax/real_mul' @ eigen__2) @ (eigen__1 @ eigen__10)) = (('const/realax/real_mul' @ (eigen__1 @ eigen__10)) @ eigen__2)),introduced(definition,[new_symbols(definition,[sP6])])).
% 49.41/49.59 thf(sP7,plain,sP7 <=> (sP2 => ('const/iterate/polynomial_function' @ (^[X1:'type/realax/real']:(('const/realax/real_mul' @ (eigen__1 @ X1)) @ eigen__2)))),introduced(definition,[new_symbols(definition,[sP7])])).
% 49.41/49.59 thf(sP8,plain,sP8 <=> (![X1:'type/realax/real']:(sP2 => ('const/iterate/polynomial_function' @ (^[X2:'type/realax/real']:(('const/realax/real_mul' @ X1) @ (eigen__1 @ X2)))))),introduced(definition,[new_symbols(definition,[sP8])])).
% 49.41/49.59 thf(sP9,plain,sP9 <=> ('const/iterate/polynomial_function' @ (^[X1:'type/realax/real']:(('const/realax/real_mul' @ eigen__2) @ (eigen__1 @ X1)))),introduced(definition,[new_symbols(definition,[sP9])])).
% 49.41/49.59 thf(sP10,plain,sP10 <=> (![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,[sP10])])).
% 49.41/49.59 thf(sP11,plain,sP11 <=> (![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)))))),introduced(definition,[new_symbols(definition,[sP11])])).
% 49.41/49.59 thf(sP12,plain,sP12 <=> ('const/iterate/polynomial_function' @ (^[X1:'type/realax/real']:(('const/realax/real_mul' @ (eigen__1 @ X1)) @ eigen__2))),introduced(definition,[new_symbols(definition,[sP12])])).
% 49.41/49.59 thf(sP13,plain,sP13 <=> (![X1:'type/realax/real']:((('const/realax/real_mul' @ eigen__2) @ (eigen__1 @ X1)) = (('const/realax/real_mul' @ (eigen__1 @ X1)) @ eigen__2))),introduced(definition,[new_symbols(definition,[sP13])])).
% 49.41/49.59 thf(sP14,plain,sP14 <=> ((^[X1:'type/realax/real']:(('const/realax/real_mul' @ eigen__2) @ (eigen__1 @ X1))) = (^[X1:'type/realax/real']:(('const/realax/real_mul' @ (eigen__1 @ X1)) @ eigen__2))),introduced(definition,[new_symbols(definition,[sP14])])).
% 49.41/49.59 thf('thm/iterate/POLYNOMIAL_FUNCTION_RMUL_',conjecture,sP11).
% 49.41/49.59 thf(h2,negated_conjecture,(~(sP11)),inference(assume_negation,[status(cth)],['thm/iterate/POLYNOMIAL_FUNCTION_RMUL_'])).
% 49.41/49.59 thf(1,plain,(~(sP4) | sP6),inference(all_rule,[status(thm)],[])).
% 49.41/49.59 thf(2,plain,(sP13 | ~(sP6)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__10])).
% 49.41/49.59 thf(3,plain,(sP14 | ~(sP13)),inference(prop_rule,[status(thm)],[])).
% 49.41/49.59 thf(4,plain,((~(sP9) | sP12) | ~(sP14)),inference(mating_rule,[status(thm)],[])).
% 49.41/49.59 thf(5,plain,((~(sP3) | ~(sP2)) | sP9),inference(prop_rule,[status(thm)],[])).
% 49.41/49.59 thf(6,plain,(~(sP8) | sP3),inference(all_rule,[status(thm)],[])).
% 49.41/49.59 thf(7,plain,(~(sP1) | sP4),inference(all_rule,[status(thm)],[])).
% 49.41/49.59 thf(8,plain,(~(sP10) | sP8),inference(all_rule,[status(thm)],[])).
% 49.41/49.59 thf(9,plain,(sP7 | ~(sP12)),inference(prop_rule,[status(thm)],[])).
% 49.41/49.59 thf(10,plain,(sP7 | sP2),inference(prop_rule,[status(thm)],[])).
% 49.41/49.59 thf(11,plain,(sP5 | ~(sP7)),inference(eigen_choice_rule,[status(thm),assumptions([h1])],[h1,eigendef_eigen__2])).
% 49.41/49.59 thf(12,plain,(sP11 | ~(sP5)),inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__1])).
% 49.41/49.59 thf('thm/iterate/POLYNOMIAL_FUNCTION_LMUL_',axiom,sP10).
% 49.41/49.59 thf('thm/realax/REAL_MUL_SYM_',axiom,sP1).
% 49.41/49.59 thf(13,plain,$false,inference(prop_unsat,[status(thm),assumptions([h2,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,'thm/iterate/POLYNOMIAL_FUNCTION_LMUL_','thm/realax/REAL_MUL_SYM_',h2])).
% 49.41/49.59 thf(14,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2,h0]),eigenvar_choice(discharge,[h1])],[13,h1])).
% 49.41/49.59 thf(15,plain,$false,inference(eigenvar_choice,[status(thm),assumptions([h2]),eigenvar_choice(discharge,[h0])],[14,h0])).
% 49.41/49.59 thf(0,theorem,sP11,inference(contra,[status(thm),contra(discharge,[h2])],[13,h2])).
% 49.41/49.59 % SZS output end Proof
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