TSTP Solution File: ITP194^1 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP194^1 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n019.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 : Sun Jul 17 00:29:28 EDT 2022
% Result : Theorem 2.06s 2.78s
% Output : Proof 2.06s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : ITP194^1 : TPTP v8.1.0. Released v7.5.0.
% 0.12/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.35 % Computer : n019.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 600
% 0.12/0.35 % DateTime : Thu Jun 2 18:19:25 EDT 2022
% 0.12/0.35 % CPUTime :
% 2.06/2.78 % SZS status Theorem
% 2.06/2.78 % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
% 2.06/2.78 % Inferences: 1
% 2.06/2.78 % SZS output start Proof
% 2.06/2.78 thf(ty_poly_real, type, poly_real : $tType).
% 2.06/2.78 thf(ty_real, type, real : $tType).
% 2.06/2.78 thf(ty_poly_real2, type, poly_real2 : (poly_real>real>real)).
% 2.06/2.78 thf(ty_zero_zero_real, type, zero_zero_real : real).
% 2.06/2.78 thf(ty_p, type, p : poly_real).
% 2.06/2.78 thf(ty_eigen__2, type, eigen__2 : real).
% 2.06/2.78 thf(ty_eigen__1, type, eigen__1 : real).
% 2.06/2.78 thf(ty_eigen__0, type, eigen__0 : real).
% 2.06/2.78 thf(ty_sturm_1076696862f_real, type, sturm_1076696862f_real : (poly_real>real)).
% 2.06/2.78 thf(ty_ord_less_eq_real, type, ord_less_eq_real : (real>real>$o)).
% 2.06/2.78 thf(ty_lb, type, lb : real).
% 2.06/2.78 thf(ty_ord_less_real, type, ord_less_real : (real>real>$o)).
% 2.06/2.78 thf(ty_sgn_sgn_real, type, sgn_sgn_real : (real>real)).
% 2.06/2.78 thf(conj_0,conjecture,(![X1:real]:((((poly_real2 @ p) @ X1) = zero_zero_real) => ((ord_less_real @ lb) @ X1)))).
% 2.06/2.78 thf(h0,negated_conjecture,(~((![X1:real]:((((poly_real2 @ p) @ X1) = zero_zero_real) => ((ord_less_real @ lb) @ X1))))),inference(assume_negation,[status(cth)],[conj_0])).
% 2.06/2.78 thf(h1,assumption,(~(((((poly_real2 @ p) @ eigen__0) = zero_zero_real) => ((ord_less_real @ lb) @ eigen__0)))),introduced(assumption,[])).
% 2.06/2.78 thf(h2,assumption,(((poly_real2 @ p) @ eigen__0) = zero_zero_real),introduced(assumption,[])).
% 2.06/2.78 thf(h3,assumption,(~(((ord_less_real @ lb) @ eigen__0))),introduced(assumption,[])).
% 2.06/2.78 thf(h4,assumption,(![X1:real]:(((ord_less_eq_real @ X1) @ eigen__1) => ((sgn_sgn_real @ ((poly_real2 @ p) @ X1)) = (sturm_1076696862f_real @ p)))),introduced(assumption,[])).
% 2.06/2.78 thf(h5,assumption,(![X1:real]:((((poly_real2 @ p) @ X1) = zero_zero_real) => ((ord_less_real @ eigen__2) @ X1))),introduced(assumption,[])).
% 2.06/2.78 thf(pax1, axiom, (p1=>![X89:real]:((fpoly_real2 @ fp @ X89)=(fzero_zero_real)=>ford_less_real @ flb1 @ X89)), file('<stdin>', pax1)).
% 2.06/2.78 thf(pax78, axiom, (p78=>(fpoly_real2 @ fp @ f__0)=(fzero_zero_real)), file('<stdin>', pax78)).
% 2.06/2.78 thf(pax53, axiom, (p53=>![X20:real, X31:real]:(ford_less_real @ X20 @ X31=>~(ford_less_real @ X31 @ X20))), file('<stdin>', pax53)).
% 2.06/2.78 thf(ax77, axiom, p1, file('<stdin>', ax77)).
% 2.06/2.78 thf(ax0, axiom, p78, file('<stdin>', ax0)).
% 2.06/2.78 thf(pax17, axiom, (p17=>![X89:real, X85:real, X79:real]:(ford_less_real @ X89 @ (ford_min_real @ X85 @ X79)=>~((ford_less_real @ X89 @ X85=>~(ford_less_real @ X89 @ X79))))), file('<stdin>', pax17)).
% 2.06/2.78 thf(pax2, axiom, (p2=>(flb)=(ford_min_real @ flb1 @ flb2)), file('<stdin>', pax2)).
% 2.06/2.78 thf(ax25, axiom, p53, file('<stdin>', ax25)).
% 2.06/2.78 thf(ax61, axiom, p17, file('<stdin>', ax61)).
% 2.06/2.78 thf(ax76, axiom, p2, file('<stdin>', ax76)).
% 2.06/2.78 thf(pax58, axiom, (p58=>![X20:real]:~(ford_less_real @ X20 @ X20)), file('<stdin>', pax58)).
% 2.06/2.78 thf(nax77, axiom, (p77<=ford_less_real @ flb @ f__0), file('<stdin>', nax77)).
% 2.06/2.78 thf(ax1, axiom, ~(p77), file('<stdin>', ax1)).
% 2.06/2.78 thf(pax36, axiom, (p36=>![X83:real, X85:real]:(~((X83)=(X85))=>(~(ford_less_real @ X83 @ X85)=>ford_less_real @ X85 @ X83))), file('<stdin>', pax36)).
% 2.06/2.78 thf(ax20, axiom, p58, file('<stdin>', ax20)).
% 2.06/2.78 thf(ax42, axiom, p36, file('<stdin>', ax42)).
% 2.06/2.78 thf(c_0_16, plain, ![X467:real]:(~p1|((fpoly_real2 @ fp @ X467)!=(fzero_zero_real)|ford_less_real @ flb1 @ X467)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax1])])])).
% 2.06/2.78 thf(c_0_17, plain, (~p78|(fpoly_real2 @ fp @ f__0)=(fzero_zero_real)), inference(fof_nnf,[status(thm)],[pax78])).
% 2.06/2.78 thf(c_0_18, plain, ![X225:real, X226:real]:(~p53|(~ford_less_real @ X225 @ X226|~ford_less_real @ X226 @ X225)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax53])])])])).
% 2.06/2.78 thf(c_0_19, plain, ![X1:real]:(ford_less_real @ flb1 @ X1|~p1|(fpoly_real2 @ fp @ X1)!=(fzero_zero_real)), inference(split_conjunct,[status(thm)],[c_0_16])).
% 2.06/2.78 thf(c_0_20, plain, p1, inference(split_conjunct,[status(thm)],[ax77])).
% 2.06/2.78 thf(c_0_21, plain, ((fpoly_real2 @ fp @ f__0)=(fzero_zero_real)|~p78), inference(split_conjunct,[status(thm)],[c_0_17])).
% 2.06/2.78 thf(c_0_22, plain, p78, inference(split_conjunct,[status(thm)],[ax0])).
% 2.06/2.78 thf(c_0_23, plain, ![X423:real, X424:real, X425:real]:((ford_less_real @ X423 @ X424|~ford_less_real @ X423 @ (ford_min_real @ X424 @ X425)|~p17)&(ford_less_real @ X423 @ X425|~ford_less_real @ X423 @ (ford_min_real @ X424 @ X425)|~p17)), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax17])])])])])).
% 2.06/2.78 thf(c_0_24, plain, (~p2|(flb)=(ford_min_real @ flb1 @ flb2)), inference(fof_nnf,[status(thm)],[pax2])).
% 2.06/2.78 thf(c_0_25, plain, ![X2:real, X1:real]:(~p53|~ford_less_real @ X1 @ X2|~ford_less_real @ X2 @ X1), inference(split_conjunct,[status(thm)],[c_0_18])).
% 2.06/2.78 thf(c_0_26, plain, p53, inference(split_conjunct,[status(thm)],[ax25])).
% 2.06/2.78 thf(c_0_27, plain, ![X1:real]:(ford_less_real @ flb1 @ X1|(fpoly_real2 @ fp @ X1)!=(fzero_zero_real)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19, c_0_20])])).
% 2.06/2.78 thf(c_0_28, plain, (fpoly_real2 @ fp @ f__0)=(fzero_zero_real), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_21, c_0_22])])).
% 2.06/2.78 thf(c_0_29, plain, ![X1:real, X2:real, X11:real]:(ford_less_real @ X1 @ X2|~ford_less_real @ X1 @ (ford_min_real @ X2 @ X11)|~p17), inference(split_conjunct,[status(thm)],[c_0_23])).
% 2.06/2.78 thf(c_0_30, plain, p17, inference(split_conjunct,[status(thm)],[ax61])).
% 2.06/2.78 thf(c_0_31, plain, ((flb)=(ford_min_real @ flb1 @ flb2)|~p2), inference(split_conjunct,[status(thm)],[c_0_24])).
% 2.06/2.78 thf(c_0_32, plain, p2, inference(split_conjunct,[status(thm)],[ax76])).
% 2.06/2.78 thf(c_0_33, plain, ![X203:real]:(~p58|~ford_less_real @ X203 @ X203), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax58])])])])).
% 2.06/2.78 thf(c_0_34, plain, (~ford_less_real @ flb @ f__0|p77), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax77])])).
% 2.06/2.78 thf(c_0_35, plain, ~p77, inference(fof_simplification,[status(thm)],[ax1])).
% 2.06/2.78 thf(c_0_36, plain, ![X381:real, X382:real]:(~p36|((X381)=(X382)|(ford_less_real @ X381 @ X382|ford_less_real @ X382 @ X381))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax36])])])])).
% 2.06/2.78 thf(c_0_37, plain, ![X2:real, X1:real]:(~ford_less_real @ X1 @ X2|~ford_less_real @ X2 @ X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25, c_0_26])])).
% 2.06/2.78 thf(c_0_38, plain, ford_less_real @ flb1 @ f__0, inference(spm,[status(thm)],[c_0_27, c_0_28])).
% 2.06/2.78 thf(c_0_39, plain, ![X1:real, X2:real, X11:real]:(ford_less_real @ X1 @ X2|~ford_less_real @ X1 @ (ford_min_real @ X2 @ X11)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29, c_0_30])])).
% 2.06/2.78 thf(c_0_40, plain, (ford_min_real @ flb1 @ flb2)=(flb), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31, c_0_32])])).
% 2.06/2.78 thf(c_0_41, plain, ![X1:real]:(~p58|~ford_less_real @ X1 @ X1), inference(split_conjunct,[status(thm)],[c_0_33])).
% 2.06/2.78 thf(c_0_42, plain, p58, inference(split_conjunct,[status(thm)],[ax20])).
% 2.06/2.78 thf(c_0_43, plain, (p77|~ford_less_real @ flb @ f__0), inference(split_conjunct,[status(thm)],[c_0_34])).
% 2.06/2.78 thf(c_0_44, plain, ~p77, inference(split_conjunct,[status(thm)],[c_0_35])).
% 2.06/2.78 thf(c_0_45, plain, ![X2:real, X1:real]:((X1)=(X2)|ford_less_real @ X1 @ X2|ford_less_real @ X2 @ X1|~p36), inference(split_conjunct,[status(thm)],[c_0_36])).
% 2.06/2.78 thf(c_0_46, plain, p36, inference(split_conjunct,[status(thm)],[ax42])).
% 2.06/2.78 thf(c_0_47, plain, ~ford_less_real @ f__0 @ flb1, inference(spm,[status(thm)],[c_0_37, c_0_38])).
% 2.06/2.78 thf(c_0_48, plain, ![X1:real]:(ford_less_real @ X1 @ flb1|~ford_less_real @ X1 @ flb), inference(spm,[status(thm)],[c_0_39, c_0_40])).
% 2.06/2.78 thf(c_0_49, plain, ![X1:real]:~ford_less_real @ X1 @ X1, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41, c_0_42])])).
% 2.06/2.78 thf(c_0_50, plain, ~ford_less_real @ flb @ f__0, inference(sr,[status(thm)],[c_0_43, c_0_44])).
% 2.06/2.78 thf(c_0_51, plain, ![X2:real, X1:real]:((X1)=(X2)|ford_less_real @ X1 @ X2|ford_less_real @ X2 @ X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45, c_0_46])])).
% 2.06/2.78 thf(c_0_52, plain, ~ford_less_real @ f__0 @ flb, inference(spm,[status(thm)],[c_0_47, c_0_48])).
% 2.06/2.78 thf(c_0_53, plain, ~ford_less_real @ flb1 @ flb, inference(spm,[status(thm)],[c_0_49, c_0_48])).
% 2.06/2.78 thf(c_0_54, plain, (flb)=(f__0), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_50, c_0_51]), c_0_52])).
% 2.06/2.78 thf(c_0_55, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_53, c_0_54]), c_0_38])]), ['proof']).
% 2.06/2.78 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h5,h4,h2,h3,h1,h0])],[])).
% 2.06/2.78 thf(fact_2__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062lb1_O_A_092_060forall_062x_O_Apoly_Ap_Ax_A_061_A0_A_092_060longrightarrow_062_Alb1_A_060_Ax_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,(~((![X1:real]:(~((![X2:real]:((((poly_real2 @ p) @ X2) = zero_zero_real) => ((ord_less_real @ X1) @ X2))))))))).
% 2.06/2.78 thf(2,plain,$false,inference(tab_negall,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__2)],[fact_2__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062lb1_O_A_092_060forall_062x_O_Apoly_Ap_Ax_A_061_A0_A_092_060longrightarrow_062_Alb1_A_060_Ax_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,1,h5])).
% 2.06/2.78 thf(fact_79__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062lb2_O_A_092_060forall_062x_092_060le_062lb2_O_Asgn_A_Ipoly_Ap_Ax_J_A_061_Asgn__neg__inf_Ap_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,(~((![X1:real]:(~((![X2:real]:(((ord_less_eq_real @ X2) @ X1) => ((sgn_sgn_real @ ((poly_real2 @ p) @ X2)) = (sturm_1076696862f_real @ p)))))))))).
% 2.06/2.78 thf(3,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[fact_79__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062lb2_O_A_092_060forall_062x_092_060le_062lb2_O_Asgn_A_Ipoly_Ap_Ax_J_A_061_Asgn__neg__inf_Ap_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,2,h4])).
% 2.06/2.78 thf(4,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,3,h2,h3])).
% 2.06/2.78 thf(5,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,4,h1])).
% 2.06/2.78 thf(0,theorem,(![X1:real]:((((poly_real2 @ p) @ X1) = zero_zero_real) => ((ord_less_real @ lb) @ X1))),inference(contra,[status(thm),contra(discharge,[h0])],[5,h0])).
% 2.06/2.78 % SZS output end Proof
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