TSTP Solution File: ITP149^1 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP149^1 : 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 : n032.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 00:29:17 EDT 2022
% Result : Theorem 3.48s 3.75s
% Output : Proof 3.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.08 % Problem : ITP149^1 : TPTP v8.1.0. Released v7.5.0.
% 0.06/0.09 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 600
% 0.09/0.28 % DateTime : Thu Jun 2 21:14:16 EDT 2022
% 0.09/0.28 % CPUTime :
% 3.48/3.75 % SZS status Theorem
% 3.48/3.75 % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
% 3.48/3.75 % Inferences: 1
% 3.48/3.75 % SZS output start Proof
% 3.48/3.75 thf(ty_a, type, a : $tType).
% 3.48/3.75 thf(ty_set_a, type, set_a : $tType).
% 3.48/3.75 thf(ty_real, type, real : $tType).
% 3.48/3.75 thf(ty_zero_zero_real, type, zero_zero_real : real).
% 3.48/3.75 thf(ty_member_a, type, member_a : (a>set_a>$o)).
% 3.48/3.75 thf(ty_elemen49976720ball_a, type, elemen49976720ball_a : (a>real>set_a)).
% 3.48/3.75 thf(ty_minus_minus_a, type, minus_minus_a : (a>a>a)).
% 3.48/3.75 thf(ty_d, type, d : real).
% 3.48/3.75 thf(ty_eigen__1, type, eigen__1 : a).
% 3.48/3.75 thf(ty_a2, type, a2 : a).
% 3.48/3.75 thf(ty_b, type, b : a).
% 3.48/3.75 thf(ty_eigen__0, type, eigen__0 : real).
% 3.48/3.75 thf(ty_ord_less_eq_real, type, ord_less_eq_real : (real>real>$o)).
% 3.48/3.75 thf(ty_inner_1173012732nner_a, type, inner_1173012732nner_a : (a>a>real)).
% 3.48/3.75 thf(ty_ord_less_real, type, ord_less_real : (real>real>$o)).
% 3.48/3.75 thf(ty_poinca659159244_rot_a, type, poinca659159244_rot_a : (a>a)).
% 3.48/3.75 thf(ty_x2, type, x2 : a).
% 3.48/3.75 thf(ty_zero_zero_a, type, zero_zero_a : a).
% 3.48/3.75 thf(ty_f, type, f : (a>a)).
% 3.48/3.75 thf(ty_x, type, x : set_a).
% 3.48/3.75 thf(conj_0,conjecture,(~((![X1:real]:(((ord_less_real @ zero_zero_real) @ X1) => (![X2:real]:(((ord_less_real @ zero_zero_real) @ X2) => (~((![X3:a]:(((member_a @ X3) @ ((elemen49976720ball_a @ x2) @ X1)) => ((ord_less_eq_real @ X2) @ ((inner_1173012732nner_a @ (f @ X3)) @ (poinca659159244_rot_a @ ((minus_minus_a @ a2) @ b))))))))))))))).
% 3.48/3.75 thf(h0,negated_conjecture,(![X1:real]:(((ord_less_real @ zero_zero_real) @ X1) => (![X2:real]:(((ord_less_real @ zero_zero_real) @ X2) => (~((![X3:a]:(((member_a @ X3) @ ((elemen49976720ball_a @ x2) @ X1)) => ((ord_less_eq_real @ X2) @ ((inner_1173012732nner_a @ (f @ X3)) @ (poinca659159244_rot_a @ ((minus_minus_a @ a2) @ b)))))))))))),inference(assume_negation,[status(cth)],[conj_0])).
% 3.48/3.75 thf(h1,assumption,(~((((ord_less_real @ zero_zero_real) @ eigen__0) => (~((![X1:a]:(((member_a @ X1) @ ((elemen49976720ball_a @ x2) @ eigen__0)) => (~(((~((((ord_less_real @ zero_zero_real) @ ((inner_1173012732nner_a @ (f @ X1)) @ (poinca659159244_rot_a @ ((minus_minus_a @ a2) @ b)))) => (~(((member_a @ X1) @ x)))))) => ((f @ X1) = zero_zero_a))))))))))),introduced(assumption,[])).
% 3.48/3.75 thf(h2,assumption,((ord_less_real @ zero_zero_real) @ eigen__0),introduced(assumption,[])).
% 3.48/3.75 thf(h3,assumption,(![X1:a]:(((member_a @ X1) @ ((elemen49976720ball_a @ x2) @ eigen__0)) => (~(((~((((ord_less_real @ zero_zero_real) @ ((inner_1173012732nner_a @ (f @ X1)) @ (poinca659159244_rot_a @ ((minus_minus_a @ a2) @ b)))) => (~(((member_a @ X1) @ x)))))) => ((f @ X1) = zero_zero_a)))))),introduced(assumption,[])).
% 3.48/3.75 thf(h4,assumption,(~((((member_a @ eigen__1) @ ((elemen49976720ball_a @ x2) @ d)) => (~((![X1:a]:(((member_a @ X1) @ ((elemen49976720ball_a @ x2) @ d)) => ((ord_less_eq_real @ ((inner_1173012732nner_a @ (f @ eigen__1)) @ (poinca659159244_rot_a @ ((minus_minus_a @ a2) @ b)))) @ ((inner_1173012732nner_a @ (f @ X1)) @ (poinca659159244_rot_a @ ((minus_minus_a @ a2) @ b))))))))))),introduced(assumption,[])).
% 3.48/3.75 thf(h5,assumption,((member_a @ eigen__1) @ ((elemen49976720ball_a @ x2) @ d)),introduced(assumption,[])).
% 3.48/3.75 thf(h6,assumption,(![X1:a]:(((member_a @ X1) @ ((elemen49976720ball_a @ x2) @ d)) => ((ord_less_eq_real @ ((inner_1173012732nner_a @ (f @ eigen__1)) @ (poinca659159244_rot_a @ ((minus_minus_a @ a2) @ b)))) @ ((inner_1173012732nner_a @ (f @ X1)) @ (poinca659159244_rot_a @ ((minus_minus_a @ a2) @ b)))))),introduced(assumption,[])).
% 3.48/3.75 thf(pax169, axiom, (p169=>![X1:real]:(ford_less_real @ fzero_zero_real @ X1=>![X3:real]:(ford_less_real @ fzero_zero_real @ X3=>~(![X4:a]:(fmember_a @ X4 @ (felemen49976720ball_a @ fx2 @ X1)=>ford_less_eq_real @ X3 @ (finner_1173012732nner_a @ (ff @ X4) @ (fpoinca659159244_rot_a @ (fminus_minus_a @ fa2 @ fb)))))))), file('<stdin>', pax169)).
% 3.48/3.75 thf(pax12, axiom, (p12=>![X77:a]:(fmember_a @ X77 @ (felemen49976720ball_a @ fx2 @ fd)=>ford_less_eq_real @ (finner_1173012732nner_a @ (ff @ f__1) @ (fpoinca659159244_rot_a @ (fminus_minus_a @ fa2 @ fb))) @ (finner_1173012732nner_a @ (ff @ X77) @ (fpoinca659159244_rot_a @ (fminus_minus_a @ fa2 @ fb))))), file('<stdin>', pax12)).
% 3.48/3.75 thf(ax2, axiom, p169, file('<stdin>', ax2)).
% 3.48/3.75 thf(ax159, axiom, p12, file('<stdin>', ax159)).
% 3.48/3.75 thf(pax1, axiom, (p1=>ford_less_real @ fzero_zero_real @ fd), file('<stdin>', pax1)).
% 3.48/3.75 thf(ax170, axiom, p1, file('<stdin>', ax170)).
% 3.48/3.75 thf(pax9, axiom, (p9=>![X77:a]:(fmember_a @ X77 @ (felemen49976720ball_a @ fx2 @ fd)=>~((~((ford_less_real @ fzero_zero_real @ (finner_1173012732nner_a @ (ff @ X77) @ (fpoinca659159244_rot_a @ (fminus_minus_a @ fa2 @ fb)))=>~(fmember_a @ X77 @ fx)))=>(ff @ X77)=(fzero_zero_a))))), file('<stdin>', pax9)).
% 3.48/3.75 thf(pax13, axiom, (p13=>fmember_a @ f__1 @ (felemen49976720ball_a @ fx2 @ fd)), file('<stdin>', pax13)).
% 3.48/3.75 thf(ax162, axiom, p9, file('<stdin>', ax162)).
% 3.48/3.75 thf(ax158, axiom, p13, file('<stdin>', ax158)).
% 3.48/3.75 thf(c_0_10, plain, ![X92:real, X93:real]:((fmember_a @ (esk7_2 @ X92 @ X93) @ (felemen49976720ball_a @ fx2 @ X92)|~ford_less_real @ fzero_zero_real @ X93|~ford_less_real @ fzero_zero_real @ X92|~p169)&(~ford_less_eq_real @ X93 @ (finner_1173012732nner_a @ (ff @ (esk7_2 @ X92 @ X93)) @ (fpoinca659159244_rot_a @ (fminus_minus_a @ fa2 @ fb)))|~ford_less_real @ fzero_zero_real @ X93|~ford_less_real @ fzero_zero_real @ X92|~p169)), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax169])])])])])).
% 3.48/3.75 thf(c_0_11, plain, ![X544:a]:(~p12|(~fmember_a @ X544 @ (felemen49976720ball_a @ fx2 @ fd)|ford_less_eq_real @ (finner_1173012732nner_a @ (ff @ f__1) @ (fpoinca659159244_rot_a @ (fminus_minus_a @ fa2 @ fb))) @ (finner_1173012732nner_a @ (ff @ X544) @ (fpoinca659159244_rot_a @ (fminus_minus_a @ fa2 @ fb))))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax12])])])).
% 3.48/3.75 thf(c_0_12, plain, ![X1:real, X3:real]:(~ford_less_eq_real @ X1 @ (finner_1173012732nner_a @ (ff @ (esk7_2 @ X3 @ X1)) @ (fpoinca659159244_rot_a @ (fminus_minus_a @ fa2 @ fb)))|~ford_less_real @ fzero_zero_real @ X1|~ford_less_real @ fzero_zero_real @ X3|~p169), inference(split_conjunct,[status(thm)],[c_0_10])).
% 3.48/3.75 thf(c_0_13, plain, p169, inference(split_conjunct,[status(thm)],[ax2])).
% 3.48/3.75 thf(c_0_14, plain, ![X2:a]:(ford_less_eq_real @ (finner_1173012732nner_a @ (ff @ f__1) @ (fpoinca659159244_rot_a @ (fminus_minus_a @ fa2 @ fb))) @ (finner_1173012732nner_a @ (ff @ X2) @ (fpoinca659159244_rot_a @ (fminus_minus_a @ fa2 @ fb)))|~p12|~fmember_a @ X2 @ (felemen49976720ball_a @ fx2 @ fd)), inference(split_conjunct,[status(thm)],[c_0_11])).
% 3.48/3.75 thf(c_0_15, plain, p12, inference(split_conjunct,[status(thm)],[ax159])).
% 3.48/3.75 thf(c_0_16, plain, (~p1|ford_less_real @ fzero_zero_real @ fd), inference(fof_nnf,[status(thm)],[pax1])).
% 3.48/3.75 thf(c_0_17, plain, ![X3:real, X1:real]:(~ford_less_eq_real @ X1 @ (finner_1173012732nner_a @ (ff @ (esk7_2 @ X3 @ X1)) @ (fpoinca659159244_rot_a @ (fminus_minus_a @ fa2 @ fb)))|~ford_less_real @ fzero_zero_real @ X3|~ford_less_real @ fzero_zero_real @ X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_12, c_0_13])])).
% 3.48/3.75 thf(c_0_18, plain, ![X2:a]:(ford_less_eq_real @ (finner_1173012732nner_a @ (ff @ f__1) @ (fpoinca659159244_rot_a @ (fminus_minus_a @ fa2 @ fb))) @ (finner_1173012732nner_a @ (ff @ X2) @ (fpoinca659159244_rot_a @ (fminus_minus_a @ fa2 @ fb)))|~fmember_a @ X2 @ (felemen49976720ball_a @ fx2 @ fd)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14, c_0_15])])).
% 3.48/3.75 thf(c_0_19, plain, ![X3:real, X1:real]:(fmember_a @ (esk7_2 @ X1 @ X3) @ (felemen49976720ball_a @ fx2 @ X1)|~ford_less_real @ fzero_zero_real @ X3|~ford_less_real @ fzero_zero_real @ X1|~p169), inference(split_conjunct,[status(thm)],[c_0_10])).
% 3.48/3.75 thf(c_0_20, plain, (ford_less_real @ fzero_zero_real @ fd|~p1), inference(split_conjunct,[status(thm)],[c_0_16])).
% 3.48/3.75 thf(c_0_21, plain, p1, inference(split_conjunct,[status(thm)],[ax170])).
% 3.48/3.75 thf(c_0_22, plain, ![X548:a]:(((ford_less_real @ fzero_zero_real @ (finner_1173012732nner_a @ (ff @ X548) @ (fpoinca659159244_rot_a @ (fminus_minus_a @ fa2 @ fb)))|~fmember_a @ X548 @ (felemen49976720ball_a @ fx2 @ fd)|~p9)&(fmember_a @ X548 @ fx|~fmember_a @ X548 @ (felemen49976720ball_a @ fx2 @ fd)|~p9))&((ff @ X548)!=(fzero_zero_a)|~fmember_a @ X548 @ (felemen49976720ball_a @ fx2 @ fd)|~p9)), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax9])])])])])).
% 3.48/3.75 thf(c_0_23, plain, (~p13|fmember_a @ f__1 @ (felemen49976720ball_a @ fx2 @ fd)), inference(fof_nnf,[status(thm)],[pax13])).
% 3.48/3.75 thf(c_0_24, plain, ![X1:real]:(~fmember_a @ (esk7_2 @ X1 @ (finner_1173012732nner_a @ (ff @ f__1) @ (fpoinca659159244_rot_a @ (fminus_minus_a @ fa2 @ fb)))) @ (felemen49976720ball_a @ fx2 @ fd)|~ford_less_real @ fzero_zero_real @ (finner_1173012732nner_a @ (ff @ f__1) @ (fpoinca659159244_rot_a @ (fminus_minus_a @ fa2 @ fb)))|~ford_less_real @ fzero_zero_real @ X1), inference(spm,[status(thm)],[c_0_17, c_0_18])).
% 3.48/3.75 thf(c_0_25, plain, ![X3:real, X1:real]:(fmember_a @ (esk7_2 @ X1 @ X3) @ (felemen49976720ball_a @ fx2 @ X1)|~ford_less_real @ fzero_zero_real @ X3|~ford_less_real @ fzero_zero_real @ X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19, c_0_13])])).
% 3.48/3.75 thf(c_0_26, plain, ford_less_real @ fzero_zero_real @ fd, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20, c_0_21])])).
% 3.48/3.75 thf(c_0_27, plain, ![X2:a]:(ford_less_real @ fzero_zero_real @ (finner_1173012732nner_a @ (ff @ X2) @ (fpoinca659159244_rot_a @ (fminus_minus_a @ fa2 @ fb)))|~fmember_a @ X2 @ (felemen49976720ball_a @ fx2 @ fd)|~p9), inference(split_conjunct,[status(thm)],[c_0_22])).
% 3.48/3.75 thf(c_0_28, plain, p9, inference(split_conjunct,[status(thm)],[ax162])).
% 3.48/3.75 thf(c_0_29, plain, (fmember_a @ f__1 @ (felemen49976720ball_a @ fx2 @ fd)|~p13), inference(split_conjunct,[status(thm)],[c_0_23])).
% 3.48/3.75 thf(c_0_30, plain, p13, inference(split_conjunct,[status(thm)],[ax158])).
% 3.48/3.75 thf(c_0_31, plain, ~ford_less_real @ fzero_zero_real @ (finner_1173012732nner_a @ (ff @ f__1) @ (fpoinca659159244_rot_a @ (fminus_minus_a @ fa2 @ fb))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24, c_0_25]), c_0_26])])).
% 3.48/3.75 thf(c_0_32, plain, ![X2:a]:(ford_less_real @ fzero_zero_real @ (finner_1173012732nner_a @ (ff @ X2) @ (fpoinca659159244_rot_a @ (fminus_minus_a @ fa2 @ fb)))|~fmember_a @ X2 @ (felemen49976720ball_a @ fx2 @ fd)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27, c_0_28])])).
% 3.48/3.75 thf(c_0_33, plain, fmember_a @ f__1 @ (felemen49976720ball_a @ fx2 @ fd), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29, c_0_30])])).
% 3.48/3.75 thf(c_0_34, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31, c_0_32]), c_0_33])]), ['proof']).
% 3.48/3.75 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h5,h6,h4,h2,h3,h1,h0])],[])).
% 3.48/3.75 thf(2,plain,$false,inference(tab_negimp,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negimp(discharge,[h5,h6])],[h4,1,h5,h6])).
% 3.48/3.75 thf(fact_11__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062s_O_A_092_060lbrakk_062s_A_092_060in_062_Acball_Ax_Ad_059_A_092_060forall_062x_092_060in_062cball_Ax_Ad_O_Af_As_A_092_060bullet_062_Arot_A_Ia_A_N_Ab_J_A_092_060le_062_Af_Ax_A_092_060bullet_062_Arot_A_Ia_A_N_Ab_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,(~((![X1:a]:(((member_a @ X1) @ ((elemen49976720ball_a @ x2) @ d)) => (~((![X2:a]:(((member_a @ X2) @ ((elemen49976720ball_a @ x2) @ d)) => ((ord_less_eq_real @ ((inner_1173012732nner_a @ (f @ X1)) @ (poinca659159244_rot_a @ ((minus_minus_a @ a2) @ b)))) @ ((inner_1173012732nner_a @ (f @ X2)) @ (poinca659159244_rot_a @ ((minus_minus_a @ a2) @ b))))))))))))).
% 3.48/3.75 thf(3,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[fact_11__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062s_O_A_092_060lbrakk_062s_A_092_060in_062_Acball_Ax_Ad_059_A_092_060forall_062x_092_060in_062cball_Ax_Ad_O_Af_As_A_092_060bullet_062_Arot_A_Ia_A_N_Ab_J_A_092_060le_062_Af_Ax_A_092_060bullet_062_Arot_A_Ia_A_N_Ab_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,2,h4])).
% 3.48/3.75 thf(4,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,3,h2,h3])).
% 3.48/3.75 thf(fact_13__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062d_O_A_092_060lbrakk_0620_A_060_Ad_059_A_092_060And_062y_O_Ay_A_092_060in_062_Acball_Ax_Ad_A_092_060Longrightarrow_062_A0_A_060_Af_Ay_A_092_060bullet_062_Arot_A_Ia_A_N_Ab_J_A_092_060and_062_Ay_A_092_060in_062_AX_A_092_060and_062_Af_Ay_A_092_060noteq_062_A_I0_058_058_Ha_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,(~((![X1:real]:(((ord_less_real @ zero_zero_real) @ X1) => (~((![X2:a]:(((member_a @ X2) @ ((elemen49976720ball_a @ x2) @ X1)) => (~(((~((((ord_less_real @ zero_zero_real) @ ((inner_1173012732nner_a @ (f @ X2)) @ (poinca659159244_rot_a @ ((minus_minus_a @ a2) @ b)))) => (~(((member_a @ X2) @ x)))))) => ((f @ X2) = zero_zero_a))))))))))))).
% 3.48/3.75 thf(5,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[fact_13__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062d_O_A_092_060lbrakk_0620_A_060_Ad_059_A_092_060And_062y_O_Ay_A_092_060in_062_Acball_Ax_Ad_A_092_060Longrightarrow_062_A0_A_060_Af_Ay_A_092_060bullet_062_Arot_A_Ia_A_N_Ab_J_A_092_060and_062_Ay_A_092_060in_062_AX_A_092_060and_062_Af_Ay_A_092_060noteq_062_A_I0_058_058_Ha_J_092_060rbrakk_062_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,4,h1])).
% 3.48/3.75 thf(0,theorem,(~((![X1:real]:(((ord_less_real @ zero_zero_real) @ X1) => (![X2:real]:(((ord_less_real @ zero_zero_real) @ X2) => (~((![X3:a]:(((member_a @ X3) @ ((elemen49976720ball_a @ x2) @ X1)) => ((ord_less_eq_real @ X2) @ ((inner_1173012732nner_a @ (f @ X3)) @ (poinca659159244_rot_a @ ((minus_minus_a @ a2) @ b)))))))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[5,h0])).
% 3.48/3.75 % SZS output end Proof
%------------------------------------------------------------------------------